Doubt about gravitational waves

[Q-reeus]

...The symmetry demands that the x- and y- tidal effects must be the same but out of phase (spatially) by \lambda/2, and that w_x+w_y=0 to reflect no change in volume. This tidal tensor will cause the squishing/stretching effect postulated for GWs ( I could be wrong on this point. Maybe some cross-terms are required because of the phase).

If this is possible then we have a wave of purely spatial nature evolving with t as the parameter, just like EM waves...

Wading in here as novice, but p13 of the article linked in #51 shows that GW has TT (transverse traceless) structure, and I know enough that that does indeed mean 'shear' type deformations only, which are there orthogonal as you say.
On another angle here, not sure where I came across the claim, but the strange thing from my perspective is that there is apparently no 'gravitomagnetic' component - only 'gravitoelectric'. So let's say we could produce narrow counterpropagating GW beams that interfere to form a standing wave pattern. In analogous EM case, there would be a standing wave structure with E and B fields in time and space quadrature phase - equipartition of energy giving total energy density. averaged over a whole spatial pattern, constant wrt time. Does absence of magnetic field analogue imply this is not possible in standing wave GW case?

 

[Mentz114]

On another angle here, not sure where I came across the claim, but the strange thing from my perspective is that there is apparently no 'gravitomagnetic' component - only 'gravitoelectric'. So let's say we could produce narrow counterpropagating GW beams that interfere to form a standing wave pattern. In analogous EM case, there would be a standing wave structure with E and B fields in time and space quadrature phase - equipartition of energy and total energy constant wrt time. Does absence of magnetic field analogue imply this is not possible in standing wave GW case?

I changed 'electrogravitic' to 'gravitoelectric' in my earlier post.

I'm not sure if gravitational standing waves are possible.

On reflection, I don't think what I've described is actually a GW. You could get a similar thing from Newtonian gravity without a wave equation involved at all. Drat.

A bit of research, and I found that the gravitoelectric tensor of a GW moving in the z-direction has all the diagonal elements equal to zero, and off-diagonal terms in the x,y positions, as Q-reeus said - it's shear. Apart from that my conjecture is right(ish)

 

[TrickyDicky]

That nice simple summary appeals to me. Maybe wrong here, but unless one assumes a priori an infinite and perfectly flat or at least uniform nature, does not requiring a higher imbedding dimension invite an infinite succession - the higher imbedding dimension in general having some structure (curvature) which in turn requires a yet higher imbedding dimension to define, and so on?

I'm not sure my set up requires an infinite succession of higher dimensions, I'd say it doesn't. But I have realized I made an unwarranted assumption that is probably causing confusion here, I'm presuming that the spatial part of the 4D spacetime curvature has curvature, now this is not the usual assumption of the corcondance model that assumes a flat 3-space as the most likely.
With that frame of mind I guess anyone that reads my question about the distinction between spacetime curvature and oscillations of curvature finds hard to make that distinction since in their mind having spacetime curvature already involves noticeable effects (tidal etc) in time without having to embed the 4D curvature in a higher dimension. (as cosmik debris said).

But IMO the core of the question remains, EM waves, or sound waves, or seismic waves have a spatial 3D component that oscillates in time, so they can be described in a 4D spacetime tensorial way or as 3d oscillations + the time parameter. In all these examples we have oscillations wrt a fixed background geometry.
In a gravitational wave we have a spacetime 4D (curvature or the spacetime metric) that is said to oscillate, and I have to ask again how can we ascertain that oscillation if time itself is also oscillating? with respect to what fixed reference can we determine the oscillation if as is widely known in GR there is no fixed background geometry since this comes determined by the metric? Remember the metric is supposed to be oscillating, but the metric is the only reference we have in GR.

There's a kind of no-mans land here at PF imo...

I',ve noticed the same thing.

BTW, was that reference to Kip Thorne's article of any use?

Well the thing is I get stuck in a previous more basic and physical step than the mathematical development of GW that the Thorne's article tackles.
I'm mostly concerned about the energy issue that you raised and with my question above.

