zotero/storage/II8QYIXX/.zotero-ft-cache

Questioning Einstein
Is Relativity Necessary?
Tom Bethell

Library of Congress Control Number: 2009923278

Tom Bethell Questioning Einstein: Is Relativity Necessary

Includes bibliographic references

ISBN

10-digit: 0-9714845-9-7

13-digit: 978-0-971-48459-7

1.

Relativity

2.

Michelson-Morley

3.

Michelson-Gale

Copyright © 2009 by Tom Bethell

All Rights Reserved. This book or any part thereof must not be reproduced by microfilm, photostat, scanner, or any other process without written permission of the publisher.
Printed in the USA Cover design by Brian Dunbar
Cover photos from http://hubblesite.org. Material from Space Telescope Science Institute (STScI) prepared under NASA contract NAS5-26555
Vales Lake Publishing, LLC P.O. Box 7609 Pueblo West, CO 81007-0609 www.valeslake.com SAN: 2 5 4—2 5 3 A

Acknowledgments
My principal debt is to Howard Hayden. Without his willingness to answer my questions, I would not have been able to finish this book. In fact, I would not have been able to start it. Petr Beckmann had shown me the big picture, but at his death there were hundreds of details that I needed to discuss, and understand. I believe that only Howard Hayden could have played that role, because he, perhaps uniquely, understood both Petr’s argument and the opposing orthodoxy. It was fortunate indeed that Petr had brought Howard around to his point of view. I doubt if anyone else could have filled in for him; not just in encouraging me, but in strengthening Petr’s own case with additional physical facts, arguments and details.
I soon learned that very few physicists are inclined to debate these issues. It’s not that they are unwilling to talk to a layman. The problem is that, where Einstein’s relativity is concerned, they have been trained to disregard all dissenting views. Only the strictest orthodoxy is allowed. Physics Ph.D.’s will have taken a relativity course, learned the Lorentz Transformations and so on. But the theory’s premises won’t be questioned. If new recruits to the academy pursue an academic career, they won’t be open to any dissent or doubt about special relativity. Inconsistent experimental results will somehow lie outside their field of vision.
Still, I have reached a number of professional physicists, usually through the air waves. (Should I call it the ether?) Among them, a few good men have been willing to answer questions. Some may prefer not to be named, and none should be suspected of heterodoxy. I would like to thank Ralph Baierlein in particular. I have also had helpful conversations or email exchanges with John Stachel, Francis Everitt, John L. Hall, Edward Teller and one or two others. In England, I have benefited from many stimulating conversations with Stephen Botcherby.
Mainly, however, I am in Howard Hayden’s debt, and so is Petr Beckmann.

Table of Contents
ACKNOWLEDGMENTS
PREFACE
Notes to Preface
INTRODUCTION BY HOWARD C. HAYDEN
CHAPTER 1. RELATIVELY EASY
On the Train Happiest Thought Electricity and Magnetism Pursuit of Simplicity Notes: Chapter 1
CHAPTER 2. THE MAGICIAN
The Central Difficulty Copernicus Revisited? Special and General Theories Notes Chapter 2
CHAPTER 3. MICHELSON-MORLEY
One-way Speed of Light “To see if light travels with the same velocity…” Translation and Rotation Michelson Papers Discarded Notes: Chapter 3
CHAPTER 4. LORENTZ AND POINCARÉ
Henri Poincaré Notes: Chapter 4
CHAPTER 5. THE SPECIAL THEORY OF RELATIVITY
Einstein’s Stage Magic The Second Postulate Revolution in Physics Deformation of Space and Time Observer-Dependent Reality Alpha and Omega Notes Chapter 5
CHAPTER 6. HOLTON’S CRUSADE
Einstein as Experimentalist Does Not Remember if he Knew Michelson pedagogically easier Notes: Chapter 6
CHAPTER 7. ON WHAT EVIDENCE?
Faraday’s Law of Induction Thought Experiments Double Stars Role of Maxwell Equations

Notes: Chapter 7
CHAPTER 8. MYSTERY OF MASS
Mass Increase, Pre-relativity Newton, Mass and Fundamentals Real Interactions Notes Chapter 8
CHAPTER 9. E = MC2
What Is Energy? Lewis’s Derivation Baierlein’s Objection E=mc2 and Nuclear Fission Notes: Chapter 9
CHAPTER 10. STELLAR ABERRATION
A Journeying Thing Breeze through the Trees Transitional Zone Notes: Chapter 10
CHAPTER 11. SPECTROSCOPIC BINARIES
Binary Mizar A Ritz Goes Ballistic Aberration or Doppler? Notes: Chapter 11
CHAPTER 12. ON BECKMANN’S THEORY
Pokorny in Prague Great Minds Alike Special, General and Real Notes Chapter 12
CHAPTER 13. THE SAGNAC EXPERIMENT
Notes Chapter 13
CHAPTER 14. THE MICHELSON-GALE EXPERIMENT
The Most Grandiose Experiment Michelson Not Enthusiastic Notes: Chapter 14
CHAPTER 15. MESONS, MUONS AND TIME DILATION
Ives-Stilwell Experiment Contraction not Observed Notes: Chapter 15
CHAPTER 16. HAFELE AND KEATING
Expect the Unexpected Einstein’s Theory Amended It’s the Clocks, Not Time Results Known Beforehand Notes Chapter 16
CHAPTER 17. GLOBAL POSITIONING SYSTEM
Relativistic Corrections?

Earth-Centered Frame Again Notes Chapter 17
CHAPTER 18. THE GENERAL THEORY
The Principle of Equivalence Light Rays in Gravitational Fields Notes Chapter 18
CHAPTER 19. BENDING OF LIGHT RAYS
Bending of starlight in a gravitational field Gravitational Red-shift Shapiro Time Delay Relativistically Incorrect Notes: Chapter 19
CHAPTER 20. MERCURY’S ORBIT
Pomeranian Schoolmaster Speed of Gravity Notes: Chapter 20
CHAPTER 21. EINSTEIN’S NEW ETHER
Lorentz’s Role Notes Chapter 21
CHAPTER 22. BRILLET AND HALL
Notes Chapter 22
CHAPTER 23. A HISTORICAL PARALLEL
Parallels and Contrasts Einstein’s Priority? Notes Chapter 23
CHAPTER 24. SYNOPSIS
THE AUTHOR
VALES LAKE PUBLISHING

Preface
The argument of this book is that the experimental consequences of relativity theory can also be reached without relativity. The equation E = mc2 was deduced from relativity theory, but it could also be reached without it and it was so derived as early as 1908. Einstein himself later arrived at the equation without relativity, and he called it his “elementary derivation.”
Readers should be warned that this book is the work of a journalist. I have been helped by professional physicists but of course that does not exclude the possibility, even the likelihood, that it contains errors. A nonspecialist has more freedom, however, and is less constrained by peer review.
My first guide was Petr Beckmann, a good friend who taught electrical engineering at the University of Colorado for twenty years. It was he who proposed the alternative to Einstein and the thesis of this book. He also made that case in a book published in 1987, Einstein Plus Two.
Petr Beckmann’s incorruptible skepticism was an inspiration to me. Born in Prague in 1924, he received his Ph.D. in Electrical Engineering from Prague Technical University, then a Doctorate of Science from the Czechoslovak Academy of Sciences. He defected to the United States in 1963, taught at the University of Colorado, and died in Boulder in 1993. He published 60 scientific papers, mostly on electromagnetics and probability theory. His popular book The History of Pi reached many readers. His more technical works included The Scattering of Electromagnetic Waves from Rough Surfaces (1963), the Depolarization of Electromagnetic Waves, and The Structure of Language (1973).
He took early retirement in 1981 so that he could concentrate on the book about relativity that he had long planned to write.
Almost as soon as he encountered the special theory of relativity he considered it unsatisfactory, and that conviction never left him. In Einstein Plus Two he outlined a theory that is simpler than Einstein’s, and (he argued) consistent with the experimental facts. It dispenses with relativity. At the same time, it accounts for two additional phenomena, ranging from

electrons to planets. They are the separation of electron orbits and the Titius-Bode series, which describes planetary distances from the sun, or lunar distances from planets. “No satisfactory explanation of the law has ever been given,” Beckmann wrote.
I was privileged to have dozens of conversations and interviews with Petr. He talked about relativity, and he told me the story of his life. He described the high school he had attended in Birmingham, England. Along with other Jewish refugees from Nazi-controlled Czechoslovakia, he had been among the “kinder-transport” of young people sent to England at the beginning of World War II. He told me of his return to a post-war Czechoslovakia, by then Communist, as were his parents. While Petr was lecturing in Colorado in 1963, his father died and he decided to stay in the United States.
When Petr talked about relativity, the difficulties that I had already encountered in “Easy Einstein” books began to melt away. Explanation replaced description, and the natural world, as I saw it, was flooded with light. But his book could not easily convey that, for it was mostly written in the technical language of mathematical physics.
Readers of his newsletter Access to Energy will know that Beckmann was a talented and entertaining writer. He could have written a popular account himself, and he considered doing so. But he believed that his ideas had a better chance of being accepted if expressed in technical language. In that he was disappointed. His book was neither criticized not refuted. Most physicists probably never even heard about it.
By the time he died, I had interviewed him extensively, but I also imagined that he would be there to review anything that I wrote. Under his guidance I had written a few articles on relativity for “lay” readers, but I hadn’t begun work on the book. Earlier, however, Beckmann had asked several figures in the academy to review the manuscript of Einstein Plus Two. One was Howard Hayden, a professor of physics at the University of Connecticut.
At first Hayden supposed that it would be only too easy to find errors. A bold challenge to the orthodoxy, Beckmann’s book was hardly believable in places. Special relativity was only tenuously confirmed by the facts, he said. When Hayden read that Einstein’s claim about the constancy of the speed of light has not been unambiguously shown to be true, he hunted for the experiments that surely would prove Beckmann wrong.

They turned out to be elusive. After much searching, Hayden concluded that they didn’t exist. He, too, became convinced that the special theory of relativity, contrary to the way it is portrayed, is based on shaky foundations. He made further discoveries of his own, and in the early 1990s, he gave talks about these ideas to the physics departments of universities in New England. No one even tried to refute what Hayden said.
One of Beckmann’s challenges came with a monetary reward, and its details are worth describing. Hayden and Beckmann offered two thousand dollars to the first person who could show where (in the scientific literature) it had been demonstrated that the speed of light is the same east to west as it is west to east. Robert Pool, a journalist at Science, heard of the offer, and published it in Science magazine. That was in 1990 (vol. 250, page 1208, for those who want to look it up). It was worded as follows:
Petr Beckmann, professor emeritus of electrical engineering at the University of Colorado, and Howard Hayden, a physicist at the University of Connecticut, will pay $2000 to the first person who offers a valid optical experiment proving that the speed of light on Earth is the same east-to-west as it is west-to-east, within 50 meters per second. The winner doesn’t even have to have done the experiment personally.
There were no takers. A reporter with the Los Angeles Times, Paul Ciotti, contacted the University of Washington’s Clifford Will, an acknowledged expert on relativity, and mentioned the offer. Will’s Was Einstein Right? had been published a few years earlier. The offer had a deadline, however. The experiment had to have been published before a certain date. Will responded that without this restriction, there were experiments that would qualify for the reward. Hayden then updated the offer and mailed it, “Special Offer to Clifford Will.” He received no reply.
It was a key test for Beckmann, because according to his own theory, the speed of light is not the same east to west as it is west to east. There should be a small difference, a function of the earth’s daily rotation.
A recent comment by the famous physicist Stephen Hawking supports this claim. In The Universe in a Nutshell Hawking describes a famous experiment in which two very accurate clocks were flown in opposite directions around the world. “When they met up again the clock that flew toward the east had recorded slightly less time,” Hawking wrote. “This might suggest that if one wanted to live longer, one should keep flying to the east so that the plane’s speed is added to the earth’s rotation.”1
He was being facetious, of course, but asymmetric time-keeping between east-bound and west-bound clocks has been observed and Einstein

had not predicted it. Chapter 16 describes the experiment that Hawking mentions.
By 1990, Petr Beckmann had founded a new physics journal, and he sought contributions from outside the mainstream. Its title was a deliberate oxymoron, although one that would be obscure to most of us: Galilean Electrodynamics. After Beckmann’s death, Hayden continued as its editor. He has since retired from the University of Connecticut and lives in Colorado, where he teaches part-time at a local college. Galilean Electrodynamics has more recently been edited by Cynthia Kolb Whitney, an adjunct professor of physics at Tufts.
Since Petr’s death I have acquired a nodding acquaintance with the world of anti-relativity physics. The encounter has not been encouraging. Those who disagree with Einstein often disagree with one another. No single theory is unanimously accepted. One can sympathize with established physicists who pay little attention. Wading through alternatives in search of the errors they probably contain is a task not to be undertaken lightly. Ignoring the whole sideshow is a time-saving strategy.
For these reasons, arguments against special relativity are not likely to persuade those who teach relativity for a living. As Howard Hayden says, if you mention alternative theories, physicists always respond: “Relativity works. And I am going to stick with it as long as it works.”2
Most observations do seem to conform to the predictions of relativity. I shall also come to anomalies. Hayden’s paper on binary stars, published at about the time that Petr Beckmann died, is of particular importance. On his deathbed Beckmann regarded it as a clear falsification of special relativity.3
The underlying physical reality that the theory asks us to accept is nonetheless strange. It has always seemed so, and now that a hundred years have passed since its publication, that is unlikely to change. But relativity will not be overthrown by the criticism that it seems paradoxical, or that it defies “common sense.” It certainly does, but physicists have little difficulty in brushing such complaints aside.
Change, if it is to come, will have to come from within the physics establishment, and probably as a result of accumulating discrepancies between theory and observation. If so, a consensus could develop around some alternative that resolves the difficulties, making the life of theory

easier for all. Beckmann’s theory is a candidate, although one cannot discount the possibility that a fatal flaw will be detected within it.
Such an upheaval will probably have to be preceded by a period of subterranean discontent within the physics profession. There are few signs of that. But storms sometimes blow up quickly, and it was interesting to read in a New York Times article not long ago that “in science no truth is forever, not even perhaps Einstein’s theory of relativity, the pillar of modernity that gave us E = mc2.”4

Notes to Preface

1

Stephen Hawking, The Universe in a Nutshell, Bantam Press, 2001, p. 9.

2

All quotations from Howard Hayden are taken from the many conversations I have had

with him, unless more specifically noted.

3

Howard Hayden, “Stellar Aberration,” Galilean Electrodynamics, v. 4 no. 5, Sept/Oct

1993, p. 92.

4

Dennis Overbye, “E and mc2: Equality, It Seems, Is Relative,” New York Times,

December 31, 2002.

Petr Beckmann (1924-1993)

Introduction by Howard C. Hayden
Hayden is an emeritus member of the Physics Department at the University of Connecticut, Storrs. He taught there from 1968 to 1999
I first became acquainted with Petr Beckmann when I read his History of Pi, a terrific book. I also read his Health Hazards of NOT Going Nuclear and subscribed to his newsletter, Access to Energy. I had long been interested in energy issues, and it was through our numerous exchanges that we got to know one another. Then, one day, he asked if I would read a book he was writing about something else—relativity theory. He wanted me, as a physicist of essentially standard education and training, to probe the book for errors. Einstein had postulated in his special theory that the speed of light is a constant, and almost everyone in physics believes that. But Beckmann disputed it. He was challenging a basic tenet of relativity, in other words.
I could see from his books that he had his head on straight, but I also knew that he was an electrical engineer, so maybe he hadn’t taken the standard physics courses. But he was inclined to trust experiment over theory, which was a good sign, and he was certainly intelligent enough to understand the experiments. So I agreed. If I could stop him from embarrassing himself, I would be doing him a kindness. All too often, people with a brief against Einstein are only acquainted with papers written before about 1920. I had in mind that I would easily be able to find the data that he might have missed.
When I got hold of the book I realized that he understood these experiments perfectly well. An initial reading suggested that, although he might be proved wrong in the details, he was raising issues that were both fundamental and that I had never encountered before.
Let me go over the background. In the 1880s Albert Michelson thought of a way to detect the Earth’s motion through the “ether.” The ether was to light what the air is to sound—the medium that vibrates as waves pass through it. In its orbital motion around the Sun, the Earth moved through this ether, it was assumed, and Michelson knew how to make this motion visible with light rays. The instrument he perfected was called an

interferometer. Similar devices are used today. They produce a set of parallel, light-and-dark interference lines. If the Earth moves through the ether, as everyone believed, the vertical lines should shift right or left by a measurable amount when the table is rotated.
Michelson tested this in 1887 in his experiment with Edward Morley. But no fringe shift could be seen. The world of physics was thrown into confusion. Then Einstein resolved it with his 1905 paper introducing special relativity. He proposed that the speed of light is constant in all directions, and if that were so, there would be no fringe shift. In the same paper he also decided that the ether itself was “superfluous.”
In his book Beckmann restored the ether that Einstein had discarded, but with a new interpretation. In the old view, the ether had been construed as one vast, rarefied substance that filled all of space uniformly. In Beckmann’s theory, it was simply the dominant gravitational field. On the Earth, obviously, the dominant field is that of the Earth itself. It merges with the Sun’s field somewhere beyond the orbit of the moon, and then the field of the Sun becomes dominant. And so on.
That would immediately explain why Michelson had been unable to detect any motion through the ether. Our gravitational field always accompanies us, as a runner’s shadow accompanies the runner. Beckmann’s theory can be classified as an “entrained ether” theory. In its orbital motion, the Earth carries its “ether” along with it. But Beckmann also argued that the Earth’s gravitational field does not swing around with the Earth in its daily rotation. If so, the Earth constantly rotates “through” its gravitational field.
Imagine a woman with a circular waist wearing a hoop skirt. She is the “earth” and her skirt is the “field.” As she walks forward, she pirouettes. But, if we eliminate friction as much as possible, her skirt does not rotate with her. So there is a “relative velocity” between her waist and her skirt; likewise between the Earth and its gravitational field. Remember, the gravitational field is the medium in which electromagnetic (including light) waves travel. That is Petr Beckmann’s theory in a nutshell.
The Earth’s rotational velocity, in the latitudes where these experiments were carried out, is roughly one hundredth of its orbital velocity. For reasons that need not detain us, that fraction has to be squared in calculating the observable effect in Michelson’s interferometer. So what Beckmann was saying was that the “fringe-shift” that should have appeared

in Michelson’s interferometer was real, but ten thousand times smaller than anticipated. Michelson had been looking for an effect caused by the Earth’s orbital motion. But if Beckmann was right, a much smaller fringe shift caused by the Earth’s rotational velocity should be present.
I had never seen this raised as an issue. And it implies something else. If the local gravitational field is indeed the luminiferous medium, the speed of light must be different to the east and to the west. Observers on the Earth would measure a higher speed of light coming from the east than from the west. The rotational velocity of the Earth would have to be either added to or subtracted from the speed of light.
Now, the constancy of the speed of light was one of Einstein’s most famous claims. It is one of the things that people know about Einstein. And that was where Beckmann’s conflict with Einstein would most obviously arise. So I went to the textbooks and looked up references to all those super high-resolution experiments that would prove the speed of light is not affected by its direction. I would explain it all to Petr and he would accept it and everything would be okay.
The first problem was that no experiments that I could find looked to see if there was any difference between the speed of light to the east and to the west. It would not have been easy to detect anyway. A sensitivity ten thousand times greater than Michelson anticipated could not possibly have been observed with his 1887 equipment. Even today it is not easy.
Eventually, I found the experiment that was said to have the highest sensitivity. That was the Brillet-Hall experiment, published in 1979. It took me some time to get through the jargon and to understand what they had done, but the experiment did have enough sensitivity. What is more, Brillet and Hall did show the effect. It was concealed, although unintentionally, by the way they had presented their data. But it was there. Their results showed the unmistakable signature of the rotation of the Earth. It could be construed as a difference in the speed of light, to the east and west. So I began to think that Petr had a point.
There were other experiments. The first was done in 1913 by Georges Sagnac. He sent light rays clockwise and counterclockwise around a tabletop, from one mirror to the next, and back to the starting point. When he rotated the apparatus, he found the fringe-shift that Michelson had looked for. This was demonstrated even before Einstein had published his general theory of relativity.

