Tuesday, May 29, 2012

Einstein's clock paradox

Galina Weinstein has posted another Einstein draft paper, Einstein's Clocks and Langevin's Twins.
2. Clock Paradox
From this Einstein derived a "peculiar consequence":3
"If at the points A and B of K there are clocks at rest which, considered from the system at rest, are running synchronously, and if the clock at A is moved with the velocity v along the line connecting B, then upon arrival of this clock at B the two clocks no longer synchronize,...".

The above "peculiar consequence" came to be known as "the Clock Paradox".

John Stachel explained that, the most new important feature of time to emerge from the special theory of relativity is the clock paradox: a comparison of one clock in a moving system with many clocks in the rest system; there is no reciprocity, but one-many relationship. The clock paradox that was predicted by Einstein embodies the difference between Einstein and pre-relativistic electrodynamics of moving bodies.4

Einstein proposed an experimental test for the clock paradox: "From this we conclude that a balance-wheel clock that is located at the Earth's equator must run very slightly slower than an absolutely identical clock, subjected to otherwise identical conditions, that is located at one of the Earth's poles".5
Lorentz and Poincare had the dilation formulas previously, but did not explicitly mention the possibility that two clocks could fall out of synchronization just because they are moving differently. The closest was Poincare's 1904 St. Louis lecture, where he explains that a moving clock runs slow compared to the other, but did not say that it led to a paradox:
The watches adjusted in that way will not mark, therefore, the true time; they will mark what may be called the local time, so that one of them will be slow of the other. It matters little, since we have no means of perceiving it. All the phenomena which happen at A, for example, will be late, but all will be equally so, and the observer will not perceive it, since his watch is slow; so, as the principle of relativity requires, he will have no means of knowing whether he is at rest or in absolute motion.
But Einstein's experimental test is wrong. Two such clocks will not show a difference.

The closely related twin paradox causes trouble for relativity students even today, but Weinstein sees it as a Jewish issue:
The clock paradox was also an excuse for anti-Semites to blame the theory of relativity as an anti-German science and blame its author as well. In Berlin, Ernst Gehrcke, Philipp Lenard, and Paul Weyland advocated an anti-relativity propaganda campaign after 1916.17

In November 1918 Einstein answered the first two by a Galilean dialogue between a relativist and a critic of the theory of relativity, "Dialogue about Objections to the Theory of Relativity" ...
Those arguments for and against the clock paradox did not involve any Jewish issues, as far as I know. Even when GPS was built a few years ago, I am told that some people were skeptical that relativity would be needed. Even today, Weinstein seems not to realize that Einstein's 1905 experiment test is wrong.

I don't deny that there was some German anti-semitism, and maybe some anti-German bias outside Germany. I just don't see what it had to do with the clock paradox, or with relativity skepticism.

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