What Happened to Dingle?



Our most trustworthy safeguard in making general statements on this question is imagination. If we can imagine the breaking of a law of physics then… it is in some degree an empirical law. With a purely rational law we could not conceive an alternative… This ultimate criterion serves as an anchor to keep us from drifting unduly in a perilous sea of thought.

                                                                                Herbert Dingle, 1940


Beginning in the late 1950's the retired British philosopher of science Herbert Dingle (1890-1978) wrote several letters to the science magazine "Nature" and other publications, claiming that special relativity did not predict asymmetric ages for the re-united twins in the famous twins paradox. Eventually he was convinced by several other correspondents that he was wrong, i.e., he became convinced that special relativity did, in fact, predict unequal ages for the re-united twins. After accepting this, Dingle began another letter-writing campaign, now claiming that special relativity is logically inconsistent. After printing many of Dingle’s letters, along with refutations from various scientists (including Max Born), these publications stopped accepting his letters, so Dingle felt compelled to write a book, “Science At The Crossroads”, in which he recounted his struggle against what he regarded as the deluded and corrupt scientific establishment. In 1972, just as his book was about to be published, he engaged in one more debate, this time with Professor Ray Lyttleton, in the “letters to the editor” section of The Times. In his final letter, Dingle presented his “irrefutable proof” as follows:


Suppose clocks A and B move along the same straight line at uniform speeds differing by 161,000 miles a second. 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… Einstein himself made just this calculation, 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 for the readings 1 and 2 o'clock of A 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 [readers] that each of two clocks can work faster than the other. I do hope he will not disappoint them.


In a nutshell, Dingle considers two systems of inertial coordinates x,t and x',t' with a relative velocity of v, and then notes that the partial derivative of t' with respect to t at constant x is equal to the partial derivative of t with respect to t' at constant x’. He declares this to be logically inconsistent. Needless to say, Dingle’s “reasoning” is incorrect. It consists of the claim that those two partial derivatives must be the algebraic reciprocals of each other, which of course is false.


To elaborate on this point, the Lorentz transformation is x' = (x−vt)g, t' = (t−vx/c2)g, and its algebraic inverse is x = (x'+vt')g, t = (t'+vx'/c2)g, where g = 1/(1−v2/c2)1/2. These equations imply t' = gt at x = 0, and t = gt' at x' = 0. Dingle alleged that these two facts are mutually contradictory, because the first implies t'/t = g and the second implies t/t' = g. However, these ratios apply to two different conditions, namely, x = 0 and x' = 0 respectively. Hence, contrary to Dingle's assertion, there is no contradiction, nor are these relations merely "appearances". They are the actual ratios of the inertial time coordinates along two different directions in space-time. (For a more on Dingle’s misunderstandings, see the note on Herbert Dingle and the Twins.)


In essence, Dingle simply noted the reciprocity of the Lorentz transformation and its inverse, which of course, far from being overlooked by Einstein, was the whole basis of the special theory of relativity. Indeed Lorentz summarized Einstein’s theory in 1909 by saying


Attention must be drawn now to a remarkable reciprocity that has been pointed out by Einstein... The behavior of measuring rods and clocks in translational motion, when viewed superficially, give rise to a remarkable paradox which on closer examination, however, vanishes.


Thus Dingle’s claim that Einstein never noticed this reciprocity is simply bizarre, as was Dingle’s "proof" of the logical inconsistency of special relativity. His reasoning can just as well be applied to “prove” that Euclidean geometry is logically inconsistent. Consider two Cartesian coordinate systems x,y and x',y' with a common origin, but rotated by an angle of q with respect to each other. Given the x,y coordinates of any point, we can compute the x',y' coordinates by means of the equations



We can also solve these equations for x and y in terms of x' and y' to give the inverse transformation



This is just elementary linear algebra. Now, if we hold y constant and vary x, how much does x' vary? In other words, what is the partial derivative of x' with respect to x? This is denoted by x'/x, and clearly we have x'/x = cos(q). Now we ask a different question, namely, if we hold y' constant and vary x', how much does x vary? This is equivalent to asking for the partial derivative of x' with respect to x, and of course we have x/x' = cos(q). Dingle's confusion is due to the fact that (like some befuddled freshman calculus students) he imagines x'/x and x/x' are algebraic reciprocals of each other, which would imply that 1/[x'/x] = x/x', and therefore cos(q) = 1/cos(q), which is impossible for any q other than 0. Does this prove that Euclidean geometry (and linear algebra) is logically inconsistent? Of course not, because Dingle's argument is obviously specious; the partial derivatives x'/x and x/x' are not the algebraic reciprocals of each other.


As noted previously, the application of Dingle's argument to the Lorentz transformation is exactly the same. Two inertial coordinate systems x,t and x',t' with a mutual relative velocity v are related according to the equations



where g = 1/(1-v2)1/2. The inverse transformation is



In this case we have the two partial derivatives t'/t = g and t/t' = g. Dingle erroneously assumed that 1/[t'/t] = t/t', and so he arrived at 1/g = g, which is impossible for any v other than 0. Again the fallacy is the erroneous assumption that partial derivatives can be algebraically inverted. Of course, we can invert total derivatives, so let's see what happens if we take the absolute differentials (for any constant v) of the time transformation equations. We have



Dividing the left hand equation by dt and the right hand equation by dt' gives



Considering the first of these equations, notice that for an object at rest in the unprimed reference frame we have dx/dt = 0 (by definition), and so we have dt'/dt = g. However, for an object at rest with respect to the primed coordinates we have dx/dt = v, which gives



This shows how we arrive at either one of the partials, depending on which direction in spacetime we are considering. Likewise for the second transformation equation we can consider the cases when dx'/dt' = 0 or -v, giving the results g and 1/g respectively. Also, since the total derivatives are reciprocals of each other, we can multiply them together to give unity, i.e.,



Notice that dx/dt is the velocity of one worldline with respect to some arbitrary reference frame, and dx'/dt' is the velocity of a different worldline with respect to that same reference frame. Let us denote these velocities by u and w respectively. Recalling that g2 = 1/(1-v2), the above equation becomes



Solving for u gives the familiar formula



which is the relativistic speed composition formula. Needless to say, there's nothing inconsistent or self-contradictory here. Dingle was simply making an elementary error.