There followed another milestone. In 1924, Michelson and Henry Gale sent light in both directions around a large rectangle, with an east-west length of over 2000 feet. It showed a fringe shift, attributable to the rotation of the Earth. But the Einsteinians now took the position that the experiment did not qualify as a valid test of special relativity. Nor did the Sagnac experiment. They had found an escape route, which I shall discuss later.
Petr Beckmann called Michelson-Gale “surely the most grandiose interference experiment ever performed.” I found that it is barely known, even among physicists. In my entire career I have met no more than half a dozen physicists who have heard of it. Misner, Thorne and Wheeler’s big book Gravitation has some 1600 references, but Michelson-Gale is not among them, even though Michelson admitted that the experiment is consistent with general relativity. It is not mentioned in the most recent papers that I have seen, claiming to measure the speed of light in various directions.
Two more experiments demonstrated the different speed of light, east and west. In 1971, Hafele and Keating transported atomic clocks around the world on commercial airliners. They found a directional difference in the clock rates. In 1985, the same asymmetry was confirmed on a global scale by Allan, Weiss and Ashby. They bounced electromagnetic signals off orbiting satellites, and found that it takes about 300 nanoseconds longer for the signal to go around the world eastward than westward.
Intrigued by the consistency of these results, I wrote a paper asking: “Is the speed of light isotropic in the laboratory reference frame?” Isotropic simply means the same in all directions. To me, that sounded like a good scientific question, even if an east-west difference was not something that Einstein expected. I cited the results from every speed-of-light paper that I could find. But I had a hard time getting it published. I tried Physical Review, Physical Review Letters, and The American Journal of Physics. Neither editors nor reviewers considered the east-west question one that was worth asking. Eventually it was published by Physics Essays, a journal that accepts dissident contributions.
At about that time, Petr Beckmann and I offered a reward of $2000 to the first person who could refer us to an experiment demonstrating that the speed of light is the same, east and west, to within 50 meters per second. All we wanted was the reference: journal and page number. A reporter at

Science magazine published the offer, so it became widely known. But no one took us up on it. Two thousand dollars may not be much, but it's a nice pile of change for a graduate student.
Finally, I discovered an earlier experiment using the extremely sensitive Mössbauer effect. It not only had the sensitivity to detect an eastwest differential, but claimed that the speed of light was isotropic to within about two meters per second. But there had been a mistake. The theorist later published an erratum saying he had neglected to take “time dilation” into account. In the end, the experiment showed that the speed of light is not the same in all directions.
I began to think that Petr might be right, but he warned me that I could be scorned by colleagues. My department at the University of Connecticut probably did regard me as if I were on a wild goose chase. But they knew that I was not idle and that I had done extensive reading of the literature. They did not make me feel uncomfortable in the least. In fact I gave a couple of departmental colloquia on the subject.
I also held colloquia with the physics faculties of about half a dozen universities, mostly in New England. The reception was mainly polite, but skeptical. The slides that raised the most incredulity were photographs of the abstract and the graph of the Hafele-Keating experiment, published in Science. The abstract said that for the westbound clocks there was a relativistic time gain, and the graph showed how they deduced that from their data.
Textbooks often mention the experiment, but I have never found one that told what actually happened. What happened was a big surprise. When I presented the facts, it was enough of a surprise that some physicists in the audience suspected I was guilty of misrepresentation. At one Canadian university that shall remain nameless one individual made a parting shot as he stomped out: “You come in and show us all this stuff, but how do we know it hasn’t been refuted by now?” By and large, however, physicists may have shaken their heads but they weren’t hostile. Curiously, however, no one has been able to raise a substantive criticism.
I have added my own little bits and pieces, experimentally. Probably the most interesting was a variation of the Trouton-Noble experiment, done in 1903. Like Michelson-Morley the experiment had a null result, and had seemed to provide strong support for relativity theory. So I redid it, with

about 100,000 times more sensitivity. Yet the effect was still “null.” But I also showed that the experiment was meaningless. Every theory in town (including Beckmann’s) predicted the same outcome. So nothing was being tested. This time, an “orthodox” journal did publish my paper.
Another thing I did was to derive the formula for the bending of starlight—using classical physics. Einstein’s most celebrated moment came when he predicted that starlight would bend slightly when passing the Sun. Photographs during a solar eclipse confirmed that, but you don’t need relativity to get there. Using a more elementary derivation, I showed that a gravitational field has an index of refraction, and that determines by how much a ray of light will be bent.
The idea here is quite simple. In Beckmann’s theory, the luminiferous medium (the gravitational field) is non-uniform. It thins out with distance from the celestial body, whether it be the Sun or the Earth. Light rays do bend by refraction when they move from one medium to another, or move into a medium of different optical density. A pencil in a glass of water appears broken at the surface. My paper on this topic was published in a new journal that Beckmann had founded, Galilean Electrodynamics.
Almost immediately, two physicists from China, Tian and Li, independently derived the same formula by another method, again without relativity. One equation they used was identical to mine for the varying speed of light in a gravitational field, but derived by a different method. They used the conservation of energy and of angular momentum to get the same deflection. I’m glad they did it independently, and that their paper was published by The American Journal of Physics.
So we have Sagnac’s table-top experiment. We have the large-scale experiment by Michelson and Gale. We have Hafele and Keating with their flying clocks. And we have the around-the-world Sagnac experiment, with satellites in Earth orbit. All gave the same result. The best interpretation is that the speed of light for someone on the rotating Earth is c – v to the east, where v is the rotational velocity of the Earth, and c + v to the west. That is the simplest explanation. The speed of light is not a constant, but must have the rotational velocity of the Earth added to or subtracted from it.
Einstein’s relativity theory begins with two simple—if counterintuitive—postulates. Here are some consequences. If A and B are moving uniformly in relation to one another, A thinks that B’s meter stick is shorter than his own, and B thinks that A’s meter stick is shorter than his own. A

thinks that B’s clocks tick more slowly than his own, and B thinks that A’s clocks tick more slowly than his own. Many words have been needed to reassure students that this is required as a result of Einstein’s postulates.
Particles called muons moving at high speed through the atmosphere, or through the vacuum of an accelerator, have longer half-lives than their counterparts at rest in the laboratory. To me, there is nothing odd about that. The bizarre part is that a hypothetical scientist traveling with those high-speed muons would conclude that the muons outside the accelerator have longer half-lives than the ones traveling with him as he speeds along. This latter result has never been tested, and neither has the equally bizarre notion of mutual length contraction.
Relativity theory also predicts dynamical results—things pertaining to mass, momentum, and energy. The most famous is E = mc2. Suffice it to say that these results are the bread and butter not only of the nuclear power industry, but of research accelerators. But physicists should not be too sanguine about how well they support relativity theory. The well-tested equations can be derived without relativity, suggesting that it is not necessary.
So has Einstein been proven wrong? Is Beckmann’s theory right? I do think that Einstein’s theory will have to be modified for various reasons. But that would require a few lessons in electromagnetics—a sermon for another day. Asymmetry in the speed of light does not in itself contradict special relativity, however. The reason is this. Special relativity theory claims only that the speed of light is constant in an inertial reference frame. No acceleration is allowed! Anything that is moving not in a straight line is non-inertial. And the rotating Earth is non-inertial by definition, because centrifugal forces and curvilinear paths are always present. In practice, however, Einsteinians use this escape route only with experimental results that don’t fit the special theory.
The Michelson-Morley experiment, for example, looked for a fringeshift predicted by classical physics. They did not find it, and that made it consistent with special relativity. But if a more accurate Michelson-Morley experiment were to find a fringe shift the Einsteinians would probably conclude that special relativity does not apply in that instance. On the surface of the rotating earth, the experiment would be seen as non-inertial.

Petr Beckmann said somewhere that the special theory is close to being inherently irrefutable. The experiments we are talking about have all been done on the surface of the Earth, or nearly so. And anything in that location is moving around in a big circle and subjected to centrifugal forces. Acceleration is present. So the theory has this built-in “catch” that prevents it from being refuted.
The first time the relativists were confronted with an awkward result— the Sagnac experiment—they responded by pointing to its non-inertial features; the same with Michelson-Gale. Perhaps the best we can do is to get them to admit that their theory is unfalsifiable. And remember, protection against refutation is not a strength but a great weakness of any theory.
As for the general theory of relativity—often called a theory of gravity —it may ultimately be shown that it gives the same results as Beckmann’s, but by a far more circuitous route.
One test that hasn’t been done and could be: a Michelson-Morley experiment on the space shuttle. In low-earth orbit, the shuttle flies at something like seven kilometers per second. This compares to 30 kilometers a second for the Earth’s orbital velocity. With the shuttle moving through the gravitational field at this speed, the fringe shift should be easily detected with modern equipment. Anyway, I predict that a fringe shift would show. The relativists would predict that it wouldn’t. If it did, I further predict they would then say that the reference frame of the shuttle is non-inertial and therefore special relativity was unscathed. So it goes.
What about Beckmann’s theory? I’m not saying it will get off scotfree either. He wrote that he was “not so naïve as to think that the first attempt to move the entire Einstein theory en bloc onto classical ground will turn out to be perfectly correct.” What he aimed for was “the return of physics from description to comprehension.”
Petr’s theory, straightforward in outline, is complicated in the zones where gravitational fields overlap. We are obviously “in” the Earth’s field, for example, but we are also in the Sun’s. As we move away from the Earth, our field gets weaker and soon we come to a place where the “dominant” field switches from that of the Earth to that of the Sun. Beckmann never worked out the mathematics of these intermediate zones. He assumed that they would be complex, but that nothing fundamental about the underlying physics would change. The transitional region is

“marked by the properties of most transients: difficult and of secondary importance,” he wrote.
I will conclude with a few thoughts on stellar aberration, which could cause trouble for relativity. The facts of stellar aberration, known since 1728, are not in dispute. As the Earth moves in its orbit, the position of a star varies slightly, depending on its direction relative to the Earth’s motion. Just as a man running in the rain must incline his umbrella forward if he is to stay dry, so a telescope must be angled forward if the starlight is to enter the telescope. The forward inclination is the angle of aberration. All stars have the same maximum angle of aberration—about 20 seconds of arc.
In his special relativity paper, Einstein used the same method to derive the formulae for the Doppler Effect (which exists for both light and sound), and for stellar aberration. Einstein argued that the aberration of starlight is simply a function of the relative velocity of the star and the Earth. But if the stars in the sky are moving at different speeds relative to us, why do they all show the same aberration? By Einstein’s theory there should be different aberrations for different stars. But that isn’t so.
In Einstein’s day, however, this was a criticism without teeth. No one knew the velocities of the stars, relative to Earth. Today, however, we have evidence from binary star systems, which revolve around each other at close range and at high speeds. At a given point in their mutual orbiting, one star must be moving more or less the same direction we are moving, and the other one in the opposite direction, irrespective of the real motion of the binary system as a whole. By Einstein’s theory, then, the two stars of the binary pair should show different aberrations. They should appear to separate, merge, and separate again, optically. Moreover, that angular separation ought to be huge compared to the small angle of aberration measured by astronomers. But that doesn’t happen. The two binary stars remain as a single unresolvable point in the sky. In fact, we only know they are binaries because of the to-and-fro Doppler shifts in their spectral lines.
The criticism was made in a recent book, and I don’t see how the relativists escape it. If relative velocity is what matters, there should be visible, alternating separation and closure between the two stars of a binary system. But it is never seen. The method that Einstein used, linking the derivation of aberration and the Doppler Effect, seemed economical at the time but it has the relativists pinned like a knight’s fork in chess. If they say

that Einstein really meant that some other velocity applies to aberration, they end up with the wrong formula for the Doppler Effect.
Well, I have covered a lot of ground. Tom Bethell takes you over much the same terrain, step by step. If you don’t understand relativity theory now —and you have lots of company— bear this in mind. Despite the simplicity of relativity’s postulates, the complications mount up in a hurry. By the time you have finished the book you may conclude that relativity is an inessential theory that introduces unnecessary complications into physics. Petr’s alternative seems far more satisfactory to me.

Chapter 1. Relatively Easy
Einstein’s special theory of relativity was published in 1905; his much more difficult general theory was completed ten years later. A strong consensus of physicists and learned laymen agrees that the special theory has been confirmed over and over again, and by now can hardly be denied. It has been verified in particle accelerators, validated by the Global Positioning System, popularized by the equation E = mc2. Accelerated particles live longer lives, GPS has relativistic corrections built into it, E = mc2 was derived by Einstein using relativity theory. And yes, atom bombs do work.
It follows that anyone who disputes the special theory does so at his peril and probably doesn’t understand the experiments that have confirmed it. When it comes to the general theory of relativity, the consensus is less confident. The theory is said to be inconsistent with quantum mechanics, and is still subjected to testing, like a patient who must go in for lab tests. Aspects of the general theory may eventually have to be revised.
These verdicts are more or less reversed in this book. I argue that the special theory is inconsistent with recent (and some not-so-recent) experiments, and that the speed of light is not a constant. It is the special theory, not the general theory that seems to need repair; perhaps even to be discarded. The general theory, on the other hand, does seem to give the right results, although by a complicated method. It takes a difficult mountain path when all along an easier route leads us to the same destination.
It was Petr Beckmann who found this easier path, although a recent book, Einstein and the Ether, shows that Einstein came close to discovering it himself. Anyway, the general theory may work well enough as long as we don’t object to its difficult route. Einstein himself was obliged to take it, lest he risk repudiating his own special theory; the repairs it needed had perforce turned his general theory into a cumbersome thing. For the rest of us, however, the pitfalls of special relativity can be skirted altogether and at that point general relativity not only becomes manageable, but begins to look a whole lot like Petr Beckmann’s theory.
That is the argument of this book.

I hope to set these things out in a way that is intelligible to nonspecialists. Public interest in relativity has always been high, and works of alleged simplification keep rolling off the presses. I call them Easy Einstein books. Sometimes I think that people just keep looking and looking—and what they are looking for is one that they can understand. People have often told me that they have found such books easy enough for the first few pages, but then, and often abruptly, they find themselves out of their depth. Something doesn’t seem to add up. At that point they are inclined to abandon their project, which was to understand relativity.
The truth is that such books are not easy. Not at all. The hardest one I ever saw, Relativity Demystified, starts out with the Maxwell equations, assumes we know what “curl” refers to, and goes on to discuss Cartan structure equations, nonholomonic bases and null tetrads. Yet the back cover claims it is “simple enough for beginners.”1 A spoof, maybe?
Yet even in books that do earnestly try to instruct us, it is not the math that is difficult. Special relativity involves nothing worse than high school algebra. But the great majority of us never master the theory. I hope to explain the source of this difficulty.
It’s fair to say that the special theory has an easy part and a difficult part. This chapter will deal exclusively with the easy part. Nothing in it will dissent from professional opinion or disturb the conventional interpretation. I shall postpone the difficult part until readers have some idea of what it’s all about. Arts majors should have no difficulties at this stage, and physicists no objections.
From the beginning, popular accounts of relativity have located everything on railroads and trains. We encounter workers outside on embankments, and guards inside. The first writer to take this approach was Einstein himself, in his popular account, Relativity: The Special and the General Theory. Its cover promises “a clear explanation that anyone can understand”; an earlier edition promised the same for those “with only a high school education.” That may have given rise to feelings of inadequacy over the years, for the book is in part easily understood, and in part quite difficult. The same could be said for just about all the other “Easy Einstein” books.
I shall follow Einstein’s lead by locating events on a railroad car, or, as his English translation puts it, railway carriage. As someone who traveled quite a bit in railway carriages in his youth, I shall follow Einstein in that

respect, too. By page 16, Einstein is alluding to “our old friend the railway carriage,” and his casual tone helps to sustain the hope, even if it proves to be short-lived, that we can expect to be comfortable with what follows.
What is important is to pinpoint the transition, when the explanation ceases to be clear and quickly turns into something that seems illogical or hard to accept. In this chapter I shall proceed up to that dividing line.

On the Train
There’s a familiar railway experience that we all have had. It is real enough, not just a thought experiment (of which there are too many in books on relativity). It allows us to encounter relativity at its most basic level. The train is waiting at a station, and you are in a window seat. Next to you is another train, almost close enough to touch. Then you see you have started to glide forward. You hardly felt a thing—but that can happen with trains. When the other train disappears from view, you see with a slight shock the stationary platform beyond. It was the other train that had been moving. You hadn’t felt a thing because you had been motionless all along.
If you had been more alert—or looking out of the window on the other side—you could easily have seen that you were stationary. Anyway, the experience illustrates the point that there are situations in which we cannot easily tell whether we are moving or not.
Assume now that it is night, the track is smooth, and the blinds are down. The train is moving in a straight line, at a constant speed. Then again, maybe it is stationary. How would you know? Your task is to conduct some experiment within the train to help you to decide whether the train is moving. The claim of relativity theory is simply that no physics experiment inside that environment would give you the answer.
That is the special theory of relativity in a nutshell. You can throw a ball straight up in the air, and it will land in your lap whether the train is stationary or racing along at a hundred miles an hour. You can try other experiments, recalled from the physics lab. You can roll ball bearings down an inclined plane, heat up water with a Bunsen burner, stir chemicals into an explosive mixture. The results will be unaffected by the motion of the train—just as long as it is uniform, in a straight line. This also helps us to establish the key distinction between the special and the general theory. In its details (and its mathematics) the general theory is much the more difficult. The special theory deals only with motion that is uniform and non-accelerated. If acceleration is involved we must turn to the general theory. Right now we shall deal only with the special theory. In the train puzzle that I have described—with the blinds down, how can we tell if the

train is moving? —you would know the answer immediately if the train headed into a curve. You would feel yourself leaning over to one side. If the train accelerated, you would feel yourself pushed back into your seat. And if you could feel those things, so could scientific instruments.
Therefore, if we want to say that “no experiment” can disclose whether the train is moving or not, we mean non-accelerated motion only. That, obviously, is a special case of motion in general; hence special theory. Most movement involves bumps, turns, or acceleration. But those kinds of motion do not meet the condition imposed by the special theory.
Einstein disliked this restriction—that relativity applied only to uniform motion. And he knew how difficult it would be to apply it to accelerated as well as to uniform motion. One of his earliest supporters, Max Planck, outright discouraged the attempt. But the “generalization” of that principle to accelerated motion is what Einstein achieved in his general theory.

