# A problem in general relativity

1. Aug 6, 2011

hello,

lets say the there are two bodies that are moving at the same speed of 50% of the light speed and they both have the same mass, which body of the two will have more time dilation ?

(Sry for the bad english its just not my first or second language :) )

thanks ;)

2. Aug 6, 2011

### ghwellsjr

It sounds like you have defined a symmetrical situation so how could one have more time dilation than the other?

3. Aug 6, 2011

### mathman

Each body observes time dilation of the other body.

Note: this is question of special relativity, not general.

Last edited: Aug 6, 2011
4. Aug 6, 2011

### bcrowell

Staff Emeritus
If they're both moving in the same direction at c/2 relative to something else, then neither observes any time dilation in the other, because they're at rest relative to one another. This may seem like a pointless quibble about something that was arguably covered by the general language of your post. However, I think the OP's post sounds like s/he isn't clear on the idea that in order to talk about time dilation, you have to specify the observer's motion relative to what is being observed.

[edit -- added "in the same direction" for clarification]

Last edited: Aug 7, 2011
5. Aug 7, 2011

### IsometricPion

I take this sentence to mean: Of the time dilation factors (relative to an observer at infinity) at the surfaces of two bodies of equal http://en.wikipedia.org/wiki/Mass_in_general_relativity" [Broken] (when considered as isolated objects) which are in hydrostatic equilibrium whose velocities (defined by the average velocity of the constituents of each body) both have magnitude 0.5c, which is the larger?

As stated, this question is ill-defined. If the compositions (density profiles/equations of state) of the two planets are not the same, the part of the time dilation factor due to space-time curvature will not be the same (at the surface). Even if the planets are assumed to have the same composition, if the directions of their velocities are not known it will not be possible to answer the question. Assuming the observer in the question is at rest in the http://en.wikipedia.org/wiki/Center_of_momentum_frame" [Broken] frame (as defined by the ADM momentum of the system) then the time dilation factor will be the same for each planet in this coordinate system (assuming surface tension is negligible). (Since the planets are in hydrostatic equilibrium the time dilation factor does not vary over their surfaces. So, in this case, the planets are entirely symmetric.)

Note that the time dilation factors will, in general, be functions of time (though in the very restricted case I have delineated I think they will remain equal to each other).

Last edited by a moderator: May 5, 2017
6. Aug 7, 2011

### HallsofIvy

50% of light speed relative to what? If they are both moving at the same speed relative to a single observer, then to that observer they will have the same time dilation.