TWIN PARADOX : A COMPLEMENTARY SCENARIO

[Pentcho Valev]

A clock on the ground is at rest but a train is moving to and fro so that the clock on the ground effectively commutes between the front and the back of the train. The speed of the train is constant except for the turn-arounds when clocks on the train suffer sharp acceleration. Will the clock on the ground run slower or faster than clocks on the moving train?

It should be noted that a clock at the front of the moving train coincides with the travelling twin's clock in the usual twin paradox scenario. Accordingly, relativity predicts that the clock at rest on the ground runs FASTER than the clock at the front of the train.

On the other hand, the same relativity predicts that, all along, except possibly for the turn-arounds (?), observers on the moving train measure the clock at rest on the ground to run SLOWER than clocks on the train.

So if the turn-arounds can be ignored, that is, if calculations are entirely based on the inertial phases of the movement, we have REDUCTIO AD ABSURDUM. The clock at rest on the ground runs faster, as judged from the ground, and slower, as judged from the train, than clocks on the train. The underlying postulate, the principle of constancy of the speed of light, is false and should be rejected.

Can the turn-arounds be ignored? Some Einsteinians, fellows of the Royal Society, say yes:

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."

Other Einsteinians may disagree but then they will have to explain, IN TERMS OF TURN-AROUND ACCELERATION, why Jill, by travelling twice as far, increases twice the amount of time gained.

Pentcho Valev

[Pentcho Valev]

In 1905 Divine Albert (more precisely, still Albert the Plagiarist at that time) ignores the turn-around acceleration and any other acceleration and shocks the world: "by the clock which has remained at rest the travelled clock on its arrival at A will be tv^2/2c^2 second slow". He forgets to add that, according to the Lorentz transforms he has just "deduced" (more precisely, plagiarized), time dilation is mutual and by the travelled clock it is the clock which has remained at rest that is tv^2/2c^2 second slow:

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. It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide. If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be tv^2/2c^2 second slow."

In 1918 Divine Albert does not ignore and does not forget anything but the world is shocked again: yes, time dilation in the inertial phases is mutual but "the calculation" shows that the turn-around acceleration of the travelling clock somehow makes the clock at rest "jump" so that the 1905 glorious conclusion is confirmed: "the travelled clock on its arrival at A will be tv^2/2c^2 second slow":

http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
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."

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."

Clever Einsteinians know that "the calculation" Divine Albert refers to in his 1918 paper does not and cannot exist, but they also know that without recourse to the turn-around acceleration the contradictory "theory" is doomed. So desperate idiotic statements like the following one, written by very clever Einsteinians, can be found in the relativistic literature:

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