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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.

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.

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,

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?

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.Т Applied 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?

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.