Hoop-Skirts of the Mind


Over the last quarter of a century (since at least 1988) a journalist named Tom Bethell has written a series of articles and a book arguing that the theory of relativity is a very bad thing. He claims, first, that special relativity is both illogical and experimentally falsified. Second, although he concedes that the predictions of general relativity are correct, he says the theory itself is incomprehensible and needlessly complicated. Third, he contends that the theory of relativity has fostered moral relativism and subjectivism. Now, anyone acquainted with the theory of relativity can see immediately that the first two of Bethell’s claims are mutually contradictory. The flat spacetime of special relativity is just a particularly simple solution of the field equations of general relativity, so all the predictions of the special theory (within its domain of applicability), including all those that Bethell claims are illogical and experimentally falsified, are also predictions of the general theory, which he concedes are correct. In view of this, any further consideration of his scientific claims may be superfluous. Nevertheless, for the sake of completeness, we’ll assess each of his claims individually on its own merits.


Disappointingly, none of Bethell’s complaints against special relativity are new or novel. He simply repeats standard misconceptions that have been common currency among anti-relativity “dissidents” (as they like to call themselves) since the early 1920s. Foremost among these is the misunderstanding of the Sagnac effect, which refers to the different times required for light pulses to travel in opposite directions around the perimeter of a rotating platform. In special relativity this effect is a trivial consequence of the invariance of the speed of light in terms of any standard system of inertial coordinates. Indeed, one of the first large-scale demonstrations of this effect, by Michelson and Gale in 1924, was performed for the express purpose of verifying the prediction of special relativity – which of course it did, as have all prior and all subsequent demonstrations. Why, then, do anti-relativity “dissidents” like Bethell claim that the Sagnac effect contradicts special relativity? Their “reasoning” is based on the erroneous belief (apparently acquired from a misreading of what Bethell calls “Easy Einstein” books) that special relativity asserts the invariance of light speed in terms of any arbitrary system of reference, including rotating systems. If this were true, the theory would indeed predict no Sagnac effect – but of course it is not true. Special relativity asserts that the speed of light is invariant when expressed in terms of any standard system of inertial coordinates, but definitively not in terms of rotating or otherwise accelerating systems of reference, so the “dissident” “reasoning” is specious. Alas, no matter how many times this is explained, the “dissidents” continue to repeat the same mistake. Bethell has taken this to an extreme: He tells of once offering a cash award to any scientist who could cite an experiment proving that the Sagnac effect doesn’t exist. Yes, he challenged relativity experts to provide evidence that relativity is wrong, and he reports with satisfaction that “there were no takers”. Clearly he is deeply confused.


The reason for Bethell’s confusion is that he conflates the Michelson-Gale experiment with the Michelson-Morley experiment, i.e., he thinks the Earth’s rotation ought to produce a non-null result in the latter as it does in the former. Of course, special relativity predicts a null result for the Michelson-Morley experiment, even down to the level of precision corresponding to the small tangential velocity of the Earth’s surface due to the Earth’s rotation. Thus Bethell’s prediction differs from the prediction of special relativity. Which one is correct?  In a 2011 article Bethell tells his readers that


The most sensitive interferometer experiment ever conducted, by John Hall in 1979, did detect a fringe shift of the correct magnitude…  Hall was not expecting to see this fringe shift and he assumed the effect was "spurious" – the artifact of a design error in his own equipment. In an interview with me in 2004, Hall agreed that his 1979 experiment should be redone…


From this we might gather that a violation of Lorentz invariance (the empirical content of special relativity) was actually detected, but was ignored because it wasn’t the expected result. (Bethell doesn’t comment on why anyone would go to the trouble and expense of performing a high-precision experiment if they were inclined to disregard the result.) If true, this would be a rather damning indictment of Dr. Hall’s scientific acumen and integrity – not to mention the fact that he missed getting another Nobel prize, this one for the astounding discovery that physics is not Lorentz invariant. But when Hall was asked about the above statements, he described the situation somewhat differently


There was a mechanical problem with the 1979 experiment because of the lack of stable leveling during rotation and, due to the brevity of the postdoc's appointment, we were not able to rework the mechanical mounting. In more recent times there have been several experiments led by a friend in Germany, Prof Achim Peters. The most recent one was by Sven Hermann and Achim Peters, and shows the correctness of the Einstein model up to two more digits. [PRL 95, 150401 (2005)] This experiment compared two length-based clocks which differed only in their angular orientation. No positive results have ever been obtained for a deviation from special relativity.


