relativity: Either of two theories developed by Albert Einstein, the special theory of relativity, which requires that the laws of physics shall be the same as seen by any two different observers in uniform relative motion, and the general theory of relativity, which considers observers with relative acceleration and leads to a theory of gravitation. (Collins Concise English Dictionary)
Professor H. Dingle, in his book Science at the Crossroads, was much concerned with highlighting the anomalies in Einstein’s theory of Special Relativity. He chronicles his arguments with the scientific establishment and his growing disquiet with the way in which his views were ignored once he had drawn attention to problems in Relativity theory and become a heretic. Actually, Dingle was as much concerned with the attitude of leading physicists and scientific journals to scientific dissidents but here I shall concentrate on Dingle’s criticisms of Relativity Theory.
The great majority of physical scientists, including practically all who conduct experiments in physics and are known to the world as scientific leaders confess, when faced with an irreconcilable criticism of Special Relativity, that they regard it as nonsense. They accept the theory because a few mathematical specialists in the subject say they should do so, or because they do not understand it at all but accept the theory as established by others and therefore a safe framework for their experiments. The response of specialists in this field is either complete silence or a variety of evasions couched in mystical language which serve to convince others that the theory is too abstruse for them to understand and that they may safely trust men with the mathematical talent to write confidently in profound terms.
Dingle outlines four basic misunderstandings which account for Special Relativity being accepted for so long despite its untenability. First, and most seriously, is the false conception of the relationship between mathematics and physics.
Galileo and Newton took observations as their starting point and used mathematics only as a tool to extract the maximum amount of information from their experiments, and as a means for expressing their new-found knowledge. The first example of the mastery instead of the servitude of mathematics in relation to physics came with Maxwell’s theory of the electromagnetic field. Maxwell showed that in electromagnetism, Ampere’s Law, expressed mathematically, did not satisfy the equation of continuity, but could be made to do so by a purely mathematical modification, which he assumed was the actual physical law. Since he knew of no physical relation which was represented by his equation he made the assumption that “displacement current existed in the dielectric, but which, unlike a conductor, could not carry electricity.”
Faraday’s ‘Thoughts on Ray Vibrations’ (Philosophical Magazine, May 1846) illustrates that he planned to ‘dismiss the ether’ which was the basis of Maxwell’s theory and endow each elementary light source with a system of rays extending indefinitely in all directions, the vibrations on the rays constituting light.
Einstein’s Special Relativity, designed to conform to Maxwell’s equations, could only do so by sacrificing the concept of the ether which was the basis of Maxwell’s theory. Had Einstein first sought to bring Maxwell’s equations into conformity with Faraday’s, which amounted to a separate ‘ether’ for each atom instead of a single universal ether, he might have produced a theory which was not subject to flaws. Mathematical theories have become increasingly abstract, to the extent that multi-dimensional universes have been accepted as reality by some experimental physicists with no physical evidence of their existence. Why do mathematicians, whose formulae belong to the realm of pure thought, tell physicists to believe such absurdities and why do physicists believe them?
The second consideration derives from the multiplicity of meanings associated with the word time. Einstein’s Special Relativity theory expounded in his 1905 paper has nothing to do with time in the sense of eternity; it is concerned with instants and durations (i.e. events and distances). Dingle states that the chief factor in creating the illusion that Relativity is unintelligible, or at least very difficult, is that it has something to say about the nature of time. Minkowski later introduced ‘eternity’ into his theory. Once the distinction between different forms of time is recognized, nearly all the literature on the subject of Relativity is seen to be in utter confusion. Writers such as Eddington in The Material Theory of Relativity (Cambridge University Press, 1930) for example, seem quite oblivious that time has different meanings and unconsciously oscillate between them.
The third of the most prominent sources of confusion that have led to the widespread illusion concerning Special Relativity is the substitution of observers for coordinate systems. In the literature on Relativity there is almost invariably a great deal about what different observers, in different states of motion, will observe. The impression is given that this is an essential feature of the theory. Writers have been prone to elevate the observer from a convenient accessory in explaining the theory’s essentials to part of its essence. This distortion has misled not only general readers but many specialists as well. In Einstein’s example of the station and the train, it can just as easily be supposed that the observer on the train is at rest while the observer on the platform is in motion.
All phenomena generally associated with Relativity – relative contraction of rods and distances when approaching light-speed, relative slowing down of clocks etc. – are not matters of observation, but are wholly concerned with coordinate systems. In Einstein’s paper the ‘observer’ is not mentioned after the first two short sections right up to the end of the description. The picturesque image of the station and the train was used to introduce concepts which were at variance with those which had formerly been taken for granted.
