Does a free falling charge radiate ?

[PAllen]

http://arxiv.org/abs/1206.6538 has interesting comments about GW from binaries.

Great find! This did not exist when I last looked (2011). It will take much time to digest...

 

[PeterDonis]

we don't have such a metric for a spacetime compatible with GWs.

Perhaps not for sources, but we do for detectors like LIGO and LISA. By the time a GW reaches such a detector, it's weak enough to be treated by linearized GR. MTW has at least one whole chapter on this IIRC (my copy isn't handy right now to check).

Yes, but that motion has to be disturbed to register a GW.

You're missing the point: the geodesic motion *is* the "disturbance". Saying that the mirrors follow geodesics that have bumps and wiggles in them, and saying that the mirrors are disturbed by the GW, are different ways of saying the same thing. There is no "disturbance" over and above the behavior of the geodesics due to the time-dependence of the metric.

 

[TrickyDicky]

Perhaps not for sources, but we do for detectors like LIGO and LISA. By the time a GW reaches such a detector, it's weak enough to be treated by linearized GR. MTW has at least one whole chapter on this IIRC (my copy isn't handy right now to check).

I thought the thread's discussion (though switching back and forth from EM source to gravitational source here and there) was more centered in the sources.

You're missing the point: the geodesic motion *is* the "disturbance". Saying that the mirrors follow geodesics that have bumps and wiggles in them, and saying that the mirrors are disturbed by the GW, are different ways of saying the same thing. There is no "disturbance" over and above the behavior of the geodesics due to the time-dependence of the metric.

This point seems worth being missed because IMO it contradicts basic concepts in GR. For instance I guess this quote from wikipedia "Spacetime" must not be righ to you:
"The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences."
I consider GWs an external influence, don't you?

Maybe it would be interesting here to consider absolute gravitometers that are a type of accelerometers that work by directly measuring the acceleration of a mass during free fall in a vacuum that includes a retroreflector and a Michelson interferometer so interferometry is also used. I don't think this is a very different mechanism ultimately (obviously the details are very different, the gravitometer is attached to the ground for one but so are all ground-based GW detectors) from that used in LIGO to detect GWs, the detector is ultimately a very specialized , very sensitive type of accelerometer.
I've read you in several threads defining geodesic motion as that which reads no acceleration in an accelerometer. But now you define geodesics as something that includes exactly the type of "bumps and wiggles" disturbances that an accelerometer should measure.
That is odd. I mean you don't bring up the time-dependence of the metric when talking about the absolute acceleration notion in GR.

 

[PeterDonis]

"The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences."
I consider GWs an external influence, don't you?

This is a good example of why Wikipedia is not to be trusted. By "external influences", they really mean non-gravitational external influences. GWs are not a non-gravitational external influence. They are fluctuations in spacetime curvature.

the detector is ultimately a very specialized , very sensitive type of accelerometer.

No, it isn't. It doesn't measure proper acceleration; it measures fluctuations in spacetime curvature, which manifest as fluctuations in the proper distance between two endpoints that are moving on geodesics.

I mean you don't bring up the time-dependence of the metric when talking about the absolute acceleration notion in GR.

Because proper acceleration is curvature of the *path*, not spacetime; it is a different thing from curvature of spacetime, time-varying or otherwise. Here we're talking about curvature of spacetime; the paths of the mirrors in the GW detector are straight, but they're straight in a manifold that's curved, and whose curvature varies with time.

 

[TrickyDicky]

No, it isn't. It doesn't measure proper acceleration; it measures fluctuations in spacetime curvature, which manifest as fluctuations in the proper distance between two endpoints that are moving on geodesics.

