Herbert Dingle: ‘Science at a Crossroads’, a critique of Special Theory of Relativity (STR) and its clocks, never answered

It is false that anyone has 'disproved' Dingle's complaint against STR, which if correct, invalidates STR and its theoretical predictions

Previous posts on STR

An overview of Special Theory of Relativity (STR)

An introduction to the underlying maths of STR

Key scientists and actors within the STR domain

James Webb Telescope observations which refute parts of STR and the Big Bang

Dingle proposed a ‘paradox’ within STR’s mathematics and formulae which rendered the theory invalid.  He focused on the heart of the theory, namely, clocks and time interval calculations.  Contrary to mainstream science and its cheerleaders, it has not been satisfactorily dealt with nor repudiated.  In essence it means that much of cosmology and arcane mathematics supporting various theories, is simply wrong. STR is a classic case study of Scientism.

Who was Herbert Dingle

Herbert Dingle (1890–1978) was an English physicist and philosopher of science, who served as president of the Royal Astronomical Society from 1951 to 1953.  Dingle became a professor of Natural Philosophy at Imperial College in 1938 and was a professor of History and Philosophy of Science at University College London from 1946 until his retirement in 1955. Thereafter, he held the customary title of Professor Emeritus from that institution.  He was one of the founders of the British Society for the History of Science and served as its President from 1955 to 1957.  He founded what later became the British Society for the Philosophy of Science as well as its journal, the British Journal for The Philosophy of Science. 

In summary, Herbert Dingle was eminently qualified to criticise anything related to physics. 

In fact, Dingle was one of the most profound experts on STR – ever.  He devoted some 50 years of his life to STR.  His 1940 textbook, when he was still a believer, entitled ‘Special Theory of Relativity’ went into many prints and was used throughout the world in university and school systems.  He spent his entire career teaching, writing, advocating, and defending the STR for much of that time. 

We can ‘safely and effectively’ presume that Professor Dingle was far from an ‘anti-science denier’.

Starting in the 1940s much to his chagrin and disappointment, Dingle noticed and comprehended that the arcane, abstract, obtuse maths of Einstein simply hid functional, and practical flaws.  In essence, Einstein, who had largely copied much of his theory from Lorentz, never proved the elemental theme of STR that 2 bodies in motion, would possess two clocks moving at different speeds.  This was the main issue for Dingle.  Dingle’s apostasy occurred probably in the early 1950s, and after 20 years of confronting the immovable ‘scientific’ establishment he finally penned his Science at the Crossroads’ in 1972, in which he outlines his main complaint and summarises the ‘debates’ with others, and their largely ad-hominem based attacks (in lieu of scientific proof).

Dingle’s Crossroads

Herbert Dingle’s book is technically and scientifically premised but it is not that difficult to get through.  He believed that ‘science’ was at a crossroads where it had to choose between two different directions and paths forward, hence the title.  One was a return to real world physical proof and experimentation to prove or disprove hypotheses.  The second path was to substitute fact and objective physical evidence, which can be replicated, with theory and mathematics. 

STR was clearly striking out on the second path.  This route easily leads to fraud, manipulation, and the creation of a system of control and totalitarianism, in which the theory and the people supporting it, assume both expertise and power.  Scientism leads to the creation of a Scientocracy which assumes the management of society.  We experienced this during the 3 years of the recent Corona totalitarianism.  C.S. Lewis in his writings during the 1930s and 40s (Abolition of Man, That Hideous Strength amongst others) also outlined the totalitarian imperative and dangers of Scientism.  Dingle was far from alone in his obloquy of Scientism. 

The 2 STR’s mixed up and confused

Dingle correctly believed that the two STR theorems of Lorentz and Einstein, though similar were different in their implications, had been conflated and merged.  This led to confusion and a lack of testability. 

“I take the earliest of all the supposed experimental verifications of special relativity — that which is described as the increase of mass of a body with velocity — not only because it is perhaps the simplest example of what is at best an extremely complex matter, but also because it serves the additional purpose of exemplifying, quite indubitably, the general oversight of the fact that all the supposed experimental verifications of special relativity can with exactly the same justification be advanced as verifications of Lorentz’s earlier and quite different theory.”