This is all quite elementary, and not terribly interesting. The more interesting question is what happened to Dingle. For most of his life he wrote approvingly about what he called “relativity”, beginning with his 1922 essay “Relativity for All”. He even wrote a monograph on special relativity (1940) in which he dutifully noted the relativity of simultaneity, and so on. But in his later years (beginning in the mid to late 1950s), after embarking on a passionate anti-relativity crusade, he exhibited a complete inability to grasp the most fundamental aspects of special relativity, culminating in the grotesquely crackpotish "Science at the Crossroads" in 1972. The obvious question is, how could he write and lecture about a theory for almost forty years, and then suddenly be unable to grasp it? Granted, Dingle was 82 when “Crossroads” was published, but can this really account for his confusion?


Dingle was born in 1890, and his father died soon thereafter, so Dingle was raised by his mother. He had to leave school at the age of 14, and worked as a clerk for the next 11 years. In 1915 he was 25 years old, and would have been subject to the conscription that was instituted in Britain just two years later, but he was a Quaker, which allowed him to claim exemption from military duty as a conscientious objector. Instead of military duty, he received a scholarship to enroll at Imperial College, where he studied spectroscopy. The circumstances of his gaining this scholarship, having previously completed only the eighth grade, at a time when all able-bodied men were being called up for military service are unclear, especially in view of the climate at that time, as recalled by Chandrasekhar in his biographical sketch of Dingle’s fellow Quaker, Arthur Eddington:


In 1917, after more than two years of war, England enacted conscription for all able-bodied men. Eddington, who was then 34, was eligible for draft. But as a devout Quaker, he was a conscientious objector; and it was generally known and expected that he would claim deferment from military service on that ground. Now the climate of opinion in England during the war was very adverse with respect to conscientious objectors: it was, in fact, a social disgrace to be even associated with one. And the stalwarts of Cambridge of those days—Sir Joseph Larmor (of the Larmor precession), Professor H. F. Newall,and others—felt that Cambridge University would be disgraced by having one of its distinguished members a declared conscientious objector. They therefore tried through the Home Office to have Eddington deferred on the grounds that he was a most distinguished scientist and that it was not in the long-range interests of Britain to have him serve in the army.


This account seems somewhat incongruous with the fact that Dingle, a poor 25 year-old clerk who never even attended high school, would be awarded a scholarship to the Imperial College in 1915, graduating in 1918. Chandrasekhar goes on to note that many Quakers were sent to camps in Northern England to “peel potatoes” for the duration of the war, and Eddington had declared himself ready to join them. Apparently this outcome was avoided only due to the intervention of Sir Frank Dyson, whose connections with the Admiralty enabled him to get Eddington deferred, under the pretext that he (Eddington) was needed at home to make preparations for an eclipse expedition to test Einstein’s light deflection prediction should the war end by 1919. Obviously no such pretext existed for Dingle, so it would be interesting to know the circumstances of Dingle’s scholarship and deferrment.


In any case, after graduating from the Imperial College in 1918, Dingle married Alice Westacott (who later bore him a son), and took a position as a Demonstrator in the Physics Department, devoting himself to the study of spectroscopy (following his mentor Alfred Fowler), especially its applications in astronomy. This is how he became an astronomer (presumably earning his doctorate during this period), and he was duely elected a Fellow of the Royal Astronomical Society in 1922. He served as member of the British government eclipse expeditions of 1927 (Colwyn Bay) and 1932 (Montreal), both of which failed to make any observations due to overcast skies. He spent most of 1932 at the California Institute of Technology as a Rockefeller Foundation Scholar. There he met both Einstein (who was visiting at the time) and the theoretical cosmologist R. C. Tolman, and studied relativistic cosmology. In 1938 Dingle became a professor of Natural Philosophy at Imperial College, and was a professor of History and Philosophy of Science at University College London from 1946 until his retirement in 1955. He was reportedly surprised to be elected President of the Royal Astronomical Society in 1951, since he hadn’t been active in astronomy for many years, having devoted himself since the 1930s mostly to the philosophy of science. He was one of the founders of the British Society for the History of Science (and particularly the Philosophy of Science Group of that Society), and served as its President from 1955 to 1957.


Dingle was no stranger to controversy, even prior to his anti-relativity crusade. In the late 1930s he engaged in a highly contentious dispute over the hypothetico-deductive method used by Milne and others in cosmology. In a polemic entitled “The Modern Aristotelians” he labeled his opponents as “traitors” to the cause of science. A few scientists (e.g., de Sitter), while not endorsing Dingle’s inflamatory rhetoric, were sympathetic to the view that cosmologists were being overly speculative (similar to the disputes today over string theory), but subsequently the methodology pioneered by Milne has become the model for the practice of cosmology.


