2869 lines
283 KiB
Plaintext
2869 lines
283 KiB
Plaintext
Frontiers of Fundamental Physics
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Frontiers of Fundamental Physics
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Edited by
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Michele Barone
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Nuclear Research Centre Demokritos, Greece
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and
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Franco Selleri
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Universita di Bari Bari, Italy
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Springer Science+Business Media, LLC
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Library of Congress Cataloging-In-Publication Data
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Frontiers of fundaNental physics I edited by Michele Barone and Franco
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Sellerl.
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p. CN.
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·Proceedlngs of an International conference on Frontiers of
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fundnentl physics, held September 27-30, 1993, In Oly.pla, Greece"-
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-T.p. verso.
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Includes bibliographical references and Index.
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ISBN 978-1-4613-6093-3
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ISBN 978-1-4615-2560-8 (eBook)
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DOI 10.1007/978-1-4615-2560-8
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1. Physics. 2. Astrophysics. 3. GeophysiCS. I. Barone,
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Michele. II. Sellerl, Franco.
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QC21.2.F76 1994 500.2--dc20
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94-38843 CIP
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Proceedings of an International Conference on Frontiers of Fundamental Physics. held September 27-30, 1993, in Olympia. Greece
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© 1994 Springer Science+Business Media New York Originally published by Plenum Press, New York in 1994
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All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher
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Preface
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The Olympia conference Frontiers of Fundamental Physics was a gathering of about hundred scientists who carryon their research in conceptually important areas of physical science (they do "fundamental physics"). Most of them were physicists, but also historians and philosophers of science were well represented. An important fraction of the participants could be considered "heretical" because they disagreed with the validity of one or several fundamental assumptions of modern physics. Common to all participants was an excellent scientific level coupled with a remarkable intellectual honesty: we are proud to present to the readers this certainly unique book.
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Alternative ways of considering fundamental matters should of course be vitally important for the progress of science, unless one wanted to admit that physics at the end of the XXth century has already obtained the final truth, a very unlikely possibility even if one accepted the doubtful idea of the existence of a "final" truth. The merits of the Olympia conference should therefore not be judged a priori in a positive or in a negative way depending on one's refusal or acceptance, respectively, of basic principles of contemporary science, but considered after reading the actual new proposals and evidences there presented. They seem very important to us.
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The confrontation between different lines of research has accompanied science from its birth. Galileo's scientific ideas were heretical, not only with respect to the dominant religious and political powers of his times, but with respect to the academic establishments of the universities as well: Well known is the example of the astronomy professor who refused to look in the telescope, but many were the centers where the heliocentric ideas were rejected. The great results obtained by Kepler, Newton, and many others, slowly transformed Galileo's heresy into the orthodoxy of modern physical science.
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Atomism had existed as an idea cultivated by few isolated people for about 2300 years when, at the end of the XIXth century, Ludwig Boltzmann presented his conception of an objectively existing atomic structure of matter. Almost all scientists surrounding him seemed to reject atomism, and the bitter struggle that went around this question probably contributed to the dramatic ending of his life (1906). In the same years, however, Albert Einstein and Jean Perrin obtained an atomistic description of Brownian motion and shortly afterwards atomism was fully accepted in physics, owing also to the discoveries made by Ernst Rutherford and Niels Bohr. In this way the isolated ideas of Boltzmann became the new orthodoxy.
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v
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The geophysicist Alfred Wegener was much laughed at for his 1912 proposal that the continents had shifted relatively thousands of km, that the Atlantic Ocean had opened as the Americas split from Africa and Europe, and that all the continents had once been united as a single supercontinent, Pangaea. Only after the confirmations found by Warren Carey in 1954 Wegener's discovery started to be accepted in the scientific community. Today there are so many independent proofs that continents have been united in the past that it seems impossible to doubt it. Here the new frontier has become the conjecture that the Earth radius has considerably increased in the past.
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In spite of these well known examples science is of course not reducible to an endless confrontation between opposite ideas, since it deals with the material reality surrounding us and uses powerful methods that allow sometimes the scientists to understand true properties of the real world. Therefore part of the orthodoxy can also be considered as valid knowledge. Such are for example the following statements: the Sun is just a star; the Milky Way is our galaxy seen from inside; in outer space there are hundreds of millions of other galaxies; there is a molecular and atomic structure of matter, and a nuclear structure of atoms; there exist subatomic entities called electron, proton, pion, etc. Many other examples of valid knowledge could easily be given. It is a fact however that today's physics seems to contain more than just valid knowledge.
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In books dealing with astrophysics and cosmology one often finds statements like: "the astronomer Edwin Hubble established beyond all reasonable doubt that the Universe is expanding", but Hubble himself wrote in several different occasions statements like the following one of 1939: "... the results do not establish the expansion as the only possible interpretation of redshifts". Moreover quasars are the objects with the largest observed redshifts, and should therefore be considered at the margins of the visible universe, but many independent pieces of observational evidence indicate that some of them are actually associated with nearby galaxies and that their redshifts cannot therefore be due to recessional motion. A recent amazing discovery is the so called "redshift quantization" phenomenon for spiral galaxies, and this is so difficult to explain within the standard cosmology that most people prefer to forget about it - a predictable reaction of modern scientific thinking confronted with radically new evidence. Important astrophysicists and cosmologists (Hannes Alfven, Halton Arp, Geoffrey Burbidge, Fred Hoyle, Jayant Narlikar, ... ) have repeatedly argued that the observed redshifts of quasars and galaxies could well have an explanation radically different from the standard one based on big bang. In spite of all this the dominant view remains the idea that the only possible explanation of galaxy and quasar redshifts is based on the universal expansion
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In relativity most people believe that the "luminiferous ether" of the XIXth century has been ruled out by Michelson-type experiments and by the development of the theory of special relativity. The situation is very different however, since
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vi
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Poincare and Lorentz were both defenders of the existence of ether, and Einstein himself after 1916 radically modified his previously negative attitude. For example in 1924 he wrote: "According to special relativity, the ether remains still absolute because its influence on the inertia of bodies ... is independent of every kind of physical influence." The minority group of people working today in the foundations of special relativity seems to be almost completely ether-oriented, and there are many proposing a reformulation of the theory along the lines dear to Lorentz: Simon Prokhovnik and the late John Bell are two examples. It has also become clear how such a reformulation should be carried out, after the 1977 realization that the conventional nature of the clock synchronization procedures opens the door to theories which are different from, but physically equivalent to special relativity.
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Also general relativity has problems of fundamental nature, in particular those connected with the right-hand side of Einstein's field equations, where only the matter stress-energy tensor, but not the field stress-energy tensor, contributes to space-time curvature. This goes against the very fundamental conclusion of special relativity that all forms of energy are completely equivalent, and gives rise to a curious conservation law of rest mass, but not of energy-momentum. A very large number of theoretical physicists seem to be happy with calculations performed strictly within the standard formulation, in spite of the fact that it has been shown that Einstein's field equations do not lead to interactive N-body solutions, if N > 1. General relativity can be considered as a test-particle theory, and as such it explains the three classical tests, but in other respects seems sometimes not to be quite satisfactory. More about this can be found in these proceedings.
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In our century the interplay between science and ideology has become more important than ever and the hystorians of physics have produced detailed reconstructions of the true scientific/cultural processes leading to the development of what we call "modern physics". From this work evidence has emerged for the existence of common cultural roots with philosophers such as S. Kierkegaard, M. Heidegger, A. Schopenhauer, and W. James. It is therefore not surprising that these philosophers developed ideas similar to some now prevailing in modern physics, in particular concerning the negative attitude toward the possibility of a correct understanding of the objective reality. In fact in quantum physics the standard teaching (after 1927) is that one cannot understand the atomic world in "classical" terms, that is by employing causal space-time descriptions. People active in the foundations of quantum physics believe instead that no good reason for such a pessimistic conclusion has ever been presented, and recall that Einstein, Planck, Schr6dinger and de Broglie could not accept it. A group of participants in Olympia try accordingly to find new space-time models of elementary particles and/ or to develop new rna thema tical tools useful for this task.
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Bell's theorem states that any theory of the physical world based on the rather natural point of view of local realism must disagree at the empirical level with the
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vii
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predictions of quantum mechanics by as much as 42%. Experiments performed in the seventies and early eighties have produced results compatible with the existing quantum theory, but Bell's theorem has actually not been checked due to the introduction in the reasoning of arbitrary (but unavoidable, given the efficiency of the used apparata) additional assumptions. In this way a confusion has been produced between Bell's original inequality and the much stronger inequality violated in those experiments, forgetting that the latter owes the very possibility of being violated by the quantum theoretical predictions to the mentioned additional assumptions. In spite of the fact that Bell's theorem could allow in principle to decide who was right in the Einstein/Bohr debate, we still do not know the answer thirty years after the formulation of the theorem.
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The confrontation between different points of view goes on, but a strange mutation seems to reduce its effects, since new ideas in fundamental physics find invariably difficulties in being accepted by the majority, no matter how well formulated and important they could be. While the ruling of the majorities is a fundamental feature of every democracy, it certainly does not apply to science where the great steps forward have always been made by isolated individuals. This dogmatic hardening risks today to make the scientific majorities impenetrable to a critical understanding of the foundations of contemporary scientific theories.
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The existence of such attitudes within modern science has been observed by many physicists and also by the best epistemologists of our century. Thomas Kuhn, for example, wrote about the education of young physicists: "Of course, it is a narrow and rigid education, probably more so than any other except perhaps in orthodox theology." Karl Popper was worried about the poor standards of scientific confrontations and stated: "A very serious situation has arisen. The general antirationalist atmosphere which has become a major menace of our time, and which to combat is the duty of every thinker who cares for the traditions of our civilization, has led to a most seri0us deterioration of the standards of scientific discussion.... But the greatest among contemporary physicists never adopted any such attitude. This holds for Einstein and Schrodinger, and also for Bohr. They never gloried in their formalism, but always remained seekers, only too conscious of the vastness of their ignorance." The understanding of the vastness of our ignorance was generally present in Olympia, but in all fairness we must add that one could also get glimpses of what our science could become in the future: in all cases these were very exciting moments.
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The choice of Olympia for helding the conference was not casual: this is the place where the Olympic games of ancient times were held for something like 1,200 years. Wars were stopped when the games started and activities included reading of poems, and discussions about science and philosophy. Olympia is not only one of the most beautiful and "interesting spots of the world, but also a positive symbol of the modern civilization.
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The generous efforts of many people have made our conference possible. First of all we wish to thank Attanassios Kanellopoulos for his encouragment and for many useful suggestions. The elected member of the Parliament Crigno Kanellopoulos-Barone has generously helped us in establishing fundamental contacts in Olympia and elsewhere. The constant help of Georges Kanellopoulos has been of tremendous importance for the success of the meeting: we thank him warmly. We are also very grateful to the physics students Rossella Colmayer, Francesco Minerva and Gabriella Pugliese, who formed an efficient and charming secretariat.
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Our thanks go also to the International Olympic Committee, and to its president Prof. X. Yzezezez, for allowing us to use, free of charge, the wonderful structures of the Olympic Academy where the conference was held. Mr. A Bababab, representative of the Greek government, brought us welcome greetings and encouragment, and Prof. R. Rapetti, president of the Istituto Italiano di Cultura in Athens, stressed the European nature of the conference. The words of Mr. X. Kosmopoulos, major of Olympia, made the participants feel at home in his marvellous town.
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Last but not least our gratefulness goes to the generous sponsors: the Greek Ministry of Culture, the General Secretary of Research and Technology of the Greek Ministry of Industry, the UniversWI di Bari and, independently, the Physics Department of the Universita di Bari, the National Tourist Organization of Greece, the Commercial Bank of Greece, the Ionian Bank of Greece, the Ellenic Industrial Development Bank S.A, and Glaxo AE.B.E. Without their concrete help the Olympia conference would not have taken place.
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M. Barone and F. Selleri
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ix
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Contents
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ASTROPHYSICS: ANOMALOUS-REDSHIFTS
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Empirical Evidence on the Creation of Galaxies and Quasars
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1
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Halton Arp
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Periodicity in Extragalactic Redshifts
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13
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William M. Napier
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Quasar Spectra: Black Holes or Nonstandard Models?
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27
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Jack W. Sulentic
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Configurations and Redshifts of Galaxies
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37
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Miroslaw Zabierowski
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Isominkowskian Representation of Cosmological Redshifts and the Internal Red-BIue-Shifts of Quasars ....................................................... 41
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Ruggero M. Santilli
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The Relativistic Electron Pair Theory of Matter and its Implications for Cosmology ................................................................................................... 59
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Ernest J. Sternglass
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Are Quasars Manifesting a de Sitter Redshift?
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67
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John B. Miller and Thomas E. Miller
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xi
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What, if Anything, Is the Anthropic Cosmological Principle Telling Us? 73 Silvio Bergia
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Large Anomalous Redshifts and Zero-Point Radiation
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83
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Peter F. Browne
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Theoretical Basis for a Non-Expanding and Euclidean Universe
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89
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Thomas B. Andrews
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Light Propagation in an Expanding Universe
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99
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Alexandros Paparodopoulos
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Fornax - The Companion of the Milky Way and the Question of Its Standard Motion ........................................................................................ 105
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Miroslaw Zabierowski
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Cosmological Redshifts and the Law of Corresponding States
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107
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Victor Clube
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RELATIVITY: ENERGY AND ETHER
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Did the Apple Fall? ................................................................................................. 115 Hiiseyin Yilmaz
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Investigations with Lasers, Atomic Clocks and Computer Calculations of
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Curved Spacetime and of the Differences between the Gravitation
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Theories of Yilmaz and of Einstein
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125
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Carrol O. Alley
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Gravity Is the Simplest Thing!
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139
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David F. Roscoe
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Fourdimensional Elasticity: Is It General Relativity? .................................. 147 Angelo Tartaglia
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Universality of the Lie-Isotopic Symmetries for Deformed Minkowskian Metrics ........ ...... ....... ...... ..... .... ..... .......... ... .... .... ......... ..... ...... .... ..... ........ ....... 153
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Ascar K. Aringazin and K.M. Aringazin
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xii
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Hertz's Special Relativity and Physical Reality
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163
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Constantin I. Mocanu
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From Relativistic Paradoxes to Absolute Space and Time Physics
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171
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Horst E. Wilhelm
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Theories Equivalent to Special Relativity
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181
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Franco Selleri
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The Physical Meaning of Albert Einstein's Relativistic Ether Concept.... 193 Ludwik Kostro
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The Limiting Nature of Light-Velocity as the Causal Factor Underlying Relativity ..................................................................................................... 203
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Trevor Morris
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The Ether Revisited .............................................................................................. 209 Adolphe Martin and C. Roy Keys
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What Is and What Is Not Essential in Lorentz's Relativity
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217
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Jan Czemiawski
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Vacuum Substratum in Electrodynamics and Quantum Mechanics Theory and Experiment ........................................................................... 223
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Horst E. Wilhelm
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The Influence of Ideal ism In 20th Century Science
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233
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Heather McCouat and Simon Prokhovnik
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GEOPHYSICS: EXPANDING EARTH
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Creeds of Physics .................................................................................................... 241 S. Warren Carey
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Earth Complexity vs. Plate Tectonic Simplicity
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257
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Giancarlo Scalera
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An Evolutionary Earth Expansion Hypothesis
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275
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Stavros T. Tassos
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xiii
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Global Models of the Expanding Earth
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281
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Klaus Vogel
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An Orogenic Model Consistent with Earth Expansion
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287
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Carol Strutinski
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Earth Expansion Requires Increase in Mass
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295
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John K. Davidson
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Principles of Plate Movements on the Expanding Earth
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301
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Jan Koziar
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The Origin of Granite and Continental Masses in an Expanding Earth
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309
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Lorence C. Collins
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The Primordially Hydridic Character of Our Planet and Proving It by Deep Drilling ........................................................................................... 315
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C. Warren Hunt
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Possible Relation between Earth Expansion and Dark Matter
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321
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Stanislaw Ciechanowicz and Jan Koziar
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Earth Expansion and the Prediction of Earthquakes and Volcanicism
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327
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Martin Kokus
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Tension-Gravitational Model of Island Arcs
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335
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Jan Koziar and Leszek Jamrozik
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FIELDS, PARTICLES: SPACE-TIME STRUCTURES
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Electromagnetic Interactions and Particle Physics
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339
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Asim O. Barut
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Isotopic and Genotopic Relativistic Theory
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347
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Asterios Jannussis and Anna Sotiropoulou
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A Look at Frontiers of High Energy Physics: From the GeV(10geV) to PeV(1015eV) and Beyond ..................................................................... 359
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Michele Barone
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xiv
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An Approach to Finite-Size Particles with Spin
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369
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Bronislaw Sredniawa
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A New High Energy Scale?
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377
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Vladimir Kadyshevsky
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On the Space-Time Structure of the Electron
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383
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Martin Rivas
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Physics without Physical Constants
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387
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Edward Kapuscik
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The Relation between Information, Time and Space Inferred from
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Universal Phenomena in Solid-State Physics
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393
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Gerhard Dorda
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Quantum-Like Behaviour of Charged Particles in a Magnetic Field and Observation of Discrete Forbidden States in the Classical Mechanical Domain ......................................................................................................... 401
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Ram K. Varma
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Unipolar Induction and Weber's Electrodynamics
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409
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Andre K. T. Assis and Dario S. Thober
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Impact of Maxwell's Equation of Displacement Current on Electromagnetic Laws and Comparison of the Maxwellian Waves with Our Model of Dipolic Particles ............ ..... ......... ................ ......... .............. ......................... 415
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Lefteris A. Kaliambos
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Direct Calculation of H and the Complete Self Energy of the Electron from Fluid Models ....................................................................... ...... ..... ............. 423
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William M. Honig
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Interbasis "Sphere-Cylinder" Expansions for the Oscillator in the Three
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Dimensional Space of Constant Positive Curvature
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429
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George S. Pogosyan, A.N. Sissakian and S.l. Vinitsky
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Pancharatnam's Topological Phase in Relation to theDynamical Phase in Polarization Optics ..................................................................................... 437 Susanne Klein, Wolfgang Dultz and Heidrun Schmitzer
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xv
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On the Connection between Classical and Quantum Mechanics
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443
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Andrzej Horzela
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Discrete Time Realizations of Quantum Mechanics and Their Possible
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Experimental Tests
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449
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Carl Wolf
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Heraclitus' Vision - Schrodinger's Version
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459
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Fitter Griiff
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OUANTUM PHYSICS: DUALITY AND LOCALITY
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Is It Possible to Believe in both Orthodox Quantum Theory and History? 465
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Euan J. Squires
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A New Logic for Quantum Mechanics?
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475
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Eftichios Bitsakis
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Dangerous Effects of the Incomprehensibility in Microphysics
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485
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Jenner Barretto Bastos Filho
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Classical Interpretation of Quantum Mechanics
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493
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Vladimir K. Ignatovich
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Rabi Oscillations Described by de Broglian Probabilities
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503
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Mirjana Bozic and Dusan Arsenovic
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A Test of the Complementarity Principle in Single-Photon States of Light 511 Yutaka Mizobuchi and Yoshiyuki Othake
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Experiments with Entangled Two-Photon States from Type-II Parametric Down Conversion: Evidence for Wave-Particle Unity...................... 519
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Carroll O. Alley, T.E. Kiess, A. V. Sergienko and Y.H. Shih Note on Wave-Particle Unity
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H. Yilmaz
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Correlation Functions and Einstein Locality
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529
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Augusto Garuccio and Liberato De Caro
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xvi
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Optical Tests of Bell's Inequalities. Closing the Poor Correlation Loophole 537 Susana F. Huelga, Miguel Ferrero and Emilio Santos
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Atomic Cascade Experiments with Two-Channel Polarizers and Quantum Mechanical Nonlocality ......................................................... 545
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Mohammad Ardehali
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New Tests on Locality and Empty Waves
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555
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Ramon Risco-Delgado
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Wave-Particle Duality
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561
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Marius Borneas
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Quantum Correlations from a Logical Point of View
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565
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Nikos A. Tambakis
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Local Realism and the Crucial Experiment
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571
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Yoav Ben-Dov
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The Space of Local Hidden Variables Can Limit Non-Locality And What Next? ...................................................................................... 575
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Milan Vinduska
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How the Quantum of Action Cannot Be a Metric one
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583
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Constantin Antonopoulos
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The Ghostly Solution of the QuantumParadoxes and Its Experimental Verification .................................................................................................. 591
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Raoul Nakhmanson
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Index .......................................................................................................................... 597
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xvii
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EMPIRICAL EVIDENCE ON THE CREATION OF GALAXIES AND QUASARS
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Halton Arp
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Max-Planck-Institut fur Astrophysik Garching bei Munchen, Germany
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Simply the arrangement on the sky of extragalactic objects has long shown that the youngest, smallest quasars and compact galaxies have been created recently in the vicinity of older progenitor galaxies. Now high energy observations in X-rays and -y-rays confirm these connections and require the creation of matter as an ongoing process marked by an initially high intrinsic redshift.
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The nearest superclusters of galaxies show creation along lines in space originating from the central, ejecting galaxy. String theory may be pertinent. The existence of preferred values of redshift (periodicity) rule out, again, an
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expanding universe. They also imply quantum mechanical effects at the m = 0
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creation points of particulate matter. No theory has been advanced, however, which numerically predicts the quantization values.
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Introduction
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The Big Bang theory of the universe precludes any scientific observation of creation because the event is so remote in time and space. But even if we could observe this singular event at a distance of 15 bilion light years this age zero universe would supposedly surround us in every direction. That leads to the rather bizarre conclusion that we are, at this moment, "inside" a point that is so small it is dimensionless (the point from which the universe is supposed to have suddenly expanded).
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Perhaps the conclusion is illogical enough to send us back to what we should have been doing all along - looking at the actual observations. If we do, we find that they all point to the incorrectness of one key assumption in the current theory. That assumption is that extragalactic redshifts measure velocities of expansion. If redshifts are not due to recessional velocities the expansion of the universe and Big
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FronJiers ofFuruiamenJai Physics. Edited by M. Barone and F. Selleri, Plenum Press, New York, 1994
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Bang is wrong and consequently creation must take place throughout the universe in events which can be observationally (hence scientifically) studied.
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Alignment of Quasars and High Redshift Galaxies Across Low Redshift Galaxies
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The clear observational pattern that emerges from systematic study of the actual sky is that galaxies occur in groups. Large, dominant galaxies tend to be surrounded by smaller younger galaxies of somewhat higher redshift (c6z~100kms-l). Even younger, more active companions tend to have higher excess redshifts. The youngest, most compact galaxies and quasars tend to be associated with active galaxies in these groups and have the largest excess redshifts (from c6z~100kms-l to c6z~2).
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Statistically these associations are overwhelmingly significant (see for review Arp 1987). In addition there are numerous instances of interactions or connections between individual low redshift galaxies and high redshift compact galaxies and quasars (see for update Arp 1993). The obvious validity of these observations has not been accepted by influential astronomers because the evidence falsifies the assumption that redshift equals velocity and hence the expanding universe to which most scientists are committed.
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As would be expected of any valid conclusion, more evidence is continually being discovered which confirms these empirical relationships between objects of widely varying redshifts. Judging from past behavior, the latest evidence will not sway the opinion of those whose interest lies with the status quo. But since the latest evidence deals with high energy X-rays and very high energy ,-rays it is of prime usefulness to those interested in real processes of matter creation in the universe.
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NGC 4258
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One of the most striking new observations is shown in Fig.I. The galaxy is an unusually active one, known to be ejecting hydrogen emission, proto spiral arms and radio material from an excited (Seyfert) nucleus. (van der Kruit, Oort and Mathewson 1972; Arp 1986a; Courtes et al. 1993). A spectacular result emerges from recent observations in X-ray wavelengths. (Pietsch et al. 1994). As Fig.1 shows, the two most conspicuous, point X-ray sources in the field pair exactly across the nucleus of this galaxy which is so well known for ejecting excited material. Any two X-ray sources in this field would only have about one chance in a thousand of accidentally pairing this exactly across the galaxy. But we have to multiply this by the small chance that two such strong X-ray sources would fall so close to the galaxy plus the extraordinary coincidence that the pairing would occur across one of the most striking examples known of an ejecting spiral galaxy. Altogether there is clearly negligible chance that the pair of X-ray sources is not associated with the galaxy. The authors of the new X-ray paper suggest they may be bipolar ejecta from the nucleus of NGC4258. The crowning result, however, is that both components of the X-ray pair are identified with blue stellar objects. One of these has been confirmed as a quasar of z rv .4 (W. Pietsch, private communication) and the other is almost certainly a quasar, probably of comparable redshift.
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NGC 4258
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Figure 1. X-ray observations by W. Pietsch et al. (1974) of the active, ejecting, galaxy NGC4258. Conspicuous X-ray sources paired across the minor axis are identified with blue stellar objects, one of which has been confirmed as a quasar with the other being investigated.
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The upshot of this one observation, by itself, is to confirm unequivocally that high redshift quasars are physically associated with and presumably ejected, from active, low redshift galaxies. This is far from the first example of this kind of association. The first one was discovered among the initial surveys of the brightest radio quasars.
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3C273 and M87
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Fig.2 shows that the brightest apparent magnitude quasars in the sky, 3C273,
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and the most active, bright radio galaxy (M87 = 3C274) - these two are aligned
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almost perfectly across the brightest galaxy in the Virgo Cluster (Arp 1967). The chance of such a configuration being accidental was calculated to be about one in a million. Many observational arguments point to the ejection origin of these two famous active objects from the central galaxy in the Virgo Cluster and, in fact, the origin of the whole cluster from this central point (Arp 1978). The Virgo Cluster is central to the Local Supercluster which is the largest aggregation of galaxies known in our sector of the universe.
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3
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DEC. (1950)
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10"
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3C274
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3C273
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O"~~----~--~----~----~--~~
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4S m
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12h30m
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14m
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R.A.{i950)
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Figure 2. The brightest apparent magnitude quasar in the sky, 3C273 and the brightest jet radio galaxy 3C274 (M87) are aligned exactly across the brightest galaxy in the center of the Virgo Cluster, M49 (from Arp 1967; 1990). (# 134 from Atlas of Peculiar Galaxies = M49)
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So just the original geometrical configuration on the sky showed 27 years ago that the quasar was a member of the relatively nearby Virgo Cluster despite its much higher redshift (cz = c x 0.16 = 48, OOOkms-1 versus cz ~ 1000kms-1 for the Virgo Cluster). Of course, during the following years all sorts of evidence accumulated to confirm that the quasars actually inhabited the Virgo Cluster. A brief summary of this evidence is as follows:
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1) A class of relatively radio bright quasars was shown in 1970 to be strongly associated with bright galaxies in the Local Supercluster of which Virgo is the center (Arp 1970).
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2) The brightest quasars in an objective prism survey by X. T. He et al. in 1984 were shown to be associated with the M87 region of the Virgo Cluster (Arp 1986b ).
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3) In the Palomar Survey of ultraviolet selected quasars brighter than V", 16.2 mag., J. Sulentic showed in 1988 that these bright quasars were concentrated in the region of the Local Supercluster (Sulentic 1988).
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4) Quasars with measured Faraday rotation show effects in the direction of the Virgo Cluster which require some to be in front of cluster (Arp 1988).
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5) An extremely unusual, low density hydrogen cloud was discovered in the Virgo cluster by R. Giovanelli and M. Haynes in 1989. It lay only 45' distant from 3C273 and was elongated accurately back toward the position of 3C273. As a clinching property the famous nonthermal jet in 3C273 pointed down the length of this extended feature (Arp and Burbidge 1990). Since the cloud had redshift of
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z = 1248kms-1 it was clearly a member of the Virgo cluster and its association
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with 3C273 therefore marked the latter as also a member. 6) When Hubble Space Telescope obtained spectra in the far ultraviolet of 3C273 it
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was found that lower redshift absorption lines were about an order of magnitude more numerous than expected from high redshift quasars in other directions (Weymann 1991). Although the conclusion was avoided, it was obvious that the extra absorption systems were most simply explained as objects in the Virgo cluster with a range of redshifts between that of the large galaxies in the cluster and the redshift of 3C273. 7) Most recent, high resolution images with Hubble Space Telescope (Nature 9 Sept. 1993) lead to an interpretation that the famous jet of 3C273 "... must be viewed in the plane of the sky nearly perpendicular to the line of sight" (Thomson et al. 1993). It is well known that, when placed at its redshift distance the quasar exhibits superluminal motion. The customary model invoked to avoid this difficulty is to have the jet aimed almost exactly at the observer. If this geometry is no longer possible then the only way to escape faster than light motion is to significantly decrease the conventional distance of 3C273.
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Virgo Cluster ROSAT PSPC
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OSQ lCl7Q
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---'___ --; lC 27)
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Figure 3. Low surface brightness X-rays connect M49 to M87 in the north and 3C273 to the south. Upper integration from ROSAT Sky Survey by Bohringer et al. 1994, lower integration by Arp from same survey.
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But now the German X-ray satellite, ROSAT, has been observing famous objects in very high energy bands and startling results have appeared. One result is the pair of quasars across NGC4258 as just described. Another result, partially in press, is shown below in Fig.3 (Bohringer, et al. 1994). A glance at the figure shows that the previously known pairing of active objects across the central galaxy in the Virgo Cluster is now confirmed by the new observation of high energy X-rays. An actual continuous path of X-rays now connects M49 northward to M87 and southward to 3C273. Southward, in the direction of 3C273 the trail of X-rays leads to another quasar of z = .334 and then to an active galaxy of cz = 2075kms- 1 (3C270) and finally, in a special analysis of an area extended further south by H. Arp (paper to be submitted), the X-ray trail leads into 3C273 where it appears to end. The appears to be the "smoking gun" where the smoke leads all the way from the active gun to the bullet which it has ejected. It is difficult to imagine what further proof one should hold out for.
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The Bright Apparent Magnitude, Active Quasar 3C279.
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Further south from 3C273 is a quasar which, although moderately faint in appearance now, was much brighter only about 40 years ago. At that time it was comparable with the brightest quasar in the sky, 3C273. Since for a long time it has been clear that 3C273 was a member of the Virgo Cluster, it was highly probable that the violently variable 3C279, falling very close in the sky to 3C273, was also a member.
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Now confirmation of this has recently been obtained from observations at even higher energy wavelengths, namely ,-rays. (The X-rays we have discussed are in the range of photon energy from 0.1 to 2.0 keV whereas the ,-ray observations shown below in Figs. 4 and 5 are in the range 0.7 to 20,000 Mev!)
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Fig.4 shows observations published by a team of observers in the 0.7-30 Mev range of ,-rays (Hermsen et al. 1993). These COMTEL observations in Fig.4 were then later confirmed by the entirely independent EGRET observations in the higher Mev range shown in Fig.5.
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The startling aspect of the publication of these results was that despite the huge team of scientists reporting the results none ventured to mention the extraordinarily important fact that the two quasars, 3C273 and 3C279 were linked together by a connection of ,-rays. The highest energy EGRET results were published in the form of a color picture in Sky and Telescope (Dec. 1992 p. 634). The strong emission from 3C279 was clearly extended to the northwest and it must have been known that it terminated on the position of 3C273. Yet the position of 3C273 was not plotted on the picture nor any mention made of it in the text.
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The intensity isophotes Fig.5 shown here were simply estimated and traced from that color Sky and Telescope picture by the present author and the position of 3C273
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and 3C279 indicated here by + signs. Although this situation has been discussed in
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meetings and privately in 1993, to date the further ,-ray observations of this crucial pair have not been released.
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In Fig.6 the X-ray observations of the Virgo Cluster have been plotted to the same scale as the ,-ray observations of 3C273 and 3C279. The extraordinary result is that the major active galaxies in the Virgo Cluster lie along an X-ray delineated extension which passes through the largest galaxy, M49 and extends southward to
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6
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Figure 4 Observations of 3C273 and 3C279 in low energy ,-rays (Hermsen et al. 1992) from COMPTEL instrument aboard the Gamma Ray Observatory (GRO)
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3C 279 z=.54
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Figure 5 Observations of 3C279 by high energy, EGRET instrument aboard GRO (I-rays 10 to 104 Mev). Isophotes of picture in Sky & Telescope (Dec. 1992) have been copied by present author who has added positions of 3C273 and 3C279 as crosses to show that these independent observations confirm the connection in ,-rays found in the observations by COMPTEL shown in Fig.4.