As Dingle elaborated, a key issue with the Maxwell-Lorentz theory is that it rests on a very limited experimental basis, particularly regarding velocities.  Velocities approaching that of light are only inferred from theoretical equations based on speeds far less than the speed of light (Lorentz entitled his paper, ‘Electromagnetic Phenomena in a System moving with any Velocity less than that of Light’).  This lack of real proof is very curious, yet simply accepted by those who support STR.

Dingle also identified that though the mathematics are similar there are some profound differences in the implications of what they propose.  They should not be conflated.  An example of this confusion is Dingle’s observation that Einstein “who had no qualms about abolishing the ether and still retaining light waves whose properties were expressed by formulae that were meaningless without it proposed to eliminate the ether and to maintain equally c as absolute constant, the idea found a favourable ground because what was perceived as the primary purpose was to preserve Maxwell’s equations, not the corresponding physical theory.”  In other words, the maths from 2 rather different STR theories are comingled to prove each other’s validity. 

Dingle wrote that many variances exist between the 2 STR’s including:

Clocks and Rods

• Lorentz ascribes the slowing down of clocks and the contraction of rods to an ad hoc physical effect of the ether on moving bodies;

• Einstein ascribes them to an ad hoc modification of kinematics at high velocities and ignores the ether

Ether

• Lorentz’s theory is impossible without an ether;

• Einstein’s (because of its relativity postulate) is impossible with one

Velocity

• Lorentz specifically restricted his theory to ‘a system moving with any velocity less than that of light’, and, from the nature of its effects, it must break down well short of that velocity;

• Einstein’s theory makes a velocity greater than c logically impossible, meaning that the macro-differences in velocities and outcomes as objects approach the speed of light is massive

Space, Time

• Lorentz’s leaves them independent, and separate with time outside of spatial reality (it is indeed a human construct);

• Einstein’s theory merges space and time into an unimaginable ‘space-time’ dimensions that has not, and cannot be proven

Supporters of STR routinely use Lorentz’s STR to justify that of Einstein, yet as given above this is completely incorrect and fraudulent.  It is because of this confusion that the ‘experimenters’ as Dingle calls them, or those who produce proofs in physical reality, have left relativity to the ‘mathematicians’.  They gave up.

Dingle’s Clock Paradox

Dingle zeroed on the crux of Einstein’s STR theory which is centred on clock-readings.  Dingle believed, quite rightly, that the speed of the Earth is the speed of the standard clock (for the standard clock of physics must be stationary on the Earth).  Therefore, we must know the speed of the Earth through the medium in which light waves travel (which is the ether, according to the Maxwell-Lorentz theory), or the speed of light in lieu of an ether as proposed by Einstein (a previous post lists issues with the supposed disproofs of an ether). 

From Dingle’s book, ‘Science at the Crossroads’ (1972), the use case issue around clocks is made clear. 

“The argument is extremely simple and fully understandable without specialised knowledge. To compare the rates of two regularly running clocks, A and B, we must find the interval recorded by one for a given interval by the other. It is immaterial which is taken as the standard: if A records 2 hrs for an interval of 1 hr by B, then A works twice as fast as B, and B must record 1/2 hr for an interval of 1 hr by A. If the clocks are in relative motion, however, they cannot be together throughout the interval, so if we remain with B to observe its readings, we can determine those of A only by means of a theory.

The special relativity theory purports to serve this purpose, and Einstein so used it, thereby calculating that (for a particular velocity of separation) A would record 2 hrs while B was observed to record 1 hr. He concluded that A worked twice as fast as B, and this result is universally accepted as the unique solution of the problem. He did not calculate the interval by B for an observed interval of 1 hr by A, but when we do so, by the same theory, we find it to be not 1/2 hr but 2 hrs, showing that B works twice as fast as A. The same theory thus requires each clock to work twice as fast as the other, which is contradictory. The necessary conclusion is that that theory must be wrong.”

The above example from Dingle is dead simple to understand. 

