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This essay is entitled Universe without Space and Time because it proposes a cosmology that discards the notion that space and time are independent entities, either in Newton's sense of absolute space and time or in Einstein's sense of a self-subsistent space-time manifold. Instead, it treats space and time as relational quantities that are wholly dependent on matter for their meaning. It develops the scholastic way of thinking about space and time, which is the fruit of meditation on the biblical account of creation, and results in a way of looking at the cosmos that is refreshingly different from that of modern cosmology. It is an essay on principles, which means that it does not propose a full-blown cosmology but starting points for a biblically-inspired cosmology. The principles are drawn from Sacred Scripture as interpreted in Catholic Tradition (as passed on by the Fathers, Doctors and Magisterium of the Church) and from the observations of empirical science. It may be that more than one consistent cosmology can emerge from these principles because they may not be powerful enough or complete enough to ptoduce a unique cosmology.
The content of the essay is conceptual and non-mathematical. It is directed to the scientifically literate reader, both professional and lay. Although written from a Catholic perspective, the book is intended to appeal to believers of all faiths that hold Genesis to be the inerrant Word of God. Even readers who do not agree with the theme of the book will find much in it that enhances their understanding of the natural world.
ISBN 978-098886030-8
51995
9 780988 860308

Warkulwiz

Universe without Space and Time

Universe without Space and Time
An Essay on Principles for Relational
Cosmology Drawn from Catholic Tradition and
Empirical Science
Victor P. Warkulwiz, M.S.S.

ABOUT THIS BOOK
This essay is entitled Universe without Space and Time because it proposes a cosmology that discards the notion that space and time are independent entities, either in Newton’s sense of absolute space and time or in Einstein’s sense of a self-subsistent space-time manifold. Instead it treats space and time as relational quantities that are wholly dependent on matter for their meaning. It develops the scholastic way of thinking about space and time, which is the fruit of meditation on the biblical account of creation, and results in a way of looking at the cosmos that is refreshingly different from that of modern cosmology. It is an essay on principles, which means that it does not propose a full-blown cosmology but starting points for a Catholic biblically-inspired cosmology. The principles are drawn from Sacred Scripture as interpreted in Catholic Tradition (as passed on by the Fathers, Doctors and Magisterium of the Church) and from the observations of empirical science. It may be that more than one consistent cosmology can emerge from the principles because they may not be powerful enough or complete enough to produce a unique cosmology.
The content of the essay is conceptual and non-mathematical. It is directed to the scientifically literate reader, both professional and lay. Although written from a Catholic perspective, the book is intended to appeal to believers of all faiths that hold Genesis to be the inerrant Word of God. Even readers who do not agree with the theme of the book will find much in it that enhances their understanding of the natural world.

UNIVERSE WITHOUT SPACE AND TIME E-BOOK

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UNIVERSE WITHOUT SPACE AND TIME An Essay on Principles for Relational Cosmology Drawn from Catholic Tradition and Empirical
Science
Rev. Victor P. Warkulwiz, M.S.S., Ph.D.
Albertus Magnus Apostolate for Religion and Science Missionary Priests of the Blessed Sacrament Bensalem, PA

Copyright © 2013 by Missionary Priests of the Blessed Sacrament Second printing 2017 (with minor revisions) E-Book 2017
ISBN for E-Book: 978-0-9888603-4-6
Front Cover: The triangular logo represents relational cosmology. It is inspired by the doctrine of the Most Holy Trinity. The triangle has long been the symbol of the Trinity. Each vertex represents a Divine Person and the lines help express their relations. These relations are what constitute the distinction between the Persons. They cannot be distinguished by any attribute because each Divine Person possesses the one unique infinite Divine Nature completely to Himself. Whatever distinction there is must be in their relations alone. Analogously, in relational cosmology each celestial body in the universe is not distinguished from the others by their locations on an absolute spacetime grid. Rather, each one possesses the one unique universal plenum completely to itself, and it can only be distinguished from others by their relations with it on its own space-time grid. And, like in the Trinity, these relations are ultimately a mystery.

CONTENTS
Introduction, 7
1. Medieval and Enlightenment Notions about Place, Space and Time, 9
Medieval Biblical Theology and Enlightenment Ideology, 9 Enlightenment Ideology and Natural Truth, 11 Medieval Notions of Place and Void, 13 Enlightenment Notion of Space, 23 Medieval and Enlightenment Notions of Time, 35
2. Sacred Scripture and the Earth as the Center of the Cosmos, 41
The Creation of Heaven and Earth, 41 The Formation of Heaven and Earth, 46 The Earth as the Center of Rest, 53 The Notion of Absolute Rest: Historical Summary, 55 Medieval Earth-Centered Cosmology and its Decline, 56
3. Empirical Science and the Earth as the Center of the Cosmos, 59
The Logic of Absolute Motion, 59 The Physics of Local Motion, 60 Astronomical Phenomena Pertaining to the Stability of the Earth, 61 Optical Experiments Pertaining to the Stability of the Earth, 63 Comments on the Nature and Motion of Light, 67 Geometrical and Physical Centricity of Earth, 68
4. The Logic of Newtonian Physics and Relativity, 71
Newton’s Laws of Motion and Inertial Frames, 71 Electrodynamics and Einstein’s Postulates for Special Relativity, 75 Kinematical Contradictions of Special Relativity, 81 Special Relativity without Contradictions, 83 General Relativity and Absolute Space, 90

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5. The Logic of Relational Physics, 97 Relational Mechanics, 97 Absolute and Relational Spaces United, 104 Relational Optics, 108 Instantaneous Action at a Distance, Cause Propagation, and Communication, 116 Extension, Timekeeping and Mass, 134
6. Conclusion: Principles for Relational Cosmology, 141 Appendix A: Spectroscopic Binaries, 153 Appendix B: Observations Pertaining to the Relative Rotation of the
Earth and the Stars, 155 Bibliography, 157 About the Author, 165 Index, 167

INTRODUCTION
This essay is a sequel to my previous work The Doctrines of Genesis 1-11: A Compendium and Defense of Traditional Catholic Theology on Origins. I call this work an “essay” because it presents a personal point of view that is not to be interpreted as religious or scientific dogma. The principles I set forth are drawn from Sacred Scripture as interpreted in Catholic Tradition (as passed on by the Fathers, Doctors and Magisterium of the Church) and from the observations of empirical science. I appeal to empirical science rather than theoretical science because the latter is often based more on ideas than facts.
I had no intention whatsoever of formulating a new cosmology, but in doing research for The Doctrines of Genesis 1–11 a new cosmological picture began to form in my mind. I also discovered that the cosmological questions asked by the ancient and medieval scholars were more pertinent to understanding the cosmos than those asked by modern scientists. Since the seeds of my thought are in The Doctrines of Genesis 1–11, I have borrowed liberally from that work, in some cases whole passages verbatim.
I’ve always found modern books on space and time boring because the ideas are drawn from impoverished and godless doctrines of the Enlightenment. Modern science, which employs those doctrines, is out of its depth when it pontificates on the nature of space and time because the true nature of space and time lies outside the set of ideas that confines it.
I hope the reader will find this work less boring than I have found those works. I made every effort to stick to the truths of divine revelation and the empirical facts, both of which work together to give us the most complete and accurate picture of the cosmos that is possible in this life. And such a picture is not boring but awesome and beautiful because it is the work of God and is recognized as such.
I entitled this essay Universe without Space and Time because it proposes a cosmology that discards the notion that space and time
7

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are independent entities, either in Newton’s sense of absolute space and time or in Einstein’s sense of a self-subsistent spacetime manifold. Instead it treats space and time as relational quantities that are wholly dependent on matter for their meaning. What all this means should become clearer as the reader proceeds through the essay. Suffice it to say now that it develops the scholastic way of thinking about space and time, which is the fruit of meditation on the biblical account of creation.
In the subtitle I say that it is an essay on “principles.” By this I mean that I am not offering a full-blown cosmology but only starting points for a Catholic biblically-inspired cosmology. It may be that more than one consistent cosmology can emerge from these principles. The principles may not be powerful or complete enough to produce a unique cosmology.
In the first chapter I discuss medieval notions of place and time and the enlightenment notions of absolute space and time. The former are based on divine revelation; the latter are based on human ideas and ignore divine revelation. In the second and third chapters I discuss the biblical notion of the earth as the center of rest in the universe and how this is misunderstood. In the fourth chapter I discuss the logic of Newtonian and relativistic physics and their common errors that lead to a false picture of the cosmos. In the fifth chapter I discuss relational physics, which treats space and time as epiphenomena (or accidents) of matter and is consistent with traditional Catholic doctrine. Finally, in the conclusion I collect and summarize the principles that have been put forth.
Rev. Victor P. Warkulwiz, M.S.S.

CHAPTER 1
MEDIEVAL AND ENLIGHTENMENT NOTIONS ABOUT PLACE, SPACE AND TIME
Medieval Biblical Theology and Enlightenment Ideology
The High Middle Ages (12th–13th centuries) was a period of great intellectual activity in Europe. Under the sponsorship of the Church, Catholic scholars pursued studies in a wide variety of subjects that included both the spiritual and physical aspects of reality. One field of interest was natural philosophy, which was concerned with knowledge about the material world. The medieval scholar observed the world with his limited technical means of observation. He interpreted his observations in light of the biblical record, using the Fathers of the Church as trustworthy exegetical guides. Thus, his foundation for the study of creation was biblical theology. He also employed the insights of Greek authors, such as Plato and Aristotle, Arabic authors, such as Avicenna and Averroes, and Jewish authors, such as Philo and Maimonides. The beginnings of experimental science are found in the work of Robert Grosseteste and Roger Bacon. The reasoning of medieval scholars was guided by divine revelation as proclaimed in Sacred Scripture, Sacred Tradition, and the official decrees of the Church. The doctrines of the faith disciplined reason and prevented it from going wild. Because of the widespread and wholehearted acceptance of the Catholic faith by the European people of that era, the High Middle Ages has come to be called the Age of Faith.
The Enlightenment (17th–19th centuries) was a period of wholesale rejection of medieval scholasticism and traditional
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authority by many of the influential intellectuals of Europe. It was characterized by scientific, philosophical, religious and rational attitudes that departed significantly from those of the Christian Middle Ages. The major figures (literary men, scientists and philosophers) of the Enlightenment were united in their belief in the supremacy of reason. In France, their verbal and written attacks on the government and the Church impelled the physically violent attacks of the French Revolution. In England the Enlightenment took the form of a cold scientific intellectualism, which produced some advances in scientific methods but also introduced seriously flawed scientific notions such as biological transformism and uniformitarian geology. Because of the divinization of the human mind by so many of the intellectuals of the era, the Enlightenment has come to be called the Age of Reason.
Enlightenment ideology is a way of thinking that was conceived in the humanism of the Renaissance (14th–17th centuries), born in the rationalism of Enlightenment, came of age in the atheism of the Modern Era (19th–20th centuries), and has reached adulthood in the neo-paganism of the Postmodern Era (21st century). It is the attitude of mind inherited by modern scientists, including the many Christian ones who compartmentalize it in their scientific work. Enlightenment ideology is
 ideological because it places total confidence in its own set of human ideas and none in divinely or humanly established authority;
 rationalistic because it holds that human reason is the supreme arbiter of truth;
 naturalistic because it holds that the world alone can tell us everything there is to know about it;
 materialistic because it asserts that all manifestations of the supernatural (such as miracles and design in nature) are explainable by physical causes, even if those causes cannot be identified;

Medieval & Enlightenment Notions of Place, Space, Time 11
 scientistic because it places exaggerated trust in efficacy of the methods of natural science, and it condescendingly applies those methods to other fields of knowledge.
Enlightenment ideology pilots modern science. The study of nature today is guided exclusively by observation, experiment, and ideologically-governed reason. Divine revelation is excluded as a source of knowledge; human ideas replace divine revelation. Observation and experiment have been enhanced by modern technical innovations, but those are products of discovery and tinkering, not of enlightenment ideology.
Enlightenment Ideology and Natural Truth
Enlightenment ideology succeeds admirably in inventing methods for squeezing facts out of nature. But it fails miserably in the interpretation of those facts. It succeeds in the former because it meticulously conforms itself to naturally revealed truth. It fails in the latter because it resolutely refuses to be informed with divinely revealed truth.
Enlightenment ideology, by not allowing itself to be guided by divine revelation, has sent science off in the wrong direction in a number of areas. By rejecting the creation account in Genesis 1 it has given a false cosmology and a false biology. Genesis 1 clearly teaches that the universe was created and formed over a period of six days; living creatures were created instantly, each with a complete fixed living nature. That picture is direct opposition to that given to us by big bang cosmology and evolutionary biology, which tell us that the celestial creatures were formed over billions of years and that the living creatures continually transform into creatures with more and more complex natures. Unbiased observation of the natural world clearly supports the biblical picture. This is shown in many places.
The rejection of the account of the creation of man in Genesis 2 by enlightenment ideology has led to false

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anthropology, false psychology and false sociology. Genesis 2 clearly teaches that the first man and woman were specially created by God, who gave them a nature that was both material and spiritual. This gave them a nature that was different in kind and not only degree from all the other members of the animal kingdom. This difference is made manifest in the intellectual and volitional life of the human being. God made the first man and woman persons, like Himself. In their intellectual and volitional life and personhood, God made the first couple images of Himself. But modern “enlightened” anthropology denies this. It sees the human being, either wholly or in its material component, as having “evolved” from lower forms of life through an innumerable (and unobserved) succession of intermediate forms. It sees the spiritual element in man (the soul) either as an illusion or as an epiphenomenon of matter, having gradually emerged from it. This view has led to a purely animalistic human psychology, which views human personhood as little more than a succession of conscious states. This aberrant psychology manifests itself in erroneous sociological notions. For example, in totalitarian states, inspired by evolutionary biology, people have been deprived of their rights as persons and treated solely as servants to the community, like a bees in a hive. Also evolutionary biology inspired the notion that animals have rights, just like human beings. Some extreme activists even see animals as having a priority in rights over humans simply because they were here first. These and other bizarre notions are the spawn of evolutionary biology.
The rejection of the biblically-attested fact that the world was completely destroyed by a universal flood as related in Genesis 6-8 has given rise to a false geology, namely uniformitarian geology. Uniformitarian geology insists that the features on the earth were produced by slow processes acting over millions of years and not by a worldwide catastrophe like the great flood. The geological data, however, provide strong evidence in favor of a worldwide catastrophe.
By rejecting the primal history of the human species as related in Genesis 9-11, enlightenment ideology has misled archaeology,

Medieval & Enlightenment Notions of Place, Space, Time 13
preventing it from giving proper interpretations to its data. And by rejecting the account of the origin of languages given in Genesis 11, enlightenment ideology has further misguided cultural anthropology.
By presuming that the earth moves absolutely in space around the sun, in conflict with Sacred Scripture, astronomers pretend to measure distances to celestial objects. Since they cannot demonstrate that the earth moves absolutely, their results are inconclusive. Yet they present their distances as if they were unquestionable facts.
Finally, by not drawing the proper inferences from the creation account in Genesis 1, modern physics has given us false notions about the nature of space (or void) and time. Medieval thinkers, like St. Thomas Aquinas, guided by the scriptural record, formed correct notions about space and time but did not develop them. The present work is a beginning of such a development in the light of current knowledge.
Medieval Notions of Place and Void
Medieval scholars did not employ the concept of free space that we have inherited from the Enlightenment, even though it had been conceived in antiquity by the Greek atomists. So to understand how they thought, we must do our best to set aside our concept of free space. This is very difficult indeed because it is so deeply ingrained in our minds and imagination. We can hardly believe that there can be any other way to conceive the universe than as being imbedded in an independently-existing threedimensional void.
To condition yourself for a change in perception do the following thought experiment: Image yourself being present on the first day of Creation. The material universe consists of the earth alone, which is completely covered with water. God equips you with scuba gear and a few devices and places you beneath the surface of the water. This is where you come to consciousness. You start to test your environment by letting go of a few hollow

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rubber balls that God gave you. You find that they float up to a certain point and go no further. Thus you deduce that where they stopped is the boundary of the universe in which you were placed. At this point you can’t imagine anything being beyond there because nothing you have experienced so far suggests that there is. You name the region where the balls stopped the “surface” of the water. It is the boundary that defines the “place” where you live.
The concept of place held much significance for medieval scholars. Their conceptions of place were built on that of Aristotle. Aristotle struggles with the notion of place in Book IV of his Physics. He concludes by defining it as follows: Place is “the innermost motionless boundary of what contains” [1, p. 278]. So in our thought experiment so far, the complete surface of the water contains the place of the earth; but that surface itself does not have a place because nothing contains it.
Aristotle goes on to say that only movable bodies have a place. The term “movable” has no meaning on the first day of Creation because then only the earth existed. At least two bodies must exist for the word motion to have meaning. So the question of whether or not the earth moves will be moot until the fourth day of Creation, when the heavenly bodies are created. Sacred Scripture tells us that God made the earth the standard of rest in the universe, but this does not mean that the earth is incapable of being moved. We can feel free to apply Aristotle’s definition of place to it, even on Day One.
For a summary of Aristotle’s views on space and place see [2]. Pierre Duhem gives a comprehensive survey of medieval notions about place in chapters 4–6 of [3]. Duhem points out that there was ample development of the theory of place at the University of Paris in the middle of the thirteenth century. Especially interesting are the views of St. Thomas Aquinas. In a discussion of the motions of the heavens around the earth, in his Expositio super libros De Caelo et Mundo, he makes the observation that the center of rotation must exist in a corporeal body. St. Thomas said:

Medieval & Enlightenment Notions of Place, Space, Time 15
There has to be something remaining immobile at the center of a body moving circularly. It is evident that any circular movement occurs around a fixed center. And it needs to be that this center is located in a fixed body, for what we call the center is not something subsisting in itself. It is an accident belonging to something corporeal; this center can only be the center of a body. [3, p. 153]
Aquinas goes on to say that the rotations of the heavens would be a meaningless notion if the earth did not exist:
This fixed body must be part of the world … but it cannot be part of the mobile orb, meaning the celestial body.… That which is at the center is eternally immobile, as heaven moves eternally.… And that which is naturally immobile at the center is the earth.… Therefore, if heaven revolves eternally, the earth has to exist. [3, p. 153]
Aquinas sees the notion of place as intimately connected with the motion of corporeal bodies. In his In libros Physicorum Aristotelis he states:
Place would not be investigated if it were not for movement; movement calls attention to place because bodies succeed each other in one place. Hence although a body does not of necessity have a place, nevertheless, a body moved with respect to place does have a place of necessity. Therefore, it is necessary to assign a place to a body moved in place insofar as one considers in that movement a succession of various bodies in the same place. Thus in things moved in a straight line, it is clear that two bodies succeed each other in place with respect to the whole. For the whole of one body leaves the whole place and into that whole place another body enters. Hence it is necessary that a body moved in a straight line is in place with respect to its whole self. [3, p. 154]

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Aquinas accepted the geocentric cosmology of Aristotle and Ptolemy, as did apparently all of his contemporaries. Thus the movements that he was primarily interested in were the circular movements of the heavens. The heavens were thought to move around the earth like spherical shells. The ultimate or final celestial sphere was thought by some to have a place; others reasoned it had no place because it did not and could not exhibit local movement but only circular movement. Aquinas, further on in In libros Physicorum Aristotelis, gives his view:
Therefore in circular movement attention is directed to the succession in the same place, not of whole bodies, but of parts of the same body. Hence for a body moved in a circle, a place with respect to the whole is not due of necessity, but only in respect of the parts.… Moreover it is much more suitable to say that the ultimate sphere is in place because of its own intrinsic parts than because of the center which is altogether outside of its substance; and this is more consonant with the teaching of Aristotle. [3, p. 154]
A paradox that vexed the medieval scholars was the notion that, according to Aristotle, place was at once both movable and immovable. It seemed moveable because it was somehow attached to the body in motion. It seemed immovable because another body moved into it after a first body left it. Aquinas resolved the paradox by considering that place has two senses, one referring to the body itself and the other referring to ambient bodies. The first means that for a place to exist there must be a body to be in place; that is, there is no such thing as absolute place, place without a physical body. The second means that a body has a relationship to other bodies that is called place. In De natura loci, which is attributed to St. Thomas, the author explains that the “set of celestial bodies” is the reference base for identifying an immobile place:

Medieval & Enlightenment Notions of Place, Space, Time 17
That is the way in which we ought to understand that the extreme parts of natural bodies form the place of other bodies; they form it in virtue of the relative position, the order, and location that they present with respect to the set of celestial bodies. The latter is the natural container, the principle of conservation and all location. [3, p. 156]
Thus if two bodies, at different times, possessed the same relationships with the “set of celestial bodies,” they can be said to have been in the same place. In De natura loci St. Thomas elaborates a bit more on the place of the ultimate sphere. He says that the ultimate sphere is in a place accidentally because its parts are in place, albeit potentially and not actually. A thing is in a place accidentally by being attached somehow to something that is in a place.
As Thomistic doctrine was developed by later medieval masters, it became clear that to be able to identify an immobile place, the reference base itself must be immobile. Thus the universe must be bounded by an immobile spherical surface. According to Duhem [3, pp. 169, 178], the “natural conclusion of the Peripatetic theory of place” is “the hypothesis of a necessarily immobile empyrean sphere.” Theologians had no difficulty with that concept. Some of them even thought that Sacred Scripture affirmed the existence of such a sphere. St. Bonaventure in commentary on Peter Lombard’s Sentences spoke of an immobile orb “which contains and is not contained” [3, 174]. This notion was taken up later by Copernicus. But he did not take the empyrean sphere as the immobile reference for movements of the celestial bodies. Rather he took the sphere of the fixed stars.
In his Writings on the “Sentences” of Peter Lombard Aquinas sets forth his view that what is called place or space is defined by the objects in it and was created with the world. He makes the further observation that what we call void is not a simple negation but a privation and is neither self-existent nor created; more will be said later about the notion of void:

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[I]t ought to be said that before the creation of the world there was no void, as there is none after, because the void is not a simple negation but a privation. Hence, in order that there be a void, as those who suppose that there is one would say, there must be a place or real dimensions, neither of which did exist before the world. [4, p. 97]
In his Summa Theologica Aquinas reaffirms his view that place or space was created in the beginning:
Whereas we hold that there was no place or space before the world was. [5, Part I, Q. 46, A. 1, Reply Obj. 4]
*
Let us retsurn now to our thought experiment. Imagine that God has also provided you with a rod. You go close to the surface of your world and poke at it with the end of your rod. To your amazement you find that the rod shortens. You then pull the rod back toward you and find that it has returned to its full length. Your first deduction might be that the rod shrinks as it makes contact with the surface. You then find that God has provided you with another rod, one that is not uniformly thick. It tapers down to a point. You now probe at the surface of the water with the point of that rod and find that the rod doesn’t shrink. Rather, the pointed end simply disappears. You then pull that rod back toward you and find that the pointed end reappears. You are amazed.
*
In 1277 a council of the doctors of the Sorbonne, which took place under the presidency of the bishop of Paris, Etienne Tempier, condemned the notion that God is unable to move the

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whole universe in rectilinear motion because the universe would then leave behind a void. It was the denial of God’s power that was condemned, not the reason given for denying that power. Actually, Aristotelians and Thomists would not have given the reason stated by the council. They would say that motion of the whole universe is a meaningless one because outside the universe there is no place or void in which to move and no reference basis against which motion can be identified. Others would say that God could create a void in which the universe could move. The end result of the condemnation, according to Duhem, was that “the theologians of the Sorbonne traced out a path to the system of Copernicus” [3, 197].
This leads us to the question of the nature of void. Is it something real? If so, was it created or does it coexist alongside God? In Book IV of his Physics, Aristotle defines void as “place bereft of body” [1, p. 270]. He argued that there is no void outside a body, no void occupied by a body, and no void in a body; that is, there is no void at all [1, pp. 280-289]. When a body moves it takes occupancy of a place previously occupied by another body. St. Thomas used the conceptual framework of Aristotle but applied his own insights. Apparently he believed in the reality of void because we heard above from him that the void is not a simple negation but a privation. A privation is the absence of something from where it naturally should or could be. For example, the lack of the power of sight is a privation in a human person or a dog because sight belongs to the nature of those creatures. But the lack of power of sight in a tree is a negation because the power of sight does not belong to the nature of a tree. So it would seem then that, according to Aquinas, a void is the absence of a corporeal body from where one could be; that is, it is an empty place. Void is not a negation; that is, it is not simply nothingness. Thus Thomas ties in the nature of void with matter.
In his rejection of the possibility of a void Aristotle, according to some interpreters, argued that if there were motion in a void, a corporeal body would move instantaneously because there would be nothing to resist its motion. (Only a plenum would

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be able to offer resistance so that it would take a period of time for a body to travel from one place to another.) And since instantaneous motion was considered impossible, it followed that a void is also impossible.
Aquinas, contrary to that interpretation of Aristotle, defended the possibility of natural motion in a void (see [1, pp. 378–380] and [6, pp. 134–142]). He held that, in addition to the resistance of a material medium in which a body moves, there is also a inclination in a body to resist motion contrary to its natural motion (violent motion) and an internal inertia of bodies that resisted being moved from one natural place to another. (Medieval scholars followed Aristotle in believing that the elements of fire, air, earth and water, had a natural inclination to move towards places in the universe reserved for those elements. Such motion is called natural motion. The natural motion of the fifth element, quintessence, of which the celestial bodies were supposed to be composed, was uniform circular motion about the earth.) So even in the absence of a material medium it would take a period of time for a body to move from one place to another because a body would provide its own resistance. Natural motion had a “natural velocity.” More than three centuries later, Galileo, in opposition to the prevailing opinion, would follow Aquinas in upholding the possibility of motion in a void.
Pierre Duhem credits Aquinas with being the first to introduce the notion of mass into physics [3, pp. 379-380]. This comes about in Aquinas’ discussions on falling bodies. Aquinas insisted that nature is not the efficient cause in the free fall of corporeal bodies; that is, the nature of a body is not the cause of its falling in the way that the nature of an animal is the cause of its movements. Rather, nature is an “active principle” in such free fall; that is, it is the nature of a corporeal body that makes it possible for it to fall. What is it in the nature of a corporeal body that makes it possible to fall? Aquinas answers that question in a lecture in his commentary on Aristotle’s Physics:
When the form, which the generator imparts, is removed from heavy and light things, a body with

Medieval & Enlightenment Notions of Place, Space, Time 21
magnitude remains only in the understanding. But a body has resistance to a mover because it has magnitude and exists in an opposite site {opposite to where the movement would lead it}. No other resistance of celestial bodies to their movers can be understood. [3, p. 378]
Thus Aquinas abstracts from a material body the notion of “magnitude,” what we today call “mass.” Duhem sees this as a revolutionary accomplishment that Aquinas managed by distinguishing in thought, “on the one hand, a form, the motor force or gravity, and, on the other hand, prime matter given determined dimensions, not prime matter bare and simple, but a quantified body occupying a certain location and resisting the force attempting to bring it elsewhere” [3, p. 379]. Duhem extols the magnitude of this achievement of St. Thomas. Referring to the passage above he states:
Thomas’s assertion, which we have just quoted, is extremely brief: let us not allow its brevity to make us misunderstand its importance. For the first time we have seen human reason distinguish two elements in a heavy body: the motive force, that is, in modern terms, the weight; and the moved thing, the corpus quantum, or as we say today, the mass. For the first time we have seen the notion of mass being introduced in mechanics, and being introduced as equivalent to what remains in a body when one has suppressed all forms in order to leave only the prime matter quantified by its determined dimensions. St. Thomas Aquinas’s analysis, completing Ibn Bajja’s, came to distinguish three notions in a falling body: the weight, the mass, and the resistance of the medium, about which physics will reason during the modern era. [3, p. 379]
In the same lecture cited above, Aquinas magically arrives at the notion of accelerated fall:

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The Commentator replies that the natural movement of light and heavy things requires this impediment from the medium so that there might be a resistance of the mobile body to the mover, at least from the medium. But it is better to say that all natural movement begins from a nonnatural place and tends to a natural place. Hence, until it reaches the natural place, it is not unsuitable if something unnatural to it is joined to it. For it gradually recedes from what is against its nature, and tends to what agrees with its nature. And because of this natural movement it is accelerated at the end. [3, p. 380]
The profundity of St. Thomas’ cosmological insights will become more apparent as we proceed through this essay.
*
Let us return once again to our thought experiment. You try to explain your observations with the rods. Your experience with the tapered rod made it clear that the rods did not shrink. Either the ends of the rods were annihilated and recreated or there was something beyond the surface of the water that “absorbed” them. You dismiss the first alternative because you know that God gives his creatures persistence; He holds them in existence; He doesn’t toss them in and out of existence. Then something must have “absorbed” the ends of the rods without destroying them. You call that something “void.” You do not know what it is or if it is material; but you now know that it is part of your world. The void provided a place for the ends of the rods.
You next test to see if the void is made of matter. You do this by attaching one of the rubber balls to the end of one of the rods. You then push the rubber ball into the void and move it laterally with the rod to see whether the void offers any continual resistance to lateral motion of the ball, which you can sense through the rod. You find out that it doesn’t, so you are convinced that the void is not material.

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You then reason that a rod is a material object with dimensionality. When one protruded through the surface of the water, it lent its dimensionality to the void it pierced. Before that the void was dimensionless nothingness, that is, it was no-thing; it was neither substance nor accident. Then you reason further. If the rod lent its three-dimensionality to the void then the whole earth must lend its three-dimensionality to the void, presuming that the earth is finite in size. That is a reasonable presumption because if the earth was infinite in size there would be no surface to its water. You then come to the final conclusion that the void is somehow part of the earth. You come to see that the void is a shadowlike extension of the earth’s existence because it provides other places in which the things of the earth can exist.
Enlightenment Notion of Space
The greatest change in cosmological thinking during the Enlightenment was the replacement of the concepts of place and void by the concept of immobile absolute empty space.
According to Max Jammer, the first major contribution to the concept of such a space was made in the sixth century A.D. by the philosopher Philoponus, also called John the Grammarian. Philoponus stated:
Space is not the limiting surface of the surrounding body … it is a certain interval, measurable in three dimensions, incorporeal in its very nature and different from the body contained in it; it is pure dimensionality void of all corporeality; indeed, as far as matter is concerned, space and void are identical. [2, p. 56]
At first sight John seems to be simply formulating the belief of the Greek atomists, who preceded him, in contrast to the belief of Aristotle. The first century B.C. Greco-Roman poet Tius Lucretius Carus enshrined the philosophy of the Greek atomists

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in Latin verse in his poem On the Nature of Things [7]. In that poem he emphatically says that nothing exists but atoms and void.
John the Grammarian’s position, however, appears to differ somewhat from that of the Greek atomists. Jammer explains Philoponus’ identification of space and void:
However this identification of space and void does not assume the existence of a void as such “in actu.” The void, although a logical necessity, is always coexistent with matter. Void and body are two inseparable correlates, each of them requiring the existence of the other. As soon as one body leaves a certain part of space, another body “replaces” the first. A certain region of space can receive different bodies in succession without taking part in the motion of the occupying matter. Philoponus’ phoronomy is completely analogous, as Duhem points out, to Aristotle’s doctrine of substance and form, where one form is succeeded by another continuously, so that substance is never void of form. Just as matter successively receives one form after another, so a section of space may be occupied by one body after another, space itself remaining immobile. [2, p. 56]
Also, John’s space does not have a favored direction, as does that of the Greek atomists. Lucretius speaks of atoms continually falling downward in infinite space. For Philoponus “down” is the direction toward the earth, which material bodies have an inherent tendency to reach; “down” is not a property of space itself.
It wasn’t until the seventeenth century, more than a millennium after John the Grammarian proposed his notion of absolute space, that Isaac Newton gave the concept of absolute space a long-enduring place of honor in physics. Newton presented his conceptual scheme of space, time, matter and motion in his Philosophiae naturalis principia mathematica (1687), known simply as the Principia. In the beginning of the Principia Newton made clear his meaning of “absolute space” by comparing it with what he called “relative space”:

Medieval & Enlightenment Notions of Place, Space, Time 25
Absolute space in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute space; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect to the earth. Absolute and relative spaces are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed. [2, pp. 99–100]
A little further on in the Principia Newton substitutes “sensible measures” for the parts of absolute space because absolute space itself is insensible and its parts indistinguishable:
But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. For from the positions and distances of things from any body as considered immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies transferred from some of those places to others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs. [2, p. 100]
Newton professed to eschew metaphysical reasoning in natural science. He said: “We are to admit no more causes of natural things than such are both true and sufficient to explain

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their appearances” [2, p. 101]. But he seeks to justify his introduction of absolute space with the famous statement: “But in philosophical disquisitions, we ought to abstract from our senses” [2, p. 101]. His notion of absolute space is purely metaphysical because absolute space is perceived only by the mind and not by the senses. The only things that we observe are relative places and motions measured against an arbitrary standard of rest. We may rightly ask whether absolute space is really a necessary abstraction or whether it is an invention, a “free creation of the human mind,” to use the words of Albert Einstein. Absolute space is not necessary for the validity of Newton’s three laws of motion and his law of gravity. Although he formulated them with absolute space in mind, they have only been experimentally verified in relative spaces, with the earth or some other celestial body as the standard of rest. Newton recognized that his laws were valid in a whole class of relative spaces that we today call “inertial spaces.” In a corollary of the Principia he says: “The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards in a right line without any circular motion” [2, p. 102]. The notions “rest,” “right line,” and “circular motion” can have an empirical meaning only with respect to corporeal bodies. In another corollary in the Principia, Newton acknowledges the necessity for an arbitrary corporeal standard of rest: “That the centre of this system of the world is immovable. This is acknowledged by all, while some contend that the earth, others that the sun, is fixed in the centre” [2, 203]. For Newton the center of the world is the center of mass of the bodies of the solar system. The center of mass of a system of corporeal bodies can, in principle, be located inside one of the bodies or inside none of them; its location depends on their relative masses, sizes, and distances. Still, a center of mass is a standard of rest that ultimately depends on the existence of corporeal bodies. To say whether the center of mass of the solar system moves, we would have to observe whether it moves with respect to the stars. The notion of the center of mass of the whole universe moving through absolute space is empirically meaningless.

