Does the following hold:

If we have:

  • person A moving at a speed of $0$;
  • person B moving at a speed of $xC$ (where $C$ is speed of light, $x$ a fraction)

And if time passes for $m$ minutes, does it hold that after those $m$ minutes

  • time passed $m \gamma$ minutes for person A;
  • time passed $m$ minutes for person B?

Where $\gamma$ is obtained using the Lorentz Transformation:


in which $v = xC$

This should imply that person B has travelled in time as a consequence of having a higher speed?


closed as unclear what you're asking by ACuriousMind, John Rennie, Kyle Oman, Kyle Kanos, yuggib Jun 23 '15 at 9:26

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  • $\begingroup$ When you say "has traveled in time" to which time are you referring to ? $\endgroup$ – Joelafrite Jun 22 '15 at 8:58
  • $\begingroup$ @Joelafrite The time for person B relative to person A. So after those $m$ minutes, how many minutes is person A older than person B (as person B should be the one that is travelling in time as he is moving at greater speed, but for him the time passed was also only $m$ minutes)? $\endgroup$ – JohnAndrews Jun 22 '15 at 9:04
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    $\begingroup$ That is correct but if you want to talk about time travel (forward time travel) You have to decelerate $B$ until $x \ll 1$ and compare the time passed for $A$ and the time passed for $B$. $\endgroup$ – Joelafrite Jun 22 '15 at 9:50
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    $\begingroup$ "person A moving at a speed of 0;" Anytime you write "at speed" in relativity without saying (or at least meaning) "relative to ..." you are making a mistake. In this case the mistake is implicitly privileging your own frame of reference above others. That is wrong and misses the whole point. $\endgroup$ – dmckee Jun 22 '15 at 14:45
  • $\begingroup$ I saw this app passing by: play.google.com/store/apps/… $\endgroup$ – JohnAndrews Jul 19 '15 at 17:17

John, have a look at the simple inference of time dilation due to relative velocity. If you and I are identical twins, and you take a fast out and back trip, when you come back we agree that you've experienced less time than me. As you pointed out, we can relate this to the Lorentz factor and write: $$\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$ But there's no time travel involved. The Lorentz factor is just a simple application of Pythagoras's theorem, which "works" because of the wave nature of matter. The hypotenuse of a right-angled triangle represents the light path where c=1 in natural units. The base represents your speed as a fraction of c. The height gives the Lorentz factor $\gamma$, where we use a reciprocal to distinguish time dilation from length contraction.

enter image description here Public domain image by Mdd4696, see Wikipedia

There's no actual time travel because I could have watched you every inch of the way through my telescope. You don't disappear from the present and end up living in the middle of next week. You just lived your life a bit slower than me, that's all. An extreme example of this sort of thing is given by the stasis box from the old Larry Niven science fiction stories. No motion at all occurs inside the stasis box. Light doesn't move, electrochemical signals don't move, nothing moves. So when I shut you inside the stasis box for five years, it's like I closed the door then opened it again immediately. You might think you've travelled to the future. But you didn't travel. Instead you didn't move at all whilst everything else did.

  • $\begingroup$ Thanks for that clear explanation. I see/saw it as time travel as the result implies that time moves quicker/slower for the persons. Moreover, if I travel at a high speed in circles arround the earth, I will age much less than the people on earth. So then we get like in interstellar that my daughter is older than I am when I return to earth. $\endgroup$ – JohnAndrews Jun 22 '15 at 22:37
  • $\begingroup$ Just a follow up: what does it mean that "time moves faster" or "slower" for one person relative to another. What is the scientific explanatiom for such a thing? Like, what do you observe through that telescope? $\endgroup$ – JohnAndrews Jun 22 '15 at 23:17
  • $\begingroup$ It isn't time per se that moves slower. It's everything that moves. Things like hearts and blood and nerve impulses, and clocks and electronics and light. We say time goes slower, but that's just a figure of speech. When I look through my telescope I can't see any actual thing called time going anywhere, or slower. But as I pan to keep up with you, I can see you going slower. And your clock, and everything else in there with you. Think of the parallel-mirror light-clock. The "local" motion inside your spaceship plus the macroscopic motion of yourspaceship cannot exceed the speed of light. $\endgroup$ – John Duffield Jun 23 '15 at 12:23
  • $\begingroup$ I saw this app passing by: play.google.com/store/apps/… $\endgroup$ – JohnAndrews Jul 19 '15 at 17:17

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