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Let there be two bodies a and b. Let a be on Earth and b in space with velocity $(√3/2)c$. Then let the time interval which has passed (on the earth) be twice that of the time interval of which passed in space for b, (i.e. the time for b is dilated for body a).

Does b also feel that the time interval which it passed with a spaceship in space is twice that of the time interval of a which passed on the earth? I ask this because for b relative to it, a is also moving with velocity $(√3/2)c$.

auden
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Ramesh Singh
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  • Yes. That said, I can't imagine where you found a source that explains time dilation without also explaining the relativity of velocity. Voting to close partly because this has been asked and answered a thousand times elsewhere on this site, but more fundamentally because it is surely answered in whatever text you were already reading when you learned about time dilation. – WillO Jul 22 '16 at 16:52
  • See What is time dilation really? – John Rennie Jul 22 '16 at 16:56

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Special relativity predicts that either clock runs more slowly than the other, as judged from the other clock'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 clock runs more slowly than the other (as judged from the other clock'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 "enough strangeness" idea (Einstein devised it in 1918) is simply idiotic.

Pentcho Valev
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  • Your last paragraph is completely out of place. Special relativity is well-tested and certainly not "idiotic". The "strangeness" is easily resolved within SR, cf. http://physics.stackexchange.com/q/2554/50583 – ACuriousMind Jul 22 '16 at 22:59
  • "The "strangeness" is easily resolved within SR" No. Read Einstein's 1918 article: http://sciliterature.50webs.com/Dialog.htm Albert Einstein 1918: "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." – Pentcho Valev Jul 22 '16 at 23:16