So, contrary to what Bethell attempts to insinuate, the prediction of special relativity has been fully corroborated by modern high-precision experiments, and Bethell’s own prediction of a non-null result has been conclusively falsified.


As with the Sagnac effect, the standard “dissident” complaint about stellar aberration relies on a misunderstanding of what special relativity actually predicts. In this case the “dissidents” contend that special relativity predicts the stars in a binary star system ought to appear at significantly different locations (contrary to what we actually observe) if the velocity parameter appearing in the relativistic aberration formula is taken to be the relative velocity between the instantaneous rest frames of the Earth and each of the stars. Once again, the “dissidents’” understanding is incorrect. When evaluating the aberration of the star’s apparent position as seen from the Earth, they fail to account for the aberration of the Earth’s apparent position as seen from the stars. When this is taken into account, the observed stellar aberration is in perfect accord with special relativity – and of course it is inconsistent with the material ether theories of the 19th century, about which we will have more to say later.


Now we come to the famous equation E = mc2. Even people who know nothing at all about physics are likely to be acquainted with that formula, and to associate it both with the theory of relativity and with some rather dramatic demonstrations of its validity. Bethell is equivocal about whether he accepts that the mass-energy relation is valid, but in any case he disputes the association with relativity. He says


We've all heard of the equation E = mc2, saying that the energy of a body is proportional to its mass. It was derived by Einstein using relativity theory. Less well known is that it was derived by him again later, without relativity. He called the later version his "elementary derivation." Relativity wasn't necessary to derive the most famous equation in physics.


This refers to a brief note entitled “An Elementary Derivation of the Equivalence of Mass and Energy” (1946), in which Einstein explained that “although this derivation makes use of the principle of special relativity, it makes no use of the machinery of the theory” [my emphasis]. Thus Bethell has misrepresented his source: he tells us the derivation was performed “without relativity”, whereas Einstein explicitly says his derivation does make use of the principle of relativity, and of course all the machinery of the full theory follows from the same premises, as Einstein had already shown. Indeed, anyone acquainted with modern physics knows that the relation mc2 = E is actually just a special case of the full relation (mc2)2 = (E)2 – (pc)2, where p signifies momentum, and that this is simply a scaled version of the Minkowski spacetime interval (dt)2 = (dt)2 – (dx)2, which entails all the well-known relativistic features of length contraction, time dilation, and relativity of simultaneity. Thus the relation E = mc2, written in full, is not just dependent on special relativity, it directly expresses the very essence of special relativity, something which Einstein himself consistently stressed, not only in the 1946 paper cited by Bethell, but in all his other writings as well. So, again, Bethell’s argument is spurious.


Bethell then goes on to consider the Hafele-Keating class of experiments, measuring the elapsed time for clocks in different states of motion. After commenting that, according to special relativity, the speed of light is the same in all directions, he says “But when atomic clocks were flown around the world in opposite directions, the clock that flew toward the east had recorded slightly less time”. This is a non-sequitur, because experiments like Hafele-Keating do not test the speed of light, they test the time-dilation predictions of general relativity (which include the effects of special relativity). And of course the results are in agreement with the predictions of relativity. As one would expect, the precision of the first attempts to measure time dilation by this method was marginal, but it has subsequently been repeated with more precise clocks, and the results continue to be in excellent agreement with the relativistic predictions. The depth of Bethell’s confusion can be seen from his comments posted on a science blog


All inertial reference frames are supposed to be equivalent to one another. The speed of light is supposed to be the same in all frames, no matter how the observer’s frame moves.  But the east-west difference in atomic clock rates showed that the speed of light indeed was not the same in all reference frames.


In the first sentence he correctly notes a fundamental premise of special relativity, i.e., that all inertial reference frames are equivalent, but in the very next sentence he drops the crucial word “inertial”, and asserts that all frames are equivalent no matter how the frame moves. This of course is absurd. As with so many “dissidents”, Bethell conflates the principle of relativity (which Einstein’s theory shares with Newtonian mechanics) with Leibnizian relationism, and he goes on to make the erroneous claim that since no object is perfectly inertial it follows (so he claims) that there is no such thing as an inertial frame of reference. Needless to say, the non-inertialness of objects – which is perfectly detectable – consists precisely of their deviation from ideal inertial motion.


