Can a Gravity Wave be detected at a point ?

[WarpedWatch]

Can a Gravity Wave be detected at a "point" ?

Greetings,

This question concerns Einstein’s Equivalency Principle, of which I confess I am mostly ignorant.

Can you measure a gravity wave with a “point-sized” detector?

Einstein’s famous “thought experiment” involving his elevator leads us to the conclusion that acceleration and gravity are the same, yet the concept only works out if we shrink the elevator down to an infinitesimal. (Otherwise we can detect the gradient of the gravitational field of the planet and thus tell the difference between the effects of gravity and the effects of a moving elevator. )

But if I allow myself to shrink a measurement device down to an infinitesimal, could I still measure the passing of a gravity wave? It seems to me that all the methods for measuring gravity waves require extremely long paths that (I’m guessing) must span the “trough and valley” of a gravity wave. Would a “point-sized” measuring system (one that does not extend across a significant part of the gravity wave) simply ride “up and down” on the ripple of space-time and thus experience zero effects? Or would such an accelerometer (one that is not allowed to look outside of its localized area) be able to tell that it is being jiggled around?

My question stems from a concept in engineering.

a = “mechanical” acceleration
g = gravitational acceleration

a = g
da/dt = dg/dt

In engineering, da/dt is known as “jerk” which is one measure of mechanical shock.
But when trying to come up with an example of dg/dt, I can only think of gravity waves, and though jerk can be measured by a “point-like” accelerometer, I don’t know about gravity waves. And is there some limit to how small an ideal detector could be miniaturized before hitting some kind of quantum limit?

many thanks for your time,
Mark

 

[Jonathan Scott]

Greetings,
Can you measure a gravity wave with a “point-sized” detector?

No, nothing interesting happens at a point when a gravitational wave disturbs it.

Gravitational waves are quadrupole and extremely weak. It is thought that one should be able to detect them using a very large L-shaped apparatus. I think the effect they are looking for is transient differences between the static length of the apparatus and the relative length as observed by interference of laser beams reflected along the two arms.

For more details see the Wikipedia article on http://en.wikipedia.org/wiki/Gravitational_wave" (with the usual caution that although Wikipedia is often very useful and helpful, it is not always entirely accurate).

Gravitational waves are only very loosely related to changing accelerations and "jerk". It's very difficult to achieve a measurable dg/dt jerk value by causing gravitational fields to change, because it is typically necessary to move a large distance in order to experience a change in gravitational field, but that motion in itself typically involves external accelerations. However, as a possible example, tides caused by the moon and sun create very slight variations in the direction and magnitude of the gravitational field experienced at the surface of the earth, and hence create the gravitational equivalent of "jerk".

 

[WarpedWatch]

Jonathan,

thanks very much for taking the time to answer my question. Much appreciated.

I remember an Einstein scholar years ago saying that the thing about Einstein that baffled him the most was his development of the Equivalency Principle. "How did he know to do that?" I remember him saying, shaking his head, utterly at a loss. Taking things to infinitesimals is a handy way of getting the math to work out, I know, but it always leaves me wondering what things of this sort really "mean". It raises that eternal question about mathematics: is math just an incredibly self-consistent system of modeling nature that just so happens to be very useful or does it say something about the way the world is really put together?

Considering your answer, I'm now stuck with conflicting images of the necessity for shrinking Einstein's elevator to a point ... and having nothing interesting happening at a point when a gravity wave passes through it. It's a problem with my intuition, I suppose. It's probably my brain comparing apples to oranges.

thanks again,
Mark