SCIENCE At the Crossroads

HERBERT DINGLE Professor Emeritus of History And Philosophy of Science,

University of London

MARTIN BRIAN & O’KEEFFE LONDON

1972

Preface

This book was written during the first half of 1971. Before arrangements for its publication had been completed, however, an independent controversy sprang up in the Listener, in which reference was made to the correspondence in that journal which is discussed in the following pages (83-87). This seemed to afford a possibility of achieving the desired end without the necessity of revealing the much fuller story told here: accordingly I withheld the typescript and gave, in the Listener of 23 September 1971, a brief account of the sequel to the former controversy. The result was another long series of letters, extending from the issue of 30 September 1971 to that of 13 January 1972, which inspired, among other things, an article by Mr Bernard Levin in The Times of 21 December 1971, which itself led to a brief correspondence in The Times.

The general interest thus brought to light, as I know from my subsequent correspondence from various parts of the world, was great and widespread, but the one essential desideratum of the whole exercise — plain evidence, through an answer to, or acceptance of, a very simple refutation of the immeasurably important special relativity theory, that the obligation to preserve strict integrity in science continues to be honoured — was still not forthcoming. Physical research, both theoretical and practical, still proceeds as though special relativity were unquestioned. There remains, therefore, no alternative to publication of the facts here recorded.

It is impossible in a brief space satisfactorily to summarise the whole of this latest phase of the matter, nor is it necessary, for the journals concerned may be consulted by interested readers, and on the one vital point no progress is made; the criticism remains unanswered and unaccepted, and its implications are unchanged. It will, however, serve to authenticate this statement, and at the same time introduce the reader at once to the central source of the book, if I reproduce the final letters, in The Times of 8 and 26 January 1972, respectively — the first from Professor R. A. Lyttleton, F.R.S., of St John's College, Cambridge, and the second my reply — and simply add that Professor Lyttleton has not responded, either privately or publicly, to my appeal to him for the one brief statement that would settle the whole matter. Lyttleton wrote as follows:

My old friend Dr. Dingle seems at last to have found in Bernard Levin (article, December 21) a kindred spirit to champion him in his lone verbal onslaughts against what he regards as a certain pernicious claim of modern physics.

In brief, what Dingle has steadfastly maintained these many years against all comers is this: That if Peter and Paul are identical twins, and Paul goes on a journey leaving Peter to stay at home, then when Paul returns he will still be exactly the same age as his brother.

The truth of this seems so self-evident as to be beyond need of discussion by any sane people. But the trouble is that it is false, and physical theory shows inescapably that Paul will arrive back having aged less than Peter. For ordinary

everyday speeds the difference is negligibly small, and it rises to importance only when velocities begin to become comparable with that of light, but such speeds are now common in much of physics.

The kinematics and mechanics (of special relativity) that hold for high- speed motions had their inception in the inspired genius of Poincare (Henri) and Einstein and others of their day, and the suggestion that such men, never mind modern exponents of theoretical physics, do not know what they are talking about is on a par with claiming that Vardon and Taylor and Hagen knew nothing of golf. But this so-called 'clock paradox' (it is not really a paradox at all) is built for friend Dingle, since the man-in-the-street does not have to deal with relativistic particles such as mu-mesons, or the design of synchrotrons, and so along with Mr. Levin can remain absolutely certain that Dingle must be right wielding his prolix pen ‘while words of learned, length and thundering sound, amaze the gazing rustics gathered round."

Dr Dingle's attitude is of a golfing enthusiastic that has read the great masters, but finding himself unable to break 100 (never mind break 70) concludes it is they that must be wrong somewhere; and what is more, that it is their bounded duty to interrupt their careers to prove to his satisfaction that they are right.

If your energetic Bernard would spend a little time learning up this branch of physics, which is not really all that difficult, he can easily discover for himself who is right and who is wrong, but he will discover also that it is not possible to convince our dear Dingle, For e'en though vanquished, he can argue still,’ — and will!

My reply was this:

My old (in affection, not alas in wisdom) friend Professor Lyttleton (January 8) has got everything wrong — even the point at issue. I have carefully avoided the 'clock', or 'twin', paradox (in which Paul, after space-travelling, rejoins Peter), knowing from experience that Paul's reversal of motion can be misused ad lib, to meet any need. In the present discussion Paul moves on, undeviating, into the intense inane.