To round out his critique of special relativity, Bethell makes the sweeping assertion that there is no empirical evidence for either length contraction or time dilation. He says these notions arise purely from a mathematical formalism with no empirical foundation, although his argument is different for time dilation than for length contraction. Regarding time dilation, he acknowledges that the temporal characteristics of physical phenomena (such as clock rates and ion half-lives, etc) do indeed exhibit the “slowing” predicted by special relativity, but he argues that we should not say time itself has slowed down for those entities. This complaint is based on a misunderstanding. If we agree (as Bethell does) that the temporal characteristics of physical entities slow down when in motion, in terms of any given system of standard inertial coordinates, by precisely the amounts predicted by special relativity (as all the evidence indicates), then we agree that physical phenomena are Lorentz invariant. It follows by simple high school algebra that relatively moving systems of standard inertial coordinates are related by Lorentz transformations. This is the entire content of special relativity, so Bethell has no substantive disagreement. Whether we choose to regard the time coordinates of standard inertial coordinate systems as representing “time” in some metaphysical sense is, well, metaphysical, and has no bearing on the validity of special relativity.


Regarding length contraction, Bethell actually denies that there is any empirical evidence for this aspect of the Lorentz invariance of physical objects. About this he is simply mistaken. The arms of the interferometer in a Michelson-Morley experiment (to give just one example) undergo measurable amounts of length contraction. Indeed it was just such experiments that first led to the recognition of length contraction. Granted the effect is extremely small in such experiments, commensurate with the relatively low velocities involved, but it’s well within the precision of interferometers to measure. Bethell bases his claim on a misunderstanding of the optical effect pointed out by James Terrell, who used the equations of special relativity (the ones Bethell says are wrong) to show that the combined effect of relativistic length contraction (which Bethell says doesn’t exist) and the different delay times for light to travel from different parts of a contracted object to any given focal point results in an optical image impinging on that point at a given time that is rotated rather than contracted. Thus Terrell’s analysis does not contradict the existence of length contraction, it is explicitly based on the existence of length contraction. Once again, Bethell has utterly misunderstood and misrepresented his source.


Incidentally, when Bethell claims that the predictions of relativity represent a triumph of mathematical theorizing over experimental evidence, he reveals that he’s unfamiliar with the history of the subject. Recall the words of Poincare, writing in 1905, describing how the principle of relativity had been viewed by experimentalists and theorists respectively:


Experimental physics has been more faithful to the principle of relativity than the mathematical theorists. The theorists, to satisfy their other general views, would not have spared it, but experiment has been stubborn in confirming it.


We may also recall the opening lines of Minkowski’s famous 1908 lecture on space and time, in which all the aspects of special relativity that Bethell finds most repugnant were given their clearest and most elegant form:


The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength.


At this point we must pause to take note of the “theory” that Bethell advocates as a replacement for both special and general relativity. His erroneous prediction of a non-null result for the Michelson-Morley experiment was based on a variant of the irrotational luminiferous ether theory proposed by George Stokes in 1845. That theory was shown to be untenable by Hendrik Lorentz toward the end of the 19th century, because it could not plausibly account for either stellar aberration or the Michelson-Morley experiment, but in 1898 Planck suggested that it might be salvaged if we assume certain extreme ad hoc variations in the density of the ether. However, in addition to there being no plausible justification for the necessary density distribution, this theory implies very extreme refractive effects that are completely inconsistent with observation. So the Stokes-Planck theory was already fully examined and refuted by the end of the 19th century. (It will be recalled that Planck was among the first to recognize the merits of Einstein’s relativity.) Unfortunately, this didn’t stop an anti-relativity “dissident” named Petr Beckmann from re-surfacing the theory in the 1980’s. Beckmann claimed that his version of the Stokes-Planck luminiferous ether (although he didn’t call it that) also somehow embodies the effects of gravity, but his writings on the subject were complete nonsense, as discussed below. After Beckmann passed away, his friend Bethell took up the cause of the compressible irrotational ether as gravitational field, touting it as a simpler and more comprehensible explanation for the effects usually attributed to relativity.


