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The Origin of the Controversy
It will, I think, help towards a general understanding if I begin with a brief picture in outline of the world of physical science as it is today, for the sake of those unacquainted with it. In accordance with what I have said at the end of the preceding chapter, I must add that this is my own description, but I do not think its essential accuracy will be questioned by anyone familiar with the situation. In any case its effect can only be to illuminate, and not to distort, the account of the facts which is to follow.
The world of physical science today cannot be defined with precision. It includes, of course, pure physicists and almost all astronomers, as well as many chemists and even a few biologists, though we may leave these out of consideration without affecting the general discussion. I shall refer to all these, for brevity, as 'physicists' or 'physical scientists'. When the editor of Nature wrote in a leading article (reproduced here in the Appendix) that 'the special theory of relativity has been enormously successful in the past half-century, and in spirit as well as in detail has come to pervade the whole of modern physics', the subjects which he included in the term 'modern physics' can with truth be said to include the work of all these scientists.
Within this field we may make a general division into two classes which I will describe as experimenters and mathematicians. There is a little overlapping, of course, and the designations arc broadly descriptive rather than meticulously exact, but the impression they give is a true one: practically everyone in whose work special relativity plays a significant part would be assigned without hesitation to one or other of these classes, and his inclusion would not be challenged. Mathematicians, in the strict sense of the word, may differ as to whether so-and-so should be called a pure or an applied mathematician, and the work of some of both kinds is mainly independent of special relativity: moreover, scientists who do experiments may indulge in mathematics at times. But in relation to the present problem the distinction is unambiguous.
Now, still keeping to my own generalisation from the whole of my experience - the reader may judge for himself how it applies to the examples which I shall give, though he cannot, of course, confirm my statement that they are truly representative -the reactions to my question from the 'experimenters' are, with almost 1 complete unanimity, either that they do not understand the theory, at all, although they assume it in their experiments, or else that they regard it as nonsensical; they take it to be true, nevertheless, in their experiments which depend on it with various degrees of directness, and justify this procedure on the ground that the theory has been tested by those who understand it (i.e. the 'mathematicians'), and therefore all questions about it should be passed to them. So long as the 'mathematicians' declare themselves satisfied that the theory is trustworthy, the 'experimenters' are satisfied to go on using it. The 'mathematicians', on the other hand, either refuse to say anything at all in answer to my criticism, or else reply in terms of politeness, mysticism, irony, (these terms arc roughly in descending order of age of the person in question) or other quality, with this alone in common, that they do not answer the question asked. In the meantime, complete trust is placed in the theory by almost everyone, and experiments proceed as though it had never been questioned.
This may seem to the uninitiated so incredible, in view of the popular image of the scientist which corresponds to Dale's description - I know from experience that it does so appear - that I am forced in my examples (which, however, will not include the least reputable ones) to give the names of those whom I quote. I do this with the greatest reluctance, but it is clearly necessary. General statements about 'modern scientists' would inevitably, and rightly, be dismissed as unconvincing. Only when those statements arc known to proceed from scientists of the highest reputation, and given in their own words, can they possibly carry the conviction that the circumstances demand. I hope it will be believed that it is this consideration alone, and nothing of personal feeling, that forces me at last to take the course which I have shunned for so long.
Another generalisation, which I think has an important significance not only for the question of the truth or falsity of special relativity but also for the matter of the education of scientists, is this: the readiness to respond to my criticism decreases steadily with increasing distinction of those who read it. The leaders in the subject reply, if at all, only when pressed, and as briefly as possible. Those of intermediate status cite experiments of greater or less irrelevance or present calculations of greater or less complication and with no relevance at all. Students and young Ph.D.s are vociferous. 'After your argument in Nature with Professor Max Born' (see p. 42), wrote the former editor of Nature to me in 1963, 'I had a large number of communications and quite a number of individual unannounced visitors at Nature office. As you implied in your letter they each one felt that he could prove you were wrong in your view and each one got about it in a different way... all the people who submitted communications or wished to discuss this problem with me, could scarcely be considered first class men of science as compared with Max Born.'
