Gravity: Effects of Curvature & Speed of Light

[tickle_monste]

General relativity describes gravity as simply the curvature of space-time. I believe that I read that the effects of this curvature are instantaneous. Is this curvature considered information? Would this mean that the information travels faster than the speed of light?

 

[mgb_phys]

The local effects of the curvature are instant - just because the curvature is already there. Changes in gravity propagate at the speed of light.

Yes a change in gravity is definitely information, if the sun disappeared we wouldn't feel a change in gravity until the loss of light was notices

 

[Nickelodeon]

The local effects of the curvature are instant - just because the curvature is already there. Changes in gravity propagate at the speed of light.

Yes a change in gravity is definitely information, if the sun disappeared we wouldn't feel a change in gravity until the loss of light was notices

Aren't the 'speed of gravity' and 'changes in gravity' different things?

The speed of gravity must vary according to how far away you are from the mass that is causing it.

 

[Fennias Bog]

Aren't the 'speed of gravity' and 'changes in gravity' different things?

The speed of gravity must vary according to how far away you are from the mass that is causing it.

seems like both terms are referring to propagation of gravitational waves, which are considered instantaneous physical responses.

 

[JesseM]

seems like both terms are referring to propagation of gravitational waves, which are considered instantaneous physical responses.

Gravitational waves move at the speed of light, what do you mean by "instantaneous physical response"?

 

[Fennias Bog]

Gravitational waves move at the speed of light, what do you mean by "instantaneous physical response"?

The curvature of s/t is essentially an instant response to the presentence of matter.
looking at the geometry visualized by s/time in SR, we see that the grav field that exists is a local instantaneous response to the presence of matter. since matter travels along geodesic lines, locality is important. the varied reasons associated with the propagation of g waves, show well that they move at c. I have seen reasonable evidence that the gravity/matter response takes place faster than gravitational propagation.

 

[JesseM]

The curvature of s/t is essentially an instant response to the presentence of matter.
looking at the geometry visualized by s/time in SR, we see that the grav field that exists is a local instantaneous response to the presence of matter.

Well, locally the electromagnetic field also responds instantaneously to the behavior of charged matter--how could it be otherwise, when "locally" means the distances you're looking at are infinitesimal?

since matter travels along geodesic lines, locality is important. the varied reasons associated with the propagation of g waves, show well that they move at c. I have seen reasonable evidence that the gravity/matter response takes place faster than gravitational propagation.

Pretty sure the curvature at any given point can be determined solely from knowledge of the curvature and matter distribution in the past light cone of that point, and likewise that it would be impossible to send a message using gravity that would arrive faster than a message using electromagnetism. If you don't disagree with either of these statements, you need to give a more precise definition of what you mean when you talk about the speed of the "gravity/matter response".

 

[atyy]

Pretty sure the curvature at any given point can be determined solely from knowledge of the curvature and matter distribution in the past light cone of that point,

Not sure about this - Minkowski and Schwarzschild solutions are both vacuum solutions (same local matter content), but their spacetime curvature is different.

 

[JesseM]

Not sure about this - Minkowski and Schwarzschild solutions are both vacuum solutions (same local matter content), but their spacetime curvature is different.

But that's why I said "can be determined solely from knowledge of the curvature and matter distribution in the past light cone of that point" rather than "can be determined solely from knowledge of the matter distribution in the past light cone of that point". I don't know for a fact that this is true, but if it wasn't it seems that by measuring the local curvature at a point you could get information about events outside the past light cone of that point, which would lead to causality violations.

 

[DaveC426913]

A field, by definition, means there is an existing value for it at every single point in the space. This is true for a gravitational field just like a magnetic field. It doesn't take time to be affected by an existing magnetic field - or gravitational field.

However, changes to the value of that field propagate at c. That includes any action that causes the field to climb from zero or fall to zero (such as switching on or off a magnetic device or creating/destroying mass).

 

[atyy]

Is this curvature considered information? Would this mean that the information travels faster than the speed of light?

