Does a free falling charge radiate ?

PeterDonis

In the general case, yes. I don't mean to say that the sort of thing I'm talking about will work in the general case. I'm trying to see if something like the binary pulsar can be treated as close enough to an idealized special case where the big problems don't arise.

I didn't mean to claim that in the first place. Sorry if that wasn't clear.

Hm, interesting. I don't suppose anything like this is available online?

PeterDonis

"Expected" in the absence of GWs.

Not necessarily. That's the question under discussion.

I think you're failing to consider that the spacetime curvature of the manifold is time-dependent; a time-dependent metric means that a geodesic curve won't look "straight" in the sense you would expect it to based on looking at geodesics in time-independent metrics. If GWs are present then the metric has bumps and wiggles in it; that's what the GWs *are*. So geodesics of such a metric will also have bumps and wiggles, which will be followed by objects lying in the path of the GWs. AFAIK the fact that the motion of the mirrors in an interferometer-type GW detector is geodesic is well-established; I'm pretty sure Kip Thorne goes into this in Black Holes and Time Warps, for example, at least at a lay person's level.

PAllen

Not that I could find.

I did find a way to visualize this surprising claim:

Imagine there is fluid wave motion inside the body. Then the locus no acceleration could reflect that some 'particle' in the wave has no proper acceleration, while a nearby particle in a slightly different phase of the wave is the 'next' particle with no proper acceleration. Then the locus of no acceleration represents something more like a phase propagation than a material propagation. I can imagine it in a spacelike zigzag through the world tube.

Perhaps under much more restrictive assumptions about the SET, you could get a nicer result. But, again, I've looked and not found any sign of such claim in the literature (but I don't have access to a university library, and don't claim to any great searching skills).

[In particular, I did a lot of searching on 'generalized equivalence principle' and 'Detweiler-Whiting' to see if there even any proposals that these could be generalized. I found none. The implications of some writers was clearly that this could only be expected for the extreme mass ratio case covered by the MiSaTaQua equation. ]

TrickyDicky

I have no problem with the geodesics in a time-dep. metric. Think of the FRW metric. I just said we don't have such a metric for a spacetime compatible with GWs.



Well the existence of such metrics as solutions of the EFE is what's being discussed.

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

atyy

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

PAllen

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

PeterDonis

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).

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

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.

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 wich 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

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.

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.

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

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?


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

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

WannabeNewton

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

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

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

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.