Outline of this series:
I. The Impetus for This Series
II. Special Relativity: The Standard Explanation
IV. A Further Look at Simultaneity
VII. Further Thoughts on the Meaning of Spacetime and the Validity of STR
VIII. Mettenheim on Einstein’s Relativity
Bibliography (appended to each part of the series)
This section draws on the Part I of Christoph von Mettenheim’s Popper versus Einstein: On the Philosophical Foundations of Physics (Tübingen: Mohr Siebeck, 1998). Mettenheim (hereinafter CM) strikes many telling blows against STR. These go to the heart of STR and Einstein’s view of science:
[T[o Einstein the axiomatic method of Euclidean geometry was the method of all science; and the task of the scientist was to find those fundamental truths from which all other statement of science could then be derived by purely logical inference. He explicitly said that the step from geometry to physics was to be achieved by simply adding to the axioms of Euclidean geometry one single further axiom, namely the sentence
Regarding the possibilities of their position solid physical bodies will behave like the bodies of Euclidean geometry.
Popper versus Einstein, p. 30
* * *
[T]he theory of relativity as Einstein stated it was a mathematical theory. To him the logical necessity of his theory served as an explanation of its results. He believed that nature itself will observe the rules of logic. His words were that
experience of course remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics.
Popper versus Einstein, pp. 61-62
* * *
STR is an unscientific, a priori, mathematical concoction. It is based on scant evidence about the supposedly constant speed of light, a speed that is purportedly independent of the speed of its source. Even assuming that the speed of light is constant and independent of its source, STR fails because of an internal contradiction in Einstein’s reasoning (among other things), which I expose in “Part VI: Getting Light Right”:
Light purportedly moves at the same (constant) speed (in a vacuum) regardless of the motion of its source or sensor. As I will discuss in this section, the meaning of that (purported) fact has been misinterpreted, and then used to draw incorrect conclusions about relativity. Even Einstein did it….
… Here is what Einstein says in the second paragraph of the 1905 paper in which he introduces STR:
[T]he phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.
Clearly, Einstein does not say that the speed of light is the same relative to all observers. He merely says that it is always the same for all observers….
… Light (in a vacuum) moves at the same, constant speed for all observers. But it must move at different speeds relative to various observers, depending on the speeds at which they are moving….
Einstein contradicts himself [in discussing his train-and-embankment thought experiment]. He insists that the speed of light relative to the train car should be c. But it can’t be, as I argue above. The speed of light is unaffected by the speed of the train car. It remains c, even though the train car is moving at v. The movement of the train car at v doesn’t affect the actual speed of light, which remains constant — the same for all observers. Therefore, Einstein wrongly rejects V = v – c as the formula for the speed of light relative to the train car. It is exactly the right formula. Rearranging, it says that c = v + V , which preserves the constancy of c (much like preserving its virtue).
I will mention below some of the other fundamental criticisms of STR that I have made in other sections of this entry. Having already laid waste to STR, I am adding this section to salt the ruins.
CM begins by discussing the state of physics and physical knowledge at the time that Einstein promulgated STR. CM follows with a standard exposition of STR and the central importance of LT.
For ease of reference, I repeat the equations of STR:
where
is the Lorentz factor and c is the speed of light in vacuum.
In the following discussion I refer to the first equation as the “time” equation and the second equation as the “distance” equation.
CM argues that STR is not a theory of physics:
[A]ll physicists believing in the special theory of relativity will agree with me that the mathematical theorems of the Lorentz transformation follow with absolute logical necessity from Einstein’s premise of the constant spreading velocity of light in combination with the fact that the principle of adding or subtracting relative velocities does not apply to light. They rest on a valid mathematical inference. Starting from these premises they can be proved to be correct.
Surprisingly, this is where their weakness lies. they are not only strong, but indeed too strong. They fall victims to Einstein’s own criterion in his … words from Geometrie und Erfabrung:
“Insofar as the expressions of mathematics refer to reality they are not certain; and insofar as they are certain the do not refer to reality.”
