THE SILLIEST EXPLANATION OF THE TWIN PARADOX

http://www.feynmanlectures.caltech.e...6.html#Ch16-S2
Richard Feynman: "Just as the mu-mesons last longer when they are moving, so also will Paul last longer when he is moving. This is called a "paradox" only by the people who believe that the principle of relativity means that all motion is relative; they say, "Heh, heh, heh, from the point of view of Paul, can't we say that Peter was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet." But in order for them to come back together and make the comparison, Paul must either stop at the end of the trip and make a comparison of clocks or, more simply, he has to come back, and the one who comes back must be the man who was moving, and he knows this, because he had to turn around. When he turned around, all kinds of unusual things happened in his space ship - the rockets went off, things jammed up against one wall, and so on - while Peter felt nothing. So the way to state the rule is to say that the man who has felt the accelerations, who has seen things fall against the walls, and so on, is the one who would be the younger; that is the difference between them in an "absolute" sense, and it is certainly correct. When we discussed the fact that moving mu-mesons live longer, we used as an example their straight-line motion in the atmosphere. But we can also make mu-mesons in a laboratory and cause them to go in a curve with a magnet, and even under this accelerated motion, they last exactly as much longer as they do when they are moving in a straight line."

It takes severe megalomania to teach that the acceleration suffered by the traveller is both responsible (in Paul's case) and not responsible (in the mu-meson case) for lasting longer. Less megalomaniac Einsteinians teach either the one or the other but never both:

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://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."

Pentcho Valev

Twin paradox without any acceleration at all:

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
Introduction to Classical Mechanics With Problems and Solutions, David Morin, Cambridge University Press, Chapter 11, p. 44: "Modified twin paradox *** 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."

Pentcho Valev

In his 1918 paper:

http://en.wikisource.org/wiki/Dialog...f_rela tivity
Dialog about Objections against the Theory of Relativity, by Albert Einstein

Einstein shows that, if the turn-around acceleration suffered by the travelling twin is 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 his theory so Einstein is forced to introduce an ad hoc absurdity (there is no other way to save relativity): 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:

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."

It is easy to show that the turn-around acceleration has nothing to do with the youthfulness of the travelling twin:

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."

There are even scenarios where there is no turn-around acceleration at all and yet the travelling twin proves younger at the end of the journey:

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 *** 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."

Conclusion: The turn-around acceleration is irrelevant and can and should be ignored. On the other hand, it is the only salvation - without the miraculous "more than compensation" caused by the turn-around acceleration, the twin paradox is a blatant absurdity: 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.

Pentcho Valev

Time dilation is mutual in special relativity, which means that the travelling twin does see the sedentary twin's clock running slow:

http://www.einstein-online.info/dict.../time-dilation
"Time dilation can be mutual: When two inertial observers speed past each other, each will find that the other's clocks go slower."

In other words, as judged from the travelling twin's system, the sedentary twin is younger - his clock is slower. However if a teacher wants to both prove and calculate the slowness of the sedentary twin's clock, he/she will have to consider a scenario in which that clock commutes between and is checked against two clocks belonging to the travelling twin's system:

http://www.amazon.com/Relativity-Its.../dp/0486406768
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."

Here lies the secret of the twin paradox: Einsteiniana's teachers simply do not want to prove and calculate the slowness of the sedentary twin's clock, and accordingly do not consider scenarios in which that clock commutes between and is checked against two clocks belonging to the travelling twin's system. Such scenarios would be taught by antirelativists but they are successfully marginalized:

http://www.informaworld.com/smpp/con...ent=a909857880
Peter Hayes "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology, Volume 23, Issue 1 January 2009, pages 57-78: "The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse."

Pentcho Valev