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3C273. The X-rays are high energy ('" 1 - 2keV) and as they approach 3C273 the photons become harder until 3C273 is conspicuous in lower energy {'-rays. The final part of the connection to 3C279 is only in high energy {'-rays and 3C279 itself is most conspicuous in the highest of all observed energy {'-rays.
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VIrVD Cluft.. ROSA' PSf'C
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Figure 6. Plot of X-ray emitting material in Virgo Cluster which ends on the quasar 3C273. The higher energy {'-rays continue on to 3C279 and are shown by approximate isophotes. The connecting material appears to rise in energy toward
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the highest energy quasar, 3C279 (z = .538).
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Trying to Understand the Observations The first order result is to confirm decisively all the previous evidence that objects of widely disparate redshifts are physically grouped together in the same assocations. Further it is confirmed that the most compact, and hence youngest, objects such as quasars have the highest intrinsic (non-velocity) redshifts. Empirically this requires the younger age to be related to the cause of the intrinsic redshift. Fortunately now there is known a solution to the field equations of general relativity which is more general than the traditional, Friedmann, expanding universe solutions. The more general solution allows creation of matter at any epoch in the universe and since the matter is created with initially low particle masses, the newly born matter has initially high intrinsic redshift which declines as it ages (Narlikar and Arp 1993). This theoretical interpretation accounts for the numerous discrepant redshift
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observations that have accumulated over the past 28 years (83 years if one wishes to count the unexplained systematic redshifts of young stars, the so called K effect).
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In particular, the discoveries reported here of intense emission of very high energy x-rays and ,-rays from quasars linked to nearby galaxies shows especially clearly that the higher redshift of these objects is connected with their extreme youth. The point is that the emission is supposed to result from acceleration processes arising from travel of charged particles through magnetic fields (synchrotron radiation). But even for the X-ray wavelengths the decay time is of the order of only 50 yrs. (Arp 1994) and for ,-rays, correspondingly shorter. This marks the higher redshift objects as characteristically in a young, active stage where they are intermittently injecting high energy particles.
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But the shocking surprise is that the low density connections between these young objects are emitting such short lived radiation. Until now the working hypothesis has been that the creation process takes place in the active nuclei of older galaxies. The new matter in compact form is then ejected in opposite directions in the form of high redshift quasars which evolve, as they age, into only moderate excess redshift companion galaxies.
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The optical connections that are occasionally observed between the older galaxies and the higher redshift companions have naturally been supposed to consist of gas, dust and or stars from the older galaxy that have been entrained during the ejection process. But now we see many more connections consisting of very high energy, short lived radiation. The only possible suggestion would seem to be that very small "retarded cores" were also thrown out with the quasar and that the quasar has left a sparkling trail of rapidly decaying high energy radiation.
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There are some difficulties with this model, however, which suggest the consideration of some fascinating alternative possibilities. The difficulties are:
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1) The lifetime of the high energy radiation is so short that it would seem difficult to sustain the emission of the connection even for the relatively short lifetime of the ejected quasar. This radiation would have to live for at least 106 - 107 years in what appears to be a low density environment.
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2) Even with low ejection speeds some of the lower intrinsic redshift ejects should show observable blue shift and red shift differences as they are ejected toward and away from us. This situation has not been ruled out by the observations but for a long time it has been estimated to be an uncomfortable restraint.
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3) Although there is abundant evidence for secondary and even tertiary ejection coming off at arbitrary angles to the original ejection lines, the development of great clusters like Virgo and Fornax seems to be in an appreciably broad filament stretching great distances and drifting somewhat irregularly from a straight line.
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All this suggests a modification of the ejection hypothesis based on reconsideration of the assumption that creation of matter takes place only in point locations in space. Dislocations in spacetime along lines in space which enable the emergence of new matter would not seem to be forbidden and could possibly explain better the newer observations. (This immediately suggests string theory although that theory has not been developed to the extent that it could make predictions of actual events in the extragalactic realm.) The possible amelioration of the aforementioned difficulties which such a "white line" theory could offer are enumerated below:
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1a) If matter wells up at one point in such a "fault line" in space this could represent the original galaxy. Later emergences, perhaps due to a creation signal from the original galaxy, could produce secondary creation along this same line. The useful point would be that smaller upwelling over an extended period all along the line could possibly account for the currently observed high energy connections between high and low redshift objects.
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2a) Since the creations take place from preexisting locations in space there need be no velocities of transport from the original galaxy nuclei and the blue and redshifts from ejection velocities could be avoided (This latter is particularly important in the matter of quantization of redshifts which would place limits of lsim20kms-1 on true translational velocities of galaxies in space).
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3a) If secondary creation lines, in analogy with strings, move through space - where ever they intersect the original creation line may promote creation nodes. If later nodes produced younger quasars and compact galaxies, the ejection lines from these secondary objects would be situated at arbitrary angles to the original creation line as observed. This interpretation suggests that jets represent material under pressure guided out of active nuclei by creation lines.
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Quantization of Redshifts.
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The one problem that seems to present unresolvable contradictions at this time are the observed quantization of redshifts. Evidence has been available for a long time which establishes that the whole redshift plane is quantized - the quasars in large steps, the galaxies in smaller (Arp 1993). Recently the smallest quantization steps of 37.5 kms- 1 seen by William Napier in the most accurate HI redshifts have become overwhelmingly statistically significant (Napier 1993).
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It is tempting to connect this quantization with periodicity in the creation process. Since the matter is created with zero mass it transitions from a a quantum mechanical realm where discretization is expected. But if they are not all at the same distance, any intrinsic galaxy redshift would be smeared out by continuously changing lookback times if the distribution of galaxies were continuously spread throughout space.
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This is presently what I would consider the most difficult unsolved problem in the subject of galaxies and galaxy creation.
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Summary Comments
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The observations push us irresistably toward a certain empirical picture of the creation of galaxies and quasars. This in turn opens exciting opportunities for theory. The creation processes of matter are no longer some kind of obscure miracle but we can actually measure the state of the matter from its radiation property at various stages in its evolution. In order to make progress, however, researchers must give up the arbitrary assumption that particle masses are constant in time. When the general case, m = m(x, t) is taken as a starting point the general solution of the Einstein field equation corresponds very well to the observed phenomena. The general connection between age and redshift becomes natural and we can hope to trace the materialization of matter from the quantum mechanical field (or material vacuum)
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to its better known state in the form of large galaxies. The problem of ultimate destiny of matter in these old galaxies lies untouched. The prediction of observed quantization of redshifts as a function of fundamental cosmic parameters forms a formidable challenge. But as a first step, before the vast majority of observers and researchers can undertake anything meaningful, they must admit the zero order result that extragalactic redshifts are not due to velocities. The empirical evidence on this point was already overwhelming and the new observation in high energy x-rays and ,),-rays now render the evidence completely inescapable. The vast observational facilities, exponentiating publication and well funded theoretical schools will continue to produce misinformation until the crucial issue of the empirical disproof of the redshift assumption is faced.
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References
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Arp, H. 1967, Ap.J. 148: 32l. Arp, H. 1970, A.J. 75: l. Arp, H. 1978, Problems of Physics & Evolution ofthe Universe, Acad. Sci., Armenian SSSR, Yerevan 1978. p.65. Arp, H. 1986a, IEEE Transactions on Plasma Science 14: 748. Arp, H. 1986b, Astrophys. Astr. (India) 7: 77. Arp, H. 1988, Astrophys. Lett. A 129: 135. Arp, H. 1994, "ROSAT Survey of an Area 10 Degrees Square around the Active Radio Galaxy Cen A", A&A, in press. Arp, H. and Burbidge, G. 1990, Ap.J. 353: Ll Arp, H. 1987, "Quasars, Redshifts and Controversies" Interstellar Media, Berkeley. Arp, H. 1990, Astronomy Now 4: 43. Arp, H. 1993, "Progress in New Cosmologies: Beyond the Big Bang" ed. H. Arp, C.R. Keys, K. Rudnicki, Plenum Press, New York p. 1-28. Courtes, G. Petit H., Hua, C.T. et al., 1993 A&A 268: 419. Hermsen, W. and 25 collaborators, 1992, A&A Suppl. in press. Napier, W. 1993, Progress in New Cosmologies: Beyond the Big Bang, ed. H. Arp, C.R Keys, K. Rudnicki, Plenum Press, New York. Pietsch, W., Vogler, A., Khabaka, P., Jain, A. and Klein, K. 1994, A&A , in press. Thomson, RC., Mackay, C.D. and Wright, A.E. 1993, Nature 365: 133. van der Kruit, P.C., Oort, J.H., Mathewson, D.S. 1972, Astron. Astrophys. 21, 169. Weymann, RJ. 1991 "The First Year of HST Observations STCI", Baltimore May 1991, p.58.
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PERIODICITY IN EXTRAGALACTIC REDSHIFTS
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W.M. Napier
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Royal Observatory Blackford Hill Edinburgh EH9 3HJ Scotland, U.K.
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ABSTRACT. Claims that the redshifts of galaxies are quantized at intervals of ~24, ~36 or ~72 km s-1 are being subjected to rigorous statistical scrutiny using new, accurate redshift data. The results of this
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enquiry to date are reviewed. The presence of a global galactocentric periodicity ~ 37.5 ± 0.2 kms- 1 is confirmed at a high confidence level. A strong redshift periodicity of ~ 71.1 ± 1.3 kms- 1 also exists
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amongst the galaxies of the outer regions of the Virgo cluster.
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INTRODUCTION
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The expression 'fool's experiment' appears to have been coined by Charles Darwin to describe the investigation of a hypothesis which no sensible individual would regard as worth testing; Darwin himself often undertook such enquiries. One imagines that, for most astronomers, the testing of 'redshift quantization' belongs firmly to this category. In essence, the hypothesis developed originally by Dr. Tifft and colleagues (e.g. Tifft 1977, 1980, 1993; Tifft & Cocke 1984) is that the redshifts of galaxies tend to occur in multiples of "'24, ",36 or ",72 km S-1 , the latter periodicity being local (applying to the redshifts of binaries or clusters of galaxies), the former two being global (depending on morphological type, and applying to the galactic redshifts after subtraction of the component due to the solar motion around the centre of the Galaxy).
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A clear verification of redshift quantization would have far-reaching consequences. In cosmology, the derivation of virial masses, and even the existence of dark matter, would be thrown in doubt; and in astrophysics, there would be a distinct shift of balance in the debate over the discordant redshifts claimed by Arp (this volume). In fact, is not clear that current cosmological and astrophysical paradigms are capable of accommodating the phenomenon. Evidently, only clearly derived, unambiguous and strong results will suffice if the phenomenon is to be taken seriously.
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However, the Tifft quantization studies, which have relied heavily on histogram binning techniques, have raised questions about the a posteriori selection of binning intervals (cf. Cocke & Tifft 1991, Schneider & Salpeter 1992) and the criteria for selection of binary galaxies; while in the case of global periodicity, a signal is in essence maximized through va,rying three parameters (the three components of solar motion), and before statements can be made about the statistical significance of the claimed periodicities, the effects of this freedom have to be assessed. Further, it is not always clear to the reader why one sample of galaxies rather than another has been chosen,
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Frontiers ofFundamental Physics, Edited by M. Barone
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and F. Selleri, Plenwn Press. New York, 1994
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and the sceptical reader may be left wondering whether negative results have gone unreported. Finally, while it is reasonable to expect an initial hypothesis to be modified with the accumulation of new or better data, several such modifications have occurred, raising the question of which version one is trying to test. For example, in its most recent manifestation it is claimed that periodicities occur over a wide range, from 2.66 km s-l upwards (but with peak power at ",36.5 km S-l: Tifft, peTS. comm.).
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These issues suggest that there is scope for a fresh approach to the quantization issue. In recent years there has been a great increase in the number of accurately measured HI profiles of galaxies; as a result, there is now a sufficient body of new data for the existence of the claimed periodicities to be settled one way or another. A colleague (Dr B.N.G. Guthrie) and I therefore embarked on a study of the quantization issue a few years ago. The philosophy adopted was to apply an objective, rigorous scrutiny to new and unbiased data, with the intention of publishing the results whether they turned out to be positive or negative. The current state of this project is summarised in the present paper: it is already clear that extragalactic redshifts are indeed strongly quantized along the lines claimed by Tifft and others.
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Methodology
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A hypothesis, once set up, may be tested against new, independent and unbiased data by asking whether they confirm a prediction unique to it. The need for lack of bias requires that any selection of the new data from a larger dataset should be carried out with prescribed, simple rules which will not affect the outcome of the enquiry. If it turns out that some modification of the original hypothesis gives a better fit to the new data, then the 'improved' hypothesis should be put to the test against further data, and so on: the protocol thus requires a clear alternation between 'playing hunches' and verifying them.
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Technique
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The statistic we have generally used in the study is I=2R2 /N, N the number of galaxies and R the length of the resultant vector in the Argand diagram when the data are wrapped round a drum of circumference P and each assigned a unit vector. A power spectrum is a plot of I against frequency l/P. For a uniform, random distribution of independent redshifts, and neglecting edge effects, the I-distribution
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has a mean value I = 2, and the probability of exceeding some value 10 by chance is
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p(I2: 10 ) = exp( -10 /2). This formula becomes inaccurate for extreme values of I, and
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the statistic is also biased and inconsistent. These problems may be circumvented by comparing the signal strength obtained for the real data with those obtained from large numbers of trials in which suitably constructed synthetic data are analyzed in identical fashion. A full discussion of the technicalities is given elsewhere (Guthrie & Napier, in preparation).
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Hypothesis
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Tifft & Cocke (1984) - TC hereinafter -claimed to observe periodicities of ",24.2 and ",36.3 km S-l in the redshift distributions of spiral galaxies with narrow and wide HI profiles respecti vely. These periodicities were global, applying to galaxies distributed over the celestial sphere, and galactocentric, emerging only when the redshift component due to the Sun's motion around the centre of the Galaxy was subtracted from each heliocentric redshift. The differential redshifts in binary galaxies (Tifft 1980) and the Coma Cluster (Tifft 1977) were said to be quantized at intervals of ",72 km S-l .
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The subsequent modifications of the above basic hypothesis have added to, rather than replaced, the above claims. A new dataset should therefore still show the above periodicities and we do not require to discuss the refinements in testing the above.
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Samples
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In our study so far, two spiral galaxy samples have been examined and are discussed here. The first comprises the nearby galaxies with the most accurately measured redshifts out to roughly the edge of the Local Supercluster; the second comprises the galaxies in the Virgo Cluster, which happens to be the nearest rich cluster of galaxies. We can see no bias in these choices of sample. Evidence for redshift periodicity is found in both of them.
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THE LOCAL SUPERCLUSTER
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Nearby Galaxies
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Guthrie & Napier (1991) first tested the global periodicity hypothesis by examining galaxies within 1000 km S-1 of the Galactic centre. The database employed was a recent catalogue of 6439 extragalactic redshifts compiled by Bottinelli et al. (1990). In the spirit of keeping the selection criteria simple and unbiased, spiral galaxies were culled from the dataset according to the following rules: (i) the quoted accuracies were (J" ::;4 km s-1; (ii) galaxies used by TC in formulating the hypothesis under test were excluded; and (iii) galaxies within 12° of M87 were excluded. The latter restriction applied because such galaxies might belong to the Virgo Cluster, which was the subject of a separate enquiry.
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By hypothesis, the global periodicity is galactocentric; thus from each observed (heliocentric) redshift one must subtract Ve cos X corresponding to the motion Ve of the Sun around the Galactic centre, X the elongation of the galaxy from the solar apex. According to TC, the solar vector yielding the periodicities was (Ve = 233.6 km S-1 Ie = 98.6°, be = 0.2°), and we first carried out a power spectrum analysis on the redshifts corrected for this vector. A prominent peak was found at a period P=37.1 km S-1 , within one of the ranges 35-37.5 km S-1 then under test. No evidence was found for the 24.2 km s-1 peak claimed by TC for narrow-line galaxies, but then only two galaxies in the list had narrow line profiles.
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The peak had a value 1=18.1 which, for a white noise distribution, has a singletrial probability,...., 10-4 according to the exponential formula. About two independent trials were involved in searching within 35-37.5 km S-1, while a signal in the range ,....,24 km s-1 (and perhaps ,....,72 km s-1 , although not strictly part of the hypothesis), would no doubt have been regarded as significant. The signal was therefore real at a confidence level C,....,0.999 according to the formula.
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An independent assessment of C was made by generating sets of 89 synthetic redshift data and determining the Imax-distribution in the range 35-37.5 km s-1. For the synthetic redshifts, the positions of the gaJaxies over the sky were preserved. The redshift data were generated by adding, to each measured redshift, the correction for the TC solar vector and then a random displacement in the range 0-8V km S-l , where 8V was small compared with the range of the redshifts and the likely dispersion within any groups and associations within the dataset. Thus the synthetic data were created by applying a 'haze' of width::; 8V to the real data, sufficient to obliterate any periodicity in the range under test but too small to have any other effect. Any significant difference between the real and the synthetic data, could thus only be due to periodicity in the former.
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15
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For each of 8V =80, 60, 40 and 20 1011 S-1 , 3000 sets of 89 data were constructed and their power spectra obtained. The distribution did not change appreciably until 8V =20 km s-1 , corresponding to synthetic redshifts within ±10 km S-1 of the real ones. Typically, one in a thousand trials yielded I-values of 18.1 or higher. Allowing for the two or three ranges under test, the periodicity hypothesis was thus again preferred over the null one (random distribution) at a. confidence level C~0.997 or 0.998, a result of high statistical significance.
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However, the motion of the Sun around the centre of the Galaxy is known with limited accuracy, and the (Vr,),P) found by TC was based on only 40 broad-lined galaxies. It therefore remained possible that the periodicity would emerge more strongly for some other solar vector in the neighbourhood of the TC solution. Guthrie & Napier (1991) therefore used published estimates of the motion of the solar neighbourhood around the Galactic centre, taking account of the solar motion relative to the neighbourhood, a probable expansion, and the ullcertainty introduced by warping of the Galactic disc, to obtain a solar vector (V0 = 2:33 ± 7 km S-1 10 = 93 ± 10°, b0 = 2 ± 10°) - the errors cannot be taken too literally. Power spectra were obtained by varying the solar vector over a wide volume of V (oj-space, 60° by 60° in longitude and latitude, and 130 km s-1 in Vr,), which adequately encompassed the error box of the solar motion. For each V 0 a set of corrected redshifts was obtained and analyzed. Several high peaks were found, the two highest being Imax =29.2 for a periodicity P=37.2 km S-1 and Imax=28.0 for a periodicity P=37.5 kms-1. The corresponding vectors were (228 kms-1 , 99°, _3°) and (212 kms- 1, 94°, -13°). Within the errors, these are reasonably close to the solar motion around the Galactic centre, but the speeds are significantly lower than estimates of the solar speed with respect to the Local Group, which lie in the range
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250:S V;v :S :310 km S-1 .
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The significance of the peaks was again assessed by comparison with closely similar synthetic data treated identically to the real data, and for each peak the periodicity hypothesis was preferred over the null one at a confidence level ~0.999.
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One further test was applied to this dataset: if the apparent periodicity was a statistical artefact, it would not in general vary with the accuracy of the data. Trials on synthetic data, on the other hand, revealed that the measured strength of the signal is highly sensitive to the redshift dispersion (Fig. 7). The resulting 89 galaxies conveniently divided up into 40 with 0'=2 or 3 km S-1 , and 49 with a =4 km S-I. For each of the two solar vectors above, trials were carried out in which 40 redshifts were randomly extracted from the 89 and I-values computed. Twenty thousand such trials were conducted, and the periodic signal was found to be significantly concentrated in the more accurat.e data, this conclusion having a confidence level 0.93 for the 228 km S-1 peak and 0.984 for the 212 km S-1 peak.
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Combining these factors, we concluded (Guthrie & Napier 1991) that the field galaxies within 1000 km S-1 of the Sun have a redshift periodicity of ~ 37.5±0.3 km S-I. The
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probability that the periodicity occurred by chance was found to be 3 x 10-6 :S p:S 3 X
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10-4 .
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Extension of the Sample
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An unexpected consequence of the study out to 1000 km S-1 was that the periodicity emerged with respect to the Sun's local galactocentric motion: the Galaxy's motion within the Local Group, or its iufall towards the Virgo Cluster, did not appear to be relevant. The phenomenon was thus nucleus to nucleus between galaxies, irrespective of large scale motions in the field. If this continued to hold out to greater distances, then the signal should appear with increasing strength as the search volume around
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16
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b0 00 I--
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• •
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'\ 292
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• 258
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W 223 206 217
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• •
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I
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I
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240 0
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1200
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10
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Figure 1. The ten highest peaks out of rv 106 in a whole-sky search (140::;
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V(0) ::;360 km S-1 ), over :W::; P ::;200 kIll S-I . • = 24 ± 3 km 8-1 , * = :37.5 ±
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0.2 kIll S-I. The formal error box of the solar galactocentric motion is shown.
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the Galaxy is increased. We have therefore extended our analysis out to 2600 km S-1 , the edge of the Local Supercluster. There is no immediate reason to suppose that the periodicity should be confined to the LSC but the cut-off was convenient as one is running out of sufficiently accurate data beyond there. The criteria for selection of galaxies from the Bottinelli et aJ. dataset were as before (essentia.lly, all accurate redshifts excluding those which TC had used). Two Virgo-like clusters (UMA and Fornax) are now incorporated in this enhanced volume, but only one eligible galaxy was found in them: for the sake of consistency, the Virgo Cluster having been excluded from the study, it too was excluded. The sample was now extended from 89 to 247 galaxies, and those with measured redshifts of extreme accuracy (0"=2 or 3 km S-1 ) increased from 40 to 97. For practical reasons we concentrated on analyzing the 97 highly accurate redshifts.
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In this extended analysis we varied the solar vector over the whole celestial sphere
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and over 140::; '/;'1 ::;:360 kIll S-1 in speed, stepping in 2 or 3° intervals and in units
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of .5 km s-l. For each pixel in this box, a power spectrum was constructed over the range 20--200 km S-1 and the highest peak recorded, irrespective of its period. About a million power spectra were generated in this search. The ten highest peaks are shown in Fig. 1. Five of the ten have P=:37.5 km S-1 (Fig. 2), and three of them lie within or very close to the error box of the solar motion. Spearman ranking of the departures of individual reclshifts from the periodicity show that all ten peaks are correlated, the three highest strongly so: thus a single underlying phenomenon is being detected. This whole-sky search confirmed that V ('.l-space is not filled with all sorts of 'periodicities' in all sorts of directions, and that indeed the only outstanding phenomenon is the TC one.
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The significa.nce of these extremely high peaks (Irv39) was assessed by constructing synthetic data as before. ThuOi each set of 97 artificial data was analyzed by varying the
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solar motion within a box of side :300 by :wo by 60 km s-1 centred on the galactocentric
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solar vector, and searching over :lO-:~9 km 8-1 . The highest peak out of tJw rv 104 power
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spectra so constructed was recorded, and the procedure repeated for ten thousand sets of artificial data. The distribution of high peaks in the 104 search volumes was then
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17
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30
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200 km/s
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20
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Figure 2. Power spectrum (1 vs frequency) associated with the solar vector (V0 ,10, b0 ) = 217 km/s,9So,--12"). The high peak occurs at 37.S kms- l .
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compared with that obtained for the true data over the same search volume. Note that this procedure, involving as it does the overall power distribution, avoids extreme value statistics of any sort.
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None of the 104 artificial datasets had statistical behaviour at all close to that of
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the real data. The real data, for example, threw up 2S peaks with 1 > 20 (n2o=2S) and 12 with 1 > 2S within the search volume, whereas none of the artificial data did.
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Extrapolation shows that, roughly, the real redshifts differ from the random ones at about. the million to one level (Fig. 3). Since periodicity is the only phenomenon which may be obliterated by the randomization procedure, it follows that the 97 galaxies possess a redshift periodicity of 37.S km S-1 at about this confidence level.
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A close examination of individual HI profiles revealed that a few of them had
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slightly asymmetric profiles. as might arise from foreground contamination. An objective criterion was used to reject 16 possibly contaminated galaxies from the list, and 24 TC galaxies which satisfied the other criteria were added. The resulting list of 103 galaxy redshifts constitutes the most accurate sample we currently have for the Local Supercluster. Its optimized power spectrum is shown in Fig. 4: I",S2 for a periodicity 37.S km S-I. A histogram of the red shift differences for this sample is shown in Fig. S: the periodicity is strong and coherent, with no sign of drift, from centre to edge of the LSC. We have not used this extraordinarily high peak to attempt a probability assessment; rather, it serves to confirm that the phenomenon in question is indeed a redshift periodicity.
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Statistical Behaviour
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The robustness of the result was tested in various ways. (a) If the periodicity arose from some obscure statistical artefact, then it might be expected to behave erratically with respect to sample size, accuracy of data and magnitude of the optimum solar vector. Fig. 6 reveals that, for a fixed solar vector (217 kIns- l , 9So, -12°), the signal strength increases linearly with N, as expected theoretically for a real signal. The observed slope is consistent with a true dispersion (J" ",8 kms- l . As can be seen from Fig. 7, this dispersion is rather critical for the detection of periodicity when the sample size is N",100, and this may account for the
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18
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-2 log P
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-8 L -________~_________L_ _ _ _ _ _ _ _~--------~~------~
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o
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10
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2S
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n 20
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Figure ;~. Probability that a set of randomized redshifts, constructed and analyzed as described in the text, would yield more than n20 spectral peaks.
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difference in behaviour between the galaxies with a formal a ~3 kms- 1 and those with a =4 km S-l, since unknown systemic errors of order several km S-l probably exist in these measurements. In this larger sample too, the signal strength was found to concentrate strongly in the best data, at a significance level ",0.998.
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(b) If, instead of holding the solar vector fixed, the optimum solar vector is derived as a function of sample size, the result shown in Table 1 is obtained. The period holds steady to within ±0.15 kms- 1 for VI') varying by only ±2 kms- 1 in speed and ±1° in direction, as the sample doubles in size from "-'50 to ",100 redshifts. This is a remarkable degree of stability, difficult to reconcile with a statistical fluke or artefact. Trials on sets of random data with in--bnilt periodicity revealed that, for a = 8 km s-1 , the r.m.s. dispersions expected are 0.2 km 8- 1 in derived period, 3 kIn 8-1 in V(.) and 1.2') in direction.
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(c) The inclusion of the Virgo galaxies, or the arbitrary exclusion of 15 redshift calibrators from the list (Baiesi-Pillastrini & Palumbo 1986) made little difference to the result. Thus the signal strength is robust to modest changes in the dataset and cannot be attributed to a particularly favorable choice of sample.
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Table 1, Optimized parameters as a function of sample size, The solution holds steady to .6.V := ±2 kms- 1 , .6.0:= ±lo atld .6.P:= ±O,15 kll1s- 1 , throughout the LSC,
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\'ma..r N V" I,;, b{.) P Imax
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1000 ,51 215 9:3 -13 37.8 :30 1400 72 213 94 -1:3 37.7 :31
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1800 86 215 94 -13 37.7 ;36
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2600 97 217 95 -12 37.5 38
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19
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Period
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200 100 70
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0.02
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0.04
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Frequency
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Figure 4. Power spectrum of the 103 most accurate, uncontaminated redshifts corrected for the optimum solar vector shown.
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20
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VI '-
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IU
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500
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CJ..
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"0
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'-
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(lJ
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..0
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E
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::J
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:z
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':::MAJ::::: 500
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1000
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~~y.i1\,1~\f.\)W\ 1'\~II \~ r. l: V: S: 2: .
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1000
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1500
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,,~MMlliMLM~o
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lIT~06n ~ An\~ : I'0
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2000
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2500
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.6.(Z (orr. (km S-l)
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Figure 5. Two-point correlation function corresponding to the redshifts and optimum solar vector employed in the previous figure. Vertical dashed lines represent the best-fit periodicity, which seems to hold over the whole of the Local Supercluster.
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21
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40
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60
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100
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N
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Figure 6. Signal strength I as a function of numbers N of galaxies. The dots are for galaxies out to ,500, 1000, 1500, 2000 and 2500 km S-1. The stra.ight line represents the mean behaviour of I(N) for an assumed true dispersion of 0'=8 km S-1 about P=37.,5 km S-1 .
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22
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10 n(I)
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o
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40
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80
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120
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Figure 7. Power distributions n(l) obtained for synthetic datasets each con-
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taining 97 redshifts distributed with periodicity 37.5 kms-1 and dispersions
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(left to right) a = 32, 12, 8 and 6 kms- 1 respectively.
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23
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(d) The data were also divided by morphological type, radio telescope employed and celestial position; no correlation was found with any of these.
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(e) Finally, a whole-sky search using synthetic data with 1'=37. 5 kms- l and 0"=8 km S-1 was conducted. The behaviour was found to have the same general characteristics as shown in Fig. l: a few peaks with the inbuilt periodicity clustered around the galactocentric solar vector, and a scattering of peaks with fractional periods over the celestial sphere and with various V",.
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Groups and Associations
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About half the galaxies in the sample of 97 belonged to loose groups or associations (Fouque et al. 1992) containing a few bright galaxies (these groupings are preserved in the Monte Carlo simulations). The data were divided into two appropriate sets to explore whether the periodicity concentrated in either the field or group galaxies. The full sample of 247 spirals was used, enhanced to 261 by the addition of a few galaxies previously used by TC. Correlation analysis revealed a strong tendency for those galaxies which belonged to groups or clusters to possess the most accurately determined redshifts. The question arises whether the periodicity truly exists in clusters, or is simply detected preferentially there because cluster galaxies have been more accurately measured. A correlation analysis supports the latter at a confidence level ~0.96.
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There are 9 doubles, 6 triplets, 3 quadruplets and a quintuplet in the sample of 97, yielding 5.5 local differential redshifts within these small groups, of which 34 are independent. The differential heliocentric redshifts are plotted in Fig. 8a, and the galactocentric ones in Fig. 8h. Becansp of the small angular extent of the groups the galactocentric correction is now second order. In effect the large number of trials involved in varying V (') are replaced by a single trial, and so in effect the differential redshifts yield a parameter-free test of periodicity. It is clearly present, power spectrum
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analysis and comparisOll with Monte Carlo trials yielding a confidence level C 2: 0.9999.
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a
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b
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o
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dV km/s
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310
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I I I I I II I
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Figure 8. Histograms of differential redshifts dV for the 53 galaxies linked by group membership. (a) heliocentric redshifts; (b) redshifts corrected for V(') = (216 kms- l , 93°, -13°). I3inwidth is 10 kIns- l . Vertical arrows mark a periodicity of 37.6 km s-1 and zero pha.se.
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Further trials involved scatkring the groups around the LSC and confirmed that the coherence in phase of the periodicity, from one group to another, is real, and not an artefact induced by the optimization procedure. Thus the ~37.5 km S-1 periodicity
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24
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is a truly global phenomenon, the galaxies being in effect test particles whose group membership is incidental
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THE VIRGO CLUSTER REVISITED
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The Virgo cluster is the nearest rich cluster of galaxies and, at the outset of the enquiry by Guthrie & Napier (1990), it had not been used in the formulation of the quantization hypothesis. It therefore constituted an unbiased and independent sample, suitable for the purposes of testing.
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In their study, Guthrie & Napier (1990) first tested for quantization in a sample of 112 Virgo spirals with relatively well-determined redshifts, initially applying a correction using a solar apex (252 km S-I, 1000 , 00 ) to obtain the galactocentric redshifts. A signal was found in the range 70-75 km s-1 then under test, but at a confidence level only 0.96::; C ::;0.99. However it was found that this signal (P=71.1 km S-1 ) was strongly concentrated in 48 galaxies situated within the less dense parts of the Virgo cluster, galaxies in the core itself showing little sign of redshift periodicity. Allowing for the a posteriori nature of the finding, and the arbitrariness involved in defining 'core' and 'less dense' regions, the periodicity was confirmed at a confidence level 0.996::; C ::;0.999. A similar result was obtained when the solar vector was allowed
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to vary over the whole sky, the speed being maintained at V(3 = 252 km s-1 .