The last of the errors permeating Relativity literature and the most effective in persuading experimental physicists that the theory must be right, notwithstanding their inability to make sense of it, is the literal interpretation of metaphors. This is best illustrated by the earliest of the supposed experimental verifications of Relativity – the increase in mass with velocity. It is the simplest example in an extremely complex matter, and in fact all supposed experimental verifications of Relativity can, with exactly the same justification, be used to verify Hendrik Antoon Lorentz’s earlier and different theory. The compatibility of the mass/velocity relation with Lorentz’s theory was pointed out by Lorentz himself, and shown to agree with observations already made before Einstein introduced his theory.
Dingle stresses that when we speak of the mass of an electron we cannot put the electron on a balance like a lump of lead and compare it with weights in the other pan. By the end of the nineteenth century electrons had been shown to be negative electricity with measurable properties, but thirty years later they were found to possess wave-like characteristics. The idea then arose that they were some sort of mist of electricity. Eddington probably gave the most candid description: “Something unknown doing we know not what.” The velocity of the electron in the electron verification procedure resembles, for example, a car in motion no more than an electron resembles a lump of lead.
Einstein developed his theory to conform to the Maxwell-Lorentz electromagnetic theory, which he regarded as fact. Einstein’s critique indicates that he believed the defect in Newton’s system was that he had assumed, on inadequate grounds, that the time by the clock of a remote event had a unique value, but neglected to say how that value could be determined. Newton’s kinematics assumed that the value at a distant event was the same as that shown by a terrestrial clock. Lorentz was the first to challenge this assumption, postulating that the motion of the clock through the ether changed its rate; but Einstein, discarding the ether, fell back on an assumption that the distant event had a unique instance of occurrence. Einstein claimed the right to determine such an instant in a form that conformed to existing electromagnetic theory without violating relativity of motion. It was a stroke of genius, but Einstein had not disproved Newton: Einstein’s theory is not consistent because it requires each of two clocks to work steadily faster than the other, which is clearly impossible.
Before the end of the First World War Einstein’s theory stood outside the mainstream. The conflict between Newtonian mechanics and Maxwell-Lorentz’s electromagnetism was best illustrated by the Michelson-Morley experiment which split a beam of light into two parts which were sent, by means of mirrors, to and fro along two equal and perpendicular arms – one of which is aligned with the direction of movement of the Earth’s orbit and one at right angles to the orbit. On returning to their starting point the light produced a pattern of dark and bright fringes. The fringes remained in the same position throughout the year both when the arm aligned with the Earth’s orbit remained in its original position or, contrary to expectations, when the arm aligned in direction of movement was moved to a position at right angles to the orbit and the other arm was brought into alignment, i.e. when the position of the arms was reversed. This is contrary to the Maxwell-Lorentz theory, in which the velocity of light is independent of the motion of its source.
There are three possibilities: that the Maxwell-Lorentz theory is wrong; that Newtonian mechanics is wrong; or that there is some unknown effect of motion which has been overlooked. The first possibility has been ignored by everyone except Ritz. Einstein, as stated earlier, adopted possibility two, which, though not primarily for the purpose of explaining the experiment, was used for this purpose. The third possibility – that there is some neglected law of motion – was adopted by Fitzgerald, who proposed that a change occurred in the dimensions of bodies caused by their motion through the ether; for example, if the length of one of the arms in the light experiment changed, a shift in interference patterns would be expected.
