Discussion:
Absurdity Called Einstein's Twin Paradox
(trop ancien pour répondre)
Pentcho Valev
2016-07-15 17:51:40 UTC
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Special relativity predicts that either twin ages more slowly than the other, as judged from the other twin's system:

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] 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."

Special relativity's prediction that either twin ages more slowly than the other (as judged from the other twin's system) leads to absurdity unless "enough strangeness occurs during the turning-around period to make A end up older". However, during the turning-around period, the traveling twin is very far away from his stationary brother so the idea that "enough strangeness" is somehow produced during the turning-around period and this "enough strangeness" miraculously affects the distant stationary twin is simply idiotic.

Pentcho Valev
Pentcho Valev
2016-07-17 11:15:57 UTC
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Einstein's twin paradox is an absurdity unless an additional ad hoc assumption is correct: the acceleration ("gravitational field", in Einstein's words) experienced by the traveling twin in the turning-around period generates "enough strangeness", and this "enough strangeness" makes the distant stationary twin age very fast:

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] 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."

http://sciliterature.50webs.com/Dialog.htm
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."

The additional ad hoc assumption (the turning-around acceleration makes the distant stationary twin age very fast) is idiotic of course, and accordingly the twin story is an absurdity, not a paradox. All clever Einsteinians know that the turning-around acceleration is immaterial and in some twin-paradox scenarios even does not exist:

http://www.scientificamerican.com/article/how-does-relativity-theor/
Ronald Lasky: "Since relativity says that there is no absolute motion, wouldn't the brother traveling to the star also see his brother's clock on the earth move more slowly? If this were the case, wouldn't they both be the same age? This paradox is discussed in many books but solved in very few. When the paradox is addressed, it is usually done so only briefly, by saying that the one who feels the acceleration is the one who is younger at the end of the trip. Hence, the brother who travels to the star is younger. While the result is correct, the explanation is misleading. Because of these types of incomplete explanations, to many partially informed people, the accelerations appear to be the issue. Therefore, it is believed that the general theory of relativity is required to explain the paradox. Of course, this conclusion is based on yet another mistake, since we don't need general relativity to handle accelerations. The paradox can be unraveled by special relativity alone, and the accelerations incurred by the traveler are incidental." [Note that in 1918 Einstein is one of those "partially informed people".]

http://www.pbs.org/wgbh/nova/blogs/physics/2015/04/physics-needs-philosophy/
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."

http://www.fnal.gov/pub/today/archive/archive_2014/today14-05-02_NutshellReadMore.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://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."

Pentcho Valev

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