Quick question about gravity/time dilation

[Mzachman]

I'm thinking about something, but I need to know this first...

Is the time dilation from gravity caused by a net gravitational force, or by the total magnitudes of the gravities added up?

For example, would a clock floating directly between two identical planets have time pass as if it were in open space, or as 2 x the difference in time that one planet at that distance from the clock would cause?

Thanks!

 

[Jolb]

As far as I know, gravitational time dilation is only dependent on your relative gravitational potential. Therefore, if you're between two planets, the gravitational potential at you is more negative than some point at infinity. So if you were directly at the center of mass of two identical bodies of mass m in circular orbits, at a distance r from both bodies, then an observer at infinity would see your clock ticking slower than a clock orbiting a lone mass m at distance r, (ignoring angular velocities). However, I don't know enough GR to tell you whether it would be 2x slower--my intuitive guess is that it's between 1 and 2 times slower.

 

[drmichael]

As far as I know, gravitational time dilation is only dependent on your relative gravitational potential. Therefore, if you're between two planets, the gravitational potential at you is more negative than some point at infinity. So if you were directly at the center of mass of two identical bodies of mass m in circular orbits, at a distance r from both bodies, then an observer at infinity would see your clock ticking slower than a clock orbiting a lone mass m at distance r, (ignoring angular velocities). However, I don't know enough GR to tell you whether it would be 2x slower--my intuitive guess is that it's between 1 and 2 times slower.

I believe you are correct Jolb. The observed time distortion is directly porportional to the position of the clock (assuming both gravitational bodies are identical in mass and distance from the clock). There is however a theory being investigated that proposes that the rotational direction of the planets could play a factor in how they manifest their gravitational fields.

 

[bcrowell]

As far as I know, gravitational time dilation is only dependent on your relative gravitational potential. Therefore, if you're between two planets, the gravitational potential at you is more negative than some point at infinity. So if you were directly at the center of mass of two identical bodies of mass m in circular orbits, at a distance r from both bodies, then an observer at infinity would see your clock ticking slower than a clock orbiting a lone mass m at distance r, (ignoring angular velocities). However, I don't know enough GR to tell you whether it would be 2x slower--my intuitive guess is that it's between 1 and 2 times slower.

You're correct that the effect depends on the gravitational potential, and this is the point that's crucial in answering the OP's question. The potential is a scalar, not a vector, so there's no vector addition going on, and the effects don't cancel, they reinforce.

Basically the reason it can't depend on the field is that according to the equivalence principle, gravitational fields are observer-dependent.

In the limit of weak fields, the time dilation effect is simply proportional to the potential, and the potential adds linearly, so the result is that it's 2x slower. For stronger fields (e.g., if we put two black holes close together, rather than two planets), you would see deviations from this behavior. There are two reasons for this. One is that approximating time dilation as [itex]\Delta\Phi[/itex] is only an approximation to [itex]e^{\Delta\Phi}[/itex]. The other is that general relativity is a nonlinear theory, so the potentials don't add linearly.

 

[Eric McClean]

Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly clocks run. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.

This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times. The effects detected in such experiments are extremely small, with differences being measured in nanoseconds.

Gravitational time dilation was first described by Albert Einstein in 1907[1] as a consequence of special relativity in accelerated frames of reference. In general relativity, it is considered to be a difference in the passage of proper time at different positions as described by a metric tensor of spacetime. The existence of gravitational time dilation was first confirmed directly by the Pound-Rebka experiment.

 

[Mzachman]

Ok, that's what I was wondering. I was guessing that was the way it worked, but i wasn't sure.

Now, assuming that gravity "travels" at the speed of light, and that time dilation is based on gravitational potential, and not the net vector for gravity... what are the implications of this for when the gravity from more and more of the tons of objects in the universe "reach" us? Will our clocks be constantly slowing down as time goes on? This seems to suggest some sort of weird thing where clocks will go infinitely slower and slower as time goes forwards and more and more gravitational potential "reaches" us, although we would not be able to sense this, correct? I'm not really sure what this would mean, but do you have any thoughts on it?