Suppose clocks A and B move along the same straight line at uniform speeds differing by 161,000 miles a second: we call A ‘stationary’ and B 'moving', but that is merely nominal. At the instant at which B passes A both read noon. Then, according to special relativity, at the instants when B reads 1 and 2 o'clock, A reads 2 and 4 o'clock respectively. Of course, A is not at B to allow a direct comparison, but Einstein's theory is based on a particular process for finding a clock-reading for a distant event, and it demands these values. Einstein himself made just this calculation, but using general symbols instead of these numerical

values, and concluded that since B recorded a smaller interval than A between the same events, it was working more slowly.

But if he had similarly calculated the reading of B (still 'moving') for the readings | and 2 o'clock of A (still 'stationary') he would have got 2 and 4 o'clock respectively, and must have reached the opposite conclusion: he did not do this, so missed the contradiction. I invite Ray to fault these calculations, or convince your 'gazing rustics' that each of two clocks can work faster than the other. I do hope he will not disappoint them.

Regarding the immeasurably less important clock paradox, Lyttleton is again wrong in saying that I have denied asymmetrical ageing for many years. Fifteen years ago, when I believed special relativity true, I indeed thought it impossible, but I soon discovered my error, and for more than 13 years have held the question open. Had we but world enough and time, or wings as swift as meditation or the thoughts of love (since I too like invoking the English, and even the Irish, poets), we could indeed make a direct test: as it is, we must await a valid determination of the true relation between the velocity of light and that of its source. Despite the mu-mesons and their kind, I think asymmetrical ageing extremely unlikely, but that is an opinion; the falsity of the special relativity theory (not necessarily of the relativity of motion) I regard as proved.

It is clear from this that, notwithstanding many years of reiteration of what my letter shows to be a simple, generally intelligible — but, if valid, fatal — criticism of the most fundamental theory of modern physics, the ultimate reaction, coming from an eminent mathematical physicist or astronomer, is simply a paraphrase of what this book will show to have been every other supposedly authoritative response during that long time — namely, first an evasion of the point by its transformation into something different, for the refutation of which justification is claimed on grounds too abstruse for general presentation; and secondly, complete silence when the transformation is exposed and an answer to the genuine, easily understandable, criticism requested. The function of this book is to provide conclusive evidence of this, and so to enlighten the public on a matter of the most profound concern to its moral and physical welfare.

It remains to summarise the necessity for this exposure, which of course is elaborated in the following pages. This necessity is twofold. First, the facts show, I think beyond question, that the traditional proud claim of Science that it acknowledges the absolute authority of experience (i.e. observation and experiment) and reason over all theories, hypotheses, prejudices, expectations or probabilities, however apparently firmly established, can no longer be upheld. The devotion to truth at all costs has gradually given place — largely unconsciously, I believe, but still undeniably — to the blind pursuit of the superficially plausible; the direction towards the most seductive, in which advance has been easiest, has been taken without regard to preservation of contact with the base, which is the truth of experience and reason; the verdict of those authorities falls on deaf ears, that of the Vardons or Hagens of physics, to question which is automatically to place oneself in a class which Lyttleton's letter makes starkly clear, having now

established itself as final; mathematics has been transformed from the servant of experience into its master, and instead of enabling the full implications and potentialities of the facts of experience to be realised and amplified, it has been held necessarily to symbolise truths which are in fact) sheer impossibilities but are presented to the layman as discoveries) which, though they appear to him absurd, are nevertheless true because mathematical inventions, which he cannot understand require them. The situation is precisely equivalent to that in which the zoologist assured the astonished spectator of the giraffe that if he understood anatomy he would know that such a creature was impossible — except that, in physical science, the layman usually believes what he is told and, unless he is enlightened in time, will be the victim of the consequences. This phenomenon, most evident in relation to special relativity, is now common in physical science, especially in cosmology, but its culminating point lay, I think, in the acceptance of special relativity, and it is with that alone that the present discussion is concerned. It is ironical that, in the very field in which Science has claimed superiority to Theology, for example — in the abandoning of dogma and the granting of absolute freedom to criticism — the positions are now reversed. Science will not tolerate criticism of special relativity, while Theology talks freely about the death of God, religionless Christianity, and so on (on which I make no comment whatever). Unless scientists can be awakened to the situation into which they have lapsed, the future of science and civilisation is black indeed.

