I can't understand time dilation in absence of absolute motion.

[Soumya_M]

According to theory of relativity there is no absolute standard of rest. Now, if Alice and Bob are two observers floating in space, so that Alice thinks that she is at rest and Bob is moving away from her at a speed comparable to that of light and Bob thinks that he is at rest and Alice is moving away from him at a speed comparable to that of light, whose time will be dilated?

 

[Dale]

whose time will be dilated?

In which frame?

 

[Doc Al]

whose time will be dilated?

The other person's.

 

[Soumya_M]

In which frame?

In both the frames. Could it be that both frames have time dilated with respect to each other? How does time dilation make sense that way?

 

[Soumya_M]

The other person's.

What will happen if Alice and Bob compare their clocks? Alice's clock will be faster than Bob's or the other way? If both show the same time - where is the dilation?

 

[Doc Al]

What will happen if Alice and Bob compare their clocks? Alice's clock will be faster than Bob's or the other way? If both show the same time - where is the dilation?

The only way for them to directly compare their clocks is for one or both of them to turn around and join the other. That changes everything. (Look up the 'twin paradox'.)

But the important point is that between inertial frames the relativistic effects (time dilation, length contraction) are completely symmetric. To ask which clock is really dilated is to miss the point.

 

[HallsofIvy]

You cannot have "absolute time" if you don't have "absolute speed". If you have relative speed then you must have relative time.

That is, Alice, observing Bob's clock as he goes whizzing past her, sees Bob's clock as running slower then hers. Bob, observing Alice's clock as she goes whizzing past him, sees her clock as running slower than his. That is what "time dilation" means.

 

[Dale]

Could it be that both frames have time dilated with respect to each other?

Yes.

How does time dilation make sense that way?

Because it is relative, as HallsOfIvy mentioned.