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Is There Really a Strictly Conserved Stress-Energy Tensor in GR?

 Quote by DaleSpam I actually disagree here. I don't think that it is even approximately true, at least not globally. If it were approximately true then that would mean that you could get a GW which was spherical plus some small higher order terms. However, the spherical and dipole terms are identically 0. You can write a realistic GW as a quadrupole term plus some small higher order terms, but no lower than quadrupole.
If you're going to actually try to model the wave fields directly as spherical harmonics, yes, I agree; the l = 0 and l = 1 terms are identically zero.

However, I can see doing a geometric optics approximation where we model the GWs, globally, as expanding spherical wavefronts of "graviton pulses", similar to the way "photon" wavefronts are modeled as spherical in SR as an approximation, even though they're really not (the lowest-order EM radiation is dipole so the spherical term is 0 for that as well). Of course the GW wavelength has to be much, much smaller than the size of the spheres for this to work, i.e., the GWs have to be high frequency. I suspect that the paper Q-reeus linked to about HFGWs was doing something along those lines. But that is still only an approximation.

Furthermore, it's a useless approximation for trying to decide if GWs carry energy, because a "yes" answer to that question is built into the geometric optics approximation in the first place. That approximation assumes that the "gravitons" are massless particles carrying some finite amount of energy and momentum (if they carried zero energy and momentum they would have infinite wavelength, which obviously violates the small-wavelength assumption).

 Quote by DaleSpam Of course, you can do local approximations, but then there is no advantage to expanding as local spherical waves rather than local plane waves. The symmetry argument doesn't apply, and you add needless complication to your approximation terms without adding accuracy.
Exactly.

 Quote by PeterDonis So you believe you can exhibit a quadrupole wave which has spherical symmetry? This should be interesting. I eagerly await the new thread.
Sorry to have to say both yourself and DaleSpam are attacking a straw man in posts #83-86. Did I not make it clear in #78 I was talking about spherical wavefronts? You are both sadly uninformed about common terminology here. Spherical wavefront (often just the term 'spherical wave' is used - without confusion by those in the know) simply means that at large r (i.e. well into radiation zone) wavefronts of constant phase have spherical symmetry. And that much I clarified for you in #80 - so you are both without excuse for attacking this straw man of your own creation. From http://en.wikipedia.org/wiki/Antenna...#Compact_range
 The CATR uses a source antenna which radiates a spherical wavefront and one or more secondary reflectors to collimate the radiated spherical wavefront into a planar wavefront within the desired test zone.
See also (perhaps you should inform author of gross ignorance in using the term 'spherical wave' in respect of antenna radiation! What an ignoramus!)
Also try
 Although the wave emitted by the oscillating dipole is a spherical wave, it does not have the same intensity in all directions.
(between (4.16) and (4.16')) Gees - yet another ignoramus! Must be crawling with em out there.

Get used to it folks - spherical wave simply refers to phase of wavefront, and need have no bearing on angular dependence of field strength or direction - savvy?! I never once used the term spherically uniform field or monopole field or monopole moment - that all came from inside your heads.
Now, assuming your bonfire for the straw man has burnt out, listen up. Have been feeling my way on this issue - beginning with #76. Some statements made in #78 I now see are wrong (phase differential bit and what flowed from that), but stand by the overall thrust. It needs considerably more refinement and better presentation, and that I intend to do, but hands are tied up at the moment elsewhere. Sufficient to say I'm now sure GW's are a phantom. One more thing. Since you and DaleSpam have not heeded my request to leave it all for now - you might as well make good on that undertaking to provide reference material for Feynman's 'strange' sticky-bead argument that had stick pointing along propagation axis. Have you found one yet?

Mentor
 Quote by Q-reeus Get used to it folks - spherical wave simply refers to phase of wavefront, and need have no bearing on angular dependence of field strength or direction - savvy?! I never once used the term spherically uniform field or monopole field or monopole moment - that all came from inside your heads.
Oh, you are correct. I was indeed thinking you were referring to complete spherical symmetry in every aspect of the wave instead of simply a spherical phase distribution. I stand corrected.

Of course, since you didn't intend to imply anything about anything other than the phase then your argument becomes a non sequiter. A GW has more than just phase, so these other components need not be spherically symmetric as your argument requires:
 Quote by Q-reeus Now please explain how each and every sticky bead decides which way to move in this situation - east or west. I'll save you the trouble - by symmetry there can be no such motions.
I was mistakenly thinking that you were making a valid argument from an incorrect premise, when you were actually making an invalid argument from a correct premise.

 Quote by DaleSpam Oh, you are correct. I was indeed thinking you were referring to complete spherical symmetry in every aspect of the wave instead of simply a spherical phase distribution. I stand corrected.
Thanks for at least admitting that - there's hope yet for you DS.
 Of course, since you didn't intend to imply anything about anything other than the phase then your argument becomes a non sequiter.
Actually it's that statement that is the non sequiter - more below.
 A GW has more than just phase, so these other components need not be spherically symmetric as your argument requires:
Wrong on last bit. My particular argument you presumably are referring to - in last section of #78, does not at all require spherical symmetry of field - merely axial symmetry in equatorial plane. And that was correctly applied.
 Q-reeus: "Now please explain how each and every sticky bead decides which way to move in this situation - east or west. I'll save you the trouble - by symmetry there can be no such motions." I was mistakenly thinking that you were making a valid argument from an incorrect premise, when you were actually making an invalid argument from a correct premise.
Actually it is you hastily making an invalid judgement. What I wrote there is just basic fact and cannot be sensibly denied. Maybe you simply have not grasped what was being said there. Perhaps you have the basic geometry confused. Are you cognizant of the arrangement: A very large circular hoop encircling at large r an axial quadrupole oscillator, with latter's axis of oscillation normal to plane of hoop? Hoop lying in equatorial plane of oscillator. I certainly described it plainly enough as such, but it never fails to amaze me how readily some folks can still misinterpret. If you did understand arrangement, how can you criticize the bit you quoted? It necessarily is true.
 Mentor This thread, like the ones before it, has degenerated to the personal. It's closed. Q-reeus, please do not start another one.