To understand the origin of Dingle’s campaign against special relativity during his retirement years, it’s necessary to examine his earlier writings, which make it quite clear that he had always fundamentally misunderstood relativity. For one thing, he believed special relativity was a relational theory of motion. This is perhaps less surprising when we learn that he was introduced to the “theory of relativity” by A. N. Whitehead (1861-1947), which illustrates the disadvantages of being taught a subject by someone who doesn’t understand it himself. Whitehead, a mathematician and philosopher, was an early critic of general relativity. In 1920, amidst the public acclaim for Einstein that followed the announcement of the eclipse expedition results, Whitehead published what was essentially a relationist critique of relativity theory, saying in part


I doubt the possibility of measurement in space, which is heterogeneous as to its properties in different parts. I do not understand how the fixed conditions for measurement are to be obtained.


In other words, he did not understand how inertial coordinate systems (which form the entire basis of special relativity) are defined. In 1922, the same year in which Dingle published his essay “Relativity for All” (in which Dingle thanks Whitehead for explaining relativity to him), Whitehead published his own alternative theory in a book entitled “The Principle of Relativity, with Applications to Physical Science”. There he wrote


I maintain the old-fashioned belief in the fundamental character of simultaneity. But I adapt it to the novel outlook by the qualification that the meaning of simultaneity may be different in different individual experiences.


This is exactly the same idea that Dingle expresses in his writings, i.e., that the “novel outlook” on the relativity of simultaneity is essentially subjective, with no objective content, and that absolute simultaneity still held good in the objective sense. It’s clear that Whitehead mistook relativity for relationism (with an implicit absolute simultaneity), and passed this misunderstanding along to Dingle. In the preface to his essay “Relativity for All”, completed in July 1921, Dingle wrote


Those who wish to pursue the subject more deeply, from either the philosophical or the scientific standpoint, are recommended to the works of Professor A. N. Whitehead, F.R.S. The author is glad to acknowledge his deep indebtedness to Professor Whitehead for invaluable help and unwearying kindness in unveiling the mysteries of a difficult subject.


Needless to say, the competing doctrines of relationism and absolute motion have been debated throughout the history of science. According to the absolutist view there exists something called absolute space and time, within which objects exist and move, whereas according to the relationist view only the relations between physical entities have physical meaning. In the famous Leibniz-Clarke debate, Leibniz argued for the relationist interpretation, i.e., he held that only relative motions between identifiable entities have meaning, while Clarke (speaking for Newton) made the case for absolute motion – a case that essentially amounts to the assertion of Galileo’s principle of inertia. Leibniz maintained that all phenomena should be explainable purely in terms of the relations between substantial entities, and hence any object could, with equal justification, be regarded as being continually at rest. In opposition to this, Clarke and Newton argued (by means of the famous spinning pail experiment, for example) that arbitrary motions are not all equivalent, i.e., it is not possible to account for all the physical phenomena associated with motion merely in terms of the relative kinematic relations between entities. Hence Newtonian mechanics gives a distinguished place to a particular set of motions, called inertial motions, and to a particular equivalence class of space and time coordinate systems, called inertial coordinate systems. In the absolute-vs-relational debate, special relativity is squarely on the absolute Newtonian side, which is to say, special relativity is based on the principle of inertia no less than is Newtonian mechanics.


To see the great distance between the principle of inertia and the principle of relationism, recall Einstein’s own statement of the relativity principle (which he carried over essentially unchanged from Newtonian physics) in 1905:


The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion [i.e., inertial coordinate systems].


This directly expresses the absolutist principle of inertia, which was anathema to (among others) Leibniz. Compare this with Dingle’s statement (in his 1940 monograph) of what he believed to be the fundamental principle of relativity:


There is no meaning in absolute motion. The principle of relativity is a generalization from the fact that all known effects, apparently caused by the intrinsic motion of a single body, depend on the motion of that body with respect to another object.


Far from being an accurate summary of the principle of relativity (which is synonymous with the principle of inertia as defined in both Newtonian mechanics and special relativity), what Dingle actually articulated was the antithesis of relativity, namely, the principle of relationism (with an implicit absolute simultaneity, on the basis of which the spatial relations are defined). Despite the unfortunate historical accident that the words relativity and relationism share a common root word, these are two entirely different – and in many respects incompatible – principles. Throughout all of Dingle’s writings, at least from 1921 until about 1959, we can see that he was laboring under the mistaken belief that Einstein’s theory of relativity was the embodiment of Leibnizian relationism, whereas in fact it is fully in the Newtonian tradition of absolute inertia. Many other philosophers during the early years of relativity theory made the same mistake, notably the French philosopher Henri Bergson who, first in 1911 (after hearing Langavin’s lecture on the ‘twins paradox’) and later in the 1920s, famously argued that the concept of “relativity” necessarily implies that a travelling twin and a stationary twin will be the same age when re-united. This is precisely what Dingle believed as late as 1956. Not surprisingly, Dingle wrote the introduction to Bergson’s 1922 book “Duration and Relativity” when it was published in English in 1965. It’s clear that Dingle’s understanding of relativity had always been in accord with Bergson’s early views, although he (Dingle) seems never to have considered the implications of the twins paradox until late in life. Of course, Bergson himself (who died during World War II) had long since acknowledged and disavowed his early misunderstandings of Einstein’s theory, but this evidently didn’t disturb Dingle’s belief in those discredited views. He seems to have suspected that Bergson’s recanting was insincere.