The second reason for the publication of this book is a practical one. Directly or indirectly — at present chiefly the latter, though none the less inseparably — special relativity is involved in all modern physical experiments, and these are known to be attended by such dangerous possibilities, should something go wrong with them, that the duty of ensuring as far as possible that this shall not happen is imperative. It is certain that, sooner or later, experiments based on false theories will have unexpected results, and these, in the experiments of the present day, may be harmless or incalculably disastrous. In these circumstances an inescapable obligation is laid on experimental physicists to subject their theories to the most stringent criticism. As this book will show, their general practice is to leave such criticism to mathematical theorists who either evade or ignore it, and the possible consequences are evident and unspeakably menacing. This alone would compel the publication of the facts here revealed.

Nothing, I think, remains to be said to enable the reader to form his own estimate of the story that follows, which he requires no special knowledge to enable him to do. My

duty is to make it known; its significance is for him to judge.

April 1972

Introduction

This is a book which I have been trying for more than thirteen years to avoid having to write: I have at last been forced to do so because it has become impossible for its purpose to be achieved otherwise and that purpose is imperative.

I am well aware that the bare summary of the matter given in this Introduction will appear so incredible that the reader will feel an almost irresistible impulse to dismiss it as illusory: that is why the evidence has to be given at such length and in such terms that doubt of its reality will be impossible; its gravity, if it is real, will need no proof. The fantastic appearance of the situation is indeed one of the reasons why it has not been rectified long since; those who could have rectified it have found it impossible to credit, and it has accordingly been allowed to persist, with the result that unless drastic action is taken, the whole community stands at a risk which is quite incalculable but might be overwhelmingly great. In introducing the matter here, therefore, I beg the reader to suspend his incredulity, which it will need the whole evidence that follows to remove, and to accept, merely as a working hypothesis at present, that what I have to say is true. Part One, which is concerned only with the ethical principles of science, not with technical details, is wholly comprehensible to any intelligent person, while Part Two needs a little elementary knowledge of physics, less than that possessed by any physics undergraduate, for its full comprehension, and only ordinary intelligence for a true idea of its general import.

I can present the matter most briefly by saying that a proof that Einstein's special theory of relativity is false has been advanced; and ignored, evaded, suppressed and, indeed, treated in every possible way except that of answering it, by the whole scientific world (the world of physical science, that is; the theory has no place at present in the biological and psychological sciences). Since this theory is basic to practically all physical experiments, the consequences if it is false, modern atomic experiments being what they are, may be immeasurably calamitous. That is why the failure of physical scientists to practise what is generally understood to be their faithfully preserved fundamental ethical principle — the subordination of all theories, however plausible, to the demands of reason and experience — compels its exposure. In the conditions of former days the falseness or otherwise of the theory could have been left to the arbitrament of experiment, which would, sooner or later, inevitably have appeared: today the possible consequences of such, equally inevitable, settlement of the question are far too dire, and nothing but the observance of strict scientific integrity, here and now, can meet the ethical demands of the case.

The reason why this has happened is largely that which will, in all probability, immediately strike the reader — namely, that the theory of relativity is believed to be so abstruse that only a very select body of specialists can be expected to understand it. In fact this is quite false; the theory itself is very simple, but it has been quite unnecessarily enveloped in a cloak of metaphysical obscurity which has really nothing whatever to do with it; the physical theory itself, indeed, is much simpler than many physical theories familiar to most educated non-scientific but interested persons in the nineteenth century;

it is wholly devoid of any mystical significance. This will be explained in Part Two, where the historical reasons for the illusions concerning the theory are fully set out. But the consequences of those illusions are the vitally important matter for the general public. They are, briefly, that the great majority of physical scientists, including practically all those who conduct experiments in physics and are best known to the world as leaders in science, when pressed to answer allegedly fatal criticism of the theory, confess either that they regard the theory as nonsensical but accept it because the few mathematical specialists in the subject say they should do so, or that they do not pretend to understand the subject at all, but, again, accept the theory as fully established by others and therefore a safe basis for their experiments. The response of the comparatively few specialists to the criticism is either complete silence or a variety of evasions couched in mystical language which succeeds in convincing the experimenters that they are quite right in believing that the theory is too abstruse for their comprehension and that they may safely trust men endowed with the metaphysical and mathematical talents that enable them to write confidently in such profound terms. What no one does is to answer the criticism.