 

[Q-reeus]

...But IMO the core of the question remains, EM waves, or sound waves, or seismic waves have a spatial 3D component that oscillates in time, so they can be described in a 4D spacetime tensorial way or as 3d oscillations + the time parameter. In all these examples we have oscillations wrt a fixed background geometry.
In a gravitational wave we have a spacetime 4D (curvature or the spacetime metric) that is said to oscillate, and I have to ask again how can we ascertain that oscillation if time itself is also oscillating? with respect to what fixed reference can we determine the oscillation if as is widely known in GR there is no fixed background geometry since this comes determined by the metric? Remember the metric is supposed to be oscillating, but the metric is the only reference we have in GR...

Best I can discern from struggling through the following somewhat more detailed treatise by KT (pages 13-15 sort of cover it) is that cosmik debris in #54 and Mentz114 in #60 are correct in that there is no temporal distortion component, at least for a plane GW: 'GW's and Experimental Tests of GR' www.pma.caltech.edu/Courses/ph136/yr2006/0426.1.K.pdf
That is something I was never clear on myself - always wondered if the LIGO-type detectors would be self-cancelling owing to temporal distortions 'fighting' spatial distortions, but that seems to not be so. I guess one must give the designers credit for thinking that one through! Which still leaves problems of course, like energy ambiguity! Kind of intriguing that an analogue to the Poynting vector does not exist, at least if comments as per #61 are correct. Not arguing though that invalidates GW energy flux, just interesting difference.

 

[Mentz114]

]with respect to what fixed reference can we determine the oscillation if as is widely known in GR there is no fixed background geometry since this comes determined by the metric? Remember the metric is supposed to be oscillating, but the metric is the only reference we have in GR.

If the metric can be decomposed into two parts, g_mn = b_mn + w_mn with the b part not oscillating, and the w part oscillating then effectively w is waving relative to the background b.

 

[TrickyDicky]

Best I can discern from struggling through the following somewhat more detailed treatise by KT (pages 13-15 sort of cover it) is that cosmik debris in #54 and Mentz114 in #60 are correct in that there is no temporal distortion component, at least for a plane GW: 'GW's and Experimental Tests of GR' www.pma.caltech.edu/Courses/ph136/yr2006/0426.1.K.pdf
That is something I was never clear on myself - always wondered if the LIGO-type detectors would be self-cancelling owing to temporal distortions 'fighting' spatial distortions, but that seems to not be so. I guess one must give the designers credit for thinking that one through! Which still leaves problems of course, like energy ambiguity! Kind of intriguing that an analogue to the Poynting vector does not exist, at least if comments as per #61 are correct. Not arguing though that invalidates GW energy flux, just interesting difference.

Thanks for the link, but as I said I can't see how it helps solve my question because it starts by assuming GW are spacetime ripples and that is what I'm trying to understand.
Can you try to specifically answer in the context of my post? Like indicating where in my phrasing I go wrong or make incorrect assumptions?

 

[TrickyDicky]

If the metric can be decomposed into two parts, g_mn = b_mn + w_mn with the b part not oscillating, and the w part oscillating then effectively w is waving relative to the background b.

The approximative linearized approach might be valid for some purposes but as I said in my first posts , I'm not sure it works here because it assumes as background a Minkowsky spacetime that being static doesn't admit GW in principle. So if the metric can be decomposed that way without loss of general validity is still a big if for me, more so when GW haven't been directly detected.

 

[Q-reeus]

Thanks for the link, but as I said I can't see how it helps solve my question because it starts by assuming GW are spacetime ripples and that is what I'm trying to understand.
Can you try to specifically answer in the context of my post? Like indicating where in my phrasing I go wrong or make incorrect assumptions?