I think this shows how, even in science, what at its beginnings is recognised as a speculation, with greater or less plausibility, develops with time into a compulsory dogma, which whosoever disbelieves thereby brands himself as an ignorant fool. To exaggerate slightly, but not to distort, it is a microscopic reproduction of the macroscopic development of the place of hypotheses in science from Newton to Eddington which was noted earlier. But, without attempting to relate it in detail to the present generalisation, I will record one instance for the reflection of the reader in this connection. Some years ago Dr. W. Cochran, now Professor of Physics at Edinburgh, but then a lecturer on relativity among other things at Cambridge, offered a prize of 10 pounds to the member of his class who wrote the best refutation of my criticism of special relativity. The winner sent me a copy of what he had written. It is not worth recording, but Professor Cochran himself has refrained from publishing what he considers a refutation, though later, in his capacity as editor of Science Progress, he rejected a paper of mine on the subject, sent to that journal for publication, the only reason given to me being that its conclusions were at variance with those of some calculations which he made, which were unrelated to the contents of my paper.
Let me now, after this preamble, record in outline the history of this matter. It began with a revival of an old problem, known as the 'clock paradox' or 'twin paradox', which dates from the early days of special relativity. I shall deal with this more fully in Chapter 9, so a brief description will suffice here. One of the earliest deductions from the theory was that if a traveller sets out from the Earth at a high speed and later returns, he will have aged less than his twin brother who has remained at home, because 'a moving clock runs slow' and the physiological processes of a man are equivalent to a clock. But equally, according to the theory, it is the Earth that might be regarded as having moved while the 'traveller' has remained at the same place, in which case the Earthbound twin would be the younger at the end of the process. These results obviously cannot both be true. In 1955 I adverted to this problem as a result of reading Sir George Thomson's book, The Foreseeable Future, in which it was stated that, according to the most authoritative view, the former result was correct and the latter therefore incorrect. In an article in Nature1 I claimed that the twins must necessarily age at the same rate because it was an essential requirement of the special theory of relativity, which I then believed to be sound, that no observation was possible that would enable one to ascribe the motion preferentially to either twin.
I need not here describe the course of the ensuing discussion, for all that is necessary will be said later. I mention the controversy here because it was the origin of my realisation that the special relativity theory (which, as I have said, at the beginning of that discussion I believed sound) was impossible: it made me see that the theory required that the twins would age both at the same rate and at different rates, which is clearly contradictory. My first presentation of the contradiction appeared in the Bulletin of the Institute of Physics2, which hardly constitutes publication since that is a journal issued only to members of the Institute Ч admittedly numerous and including many of the most distinguished physicists - and not generally available in libraries. I there expressed the contradiction, not in terms of clock readings, which Einstein had considered in his first presentation of the theory, but in terms of readings of space-measuring rods, and I showed that the theory required each of two such rods to be shorter than the other. I also ventured some speculations on electromagnetic aspects of the theory, which I should have been wiser to have left for further reflection after the kinematical question had been settled.
The immediate consequences were more evident in private correspondence than in printed discussions. They showed such failure to meet the essential point that (very shortsightedly, as I now realise) I tried to deal one by one with the purely incidental points that were raised and to show that they did not meet my criticism. I should, of course, have ignored them and pressed my correspondents to answer my argument instead of side-stepping it. During 1960 I published papers - in Science Progress3, Philosophy of Science4 (an American journal), the British Journal for the Philosophy of Science5, on various aspects of the matter Ч all, I believe, in essence sound but, from a tactical point of view, untimely since they allowed the essential contradiction in special relativity to escape attention. Being a poor psychologist, I did not realise that scientists, like other people, are far more ready to search for flaws in other people's reasoning than to eliminate prejudices from their own, and I remained in a state of bewilderment at my inability to make clear to others what seemed so obvious to me. Had I, from the beginning, pressed for an answer to the question put in the Introduction to this book, and refused to be diverted into other aspects of the matter, the question might by now have been settled. But crying over spilt milk is a useless occupation.