It would naturally be supposed that the point at issue, even if less esoteric than it is generally supposed to be, must still be too subtle and profound for the ordinary reader to be expected to understand it. On the contrary, it is of the most extreme simplicity. According to the theory, if you have two exactly similar clocks, A and B, and one is moving with respect to the other, they must work at different rates (a more detailed, but equally simple, statement is given on pp. 45-6, but this gives the full essence of the matter), i.e. one works more slowly than the other. But the theory also requires that you cannot distinguish which clock is the 'moving' one; it is equally true to say that A rests while B moves and that B rests while A moves. The question therefore arises: how does one determine, consistently with the theory, which clock works the more slowly? Unless this question is answerable, the theory unavoidably requires that A works more slowly than B and B more slowly than A --which it requires no super-intelligence to see is impossible. Now, clearly, a theory that requires an impossibility cannot be true, and scientific integrity requires, therefore, either that the question just posed shall be answered, or else that the theory shall be acknowledged to be false. But, as I have said, more than 13 years of continuous effort have failed to produce either response. The question is left by the experimenters to the mathematical specialists, who either ignore it or shroud it in various obscurities, while experiments involving enormous physical risk go on being performed.

It cannot be too strongly emphasised that this question is exactly what it appears to be, with every word and phrase bearing its ordinary, generally understood, meaning; it is not a profoundly complicated question, artificially simplified to bring it within the scope of the non-scientific reader's intelligence. It is presented here in its full scientific reality, and the ordinary reader is as fully competent to understand whether a proffered answer is in fact an answer or an evasion as is the most learned physicist or mathematician — though, of course, he may not be able to judge whether the suggested answer is true or not. For instance, the statement: 'the slower-running clock is that judged by a chosen body of experts to be the more beautiful’ would be an answer, though it is not likely to be acceptable to anyone. On the other hand, the statement: 'I cast my vote for the

special theory of relativity and the abandonment of Dingle's concept of clocks because the latter is equivalent to Newton's concept of absolute time, and relativistic physics appears to me to represent nature more closely than Newtonian physics does! (sec p. 77 for the fuller statement from which this is taken), which is the conclusion reached by one generally considered to be among the most authoritative mathematical experts on relativity, can be seen by anyone to be no answer at all, but a clear evasion of the question. Who can gather from this how to tell which clock works the more slowly? The question is by-passed, and the reader is led into a slough of metaphysical concepts which have nothing whatever to do with it. Nevertheless, the statement serves to confirm the experimenters’ conviction that the matter is beyond their understanding but has been competently dealt with by an expert authority, so they need give it no further attention.

This is typical of all responses to the criticism that have yet appeared: I choose it here because of the outstanding reputation of its author in this field and the fact that it can be expressed more briefly than most — far more briefly, for instance, than the equally evasive and far denser obscurity (given here in the Appendix) that 'convinced' the then President of the Royal Society that what he had been 'teaching' for many years but confessed he did not understand, was indeed true (see pp. 97, 100). It serves to explain why this book has become necessary — because unceasing and world-wide effort over many years has produced nothing but such evasions of a simple question needing less than six lines to answer if answer is possible, and revealing a universal attitude foreshadowing certain danger to the whole population if it is not. Any reviewer of the book can dispose at a stroke of its basic raison d'etre by giving those six lines. By the same token, his failure to do so would speak for itself.

It is no doubt generally believed that means exist for preventing the occurrence of such a situation as this, and theoretically, of course, they do. The Royal Society is a body whose function includes the safeguarding of scientific integrity in all matters, and especially those vital to public welfare in this country (the situation is of general significance, of course, but for reasons of space I deal in this book almost wholly with Britain), and accordingly, after great difficulty in overcoming the interposed obstacles,