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200
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km/s
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Figure 9. Power spectrum (I vs frequency) of 48 Virgo Cluster galaxies avoiding the core of the cluster. The high peak (1",26.5) is at 71.1 kms- l .
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The solar apex adopted in the above study was taken with respect to the Local
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Group. However the subsequent studies, described above, reveal that the global peri-
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odicity emerges strictly with respect to the Galactic nucleus: the motion of the Galaxy
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with respect to Local Group, Virgo Cluster or whatever seems not to be relevant.
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Thus in testing for periodicity within the Virgo Cluster, the Sun's galactocentric vector
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should have been subtracted. I have therefore repeated the analysis by conducting a
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box search within ±30° and ±20 kms- 1 of (220 kms- l , 960 , 00 ). A signal of strength
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I"'26.5 appears at P=71.1 km S-1 (Fig. 9), and varies little within the error box of
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the solar apex: thus there are no degrees of freedom within the error box of the latter
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and a single-trial probability exp-13.S '" 1.7 x 10-6 is obtained (the exponentia.i for-
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mula is valid to this height, against a white noise background: loco cit.). Assuming
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(J" ",10 kms- l , the periodicity which emerges is 71.1±1.3 kms- l which is, within the
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errors, the periodicity under test for a galaxy cluster.
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.
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25
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The ahove significance level should be reduced by a factor of order five to allow for the a posteriori selection of low-density regions, and a further factor of perhaps two or three to allow for the possibility of redshift interdependence through the presence of binaries (loc. cit.). Thus the periodicity hypothesis is confirmed for the Virgo cluster at a confidence level C ~ 1 - 2 X 10-5 . The earlier result yielding the same periodicity for a different vector arose because of the small angular extent of the Virgo Cluster; thus the differential solaT apex correction is small and the signal is seen over a wide range of V(0).
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CONCLUSION
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We have tested the prediction that redshifts show global periodicities ~24.2 or ~36.3 km S-1 after correction for the solar ga.lactocentric vector. We find a strong periodicity of 37.5±O.2 km S-1 to be present in accurate, independent redshift data. We have also used the Virgo Cluster to test the further prediction that a periodicity of ~72 km S-1 occurs in clusters of galaxies; we find a periodicity 71.1±1.3 km s-1 in the outer regions. The confidence levels of both these results are extremely high, and we conclude that extragalactic reclshifts are quantized. Clearly there must be a transition regime between field galaxies, loose groups and rich clusters, but this matter has still to be explored.
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The astronomer who wishes to build a cosmology based on quantized redshifts cannot be faulted on observational grounds. Thus the periodicities shown in Figs. 5, 8(b) and 9 are not 'statistica.l results': rather, they are the observed outcome of a single correction applied to the best heliocentric redshifts. Within the uncertainties, this solar correction is one which transforms our redshift catalogues to those which would be obtained by a civilization at the nucleus of our Galaxy. The phenomenon appears at about the expected strength for a given sample, it behaves as expected in respect of such matters as sample size, and it is robust to the choice of redshift data. If it is due to a gremlin in radio telescopes, then the gremlin concerned knows the galactocentric solar velocity.
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Statistical analysis enters the issue when ascertaining whether there are sufficient degrees of freedom within the error box of the solar motion for a similar result to be derived from a random redshift distribution. This question can be settled by trials, and the answer is strongly in the negative. Thus the astronomer who wishes to maintain existing cosmological paradigms must first face the challenge set by the periodicities.
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ACKNOWLEDGEMENTS
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I am indebted to Bruce Guthrie for allowing him to describe some results in advance of publication, to Franco Selleri for the invitation to address the conference, and to numerous colleagues for stimulating discussions.
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REFERENCES
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Bottinelli, L., Gougenheim, L., Fouque, p, & Paturel, G., 1990. Astr. Astrophys. Supp!. 74,391. Cocke, W.J. & Tifft, W.G., 1991. Astrophys. J. 368, 383. Fouque, P., Gourgoulhon, E., Charmaraux, P. & Paturel, G., 1992. Astr. Astrophys. Supp!. 93,211. Guthrie, B.N.G. & Napier, W.M., 1990. MNRAS 243,431. Guthrie, B.N.G. & Napier, W.M., 1991. MNRAS 253, 533. Schneider, S.E. & Salpeter, E.E., 1992. Astrophys. J. 385, 32. Tifft, W.G., 1977. Astrophys. J. 211,31. Tifft, W.G., 1980. Astrophys. J. 236, 70. Tifft, W.G., & Cocke, W.J., 1984. Astrophys. J. 287, 492.
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26
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QUASAR SPECTRA: BLACK HOLES OR NONSTANDARD MODELS?
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Jack W. Sulentic
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Dept. of Physics & Astronomy University of Alabama Tuscaloosa, USA 35487
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INTRODUCTION
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The "Big Bang" model has ascended to a powerful position in modern cosmology over the past few decades. This position has become so strong that investigation of alternate ideas has almost ceased. Observational counter-evidence certainly exists (for reviews see e.g. Arp 1987; Sulentic 1987; Tifft 1987). The general belief is that this counter-evidence consists of misinterpreted data and false clues. One could easily get the impression that all of the observations fit easily into the accepted model. In fact, at least three new concepts have assumed great importance in preserving the Big Bang against observational and theoretical challenges. In temporal order of acclamation they are: 1) black holes; 2) merger phenomena and 3) dark matter. Gravitational accretion onto supermassive black holes was required as soon as it became generally accepted that the quasar redshifts were cosmological (i.e. proportional to their distance). It provides a mechanism for producing the enormous energies implied by the assumption that quasars are at their redshift distances. Mergers came upon the scene in order to account for nearby peculiar galaxies and for the increasing luminosity and size of many objects at higher redshift. Dark matter helps to bind the groups and clusters of galaxies as well as to explain the flat rotation curves in spirals. In reality, it can help to fit almost any observation into the conventional picture. What is the observational evidence for the above three phenomena?
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Dark matter poses a very real threat to the observational astronomy profession. The fraction of matter in the universe thought to be invisible exceeds 90% in some recent estimates (e.g. Mulchaey et al. 1993). As this number converges toward 100%, astronomy may well cease to be an observational science. At the same time alternative explanations for the dynamical peculiarities are few with the most discussed being MOND (Milgrom 1983; see also Sanders 1987). Dark matter is sufficiently unconstrained at this time to handle most challenges to Big Bang theory that might arise in the forseeable future. An example of its tremendous versatility can be illustrated by the recent "rediscovery" of an association between higher redshift quasars and lower redshift galaxies (Rodrigues-Williams and Hogan 1993; see Sky and Telescope, November 1993, p.12). The reviews of counter-evidence cited above give extensive discussion to the past evidence for these associations. This evidence was
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Frontiers ofFundamental Physics. Edited by M. Barone
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and F. Selleri. Plenum Press. New York. 1994
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27
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long disputed as much because of its implications as for doubts about the observations. The excess reported in the latest study was so great that it was apparently necessary to invoke a closure density of dark matter in the galaxy clusters in order to forestall a crisis for conventional ideas.
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In recent years, almost anything that looks peculiar or that shows a luminosity excess at some wavelength has been attributed to merger activity. In fact the observational definition for a merger is quite vague. We recently studied the observational properties of compact galaxy groups (Sulentic and Raba~a 1994ab). We found that these systems show very few of the accepted observational properties of mergers. At the same time very few potential merger remnants of past compact groups are observed. This is in spite of the fact that dynamical theory predicts that compact groups should be very unstable to collapse and coalescence (Barnes 1989). If the systems most susceptible to merging show such a low level of merger activity, how can the phenomenon be common in less dense environments? The observational evidence suggests that while mergers occur, they are relatively uncommon and cannot be used to explain most peculiar extragalactic objects.
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There is no direct evidence for black holes. Indirect support comes from observation of rapid X and, ray variations in active galactic nuclei (AGN:= quasars, QSO's, Seyfert galaxies, broad line radio galaxies and BLLAC objects). Evidence for massive cores, believed to be inactive black holes, in the nuclei of nearby normal galaxies is also regarded as a form of indirect evidence. We report here on a study of the emission line properties of quasars. The motivations for this study were a) to study the frequency of occurence and magnitude of the internal redshift discrepancies observed in quasars and b) to use this data to critically test predictions of physical models for the central structure of AGN. Recently this work has become relevant to the first of the above three phenomena. The observation of double peaked emission lines in the quasar Arp 102b was interpreted as line emission arising from a radiating accretion disk (Chen, Halpern and Filippenko 1989). Direct observation of emission from an accretion disk would be tantamount to proof for the existence of black holes. Our unpopular conclusion was that the bulk of the data do not support this interpretation. We consider first the basic properties of quasar line spectra followed by the results of our study. This is followed by the results of our comparison with the predictions of line emitting accretion disk models. Finally we discuss evidence that the line shifts observed in AGN might arise from a non-Doppler cause.
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EMISSION LINES IN AGN
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Normal galaxies show spectra dominated by absorption lines that arise from the composite spectra of stars that represent their principal visual constituent. The advent of sensitive detectors in the past two decades has revealed the signature of emission from hot gas in most galaxies as well. There are two kinds of emission lines that are observed: 1) permitted lines arising from transitions following photoionization (the recombination spectrum characterized in the visual by the Balmer lines and 2) the "so-called" forbidden lines arising from transitions following collisional excitation. These lines are somewhat unique to astronomy because they arise in such low density emitting regions. The principal optical features are due to [011], [01II], [NIl] and [SII]. The critical density for [01II] )'5007A is about 106 . AGN provided an introduction to UV spectroscopy long before the first satellite telescopes opened this domain to our direct study. The higher redshift objects opened up the spectral region with rest wavelenths between 1000 and 3000 A to our view. Higher ionization broad lines such as [CIV] and [CIII as well as Lyman a are redshifted into the visible region of the spectrum (e.g. we find Lyman a at about 4800A in a quasar with redshift z=3.0). The UV lines are often referred to as high ionization broad lines (HIL's) to distinguish them from the lower ionization lines observed at lower redshift
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28
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(LIL's). In summary, optical spectra of low redshift quasars show primarily NLR and LIL-BLR lines while high redshift quasars show primarily HIL-BLR lines.
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Emission line widths in velocity units are typically less that 200 km s-1 for normal galaxies. It is the singular and unifying feature of AGN that the permitted lines are very broad (full width half maxima from 103 to 2x 104 km S-l). The forbidden lines show FWHM similar to or a little broader than the corresponding lines in normal galaxies. The Balmer lines also often show a narrow component. Figure 1 shows an example of a low redshift quasar spectrum in the region near 5000A where we find
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both broad line (BLR) Balmer features (H,B and 1') and narrow line (NLR) [0III]
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features. Broad lines in AGN show peculiarities that for a long time were only discussed
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privately in hushed tones. They were not even mentioned in the most recent textbook written on the subject (Weedman 1986). Different lines often show different redshifts in the same object. The range of redshifts in a single object can exceed 2000 km S-l. At the same time the lines can show striking deviations from symmetry. The
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Figure 1. Spectrum of Markarian 1320 in the region between HI' and [0111].\5007A. Principal lines
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are identified. Note that H,B shows both NLR and BLR components. 1A= 10-8 cm.
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keen-eyed reader will have noted a redshift discrepancy in the spectrum illustrated in Figure 1. The NLR component of H,B is centered at a higher wavelength than the BLR component in that object (Markarian 1320). Figure 2 shows an even more striking example (OQ208) where the H,B component redshifts differ by 2700 km s-l. Two kinds of internal line shifts are recognized: 1) red and blue shifting of the LIL BLR with respect to the NLR in low redshift AGN and 2) an apparent systematic blueshift (700-1000 km/s) ofthe HIL with respect to the LIL. The latter shift has to be inferred from observations of two different sets of AGN since both sets of lines (in the same object) have not, until recently, become accessible to study and measurement. Our study of the LIL vs. NLR shifts was the first of a recent flurry of activity in this area. The line shifts were originally noted by Gaskell (1982) and Wilkes (1984). It is clear that the shift and asymmetry properties of the AGN emission lines are important.
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29
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Are they giving us an invaluable clue into the internal geometry and kinematic of the line emitting region or is it possible that the shifts are evidence for a non-Doppler phenomenon? If the former is true then they pose an important challenge for current theories while the latter possibility is regarded as unthinkable. We consider both possibilities here.
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OQ 208 5
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o x 4
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A (Angstroms)
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5400
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Figure 2. Spectrum of OQ208 in same wavelength region as Figure 1. Note th" large NLR vs. BLR velocity shift (",2500 km s-1).
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SYSTEMATIC STUDY OF LINE SHIFTS AND ASYMMETRIES
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Our first study (Sulentic 1989) focused on a comparison of the redshift of HI' and [OIII]. Line asymmetry properties of HI' were also measured. We chose these lines
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for two reasons. 1) Most published data involve optical spectra of low redshift AGN
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(z~0.5) where HI' is one of the most prominent features. 2) We wanted to compare
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the (1IL) BLR vs. NLR redshift between lines that were close together but not too close to be severely blended with one another. Ha as a LIL line was ruled out because it is redshifted out of the visible at much lower redshift and is severely blended with
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NLR lines of [NIl). [OIII)A4959, 5007A are close to HI' without excessive overlap in
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most cases. There are two other important considerations for a study of this kind: 1) the
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standard of rest and 2) contamination by multiplets of Fell emission. There has been considerable confusion over which, if any, lines provide a measure of the "rest frame" for the quasar. We studied all available data that might be relevant which includes 21cm emission from neutral hydrogen (HI) surrounding the AGN and absorption line redshifts from "fuzz" surrounding some low redhift quasars. The latter is thought to be starlight from a galaxy believed to be "hosting" the AGN. This data showed agreement in redshift .6V ~ 200 km s-l of the NLR redshift (Wilson and Heckman
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1985). Usually the agreement was even better, leading us to adopt the NLR redshift
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from the lines [OIlI)A 5007 and NLR HI' (recombination emission is often observed
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from the forbidden line region) as our zero point in the line shift study. Some
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30
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recent studies have continued to use H,8 as a reference despite the fact that it shows large velocity excursions. Care should be exercized in using published data and in comparing their results with our work. The region of H,8 is infested with emission from myriads of lines arising from various multiplets of Fell. These lines inhibit accurate measurements of H,8 and [0111] as well as preclude reliable determination of the continuum level in this region. They are also a problem in other regions of AGN spectra (notably the region near rest wavelength 2800A). There are ways to
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model and correct for this contamination but we will not discuss them here. We avoid this discussion because our study focused on AGN where the presence of Fell emission was weak or absent. Figure 3 shows an example of an AGN with serious Fell contamination in this region.
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15 Q 1126-04
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Fell blends
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5200
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A (Angstroms)
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Figure 3. Spectrum of Q1126-04 in same wavelength region as Figure 1. Note the strong Fen emission blueward of H,8. Data for Figures 1,2 and 3 were obtained at Kitt Peak.
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In the end we quantified the H,8 emission line properties with the following measures: a) centroid redshift at 1/4, 1/3, 1/2 and 3/4 height; b) full width half maximum (FWHM). The centroid and width at half maximum were also measured for [0111]. The LIL line shift was then measured with respect to [0111] at each of the four heights in the line profile. In addition, an asymmetry index was defined as R= [C(3/4)-C(1/4)]/FWHM. Our first study involving 61 AGN was the largest for a sample of high resolution and SIN spectra. It revealed that LIL H,8 shows almost equal numbers of red and blue shifts (and asymmetries). This was a surprise because both were thought to be predominately red. There may still be an excess of red or blue shifts and/or asymmetries, but a larger sample will be needed to establish it. Figure 4 summarizes the kinds of line profiles that we were able to identify.
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Most other recent studies (e.g. Corbin 1989; Francis et al. 1992) have focused on the HIL line properties derived from samples of high redshift quasars observed on the ground. They suggest that HIL are generally more symmetric than 1IL and that HIL are blueshifted with respect to LI1. The magnitude of the latter shift (700-1000 km
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s-l) could only be inferred indirectly since LIL (and NLR for that matter) features
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31
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in the same objects were unobtainable. The most recent survey of the bright low redshift PG quasar sample (Boroson and Green 1992) confirm the basic results of our study. Despite a more sophisticated PCA analysis of their sample, these authors could not uncover any significant correlations between line properties that were not known (or suspected) previously. The next step is obvious; comparison of UV and optical spectra for HIL, LIL and NLR in the same objects. This has become possible because the UV sensitivity of the Hubble Space Telescope permits us to observe the HIL lines in the same sample that we have studied on the ground. Several groups, including our own, are engaged in such comparisons at this time.
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IMPLICATIONS OF LINE STUDIES
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What do we really know or think we know about quasars? We believe that they are powered by gravitational accretion onto a black hole. The only conventional alternative (the starburst model; Terlevich et al. 1992) argues that chain reactions of supernovae are responsible for the energy output. Anyone who has seen the spectrum of a supernova has been struck by the similarities with AGN emission spectra. The BLR emission line spectra in AGN are consistent with a gas at T", 1-2x104K and the size of the BLR line emitting region is constrained by variablity studies to be in the range of 10-100 light days (1 light day= 2.6 x 1010 km.). The absence of broad
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forbidden emission lines like [OIII] indicates that n;::: 109 in the LIL-BLR, while the presence of weak [CIII A 1909 indicates that n::=; 1011 in the HIL-BLR. There is growing evidence for stratification in the BLR zone with HIL emitting region closer to the ionizing continuum source. Estimates of the covering factor yield small numbers, suggesting that the BLR is made up of a collection of clouds rather than diffuse gas. The predominance of forbidden lines in the LIL argues that it lies outside the BLR. Finally there is growing evidence, already implied by radio structures, that anisotropic emission may arise from jets or cones of radiation.
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Figure 4. Combinations of emission line shift and asymmetry observed in our survey. Double peaked profiles are not included and were not found in our study.
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32
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Figure 4 shows that almost every possible combination of line shift and asymmetry is observed in AGN spectra. Both symmetric and asymmetric line profiles show (red and blue) line shifts. The only possible region of avoidance involves ones that are blue shifted and blue asymmetric at the same time (only one example was found).This stochastic property provides a very strong constraint on possible models for the kinematics and geometry of the emitting region. Favored models have invoked either a dominance of gravitational forces (infall or rotation) or radiative pressure driven outflow (ballistic models have also been considered). The stochastic nature of the line profile properties rules out such "single-force" models. It requires some hybrid explanation that can account for both red and blue shifts. We have considered the possibility that the BLR line radiation originates anisotropically (Zheng, Binette and Sulentic 1990) in a double stream model. Gaskell (1983) proposed a binary black hole model and Mathews (1993) recently proposed a model involving bouncing clouds. Any conventional model is a long way from adequately explaining the observations. It is usually possible to adequately model any single AGN but an attempt at generalization always leads to difficulties.
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Figure 5. Spectrum of Arp 102B in the region of Ha. Data obtained at San Pedro Martir Observatory, Mexico.
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Our results appear to deal a blow to models that invoke BLR line emission from accretion disks. Figure 5 shows the spectrum of Arp102b that generated considerable excitement a few years ago. It represents a kind of profile not found in our study. Its major characteristics are: 1) double peaked shape; 2) very large FWHM; 3) redshift of the line base and 4) stronger blue peak. It was quickly realized that these characteristics agree with predictions for emission originating from a rotating accretion disk. Arp102b immediately became a celebrity because it represented the nearest thing to direct prooffor black holes in the centers of AGN. Detailed models for radiating disks were developed with full relativistic treatment (including gravitational redshift and Doppler boosting) (Chen and Halpern 1989). The fit was quite good and the standard model appeared to have a boost. This idea was attractive for other
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33
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reasons 1) it provided an explanation for the strong Fell that was frequently seen
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and 2) helped solve an energy budget problem involving the ratio of 1IL to HIL emission. Unfortunately double peaked line profiles are extremely rare among AGN. A few additional cases were cited but the fits to these profiles were much poorer. In addition, some of these objects showed blue shifted bases and amplified red peaks, both of which are forbidden by the model. Epicycles were added to save the model (spotty disks are popular). It was also argued that the disk emission was only one of several components to the observed emission lines.
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We were troubled by the rarity of Arpl02b type profiles in a class of objects where an accretion disk was believed to be a standard appliance. It seemed too miraculous that Arp l02b had come along to reveal nature's secret. We decided to look at the parameter space for line shifts and asymmetries predicted by relativistic Keplerian disks. We compared these predictions with the results of our line profile analysis. Figure 6 shows a comparison of the domain of shift and asymmetry parameters that are predicted and observed. vVe tried to consider a large range of viewing angles and Schwarzschild radii for the emitting portion of the disk. It is clear that the agreement is poor. One can argue that most of the emission in most objects arises from other non-disk sources. One can argue that our model for the radiating disk is not correct or adequate. This just brings us back to the points that Arp l02b suggests most of the emission comes from a disk and that our model fits Arp l02b very well. If all of the other AGN have a hidden disk and/or different geometry and radiative properties, Arpl02b again becomes a miracle.
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Figure 6. A comparison of the shift-asymmetry domain for line profiles at FWHM. Model predictions are on the left with observational results on the right.
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NON-DOPPLER MECHANISMS
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The distribution of shift and asymmetry values actually observed and displayed in Figure 6 deserves further comment. The distribution is smooth and peaked near zero or a little redward of zero. There is no evidence for bi-modality as might be expected if there were two classes of AGN: those with and without a significant disk contribution to the line emission. If we interpret the smoothness of this distribution to a single physical model, that model would not be dominated by accretion disk line radiation. That smoothness and stochasticity must be verified with larger samples in the future.
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It is also worth noting that line shifts are observed for all classes of line profiles including those that show double peaks. If both shift and asymmetry were providing clues into the geometry and kinematics of the BLR region one might, albeit naively,
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34
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expect shifts to be observed with only certain profile types. One might expect redshifted profiles to be associated with one or more classes and blue shifted with others. In making this observation, it is important to emphasize that the shifts are real and not simply an artifact of line asymmetry. One reason we know this is that symmetric profiles also show line shifts. This ubiquity of line shifts raise the question of whether the shift property is imposed from outside. In this case it might have nothing to do with structure or motion in the quasar. This raises the subject of a non-Doppler mechanism for the production of the line shifts. Another reason to look for new explanations comes from the difficulty of any model to deal with both red and blue LIL shifts, especially if both are common. Coupling this with a systematic HIL blueshift further complicates the problem. The mere suggestion of a non-Doppler mechanism is considered offensive by the establishment. This reaction is quite independent of whether the proposed mechanism comes from conventional physical ideas or not. Perhaps the reason for this is the fear that any non-Doppler mechanism is regarded as a threat to the entire redshift-distance relation.
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Our work was originally motivated by the model for non-Doppler redshifts proposed by Wolf (1986, 1987). We discuss it here not so much as an advocate but more to demonstrate that new ideas and solutions might come from conventional physics. At this point we are only looking for a mechanism to explain internal redshift discrepancies. This solution mayor may not have a bearing on the cosmological redshift in these objects. This model and subsequent laboratory verification demonstrated that the spectrum of light might not always be invariant on propagation from the source. The idea was that partial organization or coherence in a source could produce frequency shifts in the emitted radiation, that mimic the Doppler effect. The original idea involved a static phenomenon where fluctuations in a source (or field) distribution at different points in the source region were partially correlated. Such a process could only redistribute the flux within the original frequency envelope of a line. Therefore only red or blue shifts within the original envelope of frequencies could be produced. This mechanism would produce a frequency-dependent shift. Our observational study revealed that all but two of the 61 AGN showed shifts that satisfy the former requirement. A frequency dependence of the BLR redshift might well be present in AGN considering the large scatter of line shifts that are observed and the systematic difference between UV and optical shifts.
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More recently Wolf and colleagues have investigated dynamical scattering processes (Wolf 1989; James, Savedoff and Wolf 1990; James and Wolf 1990). They conclude that "dynamic scattering in a random medium whose dielectric response function is suitably correlated in space and time" could give rise to red and blue shifts of almost any size. They originally considered only Gaussian correlation functions, but more recently (James and Wolf 1994) found that Doppler-like shifts could be generated from many random media with very different correlation functions. The relative stability of the NLR redshift suggests that, if a "Wolf" effect operates in AGN, it arises within the BLR (source) or in an envelope surrounding it (field). The dynamical model has two attractive features: 1) it produces line shifts that may be frequency independent and 2) the lines may be broadened. The best results have been produced in scattering media with a high degree of anisotropy. It is interesting that conventional models for the BLR and NLR regions have been moving in this direction for some time. BLR emission involved with jet or biconical structures is one of the few conventional ways to deal with the relatively common occurrence of both red and blue BLR line shifts. Thermal plasmas of the kind that produce the BLR radiation obey Lambert's law and should not possess any correlation properties. Therefore it is easiest to consider a component of synchrotron emission, which we know to be beamed in AGN, as the field responsible for producing the correlation induced line shifts. There is as yet no evidence for any partially coherent fluctuations of the kind required. Another problem lies in explaining why the mechanism produces almost equal numbers of red and blue shifts rather than some more restricted range of
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35
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values. This may be less of a problem for a scattering model than for the conventional explanations involving source geometry and kinematics. We look forward to more detailed comparisons between observations and model predictions of the Wolf effect. In particular, the timescale of the expected fluctuations capable of producing the observed shifts might lead to a test. While spatial fluctuations will probably be unresolvable, temporal fluctuations might be accessible at some wavelength domain.
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REFERENCES
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Arp, H., 1987, "Quasars, Redshifts and Controversies", Interstellar Media, Berkeley. Barnes, J.E., 1989, Nature 338:123. Boroson, T., and Green, R., 1992, Astrophys. J. Supp/. Ser. 80:109. Chen, K., and Halpern, J., 1989, Astrophys. J. 344:115. Chen, K., Halpern, J., and Filippenko, A., 1989, Astrophys. J.339:74. Corbin, M.R., 1989, Astrophys. J. 357:346. Francis, P., Hewett, P., Foltz, C., and Chaffee, F., 1992, Astrophys. J.398:476. Gaskell, M., 1982, Astrophys. J. 263:79. Gaskell, M., 1983, in: "Quasars and Gravitational Lenses", Liege, p. 473. James, D.F.V., Savedoff, M.P. and Wolf, E., 1990, Astrophys. J.359:67. James, D.F.V. and Wolf, E., 1990, Phys. Lett. A 146:167. James, D.F.V. and Wolf, E., 1994, submitted to J. Mod. Optics. Milgrom, M., 1983, Astrophys. J. 270:365. Mulchaey, J.S., Davis, D.S., Mushotzky, R.F., and Burstein, D., 1993, Astrophys. J.404:L9. Rodrigues-Williams, 1.1., and Hogan, C.J., 1993, Bulletin Am. Astron. Soc. 25:794. Sanders, R., 1987, in: "New Ideas in Astronomy", F. Bertola, J.W. Sulentic and B. Madore, eds.,
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Cambridge University Press, Cambridge, p. 279. Sulentic, J.W., 1987, in: "New Ideas in Astronomy", F. Bertola, J.W. Sulentic and B. Madore, eds.,
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Cambridge University Press, Cambridge, p. 123. Sulentic, J .W., 1989, Astrophys. J.343:54. Sulentic, J .W., and Raba~a, C.R., 1994a, in: "Groups of Galaxies", O. Richter, ed., PASP Confer-
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ence Series. Sulentic, J.W., and Raba~a, C.R., 1994b, Astrophys. J., July 10, in press. Terlevich, R., Tenorio-Tagle, G., Franco, J. et aI., 1992, M.N.R.A.S. 255:713. Tifft, W.G., 1987, in: "New Ideas in Astronomy", F. Bertola, J .W. Sulentic and B. Madore, eds.,
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Cambridge University Press, Cambridge, p. 173. Weedman, D.W., 1986, "Quasar Astronomy", Cambridge University Press, Cambridge. Wilkes, B., 1984, M.N.R.A.S. 207:73. Wilson, A., and Heckman, T., 1985, in: "Astrophysics of Active Galaxies and Quasi-Stellar Ob-
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jects", J.S. Miller, ed., University Science Books, Mill Valley, p. 39. Wolf, E., 1986, Phys. Rev. Lett. 56:1370. Wolf, E., 1987, Nature 326:363. Wolf, E., 1989, Phys. Rev. Lett. 63:2220. Zheng, W., Binette, 1., and Sulentic, J.W., 1990, Astrophys. J.365:115.
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36
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CONFIGURATIONS AND REDSHIFTS OF GALAXIES
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M. Zabierowski
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Technical University 50-370 Wroclaw, Poland
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11. Arp's chains of peculiar objects and Tim's bands of velocities fonn an important non-classical part of the subclustering branch in galaxy science, which (this branch) is theoretically and empirically progressive, is not degenerating.
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2. Arp recognized chains of peculiar galaxies which are different from so-called 100 Mpc filaments - they are different also in a sense of procedures which preserve different sets of hypothesis which are not subject to falsification. The branch of Arp's investigations is less connected with the readjusting the long known, old-fashioned (conservative) and "obvious" claiming that galaxies are concentrated into grains as in the case of globulars, film cennets and generally into "things" known from a cennet-like heuristic which comes from the whole tradition of Earth-bound laboratory and technical experience and from the intuitive and Newtonian-Kantian mode of growth of star clumps (Einasto et al.,1989; Grabiilska 1983, 1985, 1986, 1988, 1989, 1992, 1993; Grabiilska and Zabierowski 1987; Rudnicki 1978; LachiezeRey 1986).
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3. The Tim's bands hypothesis resembles the principle of quantum distribution of states, characterized by Zwicky as "an another statement which deals with numbers only". Is redshift proportional to k, where k=O, ± 1, ±2,... ?
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4. lwanowska (1989) was able to select five bipolar jets of galaxies in LG. She claimed explicitely that her plan of considerations favours the Arp's process but not the conventional isotropic or anisotropic collapse ofthe primordial diffusive matter.
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5. It would be rather strange to defend that there are no lwanowska's lines. It is very hard to think that the geometry of the five subgroups in LG is not highly special, that the geometrical considerations of Iwanowska are doubtful.
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6. The residual velocity dispersion 0n_lkms-1 for all galaxies classified by Iwanowska as members of the Arp's lines in LG is too great to warrant the stability of the lines and of the parts of these lines and is equal to 84. The dispersion ought to be several times smaller (Table I ).
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7. It is important to understand that - contrary to the tradition of searching the Virgo and other clusters - subclustering of the LG galaxies does not lead to any diminishing of the mean velocity
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dispersion 0n_l which is as great for the "a", "b", "A", "B" and "e" jets as for the "all galaxies"
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from the scheme ofIwanowska (1989). It seems that subdivision of the LG galaxies increases the paradox "Arp's lines - great velocity dispersion" - lwanowska did not recognized this serious discrepancy.
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Frontiers ofFundamental Physics. Edited by M. Barone
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and F. Selleri, Plenum Press, New York, 1994
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Table I. The mean residual velocities and dispersion for five lines in LG solated by
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Iwanowska (1989)
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name of the jet
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a (Milky Way) b (Milky Way) A (Andromeda) B (Andromeda) C (Andromeda)
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all galaxies
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mean residual velocity v (km/s) 44 51 5 72 88 60
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dispersion On-1 (kIn/s)
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102 78 71 120 83 84
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number of e:alaxies n 8 15 6 4 7 37
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°8. Table II shows that there is a certain possibility of substantial reduction of velocity dispersion n-1· It is of great importance for understanding the progresiveness of such searches as given by Iwanowska (1989), ofthe new scheme in astronomy.