TrickyDicky, all I can honestly answer as novice here is the following:
If one assumes GR is correct then in vacuo metric is everything and so ripples in spacetime is surely all there can be to a GW. And the only way detection is possible is via tidal distortions, in the same way a free falling observer can only detect the gradient of curvature, not curvature itself. If I had it right about there being only TT spatial components to a GW, then at least one not worry about temporal distortions messing things up.
The only other distinctly different approach I can see would be to adopt a field theory of gravity (eg. Baryshev et al). You then have a physical field propagating through a presumably flat(ish) Minkowski type background. It has an appeal re solving in principle energy ambiguities but as per comments in #49 "The latter has I suppose a real problem cosmology wise in that it doesn't seem to admit to a Big Bang, but I'm not 100% on that."
EDIT: Just caught your posting in #67 "..The approximative linearized approach might be valid for some purposes but as I said in my first posts , I'm not sure it works here because it assumes as background a Minkowsky spacetime that being static doesn't admit GW in principle."
This is out of my league, but isn't a Minkowski metric in this context just an idealization in order to simplify the calcs - one still uses the EFE's, but without the complication of sorting out curvature-on-curvature? Sorry, but more than this you need a true expert's advice. Bed time!:zzz:

 

[TrickyDicky]

Thanks Q-reeus.

 

[Mentz114]

The approximative linearized approach might be valid for some purposes but as I said in my first posts , I'm not sure it works here because it assumes as background a Minkowsky spacetime that being static doesn't admit GW in principle. So if the metric can be decomposed that way without loss of general validity is still a big if for me, more so when GW haven't been directly detected.

I wasn't thinking about the linearized, or weak field approximation where w<<b, nor need b be a flat spacetime if w=0. I don't know if such a decomposition is possible but I'm going to investigate.

 

[TrickyDicky]

I wasn't thinking about the linearized, or weak field approximation where w<<b, nor need b be a flat spacetime if w=0. I don't know if such a decomposition is possible but I'm going to investigate.

Oh, I misinterpreted you then. What were you referring to by that metric decomposition?

 

[cosmik debris]

In a gravitational wave we have a spacetime 4D (curvature or the spacetime metric) that is said to oscillate, and I have to ask again how can we ascertain that oscillation if time itself is also oscillating? with respect to what fixed reference can we determine the oscillation if as is widely known in GR there is no fixed background geometry since this comes determined by the metric? Remember the metric is supposed to be oscillating, but the metric is the only reference we have in GR.

I guess another way of looking at it then is this: we are attempting to measure the passage of GWs with LIGO. LIGO is just measuring the length of it's arms, so what is oscillating in 3D is a simple length, i.e. the transverse axis.

The thing about GR is it's background independence, that's what is making it difficult to reconcile with QFTs. QFTs can be solved in curved spacetime but don't generate it. This fundamental difference makes thinking about GR just a little bit removed from the normal thinking about fields on spacetime, which is what you're attempting to compare.

 

[TrickyDicky]

I guess another way of looking at it then is this: we are attempting to measure the passage of GWs with LIGO. LIGO is just measuring the length of it's arms, so what is oscillating in 3D is a simple length, i.e. the transverse axis.

Yes, that is what confuses me, we are measuring in no different way than if it was a "normal" 3D wave, like waves from from an earthquake, right?

The thing about GR is it's background independence, that's what is making it difficult to reconcile with QFTs. QFTs can be solved in curved spacetime but don't generate it. This fundamental difference makes thinking about GR just a little bit removed from the normal thinking about fields on spacetime, which is what you're attempting to compare.

So you would say it can't be compared? But I'm not invoking any QM effects, I'm keeping it classical.

 

[Q-reeus]