Happiest Thought
Early on, Einstein concluded that the gravitational force we all experience seems to be indistinguishable from the inertial forces we feel when we are accelerated. It was a great insight, and he referred to it as his “happiest thought.” The general theory is often referred to as a theory of gravity, and that is because the effects of acceleration can be made to “stand in” for gravity. Physicists welcome that substitution because acceleration is more amenable to investigation. We can accelerate things deliberately and see what happens. But we can neither intensify nor eliminate the gravitational force as long as we are on the surface of the Earth.
Einstein found that he could make the argument that, even if you are in a train with the blinds down, so that you feel the push or pull of acceleration or centrifugal force, you still can’t be entirely sure that your vehicle is accelerating. Perhaps, instead, you suddenly entered a different gravitational field? That is unlikely. But who could say it was impossible?
In devising the general theory of relativity, the intellectual challenge confronting Einstein was great and the mathematics complicated. Few people understood it at the time (or since). That is why it took him ten years while at the top of his game. In the end he came up with a theory that impressed almost everyone. The most important reason why scientists were impressed was that the new theory accounted for the few celestial anomalies that Newton’s theory of gravitation had been unable to account for.
At its simplest, then, special relativity is the theory that the laws of physics are unaffected by the motion of the laboratory. If so, physics experiments cannot reveal such motion either. It has become conventional to state the theory of relativity in this way.
In Simply Einstein, Richard Wolfson, a professor of physics at Middlebury College, says: “The theory of relativity is, in its barest essence, just the simple statement that regardless of one’s state of motion the laws of physics are the same.”2 He imagines a cruise ship with a tennis court. It steams forward at 30 knots, and the court is enclosed. There is no wind blowing the ball, no waves rocking the boat, no helmsman turning the rudder. Under such conditions the game will proceed exactly as if the ship were in port.

We can easily accept that. “So you already know and believe the essence of relativity,” Wolfson cheerfully continues. “In that sense, you can close this book and be done with it.” Well, no. We can’t accept that. Otherwise those Easy Einstein books wouldn’t be so confusing! There are still many hurdles to surmount. But it is true that at this point we do know something important about relativity. That is the good news. The problem is that the understanding of relativity discussed so far was already known to Galileo and Newton. Galileo even located his “relativistic” scenario on a ship. In his Dialogue Concerning the Two Chief Systems of the World, published in 1632, he wrote:
Shut yourself up with some friend in the main cabin below decks on some large ship and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle which empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions, the drops fall into the vessel beneath; and in throwing something toward your friend, you need throw it no more strongly in one direction than another. . . . [Then] have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.3
So said Galileo 377 years ago. The same idea was stated more formally and briefly by Isaac Newton in Book 1 of his Principia (1687): “The momenta of the bodies included in a given space are the same, whether that space is at rest or whether it moves uniformly in a straight line without rotation.”
And that, in a sense, is the bad news. In part, relativity theory is easily understood. Then we find out that that easy part was well known and ingeniously explained hundreds of years ago. So the difficulties all lie ahead. There’s another way of expressing the easy part of relativity, and it was discussed by Alan Lightman on PBS at the time of the centenary of Einstein’s theory.
Ray Suarez: The theory of relativity is 100 years old this month. But I’ll bet a lot of people would be hard pressed to say what it is. So, in a short, sweet way, what is the theory of relativity? Alan Lightman: The fundamental idea of relativity is that there is no condition of absolute rest—that any motion is relative to another body. If you’re traveling at 70 miles per hour, what that means is you’re going at 70 miles per hour relative to the road.

But the highway is stuck to the Earth, the Earth is spinning around, it’s orbiting the Sun at a certain speed, the Sun is moving around the center of the galaxy at another speed, the galaxy is traveling through space. And you cannot really say how fast your car is going in an absolute sense, only how fast is going relative to the highway. And that’s where the word relativity comes from.4
Lightman is making the same basic point. In the enclosed train, we can’t say if we are moving or not because we can’t say what (if anything) we are moving relative to. Lightman’s point has also been put this way: the universe has no hitching post. We can only say how fast we are moving relative to something else. There is no absolute motion.
Now we come to an important elaboration, and it will point to what is to come. Things do get a little more difficult here, but we still won’t reach the point where common sense rebels.

Electricity and Magnetism
The idea that inside an enclosed laboratory no physics experiment can tell whether it is moving or not, was true of the laws of physics as they were known in Newton’s day. By the 19th century, however, physics embraced something new: electromagnetism. Now there were new laws, and many scientists had contributed to them. The most important was James Clerk Maxwell, much admired by Einstein. His framed picture was in his Princeton study.
With electromagnetism, including the propagation of light, it was no longer expected that the old relativity principle would hold true. If your laboratory was in motion then there should be a way of detecting that motion—perhaps in some “absolute” way. There was a simple reason for this. Electromagnetic phenomena travel in waves, so it was assumed they had a medium to wave in. It was given a name: Ether. Often in the 19th century it was spelled aether.
Maxwell said that this ether filled the entirety of space. It was the largest and most uniform body of which we have any knowledge, he wrote.5 In the mind’s eye it is appropriate to think of Maxwell’s ether as composed of tiny particles, much smaller than atoms, or perhaps a fluid-like substance, which fills all of space. A ray of light is like a ripple that propagates through this ether, and does so at the enormous speed of 186,000 miles per second.
The evidence for the wave nature of light was so strong that scientists were confident they would soon detect the Earth’s passage through this ether. Since the Earth was moving around the Sun, it surely moved through this medium. To be sure, the direction and speed of the Earth’s passage through it was not known. It was not necessarily the direction of the Earth in its orbit, because, as Lightman reminded us, the Sun has its own separate motion through the galaxy. But that was a detail. The point was that the Earth’s passage through the ether could in principle be detected, much as a passenger in a moving car can feel the slipstream by putting his finger out of the window and estimate his speed.
Presumably, then, an experiment could detect and measure the Earth’s passage through the ether. If it succeeded, physicists would have found an optical way of detecting motion in the equivalent of an enclosed railroad car

with the blinds down. In the 1880s, first in Germany and then the United States, ingenious experiments were set up to detect this “ether wind.”
At the same time, if motion through the ether were detected, a divergence would have opened up between the two sets of physical laws. There were the laws of mechanics, associated with Newton and Galileo, for which (all agreed) the “principle of relativity” applied: Uniform motion could only be detected relative to something else. Secondly, there were the laws of electromagnetics, associated with Clerk Maxwell, for which uniform motion through the ether could be detected.
Could be, and (it was assumed) soon would be. If that expectation were met, nature would embody a “double standard.” The relativity principle—the idea that in an enclosed space you can’t distinguish between uniform motion and stillness—would be true of the laws of mechanics; but not true of electromagnetism. Einstein’s special theory can therefore be seen as his pursuit of the idea that there is no double standard in nature; that just as absolute motion cannot be detected in mechanical experiments, so it also could not be detected in electromagnetic experiments. A desire to impute this underlying consistency to nature was what drove Einstein. In his own popular book, written in 1916, setting forth both the special and the general theories, he more than once returns to this point. “That a principle of such broad generality should hold with such exactness in one domain of phenomena [the laws of mechanics] and yet should be invalid for another [the domain of electromagnetism] is a priori not very probable,” he wrote.6

Pursuit of Simplicity
In searching for an underlying consistency, Einstein was pursuing a goal that Isaac Newton and the classical physicists would have applauded. If there is anything that we admire in Newton’s laws of motion, and of gravity, it is their simplicity. In science, truth, beauty and simplicity do mostly seem to go together. Einstein, too, sought a simplifying unity.
So what happened? In 1881, the crucial experiment that was intended to detect the Earth’s passage through the ether was carried out by Albert A. Michelson in Potsdam. It was repeated many times, most famously in 1887 by Michelson again, this time with the help of Edward Morley. They were unable to show that our passage through the ether produced any effect at all.
According to the underlying physical theory of the time, the experiment should have produced a visible effect. Einstein’s response was to propose a revolutionary restructuring of physics. The same rule that was already accepted with respect to mechanics must now be applied to electromagnetics, he postulated. As long as motion was uniform, there was no way in principle that it could be detected by any physical experiment, whether the phenomenon was mechanical or electromagnetic.
Nothing less than “revolutionary” does the new theory justice. “All of physics had to be reformulated after Einstein,” Alan Lightman said in his PBS interview, “to incorporate this strange new notion of the relative nature of time—that different clocks in motion relative to each other tick at different rates.”
I anticipate that readers will already be waving their arms and saying they don’t understand why Lightman said that. And there is no reason why they should. His remarks have already thrown us into the deep end of the relativity pool—into the difficult part that we are going to have to master.
Notice, also, that in attempting to simplify physics by unifying its laws, Einstein seems to have ended up rewriting them and making everything more complicated. And in so doing, did he not defeat his original purpose? Certainly dissenters like Petr Beckmann, who as soon as they learned relativity were inclined to believe that there had to be an easier way, were influenced by this consideration.

So let us proceed at a more leisurely pace. I shall review the Michelson-Morley experiment and its perplexing result, but before doing so I want to take a side excursion and say something preliminary about the “relatively difficult” part of relativity theory.
Its difficulty is of a peculiar kind. If we see a page of Latin, and we know only a little of the language, translating it will be difficult. With a dictionary we may be able to do so. A page of mathematics may present us with comparable difficulties. But special relativity isn’t like that. The math is simple—in fact it need not be brought in at all. The difficulty is more like our experience when we watch a magic performance. Something unexpected happens, and our strong inclination is to respond in this fashion:
“Can you go over that again, only this time more slowly?” In case you suspect that your own intellectual shortcomings are to blame if you don’t quite get what Einstein is up to, I shall supply a few testimonials to the contrary, in the next chapter. They will be from experts in the field. Their effect, I hope, will be to persuade you that everyone encounters these difficulties. All of us are inclined to respond: Can you go over that again, more slowly? So that is what I shall do.

Notes: Chapter 1

1

David McMahon, Relativity Demystified, McGraw-Hill, 2006.

2

Richard Wolfson, Simply Einstein, W.W. Norton, 2003, p. 14.

3

Galileo Galilei, Dialogue Concerning the Two Chief World Systems, University of

California Press, 1953, p. 186.

4

Interview with Alan Lightman, “PBS News Hour with Jim Lehrer,” June 16, 2005.

5

James Clerk Maxwell, “Ether,” Encyclopedia Britannica, 9th ed., 1875 vol. 8, pp. 568-

72.

6

Albert Einstein, Relativity, the Special and the General

Theory, 15th ed, 1952, Crown, p. 14.

Chapter 2. The Magician
Here is an impressive testimonial to the difficulty that we shall encounter. It comes from a man who taught physics at Princeton University in the 1950s. His name was Eric Rogers, and he and Einstein were neighbors and friends. He was considered to be such a good teacher—he taught a popular course to non-science students—that he was made a full professor even though he didn’t have a graduate degree. He also wrote a beguiling tome called Physics for the Inquiring Mind, reprinted many times, and illustrated by himself.
In his book, he offers what he calls “an annoying, untrue fable to warn you of the difficulty of accepting Relativity.” It is “distressing to good mathematical physicists,” he says, but we shall find that what it “alleges so impossibly does occur in relativistic adding of velocities.”
In the fable he asks us to watch a “magic trick.” A conjurer takes an empty bag, which we can inspect beforehand. He puts in two balls, then two more. The bag is then found to contain five balls. It’s not an illusion, and we can repeat the exercise as often as we like. So what do we conclude? “In some cases, 2 + 2 do not make 4,” Rogers says. “The rules of mathematics must be modified.” We are not faced with this paradox in real life, he allows. But with “motion through space,” we really are.1
That from a professor who taught at Princeton. It is helpful for beginners because it allows us to believe that our puzzlement, which surely will arise, may well have nothing to do with our own shortcomings. After all, we know perfectly well that 2 + 2 make four. Apparently there is something strange that we shall have to come to grips with.
One day Rogers met Einstein coming out of his house at Princeton. Rogers told him that he was scheduled for an operation. Rogers then imitated Einstein’s German accent:
“Don’t worry,” Einstein said. “Zose doctors are vizards!”2 No, it was Einstein who was the wizard. In some cases, he could show that two and two don’t make four. This is not the last time that we shall find Einstein compared to a wizard or a magician. One of his biographers, Banesh Hoffmann, who

worked with Einstein in the 1930s, made the same comparison. We shall come to his illuminating account of Einstein’s stage-magic in chapter 5.
Here is a more recent statement of the difficulty that Rogers tells us about. Corey S. Powell, a senior editor at Discover magazine, says in God in the Equation that, despite hundreds of attempts to “translate” relativity for the lay public, “the theory remains stubbornly counterintuitive.” He gives this illustration:
If a train is moving forward at 10 miles per hour, and a passenger runs down the corridor in the same direction, also at 10 miles per hour, “Einstein argued that he is actually traveling a bit less than 20 miles per hour.”3 Relative to the ground, that is. He sounds like Rogers, but what he says is literally true in Einstein’s theory.
For a change of pace, here is a testimonial from David Mermin, who taught “sophisticated” high school teachers who met at Cornell University in the summer. The course was intended “to make them believe that special relativity was not inconsistent or paradoxical.” His book Space and Time in Special Relativity, based on these lectures, includes the following passage. I am in full agreement with what he says, except for the five-word phrase that I have italicized near the end.
The special theory of relativity, alone among the areas of modern physics, can in large part be honestly explained to someone with no formal background in physics and none in mathematics beyond a little algebra and geometry. This is quite remarkable. One can popularize the quantum theory at the price of gross oversimplification and distortion, ending up with a rather uneasy compromise between what the facts dictate and what is possible to convey in ordinary language. In relativity, on the contrary, a straightforward and rigorous development of the subject can be completely simple.
Nevertheless, special relativity is one of the hardest subjects for a beginner to grasp, for its very simplicity emphasizes the distressing fact that its basic notions are in direct contradiction to certain simple, commonplace notions that almost everyone fully grasps and believes, even though they are wrong. As a result teaching relativity is rather like conducting psychotherapy. It is not enough simply to state what is going on, for there is an enormous amount of resistance to be broken down.4
One of those commonplace notions (but wrong, according to Einstein) that we do fully grasp and believe is that a man running at 10 mph within a train that is moving at 10 mph in the same direction will be moving (relative to the ground) at 20 mph.
Obviously, we shall have to learn why Einstein says that is wrong. And having learned that lesson, we will be well on our way to understanding the special theory of relativity.

Sometimes even graduate students have a hard time with special relativity, as recent articles in the American Journal of Physics claimed.
Over a period of five years, the Physics Education Group at the University of Washington investigated the understanding of “key ideas” in relativity, including that of a reference frame. Even after instruction, the group found, “two thirds of physics undergraduates and one third of graduate students are unable to apply the construct of a reference frame in determining whether or not two events are simultaneous.” (“Reference frame” I shall come to.)

The Central Difficulty
Those doing the survey found that it was the most “basic, underlying concepts” that students find difficult. They found also that for most students, “the implications of special relativity are in strong conflict with their intuitions.”5
This is perfectly understandable, and the problem, I believe, is that the special theory of relativity itself undermines our intuitions about basic underlying concepts—the most basic of which are space and time. In fact, it could be said that teaching special relativity and teaching the “basic underlying concepts” of physics are in pedagogical conflict.
Many technical terms can be translated into something simpler, but “reference frame” is one that will keep coming up. There is nothing difficult about it other than a lack of familiarity. Essentially, a reference frame is a block of space. A simple example, as we have seen, is a railroad car. Something whose parts are rigidly connected is said to constitute a reference frame. An automobile is another. So is a second automobile that is overtaking the first. A train moving down the track is one reference frame, the track itself is another; a train going in the opposite direction is a third, and so on.
The number of possible reference frames is infinite. But if such a frame is moving in a straight line at a constant speed, it is said to be an “inertial frame,” and the rules of special relativity apply. Sometimes you see the phrase “coordinate system” instead of reference frame; Einstein used it, and it means the same thing. A reference frame can be of any size.
The crucial point is that all its parts move rigidly together, if they move at all. There is no relative motion between its parts. A train with lots of cars linked together by flexible couplings, so that it can take a curve without falling off the rails, would not be an inertial reference frame—while it was on the curve. I don’t think physicists would want to think of it as any kind of a reference frame because all the angular stresses and forces would give them too many headaches.

Copernicus Revisited?
A few words from the philosopher Bertrand Russell, whose book The ABC of Relativity was published in 1925. He anticipates on his very first page the psychological difficulty that I have mentioned. Of the popular accounts of relativity, he wrote (a few had already begun to appear) they “generally cease to be intelligible just at the point where they begin to say something important.” He exonerated the popularizers, who had done their best. Furthermore, he said, the ideas of relativity can be expressed without mathematics, but are “none the less difficult on that account.”
To overcome our difficulty, he wrote, we must “change our imaginative picture of the world.” This he elaborated upon, concluding with a prediction that has not been borne out in the 80-odd years since his book was published.
The same sort of change was demanded by Copernicus, when he taught that the earth is not stationary and the heavens do not revolve about it once a day. To us now there is no difficulty in this idea, because we learned it before our mental habits became fixed. Einstein’s ideas, similarly, will seem easy to a generation which has grown up with them; but for our generation a certain effort of imaginative reconstruction is unavoidable.7
This analogy is often made by Einstein’s popularizers, but I believe it is doubly in error. In the first place, the heliocentric system never was particularly difficult to grasp. Astronomers in ancient Greece accepted it. As to relativity, three or four generations have passed, and the difficulty that Bertrand Russell saw —comparable to accepting that simple addition no longer yields the familiar results—shows no sign of going away.
In fact, the same difficulty was restated in an article about Einstein in Natural History magazine, published in 2003.
“We live in Einstein’s universe,” Richard Panek wrote. Nonetheless, special relativity, with its high school algebra, “still does manage to defy the imagination. Try as we might, we find we find it very difficult to get our minds around it.”
He, too, compares our mystification to that allegedly experienced at the time of Copernicus. “And as we learn to change the way we think about the world, the nuances of relativity, too, can start to make as much sense as that the Earth goes around the sun.”7
Actually, it is not the “nuances” of relativity that cause problems, but the fundamentals, as we just saw with the student surveys. The truth is that

“the way we think about the world” not only has not changed in basic ways, but the difficulty embedded within relativity has emerged more plainly into view in the last century.