If I have 2 objects with 2 ‘clocks’, one at the North Pole and one at the Equator, and if they are static or not moving, I can measure the interval of time between the objects to be the same or nearly the same (some small differences would exist).  If I move them say in opposite directions at different speeds, and I choose the North Pole object as my ‘relative’ point of observation, and then calculate the interval against the clock of the object at the Equator, I will get a relative difference.  I must now do the same in the opposite direction to prove my theory.  This has never been done.

As Dingle wrote, “The criticism of Einstein’s theory made here is that his assumption is, after all, not self-consistent because it requires each of two clocks to work steadily faster than the other, which is clearly impossible. The way is now clear for a description of Einstein’s theory and an account of the circumstances that have led to the remarkable oversight of what is, in fact, a very simple defect.”

No one has refuted the observation that in STRs the two clocks must work faster than the other.  It is also clear that in Einstein’s though experiments the two clocks must also work slower than each other as well. Dingle, “…the experimental test is unnecessary because the theory itself makes the ‘stationary’ and ‘moving’ clocks interchangeable by pure thought, and so requires the impossibility that each clock works more slowly than the other. It appears astonishing that Einstein could have overlooked so simple a fact, until one realizes the mastery which mathematics had acquired over the intelligence.”

Dingle’s proofs

Dingle provided mathematical equations and explanations which were ignored by his critics and those defending the STR.  These equations are:

The key steps are as follows:

(A)     Dingle calculates the clock dial readings for the time interval between events E₀ and E₁ based upon Einstein’s solution to the Lorentz transformation equations from his 1905 paper as: t₁’ =bt₁, which he calls equation (1).

(B)      Dingle calculates the clock dial readings for the time interval between events E₁ and E₂, based upon the traditional assertion of the symmetry of Einstein’s solutions from his 1907 paper as: t₂=b^-1t₂’, which he calls equation (2).

(C)     Based on equation (1) he defines the ratio of dial readings as: t₁’ / t₁ =b (equation 3)

(D)   And based on equation (2) he defines the ratio of dial readings as: t₂ / t₂’=b¹ (equation 4)

(E) Noting that the results of steps (C ) and (D) are contradictory, Dingle concludes that the “theory from which they are derived must be invalid.”

The core of Dingle’s proof is the solution to the Lorentz transformation equations for the time intervals between three events which he defines as E0, E1, and E2.  Dingle defines the times of these events in two different ways.  The time interval between events E0 and E1 in coordinate system k, is defined in terms of time in coordinate system K using Einstein’s 1905 Lorentz transformation solution, resulting in Dingle‘s equation 3 above.  

The time interval between events E1 and E2 in coordinate system K, is defined in terms of time in coordinate k, using the reciprocal solution for the Lorentz transformation specified by Einstein in his 1907 paper on relativity, resulting in Dingle‘s equation 4.  Dingle shows that the two different solutions given by his equations 3 and 4, result in a contradiction. It is clear that all that is required to refute Dingle’s claim is to show that his solution to the problem given in his equations 3 and 4 is incorrect.  No one did this.

Valid equations

Dingle’s equations are valid mathematical expressions within the framework of the Lorentz transformation, the basis of Einstein’s STR, but their interpretation is rarely debated.  Dingle interpreted them to imply a paradox because, in his view, each clock appears to run slower than the other.

For example, using these equations there is an issue with Einstein’s observer and the relative nature of clock differences.  As Dingle concludes, this observer has no place at all if Einstein’s clocks are synchronised absolutely, for all observers and all co-ordinate systems.  The situation for Dingle based on his equations is quite clear.  If Einstein’s theory is valid the following questions arise.

How is it possible for the ratio of the intervals recorded by two identically constructed, regularly running, clocks, between the same pair of events, to vary with the events chosen?

How can the ratio of two constant quantities be variable?

Why must the events that alone give the ‘correct’ ratio be chosen from the set occurring on one and not the other of the clocks?

If they must be so chosen, how does one discover on which clock the valid set of events occurs?

The issues with STR reside with the clocks and the interpretations of variables and events by an observer and that observer’s position which will generate different results.  This contravenes the entire premise of relativity and its purpose, namely, to prove the law of inertia and velocity of light as relativistic measurements between a static and moving object, or 2 moving objects. 