Dingle’s monograph “The Special Theory of Relativity” (1940) reveals quite plainly that he always misunderstood the subject. This is evident not only in the complete absence of the actual principles of special relativity in this book, but also in Dingle’s insistence on the erroneous idea that the entirety of special relativity is entailed by the statement that “the quantity that is physically important is not L, but L(1-v2/c2)1/2”, although he distinguishes this from what he calls the Fitzgerald-Lorentz contraction hypothesis. After stressing repeatedly that “time dilation” has nothing whatsoever to do with relativity, he discusses the Kennedy-Thorndike experiment, and acknowledges that “the Fitzgerald-Lorentz contraction hypothesis will not explain the result”, but instead of going on to say that the results are explained by the combination of the length contraction and time dilation, he simply declares that the experiment falsifies the Fitzgerald-Lorentz contraction hypothesis, while still insisting that no time dilation is involved. Needless to say, both of those assertions are flatly contrary to special relativity.


Dingle’s “explanation” of the null result of Kennedy-Thorndike is, frankly, gibberish. He claims, incorrectly, that no time intervals are involved in the experiment, failing to realize that each phase of a light wave can in principle be replaced with a momentary pulse, and the phase difference at the receiver is then simply the time interval between the arrivals of two pulses. Hence the only explanation for Kennedy-Thorndike is that clocks run slow by the dilation factor. Dingle flatly denies this, so whatever he is describing, it is not the theory of special relativity. Moreover, he knows this, because he writes


This [realization that time dilation doesn’t exist] is particularly important in connexion with the Kennedy-Thorndike experiment, because it has been proposed to explain the null result obtained there by assuming, as well as the Fitzgerald contraction, a modification of the period of the atoms emitting the light, produced by their motion through the ether. Such an assumption, however, would be a purely ad hoc hypothesis, and, unlike the Fitzgerald contraction, it could not be shown to be even a possible requirement of electro-magnetic theory. It would be merely an arbitrary supposition, called in as a desperate expedient to remove an insurmountable difficulty.


Of course, Dingle is mistaken in his belief that time dilation cannot be explained in terms of electromagnetic theory. Both Larmor and Lorentz (not to mention Poincare and Einstein) had shown long before that it is quite easily explained, and indeed it emerges as a necessary requirement of electromagnetic theory, just as does the Fitzgerald contraction.


Now, one might wonder how Dingle proposed to explain Kennedy-Thorndike after rejecting time dilation. His answer is truly bizarre: He says the length of each light wave moving along either arm of the apparatus will be contracted in the same proportion as the arms themselves, and hence the same numbers of waves will always occupy the arms, so the phase difference will not change. He overlooks the fact that the speed of light is invariant, so if the wavelength is reduced from its rest value by the motion of the apparatus, the frequency must be increased from its rest value. (Note that in 1937 Ives and Stillwell had experimentally confirmed the change in frequency of a moving light source predicted by special relativity.) It follows that the null result of Kennedy-Thorndike can be consistently explained only by accounting for both the length contraction and the time dilation effects of the full Lorentz transformation. Dingle’s insistence – in what was supposed to be a competent exposition of special relativity – that no time dilation was involved is stunning.


In view of the blatent misunderstanding of the most elementary aspects of special relativity expounded in Dingle’s monograph, it is not surprising that the book was soundly criticized, e.g., by Paul Epstein. Unfortunately, editors who themselves had little or no understanding of special relativity were unable to discern Dingle’s misconceptions. In addition, his words were probably re-assuring to people who harbored similar misconceptions, so his writings continued to be published and referenced. Incredibly, when Einstein’s popular exposition of relativity was re-published in 1961 the editor Robert Lawson appended a bibliography, and the first reference was Dingle’s 1940 monograph! (Lawson thanked two obscure British professors for suggestions in the choice of books.) This is doubly ironic considering that in the preface to the 1961 edition of that monograph Dingle announces that he has now realized special relativity is both false and trivially illogical, but that he is still able to re-publish his monograph on the subject without any changes because, fortunately, he now realizes that what he described in the book was not special relativity at all.


Thus, for over 33 years (from 1922 to 1955), Dingle had written about and lectured on what he believed to be “special relativity” without ever understanding the first thing about it, and in particular, without ever having thought through the most elementary implications of the Lorentz transformation, time dilation, and the twins paradox. When he finally did think about it, he immediately concluded that no asymmetrical aging could possibly exist (when the twins were re-united), because the situation is kinematically symmetrical, i.,e., the distance between the twins increases and then decreases, and there is no meaning to the idea that their paths could be physically distinguished. This just reflects Whitehead’s claim that we have no way of making spatio-temporal measurements (and Bergon’s “perfect relativity”, by which he meant pure relationism). This is a very natural position for a relationist to take, and it leads to make exactly the kinds of arguments that Dingle made in the late 1950s. He insisted that asymmetric aging was inconsistent with the basic principle of relativity… by which he (unfortunately) meant the principle of relationism, which is nearly the antithesis of relativity. His insistent and weird pronouncements suddenly become much more intelligible if, throughout his text, the word relativity is replaced with relationism. Of course, even granted that Dingle was really talking about relationism, his position was still flawed, because each twin exists in spatial relation not just to his sibling, but to all other bodies in the universe. Thus, unless we arbitrarily rule out any kind of Machian influence, we cannot claim that the twins are even relationally symmetrical. We might propose to consider an otherwise empty universe but, as Mach stressed, no one is qualified to say what the outcome would be in such a circumstance.


One might think that Dingle’s concerns about the source of the asymmetry between the twins would have led him to be interested in the origin of inertia, but in fact he wrote a paper (in 1967) ridiculing such questions, professing to not even understand the question.


In recent years papers have appeared concerned with what is called 'the origin of inertia', and others with the associated idea of 'inertial frames of reference'. The phrase, origin of inertia is at least paradoxical. The ordinary meaning of inertia is the property (if it can be so called) which a body possesses of complete inability to change its state... But if it does not change, what sense is there in asking for the 'origin' of its immutability?