In this sense the mathematical theorems of the Lorentz transformation do not refer to reality. For the very reason that they consist in a valid mathematical inference, any uncertainty they imply can only lie in their premises…. The theorems of the Lorentz transformation may be more complicated than some other mathematical theorems; but they nevertheless consist in a truism belong to mathematics, but not to physics. This is an implication of [Karl] Popper’s criterion of falsifiability … the empirical content of a theory does not come from certainty, nor even from probability, but, on the contrary, from the possibilities which it opens to refutation by experiment. The more a theory is exposed to criticism by experiment, the more it will tell us about reality. And the more it is protected against criticism by precondition, or exceptions, the lower will be its empirical. content. In this sense the Lorentz transformation is non-empirical because it is irrefutable….
… Einstein even postulated that the situation to which the special theory applied directly had to be outside any other field of gravitation. It can be doubted with some reason whether a situation meeting this requirement is to be found anywhere in the whole universe…. But this implies according to Einstein’s own words, and according to Popper’s criterion of falsifiability, that the theory is non-empirical.
If we take Einstein’s premises of the special theory literally in the strictest possible sense without changing their original meaning, then this is the point where the special theory of relativity ends. It is a correct mathematical theorem. But it is not a theory of physics because it has nothing to do with reality. It belongs to analytical geometry….
… The logical strength of the special theory of relativity not only implies its weakness as an empirical theory. I contend that it is also the source from which its adherents take their blind faith, an often truly unshakeable conviction that, whatever comes and whichever arguments may be put forward, in the end special relativity must necessarily be victorious. They believe this not only because they think that the irrefutability of a scientific theory is a virtue…. They also mistake for truth the rules of logic and mathematics without even considering that they might be of their own making. The think, as Einstein thought, that the principle of rationality is implied in nature itself, and that a theory starting from logical principles cannot, therefore, be mistaken….
… [T]he (seeming) conflict between the view that mathematics are man-made and the indisputable fact that so many discoveries have been made by mathematical inference presents an important issue in the theory of science. In my view it is one of the most intriguing philosophical problems presently existing; and I think I have found a solution for this problem which I will try to explain in the Conclusion, below. [pp. 37-40]
CM turns to STR’s treatment of time. Referring to the “time” equation of STR, he explains that it is
an expression of the relation between the “time” t’ of the moving system and the “time” t of the system at rest. It tells us that these “times” will stand in a certain relation to each other, and that this relation depends on velocity and distance of K’ and K. But how can we use this equation? What will it tell us about reality?…
Any unique physical process may serve as a reference system to give the term “time” an unambiguous meaning. For the purpose of this essay my proposition for a nominalistic definition is as simple as it is old. It relies on the well known physical process of the motion of the Earth relative to the Sun. This amounts to using the term “time” in the normal everyday sense which we employ when we ask somebody: “What time is it?”…
There can be little doubt that any nominalistic definition of the term “time” referring to the spin of the Earth upon its axis, or its orbit around the Sun, will clash with Einstein’s theory of relativity from the very start…. This follows from the fact that [the “time” equation of STR] contains two denominators, t and t’, … while a nominalistic definition using a unique physical process … will permit only one time function for ones set of space coordinates. Relative to a random point on the globe, … the Sun can always only be in one position, but not in two positions. So there can be only one time function for this point if the Sun is to be the reference system.
But Einstein’s special theory claims that every physical body caries “its own time” with it….
… I think the following Gedankenexperiment will show that the interpretation based upon this inference is … fallacious, which implies that one of its premises must be mistaken.
Let us assume a satellite starting at Greenwich exactly when the Sun is at its zenith there. The satellite is then to circumnavigate the Earth very fast several times … and return to Greenwich where it will drop into the Thames precisely when the Sun reaches its next zenith. According to my nominalistic definition of “time” the satellite was launched at 12.00 h and returned 24 hrs. later at 12.00 h. But special relativity will claim that … the “proper time” of the satellite at its return was not 24 hrs. but some fraction of a second less. Nevertheless the duration of the trip was exactly that of one revolution of the Earth.[*]
The theory of relativity assume this “time difference” to be a logical necessity, following from the “relative nature” of time…. It simply follows from the fact that [the “time” equation of STR] contains two different symbols for the denomination of “time”, t and t’….