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Table ll. Five redshift states among Iwanowska's galaxies
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number of state
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k
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"theoretical" per analogy with Tim's
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formula
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vTifft (km/s)
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empirical v (km/s)
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velocity dispersion
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0n_1 (km/s)
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number of all galaxies in thekth
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state
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n
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IvTifft-vl
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-1
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-72
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-58
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8
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5
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14
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0
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0
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1
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17
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II
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1
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1
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72
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65
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16
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9
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7
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2
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144
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141
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20
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9
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3
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3
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216
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219
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24
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3
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3
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instead of mixing of all states
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instead of the mean
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-1,0, ...,3
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60
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84
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9. Thus all galaxies (indicated by lwanowska) are characterized by redshift regularity resembling the Tim's formula v=k*72 kms-I, v stands for velocity, k is redshift band. Our hypothesis is easily for falsification because there are many galaxies without redshift value, thus additional galaxies could destroy the narrow value of the velocity dispersion 0n_1 ~ 10 km s-l and could
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destroy the idea of fragmentation of redshfift (k-regularity). All states of redshift are well separated in statistical and also individual meaning, we cannot get the other redshift state from the dispersion On_I; 0n_1 cannot serve as a bridge between k-neighbours.
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10. Many redshifts of LG galaxies have never been predicted by astronomers, they were observed but they contradicted the smallest common part of astronomical procedures - such galaxies had been considered as "uncertain". Now, the whole "uncertain" observational material is expected.
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II. It is interesting that the Arp's branch evolved into the Tim's science. This adaptability of the two branches each other is not a priori expected, it is a new problem per se and requires an explanation. A new objective situation appeared and it contributes substantially to the network of notions in extragalactic astronomy. It is a success.
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38
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Ill. Arp did not expect short galaxy chains among normal galaxies, his famous works had been devoted to chains of peculiar galaxies. Recently Garncarek (1980, 1986, 1987, 1989) searched circular clustering, scattered distribution, pairs and chains of galaxies.
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2. Circular clustering was defined by strongcompactness index of Garncarek Z4' chain shaped galaxies - by compactness index of Garncarek Z:l. The indices correspond to Garncarek's G3 and G4 types of distribution. Gamcarek had obtained the following values for Z:l and z4 :
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Table III. Garncarek's values for circular and oblong clustering of galaxies
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R(Mpc) Z3 (R) Z4 (R)
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0.2 6.5 ± 0.13 6.7 ± 0.13
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0.4 1.7±0.14 2.2 ± 0.08
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0.6 1.4 ± 0.15 1.9 ± 0.08
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° It was widely accepted that 1 Gamcarek's values of Z:l and z4 mean that the clustering is an
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universal value at least in the Jagellonian Field, 2° the clustering drops with scale R, 3° circular-
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shaped clusters dominate over the chains. No anomaly reveals Garncarek's search.
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3. However the truth is a bit different. Z4 is indeed greater than Z:l but the relative variability index Zr = (Z4 - Z:l) / Zmean is about ten! times greater for R=0.4 - 0.6 Mpc than for R=0.2 Mpc.
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Table IV. The values of the relative variability index zr = (Z4 - z3) / zmean
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R(Mpc)
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0.2
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Zr (R)
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0.03
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Z (R) = z4 - z3 0.2
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0.4
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«
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0.26
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0.5
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0.6
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''""
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0.25
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0.4
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Because z4 and Z:l possess different sensitivities we have two parameters which cannot be directly compared. z4 and Z:l form classes for itself. Z4 is intrinsic and Z:l is, too. Thus the relative variability index is necessary for proper understanding the phenomenon of clusters. 4. Between 0.2 Mpc and 0.4 Mpc a jump in the clustering properties is observed, an excess of chains is evident. Chains dominate the smaller scales of multiclustering. This or that individual chain can of course be an effect of projection (a standard argument against Arp's scheme in galaxy science), however the idea of accidentally projected background and foreground galaxies is absolutely useless to explain Garncarek's result. 5. It is strange that such small chains still exist, they are stable on the time scale of several percent of the standard (only normal galaxies are considered) age of galaxies. The other types of Gamcarek distribution described by his non-isomorphic graphs G!, G2, and G4 do not imply troubles. 6. Iwanowska advocated lines but irregular strings, rings, loops, etc. are possible too. There is no conventional explanation of chain anomaly. Why do the chains dominate small scale? Do the velocities of galaxies are less - tens and sometimes a hundred times than the conventional theory predicts?
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III. The propositions given in this work contradict the standard understanding of observational cosmology. Such a direction requires a new metatheoretical plan of evaluation of astronomical results. In my opinion the most objective synthesis has been created and developed by GrabifIska (1992, 1993). This new synthetic view on extragalactic astronomy is essential because the old picture on astronomy is absolutely insufficient. Astronomy calls for a new truth. Note that for advocates ofthe anthropic principle the lines ofIwanowska and similar configurations are rather an illusion than an astronomical fact (PaaI 1980).
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39
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REFERENCES
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Arp, H, 1969, Sky and Telescope 38, 2. Arp, H, 1967, Astrophysics Journal 148, 321. Gamcarek, Z., 1980, Ph.D. Thesis, Jagellonian University. Gamcarek, Z., 1986, Acta Cosmologica 14, 101. Gamcarek, Z., 1987, in: "The Algorithms of Selected Problems in Cluster Analysis", Technical
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University at Kielce (K. Beres and H. Beres, Eds.), PL ISSN 0860-2077. Gamcarek, Z., 1989, Acta Cosmologica 16,37. Grabinska, T, 1983, Celebration of the Centenary (1882-1982) of the Birth of Thaddeus
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Banachiewicz, "Development of Techniques of Astronomical and Geodetic Calculations", Krak6w, 20-21 May, Scientific Bulletins of Stanislaw Staszic Academy at Krak6w, Geodezja 1000, 84 (Jan Mietelski et aI.,eds.). Grabinska, T, 1985, Astrophysis. Space Sci. ll5, 369. Grabinska, T, 1986, The Hierarchical Structure ofthe Universe, in:"COSMOS-an Educational Challenge", ESA-SP 253, European Space Agency, Paris, p.303. Grabinska, T, 1988, Astrophysis. Space Sci. 150, 75. Grabinska, T, 1989, Astrophysis. Space Sci. 161,347. Grabinska, T, 1989, The Further Search of Voids in the Jagellonian Field, in: "From Stars to Quasars":Devoted to Prof. W. Iwanowska, S. Grudzinska and B. Krygier (eds.). Astronomical Observatory at Torun, Torun University ofM. Kopemik, 125. Grabinska, T, 1992, "Realism and Instrumentalism in Contemporary Physics", Wroclaw Technological Institute Press. Grabinska, T, 1993, "Theory, Model, Reality", Wroclaw Technological Institute Press. Grabinska, T, Zabierowski, M., 1987, in: "Evolution of Galaxies", Proc. 10th European Regional Astronomy Meeting of the lAU, Praha, 24-29 August, Jan Palous (ed.), 441. Einasto, J. et aI., 1989, Monthly Notices Roy. Astron. Soc. 238, 155. Iwanowska, W., 1989, in: "From Stars to Quasars", ibid., p. 159. Lachieze-Rey, M., 1986, Fractals and Galaxy Distribution, Prep. IRF-SAp CEN, Saclay,l Paal, G., 1980, Acta Geolog. Scientar. Hungar. 23,121 and 129. Rudnicki, K., 1978,IrishAstr. Journal 13, No. 7-8,241. Tifft, w.G., 1973, Fine Structure within the Redshift- Magnitude Correlation, PRE 64. Zwicky, F., 1933, Phys. Rev. 43, 1031.
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40
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ISOMINKOWSKIAN REPRESENTATION OF COSMOLOGICAL REDSHIFTS AND THE INTERNAL RED-BLUE-SHIFTS OF QUASARS
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Ruggero Maria Santilli
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The Institute for Basic Research, Box 1577, Palm Harbor, FL 34682, USA E-mail: ibrrms@pinet.aip.org
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1. STATEMENT OF THE PROBLEM
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1.1: The main hypothesis. In this paper we study the cosmological quasar redshift and
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their internal redshifts and blueshifts via a new geometry, called isominkowskian geometrY, which is constructed as a covering of the Minkowskian geometry for the representation of electromagnetic waves and extended particles propagating within inhomogeneous and anisotropic physical media. The complementary isoeuclidean and isoriemannian geometries are also indicated.
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Recall that: I) homogeneity and isotropy of empty space are the geometric pillars of the conventional Doppler law; 2) quasars chromospheres are inhomogeneous (because of the local variation of the density) and anisotropic (because of the intrinsic angular momentum which creates a preferred direction in the physical medium, the underlying vacuum remaining homogeneous and isotropic); and 3) light is emitted in the interior of the quasars and propagates in their large chromospheres (of the order of millions of radial km) before reaching empty space.
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The isominkowskian geometry implies a generalization of the Doppler law, called isodoppler law, which predicts: I) a frequency-dependent redshift for inhomogeneous and anisotropic media of low density such as atmospheres and chromospheres (in which case light loses energy to the medium); 2) a frequency-dependent blueshift for inhomogeneous and anisotropic media of very high densities, such as those in the core of the quasars (in which case light acquires energy from the medium); and 3) lack of any shift for light propagating in homogeneous and isotropic media such as water.
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Our main hypothesis is that the difference between the cosmological redshift of quasars over that of the associated galaxies is entirely reducible to the redshift of light while traveling in the quasar chromospheres before reaching empty space, thus permitting the quasars to be at rest with respect to the aSSOCiated galaxies (or being expelled at small, thus ignorable speeds), while the internal quasar red/blue/shifts is due to the particular frequency dependence of the redshift itself. According to this hypothesis, the quasar cosmological redshifts and their internal red/blue/shifts are due to interior physical characteristics of the quasars and, more specifically, to the inhomogeneity and anisotropy of their chromospheres, i.e., to the departures from the geometry of empty space.
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1.2: Experimental verifications. In this paper we show that the isominkowskian geometry
|
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provides a numerical representation of: Ii the data by Arp [I) on the cosmological redshift of quasars, thus reducing them at rest with respect to the associated galaxy, as confirmed by a number of gamma spectroscopic data establishing the physical connection of the quasars with the
|
|
asSOCiated galaxy; IIl the data by Sulentic and others (see (2) and quoted literature) on the quasar
|
|
internal red/blue/shifts; and III) the redshift of Fraunhofer lines of light from the inhomogeneous and anisotropic chromosphere of our Sun (see Marmet's studies (3) and vast literature therein).
|
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Moreover, the isominkowskian geometry identifies intriguing interconnections between the seemingly different data I, II, III, and permits the prediction of novel, experimentally verifiable effects, such as the prediction that the dominance of red of Sun light at sunset is partially (but not entirely) an isoredshift due to the inhomogeneity and anisotropy of our atmosphere. This prediction
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Frontiers ofFundamental Physics, Edited by M. Barone
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and F. Selleri, Plenwn Press, New York, 1994
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41
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is supported by the fact that the sky at the zenith is not red, in which case the increase in redness at the horizon would be completely explainable with conventional means (scattering, absorption, etc.l. Instead, the dominance of blue at the zenith and of red at the horizon supports the
|
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isominkowskian geometry. In this paper we also present of a number of experimental verifications of the
|
|
isominkowskian geometry in particle physics which are indirectly, yet significantly related to the quasar red/blue/shifts, such as the anomalous behaviour of the meanlife of unstable hadrons with speed whose structure is fully equivalent to the isodoppler law, the data on the Bose-Einstein correlation for the UAI experiments at CERN, the anomalous total magnetic moment of few-body nuclei, and others.
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QUASAR
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Interior problem: Isogeometries
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Exterior problem: Conventional geometries
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EARTH
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zg
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ASSOCIATED GALAXY
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Fig. l. A schematic view on the main hypothesis of this paper (Sect. I.Il according to the original proposal [IOJ.
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Above all, this paper is intended to stimulate the experimental resolution of the now vexing problem of the quasar shifts via novel direct experiments, such as measure the isoredshift predicted for light from distant stars passing through the Sun's chromosphere, or a planetary atmosphere, or measure the predicted isoredshift component of the Sun's light at sunset by following a sufficient number of Fraunhofer lines from the zenith to the horizon.
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All these measures, if confirmed, would provide final evidence that a portion (but not necessarily aIIl of the cosmological redshift of quasars is of interior geometric character due to the departures from the homogeneity and isotropy of space caused by the inhomogeneity and anisotropy in their environment. The separate problem of the cosmological redshift of galaxies is only briefly conSidered.
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1.3: Connection with alternative theories. Numerous alternative theories (i.e., of nonDoppler character) have been submitted (see [1-3] and review [4]) such as Arp's theory of the creation of matter in the quasars, Marmet theory based on photon scattering, and others. These theories are capable of representing the cosmological quasar redshift, although their capability to represent the internal red/blue/shift and other recent evidence is under study.
|
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The continuation of the study of these alternative interpretations is encouraged here because each one adds valuable information to the other and, in the final analysis, all quantitative interpretations may well result to be deeply interconnected.
|
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For instance, Arp's theory emerges from our studies in a new light because the creation of matter may ultimately result to be an interplay between matter and antimatter which is prohibited in conventional geometries, but permitted in our isogeometries because of an inner conjugation indicated later on. Similarly, Marmet's representation of the data on the Sun's chromosphere [3] may essentially result to be an operator counterpart of our classical studies. We regret the inability to study these interconnections in detail at this time for lack of space.
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1.3: A historical distinction. An aspect of fundamental relevance for the studies of this
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42
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paper is the historical distinction between the exterior dynamical problem (i.e., electromagnetic waves and pOint-like test bodies moving in the homogeneous and isotropic vacuum), and the interior dynamical problem (i.e., electromagnetic waves and extended test bodies moving within inhomogeneous and anisotropic physical media). This distinction was introduced by the founders of analytic dynamics, and kept up to the first part of this century (see, e.g., Schwartzschild's two papers [4), the first famous one on the exterior problem and the second little known paper on the interior problem, or early treatises in gravitation, e.g., ref.s [6L the first with a preface by Einstein).
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Regrettably, the above distinction was progressively relaxed, up to the current condition of virtual complete silence in the specialized literature. This is due to the belief that the interior problem can be reduced to to the exterior form, which is certainly admissible as an approximation (see Schwartzchild's [5) insistence on the approximate character of his solution for the interior problem). The point is that such a reduction cannot be exact, as established by the so-cal1ed NoReduction Theorems (7) which prove that an interior system (such as a satellite during re-entry in Earth's atmosphere with a monotonical1y decaying angular momentum) simply cannot be conSistently reduced to a finite conection of ideal elementary particles each in a stable orbit with conserved angular momentum.
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With the clear understanding that the Minkowskian and Riemannian geometries are exactly valid in empty space, the above theorems establish their inapplicability (rather than "violation") for interior conditions on numerous, independent, topological, analytic, geometric and other grounds. For instance, interior systems are nonlinear in the velocities (a missile in atmosphere has a drag force nowadays proportional to the tenth power of the speed and more), nonlocal-integral (because the shape of the test body directly affects its trajectory, thus caning for integral terms), and nonpotential (because the notion of potential has no mathematical or phySical meaning for contact interior forces and the systems are variationally nonselfadjoint (7)). The inapplicability of the Minkowskian and Riemannian geometries for these interior conditions is so evident to require no additional comment. The only scientifical1y meaningful issue is the construction of appropriate covering geometries specifical1y conceived for interior conditions.
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1.4: Insufficiencies of the conventional interpretation. The conventional interpretation of quasars redshifts is based on the celebrated Doppler law
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W = Wo (I - v cos a / Co ) y , y = (I - v2 / co2 f t,
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( 1.1)
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where a is the angle between the direction of light and of motion of the source and Co is the speed
|
|
of light in vacuum. The redshift ~W = W - Wo < 0, is therefore reduced to the computation of the
|
|
speed v of the quasars with respect to Earth (see, e.g., ref.s (6)). Note that such interpretation is: J} purely classical, 2) relativistic without gravitational corrections, and 3) based on the assumption that
|
|
light is emitted by the quasars and propagates immediately in vacuum without any effect when passing through the chromospheres.
|
|
The theoretical insufficiencies of law (t. t) for interior conditions are beyond credible doubts. The homogeneity and isotropy of empty space are known to be the geometriC pillars for the derivation of the law. Its inapplicability for light propagating within inhomogeneous and anisotropic atmospheres is then unquestionable.
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Astrophysical insufficiencies of law (t. J) for the interpretation of the data on quasars redshift began to emerge with the discovery of the quasars themselves, and then progressively increased in time [1,2,31. Among the most visible inconsistencies we recal1 [Ioc. cit.) galaxies younger than their stars, galaxies older than the life of the universe, discrete variations of redshift, quasars evolving into galaxies, speeds in excess of those permitted by Einsteinian theories, etc.
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These and other inconsistencies have now reached such dimenSion and diversification to can for a revision of the fundamental geometries used in the description of the universe.
|
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1.5: Bibliographical notes. The isogeometries were constructed by this author to satisfy the fonowing conditions J) have a structure which is nonlinear (in coordinates, velocities and any needed additional quantity), nonlocal-integral (in an needed variables), nonpotential, inhomogeneous and anisotropic; 2) preserve the axioms of the original geometry at the abstract level so as to permit a geometric unification of exterior and interior problems; and 3) be coverings of conventional geometries, thus admitting the latter as particular cases when motion returns to be in vacuum.
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The methods for the construction of the isogeometries were proposed by the author back in 1978 [8) when at the Department of Mathematics of Harvard University under DOE support. They are
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43
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called isotopies from Greek terms meaning "preserving the topology", and interpreted as axiompreserving (the broader genotopies [S] are reviewed for brevity, see in this respect the contribution by Jannussis [24] in these proceedings). These methods essentially permit nonlinear-non localnonhamiltonian, but axiom-preserving generalizations (called liftings) of any given mathematical or physical structure, as outlined in Sect. 2.
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Isotopies were first applied to the lifting of classical Hamiltonian mechanics and Lie's theory into covering theories [7,S]. The first isotopic lifting of the Minkowskian geometry was proposed is ref. [9] of 1982. The isotopic lifting of the Riemannian geometry was first proposed in ref. [10] of 19S5, jointly with the proposal to elaborate Arp's data [I] (Fig. 1.1). Such elaboration was subsequently conducted by Mignani in ref. [Ill. A detailed study of the isogeometries first appeared in ref.s [121. Ref.s [13] provide a classical presentation of the isogeometries with ref.s [14] giving the operator counterpart. Mathematical reviews are available in ref.s [15-17], an independent physical review is available in ref. [ISl. A review of the isogeometries is available in ref. [19]. Preliminary. yet significant verifications are provided in ref.s [25-361. A comprehensive presentation of the content of this paper is provided in ref. [37] for flat and in ref. [3S] for curved isogeometries.
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2: BASIC NOTIONS ON ISOTOPIES
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2.1: Isotopies of the unit. The fundamental isotopies are the Iiftings of the n-dimensional
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unit I = diag. (I, I,...., [) of contemporary geometries into an nXn-dimensional matrix 1 whose elements have the most general possible, nonlinear and nonlocal dependence on time t, coordinates
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x, their derivatives of arbitrary order x, x, ..., and any needed additional interior quantity, such as the
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frequency w of the wave, the local density ~, the local temperature T, the local index of refraction n, etc. [7,S]
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I = diag. (I, I...., [) -+ 1 = 1(t, x, x, x, w, 11, T, n, .J .
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(2.1)
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under the condition (necessary for an isotopy) of preserving the original axioms of I. The above Iiftings have been classified into five topologically significant classes called KadeisviJi's Classes I-V [19,20]. In this paper we shall only consider Iiftings of Kadeisvili's Class I (with generalized units 1 that are smooth, bounded, nowhere degenerate, Hermitean and positive-definite), which characterize isotopies properly speaking), and of Class II (the same as Class I but with negative-definite isounits). For brevity we shall limit ourselves to brief comments on the remaining Class III (the union of Class I and Ill, IV (holding for singular isounits representing gravitational collapse) and V (with arbitrary. e.g., discrete, isounits).
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The isotopies of the unit demand, for consistency, a corresponding, compatible lifting of all associative products AB among generiC quantities A, B, into the isoproduct [8]
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A B -+ A * B = A T B, T = fixed ,I A = A I '" A -+ I * A = A * I '" A, 1 = T- 1, (2.2)
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whose isotopiC character is ensured by the preservation of associativity, A(BC) = (AB)C -+ A*(B*C) =
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(A*B)*C. Under the above conditions, 1 = T- 1 is called the isounit and T is called the isotopic element. Note the necessity, e.g., in number theory, of lifting the product whenever the (multiplicative) unit is lifted and viceversa.
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2.2: Isotopies of fields. The isotopies of the unit I -+ 1 and of the product AB -+ A*B demand the lifting of conventional fields F(a,+,x) of real numbers R, complex number C and quaternions Q with generic elements a, conventional sum + and product axb : = ab, into the so-
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called isofields [12]
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F(a,+,*) -+ f'(a,+,*), a = a1, ad) = aTb = (a b) 1, 1 = T- 1
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(2.3)
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with elements a = a1 called isonumbers, conventional sum + and isoproduct (2.2), under the condition (again necessary for an isotopy) of preserving the original axioms of F. All operations in F
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must be generalized for f'. We have isosquares a2 = a*a = ATa = a2), isoquotient a7b = (a/b)1,
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isosquare roots at = a1, etc. (see [12,14] for detailed studies). The above Iiftings are nontrivial inasmuch as they imply the inapplicability under isotopies
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of the entire mathematical formulations of conventional geometries. As an illustration, statements such as "two multiplied by two equals four" are generally incorrect for isogeometries. In fact, for 1
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44
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= 3, "two multiplied by two equals twelve", with the understanding that the very notion of integer number is generally lost in favor of an integro-differential notion, e.g.,!! = 2exp{NJdxtjJt(xj(p(x)) as for the Cooper pair of electrons in superconductivity with wavefunctions tjJ and <p (see Sect. 5.5).
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2.3: Isotopy of metric spaces. Liftings [ ~ 1, AB ~ A'B and F ~ P then require the
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isotopies of vector, metric and pseudo-metric spaces, evidently because they depend on the field in which they are defined. In fact, real metric or pseudo-metric spaces S(x,g,R) with Hermitean metric g over R must be subjected to the Iiftings into the so-called isospaces (first introduced in [9])
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S(x,g,R) ~ S(x,g,m, g = Tg, 1 = 'rl, x~ = (x tgx)1 E J't.
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(2.4)
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under the condition, again, of preserving the original axioms of S(x,g,R). In particular, the basis of a metric (or, more generally, vector) space is preserved under isotopies [[2], thus including the
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preservation of the basis of a Lie algebra. This results in nonlinear and nonlocal (in x, X, l<, ..J
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generalization of the original space, yet such that S(x,g,J't) ... S(x,g,R). We have indicated earlier the loss of conventional numbers under isotopies. When passing
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to isospaces, one should keep in mind the loss of conventional functional analysis into a covering formulation called functional isoanalysis [20]. In fact, the very notion of angle is lost under isotopies (see next section), thus implying the consequential loss of trigonometry, Legendre polynomials, etc. in favor of suitable, unique (and intriguing) covering notions [141.
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2.3: Lie-isotopic theory. The preceding linings demand a corresponding compatible lifting of all branches of Lie's theory into the so-called Lie-isotopic theory first submitted in [S] and then studied in ref.s [12-20]). We can here mention only the lifting of the envelope ~(g) of a Lie algebra g and related exponentiation in terms of the original (ordered) basis {Xi} of g
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~ : 1, Xi' Xi (i ~ P, Xi' Xi • Xk , (i ~ j ~ k), ...... , i, j, k = 1,2, ..., n,
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e~ iw*X = 1 + (i W ~')X/ I 1 + (i W~')X • (i w~ 'X)/ 21 + .. = {e iXTw} 1 = 1(ieWTX} ,
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(2.5a) (2.5b)
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the lifting of Lie algebra g "" [~(glr with familiar Lie~theore~, such as the 2-nd theorem [Xi, Xi ]e = Xi Xi - Xi X = CiikXk ' into the Lie-isotopiC algebras g '" ~(g)] with Lie-isotopiC theorem.s{S], e.g.,
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g: [Xi, Xi ~ = Xi' Xi - Xi * Xi = Xi T Xi - Xi T Xi = ti{(t, x, x, l<, w, II, T, n,...)* Xk' (2.6)
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where the t's, called structure isofunctions, are restricted by the Third Isotopic Theorem [S,16]; the lifting of transformations and related (connected) Lie groups G into the Lie-isotopiC transformation groups [S]
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0: x' = O(W) * x, O(w) = TIke~iXk*Wk =l{TIkeiWkTXI<) = (TIkeiXI<TWkJ1, (2.7b)
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0(0) = 1, O(io)' O(io') = O(W,)· O(W) = O(io + w'), O(W)· O(-W) = 1 ,
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(2.7a)
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{e~XI).(e~ X2}=e~ X3,X3 = XI+X2+[Xl,X2~/2+[(Xl-X2),[XI,X2~~/12 +..
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(2.7cl
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the lifting of the conventional representation theory into the isorepresentation theory of Lieisotopic algebras and groups (which is structuraIly nonlinear, nonlocal and noncanonica)); and other linings [13,141.
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Note the preservation of the Lie algebra axioms by the isotopic product [A, B~ = ATB - BTA. Note also the nontriviality of the isotopic theory from the appearance of the nonlinear-integral quantity T in its exponentiation (2.7a). We should also note that, even though structurally nonlinear, nonlocal and noncanonical, the Lie-isotopic theory verifies the axioms of linearity,. locality and canonicity at the isotopic level and, for this reason, it is called isoJinear, isolocal and isocanonical. Note finally that all nonlinear-nonlocal-noncanonical theories always admit an identical isolinear-isolocaI-isocanonical reformulation with evident advantages.
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2.5: Isosymmetries. The lie-isotopic transformation groups are turned into symmetries of isospaces, called isosymmetries, via the following:
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Theorem 2.1 [2Il Let G be an N-dimensional Lie group of isometries of an m-dimensional, metric or pseudo-metric, and real or complex space S(x,g,F), F = R or C,
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G: x' = A(w) x, (x'-d At g A (x'-y') '" (x-yY g (x-y), At g A = A g At = g,
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(2.S)
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45
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and T is derived from the deformed metric g = Tg (see the example in the next section). Note also
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that there is no need to verify isoinvariance (2.9) because ensured by the original invariance (2.8).
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It is also easy to prove that 0 ., G for all Class I isotopies (but not so for other Classes for
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which in general g ., [~(g)r", g). This property identifies one of the primary applications of
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isosymmetries, the reconstruction of exact symmetries when believed to be conventionally broken. In fact, in ref.s [2!l one can see the reconstruction of the exact rotational symmetry at the isotopic
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level 0(3) '" 0(3) for all ellipsoidical deformations of the sphere. In ref. [91 one can see the reconstruction of the exact Lorentz symmetry at the isotopic level 0(3. tl '" 0(3. tl for all signature
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preserving (T > 0) deformations of the Minkowski metric 11 = TTJ. See ref.s [13,141 for the
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reconstruction of additional exact symmetries.
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2.6: Inequivalence of the Lie and Lie-isotopic theories. Despite the isomorphism 0 "" G,
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Lie and lie-isotopic symmetries are inequivalent on numerous counts, such as: I) G is customarily
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linear-local-canonical, while C is nonlinear-nonlocal-noncanonical; 2) the mathematical structures underlying C and G (fields, spaces, etc.) are structurally different; 3) C can be derived from G via
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nonunitary transformations under which
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The above inequivalence also emerges in the isorepresentation theory [141 , e.g., because the spectra of eigenvalues of the same operator are different in the two theories (due to the necessary isotopy of eigenvalue equations Hlb> = EOlb> --+ H*If» = Hl1f» = t*If» == Elf», E ¢ EO). Also, weights, Cartan tensors, etc. acquire a nonlinear.,.nonlocal-noncanonical dependence on the base manifold, etc.
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2.7: Isodual conjugations and antimatter. The generalization of the unit permits the identification of a new antiautomorphic conjugation 1 --+ 1d = -1 introduced in [2!l under the name of isoduality. This map implies the existence of isodual images of all quantities of Class I (fields, spaces, algebras, groups, etc.) into corresponding forms of Class II.
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In particular, any positive number m or isonumber m= ml is mapped into the isodual m m, number md = mid = - m or isodual isonumber d = m1 d = - while the isodual isonorm is
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h r r given by fmfd = (m T m d = - m and it is negative-definite. The most intriguing properties
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of isodual spaces and isodual symmetries is that they describe particles with negative-definite energy moving backward in time.
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Recall that antiparticles originated from the negative-energy solutions of conventional relativistic equations, although such solutions were abandoned because the behaviour of the systems was unphysical in our space-time. Isodual spaces and isodual symmetries provide a fundamentally novel approach because the interpretation of the same negative-energy solution in isodual spaces is now fully physical [13,141.
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The isogeometries therefore permit a novel cosmological conception of the structure of the universe in which, for the limit case of an equal distribution of matter and antimatter, all total quantities, such as total energy, total time, etc., are identically null (see ref. [381 for brevity).
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3: ISOMINKOWSKIAN GEOMETRY
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3.1: Isominkowskian spaces. Consider an electromagnetic wave propagating first in empty space (exterior relativistic problem), then throughout our atmosphere (interior relativistic problem). As well known, the Minkowski space
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Then, the infinitely possible isotopes C of G characterized by the same generators and parameters of G and new isounits 1 (isotopic elements T), leave invariant the isocomposition
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on the isospaces S(x,g,f'l, g = Tg,l = T- 1,
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C: x' = A(w) * x, (x'- y,)t * AT g A * (x'-y') = (x-y)t g (x-y) , AT g A = A g AT =1 gl,
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(2.9)
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The above results yield the "direct universality" of the lie-isotopic symmetries, Le., their capability of proViding the invariance of all infinitely possible deformations g = Tg of the original metric g (universality), directly in the x-frame of the experimenter (direct universality). Note also the simplicity of the explicit construction of the desired isotransformations via rule (2.7) where w are the conventional parameters, X are the conventional generators in their adjoint representation
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46
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geometrizes the homogeneity and isotropy of empty space and, as such, it is exactly valid for exterior conditions.
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The isominkowski space (first submitted in [9]) is intended to geometrize the inhomogeneity and anisotropy of interior conditions. It is constructed via two simultaneous liftings, that of the Minkowski metric Tl into the isometric 11 = TTl of Class I and the joint lifting of the unit
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of M(x,Tl,R), I = diag. (I, I, I, J), into the 4x4-dimensional isounit 1 = T 1, and we shall write
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NI(x,11,/t): 11 = T(x, x, it,ll, T, n, .J Tl, 1 = T- 1 > 0, x~ = (xll ~v xV)1 E J't . (3.2)
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Note that isospaces NI(x,11,J't) have the most general possible nonlinear-nonlocal-noncanonical structure because the functional dependence of 11 remains unrestricted. The isometric can always be (although not necessarily) diagonalized for Class I, resulting in isoseparation of the type
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x~ = xl b12(x, x, .J x1+ x2 b/(x, x, ..J ;. + .J3 b/(x, x, .J x3 - x4bi(x, x, .J x4, tv. > 0, (3.3)
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Despite evident structural differences, the joint liftings Tl -+ 11 = TTl and I -+ 1 = T- 1 imply
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that the isominkowskian space is locally isomorphic to Minkowskian space, NI(x,11,J't) ~ M(x,Tl,R)
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[9,12,141. Owing to the positive-definiteness of the isotopic element T, it is easy to see that NI(x,11,J't)
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and M(x,Tl,R) coincide at the abstract level. Exterior and interior descriptions are therefore different
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realizations of the same abstract geometric axioms. This is the central geometric property which is
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assumed for the description of both, exterior and interior relativistic problems, and which carries
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intriguing consequences, as we shall see.
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3.2: Characteristic quantities of physical media. The b-quantities (at times also expressed
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in the form bll = I1~) are called the characteristic quantities of the medium considered. The inhomogeneity of the medium can be represented via an explicit dependence of the b's on the local
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density, and the anisotropy can be represented via different values among the b's, the factorization
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of a preferred direction of the medium, and other means.
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When the local behaviour is needed at one given interior pOint, one needs the full
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nonlinear-nonlocal dependence of the b's. This is illustrated, e.g., by the local speed of light at one
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given point when passing though our atmosphere which is given by c = cob4 = cO/n4' where n4 = b4- 1(the local index of refraction) has a rather complex functional dependence on local quantities.
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When the global behaviour throughout a given physical medium is requested, the
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(tv.), characteristic quantities can be averaged into constants, bOil =Aver.