Special and General Theories
Although special relativity is simple in its mathematics, as these things go, while general relativity is abstruse, the conceptual difficulty may actually be greater with the former. For all its complexities, there are aspects of general relativity that we can get our minds around. Most of us have seen those pictures of a heavy ball, representing the Sun, sitting on a sheet of stretched rubber. It distorts the sheet, so that a ball bearing rolled in from the periphery is forced into a circular path around the “Sun.”
The idea is that the stretched sheet is analogous to the gravitational field of the Sun. Its mass, we are told, distorts “space-time” near the Sun.
“Space-time” is not something we can easily grasp. Still, we get the idea that a distortion of space near the ball makes the ball-bearing behave as though a force emanates from the center. A distortion in space produces the same effect as a force—the force of gravity. And so we think we are at least on the way to understanding something about general relativity. Maybe we will never understand the mathematics. But that doesn’t matter. There’s a “big picture” that we partly do get. We don’t feel that it defies logic.
Many of us do feel that way, however, when we encounter the special theory for the first time. If the difficulty lay only in the math, high-school graduates would have no problems with the special theory. Yet physics graduate students, people with advanced degrees, eminent philosophers and learned laymen encounter this difficulty.
As I said earlier, special relativity is regarded as true, proved, confirmed, and repeatedly demonstrated. But general relativity still evokes questions. For over 40 years, and at a cost estimated at $750 million, Stanford University prepared an experiment—Gravity Probe B, it was called—to test in space a prediction of the general theory. Finally launched in 2004, it is now orbiting the Earth on a satellite. Implicit in this experiment, of course, is the possibility that the general theory could be shown to be false.
C. W. Francis Everitt, the director of Gravity Probe B, spent most of his professional career working on the Probe B experiment. He also wrote a hard-to-find book about Clerk Maxwell. In response to my query about the status of the two theories of relativity, he replied:

Let me give you my own general feeling. I would not be at all surprised if Einstein's general theory of relativity were to break down. Einstein himself recognized some serious shortcomings in it, and we know on general grounds that it is very difficult to reconcile with other parts of modern physics. With regard to special relativity, on the other hand, I would be much more surprised. The experimental foundations do seem to be much more compelling.
Needless to say, intuitions such as this can be wrong, and if indeed an experimentalist felt inclined to perform the test you mention, one would encourage it. One does, however, have to make choices (right or wrong) about what oneself is going to do and my own prejudice has made me concentrate on tests of the general theory.8
(I had mentioned the possibility of repeating the Michelson-Morley experiment—the topic of the next chapter—but looking for an effect very much smaller than the one that Michelson had expected to see. The proposed new experiment is central to the alternative thesis advanced in this book.)
A comparable assessment of the two theories of relativity was made by the late Edward Teller when I interviewed him in 1993. “General relativity can be questioned,” he said. “Special relativity is as firmly established as Euclid’s geometry.”
The occasion was a conference in Oakland honoring Petr Beckmann, who had recently died. Teller had known Beckmann well and told me that he loved to read Access to Energy, Beckmann’s newsletter. But he disagreed with him about special relativity. I made detailed notes as I interviewed Teller and wrote up a memorandum immediately. Here is a paragraph from that memo:
The essence of general relativity is that space is curved, Teller said. You can imagine a two dimensional thing being curved (into a third), but it is impossible to imagine threedimensional space as curved. How much harder, then, to imagine four-dimensional spacetime as curved. But general relativity says that this four-dimensional thing, which you cannot imagine, is curved. Einstein came up with the mathematics of this unimaginable thing. Teller is not entirely comfortable with the idea.9
Most physicists in this field would agree with Teller and Everitt about the relative strengths of special and general relativity. It is often said that the two “pillars” of modern physics, quantum theory and general relativity, don’t fit together properly. One or the other may have to be modified.
In any event, a physicist who expresses nuanced doubts about general relativity, or offers refinements to it, will get a hearing from his colleagues — or those who can assess what he is saying. On the other hand, a physicist who entertains doubts about the special theory might well keep

them to himself. For as the textbooks tell us, it has been tested, confirmed and repeatedly shown to be true.
I don’t think that is right. It is the special theory that will need closer scrutiny. But, first, a closer look at the most important experiment that led up to it: the Michelson-Morley experiment.

Notes Chapter 2

1

Eric M. Rogers, Physics for the Inquiring Mind, Princeton, 1960, pp. 480-81.

2

Author’s interview with Ralph Baierlein, April, 2004. He heard the story from Rogers.

3

Corey S. Powell, God in the Equation, Free Press, N.Y. 2002, p. 57.

4

N. David Mermin, Space and Time in Special Relativity, McGraw Hill. N.Y. 1968, p

vii.

5

“Student understanding of time in special relativity: simultaneity and reference frames,”

Am. J. Physics, July 2001, pp. S24-S35. “The challenge of changing deeply held beliefs about

the relativity of simultaneity,” Am. J. Physics, December 2002, pp. 1238-1248.

6

Bertrand Russell, ABC of Relativity, Harper & Brothers, N.Y. 1925, pp. 1-2.

7

Richard Panek, “And Then There Was Light,” Natural History, November 2002.

8

Letter to author from Francis Everitt, January 13, 1994.

9

Author’s interview with Edward Teller, August 14, 1993; Teller’s banquet remarks were

reprinted in a special edition of Access to Energy, v. 21, Oct. 1993.

Chapter 3. Michelson-Morley
Until the mid-1960s, most books on relativity referred the origin of Einstein’s theory to the Michelson-Morley experiment, and the great perplexity that it had provoked. Largely due to the revisionist campaign of Gerald Holton of Harvard, however, that interpretation fell out of favor.1 But I believe the older way was correct, and I shall revert to it here. Einstein’s theory is also much easier to understand if it is considered in the light of Michelson-Morley. Later, I shall discuss “Holton’s Crusade.”
In other respects, however, this chapter accepts the conventional interpretation of Michelson-Morley. The experiment was expected to show an optical effect caused by the earth’s passage through the ether, but failed to show it. From 1887 until the 1930s, the experiment was repeated under various conditions, in persistent but unsuccessful attempts to show that the anticipated effect was present.
Albert A. Michelson, born in Poland in 1852, came to the United States as a child. After high school in San Francisco he was recommended for a special appointment to the U.S. Naval Academy. Ulysses S. Grant himself interviewed him at the White House. At Annapolis, Michelson showed great ability in the sciences, leading his class in optics. He became an instructor, and found an improved way of measuring the speed of light. Hitherto the best method had been devised by Jean Bernard Foucault, known today for demonstrating the rotation of the Earth with a large pendulum.
In 1879, Michelson carried out a detailed investigation of the speed of light, with a line of sight 2000 feet long across the Severn River at Annapolis. He communicated his methods and results to Simon Newcomb, president of the American Association for the Advancement of Science.
Impressed, Newcomb persuaded the Academy to allow Michelson to join him at the Naval Almanac Office.2
At about the same time, James Clerk Maxwell wrote to the same office, inquiring about the possibility of measuring the Earth’s motion through the ether. A long series of investigations in the previous century had established beyond doubt that light is a wave form, implying the

existence of a medium for it to wave in. By the latter half of the 19th century, its existence was regarded as certain.
The ether was thought of as a uniform, attenuated substance that filled the entirety of space. It was assumed to be “isotropic,” or the same in all directions, and its parts were regarded as stationary in relation to each other. Often it was called the fixed ether. It would therefore constitute an immobile background against which the “absolute” motions of celestial bodies could be demonstrated. Therefore the Earth’s passage through it could be measured.
Although an ether was needed to constitute the medium for electromagnetic waves, its other properties—its homogeneous, uniform, fixed character—were all assumed with little evidence. Yet an ether with different properties could easily be imagined. And just such an alternative medium is central to the argument of this book.
In an article for the Encyclopedia Britannica, published in 1875, Maxwell discussed a possible experiment to detect the ether. It would be difficult to carry out, however, because it would involve measuring something very small: a time interval proportional to “the square of the ratio of the Earth’s velocity to that of light.”
At about that time Michelson took time off for the equivalent of graduate studies. He knew about Maxwell’s proposal, and pondered its technical requirements. Then he went to Berlin, where he worked under Hermann von Helmholtz. Alexander Graham Bell, frustrated by his own difficulties in raising funds for the telephone, gave Michelson a grant to proceed with the work.
In his Encyclopedia article, Clerk Maxwell had written:
If it were possible to determine the velocity of light by observing the time it takes [for light] to travel between one station and another on the earth’s surface, we might, by comparing the observed velocities in opposite directions, determine the velocity of the ether with respect to these terrestrial stations.3
If a light beam is sent from A to B, and the time taken is recorded; and then compared with the time for the beam’s return, the Earth’s motion through the ether could be demonstrated. During the time taken for the light beam’s round trip, the light would necessarily move both with, and against, the earth’s motion through the ether. If the light was sent in the same direction as the earth’s motion through the ether, then the time for the light beam’s return would be slightly shorter than for its outward journey. The observer

and his apparatus would be moving to meet the returning beam and so its measured speed would be higher than that of the beam on its outward path.

One-way Speed of Light
But there was a problem: how to determine the one-way speed of light. That depends on knowing that two remote clocks are perfectly synchronized. And it is difficult, perhaps impossible, to know that they are synchronized without knowing the speed of light measured in one direction. Experimenters could send a light beam to a mirror and note the instant of its return. But if they assume that the time taken for the beam to return is half the total time, they are already assuming that the light speed is the same in both directions. But the purpose of the exercise is to find out if the speed in one direction is any different from the speed in the other.
There is a solution, however. We do know that if a beam of light is going against the ether wind in one direction, and with it in the other, the double journey will take slightly longer than if there is no ether wind at all. How can we measure that small increase? It was here that Michelson had his inspired idea. An experimenter could compare the round-trip time taken by one light beam with the round-trip time taken by another traveling at right angles to the first.
The best analogy is to a swimmer crossing a river with a current. It can be shown by simple geometry that the time taken to cross a river in both directions will be slightly less than the time taken to swim up and downstream, over a distance equal to the double journey across the river. The swimmer struggling upstream loses slightly more time that he gains when returning downstream with the current helping him. Michelson himself was the first to put it this way, in a letter to his own children:
Two beams of light race against each other, like two swimmers, one struggling upstream and back, while the other, covering the same distance, just crossing the river and returns. The second swimmer will always win, if there is any current in the river.4
The underlying assumption was that the “ether wind” would be generated by the orbiting Earth. It moves “through” this ether (it was assumed) at about 18.5 miles per second. But light goes ten thousand times faster; at about 186,000 miles per second.
But because the experiment required that the time taken by the back and forth journey of the light beam be compared with that of another beam going at right angles to the first, the anticipated effect was much smaller still. The fraction 1/10,000 would have to be squared, giving us one part in

a hundred million. The difference in the time taken by the two light beams would be “only about one hundred millionth part of the whole time of transmission,” Clerk Maxwell wrote in his encyclopedia article. He thought this would be “quite insensible,” or undetectable.
Michelson, a great experimentalist, devised an instrument capable of detecting it. It made use of the interference pattern produced by overlapping light beams, and was known as an interferometer for that reason. A beam of light reaches a half-silvered diagonal mirror in the center of the apparatus, and this allows some light to go through in a straight line, while the rest of the light is deflected through 90 degrees. Both beams are then reflected back by mirrors, and are rejoined and observed through an eyepiece. A New York Times writer said that Michelson had split a beam of light and raced “the halves against each another.”5
The wave nature of light ensures that the reunited beams “interfere” with one another, as the British experimentalist Thomas Young had demonstrated almost a century earlier. This would appear as an array of light and dark fringes visible in the eyepiece. Where the crest of one light wave coincided with the crest of the other, the two would be reinforced, and a bright band would appear. But next to it the crest of one wave would coincide with the trough of the other, and there the two would cancel each other, creating a band of darkness. The discovery of these alternating fringes was convincing evidence for the wave nature of light.
Banesh Hoffmann, a colleague of Einstein’s, described the design this way: “Michelson solved the problem of measuring a very small time interval by converting it into a distance: the distance traveled by light in that short time. The light and dark interference fringes “in effect allowed [Michelson] to measure that small distance by using the wave length of light as a yard stick.”6
Almost everyone was confident that the ether existed, but the direction from which the ether-wind blew was less certain. It was not necessarily the direction of the Earth in its orbit. The sun itself was moving through the galaxy at a high speed, and with it the solar system. So it was difficult to say what the resultant direction of the apparatus might be, relative to the ether. The Earth’s rotation would complicate matters, because six hours after one observation, the Earth would have turned through 90 degrees. By

then the ether would be approaching the apparatus from a different direction.
Nonetheless, if the apparatus itself were rotated in the course of the experiment, the paths of light would be changed, relative to the Earth’s orbital direction. This should produce a shift in the position of the fringes. In relation to a pointer fixed to the eyepiece, a particular fringe would move slightly to one side.
Leo Sartori explains this clearly in his Understanding Relativity. Michelson had “no way of knowing how the arms of his instrument were oriented,” relative to the ether wind. But as the instrument was rotated, the emitted beam of light would at some point be in the direction of the ether flow. Then, after an additional rotation of the instrument itself through 90 degrees, the two arms would have changed places.
“One expects, therefore, that as the interferometer is rotated the fringe patterns will shift back and forth,” Sartori wrote. “By measuring the maximum shift, Michelson expected to determine [the velocity of the Earth with respect to the ether].”7
In the winter of 1880-81, Michelson set up the apparatus in a basement at the University of Berlin. But even small movements near the lab caused the fringes to shake. Helmholtz suggested that it might be better for Michelson to wait until he returned to America, “as he doubted if they had the facilities for carrying out such experiments.”8 Eventually, they moved the whole operation to an observatory in Potsdam, 30 miles away.
Here, Michelson wrote, the fringes “were sufficiently quiet to measure, but so extraordinarily sensitive was the instrument that the stamping on the pavement about 100 meters from the observatory, made the fringes disappear entirely!”9
Michelson expected to find a fringe shift of about 0.08 of a wave length of light. But he was unable to discern any significant shift at all. Later, he learned that his calculations had been in error. With that error removed, the expected fringe-shift was only half of what he had assumed.
Michelson spent time in Heidelberg, where he met Prof. Wilhelm Bunsen, the inventor of the Bunsen burner. From him, Michelson learned that each element gave off its own spectrum. Monochromatic light would make it much easier to detect the fringes, and later Michelson used the yellow light given off by sodium when salt is heated in a flame. He spent a year in Paris, at that time probably the center of the scientific world. Andre

Potier and Hendrik Lorentz discovered the error in his Potsdam calculations. Lorentz would soon be regarded as the most eminent physicist in the world, and we shall hear more of him.

“To see if light travels with the same velocity…”
The following year, Michelson obtained a position at the Case School of Applied Science in Cleveland. It must have been a come-down from Paris and Heidelberg. With his earlier error, and other room for improvement, Michelson resolved to repeat his experiment. He found a collaborator, Edward W. Morley, a professor of chemistry at nearby Western Reserve College. By adding mirrors to the table top, the light path was increased by a factor of ten. The expected fringe-shift should increase commensurately.
In 1887, Morley wrote to his father that “Michelson and I have begun a new experiment. It is to see if light travels with the same velocity in all directions,” which was as succinct a way as any of describing it. “We shall have to make observations for a few minutes every month for a year,” Morley added.
The optical parts of their equipment were mounted on a bed of stone, five feet square, and this in turn was floated in 200 pounds of mercury. It acted as a shock absorber, allowing the apparatus to be rotated smoothly without vibrations. The mercury consumed most of the grant from the National Academy of Sciences. In his fascinating account of the experiment in The Ethereal Aether, the historian Loyd Swenson wrote:
By a gentle push of the observer’s hand, the apparatus could be made to rotate very slowly, going through one complete turn in about six minutes. The observer, once his fringes could be adjusted for best ‘seeing’ and the block had started revolving on its almost frictionless liquid bearings, need not touch the apparatus at all, but could merely walk around with it and watch for any shift of the interference bands past a fiducial mark in his field of view.10
Finally, in July 1887, all was ready. “At noon on July 8, 9, and 11, and for one hour in the evening of July 8, 9, and 12, Michelson and Morley performed the simple yet amazing observations which were eventually to immortalize them,” Swenson wrote. “Michelson walked the circuit and called off his estimates of fringe shifts at each of sixteen equidistant compass points, while, usually, Morley sat by and recorded the data. Their entire series of final observations consisted of only 36 turns of the interferometer, covering only six hours’ duration over a five-day period in the summer of 1887. If Dayton C. Miller’s history [published in 1933] can be trusted, and there is no reason to doubt it, they ‘never repeated the etherdrift experiment at any other time, notwithstanding many printed statements to the contrary’.” 11

With the new apparatus, the expected fringe shift was 0.4 of a wavelength. But Michelson saw at most a shift of one hundredth of a wavelength. In their published paper, “On the Relative Motion of the Earth and the Luminiferous Ether” Michelson and Morley concluded:
if there is any displacement due to the relative motion of the earth and the luminiferous ether, this cannot be much greater than 0.01 of the distance between the fringes . . . The relative velocity of the earth and the ether is probably less than one sixth the earth’s orbital velocity, and certainly less than a fourth . . . If there be any relative motion between the earth and the luminiferous ether, it must be small.12
Notice that Michelson did not abandon the ether. He assumed that its velocity relative to the apparatus was much smaller than expected. To the end of his life—he died in 1931—he didn’t change his mind and continued to believe that the ether was real. In his Studies in Optics, published in 1927, Michelson asked: “Without a medium, how can the propagation of light waves be explained?"
In 1924, he did a more elaborate experiment with Henry G. Gale of the University of Chicago. It was intended to test the theory that the much slower rotational (as opposed to the orbital) velocity of the earth generated a fringe-shift. This time he did find one. We shall return to this important and overlooked experiment in chapter 14. Michelson wrote in Studies in Optics:
It is to be hoped that the theory [of relativity] may be reconciled with the existence of a medium, either by modifying the theory, or more probably, by attributing the requisite properties to the ether; for example, allowing changes in its properties (dielectric constant, for example), due to the presence of a gravitational field.13
Michelson’s comments are not entirely clear, but Petr Beckmann’s theory was based on something similar. I shall outline his theory later, but a brief preview here will allow readers to visualize his alternative right away.