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In modern physics, coordinate systems freestanding in absolute space are just as metaphysical as absolute space itself. Such coordinate systems and the absolute space (or space-time) they structure are fictional, but somehow they have proved quite useful. However, it will become clearer as we proceed in this book that too heavy a reliance on them has led physics up a blind alley.
Although Newton recognized that absolute space did not manifest itself kinematically, he believed that it did manifest itself dynamically. He believed that inertial effects, like the resistance of material bodies to a change in their speed and the concave surface of the water in a rotating bucket of water are caused by motion relative to absolute space. Thus uniform linear motion and accelerated motion have different manifestations in absolute space—the one relative, the other absolute. But Newton’s notion that the center of the world is at rest allowed uniform linear motion to be referred to that point of rest, so that it too could be “absolutized.” But uniform linear motion is then absolute by definition while accelerated motion is absolute by nature. To distinguish absolute motion from relative motion, Newton introduces the concept of “force” which is a “cause” that generates “true” motion:
The causes by which true and relative motions are distinguished one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist…. [2, p. 105]
Newton proceeds to admit the difficulty of distinguishing “true” motions of bodies from “apparent” motions, but he does not admit the impossibility of doing so:

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It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. [2, p. 105]
Jammer says that Newton’s forces, as presented above, are “metaphysical entities conceived anthropomorphically” and not functional entities [2, p. 106]. He says that Newton’s arguments “from causes” are based on traditional metaphysics. This is so even though Newton had strongly objected to the use of metaphysical arguments in natural science. Jammer says that there is a vicious circle in Newton’s reasoning concerning absolute motion and absolute force. He says that this can be seen by thinking of a world of moving masses in which no living organism [self-mover] existed. He says that “in such a world an absolute force can be determined, according to Newton, solely by the absolute motion of the body on which this force is exerted” [2, p. 106]. That is, the fact that there is absolute motion means that there must be a force which means there must be absolute motion, which means there must be a force, and so on—thus the circularity.
Newton’s notion of absolute space was criticized by three notable contemporaries: G. W. Leibniz and G. Berkeley (summaries of their criticisms are given in [8, pp. 97–106]) and C. Huygens (a summary of his criticism is given in [2, pp. 119–126]), none of whom accepted his dynamical arguments. Leibniz argued that space and time are not independent entities but depend on matter and material phenomena to give them meaning. Berkeley argued that since absolute space in no way affects the senses, it is useless for distinguishing motions. He argued that all motion,

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including rotational motion, requires a corporeal frame of reference:
If we suppose the other bodies were annihilated and, for example, a globe were to exist alone, no motion could be conceived in it; so necessary is it that another body should be given by whose situation the motion should be understood to be determined. The truth of this opinion will be very clearly seen if we shall have carried out thoroughly the supposed annihilation of all bodies, our own and that of others, except that solitary globe.
Then let two globes be conceived to exist and nothing corporeal besides them. Let forces then be conceived to be applied in some way; whatever we may understand by the application of forces, a circular motion of the two globes round a common centre cannot be conceived by the imagination. Then let us suppose the sky of fixed stars is created; suddenly from the conception of the approach of the globes to different parts of that sky the motion will be conceived. [2, p. 109]
However, Berkley’s argument was kinematical and does not adequately explain dynamic effects, such as the concave surface on a rotating pail of water. As we shall see later, the nineteen-century physicist, Ernst Mach, will give an explanation for that that avoids the notion of absolute space.
Leibniz, succinctly gives his conception of space, which is opposed to that of Newton, in a letter to S. Clarke, a disciple of Newton:
As for my opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistences, as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together; without enquiring

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into their manner of existing. And when many things are seen together, one perceives that order of things among themselves. [8, pp. 97–98]
Leibniz further compares Newton’s attributing a real identity to absolute space to attributing a real identity to a genealogical tree. In a genealogical tree the individuals and their generational relationships are real things, but the tree they inhabit is only a mental construct. Likewise, corporeal bodies and their spatial and temporal relationships are real things, but the absolute space they inhabit is only a mental construct.
The arguments of Leibniz, like those of Berkeley, were kinematical. Leibniz, despite much effort, was unable to explain dynamic effects by relativity of motion. Jammer, however, credits him with coming close to Mach’s solution by attempting to reduce gravity to centrifugal force. Mach also connected gravity to centrifugal force but in the opposite way, by reducing centrifugal force to an effect of gravity.
Jammer credits the third contemporary critic of Newton’s absolute space, Christian Huygens, as the first physicist who defended both kinematic and dynamic relativity. His defense of dynamic relativity, however, was faulty. He explained the effects of centrifugal forces on a rotating disk as merely an indication of the relative motion of different parts of the disk. If one took as a reference system one rotating like the disk, then the motions of the parts of the disk would disappear. However, he neglected to observe that the pressure caused by the centrifugal forces and tending to pull the disk apart would still be present and would have to be explained.
The most outstanding critic of Newton’s concept of absolute space was the nineteenth-century physicist Ernst Mach. He was the first person to credibly defend dynamic relativity. Mach said that absolute space and absolute motion are “pure things of thought, pure mental constructs, that cannot be produced in experience” [10, p. 280]. Since there is no absolute motion, the motion of bodies is determined only in reference to other bodies. Thus, since there is only one system of the world, “the motions of

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the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical” [10, p. 283–284]. Mach held that inertial effects were not the result of the action of absolute space on a body; rather they were the combined effect of all the other material bodies in the universe on the body. Thus, for example, the earth bulges at the equator not because absolute space “pulls” on it; rather, the mass of cosmic bodies rotating around it “pulls” on it. And it does not matter if one thinks of the cosmic bodies as rotating or the earth as rotating. Both views are equivalent. The inertial effects are produced by the relative rotation of the earth and the heavens. Mach wrote: “[I]t does not matter if we think of the earth as turning on its axis, or at rest while the fixed stars revolve around it…. The law of inertia must be so conceived that exactly the same thing results from the second supposition as from the first” [11, p. 10]. This idea, which has come to be known as Mach’s principle, implies that if there were no cosmic bodies there would be no inertial effects on the earth, for example, the earth would not bulge at the equator. It is not possible to test this directly because one cannot simply remove all the heavenly bodies. But, in principle, it can be confirmed indirectly by looking for inertial effects caused by the relative motions of terrestrial bodies. But such effects would be very small and very hard to measure. So far Mach’s principle has not been verified experimentally. Mach stated his principle in general terms, but he did not implement it. He said nothing about the nature of the interaction of material bodies with the rest of the universe. His principle is a simple concept, but its implementation required the rethinking of some physical concepts.
Theological considerations also were important to the seventeenth-century contestants on the issue of absolute space. Berkeley gave a cogent theological argument against absolute space. He said that space must be considered as relative “or else there is something beside God which is eternal, uncreated, infinite, indivisible, unmutable” [2, p. 112]. But Newton did not conceive

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space as coexisting with God. Rather he identified absolute space as an attribute of God. In the Principia he makes the statement:
He [God] is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present; and by existing always and everywhere, he constitutes duration and space. [2, p. 113]
Newton seems to have thought that God is spatially extended because He is able to move all the bodies in the universe. He is more able to move the bodies “within his boundless uniform Sensorium, and thereby to form and reform the Parts of the Universe, than we by our Will to move the Parts of our own Bodies” [2, p. 113]. Leibniz argued that Newton’s identification of the omnipresence of absolute space with the omnipresence of God implied that God is divisible because absolute space is divisible, a contention that was contested by Clarke. Leibniz interpreted Newton as conceiving space as an organ that God uses to perceive things. Therefore, continues Leibniz, it would follow that things do not depend altogether on God and were not produced by Him. But this argument rests on what may be a too literal interpretation of the word “sensorium.” Newton seems to have used the word in an analogous sense.
Leibniz ridicules the notion that absolute space devoid of material bodies is still not really empty. This notion was a refuge of Newton supporters who wanted to retain the concept of place in space void of matter. He asks what it is filled with. Is it filled with extended spirits or other immaterial substances capable of extension, contraction and interpenetrability? Leibniz takes issue with their fantastic theology:
Some have fancied, that Man in the State of Innocency, had also the Gift of Penetration; and that he became Solid, Opaque, and Impenetrable by his Fall. Is that not overthrowing our Notions of Things, to make God have Parts, to make Spirits have Extension? [2, p. 118]

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Critics of Newton also pointed out that while absolute space acts on a material body, the body does not react on absolute space. This would violate a general physical principle, which is embodied in Newton’s own third law, that every physical action is accompanied by a reaction that maintains balance in the universe.
Newton’s conception of absolute space involved the rejection of the conceptual scheme of substance and accident. Traditional Catholic philosophy rejects the notion of absolute space because it is incompatible with the concept of quantity as understood by the scholastic masters. The prominent sixteenth-century scholastic theologian Francisco Suarez upheld the total dependence of space on matter:
[Space is] a conceptual entity, not, however, formed at will like chimeras, but extracted from bodies, which by their extension are capable of constituting real spaces (Metaphysical Disputations 51).
Quantity is the principle of individuation. Among material substances there are many species and many individuals of the same species. The individuals are not individuated by nature (as are spiritual creatures) but by matter itself, prime matter determined by the accident of quantity. Matter so individuated is called signate matter or matter marked by quantity. Scholastic philosophy holds that absolute space is only a conceptual entity that is abstracted from signate matter. Extension is an accident of physical bodies that the mind perceives and from which the mind constructs absolute space. Extension is a necessary concomitant to quantity, and every quantity is the quantity of something. But absolute space is pure extension, which means it is quantity without a subject. In other words, absolute space is quantified nothingness, which is a contradiction in terms. It is a contradiction in reality; but it is not, however, a contradiction in the mind because it is a mental abstraction. It is an accident without a subject. It is like the shape of a statue without any material holding that shape; such can exist only in the mind and

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not in reality. Further, absolute space is not a privation, as St. Thomas Aquinas identified void, because privation implies means the absence of something where it can be. But absolute space is conceived without reference to anything but itself.
Enlightenment thinkers conceived of space as an attribute of God or as coexistent with God. But they do not seem to have considered the idea of space as a creation of God. If they did, their thinking would have led them to a more realistic vision of the universe. We saw above that St. Thomas Aquinas clearly taught that space (void) was created in the beginning of the world along with matter. When God created the earth as the first material body, He created the three-dimensional space it occupies. Space, like time, is an epiphenomenon of material creation. With the creation of the celestial bodies God created void, which separates and helps distinguish the heavenly bodies from each other and the earth. Void has no meaning except in reference to the material objects it surrounds. Matter lends its dimensionality to void. Job 26:7 confirms that the three-dimensionality of void is extrapolated from three-dimensional matter:
He stretches out the north over the void, and hangs the earth upon nothing.
Before creation there was no infinite three-dimensional absolute space into which God injected matter. The mental image of an empty three-dimensional absolute space existing before creation is abstracted by our minds from a world filled with matter. Before creation there was nothing but God. And “nothing” does not mean “three-dimensional emptiness.” It means “no thing.”
Newton’s concept of absolute space provided an amazingly successful basis for the explanation of the observed inertial behavior of material bodies and thus led to the development of classical mechanics despite the problems concerning its hypostatization. The successes of classical mechanics overshadowed objections against absolute space until the development of modern physics in the twentieth century, when

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they once again came to the fore. Among scientists who developed classical mechanics from Newton’s laws, like, for example, Lagrange, Laplace and Poisson, there was little interest in the reality of absolute space. They just accepted it as a working hypothesis. The great formulator of classical electromagnetic theory, James Clerk Maxwell, succinctly presented the paradox that the notion of absolute space introduced into physics. He said: “All our knowledge of space and time is essentially relative” [9, p. 12]. But he adds the following footnote to that statement: “The position seems to be that our knowledge is relative, but needs definite space and time as a reference for its coherent expression.” Absolute space is the phantasm of disembodied quantity that haunts classical mechanics.
Medieval and Enlightenment Notions of Time
The history of opinions about time is long and tortuous. In his cosmological dialogue Timaeus Plato calls time a “moving image of eternity” [12, p. 1167]. In his Physics Aristotle said that time is the measure of movement and movement is the measure of time; movement and time define each other [1, p. 294]. The Greek atomists said that time has no separate existence; things in motion cause time [7, p. 33]. Here we are only concerned with differences in the conception of time between the scholastic doctors and enlightenment thinkers.
The scholastic doctors, following Scripture under the guidance of the Church, rightly believed that time was created by God in the beginning. The first Christian writer to write extensively on time and whose views on time carried great weight with the scholastics was St. Augustine. Augustine explores the subject of time in Book XI of his Confessions. He declares that it is a difficult subject: “What then is time? If no one asks me, I know; if I want to explain it to someone who asks me, I do not know. I can state with confidence, however, that this much I do know: if nothing passed away there would be no past time; if there was nothing on its way there would be no future time; and if nothing

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existed there would be no present time” [13, pp. 295–296]. Thus he denies the self-existence of time. In Chapter 5 of Book XI of the City of God Augustine affirmed his belief that before the creation of the world there was no time: “It is idle for men to imagine previous ages of God’s inactivity, since there is no time before the world began” [14, p. 435]. St. Augustine refuted the idea that time existed before the creation of the world because it makes God live in time and the creation of the world look like a thought that suddenly occurred to Him, thus making Him changeable and not eternal. In Chapter 6 of Book XI of the City of God he affirms his belief that “without motion and change there is no time” [14, p. 435]. He goes on to reaffirm his belief in the creation of time: “The world was not created in time but with time” [14, p. 436]. St. Thomas Aquinas concurs with Augustine saying: “Things are said to be created in the beginning of time, not as if the beginning of time were a measure of creation, but because together with time heaven and earth were created” [5, Part I, Q. 46, A.3, Reply Obj. 1]. Lateran Council IV and Vatican Council I affirmed the creation of time. They both decreed that God “from the beginning of time created each creature from nothing…” [15, nos. 428, 1783].
Catholic philosophy, following Aristotle, Augustine and Aquinas, associates time with movement. The Catholic Encyclopedia (1914) article on time states: “In fact, say the Scholastics, we never perceive time apart from movement, and all our measures of our temporal duration are borrowed from local movement, particularly the apparent movement of the heavens” [16, article entitled “Time”].
The thinking of enlightenment philosophers on time, like their thinking on space, deviated from that of the scholastic masters. Newton, in the same scholium in his Principia that he presents his notions of absolute and relative space, also presents his notions of absolute and relative time. He describes them as follows:
Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to

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anything external, and by another name is called ‘duration’; relative, apparent, and common time is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year. [17, p. 17]
The notion that absolute time “flows” is a very peculiar one indeed. If it is intended as a metaphor, it is a very misleading one. The flow-of-time concept is circular because the concept flow already includes time, measured time. Does time flow at x seconds per second? Or perhaps there is a hierarchy of time, that is, time flows at x seconds per supersecond. But do superseconds also flow, perhaps at y superseconds per second? But now we are in a vicious circle. Then maybe superseconds flow at y superseconds per supersupersecond. We are now in an infinite regress. So where do we go with the notion of the flow of absolute time?
Newton sees absolute time as the standard for calibrating relative time, but does not show how such calibration can be done.
Absolute time, in astronomy, is distinguished from relative by the equation or correction of the apparent time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time. It may be that there is no such thing as equable motion whereby time may be accurately measured. All motions may be accelerated and retarded, but the flowing of actual time is not liable to any change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all; and therefore this duration ought to be distinguished from what are only sensible measures thereof and from which we deduce it, by means of the astronomical equation. The necessity of this equation, for determining the times of a

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phenomenon, is evinced as well from the experiments on the pendulum clock as by eclipses of the satellites of Jupiter. [17, p. 19]
Newton seems to have said that the very fact of something existing gives rise to absolute time, even if no change takes place in the existing thing. Its “perseverance” in existence causes absolute time. But how is time in that way measured, or even defined? God perseveres in existence, but He is unchanging and does not live in time but transcends time. The Scholastics understood that, but apparently Newton did not.
The only way to set up a measurable standard of time is to use a periodic physical phenomenon. That physical phenomenon can be compared with another periodic physical phenomenon to see if their periodicities synchronize. If they do, then the standard is reinforced. If they don’t, then one of the phenomena is accepted as the standard and the other is “corrected” to agree with it. In the passage above Newton said that “it may be that there is no such thing as equable motion whereby time may be accurately measured.” He would have been more on target if he removed the words “it may be that.” There is no such thing as “equable motion” because there is no way to physically define it. It cannot be physically defined because there is no way to make a comparison with something as abstract as absolute time. Absolute time, like absolute space, is disembodied quantity. It exists only in the mind but not in reality.
Newton proposes that the “astronomical equation,” which is presumably his law of gravitational attraction, is a means for determining absolute time. Mathematical equations simply describe physical phenomena. The better an equation describes an observed phenomenon, the more useful it is. But an equation does not hypostatize the quantities it employs. So the fact that the notion of absolute time is used in an equation does not mean that such exists. The notion itself is just a convenient mental construct that somehow gives answers in agreement with observations. Physical science employs a number of such constructs, for example, points and imaginary numbers.