Maybe something like this? Assume you and your measuring apparatus (laser, clock, ...) are not so massive as to significantly affect spacetime curvature. You can always measure your local curvature. Suppose you measure spacetime around you to be curved, and you are in vacuum - that certainly means you are not in Minkowski spacetime - can you use that information to deduce the distribution of matter far away? I think not, because the local curvature could be consistent with many distributions of matter (or black holes) far away in spacetime.

Roughly, to infer the matter distribution in the entire "past" and "future", you need to measure the matter and spatial curvature of one spacelike slice of spacetime. So you still have to measure properties of faraway points of this spacelike slice, and you so will be restricted by the speed of light.

Edit: this is not satisfactory, since if there is curvature where you are, then you do know immediately that you are not in globally Minkowski spacetime, which means you have eliminated the possibility of one entire past and future at arbitrary distances ...

 

[Fennias Bog]

A field, by definition, means there is an existing value for it at every single point in the space. This is true for a gravitational field just like a magnetic field. It doesn't take time to be affected by an existing magnetic field - or gravitational field.

However, changes to the value of that field propagate at c. That includes any action that causes the field to climb from zero or fall to zero (such as switching on or off a magnetic device or creating/destroying mass).

yep, all i was sayin'.

 

[Creator]

General relativity describes gravity as simply the curvature of space-time. I believe that I read that the effects of this curvature are instantaneous. Is this curvature considered information? Would this mean that the information travels faster than the speed of light?

This has been discussed (debated) much on the internet and even here I'm sure.

If you mean how fast does the force of gravity act between massive bodies (due to curvature or propagation) then a case could be made that we would have to conclude from the stability of Earth's orbit around the sun that it is extremely fast (if not almost instantaneous), otherwise a propagation delay would cause a gravitational "aberration" as viewed from Earth which would place the solar grav. force in a non-central position which would change the Earth's orbital angular momentum... which is not observed.

Not talking about gravitational radiation, (i.e., waves) here...but simply the force of normal gravity interaction between massive bodies.

 

[JesseM]

This has been discussed much on the internet and even here I'm sure.

If you mean how fast does the force of gravity act between massive bodies (due to curvature or propagation) then a case could be made that we would have to conclude from the stability of Earth's orbit around the sun that it is extremely fast (if not almost instantaneous), otherwise a propagation delay would cause a gravitational "aberration" as viewed from Earth which would place the solar grav. force in a non-central position which would change the Earth's orbital angular momentum... which is not observed.

Not talking about gravitational radiation, (i.e., waves) here...but simply the force of normal gravity interaction between massive bodies.

But there is no need to conclude any actual signal is moving that fast, this lack of aberration can be explained in terms of the local dynamics of the gravitational field...it's analogous to the way the electromagnetic force we feel from a moving charged body is always directed at its current position rather than its retarded position as long as it's moving at constant speed, no matter how far away it is (and if the body is accelerated, then the force will continue to be directed at the position it would have been if it had continued to move at constant velocity, until an electromagnetic wave created by the acceleration has had time to reach us and give us an 'update'). This is discussed in this entry from the Usenet Physics FAQ:

In general relativity, on the other hand, gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central--it does not point directly towards the source of the gravitational field--and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result.

This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations. Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light.

Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies--call them A and B--held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.

Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So, to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity.

 

[Nickelodeon]

But there is no need to conclude any actual signal is moving that fast, this lack of aberration can be explained in terms of the local dynamics of the gravitational field...it's analogous to the way the electromagnetic force we feel from a moving charged body is always directed at its current position rather than its retarded position as long as it's moving at constant speed, no matter how far away it is (and if the body is accelerated, then the force will continue to be directed at the position it would have been if it had continued to move at constant velocity, until an electromagnetic wave created by the acceleration has had time to reach us and give us an 'update'). This is discussed in this entry from the Usenet Physics FAQ:

What is this talk about 'force'? I thought the GR standpoint was that gravity was not a force.

 

[JesseM]

What is this talk about 'force'? I thought the GR standpoint was that gravity was not a force.

In that section I was talking about electromagnetism, not gravity. But the passage I quoted from this site noted that in the weak-field approximation, gravity can be treated as a sort of force similar to electromagnetism:

Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central--it does not point directly towards the source of the gravitational field--and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result.