# Who is traveling in future? [duplicate]

According to theory of relativity time dilation $$t=t_0 \gamma \text{ where }\gamma= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ suppose time for a person $$A$$ is $$t$$

and time for a person $$B$$ is $$t_0$$

Both are moving with reference to each other according to theory of relativity there is no such thing like inertial frame of reference magnitude of their velocity is $$v$$.

for $$B$$ . $$A$$ is moving with velocity $$v$$ magnitude

So time dilation for $$B$$ is $$t_0=t\gamma$$

for $$A$$ . $$B$$ is moving with velocity $$v$$ magnitude

So time dilation for $$A$$ is $$t=t_0\gamma$$

for $$B$$,$$A$$ is traveling in future

for $$A$$, $$B$$ is traveling in future

I am confused who is actually traveling in future. I am beganner so kindly explain in simple way. I have this question for long time it always confuses me .

The formula you wrote

$$t = t_0 \gamma$$

is actually incorrect, the right one is with time intervals rather than absolute time

$$\Delta t = \gamma \Delta t_0$$

where you wrote correctly that $$\gamma = \frac{1}{\sqrt{1-\beta^2}}$$ and $$\beta = \frac{v}{c}$$. This means that if a clock is moving with some speed with respect to our frame, then we would see that clock moving at a different speed when confronting it with our clock (stationary in our frame) and since $$\gamma\geq 1$$ the time interval is always dilated, namely clocks moving with some speed always tick slower.

This is true for both $$A$$ and $$B$$ traveling with a relative speed of $$v$$. On one end $$A$$ observes $$B$$ traveling at $$v$$, on the other hand $$B$$ observes $$A$$ traveling at $$v$$. Both see the other's clock moving slower.

This is of course counterintuitive, the "mistery" is resolved noticing that special relativity only works for inertial frames. If at some point $$A$$ and $$B$$ wanted to stop and check their time, at least one of them (say $$A$$) would have to accelerate (to either brake or catch up to B) and the special relativity description would no longer apply to $$A$$ since its reference frame wouldn't be inertial anymore. Then only the description of $$B$$ (who stayed in an inertial frame all the time) would be the correct one. Take a look at the twin paradox for details.

• Well explained thanks 😊 a little mistake $\beta=\frac{c}{v}$ Apr 29, 2022 at 5:32
• thanks, I corrected the formula. Apr 29, 2022 at 13:49
• "special relativity would stop working"?!??!!!?? May 3, 2022 at 4:54
• see if you like the new phrasing May 3, 2022 at 10:55