However, in 1961, in a dialogue with the late Viscount Samuel' dealing with this among more general matters, I gave at some length an account of the difficulties I had had in getting any attention paid to my criticism of special relativity, notwithstanding the fundamental importance of the matter, and I gave in an Appendix a different form of the proof that the theory contained a contradiction. It would be superfluous to repeat here what is said there (pp. 70-75). It will suffice to say that it records attempts to get publication for my criticism through the Royal Society, the Physical Society and the Philosophical Magazine, which were all rejected for reasons which the reader of the dialogue can evaluate for himself; and that not a single reviewer of the volume mentioned that the question had even been raised. I pass to a letter published in Nature of 8 September 1962,7 in which, after calling attention to the importance of either accepting or refuting my criticism, I quoted verbatim from Einstein's paper his proof that, according to his theory, a 'moving' clock, B, worked more slowly than a 'stationary' clock. A, and then gave, in exactly the same form, a proof that, in exactly the same circumstances, clock A worked more slowly than clock B. 'The conclusion of the first passage', I wrote, 'is that each reading of B is behind the corresponding reading of A, and that of the second passage is that each reading of A is behind the corresponding reading of B.' Applying the result to a particular case, I concluded: 'Hence, when B reads 6, A reads both 12 and 3. That is a contradiction. To avoid this outcome it must be explained not why the two cases are different - that is obvious - but why, consistently with the theory, the former result must be accepted as true while the latter must be rejected as false.
This brought a host of replies, from correspondents of all degrees of distinction in the subject except the highest, which had only one representative - the late Professor Max Born. The bulk of the letters were sent to me by the editor to deal with collectively, but Professor Born's letter was printed separately with my reply to it. The general article is given in Nature of 30 March 1963, which contains also Born's letter and my reply just mentioned8. I need not summarise the former, which may be looked up by anyone interested in the general sort of reaction to my very simple argument, but I must comment on my correspondence with Born, who was for many years until his death an honoured and much loved friend of mine, because of his exceptional sense of responsibility in replying to what others of comparable distinction in the subject had ignored, though it must be left to the reader to judge whether, in the end, his reaction met the full needs of the case. 'Prof. H. Dingle', he wrote, 'has sent me a reprint of his communication published under the above title' [Special Theory of Relativity] 'on p. 985 of Nature, September 8 1962, with the handwritten remark: "With kindest regards. Test case for the integrity of scientists". Though former experience has taught me that discussing relativity with Dingle leads to no agreement I have to answer a challenge which is directed against the "scientific integrity" of myself and of others.' He then proceeded to discuss the problem, and I will quote that part of his letter which bears directly on the main point. It may be verified, by reference to the original, that I have omitted nothing that modifies the significance of the quoted part, but since Part One of this book is designed to be entirely non-technical it is necessary to exclude everything that would tend to frustrate that intention, and I can assure the reader that I am giving the full essence of the matter, in so far as it concerns the central question whether my criticism has been met or not. Dingle, writes Born8,
quotes a passage from Einstein's paper, the first paragraph of which ends with the question: 'What is the rate of this clock, when viewed from the stationary system?' ... Dingle now proceeds in this way: 'And here is the passage leading to the opposite conclusion'. The first paragraph of this new passage is completely identical with that of the original including the last sentence just quoted (in italics)... The mistake is in the first paragraph quoted above (in italics); it should read, in the two cases:
1st case, clock at rest in k: What is the rate of the clock in k, when viewed from the 'stationary' system K?
2nd case, clock at rest in K: What is the rate of the clock in K, when viewed from the 'moving' system k?
Born then proceeds to answer his own questions, shows that they do not lead to a contradiction, and concludes: 'Dingle's objections are just a matter of superficial formulation and confusion.'
I need not record my reply, which can be seen in Nature immediately after Born's letter, because I think it is obvious at once that it is no answer to a criticism to say that the critic should have asked questions which he did not ask, and charge him with 'superficial formulation' because of his omission. The question which Born calls my 'mistake' is not mine; it is Einstein's. What I showed was that it had two mutually contradictory answers, equally authentic, of which Einstein had given only one which had been accepted as uniquely valid.
I believe that if Born had allowed himself to entertain the possibility that the theory might be wrong, he would have had the greatness of mind to see that it was and to have admitted the fact. Unfortunately, however, it was no longer possible for him to conceive that possibility. Although I sent him an offprint of my reply (he was then living in retirement in Germany and no longer following the English press), he would not read it.
I am completely fed up with the matter [he wrote], I don't know what you have answered to my note. As I think my argument irrefutable, I am convinced that you have made again some elementary mistake... I am sorry that I have to say such words to a man so kind and friendly as you are. But as I am over 80, the time left to me is too short to waste it on such futile discussions.
I will add only that I am equally sorry to have to say such words about a man so kind and friendly as Max Born was, but the matter is too deadly serious to leave them unsaid. The reader must form his own opinion on the matter.