Even making allowances for his age (77), this still seems rather obtuse for a self-styled philosopher of science. (Why should the "state" of an object be characterized by its velocity rather than its position or its acceleration?) Dingle seems to have been genuinely unable to grasp both the significance and the non-obviousness of inertia. He continued (in his characteristic tone)


It is to be presumed that those who discuss this subject have some definite problem in mind, but it does not appear that they perceive the desirability of stating it explicitly.


So, even if we charitably interpret Dingle’s complaint about the asymmetric aging of twins in the context of relationism (rather than relativity), his categorical claims were still wrong, and although we may be tempted to think that perhaps his concerns had a valid philosophical motivation in terms of the origin of inertia, we find that he flatly disavows any such interpretation of his motives. He is not concerned about the origin of inertia; he is fully prepared to simply accept inertia on the most naïve basis, so there really seems to be very little ground for defending or even explaining Dingle’s position as anything other than profoundly misguided and ill-informed confusion.


Ironically, critics of relativity sometimes point to the confusions of people like Dingle as evidence of a deficiency in the theory, i.e., they argue that a proper theory would not be so confusing to so many people. In this particular case that argument is rather hard to accept, because Dingle himself was one of the early expositors of the theory, i.e., one of the authors who told people that Einstein’s theory means “everything is relative”, etc., and thereby set the stage for generations of misunderstanding. Not only does it cause people to waste time critiquing a false image of the theory, but when they eventually discover an inconsistency, they often react as Dingle did himself when he finally realized that relativity actually did predict asymmetric ages for the re-united twins. By that time he had so much invested in relationism that he could never forgive relativity for not being a relationist theory.


In addition to the confusion with relationism, I think there was another, even deeper, reason for Dingle’s rejection of relativity. It’s interesting to read his essay for the Encyclopedia Britannica on the philosophical consequences of relativity (written during his pro-relativity days). This article, in retrospect, shows that his acceptance of special relativity (he never claimed to understand general relativity) was based firmly on the notion that there is no external objective reality. He believed that the essential significance of relativity was that, in his words,


... the idea of something existing objectively, which physical measurements revealed, had to be given up...  The philosopher must henceforth interpret physics in terms of operations and their results alone, leaving external existences out of account...  Physics was thus thrown back on the unadorned description of itself as the discovery of relations between the results of chosen operations of measurements.


It's clear that Dingle accepted relativity (prior to old age) as simply a collection of brute facts that need not yield any coherent picture of an objective external reality. He made the same point even more strongly in his 1954 essay on “The Sources of Eddington’s Philosophy”, in which he discussed what he believed were the implications of the theory of relativity:


Physics became a description of the relations existing between the results of certain operations which you performed, and you chose for yourself what those operations should be. Physical quantities—that is to say, those things that were represented by symbols in physical equations— were not the magnitudes of objective features of the external world. They were the results of your own definitions, and only certain of the relations between them were free from your power to change them by changing your mind. This is not generally admitted even now,* yet it is inescapable by anyone who accepts the theory of relativity as genuine physics. The argument is too simple to be deniable. Every relativist will admit that if two rods, A and B, of equal length when relatively at rest, are in relative motion along their common direction, then A is longer or shorter than B, or equal to it, exactly as you please. It is therefore impossible to evade the conclusion that its length is not a property of either rod; and what is true of length is true of every other so-called physical property. Physics is therefore not the investigation of the nature of the external world.


When he says “this is not generally admitted even now”, he refers in a footnote to articles by Paul Epstein and Max Born, both of whom had challenged Dingle’s understanding of relativity, but he obviously disregarded their explanations of his misconceptions. Ironically, Dingle’s view of relativity was similar to the modern acceptance of quantum mechanics, in the sense that there is evidently no “local realistic” model (of the classical type) of an external reality that always yields the results of our measurements; we can only describe the patterns in those results as abstract brute facts that must be accepted. In other words, Dingle's attitude (pre-1960) was that "one does not understand relativity, one merely gets used to it". This of course is a paraphrase of a famous remark that has often been applied to quantum mechanics, but Dingle was entirely mistaken in applying this attitude to relativity, because in fact relativity (unlike quantum mechanics) is an entirely classical theory, firmly based on a perfectly coherent model of objective external reality. The young Dingle never grasped this model - indeed his whole philosophy of science (in those years) was that relativity had rendered all such models unviable. Instead, he had simply told himself (like someone thinking about quantum mechanics) that when we make certain measurements we get certain results, despite the fact that he himself did not understand it. He accepted this because he believed that no one understood it, and in fact he believed that that was the whole point of relativity, that we must now believe things that cannot be "understood" in the classical sense of being manifestations of an external objective reality.


Then, in his later years, he rejected this approach (as did most of the formerly enthusiastic circle of operationalists and logical positivists), and decided that we cannot reasonably dispense with the idea of an objective reality. (Ironically, this was also Einstein's mature view.) The problem was that, once he made this change, it exposed the fact that he had never grasped the simple objective model of special relativity. In fact, he had spent much of his life trying to convince himself and others that no such model was possible, and indeed that this impossibility was the whole message of relativity. He could not, in his old age, accept the idea that, as a matter of fact, relativity has a perfectly simple objective model, and that his views on this subject, to which he had devoted much of his life, had always been fundamentally flawed and misguided.