… Time dilation is a theoretical implication of relativity, following by purely mathematical inference from the application of the Lorentz transformation….
… The empirical problems of time measurement will be discussed in a later section of this chapter. But to avoid misunderstandings I must mention even now that all empirical results indicate that clocks will in fact be influenced by velocity…. Going by the reports which I have seen, these empirical results are not to be doubted. I do not doubt them. The only question is how they are to be interpreted.
… I believe that the different performances of the clocks are indications of a real physical effect, i.e. of an external influence. [pp. 42-48]
On that point, I say this near the end of “Part VII: Further Thoughts on the Meaning of Spacetime and the Validity of STR “:
Phipps (2006, 2012) concludes that time-dilation is a fact. But it is related to the energy state of a body, and it is asymmetrical (i.e., absolute); it is not the symmetrical time-dilation of STR [emphasis added].
Returning to CM’s discussion of time, I begin with this devastating insight:
According to [the “time” equation], the “time” of the moving system, K’, stands in a certain proportion to that of the stationary system, K, and this proportion is determined by their velocity relative to each other. But the term “velocity”, v, also implies time. It is normally expressed in units of distance per time unit. So it presupposes “time” and cannot, therefore, serve to define it. [p. 51]
Relative velocity is therefore indeterminate in STR. This can be demonstrated by another Gedankenexperiment. Here’s the setup: K’ is a train car that, at rest in K, would measure 100 feet in length. The observer in K marks a distance of 100 feet along the track on which K’ will move. I will call that 1 unit of distance (d). K’ is then put in steady motion on the track, and moves past the observer in K at 0.9c.
What does the observer in K see? In the time that it takes the front of K’ to travel 1 unit of d along the track, the clock in K advances by a value that I will call 1 unit of time (t). By the “time” equation of STR, the clock in K’ (as seen by observers in K and K’) advances by 0.44t. Because of length contraction, K’ appears foreshortened (to the observer in K), so that its length in motion at 0.9c is 0.39d relative to its length at rest. These measurements yield the following estimates of the velocity (v) of K’, based on the universal formula v = d/t .
For the front end of K’, as seen by the observer in K using the clock in K, v = 1/1 = 1 .
For the front end of K’, as seen by the observers in K and K’ using the clock in K’, v = 1/0.44 = 2.3 .
For one car-length of K’, as seen by the observer in K using the clock in K, v = 0.39/1 = 0.4 .
For one car-length of K’ , as seen by the observer in K using the clock in K’, v = 0.39/0.44 = 0.9 .
Accordingly — and contrary to STR — there is no way to equilibrate “time” and “distance” between K and K’. The equations of STR yield contradictory results, even nonsensical ones (i.e., v > 1) . Only the fourth computation yields the “correct” value of v = 0.9c .
How did Einstein wander into such a morass? CM says that because Einstein was
worried by the fact that no velocity is infinite and the even light has only a measurable speed, and also by the strange physical properties of light … , he questioned the meaning of statements on simultaneity [which I will use in place of CM’s “simultaneousness”: LV]. He claimed that, for physicists, the term “simultaneity” could only “exist” if there was a possibility of finding out whether it is true or false….
The problem Einstein was really concerned about was … not the definition of “simultaneity”, but the measurement of simultaneity. This is a serious problem…. But it is an empirical problem, concerning the influence of velocity on the motion of clocks. It has nothing to do with questions of denomination or of definition, and should therefore not be confused with them….
… In order to find out whether the strokes of lighting … in Einstein’s example were simultaneous while we are observing them from the moving train, all we have to do is add, or subtract (depending on the direction), the time interval needed by the signal, or by the train during the transport of the signal…. The only problem lies in the question how to attribute a definite value to the time interval. But this a problem of measurement, not of definition. [pp. 52-54]
As I show in “Part III: A Fatal Flaw?“, Einstein’s train-and-embankment thought experiment doesn’t disprove the concept of distant simultaneity. All it shows is that an observer on a train which is moving from left to right along an embankment will see a flash coming from the right (position A) before he sees a flash coming from the left (position B), even though (a) the flashes are emitted simultaneously according to to an observer on the embankment who is situated halfway between A and B, and (b) the observer on the train is exactly opposite the observer on the embankment when the flashes are emitted.