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or nOll = Aver. (~), 11 =
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I, 2, 3, 4. This is evidently the case for the average speed of light throughout our atmosphere c =
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co/n°4, in which case n°4 is the average index of refraction. Note that bll '" bOil '" I in vacuum. A first intuitive understanding of the isominkowski spaces can be reached by noting that
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the characteristic functions bll = I1~ essentially extend the local index of refraction l/n4 to all space-time components. Equivalently, by recalling that physical media are generally opaque to light,
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the isotopies M(x,Tl,R) -+ NI(x,11,J't) essentially extend to all physical media the geometriC structure
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of Jight in vacuum. In this sense, the characteristic constant b04 geometrizes the denSity of a given medium, while the constants b\ geometrize the internal nonlinear-nonlocal effects.
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It is evident that different physical media necessarily require different isounits 1. This
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occurrence is similar to the need of infinitely possible Riemannian spaces in general relativity in
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order to represent the infinitely possible astrophysical masses. The point here is that each mass
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admits infinitely possible isounits, trivially, because each mass can be realized in infinitely possible
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different densities, sizes, chemical compositions, etc.
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3.3: Isominkowskian geometry. It is the geometry of isospaces NI(x,11,/t) and possesses
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novel characteristics as compared to the conventional geometry. Their understanding requires the
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knowledge of the inapplicability mentioned in Sect. 2 of the notion of angles, trigonometry and
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functional analysis at large in favor of covering isotopic notions.
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To study the main characteristics, let us consider first the isoeuclidean geometry which is
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evidently the space-component of the isominkowskian geometry. Consider the isoeucJidean
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subspace E(x,Il,J't) in the 1-2 plane with diagonal isometric and separation
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47
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f'(
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r,
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X,~D,1n\).•
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~ X
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-_
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XIh'12(x, x.,,x., ...) xI
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+
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X2 bi?'Jx, x., .},\, ...) X2 -_ m. v.
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As one can see, this space is curved in the most general possible form, that is, with curvature dependent on local coordinates x, velocities X, accelerations l<, etc. (see next section). The loss of the conventional angles then follows from the evident loss of intersecting straight lines.
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At this point, the isotopies playa central constructive role. Recall that the original space is flat. Its image under isotopy is then isof/at. Similarly, the images of straight lines are isostraight i.e., verify the axioms of straight lines in isospace. This implies the possibility of reconstructing angles under isotopies which is not possible for Riemann. The use of the isotopies of the group of rotation [211 permits the identification of the unique isotopic image a of a conventional angle a in
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f;(x,8,R) given by a = ablb:2. This permits the construction of the isotopies of conventional
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trigonometry, here called isotrigonometry, which is based on the following isofunctions and related properties
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isosin a = b2- 1sin (a bl b2), isocos a = bl-Icos (a b l b2),
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a a b 12 isoc0s2 + bi isosin2 a = co; + sin2 a = I.
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(3.5a) (3.5b)
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Note the deformation of the argument a --> a as well as of the magnitude of trigonometric
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functions I --> bJc-I which are intriguing for certain (e.g., nuclear) deformations of potential wells
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and wavefunctions [141. The rest of the isotrigonometry can then be constructed accordingly. The extension to the three-dimensional isoeuclidean case is consequential and it is omitted here for brevity [14].
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We consider now the hyperbolic isoplane 3-4 with isoinvariant
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x~-- x3b32(x, x.,.x., ..)x3_ x4b42(x, x.,,x., ...)x4 inv.
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(3.6)
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v v The isotopic image of a hyperbolic angle (speed) v is then given by = vbJb4, as provable via the
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use of the isorepresentations of 00. Il [13,141, with corresponding isohyperbo/ic functions and
|
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related properties
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v v isosinh = b4-1sinh (v b3 b4), isocosh = !>.i-I cosh (v b3 b4 ),
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(3.7a)
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(3.7b)
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We are now equipped to indicate a most important feature of the isominkowskian geometry, the reconstruction at the isotopic level of exact straight lines, perfect circles and conventional light cones. The loss of the notion of straight line and its reconstruction under isotopy has been indicated earlier. The preservation of perfect circles can be seen as follows. Recall that, by conception, isotopies of Class I map the circle into the infinite families of ellipses (3.4) with
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semiaxes bJc2. But the unit is jointly lifted from I =diag. (I, Il to 1 = diag. (bl- 2, b2-2). We then have the deformation of each semiaxis I --> bk2 with the joint deformation of the unit I --> bk- 2. The
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original circle therefore remains a perfect circle in isospace, while the ellipses emerge only when the figure are projected in our space (see ref.s [13,141 for details).
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We now outline the preservation of the light cone under isotopy. Let us first recall that, in the physical reality, the speed of light is not a "universal constant", but a locally varying quantity with a rather complex functional dependence on density, index of refraction, etc. As a result, the "light cone" in interior problems is not a "cone", but a rather complex hypersurfaces. The understanding of the isominkowskian geometry requires the knowledge that the "deformed cone" of the physical reality is mapped into a perfect cone in isospace, called light isocone, and the locally variable speed is mapped precisely into the original, constant speed of light in vacuum co' Consider
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the isolight cone x~ =0 in the 3-4 plane, Eq. (3.7). Then, the isotrigonometry yields Ax = D b4 sina, At
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= D b3 sin a, and
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from which we recover the conventional expression in empty space tang a = Co = const. This
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48
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occurrence is an expression of the overall unity of physical and mathematical thought achieved by
|
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isotopic technique because they allow the use of the same light cone for motion in vacuum with
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constant speed Co and motion in interior conditions with variable speed c = cob4. 3.4: Isolorentz and isopoincare' symmetries. Necessary complements of the
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isominkowskian geometry are given by the isotopies 0(3.1) and N3. j) of the Lorentz 0(3. j) and
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Poincare P(3. j) symmetries, respectively. They were constructed for the first time in ref. [9] via the
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|
Lie-isotopic theory and then studied in details in monographs [13,14] to which we must refer for
|
|
brevity. We can only recall the isolorentz transformations here presented for 11 = diag. (gil' g22'
|
|
g33' -g444) with conventional functions for simplicity (rather than isofunctions)
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(3.9a)
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x ,3 = x3 cosh [ v ( &1sg44 ) 1 ]- x4 g44 ( g33 g44 ) -1 sinh [v ( g33 g44 ) t] = 1'(xL 13 x4), (3.9b)
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x' 4 = - x3 g33 ( g33 g44 ) -1 sinh [v (g33 g44 )1] + x4 cosh [ v (~3&44 ) t] =y(x4 - T3x3l, (3.9c)
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132~ = ykgkk yk / co g44 Co, l' = II - yj 1-1,
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!3.9dl
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which are easily constructed via rule (2.7) with w = v, X given by the conventional Lorentz generators in adjoint representation, and T = diag. (gil' g22' g33' g444) > O. Note the unity and mutual consistency of the algebraic and geometric isotopies. In fact, the latter predict the hyperbolic angle
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v = v (g33g44)lI2 which turns out to be exactly that provided by the lie-isotopic theory. The
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|
addition of the isorotations and isotranslations is done via similar rules and with similar algebraicgeometric consistencies (see [13,14,21] for brevity).
|
|
Note that the absolute value is necessary in the definition of y, Eq.s (3.9d) because v"2=
|
|
vkhJc2Vk >=< co2. This is the first contact we have in this paper with the joint representation of redshift and blue shift (see below).
|
|
As expected, isotransformations (3.9) have the most general possible nonlinear-nonlocalnoncanonical structure (in which case they are called general isolorentz transforms) because of the
|
|
arbitrariness in the functional dependence of the gill! terms, as needed for the form-invariance of isoseparation (3.3). Yet the isolorentz symmetry is locally isomorphic to the original symmetry, as
|
|
expressed by their formal similarities with conventional Lorentz transformations, and confirmed by
|
|
the isotopic commutation rules [13,141.
|
|
Note finally that general isotransforms (3.9) are nonlinear and therefore noninertial, as expected for interior conditions. Nevertheless, when passing to the outside and studying the global behaviour via the average of the b's to constants b\L' they reacquire the conventional linear and therefore inertial character (in which case they are called restricted isolorentz transforms.
|
|
3.5: lsominkowskian classification of physical media. Recall that there is an infinite variety of interior physical conditions for each given astrophysical mass. This variety is classified
|
|
by the isominkowskian geometry into nine different types which play a fundamental role in practical applications (Sect. 5). Consider for simplicity the global interior cases with space isotropy
|
|
y bO 1= b02 = b03· We then have the isominkowskian classification into: Type I for b03 = b04 $ = [3, =
|
|
y), II for bO3 > bO4 ([3 > [3, y < y) and 1II for b03 < bO4 ~ < [3, y > yl. Each of these types is then
|
|
divided into three subcases depending on whether b4 = I, < I, > I. The following identifications are known at this writing. Type 1.1 (b3 = b4 = I) is therefore
|
|
empty space. Type 1.2 (b3 = b4 < j) represents the homogeneous and isotropic water with index of
|
|
refraction n° = bO4-I and speed of light c = co/n° < co' Type 11.2 (bs > b4 < j) represents our
|
|
inhomogeneous and anisotropic atmospheres with low density. Type 11.3 (b3 < b4 > I) represents the
|
|
media of the highest possible density, such as those in the interior of a star (or, equivalently, in the
|
|
interior of a hadron). Additional identifications are under study, e.g., for conductors (Type II. j), superconductors (Type 1.3), intermediately heavy astrophYSical atmospheres (Types III.l and 2), etc. [13,14].
|
|
3.6: lsospecial relativity. The abstract identity between spaces and isospaces M(x,Tj,R) '" M(x,l1,/t) and between symmetries and isosymmetries 0(3. j) "" 0(3.1), implies the isotopies of all basic
|
|
postulated of the special relativity, called isopostulates. originally proposed in [9] and studied in detail at the cIassicallevel in [13] and at the operator level. in [14].
|
|
A new relativity for interior conditions therefore emerges from the isominkowskian geometry, the isopoincare symmetry, and the isopostulates, called isospecial relativity [9,13,141. It is a covering of the special relativity in the sense that: A) it describes structurally more general
|
|
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|
49
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|
|
|
systems (nonlinear-nonlocal-noncanonical systems of the interior problem), B) via structurally more general methods (isotopic methods); and C) admits the conventional special relativity as a
|
|
particular case whenever motion returns to be in vacuum for which ~ = 1. Moreover, the special
|
|
and isospecial relativities coincides, by construction, at the abstract level. Readers not familiar with isotopic techniques should therefore be warned that possible criticisms on the isospecial relativity for interior conditions essentially are criticisms on the conventional relativity in vacuum.
|
|
A significant property of the isospecial relativity in its most general possible formulation of Kadeisvili Class V is its direct universality in the sense of applying for all possible deformations i] = TT] of the Minkowski metriC (universality), directly in the frame of the observer (direct universality). This property has significant experimental relevance. As we shall see in Sect. 5, numerous noneinsteinian time evolutions exist in the literature which, being different, create evident problems in their experimental test. Such problems are eliminated by the geometriC unification of all seemingly different laws into a unique isotopic law.
|
|
Another general property of the isospecial relativity of Class [ is its abstract identity with
|
|
the general relativity for the isotopiC element dependent on the local coordinates only, T = T(x), i] =
|
|
TTJ = TJ(x). This property can be better seen from the fact that the isopoincare symmetry for the isotopic element T(x) characterizes the symmetry of all possible Riemannian metrics i](x).As an illustration, the nonlinear symmetry of the Schwartzchild line element is given by merely plotting its glJ.lJ. elements in isosymmetry (3.9). The same holds fro all possible Riemannian line elements. The geometric unification of the special and general relativities then follows. The point important for this paper is that such unification is a mere basis for broader interior treatments because isotopic
|
|
methods naturally hold for arbitrary dependence T(x, x, x, w, 11, T, n, ... ).
|
|
3.7: Isodoppler redlblue/shifts. The prediction of the isospecial relativity most important for this paper is that light propagating within inhomogeneous and anisotropic media experiences an
|
|
alteration of its conventional Doppler's effect according to the isodoppler law (for a =0)
|
|
(3.10)
|
|
|
|
As one can see, the isospecial relativity has the following predictions: Types 1.1, 1.2, 1.3 (empty
|
|
space or water) have no deviation from the Doppler shift, as verified in the physical reality in which light does not lose energy to the medium; Types 11.1, 11.2, 11.3 (such as our atmosphere) have an isoredshift, that is, a shift toward the red in addition to the Doppler shift due to the loss of energy to the medium; and Types 111.1, 111.2, 111.3 (such as hyperdense quasars atmospheres or the interior of hadronic matter) have an isoblueshift due to the acquisition of energy from the medium.
|
|
[n order to reach a form of the isodoppler law applicable to astrophysics, we assume for
|
|
simplicity the space-isotropy b[ = b2 = b3 = b, we recall the dependence of the index of refraction
|
|
b4 from the frequency and assume the factorizability of such a dependence in the ~ term. We can
|
|
therefore write ~2 = ~(b2/bi) = ~[b02/bOi] f(wo)' where bO and b04 are constants and f(wo);;:; I is the
|
|
factorized frequency dependence. Law (3.10) for the global behaviour of light through quasar
|
|
chromosphere can be written in one of the forms
|
|
|
|
w = y Wo =--II---~-[-Wb0-o2-/ -bO-i]-f;(-~)-I-t ----,
|
|
|
|
(3.lla)
|
|
|
|
The astronomical redshift of quasars is then due to the property for a basic frequency, usually 4680 AO [2],
|
|
|
|
BO = [b02 / bO 2] f(w )I
|
|
|
|
= const. > I
|
|
|
|
4
|
|
|
|
0 Wo= 4680 AO
|
|
|
|
'
|
|
|
|
(3.12)
|
|
|
|
The internal red/blue/shift of quasars is then due to the full use of law (3.lla) which shows that frequencies smaller or bigger than the basic frequency 4680 AO have proportionately different shifts which are expected to have an approximate Gaussian behaviour owing to the condition f(wo) ;;:; J.
|
|
|
|
50
|
|
|
|
For the sun's chromosphere we recall the experimental information (Sect. 5) that the velocity dependence is restricted to the space components bk . In this latter case, the global averaging must be done on the expression ~B resulting in the form KOf(wo) = < v2tiv)2/cobl >f(wo), f(wo) ;:;; I, with isodoppler law
|
|
(3.13)
|
|
The comparison of the above laws with astrophysical data is done in Sect. 5. 3.8: Other predictions. The isospecial relativity has a number of other novel predictions
|
|
for interior conditions (Le., predictions not possible for the special relativity) which can be experimentally tested with contemporary technology, such as the isodilation law [9]
|
|
(3.14)
|
|
which is confirmed by available experimental data on the behaviour of the meanlife of unstable hadrons with speed (Sect. 5), or the isoequivalence law
|
|
(3.15)
|
|
verified by preliminary experiments on the chemical synthesis of hadrons [36] and other data [36,14].
|
|
3.9: Isodual relativities. By recalling the antiautomorphic maps I -> 1d = -I, and 1 -> 1d = -1 and their characterization of antiparticles (Sect. 2.7), isotopic methods identify four different
|
|
relativities: the conventional special relativity on M(x,TJ,R) with invariant P(3. Il for the description of particles in vacuum; the isodual special relativity on the isodual Minkowski space Md(x,TJ,Rd) with isodual Poincare symmetry pd(3.1) for the description of antiparticles in vacuum; the isospecial relativity on isominkowski spaces tv!(x;Tj,lU with isopoincare symmetry P(3.1) for the description of particles within physical media; and the isodual isospecial relativity on the dual isominkowski spaces rVld(x;Tjd,J'td) with isodual isopoincare symmetry pd(3. Il for the description of antiparticles in interior conditions.
|
|
The working hypothesis in which the total matter is equal to the total antimatter then leads to a structurally novel view of the universe in which the total energy, the total time and other total characteristics of the universe (as the sum of those for matter and antimatter) are identically null, a view confirmed by the isotopies of Riemann [23].
|
|
3.10. Connections with the studies by Arp, Sulentic, Marmet, and others. We indicated in Sect. I that Marmet theory [3] can ultimately result to be an operator version of the isodoppler formulation. A similar interconnection exists with Sulentic studies [2], and with other approaches.
|
|
A most intriguing interconnection appears to exist between the isodoppler representation
|
|
and Arp's theory [Il achieving a non-Doppler redshift via the creation of matter. This latter view is
|
|
faced with known problematic aspects and understandable resiliency in the physics community when considered within the context of conventional relativities alone. This scenario is altered by the isodual relativities. In fact, conventional relativities represent both matter and antimatter in the same space-time, with ensuing difficulties for the creation of matter from nothing. In our covering isorelativities antimatter is represented in a separate isodual universe, which is known not to be isolated from our universe because of the finite transition probabilities between positive- and negative-energy solutions of conventional relativistic equations. Rather than the creation of something from nothing, Arp's theory on the creation of matter acquires a different light in a cosmology with null total energy, time and other quantities [38] because it may result to be an interchange of energies between the two universes. We regret the inability to study these interconnections in more details at this time.
|
|
3.11: Applications. Numerous applications of the isospecial relativity are now available at the classical, operator, statistical and levels [13,14]. [n Sect. 5 we shall outline only those experimental applications which are directly or indirectly related to the quasars red/blue/shifts. [t may be important for an overall view to outline below other applications.
|
|
The simplest possible application is a static one, the representation of a straight rod when penetrating in water [14]. As well known, the rod appears to bend when entering in water, but in the reality it remains straight. Thus, the angle a of rod bending in water measured from the outside
|
|
51
|
|
|
|
a does not coincide with the physical angle in the interior of water. This occurrence is directly
|
|
represented by the simplest possible case of isoeuclidean geometry with line element (3.5) in which
|
|
b1= b2 = bO owing to the homogeneity and isotropy of water. The value bO is then determined by the
|
|
a relation = abo2. In short, the isoeuclidean geometry corrects the error in our perception that the
|
|
rod is bent by keeping it straight. The simplest possible dynamical application is the classical relativistic particle in a
|
|
resistive medium without potential interactions [13]. Consider a free, classical, extended, relativistic particle with Lagrangian L = mc and Minkowskian geodesic d2xfl/ds2 = O. The penetration of the particle within a resistive medium is described by the same Lagrangian although now written in isominkowski space L = mc = mCob4. The infinitely possible resistive forces due to shape, density, temperature, speed, etc. cannot be represented by central conception with the Lagrangian because they are nonpotential. They are then represented by the infinitely possible isotopies of the unit I -+
|
|
1. The understanding of the isospecial relativity requires the additional knowledge that the motion
|
|
of the extended particle in interior conditions remains ful/y geodesic, i.e., in isospace we still have d2xfl/ds2 = O. [n summary, the two structurally different trajectories (one free and the other with contact interactions, one linear-local-potential and the other nonlinear-nonlocal-nonpotentia\) are completely unified, and solely differentiated by the selection of the unit. The point is that all geometric, algebraic and analytic axioms are the same.
|
|
A deeper inspection soon reveals possibilities of physical applications for the isospecial relativity which are simply beyond any descriptive capacity of Einsteinian theories [13,14]. [n fact,
|
|
the isounit of the preceding example admits the factorization 1 = 10 diag. (bO 1-2, b02-2, b03-2, b04-2).
|
|
Thus, the Lagrangian L = mc in isospace can directly represent the actual "nonsphericar shape of the test body considered, such as a spheroidal ellipsoid with semiaxes bO 12, bol, boi (or arbitrary shapes with a nondiagonal isounit). The term b04 geometrizes the density of the test body and the factor 10 represents the drag force. Such a representation is manifestly impossible with the conventional relativity even after quantization. But these are the beginning of the capabilities of the isospecial relativity. A still deeper inspection shows that the same Lagrangian L = mc in isospace can represent all infinitely possible "deformations" of its original "nonsphericar shape, e.,g., via a dependence of the b\-quantities on pressure, speed, etc., which is manifestly impossible for conventional relativities even after first, second or third quantization.
|
|
These and other features we cannot report here for brevity (see ref.s [13,14]) have permitted the isospecial relativity to resolve some of vexing problems in contemporary physics, such as the first achievement of an exact numerical representation of the total magnetic moments of few-body nuclei [141 which have still remained unexplained in their entirety despite studies over three quarter of a century. The isotopic treatment is simply given by representing protons and neutrons as extended and, therefore, deformable. This implies the deformability of their charge distributions depending on the physical conditions at hand and, thus, of their intrinsic magnetic moments. The anomalies in total magnetic moments then merely represent the (generally small) deformations of the constituents in a nuclear structure. The point is that these deformations are simply beyond any possibility of the special relativity.
|
|
We should also mention the resolution of another vexing problem of contemporary physics permitted by the isospecial relativity, that of quark confinement [141. Current trends assume the same Minkowski and Hilbert spaces for the interior and exterior problems of hadrons. A finite probability of quarks tunneling free is then inescapable from the uncertainty principle irrespective of the infinite character of the potential barrier, which is contrary to experimental evidence. Now, the isotopic SO(3) symmetry is isomorphic to the conventional SU(3), and the quantum numbers of the two theories are identical, thus rendering the isotopic theory fully compatible with existing experimental data. Moreover, the use of the conventional relativity for the exterior and the isospecial one in the interior easily permits the two Hilbert spaces to be incoherent, in which case the transition probability for free quarks is rigorously proved to be identically null even for collisions. with infinite energy and no potential barrier at all (as hinted by asymptotic freedom).
|
|
[t is important also to understand that the isospecial relativity is applicable in fields beyond physics, e.g., in theoretical biology. An unexpected and suggestive application along the latter lines is in conchology [14]. Consider the growth of sea shells with minimal complexity, e.g., with one bifurcation [22]. Such a growth can indeed be inspected with our Euclidean perception of physical reality. Nevertheless, computer simulations show that sea shells should crack during their
|
|
52
|
|
|
|
growth if strictly represented in our Euclidean or Minkowskian spaces [22]. On the contrary, their growth is normal if represented in isoeuclidean or isominkowskian space, that is, with a conventional Lagrangian over a generalized unit. The representation of the bifurcations themselves is controversial in Euclidean or Minkowskian spaces because requiring discontinuous transformations into negative times [22], while the same can be continuously represented via our isorelativities of Kadeisvili Class II I. Note that the dimension of the the space is not altered. The generalization is in the structure of the geometry, as advocated in this paper.
|
|
The latter example clearly identified the limitation of our perception of Nature, and suggests caution before claiming final knowledge based on our manifestly limited three Eustachian tubes, not only in biophysics, but also in physics and astrophysics.
|
|
|
|
4: ISORIEMANNIAN GEOMETRY
|
|
4.1: Isoriemannian geometry and its isodual. The cosmological implications of this paper are studied in the separate paper [38]. We here merely mention that the isotopies and isodualities apply also to the Riemannian geometry resulting in covering structures admitting in the tangent space the isominkowskian geometry and its isodual.
|
|
4.2: Gravitational isodoppler shifts. The aspect important for this paper is that the isodoppler shift is also additive to the gravitational redshift as in the relativistic case. Our study of the quasar red/blue/shifts can therefore be restricted to the isodoppler law (3.11l because the gravitational treatment would yield conventional gravitational corrections (when appropriate).
|
|
4.3: Isogeneral relativity and its isodual. The above studies imply a step-by-step generalization of Einstein exterior gravitation for test particles in vacuum into a dual form, one called isogeneraJ relativity or isogravitation for short, for interior gravitational problems of matter, and the other called isoduaJ isogravitation for the interior gravitational problem of antimatter. The interested reader may consult ref.s [13,38]. The aspect important for this paper is that conventional gravitational theories possess no universal symmetry, as well known. On the contrary, isogravitation is based on the same symmetry at the foundation of the isodoppler law, the isopoincare symmetry. Experimental confirmations of the isodoppler law within physical media would therefore have direct gravitational and cosmological implications.
|
|
|
|
5: REPRESENTATION OF QUASARS COSMOLOGICAL AND INTERNAL SHIFTS
|
|
|
|
5.1: Representation of Arp's data [il. Isodoppler law (4.10) was originally submitted by
|
|
this author in memoir [JO] of 1988 to avoid the violation of Einstein's relativities under Einsteinian exterior conditions in vacuum, e.g., to avoid speeds of matter in vacuum higher then the speed of light. The main hypothesis of Sect. l.l can now be more technically expressed via the
|
|
characterization of quasars chromospheres with isominkowskian media of Type 11.2 with bj = b2 =
|
|
w' bs > b4, b4 < I, ~ > ~, y < y and average speed of light c = CVb4 = co/n° < co' with consequential
|
|
natural redshift = yw < w' = yw. The elaboration of Arp's data was then suggested in [1OJ.
|
|
Numerical calculations along this proposal were done by Mignani in ref. [II] of 1992 by confirming that iSodoppler's law (4.1 I) can indeed reduce the speed of the quasars all the way to that of the associated galaxies. This was submitted as a limiting case in which the difference between
|
|
the quasars redshift and that of the associated galaxy is entirely of isotopic nature. It is understood
|
|
that quasars can indeed be expelled from their associated galaxies, but at Einsteinian speeds v « CO'
|
|
This latter case implies a small correction of the b-quantities and can therefore be ignored.
|
|
The isotopic elaboration of Arp's data was conducted in ref. [II] via the relation
|
|
|
|
BO=b~O = (t.w' + 1)2 - I x (t.w' + ])2 - I
|
|
|
|
(5.1)
|
|
|
|
b04
|
|
|
|
(t.w' + 1)2 + I
|
|
|
|
(t.w' + ])2 + I '
|
|
|
|
where t.w' represents the measured Einsteinian redshift for galaxies, and t.w' represents the isotopic redshift for quasars according to law (4.lla), with resulting numerical values [I]
|
|
|
|
53
|
|
|
|
GAL.
|
|
|
|
!!.w'
|
|
|
|
NGC
|
|
|
|
0.Ql8
|
|
|
|
NGC 470 0.009
|
|
|
|
NGC 1073 0.004
|
|
|
|
NGC 3842 0.020
|
|
|
|
NGC 4319 0.OOS6 NGC 3067 0.0049
|
|
|
|
QUASAR
|
|
UBI BSo/ 68 68D BSOI BS02 RSO QSOI QS02 QS03 MARK20S 3C232
|
|
|
|
B
|
|
|
|
!!.Cl'
|
|
|
|
31.91 0.91
|
|
|
|
20.25 1.46
|
|
|
|
87.98 1.88
|
|
|
|
67.21
|
|
|
|
I.S3
|
|
|
|
198.94 1.94
|
|
|
|
(S.2)
|
|
|
|
109.98 0.60
|
|
|
|
176.73 lAO
|
|
|
|
14.S1
|
|
|
|
0.34
|
|
|
|
29.7S
|
|
|
|
0.9S
|
|
|
|
41.85
|
|
|
|
2.20
|
|
|
|
12.14
|
|
|
|
0.07
|
|
|
|
82.17
|
|
|
|
0.S3
|
|
|
|
The above results provide a clear confirmation of the isospecial relativity and underlying isominkowskian geometrization. In fact, the data show that all B values are positive and bigger than one, exactly as predicted by the geometrization of Type 11.2.
|
|
The identification of the individual values b03 = <bJ<> and bO4 requires at least one
|
|
additional experimental value, such as the average speed of light in the quasar chromospheres which would evidently fix bO4' Then bO3 could be computed from the B-ratios. As an indication, the assumption for quasar UBI of the average speed of light in its chromosphere c = 0.80 Co would yield the value b3 '" 40.
|
|
The problem of the apparent speed of the galaxies is not considered in the above analysis because it is a separate issue. The reader should be aware that isogeometries imply three independent corrections to the current estimates of the distance of galaxies from us: )) A correction due to a possible isoredshift of light in the interior of the galaxies; 2) Another correction due to the fact that space can be considered as empty only at the local (say, planetary) level because at intergalactic distances space itself becomes an ordinary medium (since it is filled up with dust, electromagnetic waves, particles, etc.), thus requiring a second, relatively smaller isotopic correction in the redshift; and 3) The very notion of distance is altered by the isogeometries [37,381 Intriguingly, each of the above corrections implies a decrease of the current estimates on the distance of galaxies from us.
|
|
Under limiting conditions, these corrections are indeed capable of interpreting the cosmological redshift itself as being of entirely isotopic origin, thus yielding a new cosmological conception of the Universe as being unlimited, composed of essential\y stationary galaxies of matter and antimatter and with a number of novel features, such as without any need for 'the 'missing mass" (from the isoequivalence law (3. IS), see ref.s [37,38)).
|
|
It should be stressed that current data are insufficient to rule out the "big bang" theory, in which framework the isotopies merely yield corrections to the current estimates on the explosion of the Universe.
|
|
5.2: Representation of Sulentic data [21. The cosmological redshift represented in ref. [III is essentially that of isodoppler law (3. IIa) under values (3.12) for a basic frequency such as 4680Ao. The representation of Sulentic [21 internal red/blue/shift requires the full use of law (3.lla) with the explicit frequency dependence. The assumption of a Gaussian realization of f(w) then leads to the isotopic behaviour
|
|
(S.2)
|
|
where k j and k2 are positive constants. Numerous fits of the experimental data are then possible. As an indication, the values k( = 10 and k2 = I yield a preliminary, yet meaningful representation of
|
|
Sulentic data of Table 4, p. 61, ref. [21 Note the shift of the center of the Gaussian as indicated by current data. Needless to say, a more accurate representation can be derived when additional measures are available such to permit the identification of the function f(w).
|
|
5.3: Representation of Marmet's data [31. The data on the redshift of spectral lines from the sun's chromosphere as studied by Marmet [31 and others are some of the most direct experimental confirmations of the isotopic character of the quasars redshift.
|
|
|
|
54
|
|
|
|
The latter data can be interpreted via essentially the same isodoppler law, only referred to form (3.13) because of the need of the different average since the sun is moving at low speed with respect to our laboratory. In fact, in first approximation, law (3.13) reproduces Marmet's expression (6), p. 240, ref. [3] identically
|
|
|
|
w / Aw = A"A /"A '" - 2 / KOf(w)1w=const. .. - 2.73 x 10-21 T2 Nc '
|
|
|
|
(5.3)
|
|
|
|
where T is the temperature of the sun's chromosphere, and Nc is the average number of collisions of photons in a given column density. Note the emergence of a dependence on the frequency which is expected to be experimentally verifiable and which, if confirmed, would establish the possibility of resolving the problem of quasar red/blue/shifts via spectroscopic measures on the Sun.
|
|
5.4: Representation of timelife behaviour. The isospecial relativity has additional experimental verifications indirectly related to the quasar red/blue/shifts which, as such, are significant for this paper. The first one is the isotopic behaviour (3.14) of the meanlife of unstable hadrons with speed which, if confirmed, would provide a clear verification of the structure of the isodoppler law (3.10).
|
|
Blochintsev and his school [25] pioneered the hypothesis that the nonlocal internal effects expected in the hadronic structure from mutual penetrations of the wavepackets of the constituents can manifest themselves via departures from the Minkowskian behaviour of the meanlife of unstable particle with speed, and computed a generalized law. The problem was subsequently studied by several authors [26], resulting in additional different laws.
|
|
This author submitted in [9] the isominkowskian geometrization of the physical medium in the interior of hadrons with isotopic law (3.14) which was proved by Aringazin [27] to be "directly universal", Le., including all possible generalizations [25,26] via different expansions in terms of different parameters and with different truncations.
|
|
The first phenomenological verification was provided in calculations [2S] on deviations from the Minkowskian geometry inside pions and kaons conducted via standard gauge models in the Higgs sector. These phenomenological studies resulted in the deformed Minkowski metric inside
|
|
hadrons 11 = diag. {(I - a/3), (\ - a/3), (\ - a/3), - (\ - a)), which is precisely of the isominkowskian
|
|
type with numerical values
|
|
|
|
PIONS 1T±: bo12 = boi = boi ;, I + 1.2 x 10-3 , boi;, I - 3.79 x 10-3 , KAONSK±: bOI2=boi=boi;, 1- 2xlO-4 , boi;, 1+ 6. Ix 10-4,
|
|
|
|
(5.4a) (5.4b)
|
|
|
|
Note the change in numerical value of the isotopic element in the transition from pions to kaons, which is necessary because of the change of the density (recall that all hadrons have approximately the same size, but different rest energies, thus having different densities and different isounits).
|
|
The first direct experimental verification was reached by Aroonson et a\. [29] who measured a clear nonminkowskian behaviour of the meanlife of the KO in the energy range 30-100 GeV. Subsequent direct experiments conducted by Grossman et a\. [30] confirmed the Minkowskian behaviour of the meanlife of the same particle in the different energy range 100-350 GeV (see review [lsD.
|
|
These seemingly discordant experimental measures were proved to be unified by the isominkowskian geometrization of the KO-partic1e by cardone et a\. [31] via phenomenological plots of both measures [29,30] in the range 30-350 GeV resulting in the following characteristic bO-values
|
|
|
|
i '" bO12 = boi = bO 0.9090S0 ± 0.0004,
|
|
|
|
boi '" 1.002 ± 0.007 ,
|
|
|
|
A bOk2 =0 0.007,
|
|
|
|
A b? =0 0.001,
|
|
|
|
(5.5a) (5.5b)
|
|
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which are of the same order of magnitude of values (5.3b). Measures (5.4b) also confirm the
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prediction of the isominkowskian geometry in the range 30-400 GeV that the b04 quantity, being a geometrization of the density, is constant for the particle considered (although varying from hadron to hadron with the density), while the dependence in the velocities rests with the ~-quantities.