Bethell says this ether is similar to a hoop-skirt that moves along with a woman as she walks, but that doesn’t spin if she performs a pirouette (assuming she has a perfectly circular and infinitely slippery waist). Likewise he says the ether responsible for the Earth’s gravity moves along with the Earth as it revolves around the Sun, but does not rotate along with the Earth – hence Bethell’s prediction of a small positive result for the Michelson-Morley experiment due to the Earth’s rotation. Unfortunately, not only is Bethell’s ether theory falsified by modern experiments as noted above, it also makes no rational sense. For one thing, if the gravitational field of each massive particle is to be represented by a surrounding materialistic ether hoop-skirt, then each of the constituent particles comprising the Earth (which exert gravitational forces on each other) must be accompanied by its own ether hoop-skirt, so such an ether would necessarily have to rotate along with the Earth. The idea that the particles shed their individual hoop-skirts and all squeeze into one giant hoop-skirt that slips freely around the aggregate is, frankly, incoherent nonsense. If we drop a hammer in the deepest mine shaft, it still falls. (Note that Michelson-Morley experiments have been conducted underground and on mountain tops, with no differences in the results.)


Of course, there is a logically self-consistent and empirically viable way of representing the effects of gravity by a (metrical) field that also serves to establish the paths of light and free material objects – it is known as general relativity – but this is precisely the theory that Bethell rejects as incomprehensible and needlessly complicated. So we must now examine his specific claims in this regard.


As mentioned above, Bethell accepts the fact that general relativity agrees with experiment (which contradicts his claims about special relativity, but never mind). His complaint against the general theory is merely that he thinks all its predictions can be matched by a theory that is much simpler and easier to understand. Unfortunately, the simpler theory he has in mind is the incoherent “hoop skirt” theory of Petr Beckmann, based on the long-ago falsified luminiferous ether theory of Stokes and Planck. In defense of Beckmann’s “theory”, Bethell again cites the authority of Einstein, who in his famous 1920 lecture entitled “Relativity and the Ether” (and in related correspondence) discussed the sense in which one could use the word “ether” to refer to the spacetime of general relativity. Of course, what Bethell fails to mention is that Einstein very carefully explained precisely why this “ether” is qualitatively dissimilar to the materialistic ethers of the 19th century – the very kind of ether that Bethell espouses. The reason Einstein’s “ether” is nothing like Bethell’s ether is that the parts of spacetime do not have persistent identities that can be tracked through time, and hence they cannot be assigned any state of motion or rest. In other words, the “ether” of spacetime must be a relativistic ether, which of course is anathema to Bethell. Einstein’s lecture makes it perfectly clear that the “ether” of spacetime in general relativity has no mechanical properties at all, i.e., none of the properties that are essential to the 19th century conception of the luminiferous ether that Bethell advocates. So, again, Bethell has misrepresented his source.


Naturally if Bethell wished to say that the ether he espouses is literally identical to the spacetime of general relativity, in the sense that Einstein described, and that Beckmann’s theory is nothing but an interpretation of Einstein’s theory (expressing the same operational theory in different words), then he would have no meaningful complaint at all, since it’s well known that general relativity has an equivalent field interpretation. In that case the only remaining question would be why Bethell wrote so many articles and a book disparaging relativity, only to admit now that he’s in full agreement with it. But of course the “field” interpretation of general relativity is mathematically identical to the usual geometrical interpretation, so this cannot be what Bethell espouses, because he insists that his hoop-skirt theory is vastly simpler and does not involve tensor calculus, etc. And of course, most of all, he insists that his ether is not relativistic. Thus his claim that Beckmann’s ether is identical to the relativistic spacetime of general relativity is both mistaken and self-contradictory.


Curiously, Bethell presents Einstein’s comments on the word “ether” as if these had just recently come to light, suggesting that they should prompt a re-appraisal of Einstein’s views. Needless to say, this is preposterous. An English edition of Einstein’s famous 1920 Leiden lecture was already published in 1922, and the earlier correspondence with Lorentz on this and other subjects has been exhaustively discussed in Einstein scholarship for nearly a century. It was even featured prominently in Pauli’s famous encyclopedia article written in 1921:


The mechanistic concept of an aether had already come to be superfluous and something of a hindrance when the elastic-solid theory of light was superseded by the electromagnetic theory of light. In the latter the aether substance had always remained a foreign element. Einstein has recently [i.e., 1920] suggested an extension of the notion of an aether. It should no longer be regarded as a substance but simply as the totality of those physical quantities which are to be associated with matter-free space. In this wider sense there does, of course, exist an aether; only one has to bear in mind that it does not possess any mechanical properties. In other words, the physical quantities of matter-free space have no space coordinates or velocities associated with them.