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Enlightenment opinions about time varied from the extreme objective view of Newton to the extreme subjective view of Immanuel Kant, who saw time as solely a creation of the human mind. Such opinions often departed widely from the commonsensical viewpoint of medieval Christendom. The majority of the medieval schoolmen conceived time as partly objective and partly subjective. Objectively, motion is something real; it is an object of experience. Subjectively, the mind divides motion into before and after and perceives time as the measure of movement according to before and after [18]. Time can be thought of as that which, to a finite mind, makes present various potentialities in a subject. Leibniz’ view of time was perhaps the closest to the medieval view since he held time as an order of successions.
God gave us natural standards of rest and time. He made the earth the standard of rest. For time He gave us natural rhythms rather than a single defined standard. The most basic is the daily rhythm determined by the stars, which gives us day and night. Following that He gave us the annual rhythm determined by the sun, which gives us the cycle of seasons. Finally the monthly rhythm determined by the moon, which gives us the tides and graduates the seasons.

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CHAPTER 2
SACRED SCRIPTURE AND THE EARTH AS THE CENTER OF THE COSMOS
The Creation of Heaven and Earth
The first three verses of Genesis relate the absolute beginning of the universe:
In the beginning God created heaven and earth. And the earth was void and empty, and darkness was upon the face of the deep. And the spirit of God moved over the waters. And God said: Be light made. And light was made. [Douay-Rheims]
The Septuagint says that the earth was “invisible and shapeless.” The Jewish Biblical Society version translates these three verses as a single sentence that highlights the state of the universe when light was created:
When God began to create heaven and earth—the earth being unformed and void, with darkness over the surface of the deep and a wind from God sweeping over the water—God said, “Let there be light”; and there was light.
The first material object created was the earth. Although “heaven” is mentioned first, it does not necessarily mean that it was the first thing created. The first verse may simply be an introductory summary, an abstract, of what follows. But if it does indeed relate the very first act of God during Creation Week, then the Hebrew word shamayim, translated “heaven,” in a physical sense could mean the void surrounding the earth (the heavenly bodies were not created until the fourth day). The void is not something that exists in itself; for then it would be coeternal with God, that is, it would have being that did not come from God,
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who is the source of all being. Nor is it an attribute of God because that would limit God by making Him somehow threedimensional. Nor was the void created alongside matter, with a separate and independent existence, because then it would be a substance without matter and form, which is senseless. Rather, the void is connected with matter, as St. Thomas Aquinas and others correctly observed. So it came into existence with the earth. Scripture may even have identified it with the earth in the second verse. Perhaps the earth being “void” means that the void surrounding the earth was actually part of it. This makes sense because the void takes its meaning and its dimensionality from the earth. The earth being “empty” or “unformed” means that the distinctions of the first three days and the adornments of the second three days had not yet been made.
The word “heaven” in the first verse might instead mean the matter of which the celestial bodies were made. St. Augustine, St. Basil, St. Gregory of Nyssa, St Ambrose and other Fathers believed that the raw material of all corporeal bodies was created at the very beginning. This is how Augustine expressed it in Genesis Defended against the Manicheans:
So then, that formless material which God made from nothing was first called “heaven and earth” where it is said: “In the beginning God made heaven and earth,” not because that is what it already was, but because it was able to be that—the making of heaven, you see, is described a little later on. It’s as if, when we examine the seed of a tree, we were to say that the roots are there, and the trunk and the branches and the fruit and the leaves, not because they are in fact already there, but because they are going to come from there. That’s how it says, “In the beginning God made heaven and earth,” as a kind of seed of heaven and earth, when the material of heaven and earth was still all unsorted; but because it was quite certain that heaven and earth were going to come from there, the material itself was already called heaven and earth. [19, pp. 45–46]

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Augustine also professes that belief in his Confessions (Book XII, no. 15):
[T]hese two things I have mentioned, heaven and earth, were what you made before all days, in the beginning. “The earth was invisible and unorganized, and darkness loured over the abyss.” These words suggest formlessness, so that the truth may gradually lay hold on the minds of those who are unable to think of an absolute privation of all form without pushing the idea to nothingness. From this formlessness were to be made another heaven and the visible, organized earth, and the beauty of fully formed water, and whatever else would thereafter constitute our world. In the making of this world a succession of days is mentioned, because the nature of these things is such that temporal succession is needed in their case to bring about ordered modifications of motion or form. [13, p. 320]
The formless matter that Augustine perceived was not what we would call “amorphous matter”, that is, matter that has a form but a form that is not well-defined. That notion he explicitly rejected (Book XII, no. 6). Neither did he perceive it as matter that has a continual succession of such forms. He also rejected the notion of formless matter as “something midway between form and nothingness” (Book XII, no. 6). He goes on to consider the mutability of corporeal bodies and begins to suspect that the “transition [of a body] from one form to another involves passing through formlessness, rather than through absolute non-being.”
It should be interjected here that in the Confessions Augustine interpreted the “heaven” of the first day of creation as the spiritual creation, that is, the creation of the angels (Book XII, nos. 2–16, 23). This is the “heaven of heaven” of Psalm 113 (115):
The heaven of heaven is the Lord’s: but the earth he has given to the children of men. [Douay-Rheims: Ps 113:16]

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The earth of the first day of creation was formless matter, from which apparently both the “visible, organized” earth and “another” heaven were made (Book XII, no. 16). The second heaven is the physical “heaven” of the second day of creation.
Augustine perceived formless matter as being in a state of quasi-eternity, that is, in a timeless state:
… the invisible and unorganized earth, where also there was no succession of time, for succession implies that one thing is followed by another, and where there is no form there cannot be any question of one thing, then another. [13, p. 320]
Augustine’s formless matter comes close to what is called in scholastic philosophy prime matter. Prime matter is pure potentiality. It has the potential to be any material thing. However, it exists separately in the mind only. In the world of real things it is always united to substantial form. In The Literal Meaning of Genesis Augustine asserts that formless matter is prior to formed matter as a source but is not prior in time. He said: “God did not first make formless material and later on form it, on second thoughts as it were, into every kind of nature; no, he created formed and fashioned material” [19, p. 181]. In this Augustine differed from other Fathers who believed that unformed (amorphous) matter was created on the first day and was “formed and fashioned” on the following five days.
St. Thomas Aquinas believed that the original condition of matter was an undefined mixture of elements waiting to be organized. St. Bonaventure’s view was closer to that of Augustine than to that of Aquinas. He saw the original condition of matter, to use modern terminology, as pure energy waiting to be transformed.
The view that all the matter of the universe was created at the very beginning, in the light of Genesis 1:1-3, 14, could mean that the earth originally contained all the matter in the universe, from which God made the heavenly bodies on the fourth day. In that case earth would be the mother of the universe. Or, it could mean

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that earth was the first thing formed from the “shapeless matter,” which would also make it a special place in the universe.
However, it is not an issue whether God created all the matter in the universe at the very beginning of Creation Week or if He created the matter along with the forms of creatures at various times during Creation Week. The important point Genesis makes is that God made the earth first and built the rest of the universe around it and for it because earth was to be the home of His masterpiece, man.
There is a question that causes wonder in some readers of Genesis 1:3. It concerns the source of the light that God created on the first day. Where did the light come from if the sun and stars were not yet made? A possible source for the light could have been chemical and nuclear reactions in the raw matter of earth itself. But according to modern physics a source really isn’t needed. Light is not tethered to a source. Once a photon of light leaves its source it is free and has an existence of its own. So modern physics has no problem with the idea that God created light without a source. And neither did St. Thomas Aquinas have a problem with it. He stated:
I answer, then, with Dionysius (The Divine Names, Book IV), that the light was the sun's light, formless as yet, being already the solar substance, and possessing illuminative power in a general way, to which was afterwards added the special and determinative power required to produce determinate effects. [5, Part I, Q. 67, A. 4, Reply Obj. 2]
Further, it will be explained in the next article why there is no problem with the fact that God set up the standard of a natural day independent of the sun, as related in verses 4–5.

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The Formation of Heaven and Earth
Verses 1:6–10 of Genesis relate God’s work on the second and third days, during which heaven and earth were given their forms. Verses 6–8 relate the formation of heaven with the creation of the firmament on the second day:
And God said: Let there be a firmament made amidst the waters; and let it divide the waters from the waters. And God made a firmament, and divided the waters that were under the firmament from those that were above the firmament. And it was so. And God called the firmament Heaven. And the evening and morning were the second day. [Douay-Rheims]
The Jewish Biblical Society version translates the verses using the words “expanse” and “Sky,” rather than “firmament” and “Heaven.”
God said, “Let there be an expanse in the midst of the water, that it may separate water from water.” God made the expanse, and it separated the water which was below the expanse from the water which was above the expanse. And it was so. God called the expanse Sky. And there was evening and there was morning, a second day.
There is no special word in Hebrew for what we call the world or the universe or what the Greeks called cosmos. Instead, Genesis uses more concrete terms like heaven, earth, waters, land and sea. The Hebrew word shamayim is translated “heaven,” in the DouayRheims version. But it does not mean God’s special abode except in a metaphorical sense, as St. Thomas Aquinas points out [5, Part I, Q. 68, A. 4]. Rather, it seems that it corresponds to our word “space,” the abode of the heavenly bodies. It is sometimes translated “sky,” as in the Jewish Biblical Society version. In verse 1:8 God names the rakia that He called into being shamayim. The Hebrew word rakia is traditionally translated “firmament,” “dome,” or “vault.” This is unfortunate because it misleads modern readers. It gives the impression that the Hebrews believed

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that the earth was surrounded by a solid dome. The Hebrew word emphasizes strength and fixity, but it does not imply solidity. The most accurate translation is probably “expanse.” More than one expanse is not excluded by the text. There may be one expanse below the separated waters and another above, the one above being the “heaven” mentioned in the first verse.
St. Thomas saw two interpretations for “firmament.” The first is the “starry firmament.” “Another possible explanation is to understand by the firmament that was made on the second day, not that in which the stars are set, but the part of the atmosphere where the clouds are collected, and which has received the name ‘firmament’ from the firmness and density of the air” [5, Part I, Q. 68, A. 1].
Genesis locates water in three places in the universe—above the expanse (1:7; 7:11), on the earth (1:7, 9), and under the earth (7:11). The waters above the expanse cannot be reckoned as clouds and vapor such as we have in our atmosphere. Clouds and vapor can hardly account for the huge mass of water that was separated from the deep. The text does not say what configuration the waters above the expanse took; it remains a mystery. Perhaps the moon was once covered by water, or maybe there were other moons that were composed of water. It may have been that such moons supplied the water that flowed through the “flood gates of heaven” (Gn 7:11) contributing to the Great Flood.
St. Thomas Aquinas held that the waters are material entities and not spiritual entities, as some authors asserted; but he was not definite about their material nature:
We must hold, then, these waters to be material, but their exact nature will be differently defined according as opinions on the firmament differ. For if by the firmament we understand the starry heaven, and as being of the nature of the four elements, for the same reason it may be believed that the waters above the heaven are of the same nature as the elemental waters. But if by the firmament we understand the starry heaven, not, however, as being of the nature of the

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four elements then the waters above the firmament will not be of the same nature as the elemental waters, but just as, according to Strabus, one heaven is called empyrean, that is, fiery, solely on account of its splendor: so this other heaven will be called aqueous solely on account of its transparence; and this heaven is above the starry heaven. Again, if the firmament is held to be of other nature than the elements, it may still be said to divide the waters, if we understand by water not the element but formless matter. Augustine, in fact, says that whatever divides bodies from bodies can be said to divide waters from waters (Genesis Defended Against the Manicheans, Book I, 5, 7).
If, however, we understand by the firmament that part of the air in which the clouds are collected, then the waters above the firmament must rather be the vapors resolved from the waters which are raised above a part of the atmosphere, and from which the rain falls. But to say, as some writers alluded to by Augustine, that waters resolved into vapor may be lifted above the starry heaven, is a mere absurdity (The Literal Interpretation of Genesis, Book II, Chapter 4). The solid nature of the firmament, the intervening region of fire, wherein all vapor must be consumed, the tendency in light and rarefied bodies to drift to one spot beneath the vault of the moon, as well as the fact that vapors are perceived not to rise even to the tops of the higher mountains, all go to show the impossibility of this. Nor is it less absurd to say, in support of this opinion, that bodies may be rarefied infinitely, since natural bodies cannot be infinitely rarefied or divided, but up to a certain point only [5, Part I, Q. 68, A. 2.].
It may be that the water above the firmament was the raw material that God used to create the heavenly bodies on the fourth day. It may actually have been real water that God transformed to make the heavenly bodies, just as Christ transformed water into wine at Cana.
St. Augustine in Genesis Defended against the Manicheans saw water as possibly being a name for the formless matter:

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He also called the very same material [formless material] water, over which the Spirit of God was borne as the will of the craftsman is borne over things to be crafted. The reason though it is not absurd to call this material “water” is that everything that is borne on the earth, whether animals or trees or grasses and anything else of that sort, starts off by being formed and nourished from moisture. [19, p. 46]
In The Literal Meaning of Genesis he says essentially the same thing: [Scripture] “may have wanted to call by the name of ‘water’ the whole basic material of the bodily creation” [19, p. 172]. Augustine points out in his Unfinished Literal Commentary on Genesis [19, pp. 120–122] and in The Literal Meaning of Genesis [19, p. 180] that nowhere in the creation account is it said that God made the water. Genesis just presumes its existence. This strengthens the argument that water is simply a name for the formless matter [or is the formless matter] from which heaven and earth were made.
Verses 1:9–10 relate the formation of the earth on the third day:
God also said: Let the waters that are under the heaven be gathered together into one place, and let the dry land appear. And it was done. And God called the dry land Earth; and the gathering together of the waters he called Seas. And God saw that it was good. [Douay-Rheims]
In Genesis Defended against the Manicheans Augustine explains this passage as follows:
But it has already been said about the earlier verse that the name of waters was given to that basic material over which the Spirit of God was being borne, from which God was going to form everything. Now however, when it says, “Let the water which is under the heavens be collected into one collection,” it means that that

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bodily material is being formed into the specific nature and appearance which these visible waters have. The very collecting together into one, you see, is the formation of these waters which we can see and touch. Every form, after all, is compressed into fitting the standard of unity.
As for its saying, “Let the dry land appear,” what else is it to be understood as saying, but that that material is to receive the visible form which this earth has that we can see and touch? So that the earth was earlier on being called invisible and shapeless [according to the Septuagint] meant that the basic material was being named as unsorted and dark; and by the water over which the Spirit of God was being borne, another name was given to this basic material. Now, however, this water and earth are being formed from that material which was earlier on called by their names, before it received these forms which we can now see. [19, p. 50]
In the Unfinished Commentary on Genesis, Augustine says essentially the same thing, adding that the formation of the land and sea was in their naming:
“And God called the dry land earth, and the collection of water he called sea.” This matter of names is still with us; not every piece of water is sea or everything dry is earth. So exactly what water and what dry land was meant had to be distinguished by names. But we can still not unreasonably take it that it was God’s naming of them which distinguished and formed these elements. [19, p. 134]
We must recall at this point that Augustine believed that everything was created at once, either in actuality or in potency, with both matter and form. He explains his position on that issue quite clearly in his Unfinished Literal Commentary on Genesis:

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So then, perhaps it is said “And there was made evening and there was made morning, one day” in the sort of way in which one foresees that something can or ought to be done, and not in the way in which it actually is done in a certain stretch of time. After all, it was in its essential nature that God’s creative work was observed in the Holy Spirit by the author who said, “The one who abides forever created all things simultaneously” (Sir 18:1). But in this book of Genesis the story of the things made by God most appropriately sets them out as it were through intervals of time; by this arrangement of the account in an orderly sequence, the divine plan itself, which cannot be directly and timelessly contemplated by our weaker intellects, is presented, so to say, as a spectacle for our very eyes to gaze on. [19, pp. 130–131]
For Augustine formless matter exists in the mind only and not in actuality. The division of God’s labors in shaping formless matter over time is a literary device to make the story of creation understandable.
Augustine’s viewpoint notwithstanding, the understanding of water as being the formless matter of Genesis 1 still makes sense if it is assumed that the whole earth had the form of real pure water and that God transformed some of the water into land and gathered the rest into the seas.
The primal earth might also be thought of as being totally murky water, with the elements of the earth mixed in with it. God then separated the earthy components to form land. Or, primal earth might have been an amorphous mixture of elements waiting to be separated and combined into substances, a la St. Thomas Aquinas, being called water because of its fluid nature. The Hebrew word mayim translated “water” is also used figuratively for other fluids.
St. Gregory of Nyssa used an analogy that may be applied here in a more direct way. He held that God created everything simultaneously; but He created them in a confused state, that is, indistinctly. Then “the work of nature” distinguished them