Translation and Rotation
In Beckmann’s theory there is a luminiferous medium and it is equivalent to the local gravitational field. Because the Earth, orbiting the Sun, carries its gravitational field with it, no relative motion between the gravitational field and the orbiting Earth is to be expected.
But as the Earth rotates, it does so “within” its gravitational field. By analogy, when a woman with a circular waist wearing a hoop skirt spins around, or pirouettes, and friction is minimal, the skirt will not rotate with her. Analogously, an “ether drift” caused by the Earth’s rotation should exist. But because the Earth’s rotational velocity is much smaller than its orbital velocity, the effect that Beckmann predicts is much smaller than what Michelson expected to see. At mid-latitudes, it would be about ten thousand times smaller. Michelson’s instrument, built in the 1880s, could not possibly have detected it. That is Beckmann’s idea in a nutshell.
Michelson left the Case School of Applied Science in 1889. He moved first to Clark University and then to the University of Chicago. He was replaced at Case by Dayton C. Miller, who became Morley’s close friend. They attended the Paris Exposition of 1900 and there met Lord Kelvin, who "strongly urged" them to repeat the ether-drift experiment. Lorentz was also lecturing at Leiden University about the Michelson-Morley experiment.14
There were various interpretations, possibilities and criticisms of the famous experiment. Michelson had at one point said they would make observations quarterly. After three months, the Earth would be moving in a direction 90 degrees different from its initial direction. But all their readings were made within a few days.
In their 1887 paper, Michelson and Morley had suggested that fringe shifts might more easily be detected at a greater height. The idea here was that the ether might be “entrained” by the earth’s motion, or swept along with the earth. This entrainment might be less effective at a higher altitude. In 1905, therefore, Morley and Miller collaborated on a new and still more accurate version of the experiment, on Euclid (later Cleveland) Heights, near Lake Erie.
Einstein himself went to Case in May, 1921, visited the site of the classic Michelson-Morley experiment, and urged Dayton Miller to keep

looking.15 He did, and regularly reported finding a fringe shift. But if it was real, and not produced by confounding factors such as temperature fluctuations, it was much smaller than the Maxwellian ether required.
In 1920, George Ellery Hale, the director of Mt. Wilson Observatory in California, invited Miller to repeat the experiment on top of Mt. Wilson. By 1924, when he was president of the American Physical Society, Miller had concluded that “the effects were shown to be real and systematic, beyond any question.”16 But the effect was only 30 percent of what was expected, and the doubts persisted.
In the end, Miller’s interpretation, that the fringe shift was real, was not accepted. It was assumed that all the experiments, whether by Michelson or Miller, and whether conducted in basements or on mountain tops, had shown a “null result.” Further, these experiments were taken to have disproved the ether hypothesis.
Michelson was awarded the Nobel Prize in Physics in 1907—the first American scientist to receive it. He was honored not for his ether-drift experiment but for another collaboration with Morley, this one to see whether wave lengths of light could provide a standard unit of length.17 Some historians have concluded that Michelson was in effect recognized for his perfection of the interferometer. Its precision was way ahead of anything achieved by others at the time, and for many years to come.

Michelson Papers Discarded
Although he was a major figure in American science, little discernible research has been done on Michelson’s papers in the almost 80 years since his death. Sadly, too, valuable material in Michelson’s office in the Ryerson Laboratory at the University of Chicago seem to have been thrown out after his death. In The Master of Light, his daughter Dorothy Michelson Livingston wrote:
In time, the Manhattan Project moved into Ryerson and all material not immediately pertinent to the creation of the atomic pile was thrown out. Ruling engine records, polarization of light records, butterfly and insect specimens, prisms, gratings, books, notebooks, and loose-leaf records of his work were all stolen or lost.
Tom O’Donnell showed me the spot where the contents of Michelson’s desk were dumped. Students rifling the letters had found a number of canceled checks bearing his signature, which were selling for a fair price even then. Tom swears that there were letters from Röntgen, Rayleigh, Kelvin, Larmor, Lodge, Gibbs, and many others, which were destroyed before the scavengers could lay their hands on them. This is why in so many instances I have found Michelson’s letters in the files of these men, but have not found their answers, unless by good fortune they were methodical enough to make duplicates, a laborious process before the days of typewriters and copying machines.18
The bulk of Michelson’s remaining papers are preserved at the U.S. Naval Academy in Annapolis today; some material is at the University of Chicago, some at Case Western Reserve and perhaps at the Mount Wilson Institute. One hopes that before too many more years elapse researchers will take an interest.
His opposition to relativity is downplayed, and today it is hardly known. Dorothy Livingston minimizes her father’s dissent, although she acknowledges it.19 It may be that undiscovered material among Michelson’s surviving papers will shed new light on these matters.
In an introduction to Loyd Swenson’s book, Gerald Holton said that Michelson’s interferometer had played a historical role “analogous to Galileo’s telescope.”20 Just as the telescope had “cast fatal doubt on the physics of its time,” so did the interferometer. It is an interesting comparison. The parallel breaks down, however, in that Galileo endorsed the new worldview ushered in by the telescope, whereas Michelson remained unreconciled to the Einsteinian worldview, from which the ether would be banished and in which waves no longer needed a medium to wave in.

A centennial symposium on the Michelson-Morley experiment was held at Cleveland in 1987. One of the participants was Dorothy Livingston. Her remarks, published by the American Institute of Physics, contain comments rarely encountered in the Einstein literature:
In 1905, when [Einstein] made his great thesis, he was disappointed that he didn’t get instant recognition from four people: Ernst Mach, H. A. Lorentz, Poincaré and Michelson. None of them came forward in 1905 and said ‘this is it.’ Well, years later [Einstein] came to America when he was widely recognized and feted from one end of the country to the other. He showed a certain coldness at meetings. My father and he would meet a various scientific gatherings and he was, you know, chilly. And of course Michelson never liked his theory, so that was another point. So they never really spoke then.21
None of those four “came forward in 1905”—or at any time, she might have added. Nonetheless, there was a personal reconciliation between Michelson and Einstein:
“Then my father retired from Chicago to California, and he was working up on Mt. Wilson when Einstein appeared out there,” Dorothy Livingston continued.
And in the evening of his life he was very happy to talk with Einstein. My father was failing in health and he was really quite ill at the end and Einstein used to come to the house. I was there when he came. My father would play him a tune on the violin and he would play the violin. Then father would get out some water colors that he had been making of California, and the whole friendship was really sealed in a beautiful way.21

Notes: Chapter 3

1

Gerald Holton, Thematic Origins of Scientific Thought, revised ed. Harvard, 1988.

Chs. 6-8.

2

The principal sources for this chapter are Loyd S. Swenson, The Ethereal Aether,

University of Texas, 1972; and Dorothy Michelson Livingston, The Master of Light: A Biography

of Albert A. Michelson, Charles Scribner’s, N.Y., 1973.

3

Maxwell, “Ether,” Britannica, op. cit.

4

Dorothy Livingston, p. 77.

5

New York Times, Nov 20, 1927, cited in Swenson, p. 220.

6

Banesh Hoffmann, Roots of Relativity, p. 76 (Michelson re. Helmholtz, Livingston, p.

75.)

7

Leo Sartori, Understanding Relativity: A Simplified Approach to Einstein’s Theories,

Univ. of California Press, 1996, pp. 36-37.

8

Dorothy Livingston, p. 75

9

Livingston, p.78-9; Michelson (1881) in American Journal of Science, v. 22, no.128.

10

Swenson, p.93.

11

Swenson, pp.93-94.

12

Michelson-Morley (1887) Am. Journal of Science, v 34, Nov. 1887.

13

A. A. Michelson, Studies in Optics, Dover, N.Y. 1995, pp 161-62; first published by

University of Chicago, 1927.

14

Swenson, p.195.

15

Swenson, p.141, 142.

16

Swenson, p. 206 et seq.

17

Albert E. Moyer, “Michelson in 1887,” Physics Today, May 1987, p.50.

18

Dorothy Livingston, p.340.

19

Dorothy Livingston, p.334.

20

Gerald Holton, introduction to Swenson, p. xx.

21

Dorothy Livingston, “Reminiscences of My Father,” in Modern Physics in America: A

Michelson-Morley Centennial Symposium, American Institute of Physics, N.Y., 1988, p. 24.

Chapter 4. Lorentz and Poincaré
Scientists in the late 19th century were “stunned” by the Michelson-Morley result, Jeremy Bernstein said. J. Robert Oppenheimer noted its “traumatic character,” while Einstein himself wrote that it had “placed [physicists] in greatest embarrassment.”1 It led to “one of the most dramatic situations in the history of science,” wrote Einstein and Leopold Infeld.2
Earlier experimenters had tried to detect the Earth’s motion through the ether. No such effects had been seen, but the equipment had been designed in the Napoleonic era, so the predicted effects were assumed to be beyond the instruments’ capacities.
But Michelson’s interferometer should have been able to do the job. His result therefore implied some basic misconception in the underlying theory. It gave rise to one of those moments when the prevailing physical “paradigm” was no longer working, although it had given satisfaction for a century or more.3
Hendrik A. Lorentz (1853-1928) had paid close attention to all this. He held the chair of theoretical physics at the University of Leiden in Holland, and in 1902 shared the Nobel Prize in Physics with Pieter Zeeman for research into the influence of magnetism on radiation. He presided over the gatherings of the Solvay Congress, welcomed new ideas, and seems to have been a model scientist. The object of physical research, he said, “was to find simple basic principles from which all phenomena can be deduced.”4
He got on well with everyone. Einstein congratulated Lorentz on his 70th birthday saying that he had found “deep consolation in your noble and outstanding personality. . . . To follow you on your path has been the most important content of my life.” This was all the more impressive in that the two scientists held strongly opposed views “on some very fundamental and important issues,” as A.J. Kox has written.5 Lorentz had seemed to lay the groundwork for relativity, but he never accepted Einstein’s theory.
Lorentz was initially at a loss to account for the Michelson-Morley result, but in the 1890s he proposed a theory in which material objects consisted of electrons, and as they passed through the ether, they were deformed. Michelson’s null result could be explained if motion through the

ether caused an object to contract, thereby accounting for the missing effect.6
But this was a “physics of desperation,” Arthur I. Miller said.7 One anticipated but unobserved effect was countered by another. So everything stayed the same. The hypothesis of contraction was “not justifiable by any electrodynamical facts,” Einstein wrote, in a rare criticism of Lorentz.8
The idea of length-contraction had also been suggested by the Irish physicist George Fitzgerald., who sent a letter to Science in 1889, proposing that idea. At first neither Fitzgerald nor Lorentz knew if it had been published. The magazine had briefly gone out of existence, leaving Fitzgerald to suppose that his letter never saw print. The ever-scrupulous Lorentz made inquiries and duly credited Fitzgerald with priority.9 The hypothesis is often referred to as the Fitzgerald-Lorentz contraction.
As the velocity (with respect to the ether) increases so does the contraction. The measuring instruments would also contract, so the fringe shift anticipated by Michelson, although greater at higher speeds, would never appear. With a quotation from Through the Looking Glass, Eddington questioned whether nature would both generate an ether wind and then go to such lengths to hide it.10
Lorentz’s contraction formula was retained by Einstein in his theory of relativity. In the next chapter, this will be described from Einstein’s point of view, showing how the idea of contraction became a mainstay of special relativity. But there was also a key difference. In Lorentz’s theory, the objects themselves physically contract as a result of their passage through the ether. There was a real material cause. In Einstein’s theory, space contracts (and time expands) in reference frames that are moving with respect to the observer. Motion itself generates an adjustment of space and time.
The Lorentz formula is such that objects contract (in the direction of motion) only to a very small extent until their speed reaches an appreciable fraction of the speed of light. The orbiting Earth, for example, “would be contracted by a mere six centimeters or so,” Banesh Hoffmann wrote.
In 1895, Lorentz published his theory in detail, stating that the arms of the interferometer contract in the direction of the earth’s motion through the ether. He regarded the contraction as real and “dynamic” — caused by physical interactions with the ether.

At the turn of the century the French mathematician and physicist Henri Poincaré criticized the ad hoc character of the various attempts to measure the earth’s motion through the ether. By then, there had been added to length contraction a further proposal of a “local time”. But there should be a more general explanation, Poincaré thought. He suggested refinements and improvements, which Lorentz then incorporated in a more thorough statement, published in 1904.

Henri Poincaré
Poincaré seemed close to formulating the theory of relativity himself. In a lecture at the Sorbonne in 1899 he said it was probable “that optical phenomena depend only on the relative motions of the material bodies, luminous sources and optical apparatus concerned,” and that absolute motion would prove to be undetectable in principle.
“A new principle would thus be introduced into physics, which would resemble the Second Law of Thermodynamics,” Edmund Whittaker commented, in his History of the Theories of Aether and Electricity. Such a principle would assert “the impossibility of doing something: in this case the impossibility of determining the velocity of the earth relative to the aether.”11
In Science and Hypothesis (1902) Poincaré referred to the “principle of relativity” for the first time. And in 1904, in a speech in St. Louis, he formulated the principle exactly as Einstein later used it:
The laws of physical phenomena should be the same for a stationary observer as for an observer carried along in a uniform motion of translation; so that we have not and can not have any means of discerning whether or not we are carried along in such a motion.12
He discussed the synchronization of clocks using a method similar to that proposed by Einstein. He even added that we might have to construct a new mechanics, “where, inertia increasing with velocity, the velocity of light would become an impassable limit.”
In fact, Leo Sartori wrote, Poincaré “articulated many of the central concepts of relativity, some of them before Einstein.”12
But they were further apart than these similarities suggest. So were Einstein and Lorentz. Einstein’s advocates are right to insist that special relativity was his alone. Both Lorentz and Poincaré retained the ether, and neither argued that the speed of light is invariant. Poincaré did express doubts about the ether, but he continued to assign it an important role. In a review article in 1908 he said: “the universe contains electrons, ether and nothing else.”13 In 1912, the year of his death, he published a paper entitled “the Relation between Ether and Matter.”
Poincaré did not mention Einstein’s relativity between its introduction and his own death in 1912. Relations between the two men seemed chilly, in contrast to Einstein’s warm friendship with Lorentz. “It is apparent that

Poincaré was tantalizingly close to a theory of relativity,” Sartori wrote. “But he either did not see the all-important final step or was not bold enough to take it.”14
Stanley Goldberg takes a different view. We are reduced to speculation, because Poincaré died suddenly at the age of 60. He didn’t write anything about Einstein’s relativity, but hardly anyone in France did before 1912. Everything we know about Poincaré’s character “belies a motive as petty as jealousy,” Goldberg writes. He adds that Poincaré and Lorentz had been working on a comprehensive theory of electrons which was going to subsume all of physics. Einstein’s second postulate, about the speed of light, “must have seemed artificial.”15
Lorentzian contraction had a real physical cause. But for Einstein, Sartori wrote, it was an inherent property of space and time:
The distance between two bodies is shortened when it is measured by observers for whom the bodies are in motion, even if no matter occupies the space between them. The Lorentz model cannot account for this contraction of ‘empty space’.16
Indeed it cannot. Maybe that is because the contraction of empty space caused by the motion of an observer relative to that space must have seemed close to an absurdity. Yet, as we shall see, we must either accept that it is true or reject the theory of relativity.
In a letter to Einstein in 1915 Lorentz reiterated his preference for retaining the ether. In fact, he “never embraced Einstein’s 1905 reinterpretation of the equations of his [Lorentz’s] electron theory,” Russell McCormmach wrote in his article on Lorentz in the Dictionary of Scientific Biography. “To the end of his life he believed that the ether was a reality and that absolute space and time were meaningful concepts.”17
In his last public appearance, a year before his death, Lorentz attended a conference in Pasadena, California, on the Michelson-Morley experiment. It was still under investigation 40 years later. Michelson himself was present. As to time and space, Lorentz said on that occasion, “there existed for me only this one true time.”18
After the total eclipse confirmed the bending of starlight and Einstein’s general relativity, Lorentz wrote an article later published as a small book by Brentano’s, The Einstein Theory of Relativity: A Concise Statement. He said something that seemed to hint at Petr Beckmann’s ideas published almost 60 years later.

It is not necessary to give up entirely even the ether. Many natural philosophers find satisfaction in the idea of a material intermediate substance in which the vibrations of light take place, and they will very probably be all the more inclined to imagine such a medium when they learn that, according to the Einstein theory, gravitation itself does not spread instantaneously, but with a velocity that at first estimate may be compared with that of light.
Speculation about the ether, Lorentz went on, had hoped to arrive at a “clear statement of electromagnetic phenomena and also of the functioning of gravitation.” It was possible that in the future this road, “abandoned at present, will once more be followed with good results, if only because it can lead to the thinking out of new experimental tests.”19
Within months of the book’s publication, Einstein gave a lecture at Leiden, with Lorentz in attendance. Einstein argued that a revival of the ether was perhaps overdue, bearing in mind that his general theory of relativity was itself a gravitational theory.20 This development, rarely noted, and its bearing on Petr Beckmann’s ideas, will be discussed in chapter 21.

Notes: Chapter 4

1

Bernstein, Einstein, Penguin, 1976, p. 52; J. Robert Oppenheimer, The Flying Trapeze:

Three Crises for Physicists, Oxford, 1964, p. 14; Gerald Holton, Thematic Origins, p. 478.

2

Einstein and Infeld, Evolution of Physics, Simon and Schuster, N.Y. 1938, p.183, 184.

3

Thomas Kuhn, The Structure of Scientific Revolutions, 2nd ed. Univ. of Chicago, 1970.

4

Russell McCormmach, “Hendrik A. Lorentz,” Dictionary of Scientific Biography, 1970,

v. 8, p. 490.

5

A.J. Kox, “Einstein and Lorentz: More than Just Good Colleagues,” Einstein in Context,

ed. Mara Beller et al, Cambridge, 1993, p. 43, 50.

6

Arthur Eddington, The Nature of the Physical World, The Macmillan Co. 1928, p. 7.

7

Arthur I. Miller, Albert Einstein’s Special Theory of Relativity, Springer 1998, p.28.

8

Albert Einstein, The Special and the General Theory, 1917, p.51.

9

Banesh Hoffmann, Relativity and its Roots, Scientific American Books, 1983, p.82.

10

Eddington, op. cit. p. 28.

11

Edmund Whittaker, A History of the Theories of Aether and Electricity, 2 vols (1953),

Harper Torchbook, v. 2, p. 30.

12

Leo Sartori, Understanding Relativity, pp. 128-130.

13

Sartori, p.132.

14

Sartori, p.132.

15

Stanley Goldberg, Understanding Relativity, Birkhauser, Boston, 1984, p. 216.

16

Sartori, 87-88.

17

Dictionary of Scientific Biography, v. 8, p. 498.

18

A. A. Michelson et al., “Conference on the Michelson-Morley Experiment, Held at the

Mt. Wilson Observatory, Pasadena, California, Feb. 4, 5, 1927,” Astrophysical Journal,

December, 1928.

19

H.A. Lorentz, The Einstein Theory of Relativity: A Concise Statement, Brentano’s,

N.Y., 1920, 60-62.

20

Albert Einstein, Essays in Science, Philosophical Library, 1934, 98-111.