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the latter analysis is important inasmuch as it establishes the possible existence of an isodoppler shift even for a medium at rest in which < v2/co2> = 0, but <v2'rf...v'f/co2bi> ¢ O.
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5.4: Representation of Bose-Einstein correlation. Another important verification has
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been recently achieved via theoretical [32] and experimental [33] studies on the Bose-Einstein's
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correlation. These studies provide a direct verification of the basic isominkowskian geometrization of physical media and, as such, are significant for the quasars red/blue/shifts.
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55
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Evidence establishes that no correlation exists for particles interactions when admitting
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effective pOint-like approximations. The Bose-Einstein correlation therefore appears to be due
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precisely to the extended character of the wavepacket of particles, which results in an evident
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nonlocal structure of the interactions at very smal\ distances. The use of the isominkowskian
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geometrization for the interior of the p-p fireball results in the two-point Boson isocorrelation
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function on K1(x,lj,R), ref. [32], Eq. (10.8), p. 122,
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L K2
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_ 2/ bO 2
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C{2) = 1 + -
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lj (e qt 11 ,
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3 11 1111
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T"J -- DJ' ag. (bO I2' bO22' bO32' - bO42 )'
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(5.6)
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where qt is the momentum transfer and the term K =bol2 + bO/ + boi is normalized to 3, under the
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sole approximation, also assumed in conventional treatments, that the longitudinal and fourth
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components of the momentum transfer are very small. Phenomenological studies conducted in [331
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via the UAI data at CERN confirm model (5.5) in its entirety, and identify the numerical values
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bO I = 0.267 ± 0.054 , b02 = 0.437 ± 0.035, b03 = 1.661, b04 = 1.653 ± O.oI5 . (5.7)
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These measures have the following important implications: A) They confirm the nonlocalnonhamiltonian origin of the correlation, which is at the foundation of these studies; B) They confirm the isominkowskian geometrization for the p-p firebal\; C) they provide a numerical value of bO4 for particles of the density of the p-p-firebal\ for use in isoequivalence principle (3.12) (see below); D) They confirm the capability of the isotopies of directly representing the nonspherical shape of the fireball and al\ its deformations; and E) They prove the reconstruction of the exact Poincare' symmetry under nonlocal-nonhamiltonian interactions.
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5.5: Cooper pair in superconductivity. This is a clear physical systems beyond any realistic capability of Einsteinian theories because it consists of two electrons of the same charge experiencing an attractive interaction. Animalu [341 has shown that the use of the isominkowskian geometry representing the mutual wave-overlapping of the two electron (with isounit given in Sect. 2.2) permits a quantitative interpretation of the attractive interactions in the Cooper pair which is in excel\ent agreements with numerous experiments (see [341 for brevity).
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5.6: Chemical synthesis of hadrons. The isominkowskian geometry also permits a speculative, yet intriguing prediction, the cold fusion/chemical synthesis of protons and electrons into neutrons (plus neutrinos). It is essentially al\owed by the rest energy of the electron when inside the hyperdense medium in the interior of the proton and computed via isoequivalence principle (3.15) with numerical value b04 = 1.653 from data (5.6). This permits a representation of al\ characteristics of the neutron [351. This prediction has received a preliminary, yet direct experimental verification by don Borghi et al [361. If confirmed, the event would permit the chemical synthesis of al\ unstable hadrons from lither (massive) hadrons. Moreover, it would permit the artificial disintegration of unstable hadrons, such as the artificial disintegration of peripheral neutrons in a nuclear structure, with realistic possibilities of a new teChnology, called hadronic technology, because based on mechanisms in the interior of individual hadrons. See Vol. III of ref.s [141 for other experimental verifications.
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5.7: Proposed experiments. A number of experiments have been proposed in classical mechanics, astrophysicS and particle physics to test the isominkowskian geometry and related isospecial relativity such as:
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Experiment 1 [131: measure the redshift of light from a quasar just before and then after passing through a planetary atmosphere or the sun's chromosphere. The isominkowskian geometry predicts in this case an additional redshift. The average data (5.2) yield <Bo> = 72.78, <AW'> = l.l5,
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<AW'> = 0.01, thus characterizing the average isoshift <AW'> - <AW'> = l.l4. The assumptions that
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the quasar atmospheres are 105 denser than the atmosphere of Jupiter (or of Earth), and that the isotopic effect is proportional to the denSity in first approximation, lead to the estimate of the isoredshift in Jupiter's atmosphere of the order of <AW'Jupiter> '" 1.14x 10-5 which is fully measurable. For smal\er ratios of the densities of the quasars and planetary atmospheres, the effect evidently becomes bigger.
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Experiment 2 [131: Follow a sufficient number of Fraunhofer lines of sun light from the zenith to the horizon to see whether or not the tendency toward the red is in part an isoredshift. The numerical estimates of the preceding experiment also apply to Earth's atmosphere, yielding a
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measurable effect.
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56
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Experiment 3 [141 Finalize the behaviour of the meanlife of unstable particles with speed [29,301. As indicated earlier, any deviation from Minkowskian time dilation is a confirmation of the corresponding isodoppler behaviour for frequencies owing to its direct universality [27].
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Acknowledgments: The author would like to thank Jack Sulentic for invaluable comments. Thanks are also due to Asterios Jannussis, Michele Barone and Horst Wilhelm for a critical reading of an earlier version of the manuscript.
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REFERENCES
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I. H. Harp, Quasars redshifts and controverSies, Interstellar media, Berkeley (1987) (see also contributed paper to this volume)
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2. J. W. Sulentic, Astrophy. J. 343, 54 (1989) (see also contributed paper in this volume)
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.m 3. P. Marmet, IEEE Trans. Plasma Science 11 238 (1988) (see also Phys. Essays, I, 24 (1988), IEEE Trans. Plasma Science 56 (1990) and ~ 958 (1992) and references quoted therein) 4. H.C.Arp, G. Burbidge, F.Hoyle, V.J.Nardikar and N.C.Wicramasinghe, Nature ~ 807 (1990). 5. K. Schwartzchild, Sitzber. deut. Acad. Wiss., Berlin. KI. Math.-Phys. Tech. 424-434 (1916)
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c. 6. P. G. Bergmann, Introduction to the Theory of Relativity, Dover Publ., New York (1942);
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M0Iler, The Theory of Relativity, Oxford Univ. Press (1952) 7. R. M. Santilli, Foundations of Theoretical Mechanics, Vol. I (1978), Vol. II (1983), Springer-Verlag
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(1978); and Hadronic J. Suppl. 1 662 (1985)
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8. R. M. Santilli, Hadronic J.l, 223 and 574 (1978; Phys. Rev. mQ. 555 (1979) 9. R. M. Santilli, Lett. Nuovo Cimento [L 545 (1983) (for a recent presentation see J. Moscow Phys.
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Soc., in press) 10. R. M. Santilli, Hadronic J. Suppl. M, issue no. 3 (1988) II. R. Mignani, Phys. Essays Q, 531 (1992) 12. R. M. Santilli, Algebras, Groups and geometries ~ 169 and 275 (1991), and.lQ, 273 (1993) 13. R. M. Santilli, IsotopiC Generalization of Galilei's and Einstein's Relativities, 2-nd edition,
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Ukraine Academy of Sciences, Kiev, in press 14. R. M. Santilli, Elements of Hadronic MechaniCS, Vols. I, II, III, Hadronic Press, in press 15. J. V. Kadeisvili, Elements of Lie-Santilli Theory, Acta Appl. Math., in press 16. D. S. Sourlas and G. T. Tsagas, Mathematical Foundations of the Lie-Santilli Theory, Ukraine
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Academy of Sciences, Kiev, (1993) 17. J. LOhmus, E. Paal and L. Sorgsepp, Nonassociative Algebras in Physics, Estonian Academy of
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SCiences, Tartu, in press 18. A. K. Aringazin, A. Jannussis, D. F. Lopez, M. Nishioka and B. Velianoski, Santilli's Lie-IsotopiC
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Generalization of Galilei's and Einstein's Relativities, Kostarakis Publ., Athens (1990) 19. J. V. Kadeisvili, Santilli's Isotopies of Contemporary Algebras, Geometries and Relativities, 2-nd
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edition, Ukraine Academy of Sciences, Kiev, in press 20. J. V. Kadeisvili, Algebras, Groups and Geometries!!. 283 and 319 (1992) 21. R. M. Santilli, Hadronic J. B, 25 and 36 (1935) 22. C. Illert, Foundations of Theoretical Conchology, Hadronic Press (J992}, and Hadronic J. in press 23. R. M. Santilli, Integral isotopies of the Riemannian geometry, in Analysis, Geometry and Groups:
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A Riemann legacy Volume, H. M. Srivastava and T. M. Rassias, Editors, Hadronic Press, in press 24. A. Jannussis, contributed paper in this volume 25. D. I. Blochintsev, Phys. leU. ~ 272 (1964) 26. L. B. Redei, Phys. Rev. HQ, 999 (1966); D. Y. Kim Hadronic J.l, 1343 (1978); 27. A. K. Aringazin, Hadronic J. ~ 71 (1989) 28. H. B. Nielsen and I. Picek, Nucl. Phys.Iill,269 (1983) 29. B. H. Aroonson et al. Phys. Rev.~ 476 and 495 (1983)
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30. N. Grossman et aI., Phys. Rev. Lett. ru!. 18 (1987)
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31. F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G1B, L61 and Ll41 (1992) 32. R. M. Santilli, Hadronic J.1Q, I (1992) 33. F. Cardone and R. Mignani, Univ. of Rome preprint no. 894 (1992), subm. for pub!.
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34. A. O. E. Animalu, Hadronic J. H. 459 (1990}, and Hadronic J. in press (1994)
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35. R. M. Santilli, in Proceedings of the International 1993 Workshop on Symmetry Methods in Physics, G. Pogosyan et aI, Editors, JINR, Dubna, in press, and JINR Communication E4-93-352 (1993)
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57
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36. C. Borghi, C. Giori, and A. dell'Olio, Hadronic J. !Q, 239 (1992) 37. R. M. Santilli, in The Mathematical Legacy of Hanno Rund, J. V. Kadeisvili, Editor, Hadronic
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Press (1993) 38. R. M. Santilli, in Analysis, Geometry and Groups: A Riemann Legacy Volume, H. M. Srivastava
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and Th. M. Rassias, Editors, Hadronic Press (1993)
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58
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TIIE RELATIVISTIC ELECIRON PAIR TIIEORY OF MATIER AND ITS IMPLICATIONS FOR COSMOLOOY
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Ernest J. Sternglass
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Radiation Physics Laboratory Scaife Hall RC- 406 University of Pittsbmgh Pittsbmgh, PA 15261
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INTRODUCTION
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Although atomic and nuclear physics have made enormous advances dming the last centmy, there has been an increasing crisis in fundamental physical theory with regard to the natme of the ultimate constituents of matter which appear to have both particle and wave-like properties and occm in a bewildering variety of types and masses. Since there is now overwhelming evidence that the universe is expanding from a highly compact state that appears to have had the dimensions of a single proton or less, fmther progress in understanding the origin of the universe and its structme cannot be made until the problem of the natme of the fundamental particles is resolved.
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If one examines the spontaneous decay process of all the newly discovered unstable mesons and baryons, one finds that ultimately they all lead to the production of electrons, positrons, protons and radiation quanta such as photons and neutrinos. Even the proton is known to annihilate with an anti-proton into mesons that in turn decay to electrons and their oppositely charged anti-particles, positrons. It is therefore the pmpose of the present paper to outline an approach to the theory of nuclear particles which reduces the number of truly elementary entities to only a single type, and to summarize the resulting implications for cosmology.
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Of all the hundreds of matter particles on the sub-atomic scale discovered dming the last centmy that have a clearly defined rest-mass and charge measmed in the laboratory, only the electron and its anti-particle possess the properties required for a truly elementary entity 1. These properties are (1) a very high degree of stability when isolated, (2) identity of all physically measmable properties under the same conditions and (3) absence of any experimental evidence for internal structme, or divisibility into fragments of smaller rest-mass, size or charge, so that the particle interacts with all other particles as if it were a mathematical point entity, requirements that have in fact been met in collisions as high as millions of limes the energy needed to create an electron - positron pair.
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The only condition under which an electron disappears is when it annihilates with a positron, resulting in purely electromagnetic radiation quanta. Likewise, electrons can be created only together with their anti-paflicles so that charge is conserved under all known physical conditions. Moreover, electrons and positrons can be. created from electromagnetic photons of sufficient energy in the well-known pair-production process. Thc;reIore, it is possible to assume that the mass of the electron is of pmely electromagnetic origin as postulated by a number of investigators shortly after its discovery, or that its mass resides entirely in its smrounding field. This allows one to regard these particles as nothing more than centers of force or stable concentrations of electromagnetic field
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energy without any "hard cores" of "ponderable matter" of unknown natme along the lines arrived at by Motz 1 . This view immediately removes the apparent contradiction between the particle and wave aspects of material
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particles since electrons are in effect taken to be stable, extended wave pulses. Thus, they can produce interference patterns characteristic of a two-slit system even when they are fired at the slits one at a time without the need to give up our usual space-time mode of describing natural phenomena on the atomic scale 3 .
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It also follows that all forces, from chemical to nuclear, must utimately tum out to be understandable in terms of the known characteristics of the electron and positron as the centers of an extended field throughout which their mass-energy is distributed. Since the gravitational interaction can be understood in terms of the distribution of mass-energy that determines the local deviations from a flat Euclidean space according to Einstein's General Theory of Relativity regardless of the natme of the mass-energy, even gravitational forces must ultimately turn out to be explainable in terms of the properties of the electron and positron alone. Fmthermore, since one must not introduce qualitatively new kinds of matter or forces in order to describe the more massive nuclear particles, one can only use purely geometric or dynamic considerations to explain their larger masses.
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Frontiers ofFundamental Physics, Edited by M. Barone
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and F. Selleri, Plenum Press, New York, 1994
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59
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TIlE RELATIVISTIC PAIR MODEL FOR NUCLEAR PARTICLES
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Of all the new nuclear particles discovered in the 1940s the neutral pion or 31:0 that is known to decay into two gamma rays bears the most obvious resemblance to positronium composed of an e+ and e- in a Bohr-type orbit Ibis led Fermi and Yang to consider amodelfor the lto consisting of a proton and an anti-proton in 1949 4 . However, within another decade, experiments had revealed that the proton had internal structure, ruling out this early model. There was however a way that a high mass could be explained with only two electrons, namely if there were a previously unknown e+e- state with very high relativistic momentum and energy. Ibis did in fact turn out to be the case, provided one makes the assumption that the force between the two particles is that calcuated by an observer at rest with respect to either one of the two particles S ftrst suggested by Eiustein in his paper on the theory of special relativity as the only way to arrive at a symmetrical result for the force between two moving particles. One then arrives at the existence of a minimum approach distance which except for a velocity dependent correction factor that ranges from 1 to 114 between low and high velocities equals the classical electron radius rcl
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= t?- /2moc 2= 1.4 x 10- 13 em, where e is the charge of the electron, ffio is its mass and c is the speed of light.
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Quantization of the orbital angular momentum as in the Bohr model leads to a mass of (21a) - 2 or 272.072
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times the electron mass tno for the ground state. Here a is the fine-structure constant e 2/ -Ii c = 11137. 036 first
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used by Sommerfeld in the relativistic treatment of the Bohr model. When corrected for the effect of the magnetic moment spin-spin and spin orbit interaction of 8ffio this leads to a mass of 264.072 mo close to the observed lto mass of 264.116 mo and life of 2xlO-16 seconds against annihilation into two gamma rays based on the analogy to positronium, again in surprising agreement with the most recent observed value of 0.87 x 10 -16.
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Besides the 31:0 which has spin 0 as a result of the spins of the electron and positron being parallel, there is
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also a spin 1 or nol meson in which the spins are anti-parallel whose mass is 12 molarger due to the difference
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in the magnetic spin-spin and spin-orbit interactions, giving a mass of about 276.072 mo s, close to the observed mass of the charged pions of 273.126 IDa , even without a correction for the addition of a charge 6. As discussed
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below, the nol has a much longer life than the no so that it forms the basic building block of all other particles.
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Thus, using only Bohr's hypothesis that a system with minimum angular momentum ~ is stable against radiation, one arrives at a model of a meson of the right order of mass and size of nuclear particles. Moreover, the
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strength of the force was found to be YI2 e2 / r122 where YI2 is given by (1-~22)-1f2,f3i2 = v 12 / c and rl2 is the
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distance between the particles. For the ground state, YI2 is equal to (2/a) or 274. 072 so that the relativistic interaction is of the correct order to explain the great strength of the nuclear force.
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Ibis surprising result is due to the high relative velocity, leading to a large magnetic interaction between two parallel currents that is much stronger than the ordinary electrostatic interaction. In this way, the strong nuclear force is seen to be a form of the electromagnetic interaction, so that this model unifies these two forces, a goal that supersymmetry theory has been trying to achieve by postulating a whole new family of particles.
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Using the basic relativistic electron pair model of the neutral pion as the analog of the Bohr positronium atom, it becomes possible to describe the heavier mesons as quasi-molecular systems composed of pions with a
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binding strength 2(2/a) e2, a Yukawa type of short-range potential of 75.7 Mev with a range of A",. =.IfI2 M" c = rei that follows from the solution of the Klein-Gordon equation, and a zero-point energy 2 M" c 2 at a fixed
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distance of rcl between them as determined by the minimum approach distance between the e+ and e- 6.7. Thus, the model gives a mass of 484 Mev for the simplest molecular system consisting of two pions compared with the observed values of 494 to 498 Mev for the K-mesons. Due to a numerical coincidence, the same mass is also obtained for a 331:, close packed structure. Likewise, a 4Jt planar structure is found to have a closely similar mass of 490 Mev, thereby explaining why one observes both 2 and 3 pion decays from what appears to be a single p,article.
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The model also gives a series of still higher short-lived systems as rotationally excited or resonant states of these molecular structures 6.7. Thus, the ftrst excited spin 1 state of the the two- pion system gives a'predicted mass of 764 Mev vs. an observed mass of 770 Mev for the p meson of spin I, and the three pion close-packed system has one of its three spin 1 states at 753 Mev compared with an observed mass of 782.6 Mev. In all the cases worked out at the time 6,7, the calculated masses agreed to within ± 6% with the measured values, even though in these simple models, the effects of magnetic moment interactions had not been taken into account.
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Moreover, the excited states of baryons that decay to protons with the emission of mesons have masses that fit some of the same basic molecular rotator levels as the meson states 8, something that is to be expected if the nucleons contain mesons. In particular, the simplest of the "mesonic molecules" , the two pion system whose ground state mass is equal to that of the K-mesons, seems to be basic to the structure of baryons since the mass of the proton of 938.28 Mev is just slightly smaller than the mass of two KO -mesons, 995.4IMev, which is also consistent with the fact that the proton and anti-proton annihilate into K-mesons as well as pions, Thus, the proton appears to be composed of two KO mesons held together by the exchange of a highly relativistic positron 9 in a state with a binding energy of 57.13 Mev in such a way that it allows internal rotational excitations as well as an unusually high degree of stability, now known to result in a half-life of more than 1032 years 10 . This results in a three quark structure, in agreement with early group-theoretial conclusions by Gell-Marm and others based on the then known groupings of baryons into multiplets which suggested that the baryons belong to an SU(3) dynamic group. But unlike the standard model that postulates fractional charges and cannot explain the exact equality of the proton and positron charge, the electron-pair model requires that the two charges are the same.
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60
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Thus, the electron-pair model for the protoo explains the excited states produced in the course of pion-protoo collisions as short-lived states in which a It is temporarily bound to ooe of the 2Jt components of the proton, forming a 3lt close packed system whose excited states fit the observed states to better than 3.7% 8 . Moreover, this model of the proton is further supported by the fact that the excited states predicted for the case where a It is temporarily bound at both ends of the protoo fit another set of predicted excited states to better than 1.3%.
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Still further, it is found that the hyperons that have the same spin 112 as stable nucleons fit excited states in which two pions or a Kz"is temporarily bound at the two ends of the basic proton structure so as to form Kmesons of the 4lt planar type rotating in opposite directions. As a result, the additional rotational momenta cancel each other, leading to total angular momenta eqnal to that of the proton. And again, the observed masses agree to within a few percent with the predicted 4lt rotational states. Finally, two different sets of excited hyperon states that are observed fit single and double- ended rotational states to the same high degree of accuracy 8.
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It remains to discuss the charged mesons, especially the relation between the muon and the pion that decay with the emissioo of neutrinos. As mentiooed above, it is the longer lived spin 1lt"1 with its anti-parallel spins and para11el magnetic moments of the two charges that forms the charged mesons. It is the net magnetic moment of the It°l that allows a charge to be bound to the pair- system'. In the case of the muon that has a spin 112, the spin of the added charge must oppose the orbital momentum of the spin 1lt"I.At the same time, the magnetic moment of the added charge must be anti-para1lel to that of the It''1 so that the sign of the charge that can be attached is fixed by the sense of the orbital angular momentum relative to the spins. But there are two different cases for this orientation: ooe in which the orbital angular momentum is parallel to the spin of the e+, and one in which it is parallel to the spin of the e·. In the former case, only a positive charge can be bound; in the latter case only a negative charge. Thus, while the It° is its own anti-particle, the It°\ can exist in two possible states: matter and anti-matter states of opposite charge, and this property appears to be related to the origin of isotopic or isobaric spin, as well as to the existence of only one kind of stable matter in the universe, as will be dicussed later on.
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The muon mass of 206.768 roo is very close to the calcnlated value of 206.7 roo, and so is the life-time of
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2.197 x 10-6 sec close to the theoretical life-time of 2.210 x 10.6 sec' . However, instead of emitting 3 gamma rays of spin 1 together with an e+ or e-, the f-lz emits two neutrinos of spin 112. The reason is that due to the relativistic orbital velocity of the pair-system, the usually small Sommerfeld precession becomes equal to the orbital angular velocity so that the angular momentum of the precessing reference frame in which the Kepler orbits are closed takes on the valueJl/2, leaving Kl2 for the orbital angular momentum relative to the precessing frame 5 . Thus, in these highly relativistic pair systems, orbital angular momenta are quantized in units of ~2 so that the centrallt"\ annihihates by emitting two neutrinos of opposite helicity that together carry away the angular momentum h. Moreover, due to the extremely relativistic motion of the two charges in the It°\, their mass is increased and the source size and magnetic moments are reduced by Y12 ' so that the rate of radiation is much less than for low velocity states', thereby explaining the origin of the weak interaction and its relationship to the electromagnetic interaction as originally described by Fermi 11 and since then observed in high energy experinlents.
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As for the decay of the ltZ to a f-lz , this is explained in terms of the preseut model as a transition from an excited state of the charge bound magnetically to the central pair with the emission of a single neutrino of spin-lfl2.
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The theoretically calculated mass of this excited state is 67.8 roo larger than the muon mass, giving a pion mass of 274.5 roo, while the theoretical mean-life is 2.49 x 10 -8 sec, in good agrement with the latest measured value of
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2.60 x 10-8 sec. It is of interest that the single neutrino emitted in the decay of the It'" to a f-l" differs from the two neutrinos emitted when the muon decays to an electron or positron in that the neutrino produced in the pion decay carries away an orbital angular momentum 11211" relative to the precessing reference frame of the It°\. Sutce the charge in the pion has to move in a direction opposite to that of the precessing frame, it carries only a small zeropoint angular momentum relative to the laboratory rather than a spin ~2. This appears to explain w~y the muon neutrino and the electron neutrino differ in their interactioo with matter '.
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Considering that these models require only the fundamental constants of electromagnetic and quantum theory e, mo, c and.ff and no arbitrary or adjustable parameters, the agreement with the masses, spins and lifetimes of the muon, the pioo and with the masses and spins of the heavier mesons and baryons must be regarded as strong support of the pair model, as well as for the assumption that the electronic charge is the smallest in nature, in agreement with the fact that all searches for fractional charges have failed 12. Thus, these results favor the suggestion of Han and Nambu that the quarks may be integrally charged, and it supports the hypothesis arrived at by a nmnber of theorists that the many different types of quarks are not truly elementary particles but instead complex structural systems composed of more fundamental entities, namely relativistic electrons and positrons.
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IMPUCATIONS FOR COSMOLOGY
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It was the unexpected discovery of yet another class of mesons in 1974, namely the J/", of mass 3097 Mev, shortly followed by the discovery of the Y with a mass of 9460 Mev, that provided experimental evidence for a possible link to the initial high density state of an expanding universe first proposed by Lemaitre in 1932 13. The most surprising characteristics of this new family of mesoos created in high energy collisions such as those of electrons and positrons were their high density, far above that of ordinary nucleons, and their loog life compared
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61
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with all previously known baryon and meson resonance states that decayed in a matter of 10.23 to 10-22 sec. Thus they produced extremely sharp, narrow resonances of less than 0.1 Mev in width, compared with lOs to l00s of Mev for the previously known massive hadrons. Moreover, they did not just decay into hadrons but also directly into electron and muon pairs without the emission of neutrinos. More unusual still, the heavier Y, instead of having a shorter life-time as in the case of ordinary hadronic resonances of increasing mass, actually proved to be longer lived than the lower mass J/",. Thus, the possibility arose that this type of particle might provide a physical model for the "primeval atom" postulated by Lemaitre as the immensely dense, massive "seed" of the universe from which all matter particles and the various cosmological structures evolved in a series of division processes.
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Since these new particles could be created in collisions between an e+ and an e' and since they sometimes decayed into an e+ and e' as well as into spin 112 muon pairs of opposite charge, it was natural to assume that they might be highly excited states of the :n;ol, or massive positronium-like states of two spin 112 particles 14. A closely
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related suggestion was that the JiIV might be composed of a pair of quarks of a new type called charmed or c
|
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quarks, forming a massive "charmonium" system 15. Likewise, when the Y was discovered, it was postulated that
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it ill turn was composed of yet another pair of quarks, called beauty, bottom or b quarks.
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However, it seemed simpler to assume that these particles were excited states of a single type of elementary entity that had already been able to explain the masses and life-times of the other hadrons instead of postulating a new type of particle every time a new resonance in electron positron collisions was observed This possibility was supported by the fact that the J/", turned out to have a mass very close to the 22nd excited state of the:rrf> , which
|
|
has a predicted mass of 3104 Mev, within ouly 7 Mev or 0.2% of the observed JiIV mass. At very nearly the same
|
|
!nass lies a system composed of two K:z,,-mesons excited to the p or J = I rotational state 7 whose theoretical mass
|
|
is 764 Mev using M" .. 140 Mev, giving a total mass of 3056 Mev. Thus, with a central:rrf>1 of mass 141 Mev
|
|
bound with an energy of 100 Mev, such a system would provide the necessary spin 1 state into which the J/", could decay, in agreement with the most frequent decay modes involving p, :n;, ro and K mesons 16.
|
|
Likewise, the Y mass is close to the n = 67 level of the :n;ol' or at 9452 Mev, ouly 8 Mev from the obsl:TVed
|
|
mass of 9460 Mev. Again there is a nearby spin 1 system into which the state Can decay to form hadrons,
|
|
composed of two excited K:z" in a J = 5 state for which the mass is 4684 Mev 7. Two such systems plus 141 Mev for a central :rrf>1 give 9509 Mev so that a binding energy of 49 Mev yields the observed mass of 9460 Mev.
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|
Thus, one can make the hypothesis that the Lemaitre atom is a highly excited, long lived state of the basic relativistic :n;olPair system 17, with a mass equal to that of the universe Mu at a density equal to the maximum possible one III', namely the Planck density PI'! = CS /-II:G2 = 5.177 x 1()93 gm. Given the effective volume Velf in which the field energy is confmed, which in the present case must be of the order of nuclear particle dimensions,
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|
one can calculate a theoretical mass of the Lemaitre atom or of the universe from the relation Mu = PI'! Velf.
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|
There are two ways in which one can arrive at a value for Velf 17 . One is to calculate the mean value of the radius in which the field energy of the relativistic pair is distributed by analogy to the case of a single electron in quantum theory following Motz 2, namely the geometric mean of the inner radius of the electron rei and the outer radius of the field given by (2/a) rei , the deBroglie wavelength. In the case of the:rrf>I' this effective radius <Ree> is the mean of rei 14 and (2/a) rei 14, or (2/a) 112 rei 14 = 4.14rel' One can then calculate the volume <Vet? using
|
|
the non-Euclidean expression for the extremely massive relativistic states as 2:n: 2<R..>J = 1400 re? The second way is to use the Dirac large number defined for the present case of electrons, N n = e2 I mo2 G =
|
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1.667 X l()42. By eliminating G, the Planck density PI'! = MulVeff becomes Nn2 (C>11104 I He4 ). Next, defming the Eddington number NE = Mu I mo one obtains NE= Verr (c5mo3 I He4)Nn2 and since both NEand Nnare dimensionless, the term in the bracket must represent the inverse of a volume V 0' given by Qre 4 I IDa3 c'). This can be rewritten as (lIa)(2 rel)3= 1096 re? and is seen to be close to the value<V..;> .For the volume Voo~ gets the radius 3.8 reI' Taking the average of the two effective radii, one obtains the value 3.98 rei or close tQ4 reI.'
