Doubt about gravitational waves

[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.