LIFESAVING ACCELERATION IN EINSTEIN'S RELATIVITY

Does Einstein's special relativity validly predict that the travelling clock runs more slowly than the stationary one (the travelling twin remains younger than his stationary brother)? The answer is NO. This "prediction" of special relativity crucially depends on an enemy-confusing acceleration phase introduced by Einstein in his 1905 paper:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
"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. It is easy to remove the acceleration phase but then the acceleration-free scenario proves sterile - the conclusion cannot be derived from the postulates.

Initially the enemy-confusing acceleration phase acted imperceptibly but in 1918 Einstein had to explicitly resort to it (otherwise his enemies would have toppled him):

http://en.wikisource.org/wiki/Dialog...f_rela tivity
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."

http://www.pitt.edu/~jdnorton/teachi...yon/index.html
John Norton: "Then, at the end of the outward leg, the traveler abruptly changes motion, accelerating sharply to adopt a new inertial motion directed back to earth. What comes now is the key part of the analysis. The effect of the change of motion is to alter completely the traveler's judgment of simultaneity. The traveler's hypersurfaces of simultaneity now flip up dramatically. Moments after the turn-around, when the travelers clock reads just after 2 days, the traveler will judge the stay-at-home twin's clock to read just after 7 days. That is, the traveler will judge the stay-at-home twin's clock to have jumped suddenly from reading 1 day to reading 7 days. This huge jump puts the stay-at-home twin's clock so far ahead of the traveler's that it is now possible for the stay-at-home twin's clock to be ahead of the travelers when they reunite."

http://van.physics.illinois.edu/qa/l...-paradox-again
University of Illinois at Urbana-Champaign: "Special relativity also gives you the tools to analyze the situation from the traveling twin's perspective. The traveling twin does not stay put in a single nonaccelerating frame of reference during his journey, however, so life is more complicated for him. Instead, at each moment of his journey, we can define a frame of reference that is moving along with the traveling twin. In this frame of reference, we can ask the question what time is read on his brother's watch. Then a moment later, we have to pick another frame of reference moving along with the traveling twin's new speed, and ask what time is read on his brother's watch. If we make a graph of the time read on the stay-at-home twin's watch in all of these different frames of reference as a function of the traveling twin's watch's reading, we will find it's not a straight line. On out outgoing part, the traveling twin thinks his stay-at-home twin's watch is running slow, just like his stay-at-home twin thinks the traveling twin's watch is runnning slow. On the turnaround part, the traveling twin thinks his stay-at-home brother's watch speeds up, and then on the return trip, he thinks the stay-at-home twin's watch runs slow again. It's a mess, but it gives the same answer as doing everything in just one frame."

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, but - note - 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 and the clock at B as moving), it is the clock at B that runs slow.

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 validly follows from the postulates (in an acceleration-free scenario) is that either clock runs more slowly than the other, as judged from the respective system. A legitimate but highly unimportant, to say the least, conclusion.

Pentcho Valev