Pentcho Valev
2013-10-06 07:45:10 UTC
According to special relativity, time dilation is mutual so each inertial observer sees the other inertial observer's clock go slower. This implies that, if the effects of the turn-around acceleration suffered by the travelling twin can be ignored, the travelling twin returns both younger (as judged from the sedentary twin's system) and older (as judged from the travelling twin's system) than his sedentary brother. This is obviously fatal for special relativity so in 1918 Einstein was forced to introduce an ad hoc absurdity (there was no other way to save the theory): According to the travelling twin, the sedentary twin's clock runs slow all along but "this is more than compensated" when the traveller sharply turns around and experiences acceleration in the process:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Dialog about Objections against the Theory of Relativity, Albert Einstein 1918: "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 [traveller sharply turns around] U2 [the travelling twin's clock] happens to be located at a higher gravitational potential than U1 [the sedentary twin's clock]. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 [traveller moves with constant speed away from sedentary brother] and 4 [traveller moves with constant speed towards sedentary brother]."
So in the last century scientists' minds had to oscillate between two contradictory wisdoms taught by Einsteinians:
Wisdom 1: The turn-around acceleration suffered by the travelling twin is responsible for her youthfulness and cannot be ignored:
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_tachyon/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."
Wisdom 2: The turn-around acceleration suffered by the travelling twin is not responsible for her youthfulness and can be ignored:
http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartI_SpecialRelativity2010.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.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics With Problems and Solutions, David Morin, Cambridge University Press, Chapter 11, p. 44: "Modified twin paradox *** [There is no turn-around acceleration at all] Consider the following variation of the twin paradox. A, B, and C each have a clock. In A's reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero. Also, in A's reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B's. Finally, when C passes A, they compare the readings on their clocks."
Nowadays scientists' minds do not oscillate between the two contradictory wisdoms anymore. Einsteinians continue to teach them but of all official scientists in Divine Albert's world not one could think of a reason why the contradiction should be discussed, let alone resolved. Just the late effects of doublethink:
Loading Image...
http://ebooks.adelaide.edu.au/o/orwell/george/o79n/chapter2.9.html
"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them. The Party intellectual knows in which direction his memories must be altered; he therefore knows that he is playing tricks with reality; but by the exercise of doublethink he also satisfies himself that reality is not violated. The process has to be conscious, or it would not be carried out with sufficient precision, but it also has to be unconscious, or it would bring with it a feeling of falsity and hence of guilt. Doublethink lies at the very heart of Ingsoc, since the essential act of the Party is to use conscious deception while retaining the firmness of purpose that goes with complete honesty. To tell deliberate lies while genuinely believing in them, to forget any fact that has become inconvenient, and then, when it becomes necessary again, to draw it back from oblivion for just so long as it is needed, to deny the existence of objective reality and all the while to take account of the reality which one denies - all this is indispensably necessary."
Pentcho Valev
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Dialog about Objections against the Theory of Relativity, Albert Einstein 1918: "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 [traveller sharply turns around] U2 [the travelling twin's clock] happens to be located at a higher gravitational potential than U1 [the sedentary twin's clock]. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 [traveller moves with constant speed away from sedentary brother] and 4 [traveller moves with constant speed towards sedentary brother]."
So in the last century scientists' minds had to oscillate between two contradictory wisdoms taught by Einsteinians:
Wisdom 1: The turn-around acceleration suffered by the travelling twin is responsible for her youthfulness and cannot be ignored:
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_tachyon/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."
Wisdom 2: The turn-around acceleration suffered by the travelling twin is not responsible for her youthfulness and can be ignored:
http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartI_SpecialRelativity2010.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.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics With Problems and Solutions, David Morin, Cambridge University Press, Chapter 11, p. 44: "Modified twin paradox *** [There is no turn-around acceleration at all] Consider the following variation of the twin paradox. A, B, and C each have a clock. In A's reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero. Also, in A's reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B's. Finally, when C passes A, they compare the readings on their clocks."
Nowadays scientists' minds do not oscillate between the two contradictory wisdoms anymore. Einsteinians continue to teach them but of all official scientists in Divine Albert's world not one could think of a reason why the contradiction should be discussed, let alone resolved. Just the late effects of doublethink:
Loading Image...
http://ebooks.adelaide.edu.au/o/orwell/george/o79n/chapter2.9.html
"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them. The Party intellectual knows in which direction his memories must be altered; he therefore knows that he is playing tricks with reality; but by the exercise of doublethink he also satisfies himself that reality is not violated. The process has to be conscious, or it would not be carried out with sufficient precision, but it also has to be unconscious, or it would bring with it a feeling of falsity and hence of guilt. Doublethink lies at the very heart of Ingsoc, since the essential act of the Party is to use conscious deception while retaining the firmness of purpose that goes with complete honesty. To tell deliberate lies while genuinely believing in them, to forget any fact that has become inconvenient, and then, when it becomes necessary again, to draw it back from oblivion for just so long as it is needed, to deny the existence of objective reality and all the while to take account of the reality which one denies - all this is indispensably necessary."
Pentcho Valev