Why doesn’t the observer on the train see the flashes at the same time as the observer on the embankment? There’s nothing mysterious about the discrepancy. The observer on the train is halfway between A and B when the flashes occur, not when they reach him an instant later. In that instant he has moved toward the flash coming from A and away from the flash coming from B. The fact that he sees the flash coming from A before he sees the flash coming from B is a manifestation of classical relativity, and it can be expressed with the use of simple algebra, as CM points out in the third paragraph of the preceding quotation. (The algebra can be found in “Part IV: A Further Look at Simultaneity“.) Einstein’s demonstration of non-simultaneity is nothing more than a fatally flawed thought experiment.
The fatal flaw notwithstanding, Einstein built up in his mind a logical edifice that had to explain the physical world:
Einstein believed in a principle of rationality residing in nature itself. The fact that some result followed with mathematical accuracy from his premises, which he treated as axioms, was therefore, to him, in itself a convincing explanation of this result. He special theory was founded on the assumption that physical effects must be explained by logical necessity. [p. 62]
But STR
is a mere hypothesis, which may be true or false like any other theory. Convincing empirical evidence could therefore be the only possible reason for adopting this particular formula.
As mentioned, the adherents of the Vulgata [the reigning, informal interpretation of STR] claim that there is, indeed, overwhelming evidence in favor of [their version of the “time” equation]….
… There is, indeed, considerable evidence showing that the effects which special relativity tries to explain exist in reality. That was one of the reasons why Einstein developed the theory…. [pp. 63-64]
The evidence doesn’t always add up. For example:
If two atomic clocks have been standing next to each other for some time without ever indicating different “times”, and if one of them is then separated from the other and taken on a fast voyage around the Earth, then their indications will be different when they are reunited….
The adherents of relativity will take the different indications of the clocks to be a ‘time difference’ resulting from [the “time” equation] and thus claim them to be empirical confirmation of the theory…. [T]he question, to me, is what happened to the clock [that went around the Earth]? [p. 64]
Again, there is the question of energy-state, which STR doesn’t address.
CM turns to the “overwhelming evidence” for STR, which really isn’t overwhelming. He discusses the Sagnac effect,
a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions…. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to the earth, the light travels at a constant speed. However, when the interferometer system is spun, one beam of light will slow with respect to the other beam of light.
CM picks up the story:
It has never been possible to reconcile this effect with the theory of relativity…. The supporters of a mathematical approach to physics will try to explain the fringe shift by the difference in the length of the light path. This will be lengthened as the light is travelling in the direction of rotation, and shortened as it travels against [the direction of rotation]. Accordingly light can be expected to take more time travelling around the disc in the direction of rotation than against it. [p. 67]
In fact, as I understand it, the time difference is resolved by simple algebra without reference to special relativity. (See the first part if the discussion here.) This is consistent with Marrett (2012):
If we now rotate the disk clockwise at velocity v, we find that the … beam [moving against the rotation of the apparatus] arrives back at the detector before the … beam [moving in the direction of the apparatus] – in fact, the difference in the velocity of light turns out to be 2*v , because the blue beam travels at c + v and the red beam at c – v .
(As discussed above and in “Part VI: Getting Light Right“, it is proper to add or subtract from the speed of light to determine the speed of an object relative to the speed of light.)
CM follows up with a comparison of the Sagnac effect and the Michelson-Morley experiment of 1887. He argues that Michelson-Morley contradicts the Sagnac effect because the Michelson-Morley apparatus was spinning with the rotation of the Earth and didn’t capture an interference pattern. However, the same is true of the Sagnac apparatus in a stationary configuration (relative to Earth). So that argument is inconclusive, as is the Sagnac effect. As CM puts it:
[T]he relations between light and velocity must be more complicated than the theory of relativity or other mathematical approaches to the problem of light will have them. [p. 69]
Next is the Hafele and Keating experiment,
which was carried out in October 1971 by two American physicists, J.C. Hafele and R. Keating. Four caesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward. It was observed that the flying clocks “lost time” (aged more slowly) during the eastward trip and “gained time” (aged faster) during the westward trip….
