# Gravitational Waves

1. Dec 4, 2005

### Spin_Network

A great recent article details the problems of GW's?

http://www.physicstoday.org/vol-58/iss-9/p43.html#ref [Broken]

So do Gravitational Waves exist?

This was meant to be placed in General forum!

Last edited by a moderator: May 2, 2017
2. Dec 5, 2005

### SpaceTiger

Staff Emeritus
I would be very surprised if gravitational radiation didn't exist. It appears in weak field GR -- a limit I think most physicists are confident with -- and we even have observational evidence for them:

It's indirect evidence, certainly, but pretty solid nonetheless. There will be some serious head-scratching if none of the upcoming gravitational wave experiments has a detection.

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3. Dec 6, 2005

### Garth

I agree that gravitational waves most probably do exist, especially as we have detected the loss of orbital energy from the PSR 1913+16 system as predicted.

However there is a question about the detection of GWs. It is similar to the question, "If the universe is expanding what exactly expands with it? Do rulers co-expand?" If so there would be no detectable expansion. The standard answer to this question is No - rulers do not expand with the universe and therefore they can detect that expansion.

However if this understanding is mistaken, and everything embedded in space-time does co-expand with the expansion of space, then any physical apparatus would not be able to detect GWs either, for they would simply 'wash over' the detectors leaving no signal. Could this be a possible explanation if the non-detection of GWs continues?

If in fact this is the case then another explanation is required for cosmological red shift, such as a mass field effect (Hoyle: F. 1975 ApJ 196:661-670 "On the origin of the microwave background") - But that is definitely not "mainstream"!

Garth

Last edited: Dec 6, 2005
4. Dec 6, 2005

### Spin_Network

I do comply with the fact that GW's exist, I also agree that their existence is not an observable fact?

Gravitational Waves exist, but their existence is not Observation Dependent.

5. Dec 7, 2005

### Haelfix

I don't understand this line of reasoning. You better believe the measuring apparatus expands as the universe expands, its just its so vanishingly small (98 orders of magnitude small for instance) that its for all intents and purposes a nonfactor.

However we aren't measuring the expansion of space, we are presumably measuring ripples from linear perturbation series from some object (like a neutron star). As they pass us, you should see a kink in the machine.

If nothing is detected as far as im concerned something is very, very wrong. In fact i'd put the blame on the experiment rather than the theory, so confident I am that it has to exist. If however it persists through generations of LIGO and others, well it would be deeply embarrasing for many of us.

6. Dec 8, 2005

### Garth

No - this is not a matter of measurement but principle.

In GR if the measuring apparatus expands as the universe expands then there would be no detectable expansion. That is why all standard textbooks carefully explain that if the expanding universe is modelled by a balloon being blown up, with galaxies modelled as spots on it, then the spots themselves do not expand, this is where that analogy breaks down as a model of the standard theory. It is normally explained that a better model is one in which the galaxies are represented by pennies/cents being glued onto the expanding balloon.

Having said that the question as to whether galaxies (and by extension rulers) really do expand with the universe is also a observational matter. But, as you say, the rate is too small to observe.

One clue that all is not right with the standard model is the Pioneer Anomaly in which the Pioneer spacecraft, now well away from the perturbations of the planets in the solar system, appears to exhibit an anomalous extra acceleration towards the Sun of
(8.74+/-1.3) x 10-8 cm/sec-2
this is very nearly equal to cH and could therefore be cosmological in nature.

[Note a simplistic equating of PA = universe expansion does not work as the acceleration is the towards the Sun, you have to think it through consistently in an alternative gravitational theory.]

Not if everything is perturbed equally. Suppose a GW causes a line of atoms to expand in one dimension (Weber detector), in GR the atoms remain of fixed size but an increase in the gap between them passes down the detector as a wave. If however the atoms, and any ruler, also themselves expand then the wave is undetectable by those atoms and ruler. I believe it was this reasoning that led Einstein to deny GWs in his rebutted paper
I concur; then we would have to see alternative gravity explanations for the PA!
Garth

Last edited: Dec 8, 2005
7. Dec 8, 2005

### EL

Comment about if "a ruler" expands when the universe expands:

The ruler does not expand simply because there are forces between the molecules in the ruler keeping it together at a fixed size, and the physical laws determining its size do not change with the expansion of the universe! As soon as the space between the molecules are expanding, the forces will pull them back to their initial distances from each other.
The same holds for galaxies.

As Garth said, if the detectors would expand with the expansion of the universe, there would be no detectable expansion, and hence the concept of an expanding universe would be meaningless. The crusial point is that the space expands, but "the physical laws" do not.

Last edited: Dec 8, 2005
8. Dec 8, 2005

### Garth

The question is situated on the problematic interface of QM and GR!

Are 'forces', and the force carrying virtual particles fundamental (QM) or are accelerations by which those forces are measured fundamental (GR)?

