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Replies: 3   Last Post: Mar 22, 2013 4:17 PM

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Pentcho Valev

Posts: 4,986
Registered: 12/13/04
Posted: Mar 22, 2013 11:40 AM
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Relativity and Its Roots, Banesh Hoffmann, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."

Since the travelling twin has to shift his frame of reference, it is technically difficult (but not impossible) to show how the travelling twin checks the sedentary twin's clock against his own and find, in accordance with special relativity, that the sedentary twin proves younger at the end of the trip. This technical difficulty allowed Einsteinians to introduce the following victorious principle:

We, Honest Einsteinians, show that, as judged from the frame of the sedentary twin, the travelling twin's clock runs slow, Divine Einstein, yes we all believe in relativity, relativity, relativity. We don't care about any means by which the travelling twin can check the sedentary twin's clock against his own. And since we do not care, the problem simply does not exist, Divine Einstein, yes we all believe in relativity, relativity, relativity.

The problem did not exist for Divine Albert in 1911 so his only concern was to minimize the effects of the acceleration suffered by the travelling twin:
Peter Hayes, in "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology, Volume 23, Issue 1 January 2009, pages 57-78, quotes Einstein writing in 1911: "The [travelling] clock runs slower if it is in uniform motion, but if it undergoes a change of direction as a result of a jolt, then the theory of relativity does not tell us what happens. The sudden change of direction might produce a sudden change in the position of the hands of the clock. However, the longer the clock is moving rectilinearly and uniformly with a given speed in a forward motion, i.e., the larger the dimensions of the polygon, the smaller must be the effect of such a hypothetical sudden change."

The acceleration-is-unimportant thesis is taught even today:
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."

Yet Divine Albert's enemies constantly referred to the fact that special relativity predicts RECIPROCAL time dilation so in 1918 he had to abandon the acceleration-is-unimportant thesis: Yes, the travelling twin does see the sedentary twin's clock running slow when the velocity is uniform but the acceleration suffered by the travelling twin at the turn-around counteracts the effect so that in the end Divine Albert's 1905 prediction (the travelling twin returns younger), even though made without any reference to acceleration, remains gloriously valid:
Dialog about Objections against the Theory of Relativity (1918), by Albert Einstein: "...according to the special theory of relativity the coordinate systems K and K' are by no means equivalent systems. Indeed this theory asserts only the equivalence of all Galilean (unaccelerated) coordinate systems, that is, coordinate systems relative to which sufficiently isolated, material points move in straight lines and uniformly. K is such a coordinate system, but not the system K', that is accelerated from time to time. Therefore, from the result that after the motion to and fro the clock U2 is running behind U1, no contradiction can be constructed against the principles of the theory. (...) 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."
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."

Pentcho Valev

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