the criticism was submitted to it for consideration. It was rejected on the basis of a report from an anonymous 'specialist' that the fallacy invalidating it was too elementary even to be instructive. The 'fallacy', however, was not revealed, nor was the simple but crucial question answered, but the customary paragraphs of mystical comment were supplied, and these satisfied the Society that the criticism was baseless. A letter to the leading scientific journal, Nature, asking, in the public interest and in accordance with the principles of the Society, that the fallacy should be published, was refused publication, on the ground that actions of the Royal Society were not open to question in Nature. An attempt was made to obtain a ruling of the Press Council (one of whose functions is 'to keep under review developments likely to restrict the supply of information of public interest and importance’) on this refusal of Nature — not, be it noted, merely on this instance, but on the general decision of the editor that no action of the Royal Society, whatever its relation to the public interest, was open to questioning in the journal — but the officers of the Council would not allow the inquiry to reach it. As will be seen in this book, other scientific journals impose a similar veto; that again is part of the reason why I

have been forced to use the medium of a book to acquaint the public with the position in which it stands: a body of scientists, in whose uncontrolled hands the physical safety of the whole community lies, is daily engaged in experiments of the greatest potential danger, based on principles which the experimenters confess they do not understand, and the Press is closed to any criticism, however well informed, of their activities, and to all questioning of their decisions.

These, then, are the circumstances that have made this book necessary. My purpose throughout is not to indict but to inform, and let the facts bring whatever indictment is necessary. This book is the only means I have of doing so. I have written it with the greatest regret, not only because iconoclasm is not an activity in which I take any pleasure at all, but also because most of those whom I am forced to present in what is bound to appear an unfavourable light — though I still believe that they do not fully realise what they are doing — are those whose friendship I value and must inevitably run the risk of forfeiting: it is largely this consideration that has persuaded me to continue so long in an endeavour which perhaps I ought long ago to have realised was hopeless. But to continue now to withhold the certain knowledge which I possess from those whose welfare, and even existence, depend on it, would be a betrayal of responsibility of which I am no longer willing to be guilty.

* * *

After the writing of this book was completed came the sad news of the death of Sir Lawrence Bragg who, as will be seen, figures prominently in one section. This raised a problem, and after reflection I have decided to leave what was written exactly as it was, without change even of tense. This seemed desirable for two reasons. First, it conforms to what I cannot too strongly emphasise — that the purpose of the book is wholly objective and what is said in it of any person relates only to the public significance of the work of that person and so is independent of whether he or she is alive or dead. Secondly, Sir Lawrence had read this Introduction and the whole passage referring to him, knowing that it would be included verbatim in the book, as it appears here down to his last letter, printed on p. 113, which was written only a few weeks before his death and now takes on an added poignancy. I know, therefore, that by leaving the passage unchanged I am saying nothing to the appearance of which he would have raised objection.

The case of Dame Kathleen Lonsdale, who died during the writing of the book, is slightly different. I should not in any case have sent her a copy of the part referring to her, knowing her well enough to be sure that there was nothing in it to which she would have taken exception.

PART ONE

The Moral Issue

11

The Basic Principles of Science

On the nature and definition of Science there has long been, and will doubtless continue to be, much disputation, but on one characteristic at least of its practice, agreement is general — its unqualified devotion to the discovery of truth at whatever cost to its expectations and tentative assumptions. Its conception of 'truth', of course, may be limited — this again is a matter of controversy — but never qualified by compromise or expectancy of any kind. Within its own intellectual sphere, however that may be conceived, its disinterestedness has been regarded as absolute, and it has often been held up as a model for other human activities — political, theological, and what not — in which throughout history has been only too evident the influence of prejudice and partisanship, from which science alone has kept itself free. Of the many expressions of this idea which may be found in the literature of the last few centuries, coming from both scientists and non-scientists, I select as a paradigm the following typical statement by the late Sir Henry Dale, O. M., a former President of the Royal Society, and one of the outstanding scientists and most universally respected representatives of his calling in this century:

And science, we should insist, better than any other discipline, can hold up to its students and followers an ideal of patient devotion to the search for objective truth, with vision unclouded by personal or political motive, not tolerating any lapse from precision or neglect of any anomaly, fearing only prejudice and preconception, accepting nature's answers humbly and with courage, and giving them to the world with an unflinching fidelity. The world cannot afford to lose such a contribution to the moral framework of its civilisation.’