It isn't exactly a regular accelerometer as I said, in fact rather than proper acceleration what GW detectors measure are variations ("fluctuations") in proper acceleration, much like gravity gradiometers do.
Even though WP is not the most reliable source this seems accurate: "Pairs of accelerometers extended over a region of space can be used to detect differences (gradients) in the proper accelerations of frames of references associated with those points. These devices are called gravity gradiometers, as they measure gradients in the gravitational field. Such pairs of accelerometers in theory may also be able to detect gravitational waves."
So of course they are not exactly the same thing but theoretically when used in groups to detect variations of proper acceleration they share a basically similar mechanism.

Also in a curved spacetime, there may be more than one geodesic between two events, so the proper length between the endpoints is not uniquely defined, and if it is not uniquely defined I wonder the sense of measuring its "fluctuations", if you are really right about GW detectors measuring varaitions in proper length, with respect to what?

Because proper acceleration is curvature of the *path*, not spacetime; it is a different thing from curvature of spacetime, time-varying or otherwise. Here we're talking about curvature of spacetime; the paths of the mirrors in the GW detector are straight, but they're straight in a manifold that's curved, and whose curvature varies with time.

See above.
Can you define what you call path? , you said that the paths of the mirrors were geodesics, I agree they are, until they are modified by the gravitational wave, something has to trigger the motion of the test masses in order to then be registered by interferometry, no?
I'm yet to understand how a mass can be made to change its state of motion without a proper acceleration being involved.

 

[WannabeNewton]

The GW detection involves the geodesic deviation equation of neighboring geodesics and is therefore related directly to the space - time curvature (the time dependent perturbations when we are talking about GW waves) as can be seen in the equation. Proper acceleration (as measured by an accelerometer) is related to a single wordline. This is exactly what PeterDonis has said already.

 

[TrickyDicky]

The GW detection involves the geodesic deviation equation of neighboring geodesics and is therefore related directly to the space - time curvature (the time dependent perturbations when we are talking about GW waves) as can be seen in the equation. Proper acceleration (as measured by an accelerometer) is related to a single wordline. This is exactly what PeterDonis has said already.

Hi WN, I made clear that difference when I spoke of the gravity gradiometer that in fact involves several accelerometers for neighbouring worldlines.

 

[WannabeNewton]

Hi WN, I made clear that difference when I spoke of the gravity gradiometer that in fact involves several accelerometers for neighbouring worldlines.

Sorry I typed up my response and left it alone for a bit before submitting so I didn't get to see your response before then.

 

[TrickyDicky]

No problem.

 

[TrickyDicky]

The GW detection involves the geodesic deviation equation of neighboring geodesics and is therefore related directly to the space - time curvature (the time dependent perturbations when we are talking about GW waves) as can be seen in the equation.

This may be just nit-picking but I always thought geodesic deviation to be caused by tidal forces is there a straight forward way to relate GWs and tidal forces?

 

[WannabeNewton]

This may be just nit-picking but I always thought geodesic deviation to be caused by tidal forces is there a straight forward way to relate GWs and tidal forces?

http://arxiv.org/pdf/gr-qc/9712019.pdf
Go to, in particular, page 159 out of 238 in the pdf itself (not page 159 in the notes).

 

[TrickyDicky]

http://arxiv.org/pdf/gr-qc/9712019.pdf
Go to, in particular, page 159 out of 238 in the pdf itself (not page 159 in the notes).

Thanks, pal. I had read those notes long ago but I think I skipped some bits.
But yes the bottom line is that gravitational waves induce a form of tidal effect on the test masses of the modified Michelson interferometer that is used in modern GWs detectors.

I think I'll start a new thread on GW detection, tidal forces and accelerometers in order not to go so much OT here.

 

[WannabeNewton]

I think I'll start a new thread on GW detection, tidal forces and accelerometers in order not to go so much OT here.

Yeah that would be cool. It is quite instructive to take a ring of test particles as your family of closely separated geodesics and see how the gravitational waves expand and shear them. There is a close relationship between the Weyl tensor as a contributor to shear and the Ricci tensor as a contributor to expansion, as codified by the Raychaudhuri equation (however they are coupled so it isn't exactly totally independent)