… I have shown … that the “time” difference in special relativity … must always be negative…. “[T]ime” never accelerates relative to the reference system. The space traveller returning home from his voyage will always be younger than his earthbound twin…. But Hafele/Keating claim to have observed a “time gain” (clocks ages faster) during the westward trip. Correctly interpreted this experiment must therefore also be considered as a refutation of special relativity….
The other possible interpretation of the “time shift” is, quite simply, that something happened to the clock on its way around the Earth — not in the sense that the results of the experiments were faked, but in the sense that the clock was exposed to some physical effect which we have not yet understood.
… This, I think, is the real issue. In my view it is an issue between the theory of relativity and empirical science….
Several indications, such as the Sagnac effect and the outcome of certain experiments by Michelson and Gale which I will discuss in more detail … below, indicate that there may be physical effects connected with the motion of light relative to matter, or of matter relative to other matter, which we have not yest foully understood. [pp. 69-70, 74-75]
See also Marrett (2013).
CM addresses the hypothesized physical effects later. His next topic is general relativity. He observes that Einstein
erroneously ascribed the deflection of light caused by the motion of two systems moving relative to each other, which is nothing but a truism of analytical geometry, to a physical property of space itself.
… This can be seen from his first introduction of the concept of “curved space”. In one of his famous Gendankenexperimente he assumes a large box, or lift, being accelerated through space at a constant rate outside any other filed of gravitation… He then lets a ray of light travelling horizontally (parallel to the bottom, or x-axis) fall into the box through a hole in its side. Due to the finite velocity of light, and … due to the constant rate of acceleration of the box, this ray …. will assume the shape of a parabolic curve inside the box.
… Einstein infers that [persons] living inside the box will ascribe the deflection of light to the influence of the gravitational field. And his further inference is that we, the human race, who are living in the gravitational field of the Earth and the Sun, without being able to “look out the window”, must therefore also assume the lines of light to be curved in this field.
Going by Einstein’s own explanation, this, and nothing else, was at the bottom of his famous concept of “curved space” when he first introduced it….
This … shows that … he considered the deflection of light as a necessary implication of acceleration, resulting from a purely mathematical operation, viz. the “changing of the system of coordinates”. [In fact, the passage of a ray of light from top to bottom of a box in horizontal, inertial motion would create the illusion of curvature: TEA.]….
As a simple truism of analytical geometry Einstein’s reasoning belongs to mathematics, but not to physics. So it falls victim to [Einstein’s] own criterion: Because it is certain it does not refer to reality. And if it does not refer to reality, then it does not describe a physical property of light, or of space. [pp. 82-85]
I was for many years convinced by Einstein’s thought experiment because I had accepted it in the way that a child usually accepts an adult’s statement of a “truth”. After reading CM’s criticism, it occurred to me that the ray of light doesn’t actually curve. It only seems to curve, if seen from inside the box, because the box is rising as the ray traverses it, so that the floor of the box moves steadily closer to the ray. But the ray remains horizontal — that is, it really continues in a straight line. So Einstein’s thought experiment fails because it relies on a particular point of view — that of the observer in the box. But Einstein to the contrary notwithstanding, that isn’t the point of view of an Earth-bound observer of the traversal of a light ray past the sun. The Earth-bound observer is standing “outside the box”, watching the ray of light approach the Sun and continue past the Sun to Earth.
Further, as I note in a parenthetical remark above, the illusory curvature of the light ray doesn’t rely on acceleration; linear, inertial movement will produce the same illusion. So one must also doubt Einstein’s equivalence principle, which states that
the gravitational “force” as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
Inasmuch as a light ray will “bend” inside a non-accelerating body, the bending of light either has nothing to do with gravity, even if acceleration and gravity are equivalent.