After finally being convinced, around 1957, that in fact special relativity does predict unequal aging for twins in certain circumstances, he concluded that special relativity must be logically inconsistent, basing this on the rather belated realization that the Lorentz transformation and its inverse possess reciprocal time dilation. He had to imagine that no one had ever noticed this before – which of course is absurd, since this reciprocity was precisely the fact on which Einstein explicitly based special relativity (as discussed above). Gradually the people with whom Dingle corresponded began to realize how profoundly confused he was, and they became dismissive of his persistent complaints that his views were not being accepted. One of the most patient was Synge, who nevertheless finally gave up trying to reason with Dingle. His last letter to Dingle shows how mystified he was at Dingle’s inability to grasp the most elementary facts of relativity theory.


I could not decide whether to pursue the argument with you or let the matter drop, leaving the last word to you. But just yesterday I had a thought. What if Dingle is pulling the leg of the world? It is to me the most reasonable hypothesis to explain what is otherwise inexplicable to me. Knowing you as well as I do (and I know you much better after our recent correspondence), I cannot bring myself to believe that you are as stupid as you make yourself out to be. If my hypothesis is correct, I salute your sense of humour. No harm has been done. Printers have had good employment. My humiliation in having been taken in is swallowed up in my admiration at the way you have put the thing across.


Dingle, of course, was not joking. His frustration over not being able to persuade anyone gradually evolved into a belief that truth was being suppressed, leading to a mounting sense of outrage over the lack of ethics by his fellow scientists. His anger boiled over in his 1972 book, “Science at the Crossroads”, a profoundly tragic and depressing document. He chronicled in detail each of his letter-writing campaigns, not only with the editors of magazines such as Nature and New Scientist, but also with numerous friends, acquaintances, and ultimately, with perfect strangers. He condensed his entire objection to special relativity down to what he called “The Question”. To convey the level of his thought, we cannot do better than to simply quote this question in full:



According to the special relativity theory, as expounded by Einstein in his original paper, 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. ‘Thence’ [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] ‘we 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.’ 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?


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.


Of course, Einstein’s phrase “under otherwise identical conditions” is understood to mean that differences in gravitational potential due to the Earth’s non-spherical shape, etc., are to be eliminated, so we are simply dealing with one inertial clock and one clock moving in a circle. Needless to say, the short answer to Dingle’s momentous question is simply: The polar clock is moving along a more nearly inertial path than the equatorial clock. This single sentence answers the question, and this answer was provided to Dingle countless times, but his response was always to disregard the answer and ask the question again, claiming that he had never been given the answer. As explained above, he failed to realize that special relativity, no less than Newtonian mechanics, is founded firmly on Galileo’s principle of inertia, not on Leibniz’s principle of relationism. Dingle was so firmly convinced that special relativity was a relational theory that he simply disregarded all the correct answers he received to his questions, because those answers did not address the principle of relationism on which Dingle had always believed (erroneously) special relativity to be founded. (The reader may recall that the reliance on the principle of inertia and the privileged place given by both Newtonian mechanics and special relativity to inertial motion had always been acknowledged as an epistemological incompleteness of those theories, in the sense that the origin of inertia was not explained. It would be tempting to think that this was Dingle’s point – had he not specifically denigrated and indeed ridiculed all epistemological scruples about the origin of inertia. Of course, this point is neither novel nor controversial, and it in no way undermines the logical consistency of either special relativity or Newtonian mechanics.)


Notice that after allowing himself half a page to state The Question, and supposedly having no idea of the answer, Dingle nevertheless felt that a single sentence should suffice for the answer, and he gives a clear indication that anything beyond a single sentence will be viewed by him as “obscuration of the essential point by irrelevant considerations”. Of course, someone who is seeking enlightenment must recognize that he may not know (or may not be able to judge at first) what is and what is not relevant. A more technical answer to Dingle’s question could be phrased like this:


The elapsed time on an ideal clock as it advances incrementally from the time and place denoted, in terms of any inertial coordinate system, by the coordinates (t,x,y,z) to the time and place (t+dt,x+dx,y+dy,z+dz) equals the square root of  dt2 – (dx2 + dy2 + dz2).


Unfortunately this answer refers to the concept of an inertial coordinate system, which Dingle never understood (as is clear from his writings throughout his life). It’s easy to give the definition (i.e., a system of space and time coordinates in terms of which inertia is homogeneous and isotropic), but Dingle would never listen to explanations, because inertia is not a relational concept (unless we posit Machian influence of distant matter as the source of inertia, which Dingle did not). And of course the digressions into irrelevancies that characterized many of the responses to Dingle were prompted by Dingle himself, since his preface to “The Question” is packed full of fallacies, non-sequiturs, and misconceptions, tempting all the respondents to address all those misconceptions before getting around to answering his question. No doubt most of them imagined that by clearing up the misconceptions revealed in his introductory comments, the answer to his trivial question would be made clear to him. But this well-meaning approach was lost on Dingle. He simply scanned the first sentence of each reply, and if it didn’t consist of an answer to his trivial question, phrased in purely relational terms (which he erroneously believed were the only relevant terms), he rejected it as unresponsive.


Just to touch on the specific misconceptions in his introductory remarks to The Question, we note that his reference to the differentials dt and dt’ erroneously assume those are total differentials, rather than partial derivatives as discussed at the beginning of this note. Also, he says Einstein’s theory “takes no account of acceleration”, so it has no way of distinguishing absolutely between the polar and equatorial clocks, but this is flatly false. Einstein’s 1905 derivation begins with the phrase “Let us consider a system of coordinates in terms of which Newton’s laws hold good”, which is to say, an inertial coordinate system, i.e., a system of coordinates in terms of which inertia is homogeneous and isotropic. Even the first principle of relativity states not that all motion is relational, but that any system of inertial coordinates is equally suitable for the formulation of physical laws. Hence Dingle’s claim that special relativity takes no account of absolute acceleration is utterly false. The existence of absolute acceleration is the very essence of the principle of inertia, on which special relativity is based. It is little wonder that, with a question prefaced by so many and such profound misunderstandings, the responses tended to be varied and discursive. Nevertheless, each respondent at some point included the simple answer to Dingle’s trivial question – but to no avail.