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|
Since the ratio <Vee> I Vo is 1.27 and therefore close to unity, it follows that the relation between NE and
|
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No2 derived above takes on the simple form NE = Nn2which is thc" Large Number Relation" that Dirac believed
|
|
would eventually require a physical explanation. It means that the origin of this relation can be explained if all !natter is composed of electrons, and that the universe began with all its mass concentrated in a volume Vo .
|
|
Thus, the relationship (e2 I mo2G )2 = M" I mo holds exactly, so that the mass of the physical universe is
|
|
fmite and can be calculated when e, IDa and G are known, giving M,,= e2 I IDa3Q2 =1.7632 x 1(J85 IDa or 9.4551 x
|
|
lOS I hlp, where Mp is the proton mass. This serves as a first test of the Lemaitre model since the luminous mass
|
|
of the universe is of the order of l()lll Mp. so that the theoretical value is consistent with the fact that visible !natter represents only about 1% of the total mass 19. Another test is whether the size of the universe is consistent with the present Hubble radius of 10-15 x 109light years. That this is the case may be seen from the fact that the
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Schwarzschild radius R, = 2GM,,1 c2 of the universe is 2480 x 109light years, large enough so as not to lead to a
|
|
significant deceleration of the expansion at the present epoch, in agreement with observation. The model explains why Nn is also a measure of the size of the universe in units of nuclear particle
|
|
dimensions. Taking the expression for the Schwarzschild radius R, and substituting Nn2mofor Muand e2 I IDaNn for G, one obtains R, = 4rel ND = <Ree>(Mu I IlIol1l2. According to Lemaitre's hypothesis, galaxies, stars and all other cosmological structures arise from similar-sized "seeds" which in the present model are relativistic pairsystems of lower mass to which the same laws apply. Thus, they all have the same value for <Ree> and Vo , so that
|
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62
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|
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leads to still another testable prediction. namely that the sizes of cosmological systems or their spacing should be proportional to M..,11l. Such a relation has indeed been found to hold empirically for the large. diffuse systems 21 . However. inspection of a logarithmic plot of size vs. mass indicates that they are not uniformly distributed but tend to cluster strongly around certain average values that tend to be about a factor of 1000 apart. Thus superclusters typically have a mass of a few hundred to a few thousand galaxies. galaxies tend to have masses some thousand times that of dwarf galaxies. and so on down to stellar associations and stars. In terms of the present model. this suggests that the decay process of the original Lemaitre atom took place in 27 major stages of
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|
= some 10 divisions by 2since 210 1024. To go from the mass of the original pair down to the mass of hadrons
|
|
therefore takes some 270 divisions. which in the present model is a form of internal pair production known to lead to the formation of pairs in nuclei when enough energy is available and other decay mechanisms are forbidden
|
|
As to the physical reason why such a halt or slow-down in the divison process might occur whenever a thousand pairs have been formed. this appears to be connected with the number of pairs that can fit into the volume Vo in which the fields are strong enough to allow pair-creation to take place. just as in the case of socalied geons or self-stabilized vortex rings of pure electromagnetic field energy investigated by Wheeler 22. From the fact that the spacing of pairs as confirmed by the rotational levels of the excited hadron states is equal to rei and the fact that the size of Vo and VefT lies between 1096 and 1400 rcl3 it appears that on average some 10 divisions by 2 fill this critical volume. and the next division process forces ejection from the rotating cluster that is held together by strong gravitational forces when each pair has the mass of a star. a galaxy or even a supercluster.
|
|
If one calculates the masses of successive clusters of 1024 pairs according to the simple relation M.. = Mol (1024)0. one arrives at a mass of 7.40 x 10 IS solar masses M 0 typical of superclusters for n =3; at 7.23 x 1012
|
|
Mo typical of large galaxies for n=4; at 7.06 x 109 M.. typical of globular clusters for n=5; at 6.73 x 103 M.. seen
|
|
= = for large stellar associations for n 7; and at 6.5 M., characteristic of the more massive stars for n 8. These
|
|
masses are about ten times greater than the average luminous masses for these objects. again suggesting that the present model is consistent with the existence of significant amounts of dark matter. This may either be in the form of baryonic matter such as brown dwarfs. planets and smaller objects in the halos of galaxies as have been recently reported using gravitational lensing 23.14.25. or it may be in the form of as yet undecayed massive pairs still trapped in the nuclei of the larger systems such as superclusters and galaxies 20. But according to the present theory this dark matter cannot be composed of any new exotic particles or neutrinos of finite rest-mass since. according to the electron pair model of matter. the neutrinos are pure electromagnetic radiation quanta.of spin 112.
|
|
Because of the relationship beween the masses and sizes of cosmological objects. there is a high regularity in the sizes or the distances between them 20. Thus galaxies are predicted to have an average distance of 4.73 x 1()6 light years between their centers when the supercluster to which they belong is relatively old so that it has collapsed to a flattened form and stopped expanding at its high initial rate of expansion. Because according to the present model all systems including the largest must rotate just as planetary systems and galaxies do 17.20. the galaxies in superclusters such as our own are in quasi-stable equilibrium while participating in the overall expansion rate of the universe. This would explain the recent finding by Napier 26 that the red-shifts seem to be quantized as if the galaxies in the local supercluster were arranged in a lattice of about the predicted spacing that maintained its regularity while expanding. Moreover. because the masses of all systems differ by factors of two from the average values due to fluctations in the decay. the model also implies that the velocities of the stars and gas clouds in the arms of galaxies should show evidence of quanti711tion as has in fact been reported by Tifft 1.7 •
|
|
Other interesting aspects of the Lemaitre model that appear to resolve certain theoretical and observational problems faced by the standard model and discussed elsewhere in more detail include the following: 1) The problem of explaining the uniformity of the universe in different regions too far apart to have ever communicated with each other after the Big Bang does not exist in the Lemaitre model since the evolutioll takes place from a single pair over a long period of some 1013 years before the Big Bang when baryons formed 20.30.
|
|
2) The need for extremely "finely tuned" initial conditions at the Big Bang to achieve a precisely "flat" universe
|
|
balanced between indefinite expansion and recollapse does not exist since all cosmological structures rotate so that any mass value can lead to stable states just as is observed for planetary systems and galaxies 17.20.21. 3) There exists no initial singularity since the initial pair has a finite size. nor do black holes contain singularities. There are no infmite physical quantities since all charges. masses. angular momenta and velocities are finite 31. 4) The problem of the early production of too much helium in the presence of a high density of ordinary baryonic matter does not exist because during the first moments after neutrons have been formed when the temperature is just high enough to fuse nucleons into helium. some 99% of all matter is still trapped in the massive central nuclei of the expanding systems. unavailable for the production of helium and other low mass elements 29,30. 5) There is no difficulty in explaining the very large coherent motions of galaxies since superclusters as well as all larger systems rotate like galaxies. leading to average rotational velocities of superclusters of 1171 kmls 30. 6) The problem of explaining how protons or ordinary matter survived the Big Bang without annihilating with anti-matter does not arise since the initial pair had either one sense of orbital motion relative to the spin of the electron or the other as explained above for the Jt"1. thus determining whether baryons or anti-baryons form. 7) The problem of understanding the presently observed ratio of photons to nucleons is solved by the possibility of calculating the kinetic energy with which baryons and pions are created in the final. 27th step of the decay process. This motional energy heats the universe to an initial temperature of about 1013 K and produces some 2.8 x 1()9 thermal background radiation quanta per nucleon at the time when radiation decouples from matter 29,30.
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63
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8) Quasars and their tendency to occur more frequently near galaxies than expected 32,33 fmd a natural explanation as delayed ejections 34, 35 of newly evolving cosmological structures from the extremely dense central nuclei of the more massive systems. as frrst suggested on observational grounds by Ambartsumian 36 but widely disbelieved because there was no theory for such enormously dense forms of matter. Therefore they seem to be "mini-bangs" in which galaxies and stars continue to be born, producing energetic baryons and relativistic jets of electrons and positrons accompanied by radiation. including powerful ganuna rays 29 as first envisioned by Lemaitre 13 .
|
|
There are other interesting aspects cf the Lemaitre model dealt with elsewhere17•29.30 such as the fact that the model requires the local value of G to be inversely proportional to the square-root of the mass of the relativistic
|
|
pair. Thus. the local gravitational constant within R.(Mee) increases by NDor 1()42 times from its initial to its
|
|
fmal value of (110. )112 (e2/m,,2 ) close to that arrived at by Motz 2 for a gravitationally stabilized electron while the
|
|
= overall valueof G for the universe remains constant. This causes the value of the Planck mass Mp\ (Kc/G)11Z to
|
|
decrease 21 orders of magnitude from its large initial value to the geometric mean of m"and (1I0.)m" while the Planck length (If 1Mpl c) increases to (2/0.) rei 14 or to the outer size of the XOI field. Therefore. the minute scale of superstrings becomes equal to that of hadrons so they that can now be identified with the lines of force between the relativistic charges confined within R.<Mee. which for the 1t"1 becomes (2/0.) rei 14. As a result. superstrings are brought from a hypothetical miniature world back to that of actual nuclear particles where they originated.
|
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CONCLUSION
|
|
It appears that we may now be on the verge of reviving the hope that all physical processes can be understood in telms of an electrodynamic theory of matter. modified by the discovery of the quantization of orbital angular momentum and spin. Since all matter and forces are aspects of the properties of electrons in the present model, one can return to the relativity theory of Poincare and Lorentz in which motions take place relative to an absolute reference frame or an ideal. fluid-like space-time continuum. This fruitful concept of an ether was taken from Anaximander in ancient Greece and revived by Descartes and Newton. Unfortunately. it was briefly abandoned by Einstein in 1905 because of the particle-like action of photons only to be found necessary for his General Theory ten years later 37.38. However. such an absolute reference frame is required for the concept of rotation of the first electron pair and its stabilization by a centrifugal force in the absence of any other matter. But once such a plenum is assumed to exist, it is possible to consider the ultimate entities to be "quantized superstrings", or stable vortices in an ideal fluid as originally envisioned by Helmholtz, Faraday and Maxwell.
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|
The Lemaitre model will soon be subjected to an important test by the Space Telescope as it looks back in time at the most distant galaxies. These newly forming "proto-galaxies" must turn out to be small and extremely bright objects similar to quasars that have since then expanded to their present spiral shape from a massive central source rather than by collapse from a diffuse gas. If this model continues to pass its tests, then there is hope that the universe can continue to exist forever since rotation will keep the systems of galaxies in equilibrium.
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|
REFERENCES
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|
1. E.I. Stemglass. in: • Proc. 10th Int Congr. Hist. of Science·, Hermann, Paria (1962).p.355
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|
2. L. Motz. Nuovo Cimcnto. 26: 672 (1962)
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|
3. E.I. Stemglaaa. in: ·Horizons of a Phil08opher·, I.FranIt d aI.• eds., E.I.Brill. Lciden (1963), p. 422
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|
4. E.Fmni.andC.N. Yang. Ph,.. Rev. 76:1739(1949) 5. E. I. Stemglaaa, Ph,..Rev.123:391 (1961) 6. E. I. Stemglaaa. in • Nucleon Structure·. R.Hofstadter and L. L Schiff,eels., Stanfonl U., Stanfonl (1964), p. 340 7. E. I. Stemglaaa, Nuovo Cimento35:227 (1965) 8. E. I. Sternglaaa, in: ·R...man! Partid...•• B. A.MIIIIir.e d., Ohio University, Athens (1965), p.33. 9. E. I. Sternglass, InL I. ThC<Jl". Phya. 17:347 (1978) 10. M. Aguilar-Benitez etal, ·Particle Data Booklet·, North HoUand, Amsterdam (1986), p.18 11. E. Fmni, Zeits. Phys. 88:161 (1934) 12. L.W. Iones and O.W. Greenberg, in "Nuclear Physics and Particle Source Book·, S.B. Pariter, ed., McGraw-Hill, NewYodt (1987) 13. G. Lcmai1re, Nature 128: 701 (1931), also "The Primeval Atmt·, Van Nostrand, New Yodt (1950 ) 14. E. I. Stemglasa, Bull. Am. Ph,.. Soc. April 1975 Meeting. 15. T. Applequist and ILD. PoIitzer, Phys.Rev.Lett. 34:43 (1975) 16. M. Aguilar-Benitez ct ai, "Particle Data Booklet·, North Holland, Amsterdam (1986), p.37 17. E.1. Sternglass, LctL Nuovo Cimento 41:208 (1984) :18. V.L.Ginzburg. Comments Astron. Astrophys. 3:7 (1971) JC9. R.P. Kirslmer, A. OcmIer and P. L. Schecterl, Astrophys. J., 84, 95 (1979)
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|
zo. E.I. Stemglass, in:"T...ting the AGN Paradigm·, Am.InsL Physics, New York (1992)
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|
2.1. B.I. Carr and MJ. Rees, Nature: 278, 605 (1979) 22. I..A. Wheeler, I'hya. Rev. 97: 511 (1955) 23. C. Alcock et aI., Nature (1993)(1n press) 24. M. Spiro, d aI., Nature (1993)(1n press) 25. B. Buczynski, eLal., (1993) Acta Aatroncmica (In JrC88) 26. W. Napier (These Proceedings) 27. W.G. Tifft, Astrop,ys. I. 206:38 (1976)
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64
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28. V.F. Litvinetal., Astropbys. Spice Sc. 202:33 (1993) 29. E. I. Stc:mglass, in "Proc. 2nd Compton Symposiwu", Am. lost. Fbysics, New York (1994) 30. E. I. Stemglass, (Unpublished tnaDlIScript)
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31. R I. Stemglass, Annals N. Y. Acad Science 480:614 (1986)
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32. G. Burbridge, A, Hewitt, I.V. Narlikar, P. Das Gnptas, Astrophys. Suppl. 74:675 (1990) 33. H. CArp, G.,Burbridge, F., Hoyle, I. V.,Narlikar sod N. C. Wickramasinghe, Nature 346:r07(I990) 34. I. D. Novikov, ,Astron. Zh. 41:1075 (1964) 35. Y. Ne'eman, Astropbys. I., 141:1303 (1965) 36. V. A.IAmbartslDDian, in "La structure et I'evolution de l'univers", Institut International de Physique Solvay, cd R. Stoops, Couder 37. A. Gnmbawu, Philos. Rev. 66:525 (1957) 38. L Kootro (These Proceedings)
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65
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ARE QUASARS MANIFESTING A DE SITTER REDSHIFT?
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John B. Miller* and Thomas E. Millert
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* 6 Benham Street
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Danbury CT 06811, USA t 2 Riverside Drive
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Cooperstown NY 13326, USA
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ABSTRACT
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In 1929, Edwin Hubble wrote in his classic paper! demonstrating a correlation between redshift and distance, liThe outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect. ..." Since the discovery of quasars more than thirty years ago, many more-or-Iess plausible explanations for the quasar redshift have been proposed. Although the de Sitter redshift was the first known cosmological redshift, it has not yet been considered as a possible etiology for the redshift of quasars. We address the question, "ls it possible that the quasar redshift is a de Sitter redshift?" Perhaps the asymptotic character of a gravitational de Sitter redshift2 could help explain the quasar phenomenon: objects with high redshifts that appear to be almost as bright as objects with intermediate redshifts. Reconsidering the possibility of a nonlinear de Sitter redshift-distance relation, we find quasar intrinsic brightness to be rather ordinary. Given a de Sitter redshift-distance law, intrinsic brightness is found to be independent of redshift over five orders of magnitude.
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INTRODUCTION
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The de Sitter redshift was most popular in the twenties3 and has now become obscure. (The de Sitter solution is distinct from the Einstein-de Sitter solution.) There are many different formulations of the de Sitter solution, depending on the choice of coordinate transformations.4 In order to use the inverse-square law so that coordinate
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e, distance equals luminosity distance, we choose cOO1:dinates (r, <p, t) that preserve the
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|
Euclidean formula for surface area: A = 41tr2. Any other coordinate transformation entails a surface area formula that does not obey strict inverse-square-Iaw dimming.
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THEORY
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Given the relativistic spacetime metric
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(1)
|
|
the de Sitter solution to the Einstein field equations can be written as
|
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|
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Frontiers ofFundamental Physics, Edited by M. Barone
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and F. Selleri, Plenum Press, New York, 1994
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67
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y = 1 - (rlR)2,
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(2)
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|
|
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with R2 =3/(81tp), where the constant R is the radius of spacetime curvature and p is the mean mass density of the universe (assuming simplified units so that G = c = 1).
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Redshift z is defined as
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|
= = Z ArlA.o - 1 y-1/2 - 1,
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(3)
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|
|
|
where Ao is the wavelength of the unshifted photon and Ar is the wavelength of the photon observed at a distance r. Distance can then be given as a function of redshift,
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r = R [1 - (z + 1)-2] 112.
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(4)
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|
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Equation (4) is the de Sitter redshift-distance law-the de Sitter equivalent of the Hubble law (Fig. 1).
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Assuming inverse-square-Iaw dimming, absolute magnitude M and apparent magnitude m are related to distance r by
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|
M + C = ill - 5 loglO (r) ,
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|
(5)
|
|
|
|
where C is a constant determined by observation. According to the Hubble law, redshift is directly proportional to distance, thus
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MH + CH = ill - 5 loglO (z) ,
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|
(6)
|
|
|
|
where MH is Hubble absolute magnitude and CH is an observational constant that incorporates the Hubble constant. Combining equation (4) and equation (5) gives the de Sitter version of the magnitude-redshift relation
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|
|
MD + CD = ill - 2.5 loglO [1 - (z + 1)-2] ,
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|
(7)
|
|
|
|
where MD is de Sitter absolute magnitude and CD is an observational constant that incorporates the de Sitter radius R.
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|
METHODS
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To compare the Hubble and de Sitter laws in the context of observation, we examined large astronomical catalogs of objects (galaxies and quasars) with published measurements of both redshift and apparent magnitude5,6,7. We transformed apparent magnitude to absolute magnitude according to the Hubble and de Sitter laws using equation (6) and equation (7) respectively. Figure 2 shows magnitude plotted versus redshift: first the raw data or apparent magnitude, second the absolute magnitude assuming a Hubble law, and third the absolute magnitude assuming a de Sitter law. As a statistical assessment, a least-squares-fit line is drawn for each set of data in the plots and the slope and the square of the correlation coefficient are given.
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RESULTS
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|
The line in the Hubble plot (Fig. 2b) is down-sloping, while the line in the de Sitter plot (Fig. 2c) is nearly horizontal. Almost all objects fall within a band spanning about ten magnitudes vertically (for a given redshift). This entire band is clearly downsloping assuming a Hubble law, but is roughly horizontal assuming a de Sitter law. De Sitter absolute magnitude is practically uncorrelated with redshift, while Hubble absolute magnitude is fairly strongly correlated with redshift. This is found to be the case not only
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68
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|
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|
for the combined catalogs, but also for galaxies and quasars considered separately (Table 1).
|
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DISCUSSION Some increase in intrinsic brightness is to be expected as a result of Malmquist
|
|
bias: more distant objects will tend to be brighter because we will only be able to s~e distant objects if they are intrinsically brighter than closer objects. However, MalmqUlst bias is generally thought to be inadequate to explain quasar intrinsic brightness. Of
|
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1.2
|
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|
|
0.8
|
|
a: -... 0.6
|
|
....
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|
0.4
|
|
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|
1/2
|
|
r ~ R[ 1 ___1 _]
|
|
(z+ 1)2
|
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|
0.2
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|
0 0
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2
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3
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|
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|
4
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|
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5
|
|
|
|
z Figure 1. Distance (rIR) plotted versus redshift (z) in a de Sitter universe (equation 4).
|
|
|
|
course, the downward slope of the least-squares-fit line in the Hubble plot (Fig. 2b) can be explained by luminosity evolution. That is, as we look out into space, we look back to a time when objects existed that were intrinsically much brighter than anything currently (or locally) extant.
|
|
An alternative is the original de Sitter redshift. Given the asymptotic character of the de Sitter redshift at large distances, quasars with high redshifts may not be much more distant than are intermediate-redshift objects. Since absolute magnitudes are
|
|
roughly the same at all redshifts assuming a de Sitter law, quasars may be considered in the context of a nonlinear de Sitter redshift-distance law without invoking luminosity evolution.
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69
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Figure 2. a, Apparent magnitudes of galaxies5,6 and quasars7 versus 10glQ(z). The corduroy texture represents lines of iso-apparent magnitude. b, Absolute magnitudes obtained by assuming a linear Hubble redshift-distance relation and applying equation (6) to the data set in Fig. 2a. The actual values are arbitrary, since the constant CH was set equal to zero. This affects the intercept, but not the slope nor the correlation coefficient. c, Absolute magnitudes obtained by assuming a nonlinear de Sitter redshift-distance relation and applying equation (7) to the data set in Fig. 2a. The actual values are also arbitrary, since CD was set equal to zero.
|
|
70
|
|
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|
Table 1. Comparison of slope, intercept, and correlation. t
|
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|
Number
|
|
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|
Hubble
|
|
|
|
Slope Intercept
|
|
|
|
R2
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|
|
|
Slope
|
|
|
|
De Sitter
|
|
|
|
Intercept
|
|
|
|
R2
|
|
|
|
Galaxies5 ,6 16118
|
|
|
|
-3.0
|
|
|
|
18.4 0.60 -0.27
|
|
|
|
18.2
|
|
|
|
Quasars 7
|
|
|
|
4197
|
|
|
|
-3.6
|
|
|
|
18.6 0.52
|
|
|
|
0.33
|
|
|
|
19.0
|
|
|
|
0.011 0.0089
|
|
|
|
Total
|
|
|
|
20315
|
|
|
|
-3.0
|
|
|
|
18.5 0.81
|
|
|
|
0.076 18.8
|
|
|
|
0.0026
|
|
|
|
tGalaxies are taken from the CfA Redshift Catalogue (n = 15597, Z < 0.33) and the ZBIG Catalog
|
|
= (n 521, Z > 0.33). Quasars are taken from A New Optical Catalog of Quasi-Stellar Objects. Slope
|
|
refers to the slope of a least-squares linear regression curve for a scatter plot of absolute magnitude versus
|
|
= 10glO(z). Intercept gives the 10glO(Z) 0 intercept of this line, assuming CH = CD = O. R2 is the
|
|
squared correlation coefficient (which is distinct from the de Sitter radius R). Only objects with published measurements of both redshift and apparent magnitude are included. A few blue-shifted galaxies have been excluded.
|
|
|
|
REFERENCES
|
|
1. E. Hubble, A relation between distance and radial velocity among extra-galactic nebulae, Proc. natn. Acad. Sci. U.S.A. 15:168 (1929).
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2. W. De Sitter, On Einstein's theory of gravitation and its astronomical consequences (third paper), Mon. Not R. astr. Soc. 78:3 (19l7).
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3. P. Kerszberg. "The Invented Universe: the Einstein-De Sitter Controversy (1916-17) and the Rise of Relativistic Cosmology," Clarendon, Oxford (1989).
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4. A.S. Eddington. "The Mathematical Theory of Relativity, Second Edition," University, Cambridge (1924).
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5. J. Huchra. "CfA Redshift Catalogue, Selected Astronomical Catalogs, Volume 1, CD ROM," Astronomical Data Center, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA (1990).
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6. J. Huchra and C. Clemens. "ZBIG Catalog," Personal Communication (1991).
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7. A. Hewitt and G. Burbidge. "A New Optical Catalog of Quasi-Stellar Objects, Selected Astronomical Catalogs, Volume 1, CD ROM," Astronomical Data Center, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA (1989).
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WHAT, IF ANYTHING, IS THE ANTHROPIC COSMOLOGICAL PRINCIPLE TELLING US?
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Silvio Bergia Dipartimento di Fisica, Universita di Bologna LN.F.N., Sezione di Bologna Via Irnerio, 46 - 40126 Bologna - Italy
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INTRODUCTION
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There can be no doubt that the evolution undergone by our ideas concerning the universe from ancient until very recent times has been characterized, on the one hand, by the removal of the earth, and of mankind, from the privileged position attributed to both of them in old cosmologies, and, on the other hand, by the rejection of any teleological point of view.
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Authors presenting or discussing the Anthropic Cosmological Principle, however, have often claimed that those ideas ought to be reconsidered; in other instances, the explicit claim has been replaced by a more or less explicit message. That we should seriously consider the possibility of a teleology of nature is the impression one receives from reading the most extensive book on the Anthropic Cosmological Principle appeared in the literature, the treatise by J.D.Barrow and F.J.Tipler, published in 1986 (BARROW and TIPLER 1986). The book's review written by W.H.Press for Nature was significantly titled "A place for teleology?" After recalling that "it is an understatement to say that teleology has been out of fashion in science in the past century, and probably not much of an exaggeration to say that the present scientific paradigm rejects the teleological hypothesis vehemently, categorically and usually with contempt", Press went on: "Now there comes a book - no crackpot tract, but a scholarly, philosophically sophisticated and mathematically high-brow monograph - that says we've all made a big mistake: there really is a place for teleology and related concepts in today's science. At least (the authors ask), give us a chance to present arguments drawn in the main from modern theoretical cosmology, which may convince the reader of an astounding claim: there is a grand design in the Universe that favours the development of an intelligent life." (PRESS 1986, p.315).
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Are we really obliged, by the arguments presented under the heading "Anthropic Cosmological Principle" [lJ to accept this conclusion? I will argue that we are not.
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We may reject the conclusion a priori advocating the postulate that science is not concerned with final causes, and that adopting a teleological viewpoint is a one man/woman decision, which depends on his/her general philosophical attitudes
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Frontiers of Fundamental Physics, Edited by M. Barone
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and F. Selleri, Plenum Press, New York, 1994
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and may in turn contribute to shape them, but which should not creep into his/her scientific work. However, this attitude may be dubbed dogmatic and we may be invited instead to face the evidence revealed by the authors who have developed the field.
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I will therefore take a different attitude and in fact examine some of this evidence. This examination leads, in my opinion, to the conclusion that the universe is indeed, in a way to be specified, "critical with respect to biology". The conclusion could be seen as a manifestation of the presence of final causes; I will however argue that the situation is similar to that concerning the evolution of life on earth. Therefore, an extended Darwinian attitude can be adopted (and in fact ought to be adopted by scientists) in analysing it. The Darwinian outlook and teleology, as I will stress once more further on, are rigorously antithetic. The confusion produced by the studies on the anthropic principle has mainly arisen, in my opinion, from the circumstance that some presentations have unduly mixed the two points of view. This is, it seems to me, only part of the confusion that has very often surrounded the subject. There is in fact, as I will argue, more to it. To begin with, in what sense, if any, are we here dealing with a principle? My second purpose is to analyse the formulation of WAP with the preliminary aim of clarifying its nature as a proposition, that is to say from a logical-syntactic point of view. This will allow me to analyse its status also from the methodological point of view, with particular attention to its predictive power, which will be compared with that of the ordinary propositions of physics. Its interest from this point of view is however limited due to its reduced ezplicative power. This difficulty is usually overcome, as I will argue, by operating a gradual shift in the meaning of the principle. This is brought about in two steps: the first one consists in viewing the WAP as an ordering principle. This step is to be considered as a positive one, as it ultimately is the one that permits us to identify, as I will argue, the objective message conveyed by the considerations which are labeled under the term Anthropic Principle: as already mentioned, this step consists in the discovery that the universe is critical with respect to biology. The second shift of meaning is brought about when one subreptitiously makes the reader develop the feeling that the principle gives a causal explanation. Since, in this case, it would be the matter of a "final cause", one would then ineluctably open the doors to teleology.
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In the exposition I will find expedient to reverse the order in which the two main points are dealt with. Hence Section 1 is devoted to analysing of WAP as a propositionj Section 2 deals with the difficulties, both objective and subjective, which are encountered when trying to ascribe an explicative power to WAPj Section 3 presents some of the evidence for the anthropic arguments and examines WAP as an ordering principlej Section 4 analyses the usual presentations, pointing out where they become misleading for lack of precision in separating Darwinian from teleological arguments; it will also be argued there that the so-called Strong Anthropic Principle represents the natural outcome of the above-mentioned process of contamination and that it amounts to stating the teleology of the universe.
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1. THE WEAK ANTHROPIC PRINCIPLE AS A PROPOSITION
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The term "Anthropic Principle" is due to Brandon Carter, of Cambridge, who coined it in 1974, in the two versions of "Weak Anthropic Principle" (WAP) and "Strong Anthropic Principle" (SAP). I will refer here to the formulations given of both by Barrow and Tipler in their book.
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I will initially concentrate my attention on WAP, and come back later to the strong version. According to Barrow and Tipler, WAP states that:
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"The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the universe be old enough for it to have already done so" (BARROW and TIPLER 1986, p. 16). Referring to formulations such as this, Wheeler, in his Foreword to the book, observes:
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"What is the status of the anthropic principle? Is it a theorem? No. Is it a mere tautology, equivalent to the trivial statement, 'The universe has to be such as to admit life, somewhere, at some point in its history, because we are here'? No. Is it a proposition testable by its predictions? Perhaps. Then what is the status of the anthropic principle? This is the issue on which every reader of this fascinating book will want to make his own judgement." [2]
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We have here a testimony of the fact that, even to the experts, it is not altogether clear what the actual meaning of the principle is.
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Before entering into any detail as regards the points I wish to analyse, let me briefly mention two questions, implied by the statement of the principle, on which I will not be able to dwell here. Note, first of all, the appearance of the notion of probability in an unusual context. Indeed, this notion makes sense only if a set of alternatives is given from which the extraction of a particular choice is possible. As P.e.Davies phrases it, one should "envisage a huge collection of possible universes a world ensemble - each varying slightly from the others so that somewhere among the ensemble would be a universe in which every conceivable value for each fundamental constant, and every conceivable initial arrangement of matter and motion, where realized to within a certain accuracy." (DAVIES 1982, p.123). The idea of the "world ensemble" can be, and has been criticized. G.Toraldo di Francia, for instance, observes: "What precisely are the possible worlds?.. .! think those scholars, like W.V.O.Quine, to be right, who doubt that it makes sense to speak of unrealized possibilities. The strong suspicion arises that, if they have not be realized, it is because they were not possible" (TORALDO 1990, p.27). The discussion of this point is certainly central for an analysis of the anthropic principle, but I will here sacrifice it in order to be able to deal at some length with the aspects mentioned above. I will thus acritically assume throughout, for the sake of the discussion, that the notion of world ensemble is a legitimate one. Note also that the statement makes an implicit reference to evolutionary cosmologies, such as the standard hot big bang cosmology, insofar as it alludes to the age of the universe. The anthropic principle allegedly provides arguments in favour of such cosmologies. The essential point seems to be the rough coincidence between the Hubble time and the age of a typical star. I have not yet analysed here the real content of the anthropic principle, but let us assume, for the sake of argument, that it implies that the value of the Hubble time is restricted by the conditions necessary for the existence of man. An essential condition is then that the universe be old enough for there to exist elements heavier than hydrogen. Now, heavier elements are synthesized in the interior of stars; as a consequence, the Hubble time of an inhabited universe cannot be shorter than the age of a typical star. On the other hand, if the Hubble time were much greater than the age of a typical star, most of the stars whose planets may sustain life would already be dead. [3]
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Putting aside, for the moment, the question as to whether the anthropic principle requires such a restriction, it seems to me that this is not an argument in favour of an evolutionary cosmology, or it is so only to the extent that it finds it (qualitatively) selfconsistent. An evolutionary cosmology is characterized by a typical time, the Hubble constant, or the age of the universe: it is found that its value is consistent with characteristic astrophysical times; no typical time exists in a steady-state cosmology and thus no problem of self-consistency arises there. What seems to me to be true, is that, since anthropic arguments deal with the origin and development of life, they
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7S
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are bound to be to some extent evolutionary. A steady-state cosmology cannot, and does not, of course, exclude evolution, at least on a local scale, and anthropic arguments can be used within its framework. However, an evolutionary view at the scale of the universe is only provided by a big bang cosmology, which is therefore more homogeneous with the anthropic viewpoint. For this reason I will consider a hot big bang cosmology as the natural background for the discussion that follows and will no longer come back on the issue of the comparison between the two cosmologies.
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My purpose here is, first of all, to analyse the formulation of WAP with the preliminary aim of clarifying its nature as a proposition, that is to say from a logicalsyntactic point of view. In J.Rosen's comment, WAP, in the version of Barrow and Tipler, "seems very incontroversial. It is simply recognition of the fact that the situation we observe in the universe must be consistent with our existence" (ROSEN 1988, p.416). My impression is that one could replace Rosen's "incontroversial" with "empty", at least until a point which I consider essential is not clarified.
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Actually, a lot depends on the value one attributes to the phrase "take on values restricted by the requirement". It seems to me that presentations of WAP are often biased by the ambiguities concerning this point. It is possible to read the sentence as the simple statement of a matter of fact. In this case it does not in fact predicate anything on the subject "the observed values of all physical and cosmological quantities", and justifies the verdict of logical emptiness. On the same grounds, it is on the other hand possible to read it as a proposition having a prescriptive value: in other words, "take on" is read as "must take on". It should of course be stressed that this value is in fact attributed to the sentence merely from a logical-syntactic point of view for the purpose of attributing significance to the proposition. Obviously, no direct operative character is, or can be, attributed to the prescription.
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This is a first, and evidently not irrelevant, discrimination. It therefore seems to me inacceptable that much of the current literature leaves it unsolved, thus justifying Wheeler's uncertainties. It we adopt the second attitude, it becomes possible to answer the question, essential for a correct collocation of WAP from the methodological point of view, as to whether a testable proposition, or a set of testable propositions, can be associated with WAP.