Came across yet another article that may or may not help here: 'Gauge invariance and the detection of gravitational radiation' http://arxiv.org/abs/gr-qc/0511083v1
...When a gravitational wave passes through the detector, it changes the lengths of the arms of the interferometer and this change is detected through its effect on the the relative phase of the two light rays. At first glance, this explanation sounds simple and clear. But on reflection some issues arise: one issue comes from thinking about the usual explanation for cosmoligical redshift, which is that the expansion of the universe causes a corresponding expansion in the wavelength of light. Applying this concept to the interferometer, if the wavelength of the light expands as much as the interferometer arm does, then there should be no change in phase and therefore no detection. Other issues arise from the fact that general relativity, as a theory of gravity, doesn’t just give predictions for the geometry of space, but also for the propagation of light and the motion of material objects. In addition to changes in the lengths of the interferometer arms then, one might expect additional effects due to the effect of gravity on the propagation of the light as it moves along the interferometer arms. Furthermore, the mirrors at each end of the arms are also subject to gravity, so one might expect an additional effect due to motion of these mirrors under the effects of the gravitational wave. Why are these additional effects not discussed in the usual explanation of how gravitational wave detectors work? Are these additional effects small enough to be negligible? But if so, then why are they? Are these additional effects absent? But again, if so, why are they absent?
It turns out that these questions can be answered by a careful consideration of the role of coordinate invariance in general relativity...
Goes on to use an interesting comparison with AB effect, which I found a little hard to understand.
EDIT: Found another one on same topic but considerably easier to follow:
'If light waves are stretched by GW's, how can we use light as a ruler to detect GW's' http://gw.aei.mpg.de/images/Saulson_1997AmJPhys_65_501.pdf

 

[TrickyDicky]

Thanks, those articles are really informative. And at the very least I can see I'm not the only one having this type of doubts.

 

[Q-reeus]

Yeah they put to rest the 'stretch - stretch = 0' problem for me. Darn long time without anything to show for the LIGO guys though - hard to say if it's them or the Supersymmetry fans at the LHC that are more nervous! :zzz:

 

[cosmik debris]

Yes, that is what confuses me, we are measuring in no different way than if it was a "normal" 3D wave, like waves from from an earthquake, right?


So you would say it can't be compared? But I'm not invoking any QM effects, I'm keeping it classical.

QFT or classical they are still fields on a spacetime, they do not generate it.

 

[PAllen]

Yeah they put to rest the 'stretch - stretch = 0' problem for me. Darn long time without anything to show for the LIGO guys though - hard to say if it's them or the Supersymmetry fans at the LHC that are more nervous! :zzz:

I think no graviational waves would be much the bigger revolution in physics. No supersymmetry would mean the most popular extensions to standard model are out the window (but LHC can't really accomplish this, as supersymmetry can easily be pushed way beyond LHC energy by adjustable parameters). No GW means all metric theories of gravity (not just GR), plus any possibility of a quantum theory of gravity are out the window. Since classical theories (pre-relavivity) are also rejected by extensive experiment, no GW would mean all known theories of physics would be discarded, with no plausible substitutes at present. LIGO might not be enough to achieve this, but the fact of no GW would mean this big a revolution in physics.

 

[Q-reeus]

...No GW means all metric theories of gravity (not just GR), plus any possibility of a quantum theory of gravity are out the window. Since classical theories (pre-relavivity) are also rejected by extensive experiment, no GW would mean all known theories of physics would be discarded, with no plausible substitutes at present. LIGO might not be enough to achieve this, but the fact of no GW would mean this big a revolution in physics.

One would assume the planners did a good job of estimating likelihood of success before collectively sinking maybe several billion $$ in the network of current GW detectors. To be fair variance may be much larger than mean and we may simply inhabit a particularly lean spacetime 'patch' for current GW detectors range as you say. Annoying that the next gen 'breakthrough' (LISA etc) seems to always be just a few years away. Came across articles by an A Loinger who claims to show GW's are an artifact of working in linearized GR and that full GR precludes them, but If right then binary pulsar finding would mean gravitational dynamics are inherently non-conservative! Doubtless considered 'crackpot' by peers, I'm not up to discerning if he has a real case.

While the gauge invariance argument as physically played out in an invariant c vs 'free-falling mirrors' explains one aspect of LIGO type detector rationale, there is another aspect that required some more thought on my part. On p 503-504 in http://gw.aei.mpg.de/images/Saulson_1997AmJPhys_65_501.pdf , it reads:
"V. LENGTHS IN COSMOLOGY AND IN LABORATORY PHYSICS
Note that the language we have been using in this paper only makes sense if we imagine that we have standards of length other than either the separations of freely falling test masses or the wavelengths of light waves. We do. A good paradigm of a length standard is a perfectly rigid rod. Such a rod does not change its length in the presence of a gravitational wave, because the arbitrarily strong elastic forces between its parts resist the gravitational force carried by the gravitational wave..."
Interesting language here from a relativist "..gravitational force..", rather than "metric distortion". And maybe this is what TrickyDicky has been on about. If spacetime is the fabric of reality, and a GW distorts the spatial component, one might think everything, from doghnut to diamond, merely follows suit exactly the same - ie there should be no such thing as GW induced material stress/strain. A swag of existing bar-type GW detectors says otherwise, but this means the TT h distortions can indeed be treated as a kind of physical stress field acting on a flat backdrop, just as for tidally induced mechanical stress in the local frame of a free falling object in Schwarzschild coords. Hope that analogy is apt.