Dingle’s paradox

Dingle’s paradox is obvious when two apparently contradictory conclusions, X and Y, follow from a premise P.  If the premise P contains an internal contradiction, it means that X and Y follow from incompatible parts of the premise and are obviously invalidated. 

For example, STR cannot provide an indication of which clock is slower.  The obvious question is - how is the slower-running clock distinguished?  As Dingle proved, either clock records the lesser time interval, depending on where the observer is situated, which is a contradiction.  In response to this complaint, it has been claimed that STR theory only requires each clock to appear to move more slowly from the point of view of the other, but not actually do so in reality.  This is specious and is ruled out by the theory’s applications, by the fact that the theory would then be useless in practice, and by Einstein’s own examples.  

Einstein’s STR is a theory which took no account of gravitation, acceleration, or any difference at all between the clocks except their relative motion.  He wrote that “We conclude that the balance clock at the equator must move more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.”  Dingle asks: “What entitled Einstein to conclude from his theory that the equatorial and not the polar clock, worked more slowly?”  No answer to that question from STR apologists was provided.

Dingle states it was almost inevitable that the clock paradox should arise from Einstein’s 1905 paper, which described Special Relativity as follows:

“If at the points A and B of the [coordinate system] K there are stationary clocks which, viewed in the stationary system are synchronous; and if the clock A is moved with velocity V along the line AB to B, then on its arrival at B, the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which remained at B by ½tv²c², t′ being the time occupied in the journey from A to B.”

The stationary clock reading is denoted by t, v is the velocity of the body and c is the speed of light. That is to say, the time recorded on the clock moved from A to B is 50% less than the clock at B.  Einstein chose ‘Y’ as the correct solution, but he did not disprove X and this disproof of X, as Dingle repeatedly stated, was never attempted because Einstein and others knew it would undermine the entire theory. 

Immutable ‘Laws’

Few scientists engaged in this debate with Dingle.  STR was just accepted as a ‘law’.  An entire industry replete with experts, publications, books, tenure, titles, accolades, awards, money, grants and expensive toys at rich institutes had been developed.  Who was going to risk that?  Also, as Dingle knew, most ‘scientists’ did not understand STR, or its maths.  Most did not understand Dingle’s clock objections nor his maths. 

Sir William McCrea’s fraudulent rebuttal

Born in Ireland, McCrea (1904-1999) was a well-known mathematician and astronomer.  He gained renown from his work outlining theories of the Sun’s composition, rising to become president of the Royal Astronomical Society from 1961 to 1963 and president of Section A of the British Association for the Advancement of Science from 1965 to 1966.  He was knighted by Queen Elizabeth II in 1985.  He won the Gold Medal of the Royal Astronomical Society in 1976 for his lifetime of efforts in astronomy.  McCrea was a stalwart defender of STR though it is clear that he did not really understand it.  McCrea’s idea of STR is very different than that of Einstein’s.  Dingle’s objection is to Einstein’s STR, not McCrea’s interpretation of it.  McCrea’s objections fall into 4 areas simplified below.

1.  Dingle’s math is wrong;

   • McCrea never shows where or why

2. Relativity does not assume a 1:1 correspondence between 2 clocks;

   • He is right on this point, given that in STR there is time dilation between 2 clocks, but this is not Dingle’s argument anyway and is a misdirection

3. Einstein’s formulae do not inform us about the rates of the clocks;

   • He is wrong on this point, and this is a fundamental mistake.  STR does provide specific formulas which explicitly detail the rates of clocks in different reference frames, an example is above, namely, time-dilation. 

4. Dingle misunderstood symbols with the mathematics of STR leading to incorrect assertions;

   • McCrae is the one who does not understand STR’s maths, #3 above is an example, more given below

Dingle’s deals with McCrea at length in his book and has a rather low opinion of McCrea’s rejoinders and lack of either mathematical or physical proofs.  The ‘debates’ were published in ‘Nature’ magazine October 14, 1967, and were intended to put the whole issue to a rest.  Needless to say, Nature and ‘the science’ claimed that McCrea decisively defeated Dingle.  There is no evidence for that.