Bethell tells us that his scientific mentor Beckmann was not aware of any of this (in the 1980s!), which simply means that Beckmann was woefully unacquainted with the literature. But the main point is that the modern view of Einstein’s rejection of mechanical ethers (of the kind advocated by Bethell), far from being called into question by Einstein’s comments in the Lorentz correspondence and the Leiden lecture, was actually based on those comments. So Bethell’s appeal to Einstein on this point is nonsense.


Of course, regardless of Einstein’s opinions, if a materialistic medium of the kind Bethell describes could accurately account for all phenomena as well as does general relativity, it would obviously have scientific merit, so we should consider Bethell’s specific claims. Unfortunately we find (again) that he brings forth nothing new, but simply repeats several of the most common misunderstandings and false allegations that endlessly circulate within the anti-relativity community, despite having been debunked countless times.


To begin, Bethell trots out the old claim (first voiced in the 1920s in Germany) that the non-Newtonian precession of Mercury’s orbit was satisfactorily derived in a classical context (though not in the context of an ether theory) by Paul Gerber prior to the development of general relativity. That claim is well known to be false. Gerber’s writings on this subject have been thoroughly examined, both when they first appeared around 1898, and also subsequently when they were re-examined in the light of general relativity. To explain the situation, it must first be mentioned that attempting to derive Mercury’s anomalous precession by tinkering with Newton’s laws was a cottage industry among physicists around the end of the 19th century. Many physicists, some famous and some not so famous, tried their hand at it. (Incidentally, Laplace had already considered the possibility of a finite speed of gravity in 1774 as the explanation for the then anomalous precession of the Moon.) Since the amount of Mercury’s precession was known, it was a matter of reverse-engineering a theory that would yield the observed precession. The form of the lowest non-Newtonian correction to an elliptical orbit is very tightly constrained by purely dimensional considerations, regardless of the cause, so only a single numerical factor remained to be determined. It was known that a numerical factor of 3 was needed to agree with the observed precession, and this factor arises from classical potential functions of a certain form. The challenge was to provide a coherent rationale for a potential of that form.


Gerber claimed that the desired potential results from assuming a finite propagation speed for gravity (which he then computed to be the speed of light). However, it’s fairly easy to show that the desired potential actually does not follow from that premise, as every competent physicist who has ever examined the matter agrees. Gerber’s “derivation” consists of nothing but some algebraic manipulation leading to one potential function, and then summarily applying another factor that is not justified on the basis of his premises. The only motivation for this factor was that it gave what was known to be the right answer. Thus Gerber’s “derivation” was no derivation at all, it was merely self-contradictory wishful thinking. In addition, Gerber’s formula for the gravitational potential, when tuned to yield Mercury’s precession, yields an incorrect prediction for light deflection, so his formulas are experimentally falsified, as well as being unsupported by any coherent argument. As Einstein succinctly put it, Gerber’s approach was “wrong through and through”.


For good measure, we can also add that Gerber’s conceptual model was actually quite abstract and not at all mechanistic. It involved the incongruity of instantaneous “spooky” communication at a distance combined with a finite propagation speed for forces, with no underlying conceptual model, so even if it had worked (which it didn’t), it would not have been any easier than general relativity for Bethell to understand. Petr Beckmann attempted to nostrify Gerber’s formulas, claiming them for his hoop-skirt ether theory (which was completely unlike Gerber’s conception), but while Gerber’s reasoning could charitably be regarded as wishful thinking, Beckmann’s was outright dishonest. His ether theory led to a particular expression for the force of gravity that gave the wrong precession for Mercury’s orbit, so he converted his force law to a potential function, and then, seeing that his potential was different from Gerber’s, he discarded his own potential and took Gerber’s as the basis for “his” precession calculation, even though it had nothing to do with his ether. Beckmann’s writing on this subject was a total sham.