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To tackle this question, I will refer to a particular phenomenon: carbon nucleosynthesis in starsJ4] The synthesis (of three helium nuclei) takes place at a particular stage of the stellar evolution, both through both a direct and an "autocatalytic" reaction, proceeding via an intermediate beryllium 8 step. These reactions must proceed resonantly to produce a non negligible yield of carbon, such as to justify the actual presence of carbon (and, incidentally, of life) in the universe. That must, which follows from the assumption of the prescriptive character of the principle's statement, is the clue the example provides us with to identify the kind of proposition we are looking for. On the basis of the datum "existence in the universe of carbon-based forms of life", which in turn requires the presence of relevant quantities of this element, and on the basis of our knowledge of the processes of stellar nucleosynthesis, we can state that certain nuclear reactions, which can be studied in the laboratory, must take place in a specific way, and namely resonantly. From a logical point of view, we are therefore in the presence of a prediction following from two premises. Up to this point, the term "prediction" has been used in a purely logical and a-temporal sense. From the point of view of the temporal sequence of events, one must distinguish between the post-diction of what must have taken place in the interiors of stars (time here is that of natural history) and the pre-diction, in a strict temporal sense, of the features of a process we can study in the laboratory (for which time is that of the laboratory life). The first one acts in an anti-temporal way, hence in a different sense from that which is customary in physics, where"the future is deduced from the past" (GALE 1981,
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p. 117), while the second one acts in a sense that is perfectly homogeneous to what normally occurs in physics; and it is interesting to note that the history, not of the universe, but of scientific activity, has followed this logical path. In 1953, Fred Hoyle, on the basis of considerations of the type reported above, formulated the prediction that, in order for the mentioned rections to be effective at the cosmological level, the carbon nucleus must have a resonant level lying near 7.7 MeV, whose existence was soon verified experimentally (BARROW and TIPLER 1986, p. 252).
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Therefore, it is not at the level of the temporal sequence of events "formulation of a hypothesis" and "experimental verification of the hypothesis" that a proposition, like the one in which Hoyle's prediction could be condensed, differentiates itself from those of the type usually employed in physics. The difference can be seen, as will be discussed in the next section, when one tries to attribute an explicative power to the proposition.
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2. EXPLICATIVE POWER
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The most marked difference between WAP, interpreted in this way and the ordinary propositions of physics is best appreciated when one wonders about the explicative power of such a proposition. Can we say that the existence of life on earth explains the carbon's resonant state? Pretending to consider this as an explanation, observes Rosen, runs into two difficulties, one of a subjective and one of an objective nature.
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The objective difficulty is what Rosen calls "the invariant context problem". "For an explanation to be an explanation, at the very least what is being explained must follow logically from what is explaining; in our case, the existence of Homo sapiens must be sufficient (emphasis added) for the coupling constants to have the value they do, or the actual values of the coupling constants must be necessary (emphasis added) for our existence, or if the values were different we could not exist". Now, can we state with certainty that, if those constants had not their actual values, man could not exist? Yes, but only if it is "tacitly assumed that no other aspect of the universe, no other law of physics, not even the form of the interaction equation, is varied. (ROSEN 1988, p. 417)" Without the assumption of the invariance of the context, the sufficiency of the existence of Homo sapiens, or, which is the same, the necessity of the constants having their actual values, does not arise.
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The subjective difficulty "is that we physicists just do not feel that any explaining is being done". We want indeed "that which is explaining to be more fundamental, simpler, more general, and more unifying than that which is being explained, and we would also like the former to be the cause of the latter. In the present case, none of these seems to hold" (ROSEN 1988, p. 417). As I have anticipated, I will argue that the difficulty experimented in accepting that the principle has an explicative power is usually overcome through a gradual shifting of its meaning.
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3. THE ANTHROPIC PRINCIPLE AS AN ORDERING PRINCIPLE
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What has been said up to this point may leave one unsatisfied, as if the subject matter had only been touched on. One tends to ask: is it all there? In fact, it is not. When reading the current literature on the anthropic principle, one gradually discovers that people are saying something more, and different, than what is contained in a proposition like that stated the WAP. What, explicitly or implicitly is being said is rather: we have discovered that "the observed values of all physical and cosmological quantities are not equally probable but they take on values restricted
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by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the universe be old enough for it to have already done so." In order to clarify this point, let us enunciate a logically equivalent proposition, which however highlights the aspect of interest: We have discovered that, if the cosmological quantities had not all the observed values, there could not exist a carbon-based life. I must say that a large part of the considerations appearing in the literature under the generic heading "Anthropic Principle" mostly stress the essential role that specific aspects of the cosmic evolution and of the laws and constants of nature have had and have in determining the conditions for the appearance of life on earth.
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The first instance I would like to briefly discuss is provided by water, whose chemical and physical structure, as Henderson had already noted in 1913, make it "a uniquely useful liquid and the basis for living things" (quoted in BARROW and TIPLER 1986, p. 524). In particular, Henderson pointed out that "the expansion of water in freezing is essential for life if it is to evolve in a constant environment. If ice were not less dense than water, it would sink on freezing. The coldest water in a lake or ocean would congregate near the bottom and there freeze. Ice would accumulate at the bottom; the amount would become greater each year as more ice formed during the winter and did not melt during the summer. Finally, all the lakes and oceans would be entirely frozen" (cited in BARROW and TIPLER 1986, p.533). Now, all properties of water can be understood in terms of the atomic structure of the water molecule and of the chemical bonds that keep it together (ibidem, p. 526). In particular, the shape of the molecule as determined by these bonds is that of an isosceles triangle in which the H-O-H angle is 104.5 degrees (ibidem, p. 526). Moreover, water molecules tend to form highly directional hydrogen bonds with each other. The above value of the bond angle is only slightly less than that of the ideal tetrahedral angle (109.5 degrees); and the anomalous density of ice is ultimately due to this fact (BARROW and TIPLER 1986, p. 532-533).
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As a second instance, we may recall that the possibility of carbon-based life rests upon a coincidence regarding the relative strength of the strong and electromagnetic forces. As discussed by Barrow and Tipler, "a 50% decrease in the strength of the nuclear force...would adversely affect the stability of all the elements essential to living organisms and biological systems. Similarly, holding the strong force constant ...the stability of carbon requires the fine structure constant a to be less than'" 0.1" (BARROW and TIPLER 1986, p.326-327).
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Finally, let me consider another instance concerning once again nucleosynthesis. To what has already been said the stellar nucleosynthesis of carbon, a lot more may be added as regards primordial nucleosynthesis. Just to give an example, we may recall that, in adition to deuteron, a proton-neutron bound state, the nuclear strong interaction could give rise to a "diproton", a two-proton bound state: for its existence, the strong interaction would have to be only slightly stronger, in order to overcome the electric repulsion. However, as stressed for instance by Barrow and Tipler, the existence of this bound state would have catastrophic consequences, since all the hydrogen of the universe would have been burnt into helium during the initial phases of the big bang so that stars would not have been formed and the synthesis of the heavy elements would not have taken place (BARROW and TIPLER 1986, p.322).
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On the other hand, the information upon which considerations of this kind are based is not new, as it has been available, often for quite a long time, in chapters of atomic and nuclear physics or astrophysics. It is clear then that, if this is the case, the term "principle" is being used improperly: from a strictly logical point of view, in fact, one is here stating no principle at all. What is being done, is that available information is being taken and ordered according to a thread which
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illustrates the above mentioned link between the physical world, its evolution and laws, and conscious life, instead of leaving it where it belongs naturally, that is in chapters of the various pertinent disciplines. In the best of circumstance, therefore, one is dealing with an ordering principle, with a 8tandpoint from which to look at known facts according to a new perspective: the perspective dictated by the wish to understand what is necessary for life.
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This operation, on the other hand, adds significance to the known facts, not by increasing their information content, but rather by making one see their relevance in a new context. It leads, and I have already used the term on purpose, to a di8covery, the discovery that:
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The univer8e is critical with respect to biology. [5] Note, by the way, that this version provides an adequate framework for the selfconsistency argument concerning the Hubble time discussed in Section 1.
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The third instance reported above shows, however, that this statement is incomplete, and should in fact be extended. What the example shows is that the criticality of the universe with respect to biology cannot be disjoined from its criticality in a wider sense. Even minor changes in the values of the fundamental constants would not only lead to a universe incapable of sustaining life: in fact they wouldn't lead to any universe at all! This aspect has been discussed at some length in particular by I.L.Rozental (ROZENTAL 1980). For these reasons Rozental prefers to speak of a "principle of effectiveness" (or "appropriateness"). While agreeing on the necessity of the extension, I will stick for convenience to the terminology in use.
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This seems to be the actual message (extension to a wider criticality included) conveyed by the complex of elements and arguments which fall under the label of "Anthropic Principle". And, from the point of view of its objective content, it is almost immaterial whether we are dealing with a principle or with a discovery. There is in fact no doubt that this way of looking at things adds significance to aspects, at times apparently marginal, of the laws of nature.
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4. DARWINISM VERSUS TELEOLOGY
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But the question is: do we want to infer some general conclusion from the mere observation that the universe is critical with respect to biology (or in a wider sense)? If we start speculating about this possibility, the message conveyed by the anthropic principle becomes more suggestive and intriguing, but also more ambiguous.
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The starting point is the feeling that a kind of conspiracy must have been operating in order for life to have emerged in some place in the universe. This feeling is enhanced by a first evaluation of the probability of the evolutionary processes, required for the development of human kind having taken place on a cosmic and astrophysical scale and in the biosphere. The possibility of reasoning in terms of probability at the cosmic level depends, of course, on accepting the idea of the "world ensemble" briefly discussed above. Even if "it is hard to quantify the improbability of the choice of our perceived world, because...we do not know how to measure probabilities between possible universes", this idea authorizes us to state that "our world is indeed extremely unlikely on a priori grounds ..." (DAVIES 1982, p. 123).
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It is difficult not to be influenced by these considerations, to the extent that they could lead us to adopt a teleological view, which could be expressed in the following terms: "The existence of life in the universe is made possible by such a sequence of highly improbable events that it appears to be the result of a project".
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However, this feeling is by no means new. For centuries throughout the course of history, human kind has never ceased wondering about the fitness of the terrestrial
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environment (on the whole, that is neglecting places like cold and hot deserts, the polar regions, etc.) for the purposes of human life.
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The advent of Darwinism implied a deep change in this attitude. No wonder if the biosphere appears suitable to host man's life: had it not reached, in the course of its evolution, a condition favourable to the development of what is necessary to life, the evolutionary process which eventually led to man could not have taken place. The change of attitude implied by the Darwinian viewpoint has been lucidly expressed, for instance, by L.Gustavsson, in the following terms: the conception about the origin of the species "to whom Charles Darwin gave a conclusive form...states that certain systems like, for instance, the mammals' internal organs, are not made as they are because [final cause) something obliged them to take the aptest form, but rather because [efficient cause) modifications of the external conditions acted as a filter with respect to the manifold of theoretically possible evolutions, leaving go through only those suited to survive and to gradually transform. The teleological principle had been led from the status of universal principle to that of a simple relation between a biological system and its transitory natural environment. Teleology could be transformed in a normal causality relation" (GUSTAVSSON 1990).
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There is therefore no need to have recourse to teleology to understand the fitness of the environment: it was not the environment to conspire to produce human kind, but it is man himself who is the result of an adaptation to the environment. Or, man is not the final cause of the earth in the universe, but it is the universe and the earth which are the efficient cause of man.
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Now, the essential point seems to me to be that these considerations can be transferred from the ambit of the biosphere to that of cosmology, as defined by the standard model of a hot big bang. The only difference of principle that arises seems to derive from the fact that most of the a priori conceivable sets of laws and data, and the corresponding evolutionary paths, would not lead to any universe at all. However, this seems to me to produce only a non essential extension ofthe Darwinian viewpoint.
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I am thus claiming that one should adopt in cosmology a Darwinian viewpoint, which essentially means replacing final causes with efficient ones, and thus, in this case, is satisfied with the conclusion that not only life could not have possibly arisen other than in a suitable universe, but also that it could not have arisen without a universe.
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We can summarize this discussion in the following terms: the statement that "the observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve" is traced back to the consideration that, would it not have been so, the evolutionary process that we can retrospectively reconstruct could not have taken place. "Discovery" and assumption of the viewpoint do not add anything to WAP, either as a verifiable proposition, or set of propositions, or as an explicative proposition. The only novelties are in the discovery and the adoption of the viewpoint. This seems to me to be what, if anything, the anthropic cosmological principle is telling us. And I would like to stress that neither the discovery nor the viewpoint necessarily outline a crime of apostasy with respect to the current theoretical and epistemological framework, nor do they necessarily imply abandoning the secular attitude which, until one has proof to the contrary, rejects teleology as redundant and extraneous to natural sciences.
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On the other hand, adopting a teleological viewpoint seems to be the only logically possible alternative to adopting a Darwinian viewpoint. It should be stressed that the issue is that of a global alternative, of an antithetic attitude, and not of a variant, or of a kind of integration of that viewpoint. This conclusion should be clear enough. And it must be said that there does not exist any version of the anthropic
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principle of which I am aware that immediately and explicitly reduces to a statement of teleology. However, some presentations have unduly mixed the two points of views. I believe this to be the essential cause of the confusion produced by the studies on the anthropic principle.
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The contamination of the Darwinian viewpoint begins when one leaves almost inadvertently creep into the discussion the idea that WAP gives an explanation in causal terms. As I have said, we encounter a subjective and objective difficulty to accept that WAP provides an explanation. "To explain" probably means to us, first of all, to find out a causal link between explanans and explanandum. Can we say that the existence of man "explains" in this sense the values of the physical constants? It does not seem necessary to associate this idea with WAP. Nevertheless, a good deal of the anthropic arguments are pervaded by the question that looks for a cause: "Why?" And, what is worse, they let the reader develop the feeling that the question has found an answer. As stressed by Press, Barrow and Tipler's book is full of implicit
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question marks: "< Why> do the physical constants have the values that they do? < Why> is the Earth the size and temperature that it is?" And so on. In this way,
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he goes on, "the seductive trap that the authors are setting is already clear: as soon
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as as we accept the < why> formulation of questions that the WAP allows us to
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address, we have entered a receptive state of mind for the Strong Anthropic Principle (SAP): The Universe must have those properties which allow life to develop within it at some stage in its history" (PRESS 1986, p.315). Or, I would rather say, we have already taken a teleological viewpoint. Indeed, I must confess that I do not understand the meaning one wants to attribute to the SAP in the above statement: and, if we try to attribute one to it, we soon discover that it amounts necessarily to claiming that the universe has a purpose. For, once more, what does that "must" mean? At the logical-syntactic level it cannot but express a necessity; but, at this level, it expresses nothing more than what is already contained in WAP, once it has been decided that as an empty proposition it does not interest us. It is then clear that the authors want the implication to be read in another way. And it does not seem to be anything else but that of a cause-effect implication, as in
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fact suggested by Press when he reads the statement as an answer to the various <
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why's >. I therefore think that the SAP either is equivalent to the WAP, or answers the question: "Why does the universe have the properties that it has?" in the terms: "The universe has the properties that it has in order that [final cause] life might develop in it at some stages of its history."
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Authors stating SAP seem to maintain that it is a proposition still possessing scientific relevance, situated somewhere in between WAP and the direct statement of teleology. On purely logical grounds, it appears a priori doubtful that an intermediate position may exist between so diametrically opposed points of view such as the Darwinian and the (neo )teleological ones. My conclusion is that, even if SAP does not immediately appear as a statement of teleology, it cannot have any other meaning.
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Rosen also considers the as "meaningless within the context of science" (ROSEN 1988, p.416). The possibility of formulating such a proposition appears illusory. That a good deal of the arguments one finds under the generic heading of anthropic principle seem to make reference to it is the result of a methodological error.
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FOOTNOTES
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[1] Unless otherwise stated, I am here referring to the so-called Weak Anthropic Principle, or WAP for short; I will come back to the Strong Anthropic Principle (SAP) in due time.
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81
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[2] J.A.WHEELER, Foreword to BARROW and TIPLER 1986, p. vii. [3] This argument was put forward by R.Dicke some thirty years ago: see Dicke
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1961. [4] This example is analysed in BARROW and TIPLER 1986, p.252. [5] My attention was drawn towards this statement of the Anthropic Principle by
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A.Masanij see, for instance, MASANI 1987.
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REFERENCES
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J.D.Barrow, F.J.Tipler, 1986, "The Anthropic Cosmological Principle," Clarendon, Oxford.
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P.C.Davies, 1982, "The Accidental Universe," Cambridge University Press, Cambridge.
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R.Dicke, 1961, Dirac's cosmology and Mach's principle, Nature 192:440. G.Gale, 1981, The anthropic principle, Sci. Am. 245:114. L.Gustavsson, 1990, L'enigmatico principio antropico, Lettera Internazionale 24:44. A.Masani, 1987, II principio antropico Il Nuovo Saggiatore, nuova serie, 2:63. W.H.Press, 1986, A place for teleology?, Nature 320:315. J .Rosen, 1988, The anthropic principle II, Am. J. Phys. 56:415. I.L.Rozental, 1980, Physical laws and the numerical values of fundamental constants,
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Sov. Phys. Usp. 23(6}:296. G. Toraldo di Francia, 1990, "Un Universo Troppo Semplice," Feltrinelli, Milano.
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82
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LARGE AlOKALOUS REDSHIFTS AID ZERO-POIIT RADIATIOI
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P. F. Browne
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Department of Physics UKIST Manchester M60 lQD
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I1TRODUCTIOI
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In de Sitter space-time using Robertson coordinates the Hubble
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redshift can be interpreted as gradual decrease of photon frequency.
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How this decrease of frequency might occur was suggested previously
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(Browne, 1962). The radiation field for each Planck oscillator is
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quantized gravitationally as a field of gravitons of minute const;ant
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energy. Scattering of a gravi ton from pne field to another toward the
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equilibrium blackbody spectrum results in a redshift, dw = - AfwUdl,
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where distance dl is propagated in a medium with radi~nt energy density
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U and A is a constant. A cross section, previously suggested (Browne,
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1976), provides a theoretical value for A. The law becomes the Hubble
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redshift dc')lc') = - dl/R if U = Kpo (.2, where Po is the gravitational mass
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density required to close the universe at radius Rand K is the ratio
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of inertial to gravitational mass (a dimensional constant with value
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unity). It is argued that zero-point radiation (vacuum fluctuations)
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have renormalized energy density KPo c 2 .
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.
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In quasars U is large enough to YIeld anomalous redshifts
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comparable with the Hubble redshift of the sources, but the sources
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must be at large distances in order to have the large values of U.
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THE PHOTOI AS A GRAVITOI FIELD
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Planck's radiation osci llators are quant ized gravitationally as
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different eigenstates of a fundamental oscillator of frequency equal to
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the Hubble constant H (w o = c/R = H). The wavelength, ~o = ltc/wo = 2ltR,
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is the circumference of the universe. Then
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(n + Y.!)'hwo
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(1)
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where n is a very large integer. A photon is treated as a field n of
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= gravitons of energy nwo' Writing nwo 2E, we have
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E <RIc)
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-hI 2
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<2 )
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Thus E may be interpreted as a basic uncertainty in all energies arising because measurement times cannot exceed the Hubble age Ric. The spectrum of Planck oscillators is quasi-continuous because E is
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unmeasurable. Selection rules, LIn = ± 1, constrain the photon to lose
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FronJiers ofFundamenJal Physics. Edited by M. Barone
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and F. Selleri, Plenwn Press, New York, 1994
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83
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gravitons one at a time, which is quasi-continuously. The process of interest is scattering of a gravi ton from photon
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field n to photon field n'. The probability for such a scattering is proportional to nn'. Introducing cross section ~o' the rate of scatterings from field n to isotropic radiation of the medium with energy density U (= Nhwo ) is
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Noting that dt
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dn/dt dllc, dn/n
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(3 )
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c/R, we obtain
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(4)
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For ~o we modify the Thomson cross section for scattering of radiation
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by a free electron. We replace the electrostatic radius of the electron
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d
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= e ~Imc 2 = 2.82
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x
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10-13cm by
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the
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gravi tatl.onal
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radius
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f
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0
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the
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electron
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a o (Browne, 1976a), obtaining
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~o
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8rra
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2 o
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/
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3
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(5)
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a
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(2K) -l(Gh/c 3) 1/2 = 8. 1 x 10-34 cm
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(6)
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o
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G being the gravitational constant, and K the ratio of gravitational to
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inertial mass (Browne, 1977). At radius a o the electron's gravitational and electrostatic fields become equal (Browne, 1977; see also Arnowitt
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et a1., 1960). By Gauss's theorem, th1/~ources of these equal fields
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are the real and imaginary charges (~c) . From (5) and (4),
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where
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A
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d(..J/w
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- AUdl
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(7)
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3.19 x 10-;21 erg -1 cm 2 '
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(8)
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the A value being for H = 50 km s -1Mpc -1 (R = 1.85 x 10 28 cm).
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Graviton scattering permits radiation trapped in a cavity with perfectly reflecting walls to attain the eqUilibrium blackbody spectrum in the absence of matter, which is not possible by recognized interactions.
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ZERO-POIIT RADIATIOI FIELD
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In order to obtain the Hubble redshift as a special case of (7) it is necessary to consider zero-point radiation (vacuum fluctuations). It will be assumed that the vacuum fluctuations have the character of classical electromagnetic radiation, which is the view of an increasing number of authors seeking to interpret quantum mechanics (Welton, 1948; Marshall, 1963; Power, 1966; de la Pena-Auerbach and GarCia-Colin, 1968; Boyer, 1975; 1978). The fluctuations are standing wave modes with random relative phases. Their energy denSity, ~w12 per mode, is
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= f = J U dw
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(~wI2)(w
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2 dw/rr
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2 C
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3 )
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(9)
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Ow
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The divergence of Uo as w tends to infinity can be eliminated by including the negative gravitational potential energy of the zero-point
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radiation which also diverges. The total energy density is
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U o
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Po ip(0)/2
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(10)
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EN. where Hr} is the Newtonian potential inside a uniformly dense sphere
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of radius
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Tolman (1934) has shown that the gravitational mass of
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disordered radiation is twice that of matter with the same energy
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density due to potential energy associated with pressure. Thus
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(11)
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84
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ir y The radi us of the universe Newtonian cosmology P is related to that
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in de Sitter cosmology by 3PN = R2. Converting to .,
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(12 ) As Uo tends to infinity, Po remain'3 finite only if
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<13 )
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which expresses tho.t Po closes the universe at radius R. If zero-point radiation closes the universe, the current search for "missing dark matter" can be abandoned.
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Zero-point radiation is not measurable because the most sensitive detector is in eqUilibrium with it. Only superiropos.ed radiation due to finite temper"ature is measurable. Adding the zero-point and Planck spectra gives,
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(14 )
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where x = exp<--h(')/kT>, and where lIo (0) i'3 given by (3).
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We postulate that radiation from a dista,nt a.stronomical source
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loses gravitons to zero-point radiation as it propagates to the Earth. Then we sub:3titute into (7) U = KP o c 2 , where Po i:;; given by (13). Then (7) and (8) yield AU liR, so that (7) becomes
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d(')/ (,)
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- dl/R,
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(15)
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which is Hubble'S law in differential and integrated forms. Quantitatively, KF'oC 2 = 6.9 x 10- 7 erg cm- 3, taking H = 50 km s-1
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Mpc -1 which implies R = 1. 85 x 10 28 cm. For compari'30n, the 2.735 UK
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cosmic blackbody radia.tion yields U = 4.23 x 10-13 erg cm-3 .
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DEFLECTION OF LIGHT
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If a photon loses a graviton to radiation propagating transversely to its path, then conservation of momentum requires that the photon gain transverse momentum h':Jo Ic, which implie'3 that it has suffered angUlar deflection o.'o/w. Interaction with isotropic radiation yields zero mean deflection, cut after loss of N graviton:3, where N = 8w/'') for redshift 8w, the angular spread is
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<88)
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<16 )
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<88> is undetectable because (,)0 is so small. If radia.tion of the medium is unidirectional and trans'"erse to the
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('}-beam, heam deflection become'3 measurable. Let the w-beam pass within dist.;mce y of a st.;)r of radius R at temperB.ture T. Then the transverse component of radiation flux h;3.s energy density UJ.. = IYT4(R/r)2Cy/r) at distB.nce r from the sta.r's center, where {J' 1:3 the Stef.:m-Bol tzmann
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constant. Noting r2 = 12 + y2,
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68
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(17)
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In the extreme case of a supergia.nt wi til T = 40,000 ('K and R find <58 = 44.5(R/y) arc sec, which i'3 detectable.
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AIOMALOUS REDSHIFTS
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The redshift formul.;) (7) integrates to ('}2/'')1 = exp(- AfUdl), where WI is the frequency at source and W2 that at reception. In the case of a quasar at distance d, U can be large enough for the 10c.;)1 redshift to
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85
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exceed the Hubble redshift w2/wl = exp(- d/R). The two redshifts are
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equal when AUl " d/R. IfF is the flux density at Earth from a quasar at distance d, then radiant energy density at source is U '" Fd 2 11 2 c.
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The condition for equality of the redshifts therefore becomes
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Fdll
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c/AR
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500 erg s -1em -2
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(18 )
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Typically F "10- 11 erg s·-.1 em - 2 and 1 '" 10 13 cm (from variability time scales - for example, see Kunieda et aI., 1990). Then (17) yields equali ty of the redshifts for d '" 5 x 1027 cm. If the source is more dh;tant the anomalous redshift is dominant, and if closer the Hubble redshift is dominant. The Hubble component of the redshift must be known in order to determine d.
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Evidence for anomalous redshifts of quasars has been accummulating for some ye8.rs CArp, 1987), Often a quasar is o.ssociated ~li th a galaxy with conSiderably smaller redshift. The association may be a very faint fil.5ment joining the bright quasar to the galaxy. Previously <Browne, 1985; 1993), it was proposed that quasar emission is beamed along the axis of a magnetiC vortex tube <MY!), which trails after the galaxy. Then the very bright quasar is seen where the line of sight is tangent to the MVT, and the faint filament is seen where the bent MVT becomes transverse to the line of sight.
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DE SITTER COSKOLOGY
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Einstein field equations, because of their general covariance, are applicable only to a perfectly isolated system, and the smallest :3uch
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system for r > a o is a universe defined by r < R (Browne, 1977; 1979).
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Clearly the source energy-momentum tensor Tcd3 in the Einstein equations is not open to free choice in the case of a tiniverse. Rather should one seek a source involving only geometrical quantities, The obvious choice is to equate KIaS to the cosmological term l\gaB' The constant A alone impo:3es a scale length on the description, Then the quat ions become
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(19)
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The static spherically symmetriC interior solution yields the metric of de Sitter space-time,
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where d0- 2 = d82 + sirf 8 df2 and A = l/R~ = 3/R2. Geodesic equations of
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radial motion for a particle released from rest at the origin are
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dr/cd'T ± r/R,
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(21)
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where ds = edT and where c(r) = (1 - / iR 2)C (from ds = 0). Thus the
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universe expands with respect to reference system (r, t). However, in
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the case of a perfectly isolated :3ystem it is impossible to distinguish
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between expansion of the system and contraction of the reference system (Browne, 1979).
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The time t 1 at which a wave crest is emitted by a source at radius r and the time t2 at which it is received at the origin are related by
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t2 = tl + Jdr/c(r). By differentiation and use of (21) it follows that
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ot2/6'tl = 1 ± r/R. Converting from ot to 81" by (21),
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(22 ) 86
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where J3 = <dr/dt)c(r)-l -:: r/R froll! (21). The factor D is the Doppler effect in special relativity, The additional factor is a gravitational redshift. Thus Hubble's effect is partly Doppler and partly gravitational. However, its interpretation is different for a different reference system, as we now show,
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The transformation of coordinates
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r(1 - r 2 IR2) -1/2exp(-ct/R)
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t + (R/2c)ln(1 - r2/R2)
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(23)
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converts the de Sitter metric to the form
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(24 )
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for which the geodesic equations are
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0,
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1
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(25)
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r Thus matter is at rest relative to <I, t). This is apparent also from
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the integral of (21) which is the first equation (23) with = const.
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= = The radial velocity of light {from ds 0) is c(t) c exp(-c~/R).
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The times of emission and reception of light signals now are related by
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r = .;r tR/c{-t) between liEits J-:2 and_- tI' yow -r is a constant so that
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= = differentiation yields 6t 2!c(t2) 6tl/c(tl)' Since 6t 6T,
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exp(-I/R)
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(26)
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where I = c(t 2 - tl)' This result agrees with (15),
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Because the metric (23) is invariant under
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(27)
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where t is a constant, the metric is unchanged by continuously varying
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time or<igin whilst appropriatly scaling radial distance. Redshift (27) can therefore be interpreted as continuous change of frequency at constant light velocity, which is the interpretation of (15),
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UIIT FIELDS AIl) ARBITRARIIESS OF GEOXETRY
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Uni hl for the three components of length and for time are of necessi ty arbitrary. By permi tUng each unit to become a field it is always possible to flatten space-time. Mathematically, the coordinate transformation is anholonomic (Browne, 1976b), and can be interpreted as projection from a curved space-time onto a flat space-time via coordinate curves in a 5-dimensional space in which both space-times are embedded. It happens that both de Sitter and Minkowski space-times can be embedded in a 5-dimensional Euclidean space.
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It is possible to derive de Sitter metric by transformation from inhomogeneous unit fields in flat space-time to homgeneous unit fields (constant units) in de Sitter space-time (Browne, 1976b), The inhomogeneous unit fields are obtained by applying Lorentz contraction to measuring rods and time dilation to clocks appropriate for the velocity field of the cosmological fluid, which is energy density of the electromagnetic field, both radiation and matter. The unit fields become the description of gravitation in flat space-time.
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87
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REFEREICES
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|
Arnowitt, R., Deser, S. and Misner, C.W., 1960, "Gravitationalelectromagnetic coupling and the classical self-energy problem", Phys. Rev. 120:313.
|
|
Arp, H., 1987, "Quasars, Redshifts and Controversies", Interstellar Media, Berkeley, Ca.).
|
|
Boyer, T.H., 1975, "Random Electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation", Phys. Rev. Dl1:790.
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|
Boyer, T. H., 1978, "Statistical equilibrium of nonrelativistic multiply periodic classical systems and random clasical electromagnetic radiation", Phys. Rev. A18:1228.
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|
Browne, P.F., 1962, "The case for an exponential redshift law", Nature 193:1019.
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|
Browne, P.F., 1976a, "A hierarchy hypothesis", Intern. J. Theor. Phys. 15:73.
|
|
Browne, P.F., 1976b, "Arbitrarines:5 of Geometry and the Aether", Found. Phys. 6:457.
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|
Browne, P.F., 1977, "Complementary aspects of gravitation and electromagnetism", Found. Phys. 7: 165.
|
|
Browne,P.F., 1979, "Universe expansion or reference system contraction", Phys. Lett., 73A:91.
|
|
Browne, P.F., 1985, "Magnetic vortex tubes, jets and nonthermal sources", Astron. Astrophys. 144:298.
|
|
Browne, P.F., 1993, "Active galactic nuclei: their synchrotron and Cerenkov radiations, "Progress in new cosmologies: beyond the big bang", ed. H.C. Arp et al., Plenum Press, New York, p.205.
|
|
De la Pena-Auerbach, L. and Garcia-Colin, L.S., "Possible interpretation of quantum mechanics", J. Math. Phys. 9:916
|
|
Kunieda, H. et al., 1990, "Rapid variability of the iron fluorescence line from the Seyfert 1 galaxy NGC6814", Nature 345:786,
|
|
Marshall, T, W., 1963, "Random electrodynamics", Proc. Roy. Soc. A276: 475.
|
|
Power, E,A., 1966, "Zero-paint energy and the Lamb shift", Amer. J. Phys. 34: 516.
|
|
Tolman, R.C., 1934. "Relativity, Thermodynamics and Cosmology", Clarendon Press, Oxford, p. 271.
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|
WeI ton, T. A., 1948, "Some observable effects of the quantum-mechanical fluctuations of the electromagnetic field", Phys. Rev. 74:1157.
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88
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