That's what I was originally thinking about, but I had to clarify that first point before I could discuss what I was actually thinking about.

 

[Al68]

Now, assuming that gravity "travels" at the speed of light, and that time dilation is based on gravitational potential, and not the net vector for gravity... what are the implications of this for when the gravity from more and more of the tons of objects in the universe "reach" us? Will our clocks be constantly slowing down as time goes on?

No. I think the key thing with gravitational time dilation is that it's not really a different phenomena than SR (velocity-based) time dilation, and it is manifested in accelerated reference frames whether a gravitational field is present or not. The role played by a gravitational field in this sense is that the only way for two clocks to be "stationary" in a gravitational field is if they are accelerated together in an accelerated reference frame, like Earth's surface.

Consider this: Say there are two clocks, one at the top and bottom of a tall tower. From an inertial reference frame (freefall), at any specified time the clock at the bottom has a higher velocity than the clock at the top, and will therefore run slower relative to the top clock. From the accelerated frame in which the clocks are stationary, that's gravitational time dilation.

The same would be the case if the clocks were at the top and bottom of an accelerating rocket in deep space instead of a tower on earth.

 

[bcrowell]

Now, assuming that gravity "travels" at the speed of light, and that time dilation is based on gravitational potential, and not the net vector for gravity... what are the implications of this for when the gravity from more and more of the tons of objects in the universe "reach" us? Will our clocks be constantly slowing down as time goes on? This seems to suggest some sort of weird thing where clocks will go infinitely slower and slower as time goes forwards and more and more gravitational potential "reaches" us, although we would not be able to sense this, correct? I'm not really sure what this would mean, but do you have any thoughts on it?

You're correct that we would be unable to sense it. If all clocks in the universe were to slow down in lock-step, then there would be no way to detect it at all. Coordinates in general relativity, such as time, are completely arbitrary. You can do any smooth, one-to-one coordinate transformation at all, and the Einstein field equations are still valid. You get a description of all the same phenomena, with no empirically testable difference.

 

[Mzachman]

No. I think the key thing with gravitational time dilation is that it's not really a different phenomena than SR (velocity-based) time dilation, and it is manifested in accelerated reference frames whether a gravitational field is present or not. The role played by a gravitational field in this sense is that the only way for two clocks to be "stationary" in a gravitational field is if they are accelerated together in an accelerated reference frame, like Earth's surface.

Consider this: Say there are two clocks, one at the top and bottom of a tall tower. From an inertial reference frame (freefall), at any specified time the clock at the bottom has a higher velocity than the clock at the top, and will therefore run slower relative to the top clock. From the accelerated frame in which the clocks are stationary, that's gravitational time dilation.

The same would be the case if the clocks were at the top and bottom of an accelerating rocket in deep space instead of a tower on earth.

That would suggest that it's based on the vector type net acceleration of gravity. Unless those can somehow add, so that in the two planet example we would be "accelerating" both directions and once, and therefore feel no "force." Hmm...

You're correct that we would be unable to sense it. If all clocks in the universe were to slow down in lock-step, then there would be no way to detect it at all. Coordinates in general relativity, such as time, are completely arbitrary. You can do any smooth, one-to-one coordinate transformation at all, and the Einstein field equations are still valid. You get a description of all the same phenomena, with no empirically testable difference.

Ok, so technically it is possible then... It just got me thinking about the "beginning of time" and all that... It's just a strange thought to me that gravity "slows down" time, but if everywhere has more gravity applied to it (and therefore should "slow down" everywhere), we just can't apply the same idea as if there was a difference in gravity between two spots causing the difference in time. So technically, to someone on the "outside" of our universe, gravity free, if they could somehow look in they would see us slowing down and slowing down infinitely slower and time progresses, but we're just going on with our daily lives happy as ever and unknowing. That's an interesting thought.

One last question. This may be dumb since I know very little about it. I just read QED by Feynman, and he talked about anti-matter being matter going backwards through time. I'm just curious, does this cause any problems with Einstein's relativity stuff?

Thanks for all the help guys, this is intriguing stuff (especially for a physicist to be... :) ).