EINSTEIN AND THE TWIN PARADOX

Einstein's 1918 paper:

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

implies that, if the turn-around acceleration suffered by the travelling twin is immaterial, 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: in the short period when the travelling twin sharply turns around and suffers acceleration (is "at a higher gravitational potential" than his sedentary brother), the sedentary twin becomes much older than the traveller who stays young thanks to the gravitational potential:

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."

It is easy to show that the turn-around acceleration ("gravitational potential") 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."

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."

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

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."

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."

Conclusion: The turn-around acceleration ("gravitational potential") is irrelevant and can and should be ignored. On the other hand Einstein shows in his 1918 paper that the gravitational potential is the only salvation for his theory. No "gravitational potential", no miraculous jumping of the stay-at-home twin's clock ("from reading 1 day to reading 7 days"), and the twin paradox becomes 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

That the travelling twin remains younger is a consequence of Einstein's 1905 constant-speed-of-light postulate. There is a specific scenario, introduced by Einstein in 1905, which favours the deduction of this consequence and not the opposite one. In a different scenario, however, the deduction of the opposite consequence is favoured - it is the sedentary twin that remains younger. Let us assume that the ants moving along the rectangular line are travelling at 87% the speed of light:

http://www.wpclipart.com/page_frames...e_portrait.png

It is easy to show that, according to Einstein's relativity, a single sedentary ant watching its brothers go by at 87% the speed of light ages half as fast as them.

Clearly we have reductio ad absurdum which means that the underlying postulate, the principle of constancy of the speed of light, is false. The speed of light (relative to the observer) does vary with the speed of the emitter, as established by Newton's emission theory of light.

Pentcho Valev

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."

Don Lincoln directly contradicts Einstein. The two frames the travelling twin inhabits correspond to "partial processes 2 and 4" in Einstein's 1918 paper. In these processes the travelling twin sees the sedentary twin's clock run slow, but, according to Einstein, "this is more than compensated" during the short turn-around period when the twins' clocks are located at different gravitational potentials and, as a result, the sedentary twin's clock runs much faster:

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."

By alternating, for more than a century, the suggestions "acceleration (gravitational potential) matters" and "acceleration (gravitational potential) does not matter", Einsteinians have converted the original absurdity into a dreadful labyrinth that sane people are reluctant to enter nowadays.

Pentcho Valev

The turning-around acceleration both matters and does not matter (in Divine Albert's world):

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. 14: "Example (Twin paradox): Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox..."

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."

This is not true or, more precisely, it is only half of the special relativity's prediction. The other half (which converts the prediction into an absurdity) says that, as judged from the moving clock's system, it is the clock at B which lags behind. The only difference between the two clocks is that the clock at A experiences acceleration at the start, but Einstein certainly did not take this initial acceleration into account in 1905. Even later, in 1918, he only considered the turn-around acceleration, not the initial one.

Pentcho Valev