What about the apparent deflection of starlight as it “curves” around the Sun enroute to Earth? Research by respectable scientists, summarized by A.D. Hall (2015), suggests that the curvature is caused entirely by atmospheric refraction.
Tests of general relativity that measure the deflection of light by the Sun are based on the assumption that the deflection is caused by gravity, as Einstein supposed. But CM reports an inconvenient fact about Einstein’s theory:
[A]s early as 1915 Einstein had read a paper before the Royal Prussian Academy of Science in which he stated that the deflection of light passing the sun was 1.7 sec. of arc relative to the passing distance from the Sun. And he adapted his general theory of relativity to this value. Therefore the value cannot have been predicted by the theory, but must have been established before….
After the publication of Eddington’s experiment [in 1919 and 1922] Einstein still spoke of a deflection of 1.7 sec. of arc. So the outcome of the experiment seems to have confirmed his expectations exactly. [pp. 88-89]
Further,
Einstein’s explanation of the redshift of light coming from distant galaxies used to be almost as famous as Eddington’s experiment…. This redshift, … so it is claimed, was predicted by Einstein’s general theory of relativity…
… [T]he redshift had already been observed at the time Einstein wrote. It was also known that the spectrum of light coming from distant stars or galaxies will always shift only in one direction, namely towards the lower frequencies. But [Edwin] Hubble discovered [in 1929] that there appears to be an order in this shift. According to Hubble’s observations, and his interpretation of them, the degree of the redshift will depend on the distance from the Earth of the respective star or galaxy. The greater the distance, the more will the spectrum of light be shifted towards the lower frequencies.
… [According to general relativity] we should expect to observe stronger redshifts in heavier, and weaker redshifts in less heavy celestial bodies. But … the degree of redshift is in fact graduated not in proportion to mass, but to distance. [pp. 91, 94-95]
Where does that leave relativity? CM closes part I of his essay in this vein:
… [I]f the theory of relativity finally breaks down, which I think it must, then the discipline of physics is likely to be left with more open problems than it ever faced before.
The problem of light is only one of them….
… [M]ost important of all is the problem of gravitation, which has also never been solved to this day, neither by Newton nor by Einstein…. [O]n this point I find myself in agreement with some of the most eminent physicists of our time. Richard Feynman, winner of the 1965 Nobel prize in physics, considered gravitation as unexplained. Leon Lederman, winner of the 1988 Nobel prize in physics, described it as our “Problem No. 1″…. Stephen Hawking, presently holding Newton’s chair at Cambridge, devoted several chapters to the problems of quantum theory and gravity….
The approach taken by the theory of relativity may at this point be characterized as a “mathematical” approach. It consists in an attempt to reduce physics to a comparatively small number of axioms from which all other statements should be deduced by purely mathematical inference. And it rests on an unfounded belief that physical hypotheses may undergo “an increase of content through translation into a mathematical language”….
… Tarksi has demonstrated that logical and mathematical inferences can never yield an increase of empirical information because they are based on nominalistic definitions of the most simple terms of our language. We ourselves give them their meaning and cannot, therefore, get out of them anything but what we ourselves have put into them…. That is why logic and mathematics alone can never lead to scientific discoveries….
… [Einstein] believed in a strict parallelism of mathematics and physics, and he thought that the laws of nature must follow from our observation by purely logical or mathematical inference….
This explains the barrenness of [Einstein’s] theory. It can never lead to discoveries. According to him
“the truly creative principle in science resides in mathematics.”
But in this he was fundamentally mistaken…. Discoveries will not come from logic, but must consist in the introduction of new empirical information….
But I must repeat that I am far from accusing Einstein of being unimaginative…. I fully subscribe to the evaluation of his merits in Lanczos’ words, as quoted by Popper, that
“if anybody asked who is the greatest modern phyysicist after Einstein, the answer would be: Einstein again…. (For) had somebody else discovered relativity his other discoveries would still make him the second greatest physicist of his time”.