Independently of this, in 1904 Lorentz proposed a much more comprehensive theory which, if valid, not only explained the null effect of the Michelson-Morley experiment but provided a supplement to Maxwell’s theory. It implied that any experiment with material systems, carried out on bodies moving uniformly with respect to each other, would give exactly the same result; so that it would be impossible to tell, from an experiment confined to a body, whether the body was at rest or moving uniformly through the ether. Lorentz proposed that the movement of a material body through the ether produced a contraction in the direction of motion and a slowing down of all rhythmical processes by a factor of:
ß = (1 − v²c²)^{½}
ß (alternatively µ) is used to denote the relative velocity coefficient between the two coordinate systems, where v is the velocity of a body and c the speed of light. Conventionally,
where L and L’ are the length of fixed and moving measuring rods in the two coordinate systems referred to below. Lorentz showed that if these physical effects were a reality the relationship between the coordinates (x,t) of an event referred to one coordinate system, and the coordinates (x,′t′) of the same event in a second coordinate system moving uniformly in the x direction relative to the first is given in terms of relative motion by:
x′ | = | x − vt |
(1 − v²c²)^{½} |
t′ | = | t − vx/c² |
(1 − v²/c²)^{½} |
These expressions became known as the Lorentz Transformations, and are as important in mathematical terms as Maxwell-Lorentz’s electromagnetic theory is invariant to them; i.e. the Maxwell-Lorentz function remains unchanged when the Lorentz Transformation is applied. If, for x and t in these equations, we substitute the values given in the Lorentz Transformation, we obtain identical equations with x′ and t′ taking the place of x and t and with v changing to -v. This guaranteed that all measurements made on the two bodies, in uniform relative motion with velocity v or -v, when interpreted in terms of the theory, would be related in the same way so that no physical observations confined to one body could distinguish the motion of one body from the other. It would still be possible, by comparing observations on the two bodies, to detect their relative motion. This proposal became known as Lorentz’s Relativity Theory.
Lorentz entitled his paper ‘Michelson’s Interference Experiment: Electromagnetic phenomena in a system moving with any velocity less than that of light’ implying that, unlike the later theory of Einstein, his proposal did not prohibit velocities greater than the speed of light. Like Maxwell, Lorentz, in order to justify his transformation equations, postulated a physical effect of interaction between moving matter and ether. Einstein had no qualms about abolishing the ether and still retaining light waves whose properties were expressed by formulae meaningless without it; he was the first to discard verifiable physical laws altogether and propose a wholly mathematical theory. A more recent example of such a scheme was that proposed by Hugh Everett, who used Heisenberg’s Uncertainty Principle of 1927 to argue that with every laboratory experiment, and also with every decision a person makes, the universe splits into additional universes.
Dingle argues that the basic principles of the theory are extremely simple. If you have two exactly similar and regular running clocks, A and B, in uniform regular motion (i.e. one is moving uniformly with respect to the other), the clocks must work at different rates. In mathematical terms dt and dt′ are the intervals, which are unequal, which the clocks record between the same events. dt and dt′ are related by the Lorentz Transformations. Hence one clock must work at a slower rate than the other.
The theory, however, provides no indication of which clock is slower and the question then arises: How is the slower-running clock distinguished? Either clock records the lesser time interval, depending on where the observer is situated, which is a contradiction. In response to Dingle’s argument it has been claimed that the theory merely 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 argument is ruled out by the theory’s many applications (detailed in Part 3), by the fact that the theory would then be useless in practice, and by Einstein’s own examples. After presenting a theory which took no account of gravitation, acceleration or any difference at all between the clocks except their relative motion, Einstein 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?”
A paradox arises when two apparently contradictory conclusions, X and Y, follow from a premise P. It can be resolved if one of four instances can be shown, as follows: firstly, the conclusions are not, in fact, contradictory; secondly, the conclusion X does not follow; thirdly, the conclusion Y does not follow; fourthly, the premise P contains an internal contradiction so that X and Y follow from incompatible parts of the premise.
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. As both clocks are in relative motion clock B could equally be held to have lagged behind clock A. Nearly everyone accepts Y as the correct solution on diverse grounds ranging from the Doppler Effect, observation by external observers in various circumstances, the influence of the rest of the universe and electromagnetic considerations.
The argument to justify ignoring X utilizes the fact that if the clock moved from A to B returns to its starting point, it must undergo an acceleration, which removes the problem from the scope of the theory, because acceleration is only considered in General Relativity. However Y, like X, is drawn from Special Relativity so that if X is nullified, then so is Y. Secondly, Einstein’s writings of this period indicate that he did not consider that acceleration affected the clock readings. Thirdly, the conclusion X is drawn from the postulate of Relativity alone, without the postulate of constant light velocity, and in his General Theory Einstein generalized the former postulate to cover both accelerated and uniform motion, so that if we accept the generalization, the acceleration cannot invalidate X.
Dingle was extremely concerned that the error in Relativity Theory would eventually lead to a major disaster. Twenty-six years after his book was published there is no sign that the scientific establishment has taken note of Dingle’s critique and its implications for theoretical physics and nuclear research.
See further Science at the Cross Roads, Bristol: Western Printing Services, 1972
This is Part 1 of a series about Special Relativity and Lorentz and Dingle’s ideas in particular. Comments are invited. paullb@totalserve.co.uk