Time Dilation: When Earth or Light Speed Travel?

[Anis SNOUSSI]

according to the general relativity, if someone stayed on Earth and another person was traveling near the speed of light, time will go slower for who's traveling faster.
but we all know that the universe has no center, so no frame of reference, then if we consider the person moving to be at rest, and that Earth is moving, wouldn't time flows slower for who's on Earth instead!?

 

[BvU]

Hello Anis,

Actually, time will go at the same rate for both (one hour per hour, so to say).
In the Twin paradox thought experiment it is clear who is doing the traveling and who is stationary: the traveller is the one who accelerates to depart, accelerates to turn around and decelerates upon arrival. That is the one who changes frames of reference, not the one who remains on earth.

The motion of the Earth around the sun is so slow that it doesn't have any influence.

 

[HallsofIvy]

according to the general relativity, if someone stayed on Earth and another person was traveling near the speed of light, time will go slower for who's traveling faster.
but we all know that the universe has no center, so no frame of reference, then if we consider the person moving to be at rest, and that Earth is moving, wouldn't time flows slower for who's on Earth instead!?

Relative to the person who is staying on earth, the person "traveling" is moving faster so his time flows slower. Relative to the person "traveling", it is the person staying on Earth who is moving faster so his time flows slower. Each observes the other time flowing slower. That is why it is called relativeity.