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according to an order fixed by God. He gives as an analogy a mixture of oil, water and quicksilver. Mixed together they are indistinguishable. But after a while the quicksilver sinks to the bottom, the water settles on it, and the oil rises to the top. The three liquids are distinct substances, but this becomes apparent only after gravity is allowed to do its work. His analogy can be applied to verses 9–10 in this way: The original unformed earth was a fluid mixture of water and other substances. God separated the other substances from the water, not necessarily by natural means, to form water and dry land.
Verses 1:14–18 relate the creation of the heavenly bodies on the fourth day of Creation:
And God said: Let there be lights made in the firmament of heaven, to divide the day and the night, and let them be for signs, and for seasons, and for days and years: To shine in the firmament of heaven, and to give light upon the earth. And it was so done. And God made two great lights: a greater light to rule the day; and a lesser light to rule the night: and the stars. And he set them in the firmament of heaven to shine upon the earth. And to rule the day and the night, and to divide the light and the darkness. And God saw that it was good. [Douay-Rheims]
The heavenly bodies may have been created completely, matter and form, on the fourth day; or they may have been made from the raw material created on the first day. Perhaps God made them from the waters that were raised above the expanse. Or, perhaps the expanse was a plenum that contained the raw materials for the cosmic bodies.
It has been a cause of wonder that day and night were created before the sun and the moon. Some readers of Genesis can’t understand how there was a first day before the sun was created and so dismiss the creation account as myth or allegory. But verse 16 says that God created the sun and the moon to “rule” the day and the night, not to determine them. This means that the periods of day and night ontologically precede the sun and moon. The sun and moon were created to regulate periods of time that had already been determined. St. John Chrysostom expressed this way:

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“He created the sun on the fourth day lest you think that it is the cause of the day” [20, p. 16].
The Earth as the Center of Rest
Genesis 1 makes it clear that God made the earth first and built the rest of the universe around it. Scripture elsewhere makes it clear that God also defined the earth to be the standard of rest in the universe. This is made clear in Psalms 92 (93):
For He hath established the world which shall not be moved. [Ps 92:1 (Douay-Rheims)]
The Hebrew word kun translated “established” has a variety of applications, including “ordain,” “appoint.” The Hebrew word tebel translated “world” means the earth and not the universe.
The stationary earth standard is confirmed by Psalms 103 (104):
Who hast founded the earth upon its own bases; it shall not be moved for ever and ever. [Ps 103:5 (Douay-Rheims)]
It cannot be said that the earth is absolutely at rest because that means that it would be at rest with respect to something else that is absolutely at rest. What would be that something be other than absolute space? But it was shown above that there is no absolute space. So a standard of rest must be defined; it is not given by nature. God defined it to be the earth.
Sacred Scripture applies the stationary earth standard concretely in describing two famous miraculous events that occurred in the history of Israel. Both attested to the movement of the sun in the heavens.. The first event is “Joshua’s long day.” It is recorded in Joshua 10: 12–14:

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Then Josue spoke to the Lord, in the day that he delivered the Amorrhite in the sight of the children of Israel, and he said before them: Move not, O sun, toward Gabaon, nor thou, O moon, toward the valley of Ajalon. And the sun and the moon stood still, till the people revenged themselves of their enemies. Is not this written in the book of the just? So the sun stood still in the midst of heaven, and hasted not to go down the space of one day. There was not before nor after so long a day, the Lord obeying the voice of a man, and fighting for Israel. [Douay-Rheims]
Joshua’s long day was observed around the world, as indicated in the folklore of various nations.
The second event is “Hezekiah’s sign.” It is recorded in Isaiah 38:7–8:
And this shall be a sign to thee from the Lord, that the Lord will do this word which he hath spoken: Behold I will bring again the shadow of the lines, by which it is now gone down in the sun dial of Achaz with the sun, ten lines backward. And the sun returned ten lines by the degrees by which it was gone down. [Douay-Rheims]
This event involving the backward movement of the sun is also recalled in 4 Kgs (2Kgs) 20:8-11 and 2 Par (2 Chr) 32:24.
In these depictions Sacred Scripture is doing more than simply describing the events as they appeared to observers on earth. It is making the profound implication that the earth is the center of rest in the universe. If there were such a thing as absolute rest in the universe, and if the sun were at absolute rest with the earth moving around it (as per the Copernican system), then the Sacred Author would be deceiving us in these verses, which is unthinkable.
The essential misunderstanding in the Galileo affair was the mistaken notion that there is a natural condition of absolute rest. In both the systems of Ptolemy and Copernicus it was presumed that there is a place of absolute rest. The major difference between them was the location of that place.

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The earth is said to be at the center of the universe because it is a place in the universe with special properties, just as geometric centers and centers of mass are places with special mathematical and physical properties. God created the earth first, built the rest of the universe around it, defined it as the center of rest, and made it the home of man, who is a unique union of matter and spirit. The centrality of earth in the universe might also be expressed geometrically and/or physically, but it need not be so to be in accord with Scripture and Tradition.
The Notion of Absolute Rest: Historical Summary
The medieval schoolmen saw the universe as a finite, bounded plenum or quasiplenum with the earth at rest in the center with the heavenly spheres rotating about it. They had a notion of void but no notion of absolute space in the Newtonian sense. Their notion of the earth being at rest meant that the heavens were moved around the earth by some efficient cause distinct from the spheres. And the earth was not moved with respect to the heavens by any such efficient cause. Thus they had a notion of absolute rest. This cosmology colored their interpretation of the Scriptural passages that relate to the stability of the earth.
Newtonian physics also has a notion of absolute rest because it has a notion of absolute space to which all motion is referred. Newton, however, following Copernicus, set the sun at absolute rest with the earth moving around it, its motion being caused by its inertia, which was given to it by God in the beginning [see 17, pp. 47–49].
The modern view, following Einstein, sees the universe as an unbounded three-dimensional absolute space with a geometrical structure determined by the masses that occupy it. The cosmological principle, which states that the universe looks pretty much the same from wherever in it you view it, makes the notion of rest relative. Any body in the universe can be defined to be at rest.

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Without subscribing to Einsteinian cosmology and the cosmological principle, one can still interpret rest as relative. The passages in Scripture referring to the stability of the earth can be interpreted to mean that the earth is at rest because God defined it to be so. He made the earth the standard of rest in the universe because it was the first body created and is the home of man. This requires rejection of the notion of absolute space because that notion contains within it the notions of absolute rest and absolute motion.
Medieval Earth-Centered Cosmology and its Decline
Sacred Scripture makes it clear that man and his home, earth, are the focus of the universe. The centrality of man was expressed geometrically in the Christian medieval cosmos by having the earth at rest with the sun and the heavens moving around it, using a model that came from the Greeks but was in harmony with Scripture. In the medieval cosmos there was order and hierarchy. God encompassed all and man, His steward, was at the center. Love was the great mover. The medieval universe had a rational structure with a purposeful place for everything. Philosopher of science E. A. Burtt nicely summarizes the medieval Christian vision:
For the Middle Ages man was in every sense the center of the universe. The whole world of nature was believed to be teleologically subordinate to him and his eternal destiny. Toward this conviction the two great movements which became united in the medieval synthesis, Greek philosophy and Judeo-Christian theology, had irresistibly led. The prevailing world-view of the period was marked by a deep and persistent assurance that man, with his hopes and ideals, was the all-important, even controlling fact in the universe. [21, p. 18]

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Medieval Catholic astronomy testified to the deeply-engrained belief that man is the masterpiece and center of creation. His good is the end of all creation. Nature exists for his use, to help him attain his end, which is to serve God here on earth and to spend eternal life with Him in heaven.
Nicholaus Copernicus disturbed that worldview by having the earth move, and the theological confusion caused by Galileo’s aggressive advocacy of Copernicus’ cosmology had the sad effect of clouding the truth of man’s centrality and shattering the medieval vision. This decline was further advanced by enlightenment ideology, which produced a cosmology with man removed from the center of creation.
Burtt contrasts the drab view of man in the universe advanced by Galileo and developed by enlightenment thinkers with the bright picture of the medievals:
Note, however the tremendous contrast between this view of man and his place in the universe, and that of the medieval tradition. The scholastic scientist looked out upon the world of nature and it appeared to him a quite sociable and human world. It was finite in extent. It was made to serve his needs. It was clearly and fully intelligible, being immediately present to the rational powers of his mind; it was composed fundamentally of, and was intelligible through, those qualities which were most vivid and intense and his own immediate experience—colour, sound, beauty, joy, heat, cold, fragrance, and its plasticity to purpose and ideal. Now the world is an infinite and monotonous mathematical machine.… It was simply an incalculable change in the viewpoint of the world held by intelligent opinion in Europe. [21, pp. 123-124]
The modern view, held by many scientists and scholars today, was clearly expressed by Bertrand Russell in A Free Man’s Worship (Mysticism and Logic); it is the wretched fruit of enlightenment thinking:

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Such, in outline, but even more purposeless, more void of meaning, is the world which Science presents for our belief. Amid such a world, if anywhere, our ideals henceforward must find a home. That man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspirations, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins—all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built. [21, p. 23]

CHAPTER 3
EMPIRICAL SCIENCE AND THE EARTH AS THE CENTER OF THE COSMOS
The Logic of Absolute Motion
In the first chapter it was explained why scholastic philosophy considers absolute space a contradiction in reality, although not in the mind. Thus there is no such thing as absolute space. And since there is no such thing as absolute space, it logically follows that there is no such thing as local motion in absolute space and no such thing as a change in local motion in absolute space. That is, there is no uniform local motion and no accelerated local motion in absolute space. And since there is no such thing as absolute accelerated motion, there is no such thing as absolute force. All motion and all forces are relative to physical bodies, as Ernst Mach correctly argued [10, p.279].
Isaac Newton realized that the existence of absolute space cannot be demonstrated by uniform local motion, but he argued that the inertial effects associated with rotational motion demonstrated it. He gave his famous example of the concave surface of a rotating pail of water. Modern geophysicists follow Newton in considering phenomena such as the oblate shape of the earth, the rotation of the plane of vibration of the Foucault pendulum, and the diminishing of gravity at the equator as inertial effects associated with the absolute rotation of the earth.
Mach refuted Newton’s argument by pointing out that, even in the case of rotational motions, we have knowledge only of relative places and motions. We observe only the relative rotational motion between a rotating body and the rest of the universe. We cannot logically conclude that the inertial effects associated with rotation would occur without the rest of the universe present, which would be the case if rotational motion
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were absolute. According to Mach, rotational effects can be explained with reference to relative frames. He argued: “The principles of mechanics can, indeed, be so conceived that even for relative rotations centrifugal forces arise” [10, p. 284]. A. K. T. Assis implemented this insight in his development of relational mechanics [8].
The Physics of Local Motion
The physical science that deals with motion in itself, without the consideration of masses and forces, is called kinematics. Kinematics is concerned solely with the locations, velocities and accelerations of physical objects that move locally in any way. These are entities that are subject to measurement, and there must be standards for their measurement.
Measurements of distances and angles, on a material object or in a void, ultimately depend on the use of rigid material rods on rigid material frames of reference. Even methods that use light to measure distance must be calibrated according to such a standard. Rigid rods and frames of reference have parts that remain fixed with respect to each other.
The surface of the earth provides a basis for rigid frames of reference for terrestrial measurements and for the calibration of astronomical measurements.
The fixed stars provide a rigid frame of reference for astronomical measurements. The fixed stars do not appear to us to move with respect to each other. This is because 1) they actually do not move with respect to each other; or 2) they move with respect to each other with a motion too slow to perceive; or 3) they are so far away that, even if they do move with significant speed with respect to each other, their motion is imperceptible to us.
The measurement of motion also requires a standard for the measurement of intervals of time. Since there is no such thing as absolute time (time is an accident, not a substance) all intervals of time are relative. Time is measured by comparing physical processes. Intervals of time are measured by comparison with

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some physical process presumed to be uniformly periodic. At one physical extreme we have an astronomical standard (the sidereal day). At the other extreme we have atomic clocks. In between we have pendulum and other mechanical clocks. If we compare the uniformity of two clocks and they agree (that is, m cycles on one always corresponds to n cycles on the other), then we can interchange them as standards. However, if they do not always agree, then we must assume that one is the standard and that the other drifts. If we can give a good physical explanation why the second clock drifts, then we are satisfied. But if not, then we reverse the process. However, it seems that God gave us astronomical time as the ultimate standard.
Astronomical Phenomena Pertaining to the Stability of the Earth
Believers in a mobile earth point to two well-known astronomical phenomena that they suppose convincingly demonstrate motion of the earth through absolute space. Those phenomena are stellar aberration and stellar parallax. Arguments for a moving earth based on them can easily be shown to be inconclusive.
The phenomenon of stellar aberration was discovered by James Bradley in 1726. It is the apparent displacement in the positions of stars attributed to the finite speed of light and to the transverse motion of the earthbound observer with respect to the ray of light from a star. The effect requires the slanting of a telescope at an angle away from the target star to allow light entering the objective lens to reach the eyepiece. The telescope must be tilted to allow the ray to travel down the axis of a transversely moving telescope. If the speed of light were infinite, that would not be necessary. Stellar aberration has long been used as evidence for motion of the earth through absolute space. Those who advance it as evidence for absolute motion of the earth assume two things. They first assume that light propagates like a wave through a medium called the ether. Second, they assume that

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the ether is at rest in absolute space. According to that view, motion of the star through the ether would not cause the effect; only motion of the earth through the ether would cause it. But, if the ether moved like a breeze through absolute space, the same effect would be produced. One could conceive of the earth at rest with the ether moving around it with the sun. Also, if the light is conceived as a beam of particles, which is the quantum mechanical view, then the effect is only one of the relative motion of the earth and star.
Albert Einstein, in his 1905 paper on special relativity entitled “On the Electrodynamics of Moving Bodies,” treated stellar aberration as a phenomenon caused by relative motion of the earth and star [22, pp. 55-57]. Einstein calculated the first-order stellar aberration, which is caused by a “wobble” of the celestial sphere with respect to earth. The first-order effect is of equal magnitude for all the stars. Higher order aberration effects are caused by additional motions of stars with respect to the celestial sphere.
Stellar parallax is the angular displacement of certain stars against the background of the fixed stars. It was first observed by Friedrich Wilhelm Bessel in 1838. Astronomers attribute this to the optical effect called parallax, which is the apparent displacement of two objects when viewed from two different positions. This occurs, for example, when one holds a pencil in front of his nose and views it with one eye and then other. The pencil appears to move relative to the background. In the case of stellar parallax, the two observations are made from the earth six months apart. The earth in then pictured as being at two different ends of its apparent orbit around the sun. It is assumed that earth moves with respect to the stars and that the sun remains fixed with respect to the stars. This means that there would be no parallax on the sun, something that has not been demonstrated. This explanation further assumes that the stars themselves are fixed in absolute space, something else that has not been demonstrated. The phenomenon of stellar parallax, therefore, does not conclusively demonstrate absolute motion of the earth.

