Deflection of light and gravity

[Thinkor]

Light is deflected in a gravitational field and this effect has been measured empirically, confirming the predictions of GR.

Gravity is also deflected in a gravitational field according to GR, the geodesics for light and gravity being the same, but has any deflection of gravity ever been empirically detected? If so, has it been confirmed to be close to the deflection of light?

(My guess is the answers are No and No, because of the difficulty of detecting deflection, but experimentalists are sometimes very clever in finding indirect confirmations of theoretical predictions.)

 

[PAllen]

Light is deflected in a gravitational field and this effect has been measured empirically, confirming the predictions of GR.

Gravity is also deflected in a gravitational field according to GR, the geodesics for light and gravity being the same, but has any deflection of gravity ever been empirically detected? If so, has it been confirmed to be close to the deflection of light?

(My guess is the answers are No and No, because of the difficulty of detecting deflection, but experimentalists are sometimes very clever in finding indirect confirmations of theoretical predictions.)

The closest thing to what you are describing would be deflection of gravitational waves (rather than gravity per se). Gravitational waves do not exactly follow null geodesics except in approximations (that are highly accurate for plausible scenarios). Anyway, no gravitational waves have been detected at all, and from there to detecting deflection would be mind bogglingly harder.

 

[Thinkor]

The closest thing to what you are describing would be deflection of gravitational waves (rather than gravity per se). Gravitational waves do not exactly follow null geodesics except in approximations (that are highly accurate for plausible scenarios). Anyway, no gravitational waves have been detected at all, and from there to detecting deflection would be mind bogglingly harder.

Yes, but the existence of gravitational waves has at least been supported by observation of how fast certain binary star systems are losing energy, if I remember correctly. Aren't there any consequences of the deflection of gravity that can be detected in such an indirect way?

 

[PAllen]

Yes, but the existence of gravitational waves has at least been supported by observation of how fast certain binary star systems are losing energy, if I remember correctly. Aren't there any consequences of the deflection of gravity that can be detected in such an indirect way?

Yes, that is strong indirect evidence of their existence, but you can't measure anything about deflection that way. You need to be able to detect precise direction of source as it passes behind some large mass. We are very, very far from being able to do that with gravitational waves.

 

[pervect]

At the risk of making this thread longer, but in the interest of clarity, I should make a few comments. If we consider first the case of electromagnetism, we see that light, or electromagnetic radiation, aberrates, as has been measured experimentally, but the coulomb force between charges does NOT aberrate in the same manner. To be more specific, see Steve Carlips paper http://arxiv.org/abs/gr-qc/9909087

lt is well known that if a charged source moves at a constant velocity, the electric field experienced by a test particle points toward the source’s “instantaneous” position rather than its retarded position. Lorentz invariance demands that this be the case, since one may just as well think of the charge as being at rest while the test particle moves. This effect does not mean that the electric field propagates instantaneously; rather, the field of a moving charge has a velocity-dependent component that cancels the effect of propagation delay to first order and furthermore cannot aberrate if angular momentum is to be conserved.

Similar results apply to gravity, though the details are more complex, and the absence of dipole gravity means that the propagation delay effects are canceled to a higher order. This is discussed in the reference above. The main point is that one should not expect the "force" of gravity to aberrate in the same manner as waves would, while one should expect that gravity waves would aberrate in the same manner that light waves do.

This "debate" historically occurs with respect to the "speed of gravity" rather than its "deflection".

 

[Bill_K]

Gravitational waves do not exactly follow null geodesics except in approximations (that are highly accurate for plausible scenarios).

Doesn't the same qualification need to be made for electromagnetic waves?

 

[PAllen]

Doesn't the same qualification need to be made for electromagnetic waves?

Strictly, yes, but I was referring to GW tails, which, so far as I know, are not associated with EM radiation.

http://arxiv.org/abs/gr-qc/9710038

 

[Thinkor]

Yes, that is strong indirect evidence of their existence, but you can't measure anything about deflection that way. You need to be able to detect precise direction of source as it passes behind some large mass. We are very, very far from being able to do that with gravitational waves.

I'm beginning to think that I have a major misunderstanding here. I assumed that in any configuration of masses, the deflection of gravity is going to have an effect, for example, in the Earth and moon system, but any such effect has to be accounted for in the minimization of the action (as in Einstein-Hilbert action).

Minimization of the action is minimization of the curvature of spacetime. There is no concept of deflection in GR. That exists only in coordinate space and time, where the image of a geodesic appears as a curving trajectory. To test it we'd have to find an exact solution, or a close approximation to one, in coordinate space and time, where we would see a deflection, and then we'd have to compare it with observation.

For example, maybe this could be done with the Earth-Moon. You might then find an error in GR, but I don't see how that could be traced to deflection rather than some other problem.

 

[pervect]

I'm beginning to think that I have a major misunderstanding here. I assumed that in any configuration of masses, the deflection of gravity is going to have an effect, for example, in the Earth and moon system.

The conservation of angular momentum means that the Earth and moon will essentially be attracted along the line joining their centers of mass, according to the instantaneous position and not the retarded position.

A *very small* amount of angular momentum is carried away by gravitational radiation, so it's not exactly along the instantaneous line connecting the center of masses. But for all practical purposes the difference is negligible. The electromagnetic case is similar when there is no significant emission of electromagnetic radiation, the attraction is not retarded in that case either.

 

[Thinkor]

The conservation of angular momentum means that the Earth and moon will essentially be attracted along the line joining their centers of mass, according to the instantaneous position and not the retarded position.

A *very small* amount of angular momentum is carried away by gravitational radiation, so it's not exactly along the instantaneous line connecting the center of masses. But for all practical purposes the difference is negligible. The electromagnetic case is similar when there is no significant emission of electromagnetic radiation, the attraction is not retarded in that case either.

I think my problem is that I didn't understand gravitational radiation. Suppose you have two rigid planets connected by a rigid bar of negligible weight, isolated in space. Then there would be no gravitational radiation, right? In general there is no gravitational radiation in any isolated static system, right?

 

[PAllen]

I think my problem is that I didn't understand gravitational radiation. Suppose you have two rigid planets connected by a rigid bar of negligible weight, isolated in space. Then there would be no gravitational radiation, right? In general there is no gravitational radiation in any isolated static system, right?

Correct, no GW in a static set up.

 

[Thinkor]

Thank you.