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So, am I supposed to accept the fact the time dilation may not just be a relative effect, as in: it's just as an illusion, but rather, the time that is elapsing for me is actually $\gamma$ times the time, what is elapsing for the other moving person?

If so, won't he feel the same(Since, I will be moving at a speed of $-u$ relative to him)? As in, won't even he feel that he's experiencing time $\gamma t_0$ to be elapsing, and feel that only $t_0$ seconds elapses for me?

So what is 'actually' happening? Because either of them feels that time is running faster for them, compared(aka, relative?) to the other person

Qmechanic
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Swaroop Joshi
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  • They both observe the same time dilation. It is symmetric, as you point out. I'm sorry it doesn't make sense to you. If it's any consolation, it doesn't make sense to anybody, but nonetheless it is a fact. – garyp Feb 21 '20 at 03:22
  • Recommend reading the Wikipedia article on the Twin Paradox, which seems like what you're asking. https://en.wikipedia.org/wiki/Twin_paradox – Allure Feb 21 '20 at 03:38
  • Time dilation does not "absolutely happen" in either case. It is relative. – m4r35n357 Feb 21 '20 at 10:39

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Time dilation is indeed symmetric. But to get a coherent picture, you must look at all implications of the Lorentz transformation, not time dilation only

TO clarify things, suppose you and I are moving at a certain constant velocity with respect to each other and that initially we are at the same location x=0 and our clocks indicate the same time t=0.

Then, I will observe that your clock runs slower than mine, and you will observe that my clock is running slower than your. This is a fact, not an optical illusion, because time is actually a relative quantity (just as velocity is).

Consequently, while initially our clocks were synchronized, after a while we are at a certain distance from each other, and our clocks are no longer synchronized (I observe your one runs slower, you observe mine runs slower). But this is perfectly normal because in general clocks that move with respect to each other cannot be synchronized. This is called Relativity of simultaneity, which can be inferred from the Lorentz transformation:

t' = (t + ux) / sqrt(1-u^2)

The term ux here implies a delay between clocks that are far apart.

I hope this gives you a clearer picture.

Giuseppe
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