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E. Whittaker summarizes nineteenth-century optical astronomy and concludes that optical methods had been unable to detect the earth’s alleged absolute motion through space:
Fresnel inferred from his formula that if observations were made with a telescope filled with water, the aberration would be unaffected by the presence of the water—a result which was verified by Airy (*) in 1871. He showed, moreover, that the apparent positions of terrestrial objects, carried along with the observer, are not displaced by the earth’s motion; that experiments in refraction and interference are not influenced by any motion which is common to the source, apparatus and observer; and that light travels between given points of a moving material system by the path of least time. These predictions have also been confirmed by observation: Respighi (*) in 1861, and Hoek (*) in 1868, experimenting with a telescope filled with water and a terrestrial source of light, found that no effect was produced on the phenomena of reflection and refraction by altering the orientation of the apparatus relative to the direction of the earth’s motion. E. Mascart (*) in 1872 studied experimentally the question of the effect of motion of the source or recipient of light in all its bearings, and showed that the light of the sun and that derived from artificial sources are alike incapable of revealing by diffraction-phenomena the translatory motion of the earth. [23, vol. I, pp. 113-114] [An asterisk indicates that a source is cited by the author.]
Optical Experiments Pertaining to the Stability of the Earth
The most famous attempt to measure the alleged motion of the earth through the ether by optical means was the MichelsonMorley experiment, first performed in 1887. The logic of the experiment is as follows: two coherent light beams are sent out

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from a beam splitter in mutually perpendicular directions, one in the direction of the earth’s supposed motion and one perpendicular to it. After traveling equal distances on the apparatus, the two beams are reflected back to the beam splitter and into an interferometer. Calculations indicated that the roundtrip “upstream and downstream” and the roundtrip “cross stream” would take different periods of time, the upstreamdownstream trip taking more time. So they should both arrive back at their origin out of phase and thus cause a shift in the interference fringes (from that expected for a null result). But no such fringe shifts were observed, which implied that earth does not move. But physicists like G. F. Fitzgerald and H. A. Lorentz, who were totally imbued with the notion of absolute space filled with ether, attempted to explain the null result of the experiment by making the incredible proposal that the apparatus “shrunk’ in the direction of the motion just enough to conceal the earth’s motion. According to J. S. Bell, Lorentz, rather than rejecting the notion of the motion of the earth through the ether, “preferred the view that that there is indeed a state of real rest, defined by the ‘aether’, even though the laws of physics conspire to prevent us from identifying it experimentally” [24, p. 77]. A. Assis explains the null result of the Michelson-Morley experiment in terms of relational mechanics. Assis maintains that the most straightforward explanation of that experiment is that there is no ether. He says: “Only the relative motion between the light, the mirrors, the charges in them and the earth are important, no matter what the velocity of these bodies relative to the ether or to absolute space” [8, p. 145].
Einstein expressed his belief in the fruitlessness of attempting to measure absolute motion of the earth. In the introductory paragraph of his 1905 paper on special relativity Einstein refers to “unsuccessful attempts to discover any motion of the earth relatively to the ‘light medium,’ which “suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest” [22, p. 37]. The attempts that he alludes to include stellar aberration, stellar

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parallax and the Michelson-Morley experiment, all observations that predate publication of that paper.
Gerardus D. Bouw [25] describes a geostationary model of the universe that exhibits all observable astronomical kinematic phenomena, including the phases of Venus, stellar aberration and stellar parallax. It is a modified version of that of Tycho Brahe with the planets and the stars moving around the sun, which, in turn, moves around the earth.
*
Accelerated motion can be detected by actual physical effects, for example, compression or tension in an elastic material. However, the effects cannot tell us whether the acceleration is caused by motion with respect to absolute space or motion with respect to the rest of the universe.
In 1913 G. Sagnac, following a suggestion by A. Michelson, used light in an attempt to determine absolute rotational motion. The experiment was conducted as follows: Four mirrors were arranged in a square centered on the axis of a turntable so as to reflect a beam of light around the square. A light source, a beam splitter, and an interferometer were also placed at appropriate locations on the turntable. Two coherent beams of light were sent out from the beam splitter in opposite directions around the square back to the beam splitter and into the interferometer. When the turntable was at rest the beams arrived at the interferometer in phase with each other and produced a fringe pattern. When the turntable was rotated, however, shifts in the fringes were observed, which indicated that the optical lengths of the two paths were different. (The same observation was made later by different experimenters with the light source and observer standing off the rotating platform.) This was taken as a demonstration that the platform was rotating in absolute space [25, pp. 281–284; 26, pp. 55–58]. However, the same arguments apply for this experiment as were made above for mechanical effects of acceleration; that is, we do not know whether the

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Sagnac effect is caused by motion with respect to absolute space or motion with respect to the rest of the universe. It is not possible to test this directly because one cannot simply remove all the heavenly bodies. H. E. Ives seems to have recognized this, although he argued against the Sagnac effect as being an effect of the relative rotation of material bodies. In a 1938 paper that deals with the Sagnac effect he concludes:
The observer on the apparatus has just one reference framework by which he can predict whether the Sagnac effect will appear or not; that framework is the pattern of radiant energy from the stars. If his apparatus rotates with respect to the stars he will observe a Sagnac effect, if it does not, then no matter how great a relative rotation it exhibits with respect to its material surroundings, there will be no Sagnac effect. [27, p. 44]
The results of optical experiments like the Sagnac experiment must be interpreted with great care because we do not have a clear understanding of the nature of light and its inertial effects. Light has been observed in various experiments to behave with apparently irreconcilable wave properties and particle properties. Waves are propagated; particles are projected or propelled. Any particular experiment must be interpreted according to whether a wave property or a particle property is being observed. If a wave property such as interference or diffraction is being observed, then light must be presumed to be a wave. Since a wave is propagated, it requires a medium. The medium that propagates light waves is called ether. Assumptions must be made about the ether, for example, whether it is at rest or moving and in respect to what. Particle properties of light manifest themselves in experiments that involve the exchange of energy and momentum between light and matter. Another consideration is the speed of light. Is it the same for all sources? How does reflection of light from a moving mirror affect its properties of wavelength, frequency and speed? Einstein, in his 1905 paper on special theory of relativity, assumed that the speed of light in a vacuum is always the same for everybody [22, p. 41]. However, others interpret

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empirical evidence to the contrary [8, pp. 139-140]. In his 1905 paper, Einstein interpreted light as a wave phenomenon and the constancy of the speed of light for all observers as a kinematical effect. That interpretation generates contradictions. However, in the next chapter a dynamic interpretation for the constancy of the speed of light will be given that is free from contradictions. That interpretation employs particle properties of light.
Comments on the Nature and Motion of Light
At this point it would be sensible to consider the general nature and the motion of light itself because its nature and its means of moving determine the interpretation of optical observations.
St. Thomas Aquinas following Aristotle held that light is an accidental form. St. Bonaventure held that it is a substantial form. It is interesting that neither held light to be a substance. Being a form, it exists in something else. As an accidental form, would the underlying “subject” be a material object or the void? And, as a substantial form, what is the underlying “matter”? St. Bonaventure believed in the plurality of substantial forms (more than one substantial form in a substance) and that the same matter underlies both material and spiritual substances. He believed that light is the common form of all things. The nineteenth-century view was that light is a disturbance of an ethereal medium that is propagated. Thus light was considered accidental in nature. The modern view is that light is substantial. Photons of light possess energy that can be transformed into matter.
There are three ways in which light might move: propagation, projection, and propulsion. In the so-called “wave theory,” light is propagated as a wave, analogous to water and sound waves; this is the classical electromagnetic view. In the so-called “ballistic theory,” light is viewed as a projectile that is given motion by its source and continues to move along by inertia; this is the picture we are given, rightly or wrongly, by quantum mechanics. A third view, which does not seem to have been given much attention by physicists, might be called the “self-propulsion theory.” It is a

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combination of the modern and classical views. Light is seen as an independent entity like a photon. But it propels itself through the ether, analogous to a fish in water or a snake on land. There is a hint of this in the classical explanation for the propagation of an electromagnetic wave. In that view a varying electric field produces a varying magnetic field in its immediate vicinity, which in turn produces a varying electric field in its immediate vicinity, and so on. In this way light “wiggles,” “crawls,” “swims,” “steps” or “walks” through the ether.
Geometrical and Physical Centricity of Earth
The earth is at the center of the universe because it is a place in the universe with special properties, just as geometric centers and centers of mass are places with special properties. The definition of “center” is not unique; for example, geometers have a number of different definitions for the “center” of a triangle. The earth is considered to be at the center of the universe because God created it first, built the rest of the universe around it, defined it as the standard of rest, and made it the home of man, who is a unique union of matter and spirit.
The centrality of earth in the universe might also be expressed geometrically and/or physically. And, as we shall see, there is evidence that it is; although it need not be so to be in accord with Scripture. Striking evidence that the earth is at or near the center of the universe comes from the observation of galaxies and quasars. (Quasars, from “quasi-stellar objects,” are star-like sources of light of unknown nature whose red shifts are large. They must be very bright to be visible at the great distances astronomers assign to them.) In the early 1970s, William Tifft at the Steward Observatory in Tucson, AZ analyzed red shift data from galaxies in all directions. His analysis showed that the red shifts are quantized. This can be interpreted to mean that the galaxies are arranged on concentric spherical shells. The quantization effect could be clearly observed only if the earth was close to the center of the shells. [See Russell Humphreys, “Our galaxy is the centre of the universe, ‘quantized’ redshifts show,” TJ

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16(2):95–104 (2002).] Y. P. Varshni studied the red shifts of 384 quasars. Varshni concluded that if the quasar red shifts are real and distance related then “the Earth is indeed the center of the Universe. The arrangement of the quasars on certain spherical shells is only with respect to the Earth. These shells would disappear if viewed from another galaxy or a quasar. This means that the cosmological principle will have to go. Also, it implies that a coordinate system fixed to Earth will be a preferred frame of reference in the Universe. Consequently, both the Special and the General Theory of Relativity must be abandoned for cosmological purposes” [Astrophys. Space Sci. 43:3 (1976); 51:121 (1977)].
Other evidence offered as suggesting that the earth is at or near the center of the universe comes form the study of ambient microwave radiation. In 1965 A. A. Penzias and R. W. Wilson discovered that the earth is immersed in a bath of microwave radiation corresponding to that found inside a box kept at a temperature of 2.7 Kelvin. This radiation, called cosmic microwave radiation (CMR), is very isotropic, having intensity variations with direction no greater than one part in one hundred thousand. Physicist V. F. Weisskopf made this observation concerning the isotropy of this radiation: “It is remarkable that we are now justified in talking about an absolute motion, and that we can measure it. The great dream of Michelson and Morley is realized. They wanted to measure the absolute motion of the earth by measuring the velocity of light in different directions. According to Einstein, however, this velocity is always the same. But the 3 K radiation represents a fixed system of coordinates. It makes sense to say that an observer is at rest in an absolute sense when the 3 K radiation appears to have the same frequencies in all directions. Nature has provided an absolute frame of reference. The deeper significance of this concept is not yet clear” [Am. Sci. 71, no. 5: 473]. However, observations show that the CMR wavelength spectrum is not isotropic in wavelength. Its wavelength spectrum is shifted down in one direction of the sky and shifted up by the same amount in the opposite direction. This phenomenon is called dipole anisotropy. It is attributed to the Doppler effect caused

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by a speed of about 260 kilometers per second of the earth relative to the radiation. Weisskopf’s enthusiasm is premature. There is not enough known about CMR to qualify it as an absolute frame of reference. Is it isotropic, stationary and thermally uniform throughout the whole universe? Or is it like our oceans, hotter in some places, cooler in others, with streams flowing through it? Dipole anisotropy suggests such streams when we take the earth as the center of rest. It seems then that CMR can no more provide a standard of absolute rest for the universe that can ocean water provide a standard of rest for the earth.

CHAPTER 4
THE LOGIC OF NEWTONIAN PHYSICS AND RELATIVITY
Newton’s Laws of Motion and Inertial Frames
The science of matter and motion, called mechanics, was greatly advanced by the work of Isaac Newton. In the Principia Newton encapsulated the dynamics of material bodies in three laws [17, pp. 25–26]:
LAW 1: Every body continues in its state of rest or of uniform motion in a right line unless it is compelled to change that state by a force impressed upon it.
LAW 2: The change of motion is proportional to the motive force impressed and is made in the direction of the right line in which that force is impressed.
LAW 3: To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
The first law is called the law of inertia. It states that a material body, by virtue of its inertial mass (“quantity of matter”) alone, will not change its state of rest or uniform linear motion without an outside influence being impressed upon it.
Newton defines the “quantity of the motion” (momentum) of a material body as the product of it mass and velocity. An applied force changes the momentum along the direction of the force. The second law states that if a force produces a change in the quantity of motion, then twice that force will produce twice the change, three times the force three times the change, and so on.
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The third law is called the law of action and reaction. Whenever one material body “pushes” on another, the second pushes back with an equal force.
Newton did not give an adequate definition for the inertial mass of a body. He simply defined it as the product of the volume of a body and its density. Ernst Mach gave a much better definition by employing the third law. He stated: “All those bodies are bodies of equal mass, which, mutually acting on each other, produce in each other equal and opposite accelerations” [10, p. 266]. For example, consider two masses at the two ends of a constrained compressed spring on a level frictionless surface. When the constraint is removed, the expanding spring will cause both masses to accelerate along the surface. If the accelerations are equal, the masses are equal. This definition would seem to work well on any rigid material frame of reference in which both masses start out at rest with respect to each other and with respect to the frame of reference and no external forces are present that produce a bias. Such a bias would be present, for example, if one performed the above procedure on an inclined surface rather than a level one. Then gravity would decrease the acceleration of the mass going uphill and increase the acceleration on the mass going downhill. In the case of unequal accelerations, the ratio of the masses is inversely proportional to the ratio of the magnitudes of the accelerations.
Newton said that his laws of motion apply in any frame of reference that is at rest in or moves in uniform linear motion in absolute space. These are called inertial frames. Today the term inertial frame is used simply to mean a frame in which Newton’s laws of motion apply directly, without any reference to absolute space. Frames of reference in which Newton’s laws do not apply directly (such as rotating rigid platforms) are called non-inertial frames. In such frames Newton’s laws of motion have to be modified by the introduction of “fictitious forces,” such as centrifugal and Coriolis forces. According to Newtonian mechanics, fictitious forces are forces that cannot be traced to physical interactions with other material bodies; they are the result of nonuniform and/or nonlinear motion of a frame of reference

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with respect to absolute space. According to Machian mechanics, the so-called fictitious forces are actually real forces that are associated with interactions arising from nonuniform and/or nonlinear motion of a frame with respect to the rest of the universe. A specific nature is given to those interactions by Andre Assis in his Relational Mechanics [8].
Ultimately, fictitious forces are explainable in terms of Newton’s three laws because they derive from the inertial properties of matter contained therein. Therefore they are also called inertial forces. Newtonian mechanics does not give a reason for these inertial properties of matter; it only states them. Machian mechanics, on the other hand, attributes the inertial properties of a material body to the other matter in the universe. In the Machian view, every material body resists any change in the arrangement of the universe, and this is a collective phenomenon.
Newton’s referencing his laws to absolute space introduces a certain ambiguity in his first law. In that law he refers to motion in a “right” (straight) line. But what is a straight line? How can a straight line be defined in absolute space? If it is defined as the trajectory of a mass that has no force impressed on it, then his law suffers from circularity. And how would “trajectory” be defined in the first place? How does one determine geometrically whether or not a force is being impressed? In empty absolute space no coordinate grid can be established because there is no place to anchor such a grid and no standard for the measure of distance. Therefore the concepts of trajectory and straight line are meaningless.
Despite this Newton was immensely successful in using his laws to explain observed terrestrial and celestial motions. That is because his laws of motion do not require the notion of absolute space, as Ernst Mach pointed out. Newton’s laws of motion only require rigid frames of reference in which they work. All the frames of reference in which his laws of motion have been empirically confirmed are frames fixed to material objects, which are relative frames not absolute ones.

