In his 1905 paper on special relativity, Einstein made it clear that there are two aspects to the strange principle of the constancy of the speed of light for every observer.
First, the observation that the two-way speed of light has the same value, c, in every frame of reference in which the laws of mechanics hold if clocks of identical construction are used.
Second, the decision to adjust clocks in every such frame such that the "one-way speed of light" in those frames is always the same in opposite directions. I have put "one-way speed of light" in quotation marks here to indicate that this is a purely formal "coordinate speed", calculated using readings of clocks that are not necessarily synchronized.
It is true that Einstein repeatedly said that clocks adjusted in line with his procedure could be declared to be synchronous "by definition", as if there were no substance to the concept of synchronization, or distant simultaneity, other than the existence of some systematic procedure to adjust distant clocks. But an article by Einstein published in a French journal in 1910 shows that he knew that not every clock adjustment procedure is a synchronization procedure. Einstein even specified a symmetry requirement that must be met for a clock adjustment procedure using signals to qualify as a synchronization procedure. However, as explained in a previous post, he failed to realize that his procedure using light signals does not meet that requirement and is therefore not a synchronization procedure.
In light of all this, a hundred years on, what would I expect from a textbook on relativity in which the "logical arguments" underpinning the theory are said to be "presented in a rigorous manner" and in which "the major conceptual difficulties are addressed"?
More than anything else, I would expect to see a detailed explanation of the reasons for adopting a clock adjustment procedure which is not a synchronization procedure and which therefore leads to strange results, such as the principle of the constancy of c. Specifically, I would like to see a detailed and probing discussion of
- how decision-making contributes to the principle of the constancy of the speed of light;
- why it may be useful or advisable to adjust clocks in line with Einstein's procedure;
- whether or in what sense Einstein's clock adjustment procedure can be regarded as a synchronization procedure and whether, therefore, it leads to meaningful statements about one-way speeds, simultaneous existence and causality.
Sadly, in Leo Sartori's book (1996), which is promisingly entitled "Understanding Relativity", I have found nothing, nought, zilch, rien, nichts, niets on these issues.
Let me be clear: I like Sartori's book. It is perfectly lucid and refreshingly detailed on the various paradoxes relativity appears to imply. I can recommend it to anybody wishing to understand why, in the framework of relativity, there is nothing paradoxical about those paradoxes. But readers of Sartori's book should not expect to find a detailed and probing discussion of the framework itself.
For example, on page 49 Sartori maintains that there has been "direct experimental confirmation of the second postulate", but he never mentions that the light speed postulate is not just a matter of empirical fact but also of clock adjustment decisions.
And in a nine-page section on "the synchronization of clocks" starting on page 60, Sartori cheerfully asserts that "Einstein's second postulate provides the solution" to the issue of how to synchronize clocks since "two separated clocks can be synchronized by exchanging light signals between them, taking advantage of the fact that all light signals travel at the same speed c."
Sartori has got the wrong end of the stick here since the light speed postulate depends on Einstein's clock adjustment procedure and can therefore not be used to justify that procedure or the idea that it represents a synchronization procedure. In his book on the concept of simultaneity, Max Jammer (2006, p. 135) says the kind of reasoning put forward by Sartori suffers from "a vicious circularity". He points out that the notion of one-way speed presupposes the concept of distant simultaneity, which must therefore be defined before meaningful statements about such speeds can be made.
Sartori is, of course, not alone in making this mistake. I have seen it in many other expositions of special relativity, including at least one by Einstein ("Le principe de relativité et ses conséquences dans la physique moderne", published in Archives des sciences physiques et naturelles 29 (1910) pp. 5-28 and 125-144, discussed in this post), and this raises a serious concern in my mind: could it be that ever since 1905 many physicists have simply not understood the foundations of special relativity? Could this be the reason why some of their writings contain basic errors of interpretation concerning one-way speeds, causality and simultaneous existence in the framework of relativity, as suggested in my previous post?
To be explored further with reference to the specialized literature, starting with Wolfgang Rindler's 2001 textbook on Relativity - Special, General, and Cosmological, in my next post.
