FATAL ACCELERATION IN EINSTEIN'S SPECIAL RELATIVITY

[Pentcho Valev]

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the 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 has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

The moving clock experiences acceleration at the start of its journey from A to B so Einstein's conclusion ("the clock moved from A to B lags behind the other") is invalid - it is not a consequence of the postulates of special relativity. Einsteinians will have to remove the acceleration phase from the scenario and consider clocks that are inertial all along.

If Einstein's conclusion cannot be made in an acceleration-free scenario, then... what then, Einsteinians?

Pentcho Valev

[Pentcho Valev]

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the 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 has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

The moving clock experiences acceleration at the start of its journey from A to B so Einstein's conclusion is unjustified. Yet the acceleration phase is easy to remove. Let us assume that both the clock at A and the clock at B remain stationary but a third clock, moving with constant speed v, consecutively passes them so that its reading can be checked against theirs. For the third clock Einstein's relativity does indeed predict that it runs slow, as judged from the stationary system.

The last phrase, "as judged from the stationary system", is crucial and reminds us of another prediction of Einstein's relativity: As judged from the third clock's system (the one in which the third clock is regarded as stationary), it is the clock at B that runs slow. That is, observers in the third clock's system are entitled to regard their own clocks as stationary and the clock at B as "the moving clock" from John Norton's scenario:

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Reciprocity/index.html
John Norton: The figure shows the bare essentials of the moving clock and all the other clocks spread out through space. The moving clock agrees with the reading of the leftmost clock--my wristwatch--as it passes by. However when it passes the rightmost, it now reads much less:
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Reciprocity/clocks.gif

Clearly, Einstein's 1905 conclusion that the moving clock "lags behind" the stationary one CANNOT be derived from the postulates of special relativity if the scenario is acceleration-free. What follows from the postulates is that either clock runs more slowly than the other, as judged from the respective system.

Pentcho Valev

[Pentcho Valev]

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the 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 has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

By using a scenario involving an acceleration phase, in 1905 Einstein managed to hide the fact that his conclusion ("the clock moved from A to B lags behind the other") does not follow from the postulates of special relativity. Elated by his success, in 1918 Einstein explicitly referred to essentially the same acceleration phase in order to justify his unjustifiable conclusion that the travelling twin returns younger than his sedentary brother:

http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Albert Einstein 1918: "During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2. However, this is more than compensated by a faster pace of U1 during partial process 3. According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4. This consideration completely clears up the paradox that you brought up."

Pentcho Valev

[Pentcho Valev]

Let us consider, again, the initial acceleration of the clock at A as it starts moving towards the clock at B:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the 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 has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

By using a scenario involving acceleration, Einstein in fact blocked any derivation from the postulates of special relativity. His conclusion ("the clock moved from A to B lags behind the other") was purely arbitrary, an outcome of his personal ambition to become a celebrity. If the scenario is acceleration-free, only the embarrassing, far-from-converting-the-author-into-a-celebrity, conclusion that either clock runs more slowly than the other (as judged from the respective system) can be derived from the postulates.

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