What about the deflection of light near a gravitating body? The eclipse expeditions of 1919 and the support they gave to the theory of relativity are well known. Within the “dissident” community it’s common to emphasize the difficulties and inaccuracies of eclipse observations, and to question whether the conclusion reached by Eddington and Dyson in favor of general relativity was justified. Of course, subsequent observations – of both optical and radio sources – have confirmed beyond all doubt that the predictions of relativity are correct to extraordinary levels of precision, far greater than was possible in 1919. Bethell seems to concede that Einstein’s prediction for the amount of light deflection was correct, but he claims that this same deflection is also to be expected from simple considerations of ordinary refraction in Beckmann’s hoop-skirt ether. This is false for two reasons. First, Beckmann’s account of Mercury’s precession was based on the potential function from Gerber’s theory, which was not an ether theory at all. Second, the consistent application of that potential function leads to an incorrect prediction for the deflection of light, as noted above. Despite this, Bethell assures us (on the word of his friend, the “dissident” Howard Hayden) that the deflection of light in a gravitational field can be derived in the hoop-skirt model


…with a few lines of high school algebra… and derived exactly, [whereas] the tensor calculus and Riemannian geometry of general relativity gives only an approximation.


Thus, not only is Bethell claiming that the hoop-skirt ether model gives answers as good as the answers of general relativity, he is claiming that it gives better answers. Now, the answer given by general relativity is already correct to within the limits of observational precision, so it’s unclear how anyone can claim that a different answer is exactly correct. Moreover, those “few lines of high school algebra” are not in evidence, and when the deflection of light produced by ordinary refraction in a medium of varying density is examined in detail, the results do not agree with the predictions of general relativity over the whole range of conditions that have already been empirically verified. In fact, in the same letter where Lorentz first congratulated Einstein on the eclipse results, he commented on how the deflection pattern predicted by general relativity differs appreciably from the pattern that would be produced by ordinary refraction in any remotely plausible density distribution for a material medium, so we can be sure the observed effect is really the relativistic effect. More recently, gravitational deflection of electromagnetic signals has been verified by examining radio sources over a wide range of angular positions far from the Sun, and it exhibits the precise variation predicted by general relativity. Furthermore, refraction in a materialistic ether would give rise to dispersion effects for light of different frequencies – effects which do not occur. So the materialistic refraction model does not work, and Bethell’s specious claim to be able to reproduce these results “with a few lines of high school algebra” based on ordinary refraction is simply false.


As an aside, we note that Bethell’s adherence to the refractive ether concept makes it difficult for him to exploit one of the other perennial topics from the anti-relativity literature dating back to the 1920s, namely, the 1801 calculation of Georg von Soldner. This was a Newtonian calculation based on the assumption of a corpuscular theory of light, so it wouldn’t make sense for Bethell to claim it for his ether theory. Of course, it gives only half of the deflection predicted by general relativity. (The weird claims of some of Bethell’s predecessors, such as Arvid Reuterdahl, that Soldner actually predicted the full relativistic deflection have long since been debunked.)


Another perennial misconception promoted by Bethell is the idea that the absence of low-order aberration in the direction of the force of gravity implies that gravitation must propagate almost instantaneously (billions of times faster than light), thereby contradicting special relativity. The fallacy in this reasoning was already pointed out in 1905 by Poincare, who explained that all relativistic forces, including electromagnetism, necessarily have velocity-dependent components that cancel the low-order aberration effects, even though all effects propagate at (or below) the speed of light. The absence of low-order aberration in the direction of gravitational acceleration is entirely consistent with general relativity, so Bethell’s claim is invalid. (Amusingly, Bethell’s source for this claim is a paper in which Eddington is quoted for a description of why one might think the lack of aberration implies superluminal force propagation. Bethell’s source omits the fact that Eddington’s next sentence was “But that reasoning is fallacious, because…”, followed by an explanation of the fallacy. This is just another example of how the anti-relativity community habitually misrepresents its sources.) We should also mention that Bethell’s advocacy of the idea that gravity propagates millions of times faster than light directly contradicts his advocacy of Gerber’s alleged derivation of Mercury’s precession from the premise that gravity propagates at the speed of light.


