Can Interferometers Measure Gravitational Waves Despite Being Made of Matter?

[VantagePoint72]

I'm currently reading the chapter in Schutz about gravitational waves (though knowledge of/access to Schutz shouldn't be necessary to answer my question). After demonstrating how a passing gravitational wave will cause the proper distance between two points to change temporarily, he says:

"A frequent question is, if space is stretched, why is a ruler (which consists, after all, mostly of empty space with a few electrons and nuclei scattered through it) not also stretched, so that the stretching is not measurable by the ruler?"

He explains this by saying that the changing metric due to the wave manifests as a tidal force acting on particles at the two points in space. As in classical mechanics, this force will pull the particles apart or push them together. However, rulers (and other physical objects) are made of matter which is held together by electromagnetic, etc., forces. These forces are much stronger than the tidal forces induced by the wave. Thus, it's only the distances between things that gets stretched, rather than the things themselves.

This makes good sense to me. But then he goes on to discuss various ways of trying to measure gravitational waves. In particular, he goes on at length about interferometers. But the end mirrors of interferometers aren't just floating in space (at least, not yet). Apparati like LIGO are made of large tunnels made of matter, to which the mirrors are fixed. So, by the earlier arguments, shouldn't the distance between the mirrors remain unchanged since they're attached to matter that's held together by other forces? How are these detectors able to (in theory) detect an incoming wave?

 

[Passionflower]

"A frequent question is, if space is stretched, why is a ruler (which consists, after all, mostly of empty space with a few electrons and nuclei scattered through it) not also stretched, so that the stretching is not measurable by the ruler?"

He explains this by saying that the changing metric due to the wave manifests as a tidal force acting on particles at the two points in space. As in classical mechanics, this force will pull the particles apart or push them together. However, rulers (and other physical objects) are made of matter which is held together by electromagnetic, etc., forces. These forces are much stronger than the tidal forces induced by the wave. Thus, it's only the distances between things that gets stretched, rather than the things themselves.

This makes good sense to me.

It does not to me.

"the distances between things that gets stretched, rather than the things themselves"
??

This frankly sounds to me like absolute rubbish.

Schutz is absolutely a brilliant mind but it is not the first time I heard "off center" ideas from him. See for instance:
http://books.google.com/books?id=jR...v=onepage&q="accelerate a solid body"&f=false

Or this from the same book:

"The inertia of pressure can be traced to the Lorentz-Fitzgerald contraction. In Investigation 15.4 on the next page we show how to calculate the extra inertia, but even without much algebra it is not hard to see why the effect is there. Consider what happens when we accelerate a box filled with gas. We have to expend a certain amount of energy to accelerate the box, to create and maintain the force of acceleration. In Newtonian mechanics, this energy goes into the kinetic energy of the box; as its speed increases so does its kinetic energy. This happens in relativity too, of course, but in addition we have to spend some extra energy because the box contracts.
The Lorentz-Fitzgerald contraction is inevitable; the faster the box goes, the shorter it gets. But this shortening does not come for free. The box is filled with gas, and if we shorten the box we reduce the volume occupied by the gas. This compression is resisted by pressure, and the energy required to compress the gas has to come from somewhere. It can only come from the energy exerted by the applied force. This means the force has to be larger (for the same increase in speed) than it would be in Newtonian mechanics, and this in turn means that the box has a higher inertia, by an amount proportional to the pressure in the box."

Granted "Gravity from the Ground up" is a book for the layman but that does not mean it should contain nonsense.

 

[Matterwave]

The mirrors are actually not rigidly set to the walls or anything, they are attached, I believe, by some very sensitive apparatus (piano strings I think) and so they are free to move.

Indeed, the gravitational wave changes geodesic motion, and objects which are rigid do not follow geodesic motion due to the forces in between them. To be absolutely precise, one should solve the Lorentz force law in curved units...but that is quite a bit of work. I see no problem in Schutz making order of magnitude estimates in this area.