Normally QM and GR are kept well apart in their respective domains of influence, however when the BB itself is approached the two become of equal importance, so which is to be the most fundamental?

In the normal expanding cosmological solution of GR what exactly is it that is expanding? If it is space-time itself, as demanded by the theory, then what expands with it?

As the Schwarzschild solution for gravitational orbits is embedded in that space-time should not its solutions co-expand?

Also as the Bohr/Schrödinger/Dirac equations of atomic physics are also so embedded then should not their solutions expand?

If, as a consequence, gravitational orbits and atoms together with the physical rulers constructed of those atoms so co-expand with the universe, then surely there would be no detectable expansion?

As I said above in that case gravitational red shift would have to be interpreted by another cosmological effect, such as a secular increase in atomic masses.

Garth

Last edited: Dec 8, 2005
9. Dec 8, 2005

### EL

I have always thought of it like that every distance between every pair of objects expand. Then for objects close to each other the distance between them increases quite slow, and also the force between them usually are quite strong, and hence the forces can keep up with the expansion rate rather easy. For objects further away from each other, the distance between them increases faster and also the forces are weaker, and hence cannot keep up with the universal expansion.
So this is my explanation of why galaxies and rulers don't coexpand with the universe, while larger structures do.

But the Schwarzschild solution is time independent and does not expand. Of course in reality you have some kind of overlap between the SS and the expanding universe solution, but for small enough systems the SS clearly dominates. Hence neither the solarsystem, or not even the galaxies, coexpand. So it really works in the same way as for forces.

Regards /EL

Last edited: Dec 8, 2005
10. Dec 8, 2005

### Labguy

Last edited by a moderator: Apr 21, 2017
11. Dec 8, 2005

### Garth

The Schwarzschild solution is a static spherically symmetric solution embedded in a Minkowsian space-time, the GR solution tends to SR as r tends to infinity.

However in the real universe the spherically symmetric solution should be embedded in a R-W metric, whether this makes a significant difference or not is a matter of debate, but as Labguy's link to Ned Wright says the consensus opinion is that it does not. The problem is that an accurate model of the solar system gravitational field has to be embedded in the galactic field which has to be embedded in the cluster field etc. up to the cosmological R-W field. Whether or not the GR cosmological expansion affects the solutions embedded hierarchially within it or not is not clear.

But certainly in the standard model, GR, because of the equivalence principle and constant particle masses, atomic rulers do not expand with the universe. However, it may be informative to consider conformal gravity theories in which they do.

Garth

12. Dec 8, 2005

### Labguy

And THAT is a very good point that must be considered.

13. Dec 8, 2005

### EL

Well my intuition strongly tells me the expansion would not affect the solar system very much. But, of course it's just a guess...

14. Dec 9, 2005

### pervect

Staff Emeritus
I seem to recall someone has looked at this issue (fitting the Schwarzschild solution to an expanding universe).

http://arxiv.org/abs/astro-ph/0112320

which I've only skimmed, but looks good so far. The solution I find of interest is the one which assumes a cosmological constant (i.e. a vacuum energy density and an associated negative pressure) for "empty" space.

15. Dec 9, 2005

### Garth

The more basic problem was examined by no less than Einstein and Straus "The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars" Rev. Mod. Phys. 17, 120–124 (1945).
in which they embedded a Schwarzschild mass in a sphere of vacuum cut out of the background cosmological representative medium. This is because the Schwarzschild solution is for a spherically symmetric and static mass surrounded by vacuum whereas in the cosmological solution the mass is distributed as a homogeneous density.

Note that in the real universe the opposite is true; the density of the Solar System medium is higher than the ISM or IGM. It is not surprising therefore to read W. B. Bonnor's paper: "Local Dynamics and the Expansion of the Universe" GRG Volume 32, Number 6 June 2000 Pages: 1005 - 1007 .
Garth

16. Dec 9, 2005

### EL

Baker Jr concludes:
I find this very reasonable.

17. Dec 9, 2005

### Garth

To go back to the OP - if GW's are detected in the next few years there will be nothing to worry about, however if they are not, and continue to be undetected even as sensitivities increase by OOMs, then the above discussion may be relevant in explaining their invisibility.

Garth

18. Dec 9, 2005

### Haelfix

Im in complete agreement with the link, although there is a bit of a messy continuity problem. When you imbed local metrics into larger ones you really want to require asymptotia to match precisely, the details of this matching can be messy and linear perturbation theory can break down (the root and source of the problem).

At one point you really want to say, at what distance scale do rulers start to coexpand. Then take a local neighborhood of that point, and observe the differential structure. Since we are still working with manifolds here by assumption, everything has to be smooth in some localized coordinate system.

19. Dec 9, 2005

### pervect

Staff Emeritus
I have big semantic problems with this statement. Rulers are the means by which we define and measure distances, so they never expand or contract.

A pair of massive particles will either get closer together because of their mutual gravitational attraction (be bound), or move further apart because of the expansion of the universe (be unbound).