To conclude our review of the “dissident” challenges to the empirical foundations of relativity, it’s worth commenting on one rather odd characteristic to be found throughout the anti-relativity literature. We mentioned above how anti-relativity enthusiasts often focus on certain historical questions, such as whether the original Michelson-Morley experiment in 1887 was precise enough to completely rule out any ether wind, and whether the 1919 eclipse observations were precise enough to support the conclusions, and whether the clocks in the original Hafele-Keating experiment of 1971 were precise enough to give conclusive support for relativity. The same applies to many other classes of experiments, such as the original gravitational time dilation observations from solar spectroscopy, the Kaufmann ion experiments, and so on. In all cases, the anti-relativity “dissidents” try to discredit relativity by arguing that the first attempts to test various predictions of the theory were performed at the limits of achievable precision, and were therefore perhaps not conclusive. These “dissidents” completely disregard the fact that subsequent tests have fully and conclusively corroborated the theory.


The reader may have noticed a certain symmetry in the above discussion. There is a body of scientific knowledge and a contrary body of “dissident knowledge”. If one believes in subjectivism and moral relativism, one might think that both of these “schools of thought” are equally valid. However, the validity of physical theories shouldn’t be evaluated on the basis of sociological relativism. Bethell’s claims were all empirically falsified long ago, and they are also objectively incoherent and self-contradictory. In contrast, the theory of relativity has passed all empirical tests, and all of Bethell’s objections to its conceptual coherence are easily shown to rest on blatant misunderstandings and misrepresentations, as explained in the preceding discussion.


Speaking of moral relativism, in some of Bethell’s most recent writings, and in an illuminating webcast interview, he reveals something that he admits he intentionally suppressed in earlier writings (on the advice of friends to avoid damaging his credibility), namely, the fact that his underlying complaint is ideological rather than scientific: He believes the theory of relativity is allied with moral relativism, and he hopes to hasten the demise of both. He says


Relativity and relativism arose at about the same time, and the scientific claims surely bolstered the cultural applications. Now there is skepticism about both. Maybe, in time, they also will fade together.


This, of course, is a straw man. As the Stanford Encyclopedia of Philosophy observes


Moral relativism has the unusual distinction—both within philosophy and outside it—of being attributed to others, almost always as a criticism, far more often than it is explicitly professed by anyone.


But even if we accept that someone, somewhere, actually espouses moral relativism, it obviously has nothing to do with the scientific theory of relativity, despite the common root word in their names. Bethell isn’t the first person to imagine a connection between relativity and moral relativism, but the idea is utterly misguided. If Einstein’s theory had been named “The Theory of Invariants” (as Klein and Einstein proposed) or “The Theory of the Absolute World” (as Minkowski suggested), then people like Bethell, who deal on a purely verbal basis, might have found it less offensive. Admittedly the theory entails relativistic features, but the scientific concept of relativity goes back thousands of years, so Bethell is mistaken in thinking that it originated with Einstein. Euclid’s geometry, Copernicus’ heliocentric model of the solar system, and Newton’s physics are all examples of relativistic theories, and special relativity lends no more support to moral relativism than do any of those other theories. Of course, this doesn’t exonerate special relativity in the minds of some people. For example, there are self-proclaimed geocentrists even today (I’m not joking) who contend that the only conceivable system of coordinates is one in which the Earth is immobile, and that the Catholic Church was correct in condemning Galileo’s defense of Copernican theory. Like Bethell, such individuals argue that we have a moral imperative to reject the notion that physical laws can take the same form in terms of relatively moving systems of reference.


Needless to say (or so one would have thought), the denial of plain and indisputable facts of everyday experience is a poor foundation on which to base our spiritual beliefs. The fact that Cleveland may be to the south of Mr. Smith and to the north of Mr. Jones is neither self-contradictory nor does it imply that “truth is subjective”. It merely means that some attributes of the world are inherently relational. Our spiritual beliefs and moral compasses shouldn’t be so fragile that they can’t withstand an awareness of simple spatio-temporal relations, such as the fact that inertial coordinate systems are related by Lorentz transformations.


Bethell mentions that Cardinal Joseph Ratzinger (later Pope Benedict XVI) has expressed his abhorrence of “relativism”. Not surprisingly, Cardinal Ratzinger has also spoken on the subject of Galileo and the Copernican model of the solar system. In 1990 he gave a speech in which he cited the philosopher Paul Feyerabend for the belief that


The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo's teaching too. Her verdict against Galileo was rational and just, and the revision of this verdict can be justified only on the grounds of what is politically opportune.