 

[VantagePoint72]

Passionflower—what you quoted was my own summary. Allowing that I may have distorted it, here is how Schutz puts it:

"Since the atoms in the ruler are not free, but instead are acted upon by electric forces from nearby atoms, the ruler will stretch by an amount that depends on how strong the tidal gravitational forces are compared to the internal binding forces. Now, gravitational forces are very weak compared to electric forces, so in practice the ruler does not stretch at all. In this way the ruler can be used to measure the tidal displacement of nearby free particles, in other words to measure the ‘stretching of space’."

He's not the only one who explains it that way. That's the standard answer I've received when asking the related question of how cosmological stretching is measurable.

 

[VantagePoint72]

Matterwave—that's a good point, though Schutz only ever refers to the suspension of the mirrors in the context of explaining how they're isolated from vibrations. I guess it makes sense that, if they can prevent the mirrors from moving due to undesirable forces, they can allow them to move due to desirable forces for the same reason.

 

[Matterwave]

I think the mirrors are about as "free hanging" as they can make them. Obviously, they can't just levitate the things, but very thin piano wires provide almost no transverse (horizontal) force.

 

[Passionflower]

Passionflower—what you quoted was my own summary. Allowing that I may have distorted it, here is how Schutz puts it:

Thanks for mentioning that.

By the way I forgot to provide a reference to the source of the quote above from member Matterwave:
https://www.physicsforums.com/showpost.php?p=3674576&postcount=1

 

[Passionflower]

"Since the atoms in the ruler are not free, but instead are acted upon by electric forces from nearby atoms, the ruler will stretch by an amount that depends on how strong the tidal gravitational forces are compared to the internal binding forces. Now, gravitational forces are very weak compared to electric forces, so in practice the ruler does not stretch at all. In this way the ruler can be used to measure the tidal displacement of nearby free particles, in other words to measure the ‘stretching of space’."

I can certainly agree with that.

 

[bobc2]

I'm currently reading the chapter in Schutz about gravitational waves...

This comment is probably not worth posting, since my information is so sketchy... But, I recall reading about research by Wheeler at The University of Maryland (not Archibald at Princeton and Univ. of Texas). I think he must have performed this in the mid-60's. He constructed a gravitation wave antenna consisting of a huge aluminum cylinder with piezo-electric crystals bonded to the surface for measuring strain. The cylinder was designed for resonanant vibration in modes with resonance frequencies thought to be in the neighborhood of expected gravitation wave frequencies (it seems like those frequencies were in the 10 - 20Hz range). The cylinder was supported by a very soft suspension system to filter out external structural vibrations. I assume it was enclosed in a quiet chamber to avoid vibrations excited by sound. The challenge was to bring the signals up out of the noise floor (or, suppress the noise below the threshold of the targeted signal levels).

Spectral averaging was applied to the processed data (perhaps using analog tape loops in that time period--I'm not sure). It seems like there was to be a companion antenna across the country at another university somewhere so they could do statistical spectral cross-correlations between the pair.

I considered following up on Wheeler's ideas with the idea of putting antennas in orbit; my preliminary calculations didn't look very promising for the cylinder geometry that I was contemplating, and my advisor suggested it would not be a very practical doctoral project at the time, considering resources and magnitude of collaboration required.

 

[Vorde]

I believe the piezo-electric gravitational wave detectors still exist, but the general (or at least common) consensus is that the level of preciseness isn't enough to isolate gravitational waves from the surrounding vibrations.

As for LIGO, I actually have been to the LIGO Livingston Detector and saw the beam apparatus first hand (though not the mirror itself- it's significantly enclosed), the endpoint mirrors and I believe also the beam splitter are isolated from the surrounding tunnel by suspension wires, and are further actively isolated from vibrations with magnetic controls.

 

[Afisamuleal]

The reason LIGO can detect a gravitational wave is because the distance is rigid, like a ruler, and thus the phase offset of the returning laser is either proportional to the length of the arm of the interferometer/c, or not. And if the phase offset of the beam is not what is calculated, then space must have been stretched or contracted between the ends of the interferometer.

Light does not propagate via matter, but rather with respect to space. Space is contracted and expanded, whereas the matter is not.