On reflection several years later on the course which this controversy has taken, I realise that, in my ignorance in the earlier stages of the degree to which conviction of the final truth of special relativity had displaced, in the minds of physicists, the openness indicated in Dale's description of Science, I took the less effective of two possible courses. I could have put my criticism of the theory in the form of a statement and invited critics to find a flaw in it; or I could have pointed out that the theory left open a question and asked for an answer to that question. Put more specifically, I could have pointed out that the theory contained a contradiction - that it required each of two clocks to work faster than the other - or asked the question: how does one tell from the theory which clock works the faster?
The difference seems slight, but its effects have been wholly different. Unfortunately, throughout most of the controversy I took the first course, and that opened a way for all sorts of spurious 'faults' to be found in my statement - quibbles over words, and so on: for instance, those of Born just mentioned, and the innumerable others to which the then editor of Nature, Mr L. J. F. Brimble, referred (p. 39); a notable example is that given in the Appendix, in which it will be seen how Professor McCrea smothers the simple passage given in my article, to which I asked for exclusive attention to be given, by entirely superfluous comments including a space-time diagram, to dispose of a consideration that had not been raised except by himself.
As soon as I took the other course, however (the asking of a question), the effect was completely opposite; instead of bringing on myself a flood of discordant 'refutations' I was met by complete silence. This is illustrated by what followed my letter to Science (p. 81); by the successive failures of the present editor of Nature to fulfil his repeated promises to deal with the matter in an editorial (p. 90); and by a reply from Professor Bondi (a well-known mathematical authority on relativity, who, as Chief Scientific Adviser to the Ministry of Defence, may be held to have a special responsibility in such a matter) who simply wrote:
It is kind of you to invite me to participate through adding a reply, but I do not feel able to accept your offer. In my view my published work (particularly 'Relativity and Common Sense', also 'Assumption and Myth') amply refutes your views. I do not think I can usefully add to what I said there; I am only sorry that you do not find it convincing.
The sentence I asked for would have occupied less space than this.
I think the difference is most instructive - a deluge of evasive replies in one case and total silence in the other. It will greatly assist the full appreciation of what follows if I give here the two forms of criticism of the theory in what seem to me to be the terms in which they can best be understood and, if possible, answered: I call them 'The Argument' and 'The Question' respectively.
According to the special theory of relativity, two similar docks, A and B, which are in uniform relative motion and in which no other differences exist of which the theory takes any account, work at different rates. The situation is therefore entirely symmetrical, from which it follows that if A works faster than B, B must work faster than A. Since this is impossible, the theory must be false.
Since I wish in this book to concentrate on The Question, and let the reader judge the cogency of any answer that may be offered (none has been offered yet), I put this in more extended form, to anticipate as far as possible comments which are not answers; but I think it will be realised that The Question could have been put as briefly as The Argument (it is in fact summarised in the Introduction) and that a valid answer would be equally brief.
According to the special relativity theory, as expounded by Einstein in his original paper,9 two similar, regularly-running clocks, A and B, in uniform relative motion, must work at different rates. In mathematical terms, the intervals, dt and dt', which they record between the same two events are related by the Lorentz transformation, according to which dt ? dt'. Hence one clock must work steadily at a slower rate than the other. The theory, however, provides no indication of which clock that is, and the question inevitably arises: How is the slower-working clock distinguished? The supposition that the theory merely requires each clock to appear to work more slowly from the point of view of the other is ruled out not only by its many applications and by the fact that the theory would then be useless in practice, but also by Einstein's own examples, of which it is sufficient to cite the one best known and most often claimed to have been indirectly established by experiment, viz. СThenceТ [i.e. from the theory he had just expounded, which takes no account of possible effects of acceleration, gravitation, or any difference at all between the clocks except their state of uniform motion] Сwe conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.ТApplied to this example, the question is: what entitled Einstein to conclude from his theory that the equatorial, and not the polar, clock worked more slowly?
A single sentence would be sufficient for an answer, and such a limitation is highly desirable to prevent obscuration of the essential point by irrelevant considerations. To guarantee its relevance it should be applied to justify Einstein's choice.
Failing an answer the theory clearly becomes untenable, for, as Professor J. L. Synge has said after long consideration (p. 77),either the theory or the conception that a regularly running clock cannot work both faster and slower than another must be abandoned.
The remainder of this book is concerned with The Question and the attitude of the scientific world to it. That being understood, I resume the story and describe what followed my exchange of letters with Born.