It is not, of course, to be supposed that every scientist has on every occasion lived up to the counsel of perfection which this statement represents; far from it, although it is true that, on the whole, the history of science compares very favourably indeed with the history of most, if not all, other human activities. Nevertheless, there are examples enough of prejudices and preconceptions, on the part of both individual scientists and scientific organisations — it is sufficient to mention the general dismissal during the eighteenth century of authentic evidence for the reality of falls of meteorites, on the sole ground that such things could not happen: for belief in the inviolability of laws of nature was substituted belief in the inviolability of the existing conception of what those laws were. It would be a gross error to imagine that scientists, as a class, are inherently more honest in their thinking and actions than men in other classes — a fact evident enough when we compare their extra-scientific activities with those of others. They are human, all too human, neither better nor worse on the whole than politicians and theologians, than historians and business men, than artists and artisans. What makes scientists behave so much more consistently in accordance with their ideals is not a unique ‘original virtue’ but the nature of their job.

12

This, as I have said, is, in its fundamental essence, a matter of dispute and academic discussion, but, speaking in general terms— which is not to say false terms so far as they go — it may be said that the aim of science is to discover what actually exists in nature and to express the relations between natural phenomena in rational form, '1.e. in statements which, when established by sufficient evidence and found to hold good over a sufficiently wide range of experience, we call laws of nature, and when less completely supported but still possessing some measure of plausibility, we call theories or hypotheses. The evidence is never complete, and experience is never exhaustive, so all these statements are subject to change, but, however tenaciously scientists may wish to retain those which they have learned to trust, there is a finality about both experience and reason that ultimately overrides all opposition and forces the scientist to acknowledge the error of his preconceptions, however reluctant he may be to do so. The historian may defend or condemn the execution of Charles I; the theologian may assert or deny justification by faith; and nothing that any of them can do can finally refute his opponent. But the astronomer who asserts the existence of seven planets and denies the possibility of more, is silenced when an eighth is discovered; the experience on which he relics for the reality of the seven must have the same validity with regard to the eighth, and he has no option but to yield. The mathematician, in whose calculations leading to what he has asserted to be a proof of a theory the accidental omission of a factor 2 is discovered, must likewise acknowledge his error: no matter how strong his belief in the theory may be, the demands of reason which he has trusted to establish it now demand its abandonment. Scientists must be honest in the long run because the nature of their occupation makes them so: experience and reason are irresistible.

There is, however, one striking difference between the refutation of a hypothesis by experience and by reason which we must acknowledge, though it may be left to the psychologist to explain. Experience — 1.e. observation or experiment — usually carries much greater conviction than reason, though ultimately they have equal authority. When a hypothesis is used to predict a certain experimental result, and the relevant experiment when performed yields the opposite result, there is generally no further discussion; the hypothesis is dismissed, or at least changed. But when the reasoning involved in a hypothesis is disputed (the example just given of an accidental mathematical error is of course a very special case, though it differs only in degree from reasoning processes much less obviously erroneous) there is usually no such general agreement on the truth of the matter, although, according to the strict principles of science, there should be. Newton, albeit with an ill grace, acknowledged an error in his reasoning concerning falling bodies which was detected by Hooke; he did not insist on an experimental test. But there has frequently been less readiness to abandon a cherished idea on rational than on experimental or observational grounds. In the nineteenth-century controversy on the age of the Earth between the geologists and the physicists, both sides had all the available evidence before them, and the difference in their conclusions arose wholly from the reasoning which they applied to it. We can see now, not only why equally intelligent reasoners reached widely different conclusions from the same evidence, but also that a stricter regard for the difference between necessary and probable conclusions from the evidence would have enabled a disinterested adjudicator to form a single judgement even then. It was, of course, a matter which could not be tested by experiment; had it been so,

i:

the dispute would have ended. In the event, only further experience, not then available but the possibility of which might have been anticipated, led to an agreed conclusion.

