The apparently widespread belief that Einstein's 1905 clock adjustment procedure is a synchronization procedure has led some physicists to draw spectacular but misguided conclusions on issues such as causality and existence. These conclusions are the result of what I will call the "simultaneity syndrome" in modern physics: the continued and uncritical application of concepts depending on synchronization, such as one-way speed, causality and distant simultaneous existence, in the framework of a theory in which clocks have not in fact been synchronized.
My first example is a passage in Wolfgang Rindler's textbook Relativity - Special, General and Cosmological (2001), in which the author suggests that superluminal signals cannot exist since they would give rise to intractable causality paradoxes (pp. 54-56). When I first read this passage, it didn't seem right to me because superluminal signals are logically perfectly conceivable while true causality paradoxes are not. Therefore, superluminal signals could not possibly give rise to such paradoxes.
But I didn't know where the flaw in Rindler's reasoning was. Today I think I know that his argument is a case of simultaneity syndrome.
Rindler says that if P is the event of sending out a signal along the x-axis of a first frame of reference S at superluminal speed U and L the event of that signal arriving somewhere else, then there are other frames, for example S', "in which L precedes P, in which cause and effect are thus reversed and in which the signal is considered to travel in the opposite spatial direction". "So, if L were, for example, the breaking of a glass somehow caused in S by the signal from P, then in S' the glass would break spontaneously and at the same time emit a signal to P. Since in macro-physics no such uncaused events are observed, nature must have a way to prevent superluminal signals."
Let me analyse the sequence of events sketched out by Rindler in greater detail. Suppose that S is a frame in which light signals propagate in symmetrical conditions in all directions and that thus Einstein's clock adjustment procedure can be used to synchronize clocks in S. Suppose further that Rindler's signal is an arrow which is initially stationary at x = 0 in S and then fired from (x; t) = (0; 0) in the positive direction of the x-axis at the superluminal speed of U = 2x1018 m/s. Suppose further that S' and S are in standard configuration - i.e. the events (0; 0) in the two frames coincide - and that S' moves at the speed of 9m/s relative to S. Finally, suppose the glass is a strong glass wall located at x' = 100m in S' and that the arrow gets lodged in it upon impact. From the point of view of S, we thus have the following situation at t = 0:
Diagram 1
In this diagram, an Einstein-adjusted S' clock at the glass wall would show a time of about
-10-16s. If the arrow is now fired from (0; 0) in S at the speed U, it will hit the glass wall when the S' clock there shows about -0.5x10-16s, i.e. in terms of S' coordinates the arrow arrives "before it was fired". In reality, of course, it arrives after it was fired, as it must, it's just that the clock located at 100m in S' is not synchronized with the one at 0m in S'. A diagram of the arrow's progress in terms of S' coordinates shows what happens if we treat those coordinates as if they defined a relationship of simultaneity:
Diagram 2 - I have exaggerated the angle between the incoming world line of the arrow and the t'-axis for clarity
In this diagram, at the time t' = -0.5x10-16s in S', while the arrow is still lodged in the firing mechanism and moves at -9m/s towards the (0; 0) position in S', a copy of the arrow mysteriously pops up from nowhere at 100m and instantly splits into two arrows, one of which remains lodged in the glass while the other moves backwards towards the arrow firing mechanism, where it merges with the first copy just as the arrow is fired at (0; 0). All this is of course nonsense, resulting from the application of the language of simultaneity to a situation in which clocks are not synchronized. Trying to make sense of the diagram in terms of "simultaneity" and "cause and effect" is like trying to make sense of a text in which words have been strung together arbitrarily. It means trying to find meaning where there is no meaning. It is an example of simultaneity syndrome.
As Rindler points out, in the framework of SR "superluminal" signals could even be used to tamper with the past in one and the same location. The arrow could, for example, be plucked out of the glass wall in S', hurled back towards the arrow firing mechanism at "superluminal speed" in S' and hit and destroy that same arrow before it was even fired! People in S and S' would be left with two broken arrows, a shattered glass wall and a lot of unanswered questions. Rindler is right to say that this kind of scenario is fraught with paradox. But it does not follow from this, as he suggests, that superluminal signals cannot exist. It merely follows, much less spectacularly, that faster-than-instantaneous signals cannot exist. There may, of course, be physical barriers to any signal moving faster than light, at least locally. However, the idea that superluminal signals could create time paradoxes is based on the misguided belief that in special relativity Einstein-adjusted clocks in any particular frame of reference are necessarily synchronized and all "speeds" are meaningful.
The simultaneity syndrome strikes again in Vesselin Petkov's book Relativity and the Nature of Spacetime (2005), where it leads to astounding conclusions about simultaneous existence.
Petkov argues that the indisputable empirical validity of special relativity means that we live in a four-dimensional "block universe" in which the flow of time is just an illusion since in SR every event exists simultaneously with every other in some frame of reference (see for example pp. 123-134). In a blog post published in May 2008, Sabine Hossenfelder pretty much hit the nail on the head when she said that Petkov's argument is wrong because "existence" is not a concept that is part of SR, so "everything that can be said about 'existence' in SR is a completely empty statement". I'd add that the reason why SR has nothing to say about distant simultaneous existence is that clocks in SR are in general not synchronized.
What these examples show is that, for a proper understanding of special relativity, it is crucial to realize that Einstein's clock adjustment procedure is not a synchronization procedure. Once this has been understood, everything else falls into place:
- the principle of the constancy of the "speed of light", for example, since it becomes clear that the "speed" it refers to is a purely formal "coordinate speed" obtained from clocks which are not necessarily synchronized;
- or the "time quakes" which occur in SR when distant observers begin to move relative to each other, since, again, the only "time" that is subjected to such swings is a purely formal "coordinate time" shown by clocks which are not synchronized.
To illustrate once again the effects of adjusting clocks in ways which do not synchronize them, take the case of two runners who set off from the mid-point between two clocks at the same time and who set those distant clocks to the same time when they arrive there. If they were equally good runners, equally well motivated, rested and fed, making equal efforts, traversing equally difficult terrain in equal weather conditions and so on, we might be willing to consider that their clock adjustment has probably roughly synchronized those clocks.
If, on the other hand, one of them sprinted to her clock and the other took a leisurely stroll, we would not regard those two clocks as synchronized and it would not be possible to measure one-way speeds using such clocks. If we did so in purely formal terms for people walking from one clock to the other, by dividing the distance between the clocks by the difference in clock readings, we'd get nonsensical results, such as "infinitely fast" or even "faster-than-infinite" walking speeds.
Those clocks would not be synchronized because, in abstract terms, the conditions in which the signals used are emitted or propagate are not symmetrical. And that's exactly why, in general, clocks in SR are not synchronized, either. The idea that we could define simultaneity by declaring that those clocks are to be regarded as synchronized "by definition" reminds me of an often-quoted passage in Lewis Carroll's Through the Looking-Glass (1871), in which Humpty Dumpty declares: "When I use a word, it means just what I choose it to mean - neither more nor less." It doesn't, of course, and it would take more than the choice of the entire community of physicists to make true Werner Heisenberg's suggestion, in his book Physics and Philosophy published in 1958, that "language" has already evolved in such a way that today "the word 'simultaneous' is used in line with the definition given by Einstein" (p. 163).
As I have attempted to show, the truth is that even contemporary specialists on relativity, such as Rindler and Petkov, use the concept of simultaneity in a rather confused and confusing way. If that is so, how do they explain the principle of the constancy of the speed of light to their readers? And how do they tease out the role of definition, stipulation or convention in that principle? My next post will tell.