By 1971 Dingle had convinced himself that the entire world was in “grave danger” from the prevalent belief in the theory of special relativity, and he frequently referred to on-going (but unspecified) “dangerous experiments” being conducted on the basis of special relativity, the result of which could be catastrophic for the whole world. Those who continued to deny the logical inconsistency in special relativity revealed “a universal attitude foreshadowing certain danger to the whole population”.


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.


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…


I write this letter, as a member of the public and as spokesman for those who have expressed to me their grave misgiving at the state in which this matter now stands, to request that the Royal Society [which had said Dingle’s error was too trivial to even be instructive] shall publish in Nature a statement of the fallacy in the argument expressed in my letter in this journal and summarized above; or, alternatively, acknowledge that there is in fact no fallacy and therefore that the special relativity theory can no longer safely be used as the basis for dangerous experiments.


I wish also to emphasize that, although there are details of the matter in which I think I should have personal ground for complaint against the present editor, Mr. John Maddox, I am here making no such complaint: my charge is entirely that his actions, and the principles underlying his conduct of the journal, constitute a grave public danger.


The answer to the point in question (which is one of the two foundation stones of the special relativity theory) must be sought immediately and, whatever it is, accepted, made known, and acted upon. In the meantime, dangerous experiments based only on evidence that is possibly irrelevant or inconclusive should be suspended.


And so on. One of the magazine editors, in declining to publish Dingle’s letters, commented on this aspect of Dingle’s concern.


I do not find in your letter any clear statement of the nature of the dangers which you imagine might follow the use of the special theory of relativity. You say the possibility of danger is vividly real to you and yet I cannot find in your letter, or in anything you have written, a clear statement of the nature of the danger you anticipate...


Dingle replied


On the matter of specifying the danger involved, I can only say that if this could be foreseen, steps could be taken to prevent it, but since we know only of what character this might be, it seems wiser to start at the shadow than passively to await the arrival of the substance casting it.


The most heart-breaking aspect of Dingle’s book is its account of his correspondence with former friends and associates. Most of these people were octogenarians, like Dingle himself, and in poor health. In each case he begins by describing how he had always held the person in high regard, but then gradually, after the exchange of a few letters, in which Dingle tries to persuade them of their moral and ethical responsibility to join him in his campaign against special relativity, the person can be seen painfully struggling to extricate themselves, and Dingle concludes regretfully that yet another person has been unmasked as a co-conspirator in the worldwide pro-relativity fraud. One of these was Max Born, whose last reply to Dingle read


I am completely fed up with the matter, 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 to 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.


Eventually Dingle began to harass the elderly Lawrence Bragg, entreating him to demand that the journal Nature publish an acknowledgement of their misdeeds. When Bragg politely declined, Dingle wrote back, threatening to expose Bragg’s moral bankruptcy in a forthcoming book (i.e., Science at the Crossroads). Remarkably, Bragg responded again in polite terms


It seems to me that you have had a very fair and patient hearing from a number of people who are competent experts. I trust their judgment and I think no useful service to science is done by reopening the correspondence. I think it best to be frank.


Dingle very accurately characterized this response as follows


…the tenor of Sir Lawrence's letter … is that of one written to a misguided, though perhaps well-meaning, ignoramus whose delusions have received sufficient, if not over-generous, attention…


This leads Dingle to present his credentials, pointing out that he learned relativity from A. H. Whitehead (who, as Dingle himself acknowledged previously, was an opponent of Einstein’s theory) fifty years previously. Overall, Dingle’s book and his writings throughout his life make it very clear that he never understood even the most elementary aspects of Einstein’s theory, or rather, he mis-understood them. His writings are a stark example of how some academicians can make an entire career out of stringing together words that fundamentally make no sense, but that conform superficially to the appearance of plausible prose, acceptable within some peripheral academic sub-group (in this case, philosophers of science).


Dingle and a few others like him were responsible for obfuscating the theory of relativity beginning in the 1920’s, spreading false and confused ideas about it in popular accounts, only to complain years later that many false and confused ideas about relativity were in circulation, citing this as evidence that there must be something wrong with the theory. This may explain how, after fifty years, Dingle could be so ignorant of the subject. Still, it seems to me this can’t entirely explain the obsession which overtook him in his last years. The impression given by “Science at the Crossroads” is one of a mild form of mental illness. The words are strung together in superficially coherent sentences, but all underlying thought processes have clearly broken down. For example, he alludes to a single quote from Henry Dale not once, not twice, but twenty times. He also refers repeatedly to the “Aberfan” tragedy (in which over 100 school children were killed by an avalanche near a coal mine), stating that this kind of event will surely reoccur if the world’s scientists don’t immediately acknowledge the invalidity of Einstein’s special theory of relativity. The book is almost unbearable to read, but it is recommended to anyone who contends that Dingle was not suffering from some kind of dementia during his last years.


Professor McCrea, with whom Dingle battled on several occasions, passed away in 1999 at the age of 94. Obviously McCrea was on the right side of the debate, although his rebuttals of Dingle's position may not have been as clear and direct as they could have been. Of course, any false premise can be refuted in infinitely many ways, so there is always a temptation to pile refutations on top of each other, and McCrea fell into this trap to some extent, giving not just one but several reasons why Dingle was wrong. The effect of this approach is often to blunt rather than sharpen the refutation. It’s also worth noting that neither Dingle nor McCrea were theoretical physicists, nor were they educated in the philosophy of science; they were both astronomers. They also had a long history of publicly disagreeing with each other on a variety of subjects, beginning several decades prior to their dispute over special relativity. (Oddly enough, they were both protégées of R. H. Fowler, and both were professors at Imperial College in London.)