Chapter 5. The Special Theory of Relativity
The special theory was Einstein’s solution to the problem that arose as a result of the “unsuccessful attempts to detect a motion of the earth relative to the light medium,” to use his own words in 1905.1 He didn’t single out the Michelson-Morley experiment, but almost certainly he had it in mind. This itself is disputed, and I explore that later. But it is of secondary importance. More important is to discover what Einstein’s theory is claiming.
In outlining his theory, Einstein proceeded by the method of postulates. Certain propositions are assumed to be true. Einstein says, in effect, “let us assume that they are true.” He then works out their consequences. If the (two) postulates are true, various physical phenomena should be observed. They amount to predictions of the theory. If they are observed, then Einstein can claim that his theory has been confirmed. Observations in conflict with those predictions, on the other hand, will tend to falsify the theory.
That is the perfectly conventional method that Einstein uses. He states his theory, predicts its consequences, and looks to see if the physical world corroborates them.
The core of his theory is found within five sentences early in his paper, “On the Electrodynamics of Moving Bodies.” The passage is written in plain language, mostly, with little technical jargon. But we need to be warned that it is less straightforward than it appears. At one point Einstein doesn’t quite say what he means, and that has been the source of much confusion. If we are to understand relativity, it is essential to know what is going on in this passage. Everything else in the theory follows from it.
… [N]ot only the phenomena of mechanics but also those of electrodynamics have no properties that correspond to the concept of absolute rest. Rather, the same laws of electrodynamics and optics will be valid for all coordinate system in which the equations of mechanics hold, as has already been shown for quantities of the first order. We shall raise this conjecture (whose content will hereafter be called the “principle of relativity”) to the status of a postulate and shall also introduce another postulate which is only seemingly incompatible with it, namely that light always propagates in empty space with a definite velocity V that is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent electrodynamics of moving bodies based on Maxwell’s theory for bodies at rest. The introduction of a ‘light ether’ will

prove to be superfluous, inasmuch as the view to be developed here will not require a ‘space at absolute rest’ endowed with special properties… 2
In his book Understanding Relativity, Leo Sartori says that “all of special relativity follows by logical deduction from these two postulates.”3 It is an important point and rarely stated so plainly. Students soon find themselves grappling with the proposition that there is no universal time, for example, or that the simultaneity of clocks in relative motion cannot be established. They learn also that these things are somehow entailed by relativity.
They are, but we need to know that they are deductions from Einstein’s postulates. They were not independently observed and built into the theory for that reason. If for any reason we reject either postulate, then nonsimultaneity and a multiplicity of times will also disappear. We will no longer have to ponder them. They are not empirical realities that have been independently verified.
The first postulate can be read as a summary statement of the theory of relativity itself. We have already discussed it earlier, but here it is again, extracted from the passage above.
… not only the phenomena of mechanics but also those of electrodynamics have no properties that correspond to the concept of absolute rest. Rather, the same laws of electrodynamics and optics will be valid for all coordinate systems in which the equations of mechanics hold …
What Einstein is saying is that inside a smoothly moving railway carriage, the phenomena of electricity and light will no more be affected by the motion of the carriage than the passengers are, or any mechanical experiments that they might perform. It extends to all physical phenomena the observations that Galileo had already made about mechanical phenomena. So the first postulate simply says: Let us assume that this claim is true.
In the first place, the postulate has the merit of being consistent with the Michelson-Morley “null result.” It had failed to detect the effect of motion on light waves, possibly because there was no such effect. (That is the usual interpretation of the experiment.) Another possibility was that the effect was present but too small for Michelson’s equipment to detect.
Anyway, in his first postulate Einstein assumes that the effect was not there. Michelson showed that moving his apparatus through the ether had no effect, and the First Postulate predicted that.

But there was also a problem with this postulate, on its own. It was in conflict with the prevailing theory of electromagnetism. Motion through the light medium should have produced an effect, as just about everyone at the time expected it would. That it had not done so suggested that something quite basic in physical theory might be wrong.
Therefore, Einstein proposed a second postulate, worded as follows. (The letter V was by convention changed to the more familiar c a year or two after his paper was published.)
Light always propagates in empty space with a definite velocity V that is independent of the state of motion of the emitting body.
Immediately following this, Einstein went on to say that these two postulates would “suffice for the attainment of a simple and consistent electrodynamics of moving bodies.” (We won’t need any more postulates, he was saying.) Then, in a casual aside, he added that “the introduction of a light ether will prove to be superfluous.”
Confusion may already be setting in, so here is a brief recap: First of all, linear, unaccelerated motion doesn’t affect the laws of
mechanics—as was known to Newton and Galileo. Within the hold of a smoothly sailing ship, a sailor lacking port holes cannot tell whether he is moving or not. But by the 19th century electromagnetic theory predicted that smooth motion would generate measurable effects for electricity and light. Motion through the light medium should produce visible effects. But Michelson had not found them. Lorentz had suggested an explanation: motion through the ether caused the measuring equipment itself to contract in the direction of motion, and this exactly offset the anticipated effect.
In his new theory, then, Einstein was saying there really was no effect. He was claiming that the laws of electromagnetism are as indifferent to motion as are the laws of mechanics. He achieved this parsimonious and ostensibly desirable outcome with the help of his second postulate. This is where we have to pay careful attention.
The second postulate lies at the heart of the mystery of special relativity. It blandly tells us something that we have all heard—that the speed of light is a constant—but Einstein was nonetheless saying something that tends to remain opaque, sometimes even to students of relativity. An important reason is that Einstein himself stated his own postulate in a misleading way.

Einstein’s Stage Magic
We must approach the second postulate as circumspectly as we would the performance of a conjuror or magician. The man pulls a rabbit out of a hat in front of our eyes, and we know something isn’t as it appears. But we can’t quite see what it is.
But don’t take my word for it. Let us hear from one of his greatest admirers and best expositors, Banesh Hoffmann. For a while he was Einstein’s colleague at Princeton’s Institute for Advanced Studies and later his biographer. He cannot be suspected of even a trace of heresy. He is the best known commentator to have drawn attention to Einstein’s brilliant stage magic.
Here is what Hoffmann says in Albert Einstein: Creator and Rebel. He is about to explain the inner workings of the special theory. But first he gives us this warning:
Watch closely. It will be worth the effort. But be forewarned. As we follow the gist of Einstein’s argument we shall find ourselves nodding in agreement, and later almost nodding in sleep, so obvious and unimportant will it seem. There will come a stage at which we shall barely be able to stifle a yawn. Beware. We shall by then have committed ourselves and it will be too late to avoid the jolt; for the beauty of Einstein’s argument lies precisely in its seeming innocence.4
What does “we might commit ourselves” mean? He means that once we accept those two postulates, we shall have to accept their consequences. Then it will be “too late” to insist, as we may want to do, that what follows seems unacceptable. Heed the warning, therefore. Recall Leo Sartori’s comment that “all of special relativity follows by logical deduction from these two postulates.” The special theory is like a legal contract containing a tricky clause. Before signing on the dotted line, let us examine it with care.
If indeed there does turn out to be something wrong with the special theory, we can be sure that it is hidden in these postulates. A few years later, in 1912, Einstein said that “the theory of relativity is correct insofar as the two principles upon which it is based are correct.”5 That is a fair comment. In effect he is acknowledging the provisional nature of his own postulates.
Hoffmann went on to say—still in a cautionary vein—that Einstein’s 1905 argument is based on “concepts of beguiling acceptability.” Accept

them, and we shall have “unknowingly committed ourselves to a staggering consequence.”6 He repeated a comparable warning in his later book Relativity and Its Roots (1983). Einstein’s two postulates are “cunningly chosen,” he wrote, for “each by itself seems harmless, yet the two together form an explosive mixture destined to rock the very foundations of science.” In fact, the consequences that follow are “revolutionary.”7
I agree with Hoffmann’s analysis, excepting only the admiration that he bestows. For the use of “beguiling” procedures that only “seem” innocent to the reader is not normally regarded as an admirable modus operandi within science.

The Second Postulate
It seems plain enough—the speed of light is always the same “irrespective of the motion of the emitting body.” But this formulation is far from straightforward. Our gratitude to Banesh Hoffmann, who put his finger on the problem:
Einstein’s second principle takes on the aspect of an utter triviality. For no matter how a light wave is started, once it is on its way it is carried by the ether at the standard speed with which waves are transmitted therein.8
In Relativity and Its Roots, Hoffmann expressed the same idea in a slightly different way.
For if a source of light generates light waves in the ether, once the waves are launched they are no longer linked to their source; they are on their own, moving at the rate set by the elastic properties of the ether.7
The idea that a wave travels at a definite speed unaffected by the movement of its source was, and remains to this day, an everyday feature of wave theory. It is something that was once taught in high-school physics. Physicists reading Einstein’s paper in 1905 must have considered the second postulate unremarkable—hardly worth postulating, in fact.
In the medium of air, the sound wave of a plane proceeds through the skies at about 750 miles per hour, whether the plane is traveling at 100 or 600 mph through that air. Petr Beckmann would illustrate the point by saying that if a seagull skims over the sea and taps the water with the tip of a wing, the resulting wave proceeds at a speed that is unaffected by the speed of the gull. The speed of sound in air is not an absolute, because it depends on air pressure; the speed of water waves depends on the depth of the water. But in neither case is the speed affected by the speed of the wave source.
Einstein “extracts from the ether the essential that he needs,” Hoffmann wrote. Two sentences later the ether is whisked away, because it is now “superfluous.” Here indeed we see the magician in action. Einstein had taken as his second postulate “something inherent in the wave theory of light, even as he declares the idea of an ether superfluous.” In so doing, Hoffmann added, he “gave a striking indication of the sureness of his physical intuition.”

In that indulgent comment Hoffmann goes astray, surely. Einstein knew perfectly well that a light speed independent of the motion of the source was uncontroversial. Physicists fully expected that. But with the ether removed, we were in a very different world.
Without the ether, all we have is the source of light and the observer of the light; if one is moving, all we can say is that there is relative motion between source and observer. It is no longer possible to say, in any absolute sense, which is moving. Without the ether as physical substrate, the first postulate gains the upper hand. It forces us to accept that if one thing is moving relative to another, and there is no medium, then any attempt to distinguish between the motion of the source and the motion of the observer is futile.

Revolution in Physics
Henceforth, therefore, without the ether, accepting the second postulate will oblige us to accept that the speed of light is a constant, not just irrespective of the source’s motion, but also irrespective of the observer’s.
And that does introduce a revolution into physics. It leads to Hoffmann’s “staggering consequence.” Move the source, and the speed of the wave is unaffected. Move the observer (in conventional wave theory), and the motion of the observer must be added to or subtracted from the speed of the wave, in order to know the speed with which the wave approaches the observer.
When Einstein said “source,” then, what he really meant was “source or observer.” We know he meant that because he plainly said so himself— some years later. In November 1919, following the immense publicity surrounding the confirmed bending of starlight near the sun, he wrote in an article for the Times of London:
The second principle, on which the theory of relativity rests, is ‘the principle of the constant velocity of light in vacuo.’ This principle asserts that light in vacuo always has a definite velocity of propagation (independent of the state of motion of the observer or of the source of the light).10
I believe this was the first time that Einstein said plainly that the speed of light is a constant irrespective of the observer’s motion.11
Einstein addressed the subject again in his popular account, Relativity, The Special and the General Theory. He ambiguously referred to “the constancy of the velocity of light,”12 without explaining: constant with respect to what? He then had the audacity to continue: “Who would imagine that this simple law had plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties?” He wondered “how these difficulties arise.”13 Yet he still had not plainly said that the velocity of light, in his theory, is assumed to be unaffected by the motion of the observer.
Think of it this way. From the constancy of the speed of light irrespective of the movement of the source (with an ether) Einstein had inferred the constancy of the speed of light, irrespective of the movement of the observer (without an ether).

Deformation of Space and Time
Why is this so important? The former is an everyday feature of wave theory. The latter undermines the fundamentals of physics—space and time.
By analogy, let us apply these ideas to sound waves and see how accepted physical theory treats them. Then we can move on to light. For the sake of argument, assume we have a (stationary) vehicle with a siren. Observers down the road measure the speed with which the siren’s sound approaches them, and all agree that it is, say, 750 mph. Now the vehicle moves forward (at a constant speed), and all observers continue to find that the speed of the approaching sound wave remains unchanged—unaffected by the motion of the source. Sound waves behave just as Einstein said light waves do. Their speed is “independent of the state of motion of the emitting body.”
Now, we put observers in two cars down the road and they are moving either toward or away from the approaching sound wave. Both cars are moving at 50 miles per hour, with respect to the road. The one moving toward the sound source finds the siren wave approaching at 800 miles per hour, while the other measures the wave approaching at 700 miles per hour. Common sense, physical theory and observation are all in agreement. We simply add (or subtract) the observers’ motion to (or from) the speed of the sound wave to find its speed relative to the observer.
But when it comes to measuring the speed of light, Einstein says, we don’t add or subtract the observers’ motion. We assume—or rather, he postulates—that all observers, however they are moving (providing that motion is unaccelerated) will measure the light wave approaching at a uniform, constant speed, c.
How can this be? There is of course an important distinction between the sound and light examples. Sound waves are transmitted in the medium of air, so sound certainly has its “ether.” This means that the motion of the sound source relative to the ground is irrelevant. For a sound wave (as Hoffmann noted) proceeds at its own speed, depending only the “elastic properties” of the medium (air). It will be unaffected by the motion of the source—the vehicle with the siren.

In measuring light waves, however, we no longer have an ether; Einstein has banished it. Therefore, the only speed we must deal with is the relative speed of the light source and the observer. Let us assume we now have two moving vehicles with observers who are measuring the speed of an approaching beam of light. One vehicle is moving toward the light wave at 100 mph, the other moving toward it at 50 mph.
If light waves behaved like sound waves, we would expect to add the speed of each vehicle to that of the light wave. Since the speed of light is so enormous compared to the vehicles’, the difference would be very small. It would be the speed of light in a vacuum, plus 100 mph in one case; plus 50 miles per hour in the other. (These additions are almost negligible, of course, compared with the nearly 500 million miles that light travels in an hour.)
Yet Einstein’s second postulate decrees that any vehicle on the ground, however moving, in whatever direction at whatever speed, will record the light beam as approaching at an unvarying, constant speed, c. How can this be? Well, to be tiresomely repetitive, it has been postulated. For the sake of argument, then, we must proceed as though it is true. Speed is simply distance divided by time, so the required procedure, adopted by Einstein’s theory, is to adjust space and time by an appropriate factor, so that distance divided by time always yields the same quotient, c.
The “appropriate factor” is itself determined by the speed at which the light source and the observer are approaching one another.
Both observers must find that, in the reference frame of the light source, as seen by them, space is foreshortened and time is dilated, but to a different extent for each observer. The greater the approach speed, the more space is said to contract, the more time is said to expand. Consequently, the adjusted distance divided by the adjusted time always yields the same quotient, c—the ever-constant speed of light, for both observers. And this will hold true for any number of observers who may be moving in relation to the light source.

Observer-Dependent Reality
Reality has become observer-dependent, as Petr Beckmann used to say, summarizing the principal reason why he was unable to accept relativity. Space and time become the handmaidens of a particular speed. They must henceforth “cater to” the speed of light, Beckmann said, forever adjusting themselves so that the one divided by the other yields the same constant, c.
The mathematical formulae, giving the extent to which these contractions and expansions are said to occur, were published by Hendrik A. Lorentz a few years before 1905. In relativity theory they are called the Lorentz Transformations.
Notice that all along we have been proceeding purely within the realm of logical deduction. Space contraction and time dilation are simply dictated by Einstein’s second postulate, properly understood. That is why Banesh Hoffmann warned us that once we accept those postulates, we set ourselves up for a “staggering consequence.”
When the observer moves toward the sound wave, we simply add their speeds to find the speed of the approaching wave: 750 mph + 50 mph = 800 mph. That is called the Galileian transformation. But with light, things don’t quite add up any more and the Galileian must be replaced by the Lorentz transformation.
Usually given as mathematical formulae, the Lorentz transformations lie at the heart of the special theory. They describe the extent to which space and time must be adjusted in the reference frame that is moving with respect to the observer. Notice that, in accordance with the first postulate, the observer’s own reference frame can always be regarded as stationary, as long as we confine ourselves to non-accelerated motion (as special relativity dictates). Therefore, no changes in space or time are to be expected within the observer’s own frame. It is always in the other reference frame that space is seen to be shrinking or time slowing down.
The Lorentz formulae are based on the Pythagorean Theorem. As they can look daunting to laymen I omit them here. They are uncontroversial in themselves—no one claims that mathematical errors are involved in the theory; the math never rises above high-school algebra anyway. Again, if there is any error, it’s in the postulates, not in their mathematical elaboration.

These deduced adjustments or transformations of space and time amount to predictions of relativity theory. Have they in fact been observed, experimentally? That is a crucial question, and I shall address it in later chapters. But before doing so, I ask the reader to consider how bizarre it is even to entertain such an idea: Because I move, your watch slows down.

Alpha and Omega
Time and space are the alpha and the omega of physics. They are to physics what the clock and the yard lines are to football. Yet they must be distorted, to maintain the constancy of a velocity, as differently seen by observers in motion. Space contracts and time dilates whenever a body moves in relation to an observer (or—same thing, without an ether— whenever the observer moves in relation to the body). Motion through what? Motion through nothing. As long as one thing moves relative to another, space contracts and time dilates in the “other” reference frame.
You and I are standing in the same room, both of us wearing identical synchronized watches. I move towards you, and as I move, I observe your watch to run more slowly than my watch. And you observe my watch to run more slowly than your watch.
Notice how implausible this is. You are there, and I am here, and you are moving in relation to me. In consequence of that motion and nothing else, distances contract in your reference frame and time slows down.
The Einsteinians are well aware of this implausibility and so they reassure us. Don’t be alarmed, they say. The time and length corrections are minuscule (as long as we are confined to everyday velocities). So the laity is urged go on thinking in the same old way. Our old clocks and rulers will still give us serviceable readings. The professionals on the inside know that everything has been remade, but the laity need not be disturbed.
So we are placated. We overlook the injury to common sense implicit in the theory. But many students of the theory still do find it difficult to sustain this mental acceptance, which I think is why few people ever feel that they really understand the theory of relativity. For it is the principle that matters, not the magnitude. Why, in principle, should we accept that any such a change in space or time really does occur?
It is important to realize that these adjustments to space and time are said to be real. They are not merely apparent. It’s not like perspective, where receding objects appear to shrink. Lengths really do contract, in the Einsteinian scheme, and time really does slow down. An observer moving in relation to you really does see your time slowing down, and your space contracting (even though, within your own reference frame, you detect no such changes.)