The Cardinal indicated that, considering the “deep self-doubt of the modern age, of science and technology… it would be foolish to construct an impulsive apologetic [regarding the Church’s condemnation of Galileo’s teachings]…" Nevertheless, in 1992, Pope John Paul II publicly expressed regret for how the Church had handled the Galileo affair, and on the basis of a study conducted by the Pontifical Council for Culture he acknowledged that errors had been committed by the Church tribunal that had judged Galileo. In 2008 (the 400th anniversary of Galileo’s first astronomical observations) the Church actually proposed placing a statue of Galileo inside the Vatican, and Pope Benedict XVI praised Galileo’s contributions to astronomy. Now, if Bethell wants to argue that Galileo’s belief in the relativity of motion was wrong and/or morally subversive, he is obviously free to do so, but he shouldn’t suggest that he is expressing the views of the Catholic Church, and he should get his facts straight about when the principle of relativity arose:  2400 years ago for Euclidean geometry, and 400 years ago for Galilean dynamics.


As noted above, Bethell admits that he sometimes intentionally concealed his true motivations to avoid damaging his own credibility, and this seems to be another example of the same strategy: His real argument is with the relativity of Copernicus and Galileo, which he may associate with the religious schism that arose at about the same time (Copernicus and Martin Luther were contemporaries), but he hopes to disguise this and make his position appear less embarrassing by expressing his complaints in the arcane context of special and general relativity (theories which he utterly misunderstands), as if this were a new topic that arose in the 20th century.


Bethell’s antagonism toward the theory of relativity also contains a strong anti-elitist component. He complains about what he sees as the intentional obscurantism of members of the “scientific priesthood”, who seek to defend their unjustified position and prestige by suppressing any efforts to expose the obvious failures and fallacies (as he sees it) of the theory. This kind of sentiment is perhaps understandable in someone who has found himself unable to grasp something. During the webcast mentioned above, Bethell commented on how, after reading all the “Easy Einstein” books, he was never able to understand the subject. One imagines it was a relief to his ego to discover the community of “dissidents” claiming that the subject simply doesn’t make sense, and that failure to understand such nonsense actually signifies superior intelligence. (As Emerson once wrote, “If I cannot brag of knowing something, then I brag of not knowing it.”) The description of his book on Amazon begins


Questioning Einstein… is a serious scholarly work … absorbing the reader in a tale of long-neglected experimental results that plays out to a deep satisfaction in finally answering the question, "Why can't I understand relativity?"


The deeply satisfying answer offered by Bethell is, of course, that you can’t understand relativity because it is not understandable. In place of the actual theory of relativity, Bethell provides a substitute “recasting”, devoid of scientific content, consisting of hoop skirts, misinformation, and complete disregard for both conceptual coherence and quantitative empirical evidence. He reassures his readers that they needn’t trouble themselves to actually understand the subtleties of modern physics, because the egghead professors are just perpetrating a gigantic conspiracy designed to bewilder and mislead the common man in an insidious campaign to promote moral relativism.


On one point it’s possible to have some sympathy for Bethell, because it’s undeniably true that special relativity is often badly taught, especially in the “Easy Einstein” books to which Bethell so often alludes, and which he admits he could never understand. His misreading of these popularizations is evident in many of his erroneous statements. Moreover, he had the misfortune of coming under the influence of Petr Beckmann, who evidently imbued Bethell with all the well-known anti-relativity misconceptions dating back to the 1920s. But this can’t excuse his spreading of so much misinformation and misunderstanding for so many years. Surely Bethell’s misconceptions have been explained to him many times by now, and he has had ample opportunity to avail himself of the serious scientific literature and actually learn the subject – which, after all, is not so difficult.


I’m reminded of another book, remarkably similar to Bethell’s, entitled “Challenging Einstein’s Relativity”, by someone named John Doan.  After outlining his book’s challenge to relativity (which is intellectually on a par with Bethell’s), Mr. Doan concludes his prospectus with the stirring words


Surely that sounds absolutely nonsense. But wait until you read my book. I might convince you better and make you understand clearer what has been written for years in many scientific books by famous professors about things you know they can never make you understand.


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