This greater degree of conviction which experience provides has had an important consequence in the progress of science. It has led to a relaxing of the demand that scientific hypotheses shall be strictly rational and a greater reliance on the ultimate verdict of experiment. This is not merely a development of the chief characteristic of the modern scientific movement that began in the seventeenth century and was marked by an exchange of interest solely in a priori reasoning prevalent in the Middle Ages for an interest primarily in experience. The pioneers of that movement — Galileo and Newton in particular — indeed insisted on the primacy of experience, but they relied no less than the Schoolmen on faithful obedience to the demands of reason in their ordering of experience and their deductions from what it revealed. Galileo has been criticised for his reasoning from 'thought experiments’, and not only were these 'experiments', which were a novelty at that time, but also they involved rational thought and permitted nothing that violated the strict rules of reasoning. Newton, though he declared, in a famous phrase, that he did not make hypotheses, and in fact did make numerous experiments, nevertheless also laid down 'Rules of Reasoning in Philosophy’, and did not hesitate to use what many today would regard as hypotheses. The scientific movement of the seventeenth century was a blend of experience and reasoning, in which both were essential but the reasoning was confined to what was derived from experience, and everything that was derived from 'principles' that had no justification except that they seemed necessary or good to those who adopted them, was firmly eschewed. But what gradually developed later, as a result of the greater degree of conviction that an experimental result brought with it, was a permissiveness in the framing of hypotheses, arising from the certainty that, if they were wrong, experiment would inevitably reveal that fact, and there was always a chance that, however improbable they might seem, they might turn out to be right.

There is much that can be said in defence of this — or at least there was — so long as the hypotheses are recognised for what they are — namely, a means of arriving at truth and not truth itself. Anything imaginable might be true — there are more things in heaven and earth than are dreamed of in our philosophy — and a few more dreams, which are not accepted as reality until waking experience confirms them, can do no harm, apart from a possible waste of time and money in a good cause, and might lead to the discovery of truths that would otherwise remain hidden. This indeed has happened not once or twice in the history of science. But it is attended by two dangers. The first, which was evident many years ago, is that the dreams shall be substituted for reality and accepted as true, not only before experience verifies them but wholly in their own right, regardless of whether experience verifies them or not. The second danger, which is relatively new, and demands far more urgent attention, is one reason why this book has had to be written: it lies in the fact that the experimental testings of the hypotheses of modern physics are attended by such possibly catastrophic results if the hypotheses are wrong, that the preliminary confirmation, that they are not necessarily wrong through violating the laws of reasoning, becomes imperative. Anything imaginable might be true: what is not imaginable — such as that Hitler both is and is not dead, or, to take a

14

requirement of the hypothesis with which this book is chiefly concerned, that one clock can work steadily both faster and slower than another — cannot be true, and experiments based on the assumption that it is, are bound to lead, sooner or later, to anomalous results.

The first danger — the substitution of imagination for experience — was, as I say, realised long ago; this is how I exemplified it in a book published in 1931:7

I will give three quotations from representative scientists, covering the period from Newton to the present time and separated by roughly equal intervals. The first is from Newton himself (1687): 'I frame no hypotheses. For whatever is not deduc'd from the phaenomena, is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.' The second is from Laplace, referring to his famous 'nebular hypothesis’ (1796): 'I will suggest an hypothesis which appears to me to result with a great degree of probability, from the preceding phenomena, which, however, I present with that diffidence, which ought always to attach to whatever is not the result of observation and computation.' The third is from Eddington (1926); 'Care is taken to provide "macroscopic" equations for the human scale of appreciation of phenomena as well as "microscopic" equations for the microbe. But there is a difference in the attitude of the physicist towards these results; for him the macroscopic equations — the large-scale results — are just useful tools for scientific and practical progress; the microscopic view contains the real truth as to what is actually occurring.’ The course of development is from a categorical rejection of hypotheses of any kind whatever, through a diffident presentation of one which results ‘with a great degree of probability’ from phenomena, to the confident assertion that a hypothesis contains 'real truth' and phenomena are just ‘useful tools.' The question of the validity of this process is the most vital question, both for the philosophy of Science and for the application of scientific ideas to other departments of thought, at the present time.

Since that was written the process has gone even further. Not only are hypotheses held to contain the ‘real truth’; it is now claimed that any (mathematical) hypothesis is necessarily true. In a recent paper, two physicists, 0.Bilaniuk and E.C.G. Sudarshan, write:3 'There is an unwritten precept in modern physics... which states that in physics "anything which is not prohibited is compulsory". Guided by this sort of argument we have made a number of remarkable discoveries, from neutrinos to radio galaxies.''We', of course, means scientists in general, and it is evident from the context that ‘prohibited’ means mathematically impossible. The statement that neutrinos and radio galaxies, or anything else, were so discovered is, of course, nonsense, but the statement is taken seriously and has instigated experiments directed towards the observation of 'tachyons' — hypothetical particles that travel faster than light — and stimulated a serious discussion in Nature on whether an effect can precede its cause. The relation between mathematics and physics is discussed in Chapter 6; in the meantime, this is sufficient to indicate how far we have gone along the path that started with the recognition that hypotheses might assist in the discovery of phenomena: first phenomena became 'useful tools' for the creation of hypotheses, and now hypotheses themselves are enthroned as necessary phenomena.