McCrea’s failure

In fact, McCrea failed to demonstrate that Dingle was wrong.  He, not Dingle, lost.  The basis of McCrea’s assertion is that he specifically denies that the Lorentz transformation equations can be used to define simultaneous events in the relatively moving reference frames.  This is incorrect.  Dingle correctly asserted that this is the key function of the Lorentz transform equations and that without the claim that they do transform events in a way that transforms simultaneity, then the theory is falsified.  Either McCrea did not read or understand Dingle’s proofs, or he lied about the core of Dingle’s claim. 

An example of obfuscation (to be diplomatic) is that McCrea’s argument established a restrictive model which required the moving B clock to only record an event, when it passes next to a clock at rest.  When the A clock passes clocks at rest in the unprimed frame, McCrea claims that there is a different event involved so that the symbols t and t’ used in the equations can be assigned different meanings in the two different events, so that the claim of contradiction can be invalidated.  This is sheer sophistry and is incorrect. This is not what STR predicts and this is not what the maths state.  There is much else that is wrong with McCrea’s thesis but the above is enough to destroy it. 

So, unfortunately for McCrea, his argument is invalid. There is indeed a deficiency in the theory as Dingle asserted. 

Scientism and sources

The attack on Dingle, evidenced by McCrea, devolved as one would expect to largely slander and ridicule.  As Dingle offered, the paradox is a simple question, if he is wrong, surely it takes only a simple answer to refute the allegation that the STR is incorrect.  If I dispute that 2+2 = 4 and that like O’Brien in 1984, I demand it is 5, you don’t need to issue abstruse objections to my criticism as given above.  You simply, clearly and logically prove that 2+2 =4.  That is all Dingle is asking. 

McCrea is always referred to by other critics as the source of Dingle’s disproof.  So even if 20 get involved and criticise Dingle, the foundation of their complaint is McCrea’s fallacious analysis.  This is common in Scientism.  When you trace back the ‘source’ of a ‘proof’ invariably you collide into one person, one experiment or one key ‘study’.  Thus, we have one mathematician-astronomer arrayed against what is likely history’s foremost authority of STR. 

Clock conclusion

In reading the correspondence between Dingle and STR’s defenders, including published material in various journals and in looking at Dingle’s examples and equations, it is obvious that not a single proponent of STR dealt with either the mathematics of Dingle, nor the details and flows of his clock paradox.  In other words, they ignored the substance of the complaint and tried (and failed) to use more maths to prove STR’s maths.  This is not scientific.

Dingle is undoubtedly correct when he asserts that if this criticism of STR had been made in 1906, it would at once have been seen to be fatal and Einstein would have been the first to acknowledge that it was dead:

(Dingle) Suppose the relative velocity is 161,000 miles a second. Then, according to the theory, the time according to one clock (A, say) between the readings 1.0 and 2.0 o’clock of B is 2 hrs., so that A works twice as fast as B. This is a particular case of a general result obtained by Einstein in 1905 and universally accepted. But, similarly, the theory requires that the time according to B between the readings 1.0 and 2.0 o’clock of A is 2 hrs., so that B works twice as fast as A. (Einstein did not consider this case). These results are clearly contradictory.

This objection still stands today.  In fact, there might be 3 clocks in play which further degrades STR.

Bottom Line

Dingle’s paradox, notwithstanding ChatGPT answers, textbooks, documentaries, and mainstream science articles has not been answered.  It is a major issue with STR.  There are however many other problems with STR (previous posts have illumined some, and the next post will summarise them) that only add to the problems with the theory.  

As Einstein purportedly stated, maybe 12 people on the entire planet understood the maths of STR and one of them was Dingle.  This is an obvious issue.  Scientism or the cult of science, which is aligned with power and money, usually relies on a small, controlled group of ‘experts’ and ‘scientists’ to push the dogma and assertions or laws.  They hide behind impenetrable screens of maths, manufactured data, models, and word-salads which confuse and misdirect.  The Climate change nonsense and Corona plandemic are two obvious examples of this implementation pattern.  STR whilst not a purposely fraudulent exercise, is certainly an elaborate and abstract theory with little objective proof and physical reality.