EINSTEIN'S RELATIVITY : TRAVELLING TWIN BOTH YOUNGER AND OLDER

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..."

As many authors show, the turning-around period is immaterial (no "strangeness" occurs during it), so, for more than a century, the whole trick has consisted in stubbornly teaching a scenario in which only a half of the mutual time dilation can be demonstrated. In this scenario, the travelling (twin's) clock moves from place to place where synchronous stationary clocks can be located - then it is easy to show that, according to special relativity, the travelling clock runs slower and the travelling twin ends up the younger. The other half of the mutual time dilation - the stationary clock runs slower and the stationary twin ends up the younger - is impossible to demonstrate.

Yet David Morin admits, in conformity with Einstein's 1918 confession, that "for the entire outward and return parts of the trip, B does observe A's clock running slow". Since the turning-around period is immaterial, this implies that the stationary twin ends up the younger, and that Einstein's relativity will have to be rejected as inconsistent. Here is a setup allowing both scenarios - the travelling twin is the younger and the stationary twin is the younger - to be run:

Consider stationary ants spread out in the rectangular line:

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

If a single ant is travelling along the rectangular line, consecutively meeting its stationary brothers, this is the original twin-paradox scenario. The travelling ant is the travelling twin which, according to Einstein's relativity, is gradually getting younger than its stationary brothers. In other words, the difference in age between the stationary ant/twin just being met and the single travelling ant/twin increases with the number of meetings..

If the single ant/twin is stationary, located in the middle of one of the sides of the rectangle, and if the other ants/twins are travelling along the rectangular line, the scenario becomes dangerous for Einstein's relativity.. In this case the theory predicts that the single stationary ant/twin is gradually getting younger than the travelling ants/twins. That is, the difference in age between the travelling ant/twin just being met and the single stationary ant/twin increases with the number of meetings.

Clearly Einstein's relativity is an inconsistency - it predicts both that the travelling twin is getting younger and that the stationary twin is getting younger.

Pentcho Valev

References showing that the turning-around period is immaterial (no "strangeness" occurs during it):

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."

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."

Pentcho Valev

According to Einstein's special relativity, time dilation is reciprocal - if two inertial observers move relative to one another, either sees the other's clock running SLOWER than his own. This is absurd but there is no formal way to prove the absurdity for the simple reason that, if both clocks are inertial, they are expected to meet only once.

In the rotating disc scenario one of the observers and his clocks are not inertial and this makes multiple meetings possible:

http://www.bartleby.com/173/23.html
Albert Einstein: "An observer who is sitting eccentrically on the disc K' is sensible of a force which acts outwards in a radial direction... (...) The observer performs experiments on his circular disc with clocks and measuring-rods. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc K', these definitions being based on his observations. What will be his experience in this enterprise? To start with, he places one of two identically constructed clocks at the centre of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it. We now ask ourselves whether both clocks go at the same rate from the standpoint of the non-rotating Galileian reference-body K. As judged from this body, the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to K in consequence of the rotation.. According to a result obtained in Section XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i.e. as observed from K."

Einstein refers to Section XII but this Section does not contain any results explaining why the (inertial) clock at the centre of the rotating disc should run FASTER than the (non-inertial) clock placed on the edge of the disc. Rather, the results in Section XII are all based on the Lorentz transformation which predicts RECIPROCAL time dilation for two INTERTIAL clocks: either INERTIAL clock (more precisely, the observer in this clock's system) sees the other INERTIAL clock running SLOW by a factor of 1/gamma = sqrt(1-(v/c)^2). The Lorentz transformation does not predict anything about a system of two clocks one of which (in this case the one on the edge of the disc) is not inertial. Yet in the above text Einstein claims (more precisely, lies) that, IN ACCORDANCE WITH THE LORENTZ TRANSFORMATION, the inertial K-clock (at the center of the disc) is running FASTER than the non-inertial K'-clock (on the edge of the disc) by a factor of gamma = 1/sqrt(1-(v/c)^2).. A similar unjustified claim (lie) can be found in Einstein's 1905 paper:

http://blog.hasslberger.com/Dingle_S...Crossroads.pdf
Herbert Dingle, SCIENCE AT THE CROSSROADS, p.27: "According to the special relativity theory, as expounded by Einstein in his original paper, two similar, regularly-running clocks, A and B, in uniform relative motion, must work at different rates.....How is the slower-working clock distinguished? The supposition that the theory merely requires each clock to APPEAR to work more slowly from the point of view of the other is ruled out not only by its many applications and by the fact that the theory would then be useless in practice, but also by Einstein's own examples, of which it is sufficient to cite the one best known and most often claimed to have been indirectly established by experiment, viz. 'Thence' [i.e. from the theory he had just expounded, which takes no account of possible effects of accleration, gravitation, or any difference at all between the clocks except their state of uniform motion] 'we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.' Applied to this example, the question is: what entitled Einstein to conclude FROM HIS THEORY that the equatorial, and not the polar, clock worked more slowly?"

It is easy to see that the rotating disc scenario actually refutes special relativity. By increasing the perimeter of the disc while keeping the linear speed of the periphery constant, one can convert clocks fixed on the periphery into VIRTUALLY INERTIAL clocks (the "gravitational field" they experience is reduced to zero). Now, in accordance with the Lorentz transformation, the (virtually inertial) observer "sitting eccentrically" on the edge of the disc (the K'-observer) sees the clock at the center of the disc (the K-clock) run SLOWER than clocks fixed on the periphery (K'-clocks).

The absurdity is demonstrated now - the clock at the center runs both FASTER than clocks on the periphery (as observed from K) and SLOWER than clocks on the periphery (as observed from K'). We just have REDUCTIO AD ABSURDUM: the consequent (reciprocal time dilation) is absurd, therefore the antecedent (Einstein's 1905 constant-speed-of-light postulate) is false.

Pentcho Valev