15

But it is the second danger that calls for immediate attention and, as indicated in the Introduction, has made this book necessary: it arises from the fact that modern physical experiments are such that the unexpected results which they produce might be catastrophic. Ironically enough, it is the very safeguard against the first — the certainty that experiment will ultimately show up the falsity of bad reasoning — that constitutes the essence of the second. We can contemplate with equanimity a temporary disregarding of truth, for we know that truth is great and will prevail, but the means by which its triumph is achieved may now ensure that there shall be no one left to care whether it prevail or not. When Rutherford's early experiments with atoms produced a result quite impossible if atoms were as he had conceived them, he declared that he was as surprised as if he had fired a bullet at a piece of tissue paper and it had rebounded and hit him. Similar misconceptions today, when chain reactions may occur that were not possible in Rutherford's experiments, may cause unimaginably great disasters, and the necessity that the hypotheses on which modern physical experiments are planned shall be scrutinised with the utmost care and freedom from prejudice is thus paramount. In fact, as later chapters will show, it is ignored. All unconsciously, scientists have allowed themselves to relapse into the mental state which science is usually regarded as having displaced — that of imagining how nature ought to behave and then assuming that she does so, instead of examining nature with an open mind and then expressing her observed behaviour in rational terms.

The factor that has made this possible, if one may use metaphorical terms to express the idea more vividly, is the exchange by reason of the cloak of Aristotelian logic for that of mathematics. Both begin with so-called 'axioms' which are conceived in the mind without reference to experience, and their implications are developed into extended systems of thought which necessarily follow from the axioms but may or may not correspond to what can be observed in nature. For example, it was a mediaeval axiom that all celestial bodies moved in circles or in orbits that could be analysed into circular movements. This had nothing to do with observation: it was assumed before any regard was paid to observation of the actual movements of the bodies, and when those movements were observed it was regarded as a necessity to analyse them into circles of which their obviously quite different paths were the resultants. The essence of the scientific approach, applied to this particular example, consisted in taking the observed movements as the starting point, and expressing them in the simplest terms, without restriction to any preconceived notions of what those terms should be.

I shall consider in more detail in Chapter 6 the relation between mathematics and physics, but the matter is so fundamental for our present considerations that some preliminary remarks on it are desirable here. It was particularly Galileo who realised that mathematics provided the most effective terms in which to express physical observations, and it was he who contributed most to the introduction of those terms into science. The book of nature, he wrote, ‘is written in the mathematical language’. But there are two things that should be said about this oft-quoted aphorism. The first is that 'nature', or 'the universe’, as Galileo conceived it was a much more restricted concept than that which we hold and that with which modern science is concerned. It comprised only what we study in mechanics; all other phenomena — sights, sounds, smells, etc. — belonged in his view

16

not to the external world but to the observing subject, and it was not at all his idea that mathematics played the all-comprehensive role in science that it is nowadays often assumed to do. Secondly, a language is a medium for expressing ideas, and it is just as capable of expressing false ideas as true ones. The fact, therefore, that something can be expressed with rigorous mathematical exactitude tells you nothing at all about its truth, i.e. about its relation to nature, or to what we can experience.

The most dangerous intellectual error of modern science, with which this book is concerned, lies in the fact that this has been overlooked. Mathematics is an immensely more powerful tool than the Aristotelian syllogism, and its use as a language in which to express the facts of experience has been so successful that the idea has crept unperceived into the minds of physicists that whatever it says must be true. This is openly expressed in the statement already quoted, that everything that is not mathematically forbidden is necessarily observable. Accordingly the habit has developed of assuming that a physical theory is necessarily sound if its mathematics is impeccable: the question whether there is anything in nature corresponding to that impeccable mathematics is not regarded as a question; it