It was a rearrangement of the physical world far more sweeping than anything that Lorentz or anyone else had in mind. When things move, in relation to one another, space and time are affected. And this applies across the board in physics, not just to phenomena involving light. In consequence of the special theory, all relative motion has to take into account the Lorentz transformations.
This is one of the least understood aspects of relativity. It is tempting to think that only electromagnetics are affected, because we start out by referring the moving observer to a beam of light. But all of physics is affected—mechanical laws as well as electromagnetic. It is not electromagnetic particles that contract because the observer moves relative to the light ray. It is space that contracts because Einstein has postulated that light rays approach all moving observers at the same speed.
Once we accept that space contracts whenever a reference frame moves in relation to an observer, then everything in that space will contract along with it. Contraction will shrink large objects like tables and chairs just as easily as electromagnetic particles.
The eminent British physicist Paul Dirac emphasized this point when he spoke at the Einstein centennial of 1979. He seemed mildly incredulous himself:
In one respect, Einstein went far beyond Lorentz and Poincaré and the others, and that was in asserting that the Lorentz transformation would apply to the whole of physics and not merely to phenomena based on electrodynamics. Any other physical forces that may be introduced will have to conform to Lorentz transformations, which is going far beyond what the people who were working with electrodynamics were thinking about.14
A more controversial British physicist, Herbert Dingle, said the same thing. He taught relativity at Imperial College, London, and wrote a short book, The Special Theory of Relativity in 1940. He knew Einstein and for years accepted the theory without question. Two decades later, however, he concluded that it was “untenable.” Then he disputed it in a second book Science at the Crossroads. In the earlier work, still accepting the orthodoxy, Dingle had written:
This substitution [of length] must be made whenever length occurs, explicitly or implicitly, in a physical relation. And since every physical measurement that is made depends in part on the measurement of length, all physical measurements are thereby affected… The subject known as the Special Theory of Relativity is thus a revision of the basic principles of physics.15

The consequence of applying the Lorentz transformations to “the whole of physics” is that things don’t quite add up any more. When a man runs inside a train in its direction of motion, we can no longer say that his speed relative to the ground is the addition of those two velocities. It is slightly less than that. Ten miles per hour plus another ten miles per hour don’t quite add up to twenty. Yet the speed of light has not entered into it.
The science writer Isaac Asimov considered these matters and briefly wavered. “It seems strange and uncomfortable to accept so unusual a set of circumstances just to save Einstein’s assumption of the measured constancy of the velocity of light,” he said. In tracing these strange consequences to “Einstein’s assumption,” Asimov had it exactly right. But he quickly fell into line. “Nevertheless,” he added. “whenever it has been possible to measure the velocity of light, that velocity has always been placed at one constant value…”16
Meanwhile, we may ask: What physical evidence supported relativity when the theory was proposed? Had anything comparably strange been observed in nature? I address this question in the next chapter. I believe the answer is that the only anomalous observation was our old friend, the Michelson-Morley experiment.
In later chapters I shall deal with more recent observations. Has time dilation, or space contraction actually been observed? It has been shown that clocks slow down as they move through the gravitational field, and that they speed up at a higher elevation. But no contraction of space has been observed in any experiment.

Notes Chapter 5

1

“On the Electrodynamics of Moving Bodies,” John Stachel ed., Einstein’s Miraculous

Year, Princeton, 1998, p.124.

2

Stachel ed. p. 124.

3

Leo Sartori, Understanding Relativity, p. 48.

4

Banesh Hoffmann, Albert Einstein: Creator and Rebel, Viking Press, New York, p. 72.

5

Albert Einstein, “Reply to Comment by M. Abraham,” August 1912, Collected Papers,

Princeton, vol. 4, Doc. 8

6

Hoffmann, Creator and Rebel, p.75.

7

Hoffmann, Relativity and its Roots, p. 92.

8

Hoffmann, Creator and Rebel, pp.71-72.

9

Hoffmann, Relativity and its Roots, p. 92.

10

Einstein’s article appeared in The Times on Nov 28, 1919. Reprinted in Einstein,

Essays in Science, Philosophical Library, 1934, pp.53-60.

11

In 1907 Einstein published a more elaborate version of his special theory in a journal

called Jahrbuch der Radioaktivität und Electronik. His description of the second postulate can be

construed as saying that the speed of light is a constant, whatever the observer’s motion. See

Einstein’s “Jahrbuch,” (1907) The Collected Papers of Albert Einstein, vol. 2, Doc. 47, p.256.

But his comment is still unclear. Einstein postulates that “the propagation velocity of every light

ray in vacuum… becomes everywhere equal to a universal constant c…” This is to hold true

“whatever the motion of the light source emitting the light ray or the motion of other bodies may

be.” What “does the motion of other bodies” refer to? The observer? Einstein then made it even

more confusing. The principle of “the constancy of the velocity of light” is made plausible by

“the confirmation of the Lorentz theory, which is based on the assumption of an ether that is

absolutely at rest, through experiment.” This must have confused everyone, for while Lorentz’s

theory indeed was based on “the assumption of an ether,” Einstein’s theory was based on the

assumption that there is no ether.

12

Albert Einstein, The Special and the General Theory (1917), p.17

13

Ibid.

14

P. A. M. Dirac, in Some Strangeness in the Proportion; A centennial symposium, ed.

Harry Woolf, Addison-Wesley, 1980, pp.110-11.

15

Herbert Dingle, The Special Theory of Relativity, Methuen, London, 1940, pp.8-9.

Dingle, Science at the Crossroads, Martin Brian & O’Keefe (1972).

16

Isaac Asimov, Understanding Physics, vol. 2, Dorset Press, 1966, p.104

Chapter 6. Holton’s Crusade
We see, then, that the special theory really was revolutionary. Those innocent-seeming postulates brought us to a strange place. The usual way of adding velocities no longer applied; universal time was to be replaced by multiple times, while others in motion relative to us had their own times, too; simultaneity between reference frames in motion could no longer be established.
What evidence in 1905 supported so disruptive a theory? Only one experiment seemed to require so great an upheaval. That was the Michelson-Morley experiment. Its unexpected result did imply that some basic conceptions in physics needed to be rethought.
There is much support for the view that Michelson-Morley was in fact the crucial precursor. One of relativity’s earliest backers was Max Planck. According to Arthur I. Miller, Planck’s support for relativity came even though he believed “the supporting data came only from the MichelsonMorley experiment.”1
What evidence tended to support relativity when it was published? Not much, replied Caltech’s Kip S. Thorne.
Clocks of his era were too inaccurate to exhibit, at the low speeds available, any time dilation or disagreements about simultaneity, and measuring rods were too inaccurate to exhibit length contraction. The only relevant experiments were those few, such as Michelson and Morley’s, which suggested that the speed of light on the Earth’s surface might be the same in all directions. These were very skimpy data indeed on which to base such a radical revision of one’s notion of space and time!2
Yet, increasingly, we read that Einstein may not even have known about the Michelson-Morley experiment when he proposed his theory. We are certainly encouraged to believe that it played a minor role.
The man who has most vigorously pressed this interpretation is Gerald Holton, the Mallinckrodt Research Professor of Physics at Harvard, founder of the quarterly Daedalus, and a former editor of The Collected Papers of Albert Einstein. In recent decades he has been the most influential shaper of opinion about the origins of Einstein’s special theory. His key articles on the topic were collected in his book Thematic Origins of Scientific Thought.3

For many years, the accepted interpretation was that Einstein was well familiar with Michelson-Morley before 1905. The primary evidence is Einstein’s own comment, in his 1905 paper, about “the unsuccessful attempts to discover any motion of the earth relative to the ‘light medium’.” True, there had been a number of attempts. But the two by Michelson were by far the best known. Einstein surely was referring to Michelson-Morley, even if he didn’t identify the experiment specifically. (The paper had no references of any kind.)
Today, nonetheless, Holton has succeeded in winning over many within the profession to a different position.
To gauge his success, we need only look at the article “History of Physics” in the Encyclopedia of Physics. At the end of the article we find a “see also” list of 29 additional topics. Among them is listed only one experiment: Michelson-Morley. But in the article on the history of physics, Lewis Pyenson writes: “There is strong evidence that, in 1905, Einstein was not aware of the Michelson-Morley experiments that had failed to detect the presence of ether drag relative to the earth’s motion.”4
Holton allowed that Michelson’s experiment was “one of the most fascinating in the history of physics,” and its “beauty and mystery” has been appreciated equally by “textbook writers and research physicists.”5 But he concluded that the role of the experiment “in the genesis of Einstein’s theory appears to have been so small and indirect that one may speculate that it would have made no difference to Einstein’s work if the experiment had never been made at all.”6
Why is this important? Einstein himself cited the Michelson-Morley result as supporting evidence for special relativity. But if the theory was in fact inspired by that experiment, it should not entirely surprise us to find that the experimental result is compatible with the theory.
In his popular account of relativity Einstein had asked: “To what extent is the special theory of relativity supported by experience?”7 He wrote that, at last, in his theory, Michelson’s negative result—“a fact very perplexing to physicists”— was furnished with an explanation “incomparably more satisfactory” than anything earlier proposed by others.
Einstein, I submit, preferred to represent Michelson-Morley not as inspiration but as confirmation for his theory, precisely because in 1905 confirmation of the type that he needed was otherwise lacking. Holton recognizes this himself. He says at one point that Einstein

… accurately saw that the Michelson-Morley experiment could be used to gain credibility for the relativity theory in the community of physicists, and he wrote to Sommerfeld on January 14, 1908: “If the Michelson-Morley experiment had not placed us in greatest embarrassment, nobody would have perceived the relativity theory as (half) salvation.”
Einstein later repeatedly made such references to the justificatory and pedagogic usefulness of the Michelson-Morley experiment.8
In looking for evidence supporting Einstein’s theory, we do need something dramatic. Relativity distorted space and time. Holton always downplays the revolutionary character of relativity, arguing that Einstein instead sought continuity. Unconvincingly, he maintains that “the so-called revolution which Einstein is commonly said to have introduced into physics in 1905 turns out to be at bottom an effort to return to classical purity.”9 Holton, however, fails to show us just how revolutionary Einstein’s theory was. Nor does he show how it restored classical purity.
James Bradley’s discovery of stellar aberration (see chapter 10) had caused no upheavals. Fizeau’s experiment on the speed of light in moving media (water) had no revolutionary implications. Nor did Michael Faraday’s induction experiments, with which Einstein had opened his 1905 paper. In 1911, William F. Magie, the president of the American Physical Society, said that relativity was not essential to explain many experiments then under discussion, including Fizeau’s. On the other hand “the negative result of the famous experiment of Michelson and Morley” did require an explanation.10
For over half a century, as Gerald Holton allowed, “historians of science as well as textbook writers were in almost unanimous agreement that the Michelson-Morley experiment was a crucial guide for Einstein in the genesis of his relativity theory.” Both the physicists and the textbook writers were “virtually unanimous” on the point.11 Among them was Max von Laue, a major supporter of Einstein and the author of the first textbook on relativity (published in 1911).
We know also that before 1905 Einstein was keenly interested in the attempts to detect an ether wind. He even planned experiments of his own (although by inclination he was not an experimentalist). In 1899, according to the second volume of his Collected Papers, Einstein “designed an experiment to test the effect of the motion of bodies relative to the ether on the propagation of light; in 1901 he designed a second such experiment, but was unable to carry out either.”12

Einstein as Experimentalist
In one biography, we learn that from the time Einstein arrived at the Institute of Technology at Zurich, he “had the desire to conduct experiments on the Earth’s movement against the ether.” He did set up such an experiment in the lab, in mid-July, 1899. But he “pushed the equipment beyond its limits and something gave,” and as a consequence, “he seriously injured his right hand, which needed several stitches at the city clinic.”13
Michelson himself was not in doubt. In 1923, he told a reporter for the Chicago Tribune that “I think most people would say that [MichelsonMorley] was the experiment which started the Einstein theory of relativity. That experiment is the basis of Einstein.”14 Likewise a book Einstein coauthored with Leopold Infeld discusses “the starting point of relativity theory.” The only experiment mentioned in a fairly lengthy discussion is the “famous Michelson-Morley experiment.”15
Robert A. Millikan, Michelson’s colleague for many years at the University of Chicago and winner of the Nobel Prize in 1923 wrote:
The special theory of relativity may be looked upon as starting essentially in a generalization from Michelson’s experiment. . . [which had shown that there was] no observable velocity of the earth with respect to the aether. That unreasonable, apparently inexplicable experimental fact was very bothersome to 19th century physics, and so for almost 20 years after this fact came to light physicists wandered in the wilderness in the disheartening effort to make it seem reasonable. Then Einstein called out to us all, “Let us merely accept this as an established experimental fact and from there proceed to work out its inevitable consequences,” . . . . Thus was born the special theory of relativity.16
Einstein’s biographer Abraham Pais cannot resist an exclamation point when he writes that Einstein allowed that he had read Lorentz’s paper of 1895, which discusses Michelson-Morley at length. Einstein had also read a paper published in 1898 by Wilhelm Wien, briefly describing experimental attempts to detect the motion of the earth through the ether. The Michelson-Morley experiment is among them.17
Einstein and Michelson met for the last time in Pasadena in 1931. Michelson, who was within weeks of his death, had already referred to relativity as a “monster” and had not stopped looking for new interpretations of the ether. Many eminent physicists were present, including Millikan, Hale and Hubble. After an elaborate dinner Einstein

gave a short speech in which he addressed Michelson and the assembled company.
It was you who led the physicists into new paths, and through your marvelous experimental labors prepared for the development of the theory of relativity. You uncovered a dangerous weakness in the ether theory of light, as it then existed, and stimulated the thoughts of H. A. Lorentz and Fitgerald from which the special theory of relativity emerged.18
But as the years went by, Einstein became more and more vague about his prior knowledge of the experiment. Increasingly, he gave the impression that the special theory had occurred to him as a result of pondering universal principles—his mind untrammeled by experimental minutiae. In 1942 he wrote to Bernard Jaffe: “I was pretty much convinced of the validity of the principle before I did know this experiment and its results.” Michelson’s result, he added, “showed that a profound change of the basic concepts of physics was inevitable.”19

Does Not Remember if he Knew
In a 1953 letter to Michael Polanyi Einstein wrote: “In my own development Michelson’s result has not had a considerable influence. I even do not remember if I knew of it at all when I wrote my first paper on the subject (1905).”20
Starting in 1950, R. S. Shankland, Professor of Physics at CaseWestern Reserve, corresponded with Einstein on the role of MichelsonMorley. He had worked with Dayton Miller on some of the later versions of the experiment. Einstein at first said that only after 1905 had MichelsonMorley come to his attention. “Otherwise I would have mentioned it in my paper.” The experimental results that had most influenced him were the observations on stellar aberration (first made by James Bradley), and Armand Fizeau’s experiment of 1851. “They were enough,” he said.21
Two years later, however, Shankland went to see Einstein and asked the same question. When did he first hear of Michelson-Morley?
“This is not so easy,” Einstein replied. “I am not sure when I first heard of the Michelson experiment. I was not conscious that it had influenced me directly during the seven years that relativity had been my life. I guess I just took it for granted that it was true.”
Then, in a later letter to Shankland, in December, 1952, Einstein said he learned of Michelson-Morley “through H. A. Lorentz’s decisive investigations of the electrodynamics of moving bodies (1895), with which I was acquainted before developing the special theory of relativity.”22
Abraham Pais seemed critical of Einstein about all this. He quotes Einstein’s letter saying he didn’t recall whether he knew of Michelson’s experiment and comments: “Why this need not to remember, or, at best, to underplay this influence?”23
Pais also gives a firm answer to the questions: Did Einstein know of Michelson’s work before 1905? Did it influence his creation of the special theory of relativity? “Yes, unquestionably,” to both questions.24
John Stachel, the first editor of the Einstein Papers, thinks “there is strong indirect evidence that [Einstein] must have known of the MichelsonMorley experiment by 1899.”25

Michelson pedagogically easier
In his own textbook, Holton proved to be more cautious than some of his followers. Describing the theory of relativity for those who have not already encountered it, he first reassured his readers that Einstein himself “did not rely on” Michelson-Morley. Nonetheless, it would be “pedagogically easier” for him to present that experiment as a prelude to any explanation of relativity.26 He then describes the experiment as a logical precursor, much as the textbooks of old had done.
More recently, Holton seems to have been abandoned by his former graduate student, Arthur I. Miller, who published a study of the special theory in 1982. Then he revisited the question in his later book comparing Picasso and Einstein. He had earlier “systematically set up a classification of the books, monographs and journals Einstein had definitely read, very probably read,” and so on. By the time he published his Picasso book (2001), Miller seemed adamant: “The objective historical fact is that Einstein had studied the Michelson-Morley experiment prior to 1905.”27
In the end, perhaps it is not of crucial importance whether we view the famous experiment as confirmation or as inspiration for Einstein. But if it was the latter, it cannot easily do duty as the former. Reenlisting it as a confirming result is circular.
One thing is clear, as Holton showed in his own textbook. Debate over the origins of special relativity has made life harder than ever for authors of “easy Einstein” books. How was it that Einstein came up with so disruptive a theory if he was unaware of its comparably disruptive experimental precursor?
Those deferential to Holton’s Crusade are sometimes forced into implausible or untenable accounts of the origins of relativity. Increasingly, for example, we are told that Einstein relied on his own intuition about the way the speed of light must behave. What, other than Michelson-Morley, obliged Einstein to propose so revolutionary a theory?

Notes: Chapter 6

1

Arthur I. Miller, Albert Einstein’s Special Theory, p. 239, 341.

2

Kip Thorne, Black Holes and Time Warps, W.W. Norton, 1994, pp.78-9.

3

Gerald Holton, Thematic Origins, Chapters 6, 8.

4

Lewis Pyenson, “History of Physics,” Encyclopedia of Physics, Addison- Wesley, 1981,

p. 407

5

Holton, Thematic Origins, p.282; next sentence, Ibid, 478

6

Holton, Thematic Origins, p. 345.

7

Einstein, Relativity, The Special and the General Theory, p 49.

8

Holton, Thematic Origins, p. 479.

9

Holton, Thematic Origins, p. 195.

10

William F. Magie, “The Primary Concepts of Physics,” Science, Feb 23, 1912, p. 288.

11

Holton, Thematic Origins, pp. 477-78; 288; 290.

12

Collected Papers of Albert Einstein, v 2, 259. See his letter to Mileva Maric, 10

September 1899, and to Marcel Grossman, 6 Sept 1901.

13

Michael White and John Gribbin, Einstein: A Life in Science, Plume, 1995, p. 40.

14

Loyd Swenson, Ethereal Aether, pp. 203-4.

15

Albert Einstein and Leopold Infeld, Evolution of Physics, 1938, p. 172, 183.

16

R. A. Millikan, “Einstein on his 70th Birthday,” Rev. Modern Physics, 1949, pp. 343-

44.

17

Abraham Pais, ‘Subtle is the Lord’: The Science and the Life of Albert Einstein, Oxford

Univ. Press, 1982, p. 118.

