2017-06-04 10:59:51 UTC
Einstein was a powerful doublethinker. He was able to defend both thesis and antithesis with the same conviction, without any hesitation. So in 1911 he explained to the gullible world that the "sudden change of direction" is immaterial with respect to the clock (twin) paradox:
Albert Einstein 1911: "The clock runs slower if it is in uniform motion, but if it undergoes a change of direction as a result of a jolt, then the theory of relativity does not tell us what happens. The sudden change of direction might produce a sudden change in the position of the hands of the clock. However, the longer the clock is moving rectilinearly and uniformly with a given speed in a forward motion, i.e., the larger the dimensions of the polygon, the smaller must be the effect of such a hypothetical sudden change."
In 1918 the "sudden change of direction" involving acceleration, which had been immaterial a couple of years before, became crucial and produced a miraculous HOMOGENEOUS gravitational field:
Albert Einstein 1918: "A homogeneous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field. [...] 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."
Today's theoretical physicists prefer Einstein 1911 argument and teach that the "sudden change of direction" involving acceleration is immaterial, but an important minority sticks to Einstein's 1918 idiocy and teaches that the "sudden change of direction" is crucial:
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."
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."
Tim Maudlin: "...so many physicists strongly discourage questions about the nature of reality. The reigning attitude in physics has been "shut up and calculate": solve the equations, and do not ask questions about what they mean. But putting computation ahead of conceptual clarity can lead to confusion. Take, for example, relativity's iconic "twin paradox." Identical twins separate from each other and later reunite. When they meet again, one twin is biologically older than the other. (Astronaut twins Scott and Mark Kelly are about to realize this experiment: when Scott returns from a year in orbit in 2016 he will be about 28 microseconds younger than Mark, who is staying on Earth.) No competent physicist would make an error in computing the magnitude of this effect. But even the great Richard Feynman did not always get the explanation right. In "The Feynman Lectures on Physics," he attributes the difference in ages to the acceleration one twin experiences: the twin who accelerates ends up younger. But it is easy to describe cases where the opposite is true, and even cases where neither twin accelerates but they end up different ages. The calculation can be right and the accompanying explanation wrong."
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."
John Norton: "We read from these hypersurfaces that the traveling twin judges the stay-at-home twin's clock to be running at half the speed of the travelers. When the traveler's clock reads 1 day, the stay-at-home twin's reads 1/2 day; just before the turn around, when the traveler's clock is almost at 2 days, the stay-at-home twin's clock is almost at 1 day. 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. Careful attention to the differing judgments of simultaneity of the two twins shows that there is nothing paradoxical in the twin effect. The brief moment of acceleration of the traveling twin completely alters the traveler's judgments of simultaneity and this alteration is key to seeing how relativity provides a consistent account of the effect."
"The Twin Paradox is a scenario that, at first glance, seems to make nonsense out of Einstein's theory of special relativity. The situation is that a man sets off in a rocket travelling at high speed away from Earth, whilst his twin brother stays on Earth. [...] What happens is that the twin on Earth, viewing himself as stationary and his brother as moving at high speed, sees his brother experiencing time dilation and thus ageing more slowly. At the same time, the twin in the spaceship considers himself to be the stationary twin, and therefore as he looks back towards Earth he sees his brother ageing more slowly than himself. Each sees the other as moving, and therefore as experiencing time dilation. But which brother is "correct" in the way he perceives the situation? Both are. Each sees the other as being younger than himself. How they were perceived by any onlooker would depend on which frame of reference the onlooker was in. It doesn't make sense to ask which brother is "really" older, because the answer depends on where you stand to ask the question! But what about when the brother in the spaceship returns to Earth? Surely the contradiction will be apparent then? Ah, but in order to return to Earth, the spaceship must slow down, stop moving, turn around and go back the other way. During those periods of deceleration and deceleration, it is not an inertial frame and therefore the normal rules of special relativity don't apply. When the twin in the spaceship turns around to make his journey home, the shift in his frame of reference causes his perception of his brother's age to change rapidly: he sees his brother getting suddenly older. This means that when the twins are finally reunited, the stay-at-home twin is the older of the two."
The sudden ageing syndrome described in the last two quotations (and in Einstein's 1918 paper) deserves special attention - this is perhaps the greatest idiocy in the history of science:
"When the twin in the spaceship turns around to make his journey home, the shift in his frame of reference causes his perception of his brother's age to change rapidly: he sees his brother getting suddenly older. This means that when the twins are finally reunited, the stay-at-home twin is the older of the two."