One point of interest in Dingle’s book is the reference to Einstein’s 1918 paper on the subject of the twin paradox, “Dialogues about Objections to the Theory of Relativity”, Naturwissenschaften, 6, 697 (1918). In this paper Einstein explained (among other things) how to reconcile the usual resolution of the twin paradox with the general theory. In the context of special relativity, it is customary to “resolve” the paradox simply by noting that the twin who travels away and back has accelerated, whereas the twin who stays at home has not, and this asymmetry (somehow) accounts for the difference between their elapsed times. Now, the privileged role of inertial motion was always seen by Einstein as a defect of the special theory (just as in Newtonian theory), and the general theory was supposed to provide a more satisfactory framework, in which the laws of physics were equally well expressible in terms of accelerating or non-accelerating coordinate systems. Einstein’s task, then, was to explain why the twins were still asymmetrical, even in the context of the general theory. The answer, of course, is that the “equivalence” of all systems of coordinates entails the appearance of pseudo-gravitational fields with respect to accelerated coordinates, and the general theory gives a quantitative account of how these fields affect the elapsed proper time along any given worldline. Einstein demonstrates that, when these effects are taken into account, the original conclusion about the twins based purely on special relativity remains valid. This explanation of Einstein’s is very closely reproduced in Max Born’s popular book published a couple of years later (in 1920).


It’s been suggested that Dingle’s disaffection with relativity might have begun in 1950 as a result of the unfavorable review that Einstein gave to Dingle’s essay contained in Schlipp’s volume entitled “Einstein, Philosopher-Scientist”. This book was comprised of essays, on various aspects of Einstein’s work, contributed by several prominent thinkers, including Bohr, Pauli, Born, von Laue, Reichenbach, Margenau, Bridgeman, Infeld, Milne, Lemaitre, Menger, and Godel. At the end of this book honoring Einstein appears a chapter in which Einstein himself “replies to his critics” – a droll reference to the fact that many of the essays respectfully take Einstein to task, mainly for his “rigid adherence to classical theory, i.e., his failure to fully embrace quantum mechanics. He gave thoughtful replies to these essays, acknowledging the valid points of the authors, and defending his “realist” views as best he could. He also praised a few of the other essays, especially the one by his old friend von Laue. However, when it came time to address himself to the essay contributed by Dingle, Einstein had only this to say:


In spite of serious efforts I have not succeeded in quite understanding H. Dingle's essay, not even as concerns its aim. Is the idea of the special theory of relativity to be expanded in the sense that new group-characteristics, which are not implied by the Lorentz-invariance, are to be postulated? Are these postulates empirically founded or only by way of a trial "posited"? Upon what does the confidence in the existence of such group-characteristics rest?


Dingle might well have been humiliated by this appraisal, especially since his was the only essay to be essentially dismissed out of hand in Einstein’s remarks. Interestingly, after contributing that essay to Schlipp’s book on Einstein, Dingle thereafter frequently cited it among his main credentials for being a “recognized expert” on Einstein’s theory – despite the fact that Einstein himself lambasted the essay as unintelligible. Even more remarkable is the fact that when Dingle subsequently contributed an essay to the Encyclopedia Britannica on the subject of the “philosophical consequences of relativity”, he essentially repeats his 1949 essay from the Schlipp book, and even says


It has been shown, indeed, that when the phenomenon of radiation is treated in the same manner as the phenomenon of motion, an “entropy-time” emerges which is of precisely similar character to the space-time of mechanics. Neither of these concepts is to be regarded as objective…


If any readers of the encyclopedia are curious to know where this “has been shown”, the references point to Schlipp’s book of essays, which is to say, to Dingle’s own unintelligible essay, an essay which Einstein himself repudiated in the very same book. The only other reference cited in the encyclopedia article (aside from Eddington’s book on philosophy which is cited mainly to be criticized) is Dingle’s own 1940 monograph on special relativity, a book which he himself later acknowledged did not accurately represent the subject (thus enabling him to continue re-publishing the book after he had repudiated the subject). Naturally he always listed this book, too, as one of his main credentials for being an expert on the subject.


Despite Einstein’s rather blunt repudiation of Dingle in 1949, Dingle ostensibly continued to admire Einstein, and didn’t turn against relativity (or what he understood of relativity) until about six years later. In his “Crossroads” book he wrote about how, after a lifetime of being a proponent and teacher of special relativity, he had first begun to lose confidence in its soundness:


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. 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 re-united twins would have aged differently]. In an article in Nature 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.


At this point he still claimed to be adhering to “special relativity” (obviously conflating it with relationism), but drawing from it different conclusions than the ones he had formerly believed. Only subsequently (around 1957) did he finally realize that special relativity did indeed predict unequal ages for the re-united twins, leading him to conclude that it was special relativity itself that was logically inconsistent. But what intrigues me is the date of his initial doubts, 1955, the year Einstein died. Dingle was 65 at this time. Thereafter his writings began to feature frequent claims about what Einstein had meant and how Einstein would have responded to various things, claims which he wisely avoided making while Einstein was still alive (since it’s clear from the Schlipp episode that Einstein found Dingle’s interpretation of relativity to be unintelligible). Could there have been some psychological connection between the death of Einstein and the onset of Dingle’s unraveling, or was this just coincidental?


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