 

[TrickyDicky]

One would assume the planners did a good job of estimating likelihood of success before collectively sinking maybe several billion $$ in the network of current GW detectors.

That is a lot to assume, just look at the 800 million$ spent in the Gravity probe B and how the whole thing has ended up, it neither improved much the precision of an already experimentally previously confirmed geodetic effect, nor was able to confirm or falsify one of the few predictions of GR that has no experimental confirmation to date: the Lense-Thirring effect (frame-dragging)-see http://www.springerlink.com/content/w67u3842122871r1/
Apparently GPB team is still swamped trying to make sense of the data, but NASA withdrew funds in 2008. From WP: "A review by a panel of 15 experts commissioned by NASA has recommended against extending the data analysis phase beyond 2008. They warn that the required reduction in noise level (due to classical torques and breaks in data collection due to solar flares) "is so large that any effect ultimately detected by this experiment will have to overcome considerable (and in our opinion, well justified) skepticism in the scientific community".

While the gauge invariance argument as physically played out in an invariant c vs 'free-falling mirrors' explains one aspect of LIGO type detector rationale, there is another aspect that required some more thought on my part. On p 503-504 in http://gw.aei.mpg.de/images/Saulson_1997AmJPhys_65_501.pdf , it reads:
"V. LENGTHS IN COSMOLOGY AND IN LABORATORY PHYSICS
Note that the language we have been using in this paper only makes sense if we imagine that we have standards of length other than either the separations of freely falling test masses or the wavelengths of light waves. We do. A good paradigm of a length standard is a perfectly rigid rod. Such a rod does not change its length in the presence of a gravitational wave, because the arbitrarily strong elastic forces between its parts resist the gravitational force carried by the gravitational wave..."
Interesting language here from a relativist "..gravitational force..", rather than "metric distortion". And maybe this is what TrickyDicky has been on about. If spacetime is the fabric of reality, and a GW distorts the spatial component, one might think everything, from doghnut to diamond, merely follows suit exactly the same - ie there should be no such thing as GW induced material stress/strain. A swag of existing bar-type GW detectors says otherwise, but this means the TT h distortions can indeed be treated as a kind of physical stress field acting on a flat backdrop, just as for tidally induced mechanical stress in the local frame of a free falling object in Schwarzschild coords. Hope that analogy is apt.

Yes, that is exactly what I have been talking about, too bad I am not very good at explaining myself thru analogies.
But, hey if the "expert relativists" don't have any problem with this why should we?
Glad someone else can see this though

 

[Q-reeus]

That is a lot to assume, just look at the 800 million$ spent in the Gravity probe B and how the whole thing has ended up, it neither improved much the precision of an already experimentally previously confirmed geodetic effect, nor was able to confirm or falsify one of the few predictions of GR that has no experimental confirmation to date: the Lense-Thirring effect (frame-dragging)...

Yes not the first or last time unfortunately. We could hark back to the SCSC, or Hubble mark1 etc. Wonder if there is a taxpayer funded GPC in the pipeline...

Yes, that is exactly what I have been talking about, too bad I am not very good at explaining myself thru analogies.
But, hey if the "expert relativists" don't have any problem with this why should we?
Glad someone else can see this though

And I really think this aspect has a 'standard answer' (this-or-that metric component's property means such and such), just maybe the energy issues too, but they're a long time coming bud! Good thing we have the internet at our fingers - but there's a certain fatigue factor to that.