18

Holton, Thematic Origins, p. 368.

19

Bernard Jaffe, Michelson and the Speed of Light, Doubleday & Co., 1960, pp. 100-101.

20

Holton, Thematic Origins, p. 340; 343.

21

Einstein to Shankland, Holton, Thematic Origins, p. 300, 301.

22

Einstein letter to Shankland, Am. J. Physics, 32 (1964), p. 16.

23

Pais, Subtle, p. 172.

24

Pais, Subtle, p. 116.

25

John Stachel, “Einstein and Ether Drift Experiments,” Physics Today, 40, 1987, p. 45.

26

G. Holton and Steven Brush, Introduction to Concepts and Theories in Physical

Science, 2nd ed. Princeton, 1985, p. 505.

27

Arthur I. Miller, Einstein, Picasso, Basic Books, 2001, p. 184.

Chapter 7. On What Evidence?
Faraday’s Law of Induction
The only anomalous result that Einstein mentioned in 1905 (other than the “unsuccessful attempts to discover any motion of the earth relative to the ‘light medium’”) was one that he put right at the beginning of his paper. It was well known that whether a wire conductor is moved in relation to a magnet, or a magnet is moved in relation to a wire, he wrote, the same electric current is induced in the wire. The observed phenomenon “depends only on the relative motion of the conductor and the magnet.”
As the Einstein scholar John Stachel put it:
the ether theory gives a different explanation for the origin of the current in the two cases. In the first case an electric current is supposed to be created in the ether by the motion of the magnet relative to it (Faraday’s law of induction). In the second case, no such electric field is supposed to be present since the magnet is at rest in the ether, but the current results from the motion of the loop through the magnetic field (Lorentz force law). This asymmetry of explanation [is] not reflected in any difference in the phenomena observed…1
Despite its prominent place in Einstein’s paper, books on relativity usually omit induction entirely in accounting for the origins of the theory. The symmetry of the induced current “had been known ever since Faraday first described the effect in 1831,” as Gerald Holton wrote. “Few physicists, if any, can have thought in 1905 that there was something of fundamental importance in the asymmetry [of the explanation] to which Einstein pointed.”2
Einstein later wrote that the current’s indifference as to which is moved led him to postulate the first or “relativity principle.” The main difficulty that still “had to be overcome was in the constancy of the velocity of light,” he added. At first Einstein thought he “would have to give [this] up,” but he found a way around his problem by postulating a constant light speed and then “relativizing the concepts of time and length.”3 Faraday’s induction, known for decades, supported the first, or relativity postulate but was not something so earth-shaking as to oblige us to reconstruct space and time. That was deduced purely in consequence of Einstein’s second, speedof-light postulate.

Thought Experiments
In accounting for the origins of the theory, a famous thought experiment is cited more and more frequently. Einstein recalled, late in life, that at the age of 16 he hit upon a “paradox” within which “the germ of the special relativity theory is contained.” If he were to pursue a beam of light with the velocity c, he speculated, he “should observe such a beam as a spatially oscillatory electromagnetic field at rest.” But there “seems to be no such thing, whether on the basis of experience or according to Maxwell equations.”
This he viewed as a paradox, and by then (he was writing in 1946), “everyone knows” that “all attempts to clarify it were condemned to failure.” That failure persisted just as long as the “axiom of the absolute character of time, viz., of simultaneity, unrecognizedly was anchored in the unconscious.” So he came to see the “arbitrary character” of this axiom, and that in turn led him to see “the solution of the problem.”4
But such “experiments,” in which impossibilities are imagined, cannot be treated as evidence. Similarly, in this book I have disregarded Einstein’s famous thought experiment about twins, in which one of the pair travels at high speed, turns around and returns younger than the stay-at-home twin. No such experiment has ever been done, and its imagined outcome entails acceleration which disqualifies it from the realm of special relativity anyway. A famous experiment with traveling atomic clocks was carried out, however, and this important experiment is discussed later.
In his “beam of light” paradox, Einstein was really saying nothing more than that imagining something impossible allowed him to conclude that a false axiom about time had been embedded in the unconscious mind. Therefore, that axiom was rejected.
In contrast, illustrating the indulgent trend of modern commentary, Discover’s Corey S. Powell, an adjunct professor at New York University, thinks that Einstein’s thought experiments shows “the universal nature of his thinking.” It enabled him to unearth “shortcomings in current physical theory,” and respond to them by “inventing his own physics and finding new ways to measure space and time.”5 Creativity is to be admired, certainly, but not even Einstein can be permitted to invent his own physics.

Double Stars
A further piece of evidence is worth putting on the table, even though it wasn’t available until several years after the special theory was published. But Einstein promptly incorporated it into his popular work, Relativity: The Special and the General Theory (1917), and it deserves to be considered.6
In 1913, the Dutch astronomer Willem de Sitter had analyzed the light coming from certain double stars, whose orbital plane is aligned so that, in the course of their mutual circling, one star is moving generally toward the Earth while the other is moving away. But if the light from these stars proceeded toward us at different speeds, one with the star’s orbital velocity added to the speed of light, the other with its velocity subtracted, they would not appear to us as two distinct stars. We would see time-delayed images, sometimes resulting in three apparent stars, as the faster moving light from a star that has turned toward us in its orbit catches up with the earlier, slower light when the star was receding. But we never see that. They always appear as double stars.
Einstein drew attention to De Sitter’s observation as a way of confirming his second postulate: the speed of light is unaffected by the motion of the light source. If by then the ether had remained in good standing among physicists, this claim might well have been considered unremarkable, because with a luminiferous medium, the light from both stars would have launched forth at the standard velocity of light in that medium. By 1913, moreover, the ether was still widely accepted, as Einstein’s special theory had not yet transformed public opinion on the topic. Etherists would have no trouble believing that the speed of light from double stars would be unaffected by their motion.
De Sitter’s claim was nonetheless important, because the wave theory of light was still contending with the emission theory of Walter Ritz (and others). Ritz claimed that light traveled in particle streams, as indeed Newton had thought. But double stars seriously weakened the emission theory. As the light source approached the Earth, the speed of particle stream should increase, just as bullets go faster if fired from a gun moving toward the target. De Sitter’s evidence therefore strengthened the competing wave theory.

But as Einstein could see, with no further role for the ether — abolished by his special theory—the new double-star data showed that light, whether rays or particles, definitely did not approach at differing speeds from moving sources. Therefore it was true that De Sitter’s analysis tended to support both the wave theory of light and Einstein’s speed-of-light postulate.
In Special Relativity, A. P. French adds an interesting footnote. It has been more recently argued, he says (citing an article in the American Journal of Physics) that “since these binary star systems are usually surrounded by a gas cloud, which absorbs and then re-radiates the light from the stars, the speed of the light that crosses interstellar space may in any case be independent of any possible influence of the original moving sources.”7
French’s comment is of interest to the proponents of Petr Beckmann’s theory—that the local gravitational field is the luminiferous medium— because in this theory, too, twin stars would tend to be enveloped in a blended gravitational field. It would absorb and re-radiate the light from the orbiting stars at a speed determined by their joint gravitational medium, not by the stars’ separate motion. Therefore the binary star result is consistent with Beckmann’s theory in addition to Einstein’s.

Role of Maxwell Equations
Commentators today are ever more inclined to say that Einstein’s speed of light postulate is implied by the Maxwell equations.[1] If so, however, one could also claim that the special theory itself is little more than a deduction from Maxwell’s electromagnetic ideas.
The modern fashion is to put as much distance as possible between special relativity and Michelson-Morley, and then to attribute the second postulate to Maxwell’s electrodynamics. In My Einstein, for example, Janna Levin, a professor of physics and astronomy at Barnard College, says that Einstein “realized that space and time are relative.” She continues:
He came to this incredible conclusion through the idea that the speed of Maxwell’s electromagnetic light is a fundamental constant. This simple assertion is actually outrageous. Our familiar experience is exactly contrary. For instance, if you race toward a moving train, its speed relative to you changes. But if you race toward a beam of light, its speed, as measured by you will, remarkably, always be c. … The implications are surreal and Einstein worked them out in imaginative thought experiments.8
The idea that relativity theory flowed from Maxwell has also been adopted by John and Mary Gribbin. “Einstein had realized that no experiment involving Maxwell’s equations could ever detect motion relative to this hypothetical absolute rest frame.” His second postulate, in fact, “comes straight from Maxwell’s equations.”9
In the same vein, John Gribbin wrote in Deep Simplicity (2004):
It is this requirement from Maxwell's equations that the speed of light is a constant for all observers, no matter how they are moving, that led Albert Einstein to develop the special theory of relativity in 1905.10
The most eminent recruit in support of the Maxwell-equation view is Stephen Hawking. In 2007, he contributed introductions to a volume of Einstein’s scientific writings. In one commentary he wrote:
… . Einstein’s 1905 special theory of relativity grew out of a simple observation. The theory of electromagnetism discovered by James Clerk Maxwell in the 1860s showed that whether we are moving toward or away from a beam of light, the light will always approach you at the same speed. This is not true of our experience in the everyday world.11
But it is not clear that Einstein ever did make such a claim, although he undoubtedly set such an interpretation in motion. In an unadorned footnote to his E = mc2 paper, published later in 1905, he wrote: “The principle of

the constancy of the velocity of light is of course contained in Maxwell's Equations.”12
As it stands, however, this is ambiguous. Read one way, it is uncontroversial. Read another, it is problematic. The point is that Maxwell accepted the existence of the ether and assumed that light was propagated in the ether at a constant speed. It would be unaffected by any motion of the light source within that medium. By 1905, however, Einstein had rejected the ether. It is not clear whether Einstein in this paper assumes an ether or not.
But our more recent authors all accept that the ether is no more. Yet they insist that without an ether the speed of light is a constant according to Maxwell, no matter how the observer moves. That does correspond to Einstein’s second postulate, but it is not something that can be deduced from the Maxwell equations. If it could be, Einstein would not have needed to postulate it in 1905.
Furthermore, Maxwell himself would have had no reason to believe that the Earth’s motion through the ether could be detected. Yet he argued that a reflected light beam would have different speeds, coming and going, and his communications on this subject first inspired Michelson to carry out his experiment. If these recent interpretations of Maxwell were correct, his own equations should have told him that no such speed differentials were to be expected.
Not only did Maxwell assume that there was such a difference, he published an article claiming as much in the Encyclopedia Britannica. Maxwell wrote: “If it were possible to determine the velocity of light by observing the time it takes to travel between one station and another” on the earth’s surface,
we might by comparing the observed velocities in opposite directions, determine the velocity of the aether with respect to these terrestrial stations. All methods, however, by which it is practicable to determine the velocity of light from terrestrial experiments depend on the measurement of the time required for the double journey from one station to the other and back again, and the increase of this time on account of a relative velocity of the aether equal to that of the earth in its orbit would be only about one hundred millionth part of the whole time of transmission, and would therefore be quite insensible.13
Because he thought the difference would be too small to measure he proposed another method, this one yielding a potentially larger, “first order” effect; not depending on reflected light. It involved timing the eclipses of Jupiter’s moon at different stages of its orbit, relative to the earth’s

position. Maxwell wrote a letter to D. P. Todd of the Nautical Almanac Office and the editor of American Ephemeris in Washington, about the possibility of confirming this experimentally.
Maxwell died soon after that, in November 1879. Recognizing the letter’s importance, Todd sent it to Nature, which published it.14
It was about the last thing that Maxwell wrote. A. P. French is one of the few authors to have discussed it.15 Maxwell’s letter and encyclopedia article plainly undermine the claim that he believed, or that his equations predicted, that the speed of light would be the same in all reference frames.
Michelson saw Maxwell’s letter and it inspired him to carry out his first experiment. He realized that the effect that Maxwell thought would be “quite insensible” was in fact “easily measurable” with his improved interferometer.16 (But Maxwell’s later suggestion, timing the eclipse of Jupiter’s moons, really was not feasible.)
So the Michelson-Morley experiment was born. It is an irony, surely, when one delves into Maxwell’s ideas about the ether and the speed of light, that instead of leading us away from Michelson’s experiment, they lead us straight back to it. Far from rendering the Michelson-Morley experiment superfluous, as far as the origin of relativity is concerned, Maxwell’s ideas actually gave rise to the famous experiment, historically.
The mistake made by recent commentators, surely, is to assume that in thinking about Maxwell’s electrodynamics it is all the same whether the ether exists or not. If there is a medium, light speed is a constant with respect to that medium. If there is no medium, and either the light source or the observer moves, the speed of the approaching light beam will vary. If one then decides, for theoretical reasons, that the speed of light must be a constant, and one postulates it —”let’s assume that the speed of light is a constant for all observers”—then space and time logically must be corrected so that they always produce, mathematically, the unvarying speed that has been postulated. That is the path that Einstein took.
In my view, then, the claim that Einstein’s second postulate is implied by the Maxwell equations must be rejected. If it were true, we would be reduced to claiming that Maxwell didn’t understand his own theories. This leaves us, as we began, with the Michelson-Morley experiment as the sole support for the theory of relativity at the time it was published.

Notes: Chapter 7

1

John Stachel, Einstein from ‘B’ to ‘Z’, Birkhauser, Boston, 2002, p. 162.

2

Gerald Holton, Thematic Origins, p. 381, 383.

3

John Stachel, Einstein’s Miraculous Year, p. 111.

4

P. A. Schilpp ed., in Albert Einstein, “Autobiographical Notes,” 1949, p. 53.

5

Corey Powell, My Einstein, Pantheon Books 2006, p. 101.

6

Einstein, Relativity: The Special and the General Theory, p. 17.

7

A. P. French, Special Relativity, W.W. Norton & Co., 1968, p. 74.

8

Janna Levin, My Einstein, p. 183.

9

John and Mary Gribbin, Annus Mirabilis, Chamberlain Bros, N.Y. 2005, p. 96.

10

John Gribbin, Deep Simplicity, 2004, p. 20.

11

A Stubbornly Persistent Illusion: The Essential Scientific Works of Albert Einstein,

commentary by Stephen Hawking, Running Press Book Publishers, Phila. Pa., 2007, ix.

12

Einstein et al, The Principle of Relativity, (1923), Dover, p. 69.

13

Maxwell, “Ether,” Encyclopedia Britannica, op. cit.

14

The Scientific Letters and Papers of James Clerk Maxwell, vol.3 (2002) ed. P.M.

Harman, Cambridge University Press 2002, item # 734. p.767. Nature, Jan 29, 1880.

15

French, Special Relativity, p. 49.

16

Michelson’s paper, see Loyd Swenson, Ethereal Aether, pp. 249-50.

Chapter 8. Mystery of Mass
Consider a spaceship passing overhead. According to Einstein’s theory, as its speed increases its mass increases. It becomes greater and greater, until at the speed of light (in theory) it becomes infinite. Since this is impossible it implies that the speed of light is unattainable … As the spaceship (as viewed from Earth) gets shorter, it physically becomes more massive. In fact, when it is one-tenth its original length, it is ten times as massive … Of the three dramatic changes with speed, the change in mass is the easiest to observe experimentally. In fact, scientists observe it every day around the world in high energy accelerator labs. … Again, we have to be careful. This change is only evident to the observer on Earth; the observer on the spaceship notices nothing out of the ordinary.1
Barry Parker, Einstein’s Brainchild: Relativity Made Relatively Easy!
We have already seen that special relativity reduces space and time, previously regarded as autonomous, to a state of dependency; waxing and waning depending on the speed with which the observer moves. Now—in the comment by Barry Parker above—we find that mass meets the same fate.
Einstein and Infeld wrote in The Evolution of Physics:
We know from mechanics that every body resists a change in its motion; the greater the mass the stronger the resistance … But in the relativity theory, we have something more. Not only does a body resist a change more strongly if the rest mass is greater, but also if its velocity is greater. Bodies with velocities approaching that of light would offer a very strong resistance to external forces. In classical mechanics the resistance of a given particle was something unchangeable, characterized by its mass alone.2
In this chapter, I shall explore what happens when masses are moved. Later I will turn to the experiments claiming that time slows down in moving reference frames. (The space ship “gets shorter,” in theory and in drawings. But space contraction has not yet been observed experimentally.)
Prof. Parker was not misstating the doctrine of the relativists, however. Jeremy Bernstein, in his book Einstein, published decades earlier, wrote: “A moving electron, or any massive object, becomes more massive when it is in motion with respect to an observer than when it is at rest with respect to the same observer.”3 [My italics.]
This is bound to leave readers puzzled. Parker (deliberately) begs the question of what is “really” going on. The observer on the ground thinks that the mass of the spaceship has increased, but the observer on the spaceship sees nothing out of the ordinary. Which is it? That is not a

meaningful question, say the Einsteinians. The mass is either increasing, or not, depending on your point of view. In fact, as Parker did not say but might have, from the point of view of the fast-moving spaceship, the mass of the Earth, rushing back in the opposite direction, will be seen to have increased by a factor of ten. But earth-dwellers will notice nothing unusual.
By the rules of relativity, remember, no reference frame is privileged. Symmetry must reign. It is always permissible to assume that the observer is located within the “other” inertial frame—that of the spaceship or the high-speed particle. And from these points of view the observer will see no change within his own environment.
In The Nature of the Physical World, Arthur Eddington takes us on this imaginary journey. He examines a fast-moving particle from its own point of view.
It is an ordinary electron in no wise different from any other. But is it travelling with unusually high speed? ‘No,’ says the electron, ‘that is your point of view. I contemplate with amazement your extraordinary speed of 100,000 miles a second with which you are passing me. I wonder what it feels like to move so quickly. However, it is no business of mine.’
So the [electron] smugly thinking itself at rest, pays no attention to our goings on, and arranges itself with the usual mass and charge. It has just the standard mass of an electron, 9 ·10 -28 grams. But mass and radius are relative quantities, and in this case the frame to which they are referred is evidently the frame appropriate to an electron engaged in self contemplation, viz. the frame in which it is at rest.4
Eddington’s intent was not to raise doubts about observer-based physics, nor about relativity, which he admired. Nonetheless, his account is bound to raise questions about a theory in which something as basic as mass depends on the observer’s point of view. At the least we may wonder whether Einstein’s theory really did simplify physics.
When we talk about mass in this context, we are not talking about matter. It is a point repeatedly stressed by Ralph Baierlein, the author of Newton to Einstein. When describing what it is that changes with velocity, we are talking about an attribute of a thing, not the thing itself.5 The matter of a particle has the same number of atoms whatever its speed. We are talking about an attribute, its inertia, or inertial mass. It is a measure of the reluctance of a given piece of matter to change its state of motion.
The increase of inertial mass with velocity is observed in particle accelerators, and we are told that this gives us the best confirmation of special relativity. Relativity indeed does provide an explanation of sorts. But there was all along a better one—one that does not oblige us to believe

that if we travel alongside a fast-moving particle, its mass stays unchanged even as the mass of everything else outside it is observed to increase.