This doesn't have anything, in my book, with rulers expanding or contracting. In fact, we need the rulers to be able to *measure* the distance between the pair of interacting particles to determine whether or not the distance is increasing, or decreasing.

20. Dec 9, 2005

### Garth

Absolutely; if rulers or clocks are said to vary then that statement makes no sense unless it is also stated against what standard are they measured to vary.

Notice that the size and de Broglie wavelength (inverse frequency) of an atom is inversely proportional to its mass and proportional to Planck's constant, so if either of these 'constants' should in fact vary then that variation itself would require a non-varying standard of mass, length and time.

Note: SCC suggests that such a standard is to be found in a free photon, travelling along a null-geodesic, (after Doppler effects are allowed for). As photons in the CMB and other cosmological radiation 'expand with the universe' [$$\lambda = \lambda_0\frac{R(t)}{R(t_0)}$$]
then as measured by such photons the universe is non-expanding and so local 'rulers'/orbits also do not co-expand. (In the SCC Jordan conformal frame) Cosmological red-shift is caused by a secular increase in atomic masses.

Garth

21. Dec 10, 2005

### Haelfix

Umm, its fairly obvious the notion of 'distance' is parameter dependant. On cosmological scales, they can run proportional to things like the scale factor and so forth.

Either way, we can be precise about this. Are we all in agreement that gravitational waves should be seen as tidal forces on some local measuring apparatus (say an interferometer like LIGO)? Eg this is a case where the principle of equivalence is violated, as we now have acceleration affects that are second order in the geodesic eqn.

I think they call this geodesic deviation.

Anyway you should 'observe' a nonzero tidal tensor, which should make sense assuming we have gravitational wave energy lose from the source object (again here we have to go to much higher order in linearized perturbation series to see the 'loss' from say an oscillating relativistic object).

Assuming the interferometer is large enough, then the kink will manifest itself in errors between signal transfers as the wavefront passes through the arms.

So I still don't quite see how much smaller effects (like tiny distortions from scale factor effects should in any way effect the results gross order of magnitude)

22. Dec 10, 2005

### Garth

Physical measurements are a comparison of an observable with a standard unit. If the standard unit varies with the observable then no variation is detected. This applies both to the size of the universe on the large scale and also to a fluctuation in a GR detector, or even just an atom, on the small scale.

Garth

Last edited: Dec 10, 2005
23. Dec 10, 2005

### Haelfix

Yea sorry I still dont see why thats the case, the distance between the two arms of the interferometer is inconceivably tiny relative to any FRW scale parameter effect, for all intents and purposes you can just assume that length is a 'constant' ruler. Otoh, a much larger tidal 'kink' from a spacetime ripple (which has strictly nothing to do with universe expansion rates) that is traversing it should register as a potential difference in xing times, assuming the accuracy of the lasers is good enough and so forth.

In the previous posts I mentioned that I still think this 'constant' ruler does expand with say the scale parameter, its just so vanishingly, vanishingly small relative to every other local effect (solar system Schwarschild metric variables, that are also tiny), much larger stress energy tensor asymetries from EM effects and so forth that it makes strictly zero difference for an experiment (and heck LIGO has much larger local effects to deal with and damp out, like the local vibrations from train stations 30 miles away).

24. Dec 10, 2005

### Stingray

And this is why people have rigorously extended Newtonian elasticity theory to curved spacetime. Everything works out according to the standard expectations, even if these justifications are rarely mentioned.

Arguments of how things are "dragged along" when space "expands" or "contracts," were some of the original reasons that gravitational waves were debated (as the original article here discusses). But these arguments have been conclusively settled for decades.

Anyway, here's a nice starting point for the discussion (though definitely not in the class of rigorous results I referred to above):
http://xxx.lanl.gov/abs/gr-qc/0508052"

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25. Dec 11, 2005

### pervect

Staff Emeritus
The way I see it, the notion of distance requires two things. One is easy, a knowledge of the Lorentz intervals between any two points, which we get from the metric. The other is more subtle - we need a notion of time, relative to which the distance will always be orthogonal. We then find the distance by integrating the lorentz interval along the appropriate curve of "simultaneity".

There are at least two possible notions of time to use for an extended body. One is to base a time coordinate on Einsteinian clock synchronization (so that all clocks on the body will be synchronized with each other via the Einstein convention). This is the notion of synchronization that I associate with a ruler, though it appears to be little used in cosmology. The other notion of time is to use cosmological time. This gives us the usual notion of "proper distance" in cosmology.

I agree with the description in terms of tidal forces.

This remark puzzled me for quite a bit. Do you mean that the region of space-time is too large to apply the principle of equivalence because of the curvature induced by the gravitational waves?

My main objection was to the idea that rulers changed length. I will agree that the tidal forces due to the expansion of the universe are extremely low and not detectable with any sort of practical measurement.