My objections chiefly concern the theory of relativity as it is being taught in our days. It is this present dogmatic attitude which I consider to be as unscientific as can be. If we wish to overcome dogmatism in physics, then the theory of relativity must be given up. [pp. 99-107, passim]
I agree.
* Here’s another thought experiment to the same effect: Return to Einstein’s train-and-embankment setup, with a clock at M on the embankment. Along comes a very fast train with a clock at M’ (the front of the train) which reads 00:00:00 when M’ is directly opposite M; the clock at M also reads 00:00:00 at that instant. A second later, on a parallel track comes an even faster train with a clock at M” (the front the train) which reads 00:00:01 when M” is exactly opposite M; the clock at M also reads 00:00:01 at that instant. A second after than that, at 00:00:02 according to the clock at M, the clocks at M” and M’ are exactly aligned with another clock at W on the embankment, which is perfectly synchronized with the clock at M and also reads 00:00:02. Perpendicular to W is a wall of such strength that the two trains stop immediately and with such force that the clocks at M’ and M” are crushed. But there is no question that they hit the wall at 00:00:02 by the clocks at M and W. Further, there is no question that they hit the wall at the same time at the same (extended) point in space (the wall reaches from the embankment to the far side of the tracks), which can be treated as an extended point in space. (Alternatively, the “trains” could be point-particles running through M and stopping at W.) A point in space-time is unique, by definition, and cannot have more than one space-time coordinate. Each train’s clock agreed with the clocks at M and W as it passed M, and each train’s clock had to agree with the clocks at M and W as it reached the unique space-time point W-00:00:02. That is, the clocks on the trains actually moved at the same rate as the clocks at M and W, STR to the contrary notwithstanding. If, for any reason, the clocks moved at different rates, those rates had nothing to do with geometrical relationship depicted by STR. And it would be purely coincidental if those differing rates were the same as rates computed in accordance with STR.
BIBLIOGRAPHY
Online courses in special relativity
Lecture 1 of “Special Relativity”, Stanford University
All lectures of “Special Relativity”, Khan Academy
All lectures of “Understanding Einstein: The Special Theory of Relativity”, Standford University
Selected books, articles, and posts about special relativity
Barnett, Lincoln. The Universe and Dr. Einstein. New York: Time Incorporated, 1962.
Bondi, Hermann. Relativity and Common Sense: A New Approach to Einstein. New York: Doubleday & Company, 1946.
Buenker, Robert J. “Commentary on the Work of Thomas E. Phipps, Jr. (1925-2016)”. 2016.
Einstein, Albert. “On the Electrodynamics of Moving Bodies”. Annalen der Physik, 322 (10), 891–921 (1905).
———. Relativity: The Special and General Theory. New York: Henry Holt, 1920.
Epstein, Lewis Carroll. Relativity Visualized. San Francisco: Insight Press, 2000.
Hall, A.D. “Lensing by Refraction…Not Gravity?“. The Daily Plasma, December 23, 2015.
Marrett, Doug. “The Sagnac Effect: Does It Contradict Relativity?“. Conspiracy of Light, 2012.
———. “Did the Hafele and Keating Experiment Prove Einstein Wrong?“. Conspiracy of Light, 2013.
von Mettenheim, Christoph. Popper versus Einstein. Heidelberg: Mohr Siebeck, 1998.
———. Einstein, Popper and the Crisis of Theoretical Physics (Introduction: The Issue at Stake). Hamburg: Tredition GmhH, 2015.
Noyes, H. Pierre. “Preface to Heretical Verities [by Thomas E. Phipps Jr.]”. Stanford: Stanford Linear Accelerator Center, Stanford University, June 1986.
Phipps, Thomas E. Jr. “On Hertz’s Invariant Form of Maxwell’s Equations”. Physics Essays, Vol. 6, No. 2 (1993).
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, first edition, 2006.
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, second edition, 2012 (The late Dr. Phipps — Ph.D. in nuclear physics, Harvard University, 1950 — styled himself a dissident from STR, for reasons that he spells out carefully and exhaustively in the book.)
Rudolf v. B. Rucker. Geometry, Relativity, and the Fourth Dimension. New York: Dover Publications, 1977.