ELEMENTARY ERRORS IN EINSTEIN'S RELATIVITY

In his 1918 paper Einstein made two important statements:

(A) During the inertial phases of the travelling twin's trip, the sedentary twin's clock "runs indeed at a slower pace" than the travelling twin's clock. That is, if no other factor affects the clocks, the travelling twin will return older than his sedentary brother.

(B) The "other factor" that brings about the youthfulness of the travelling twin is the acceleration (or gravitational potential) experienced by him during the short turn-around period. In this period the sedentary twin's clock runs much faster than the travelling twin's clock, and "the calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind" during the inertial phases of the trip:

http://en.wikisource.org/wiki/Dialog...f_rela tivity
Dialog about Objections against the Theory of Relativity, 1918, Albert Einstein: "During the partial processes 2 [traveller moves with constant speed away from sedentary brother] and 4 [traveller moves with constant speed towards sedentary brother] the clock U1 [the sedentary twin's clock], going at a velocity v, runs indeed at a slower pace than the resting clock U2 [the travelling twin's clock]. However, this is more than compensated by a faster pace of U1 during partial process 3 [traveller sharply turns around]. 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."

Einstein's error is elementary again - the turn-around acceleration (or gravitational potential) can obviously play no role in determining the age of the twins:

http://www.damtp.cam.ac.uk/research/...tivity2010.pdf
Gary W. Gibbons FRS: "In other words, by simply staying at home Jack has aged relative to Jill. There is no paradox because the lives of the twins are not strictly symmetrical. This might lead one to suspect that the accelerations suffered by Jill might be responsible for the effect. However this is simply not plausible because using identical accelerating phases of her trip, she could have travelled twice as far. This would give twice the amount of time gained."

http://www.fnal.gov/pub/today/archiv...lReadMore.html
Don Lincoln: "Some readers, probably including some of my doctoral-holding colleagues at Fermilab, will claim that the difference between the two twins is that one of the two has experienced an acceleration. (After all, that's how he slowed down and reversed direction.) However, the relativistic equations don't include that acceleration phase; they include just the coasting time at high velocity. For the professional (or the brave), I work out the predictions of relativity. That one twin inhabits two frames is the only thing that matters."

http://sciencechatforum.com/viewtopic.php?f=84&t=26847
Don Lincoln: "A common explanation of this paradox is that the travelling twin experienced acceleration to slow down and reverse velocity. While it is clearly true that a single person must experience this acceleration, you can show that the acceleration is not crucial. What is crucial is that the travelling twin experienced time in two reference frames, while the homebody experienced time in one. We can demonstrate this by a modification of the problem. In the modification, there is still a homebody and a person travelling to a distant star. The modification is that there is a third person even farther away than the distant star. This person travels at the same speed as the original traveler, but in the opposite direction. The third person's trajectory is timed so that both of them pass the distant star at the same time. As the two travelers pass, the Earthbound person reads the clock of the outbound traveler. He then adds the time he experiences travelling from the distant star to Earth to the duration experienced by the outbound person. The sum of these times is the transit time. Note that no acceleration occurs in this problem...just three people experiencing relative inertial motion."

Pentcho Valev