What does GR say about time dialation when one is falling vs. on the ground?

[gib65]

So, I understand that in a gravitational field, time slows down the deeper one goes into the field, but what difference does it make whether one is falling or on the ground? If I understand GR and SR correctly, then I'd assume when one is falling, you simply sum up the time dialation due to the process of falling (SR) and due to how deep one is at any point during the fall (GR). That is, when one is falling, time slows down because of the principles of SR. But in addition to that, when one falls, one ends up at deeper and deeper points in the gravitational field, and at each point, time slows down because of the principles of GR. When one is on the ground, SR would say time dialation = 0, so only GR must be taken into account. So am I right in assuming the net time dialation is the sum of the SR and GR?

 

Gib

[timo]

Good question. But not a valid one in GR. Time dilatation and length contraction can be considered as an effect of changing your base-vectors when switching from one coordinate system to another. But in GR vectors are only defined in a point of spacetime. So you -usually- can compare only vectors in the same point. And the effect of graviational time dilatation (whatever that´s supposed to be) is of course the same for all observers in one point.

 

Also note that the statement "in a gravitational field, time slows down" is vague at best. It sais that Eigentime increases slower with the time-coordinate of your coordinate system. The time-coordinate of your coordinate system, however, has little to no physical meaning.

[TrueHeart]

.. That is, when one is falling, time slows down because of the principles of SR. But in addition to that, when one falls, one ends up at deeper and deeper points in the gravitational field, and at each point, time slows down because of the principles of GR.

There you go again using sloppy wording - tsk tsk! "Time slows down" is not a truism; time slows down relative to the clock of an observer higher up in the gravitational potential field, and time slows down relative to the clock of a presumed still observer, when you are falling ie. in motion. Time dilation attributable to relative motion is a purely mutual effect, ie. he sees your clock run slow and you see his clock run slow. Gravitational time dilation (as its called) has an unambiguous orientation: the one deeper down in the G-field perceives clocks of one higher up to run fast, while the higher up one perceives the deeper down one to run slow.

[gib65]

Okay, okay, sorry about the wording. But from what you're saying, it seems like the concept I was trying to get across is correct. From the POV of someone higher up in the gravitational field, a clock that is deeper into the gravitational field will appear to be running slower than one that he is carrying. If the deeper clock is also falling then the observer higher up in the gravitational field will see the deeper clock, at a given point, moving even slower than if it was still at that same point. Right?

[TrueHeart]

Yes, correct; at least that's how I understand it to be!

[CPL.Luke]

but then the question of time dialation do to velocity, to those who know more about relativity is the question not applicable? or...

[Pete]

So, I understand that in a gravitational field, time slows down the deeper one goes into the field, but what difference does it make whether one is falling or on the ground? If I understand GR and SR correctly, then I'd assume when one is falling, you simply sum up the time dialation due to the process of falling (SR) and due to how deep one is at any point during the fall (GR). That is, when one is falling, time slows down because of the principles of SR. But in addition to that, when one falls, one ends up at deeper and deeper points in the gravitational field, and at each point, time slows down because of the principles of GR. When one is on the ground, SR would say time dialation = 0, so only GR must be taken into account. So am I right in assuming the net time dialation is the sum of the SR and GR?

There are two time dilation effects in relativity. One is gravitational time dilation and there is time dilation due to a motion. The specifics of the problem and question will determine the exact response that you're looking for. I.e. who is measuring what etc.

 

Let consider a specific example ("time orthogonal spacetime"/no frame dragging). In such a field time intervals dt (time measured by 'coordinate' observer - precise meaning depends on exact situation) are related to proper time intervals, dT (time read by clock which is in g-field and moving), by

 

dt/dT = 1/sqrt(1 + 2*Phi/c² - v²/ c²)

 

where v = speed of particle and Phi = gravitational potential.

 

Consider, for example, a person who is in free-fall in a uniform g-field. Then to that free-fall observer no gravitational field exists anywhere (Phi = 0 everywhere in region where field is uniform) so there is no gravitational time dilation to speak of. There is only time dilation due to motion. If, however, the gravitational field is not uniform then the gravitational field does not vanish everywhere for a free-fall observer and in general there will be gravitational time dilation.

 

In case I made an error please see the Global Positioning System (GPS) example in Taylor and Wheeler's book at

http://www.eftaylor.com/pub/projecta.pdf

 

Pete