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Even though Newton’s mechanics gave the science of physics a great boost, his faulty metaphysics pointed physics in the wrong direction. Newton’s rejection of the scholastic view of space and time led the way to the plethora of esoteric and confused relativity-based cosmologies that we are plagued with today. His opposition to the scholastic view is clearly presented in the following passage from his paper De gravitatione (c. 1670), in which he defends the reality of absolute space:
… we can clearly conceive extension existing without any subject, as when we may imagine spaces outside the world or places empty of body, and we believe {extension} to exist wherever we imagine there are no bodies, and we cannot believe that it would perish if God should annihilate a body, it follows that {extension} does not exist as an accident inherent in some subject. And hence it is not an accident. And much less may it be said to be nothing, since it is rather something, than an accident, and approaches more nearly to the nature of substance. There is no idea of nothing, nor has nothing any properties, but we have an exceptionally clear idea of extension, abstracting the dispositions and properties of a body so that there remains only the uniform and unlimited stretching out of space in length, breadth and depth. And, furthermore, many of its properties are associated with this idea; these I shall enumerate not only to show that it is something, but what is. [28, p. 618]
The scholastic argument, given in Chapter 1, is much sounder; it does not confuse abstraction with reality.
Furthermore, Newton’s theology of creation was decidedly non-Catholic. He considered void not as a freely created entity but as a necessary effect of God, existing eternally along with Him, and, like God, perfectly simple and immutable. God had no alternative to creating matter in three-dimensional space. (That would seem to put an unreasonable limitation on God’s power to create. He would not be free to create a higher-dimensional world,

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which does not seem to be an inherently contradictory notion.) Likewise, Newton considered absolute time to be uncreated. He viewed the eternity of God not as transcending time but as the enduring existence of God in absolute time. Newton perceived God as distinct from but effecting and living in infinite space and time. Moreover, he held that infinite space is the “sensorium” of God, in which He observes the world. Newton spelled out these views in De gravitatione, the Principia and elsewhere [see 17, pp. 41– 67; 28, pp. 617–644].
Electrodynamics and Einstein’s Postulates for Special Relativity
The notion of absolute space was to be looked at in a new light in the nineteenth century with the development of a completely new science, electrodynamics. This science dealt with the newlyidentified electric and magnetic forces, which, although similar in some ways, were quite different from the familiar gravitational force. At the center of electrodynamics is a physical entity called electric charge, of which there are two kinds, positive and negative. If a material body possesses such a charge, it will exert a repulsive force on other bodies that possess the same kind of charge and an attractive force on bodies that possess the other kind of charge. All uncharged material bodes contain equal amounts of positive and negative electric charge, which cancel out the effects of each other making the body overall electrically neutral. Uncharged metals carry “free” negative charge, that is, charge that is free to move within the metal. But that charge is balanced by an equal amount of “fixed” positive charge, which makes the metal overall electrically neutral. Charged metals carry either a deficiency or an excess of negative charge, making them either positively or negatively charged. The free charge in a metal can move to constitute what is called an electric current. Because of their ability to conduct an electric current, metals are called

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conductors. Materials that do not possess “free” charge, and therefore cannot conduct an electric current, are called insulators.
There was yet another kind of material, called lodestone, which possessed a strange property. Pieces of lodestone were observed to attract or repel other pieces of lodestone, even with nothing in between them. And it was found that it could give this property to iron without losing it itself. This property came to be known as magnetism. Bodies that possess it are called magnets. Magnets were also observed to produce effects on electrically charged bodies, but those effects were different from the effects electric charges produced on each other. Magnets exerted forces on electrically charged bodies, but only on charged bodies that move relative to the magnet. If was observed that if a metal wire was moved toward or away from a magnet an electric current would be induced in the wire. If instead the magnet was moved in the same way relative to the wire an identical current would be induced. Thus the induced current was observed to depend only on the relative motion between the wire and the magnet.
A key figure in the development of the science of electrodynamics was Michael Faraday, who performed experiments with charged bodies, wires and magnets. In his attempt to understand what he observed he invented the concept of a field, which was mathematically developed by James Clerk Maxwell. The concept of a field eliminated the need to talk about action-at-a-distance. That is, one no longer had to think of charged bodies and magnets as exerting their effects instantly across empty space. Instead, they produce fields of force in the space around them, which in turn exert their effects by immediate contact. So there developed two approaches to electrodynamics, the action-at-a-distance approach, which was developed by Wilhelm Weber, and the field approach of Faraday and Maxwell. The latter won out in the minds of physicists, but not without the introduction of new perplexities that replaced those of action-at-adistance.
The great achievement of the field approach to electrodynamics was the discovery that disturbances in an electromagnetic field are propagated as waves that travel at the

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same speed as light. Thus light came to be identified as an electromagnetic phenomenon. The perplexities introduced were associated with the notion of the luminiferous ether, the mysterious medium required for the propagation of electromagnetic disturbances. Is it identical to absolute space or distinct from it? If distinct, of what is it composed? Does it have a solid or fluid nature? Does it exist in absolute space; and, if so, is it at rest or does it move in the manner of an ocean current or perhaps multiple ocean currents? Does it travel with the source of the fields it propagates? Does it resist the motion of material bodies through it, thus giving rise to the phenomenon of inertia? Nineteenth century physicists tended to think of the ether, whatever they perceived its substantial nature to be, as being at rest in absolute space and as pervading all of space. H. A. Lorentz was the great champion of the ether notion. Albert Einstein was its great opponent.
The notion of ether also raises interesting questions for the scholastic philosopher. If the ether exists, is it a substance or an accident? If it is a substance, is it material or immaterial? If it is a substance, then arguments that deny the existence of absolute space, which is nothingness, would not apply to the ether, which is a created something. If the ether is a substance that pervades the whole universe, then the universe is a plenum and there is no void. If the ether is an accident, then in what subject does it exist? Is the ether a potency and, if so, to what? If it is a potency, what is its relation to pure potency, that is, prime matter? Is the ether an incomplete substance, analogous to a disembodied human soul, and, if so, what completes it? Consideration of such questions could lead to a better understanding of electromagnetic phenomena.
Einstein presents the ethereal point of view at the beginning of his 1905 paper on special relativity [22, pp. 37–38]. He gives the Lorentzian explanation for the induced current in a conducting wire moving with respect to a magnet. According to the Lorentzian interpretation of Maxwell’s field theory, the same current can be produced in the wire for two different reasons,

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depending on motion with respect to the ether. If the wire moves with respect to the ether, then the current is induced simply by the motion through the magnetic field. If the magnet moves, the current is induced by an electric field produced by the moving magnetic field. Thus in one case a magnetic field produces the current; in the other case an electric field produces the current. This is an asymmetry that is not inherent in the phenomenon itself because the exact same effect takes place no matter which object is moved. The asymmetry results from a misinterpretation of Maxwell’s field equations. Maxwell’s field equations state that a varying electric field at a point produces a magnetic field in the vicinity of the point and vice versa. However, the fields must be referred to their source (as Faraday and Maxwell did) and not to the ether (as Lorentz and Einstein did). And since the field of the magnet does not change with respect to the magnet when the magnet is moved there is no electric field produced by the moving magnet. So the current in the wire is induced by magnetic force in both cases. This is explained clearly and in detail by Andre Assis [8, pp.127–131 (also see 43, pp. 148-149 and 48, pp. 7-9)].
Einstein believed that elimination of the asymmetry required elimination of the notion of ether. If he had adopted the view of Faraday and Maxwell instead of the view of Lorentz, he would have been able to retain both the symmetry and the ether. Elimination of the ether was a drastic step that led to the theory of relativity of space and time with its confused notions and inherent contradictions.
Einstein built his theory of special relativity on two postulates. The first he called the “principle of relativity.” It can be stated as follows: The fundamental laws of physics (mechanical and electrodynamic) have the same formulation on all rigid material frames of reference that move in uniform translatory motion with respect to each other. That would make uniform translational motion through the ether undetectable by physical experiments. However, the postulate says nothing about accelerated motion. Accelerated motion could still be detected by inertial effects, as Newton had observed. So the notion of ether cannot be totally ruled out by this postulate.

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The second postulate in that of the constancy of the speed of light in a vacuum. The first postulate already implies that the speed of light is constant with respect to the source. Otherwise, the fundamental laws of electrodynamics would differ from frame to frame and one could detect uniform motion in the ether. But for the speed of light to be constant with respect to the source each source would have to be accompanied by its own ether. Einstein went a step further because he wanted to eliminate the ether altogether. He said that the speed of a beam of light will have the same speed for all observers that move in uniform translatory motion with respect to each other, no matter in which frame it was emitted. Assis points out that this postulate makes light an oddity in the physical world. The speed of bullets shot from a gun with respect to a flatcar on which it rides does not depend on the speed of the flatcar, but their speed with respect to any observer depends on the speed of the observer relative to the flatcar. The speed of a wave is constant with respect to the medium in which it travels, as long as the medium is homogeneous. But its speed relative to an observer depends on the speed of the observer relative to the medium. However, in special relativity the speed of light does not depend on the speed of the observer relative to anything. According to Assis, that has never been empirically demonstrated. In fact, Assis cites evidence to the contrary [8, pp. 139–140]. In physical experiments light always shows similarities to projectiles or waves. But Einstein made light behave differently than either projectiles or waves. That is the source of the “paradoxes” and the counter-intuitional concepts of space and time generated by special relativity because in order to maintain the constancy speed of light for all observers one is forced to deny the possibility of common standards for measuring distance and duration.
Thus Einstein’s second postulate gives light a privileged place among physical phenomena. Making the speed of light constant for all observers makes it simulate infinite speed. According to classical physics only something traveling at an infinite speed would have the same speed with respect to all observers,

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independent of their states of motion. The speed of light being the same for all observers gives rise to relativity’s bizarre notions of space and time.
One such notion is called “relativity of simultaneity.” Classically, simultaneity can be defined in terms of events that can be “connected” with signals that travel at infinite speed. This means that if a clock, at a certain instant, sends out an infinitely fast signal throughout the universe, events occurring at places throughout the universe when that signal is received are occurring simultaneously. But in Einstein’s relativity, such simultaneous events are also connected by signals that travel at finite speeds. Consider a transmitter at rest with respect to a receiver located at another distant place. Assume next that, at a certain instant, the transmitter sends an infinitely fast signal to the receiver that contains information about events then occurring at its place. So the “observer” at the receiver can know what is happening at that instant at the place of the transmitter.
Next consider an “observer” moving at velocity v with respect to the rest frame of the transmitter and receiver. According to classical kinematics the signals exchanged between the transmitter and receiver would still be infinitely fast for such an observer. But according to relativistic kinematics that would not be so. The transmission and reception events would not be connected by a signal of infinite speed, but by a signal of finite speed, and therefore the transmission and reception of the signal would not be simultaneous events to such an observer. The formulas for the addition of velocities of special relativity transform the infinite speed of the signal sent by the transmitter to the receiver to a signal of finite speed for such an observer. The speed of the signal can take on a range of finite values, the value depending on the magnitude of v and its direction with respect to the line connecting the transmitter and receiver.
Consider a special case in which the observer travels in a straight line at speed v in the direction from the transmitter to the receiver. Then the infinitely fast signal appears to the observer to be traveling at the at the finite speed c2/v, where c is the speed of light. Relativistic kinematics does not allow v to exceed c because

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that produces mathematically imaginary effects. Therefore the speed of the signal that the moving observer observes, although finite, is still equal to or greater than c. Furthermore, the fourth Lorentz equation, the time transformation, indicates that if the observer were to clock a signal speed greater than c2/v he would see the temporal sequence of the events reversed; that is, the observer would see the receiver receiving the signal before the transmitter transmits it. Since c2/v is the transformation of the highest signal speed possible in the rest frame of the transmitter and receiver, it is the highest signal speed that can be clocked by the observer, so the reversal of cause and effect in his frame is not possible.
The above example should make it clear that although relativistic kinematics puts a limit on the relative speed of inertial frames, it does not put a limit on the speed of a signal sent within an inertial frame or even between inertial frames. However, relativistic dynamics puts a limit on the speeds of signals that are conveyed with objects that have inertial mass because a massive object cannot move faster than the speed of light in an inertial frame.
There are indications that some natural effects are transmitted with infinite or near-infinite speed. Physical observations provide strong evidence that certain gravitational, electromagnetic and quantum mechanical effects are communicated instantly or near instantly. But these effects cannot be used by intelligent agents to communicate information. This will be discussed at some length in the next chapter.
Kinematical Contradictions of Special Relativity
If something were to travel instantaneously it would appear so to all observers because that is a property of infinite speed. Postulating that a finite speed of light is the same to all observers is applying a property proper to an infinite thing to a finite thing. This is the source of contradictions in special relativity. It is analogous to postulating that the center of every finite circle is

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everywhere within the circle, a property that belongs only to infinite circles. A geometry based on such a postulate would produce contradictions.
Two results of special relativity are length contraction and time dilation. According to Einstein, observers moving with uniform linear motion with respect to each other will observe the other’s measuring rod to be shorter and clock to be slower; both would observe the exact same effects in the other’s instruments. This notion leads to contractions. The most famous contradiction is the “twin contradiction.” It is usually called the twin “paradox.” But it is not a paradox because a paradox is only an apparent contradiction. It is a genuine contradiction if presented in the proper way. It goes as follows:
Twins occupy two identical space rockets facing back to back. They both fire off at the same time and follow the same flight program. They rapidly accelerate away from each other to close the speed of light, move on uniformly for a time, slow down to a stop, reverse direction, accelerate to close the speed of light again, move on uniformly for some time, slow down and return together. According to special relativity, each pilot says that the other has aged more slowly and will be younger on the return. Because of the perfect symmetry of the arrangement, this can be nothing other than a genuine contradiction.
This “paradox” is usually presented in a non-symmetrical form. The one twin stays home on earth while the other goes off in a rocket and returns. Relativists resolve the paradox by saying that the twin who stayed at home remained at rest or in a state of uniform motion in space while the other was subjected to forces during acceleration and deceleration. So he’s the one who really moved, and he will indeed be younger than his brother when he returns home. Here relativists resort to the concept of absolute space (or ether), which Einstein’s theory was supposed to make “superfluous.”
Here is a contradiction involving length contraction that might be called “the incredible shrinking bobsled contradiction”: A bobsled is made to slide in a long straight frictionless track. At midlength along the track a hole made equal to the length of the

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bobsled when the bobsled is at rest in the track. The bobsled is then taken to the end of the track, equipped with rockets, and accelerated down the track to close to the speed of light. An observer sitting at rest alongside the track will observe that the bobsled is shorter than the hole and that the bobsled will fall through the hole. The pilot of the bobsled will find the hole much shorter than the bobsled and the bobsled will pass right over the hole.
These and other inconsistencies in the special theory of relativity call for a rethinking of the problem of relative versus absolute motion.
Special Relativity without Contradictions
The most fundamental formulae of field electrodynamics are Maxwell’s four field equations and Lorentz’s force equation. Maxwell’s equations describe the electric and magnetic fields of a source relative to the source. The Lorentz force equation describes the effects of an electromagnetic field on an electrically charged body moving relative to the source of the field. If the principle of relativity is a genuine feature of nature, what can we learn about nature by applying it directly to Maxwell’s and Lorentz’s equations? That and related questions were investigated by Nizar Hamdan in a series of five papers [30]. Hamdan conceives a dynamic relativity that is free of the contractions inherent in Einstein’s kinematic relativity. He obtains the verified results of special relativity without employing its bizarre conceptions of space and time.
Hamdan distinguishes his principle of relativity from that of Einstein. For Einstein, a fundamental physical law is one that remains invariant (that is, retains the same mathematical form) under a Lorentz transformation, which is a set of transformation formulas that give Maxwell’s equations the same mathematical form in all frames of reference moving in uniform linear motion with respect to each other. For Hamdan, any physical equation is a candidate to describe a fundamental law. The Lorentz

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transformation is a transformation of space and time coordinates that leads to the notions of length contraction and time dilation. Hamdan removes Einstein’s constraint and thereby eliminates the need to refer to the Lorentz space-time transformation and its associated contradictions. For a given physical equation, the transformation rule is not imposed; rather it is sought.
Hamdan arrives at the constancy of the speed of light for all observers by applying his principle of relativity to both the Lorentz force law [30a] and to Maxwell’s field equations [30e]. He shows that the constancy of the speed of light for all observers is a consequence of the relativity principle alone and need not be postulated additionally as Einstein did. But he argues that the constancy of the speed of light is not a kinematic effect, as it is in the special theory of relativity, but a dynamic effect. That is, it is not an effect of the properties of motion but an effect of the properties of light itself. The wavelength (which is inversely proportional to the momentum) and frequency (which is proportional to the energy) of a photon of light may vary from observer to observer, but their product (which is the speed of light) remains constant. In Hamdan’s analysis the notions of length contraction and time dilation and the contradictions associated with them have no physical significance. They have no significance because they are rooted in the notion that the constancy of light is a kinematic phenomenon, as Einstein proposed. If the constancy of the speed of light is a dynamic phenomenon, as Hamdan proposed, then length contraction and time dilation do not follow as necessary consequences.
In both Einstein’s and Hamdan’s dynamics a massive body cannot move in any inertial frame faster than the speed of light. But in both relativities massless signals can move faster than the speed of light within an inertial frame or between inertial frames. It seems that gravitational and electromagnetic interactions are such massless signals and thus are not constrained to speeds less than or equal to the speed of light.
In Hamdan’s analysis the fundamental entities in the universe are energy and momentum. Space, time and mass are secondary. This is consistent with the scholastic notion that matter and

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motion are the two fundamental created entities. Place, time duration and quantity of matter are accidents of matter and motion. Hamdan shows that the invariance of the speed of light is rooted in the transformation properties of its energy and momentum for observers in relative motion. From his application of the relativity principle alone to the Lorentz force alone he arrives at the two great triumphs of Einstein’s theory: the formula describing the increase of inertial mass with velocity and the formula identifying inertial mass and energy. Those formulas are also rooted in the transformation properties of energy and momentum and manifest a close relationship between inertial and electromagnetic phenomena.
Einstein altered classical mechanics to make it compatible with the Lorentz transformation. Newton’s second law conformed if the velocity-dependent mass formula is used to define momentum rather than a velocity-independent mass. Hamdan obtains the same mechanical results as special relativity without the use of the Lorentz transformation [30c]. He first argues that his principle of relativity calls for a variable mass in Newton’s second law. He argues that the variation of mass with velocity is a dynamical effect, not a kinematical one, as in special relativity. The work performed on a massive body by a force changing its location is absorbed as kinetic energy, which is expressed in the form of mass. The kinetic energy does not reside in the motion but in the body; it is the material body itself that has the ability to do work, not its motion.
It must be admitted that in Einstein’s analyses the connection of mechanics and electrodynamics seems more natural. The speed of light enters into the mechanical calculations by means of the Lorentz transformation, which connects with Maxwell’s equations. However, in Hamdan’s analyses the speed of light seems to be artificially introduced.
Proponents of Einstein’s theory of special relativity claim that time dilation is experimentally confirmed. They point especially to two phenomena as confirming it: the transverse Doppler effect and the radioactive decay of mesons. The transverse Doppler

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effect is a shift in the wavelength of light that occurs to an observer viewing light from a source moving perpendicular to his line of sight. The transverse Doppler effect is predicted by the special relativity theory. There are explanations for the effect, however, that employ classical physics [see citations in 30d], but relativists have long claimed it as a unique feature of special relativity. The transverse Doppler effect is attributed in Einstein’s relativity to time dilation. The transverse Doppler effect has been observed experimentally, and relativists claim that time dilation is thereby empirically confirmed. In his fourth paper [30d] Hamdan explains the effect using only the Lorentz force law and the principle of relativity, without the notion of time dilation. He thus shows that the transverse Doppler shift is not a kinematic effect, that is, it is not caused by motion; but it is a dynamic effect, an effect of the nature of light.
The transverse Doppler effect as a dynamic effect has a mechanical analog. The longitudinal tension in a cord held to a fixed center of rest might be caused by one of two things. First, it might be caused by a mass at the other end of the cord that is trying to increase its distance from the center of rest in the direction in which the cord is stretched. Second, it might be caused by a mass at the other end of the cord that is traveling in a circle around the center of rest, perpendicular to the direction in which the cord is stretched. If the mass was moving in a circle and the cord was very long and the speed of rotation was very slow, an observer at the center of rest might not be able to perceive the angular rotation of the cord and would, therefore, be unable to discern the cause of the tension.
Experiments have been performed in which radioactive mesons are accelerated to high velocities in particle accelerators. In those experiments it has been observed that the half-lives of the accelerated mesons are greater than the half-lives of mesons at rest in the laboratory. Relativists claim that those experiments are confirmations of time dilation. They say that the experiments show that clocks “riding” on the accelerated mesons run slower than the clocks at rest in the laboratory. However, an analysis like Hamdan’s analysis of the transverse Doppler effect might possibly

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explain that as an effect caused by the difference in internal energy between the speeding mesons and those at rest. The speeding mesons would have larger masses, and the larger masses might be associated with stronger binding forces, which mean greater halflives.
E.A. Milne [31, pp. 34–48] argues that the Lorentz transformation formulas of special relativity express kinematical observational effects connected with the finite speed of light and do not reveal any deep secrets about the nature of space and time.
And now a few words about energy and momentum, the fundamental entities in Hamdan’s perception of relativity: First, let us consider the intangible nature of energy. Recall that energy is the ability of something to do work on a material body. This “ability” is communicated, without loss, to the body on which it works. James Clerk Maxwell observed that energy is not capable of identification. He states:
We cannot identify a particular portion of energy, or trace it through its transformations. It has no individual existence, such as that which we attribute to particular portions of matter.
The transactions of the material universe appear to be conducted, as it were, on a system of credit (except perhaps that credit can be artificially increased, or inflated). Each transaction consists of the transfer of so much credit or energy from one body to another. The act of transfer or payment is called work. The energy does not retain any character by which it can be identified when it passes from one form to another. [9, p. 90]
The modern notion of energy echoes the scholastic notion of prime matter, which is matter out-of-which something exists. Prime matter is that which is in potency to substantial existence. It is pure potency because it has the potential to be any material thing, and it is the principle of permanence because it perseveres through any change. It exists separately in the mind only. It does

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not exist separately in reality. It has no form in its rational character, yet it is never stripped away from form in reality. St. Thomas Aquinas in On the Principles of Nature points out that prime matter is “numerically one in all things.” That is, it “exists without dispositions making it numerically different.” Prime matter, like energy, is not capable of identification because it does not possess a character that can be identified when it passes from one form to another. And energy is like prime matter because it does not exist in itself but only in physical entities; it perseveres through physical transformations without a specific identity.
Another important property of energy is that it is strictly relative. The calculation of energy transfer takes into account only the communication of “parcels” of energy between one thing and another. It makes no use of an absolute source of energy. Maxwell points out that we cannot know the absolute energy of a body (if indeed such a notion makes sense):
The energy of a material system can only be estimated in a relative manner.
In the first place, though the energy of the motion of the parts relative to the centre of mass of the system may be accurately defined, the whole energy consists of this together with the energy of a mass equal to that of the whole system moving with the velocity of the centre of mass. Now this latter velocity—that of the centre of mass—can be estimated only with reference to some body external to the system, and the value which we assign to this velocity will be different according to the body which we select as our origin.
Hence the estimated kinetic energy of a material system contains a part, the value of which cannot be determined except by the arbitrary selection of an origin. The only origin which would not be arbitrary is the centre of mass of the material universe, but this is a point the position and motion of which are quite unknown to us. [9, pp. 90-91]

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One could go further and say that the notion of absolute energy is meaningless because the notion of motion of the center of mass of the universe means its motion through absolute space, which is meaningless.
Maxwell gives us another reason for considering the notion of absolute energy meaningless, although he does not reject the idea:
But the energy of a material system is indeterminate for another reason. We cannot reduce the system to a state in which it has no energy, and any energy which is never removed from the system must remain unperceived by us, for it is only as it enters or leaves the system that we can take any account of it.
We must, therefore, regard the energy of a material system as a quantity of which we may ascertain the increase or diminution as the system passes from one definite condition to another. The absolute value of the energy in the standard condition is unknown to us, and it would be of no value to us if we did know it, as all phenomena depend on the variations of the energy and not on its absolute value. [9, p. 91]
The relative nature of energy is manifested in the observation that its transfer is a local phenomenon; that is, the giver and the receiver of a “parcel” of energy are in the same place at time of the transaction.
Adding the accidents of place and time duration to the notion of energy leads to the complementary fundamental notion of momentum. If energy corresponds to matter in place, momentum corresponds to matter in motion. Momentum has the same relation to time as energy has to position, namely, the rate of change of the momentum of a body with respect to time is the same as the rate of change of its energy with respect to position. And like energy, it is a relative quantity that is conserved in energy transactions.

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Again, recall that the energy possessed by a body actually resides in the body itself and not in its position or speed, although it depends on them in an accidental way. The same is true for momentum.
General Relativity and Absolute Space
In his theory of general relativity, Albert Einstein proceeded to formulate the laws of physics so that they look the same in all coordinate systems moving relative to each other, whether uniformly or nonuniformly, linearly or nonlinearly. To do this the notions of absolute motion in space and absolute rest in space had to be eliminated. This was made possible by the equivalence of inertial and gravitational mass, which allowed for gravity to eliminate absolute motion. Motion of massive bodies could then be looked at as being determined by the geometry of space-time that was shaped by gravitating masses. The first law to be formulated for all possible coordinate systems had to be that of gravity itself because of its central importance. Einstein put a lot of effort into this problem. His work resulted in the formulation of his famous gravitational field equations, a set of ten differential equations for the metric of space-time. These are the equations modern cosmologists use to model the universe.
Einstein was strongly influenced by the thinking of Ernst Mach. He wanted to incorporate Mach’s ideas into his theory of general relativity but was not able to do so satisfactorily [see 2, pp. 192-199; 8, pp. 125-159; 11, pp. 242-244; 28. p. 6; 32, pp. 284288]. For Mach, the concept of space as an independent entity has no place in physics, and Einstein did not succeed in removing it. In his theory of general relativity, Einstein did not eliminate space and time as independent entities even though he combined them into space-time. But he still treated space and time as realities that are independent of the matter that determines them. So one could contemplate removing all the matter from the universe and yet have space and time remain. That is metaphysical thinking, not physical thinking. But his space-time differed from absolute space in that it was something that both acted and was acted upon.

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Masses in their passive inertial role are “guided” by space-time and in their active gravitational role “shape” space-time. General relativity did not eliminate space, but it did deprive space of its Newtonian absoluteness by giving it a passive quality.
The reason that Einstein failed to eliminate an independent space-time seems to be that he actually started out with one. In general relativity Einstein starts out with a four-dimensional spacetime manifold that is anchored to nothing. A manifold is a topological space (a continuous set of points with certain properties) with a Euclidean structure. That means that it is a space on which a constant Pythagorean metric is imposed (the metric gives a non-negative number for the distance, or separation, between two points). That Euclidean structure is then deformed by matter/energy imbedded in the space. This deformation is manifested by a varying metric described by his ten gravitational field equations. Einstein’s space-time is not generated by matter/energy but is co-existent with it and given shape by it.
At this point let us recall what was said about Newtonian absolute space. It was mentioned earlier that in empty Newtonian absolute space no coordinate grid can be established because there is no place to anchor such a grid and no standard for the measure of distance. Therefore the concepts of trajectory and straight line are meaningless. Newtonian absolute space might be called a reverse abstraction. The notion of extension is abstracted from material bodies, in which it has real intrinsic meaning, and applied to empty space, in which it has no real intrinsic meaning. Extension is an accident of matter, whose ultimate standard of measurement is a material measuring rod. The notion of extension in empty space without matter is meaningless because it an accident without a subject in which to inhere. Furthermore, the notion of three-dimensional emptiness is theologically objectionable when it is paired with the notion that before creation empty three-dimensional space existed alongside God as a parallel infinity. As previously noted, sound theology informs us that before creation there was no infinite three-dimensional void

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into which God injected matter. Before creation there was nothing but God.
The Catholic Encyclopedia (1914) nicely expresses the position of the scholastic masters on absolute space:
The traditional philosophy of the Catholic schools rejects absolute space. Newton's idea is incompatible with the concept which the great doctors of the school, following Aristotle, formed of quantity. Suarez declares that space is only "a conceptual entity [ens rationis], not, however, formed at will like chimeras, but extracted from bodies, which by their extension are capable of constituting real spaces" (Met. disp., 51). The expression ens rationis may be equivocal, but it expresses somewhat exaggeratedly the very active part played by the human intellect in the construction of space. Space is not material bodies themselves, since it appears to be rather a receptacle containing them. From this point of view it must be pure extension, an unqualified quantity. In the strict sense of the terms a quantity without quality is contradictory; for quantity is only the multiplicity of the homogeneous parts in the unity of a body; it is the distribution of an essence, simple in its formal determination. Multiplicity implies a thing that is multiplied, and distribution something that is distributed. Every quantity is the quantity of something; all extension is therefore, in itself, the extension of an extended substance. Yet quantity is something more than a modal accident; it is in truth the absolute accident par excellence; it confers on a substance a perfection such that, granted the existence of a substance, the corporeal body is measured by its quantity. It is none the less true that quantity postulates a quantitative substance; and, in a sense, entirely different however from the fancies of ancient physics, it may always be said that an empty quantity is a contradiction in terms. From this we must conclude that extension is only a derivative of quantity; a nonqualified extension, pure extension, pure space in the reality of the corporeal world is contradictory. We

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conceive it, however, and what is, properly speaking, contradictory is inconceivable. The contradiction arises when we add the condition of existence to pure space. Space is not contradictory in the mind, though it would be contradictory in the real world, because space is an abstraction. Extension is always the extension of something; but it is not the thing extended. Mentally we can separate extension from the substances from which we distinguish it; and it is extension thus separated, conceived apart, which constitutes the space of the universe. Space is therefore as real, as objective, as the corporeal world itself, but in itself it exists apart only in the human mind, seeing that in the reality of existing things it is only the extension of bodies themselves. [16, article entitled “Space”]
The above critique of Newton’s absolute space can be also applied to the inertial spaces of special relativity because conceptually they are either simply subdivisions of absolute space that move in absolute space or, more confusing yet, an infinite set of independent absolute spaces that move at all speeds relative to one another.
Einstein’s four-dimensional space-time is also subject to the same critique. It is in no way clear how Einstein makes the transition from topological space to physical space. In his paper “The Foundation of the General Theory of Relativity” (1916) Einstein states that his “introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences.” The “coincidences” are “the meeting of the material points of our measuring instruments with other material points” [22, p. 117]. But he treats the reference (coordinate) system that “facilitates” the description of such coincidence as a free agent, not as something that depends on those coincidences for its existence. Thus it differs little in its conceptual fundamentals from Newton’s absolute space. Further, in general relativity, matter/energy imposes a metric, which is accidental, on the four-dimensional manifold (system of

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reference), which is a mathematical (mental) object that has no substantial existence.
General relativity failed to give a cosmic origin to the inertia of a body. [see 8, pp. 148-159] According to Mach’s principle, a body in otherwise empty space should possess no inertia. But Einstein was not able to achieve that result. According to general relativity such a body would possess inertia. Also, general relativity predicts that the surface of a rotating pail of water would retain its concave shape if the rest of the matter in the universe disappeared. That too violates Mach’s principle. Further, although general relativity employs the proportionality of gravitational and inertial mass, it is unable to give a reason for it.
St. Thomas Aquinas said that space is a privation and not a negation, that is, it is the absence of matter from where it ought to be and not its absolute absence. He said that before the creation of the world there was no space because there were no “real dimensions” and no “place” [4, p.97; 5, Part I, Q. 46, A. 1, Reply Obj. 4]. One can apply St. Thomas’ reasoning to the consequences of general relativity. The fact that in general relativity a body has inertia in the absence of other masses implies that there is a coordinate system in which acceleration is measured. But it is impossible to construct such a coordinate system because there are no physical objects on which to fix it (no “real dimensions”) and no measuring rod to measure it. The isolated body itself could not be a measuring rod because to make measurements it would have to be moved from one place to another. But in such a situation there is no such thing as “place,” and thus moving it from place to place is meaningless. Also, the object itself could not be the origin of a coordinate system in which its acceleration is measured because the body always remains at the origin.
It seems that freestanding (independent of matter) coordinate systems have introduced immense complications and confusion into physics that far outweigh any simplifications they may have produced. J. B. Barbour noted:
Einstein himself commented [citation given] that the simplest way of realizing the aim of the theory of

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relativity would be to formulate the laws of motion directly and ab initio in terms of relative distances and velocities—nothing else should appear in the theory. He gave us the reason for not choosing this route its impracticability. In his view the history of science had demonstrated the practical impossibility of dispensing with coordinate systems. He therefore adopted an indirect approach and was guided, it seems, more by gut intuition than a clear formulation of principles that would of necessity lead to the realization of his aims. [28, p. 6]
This leads us into the subject of the next chapter, namely, relational mechanics, in which the laws of motion are formulated directly in terms of relative distances, velocities and accelerations.

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CHAPTER 5
THE LOGIC OF RELATIONAL PHYSICS
Relational Mechanics
The Catholic Encyclopedia (1914) reduces the views of philosophers concerning space to two fundamental notions:
To recall all the successive explanations of the nature of real space given by the great philosophers it would be necessary to go through the history of philosophy; but, leaving aside the complete negation of extension, all the doctrines, from Hesiod (cf. Aristotle, IV Phys., vi, 213b) to our day, fluctuate between the idea of absolute space, a real substance independent of the bodies it contains, and purely relative space, a mental fiction based on the real extension of material bodies. The most radical expressions of these two conflicting views are those of Newton and Clarke, on the one hand, who consider space as the sensorium of God, and on the other, of Leibniz, who asserts that there is no space independent of extended bodies, and reduces it to "the order of co-existing things." [16, article entitled “Space”]
In his much cited foreword to Max Jammer’s Concepts of Space: The History of Theories of Space in Physics [2], Albert Einstein clearly and succinctly presented those two conflicting notions of space as “container of all material objects” and as “positional quality of the world of material objects.” Philosophers and historians of science use the word “absolute” space when referring to the first notion and “relational” space when referring to the second. The two notions of space give rise to two different ways of doing physics. This first way employs the notion of absolute space and its derivatives, such as inertial spaces, and the consequent notion of
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freestanding coordinate systems, which is the cause of much confused thinking in physical matters. The second employs only direct physical quantities and their relations, without the intermediary of freestanding coordinate systems.
Albert Einstein recognized the limitations of using the elusive notion of freestanding coordinate systems in physical systems but argued that it was unavoidable:
We want to distinguish more clearly between quantities that belong to a physical system as such (are independent of the choice of coordinate system) and quantities that depend on the coordinate system. One’s initial reaction would be to require that physics should introduce in its laws only the quantities of the first kind. However, it has been found that this approach cannot be realized in practice, as the development of classical mechanics has already clearly shown. One could, for example, think—and this was actually done—of introducing the laws of mechanics only by the distances of material points from each other instead of coordinates; a priori one could expect that in this manner the aim of the theory of relativity should be most readily achieved. However, the scientific development has not confirmed this conjecture. It cannot dispense with coordinate systems and must therefore make use in the coordinates of quantities that cannot be regarded as the results of definable measurements. [8, p. 147]
It seems strange that Einstein should so readily dismiss the employment of relational quantities, considering the conceptual simplification they offer, for simplification is what he sought. Instead he pursued the complex way to simplification. He describes the agony of his pursuit for the equations of general relativity as follows: “In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion and the final emergence