Measuring Gravity Wave Time Distortion Accuracy

[Ratman101]

TL;DR Summary

Has/Can gravity wave time distortions be measured to any degree of accuracy as does LISA measures space distortions? If not, why not?

Has/Can gravity wave time distortions be measured to any degree of accuracy as does LISA measures space distortions? If not, why not?

 

[Orodruin]

Gravitational waves are spacetime distortions. How the space/time split of spacetime is made is largely a question of convention. The signal you see in an experiment is not.

 

[Ratman101]

Could you please explain a little more detail. If I wanted to measure the time distortion, how much distortion does the theory predict and is this measurable with existing capabilities?

 

[Nugatory]

If I wanted to measure the time distortion...

It's spacetime that's being distorted by the gravitational wave; there is no separate "time distortion" and "space distortion". The experimental fact is that the relative phase of the two laser beams changes as the wave passes through. We can explain this experimental fact by saying that the distances covered by the beams change slightly as the wave passes through, or that the amount of time that passed for the two beams is slightly different, or as a combination of those effects. All such explanations are equivalent - they're just different words wrapped around the same distortion of spacetime.

As a (dangerously simplistic) analogy: I draw a horizontal line one centimeter long on a piece of paper. I then draw ordinary Cartesian x-y axes (the same things you used in first-year algebra class) on the sheet of paper in the ordinary way with the x-axis horizontal, and then announce that my line extends one centimeter in the x direction and zero centimeters in the y direction. You grab the pencil and draw a new set of xy axes at a 45 angle to mine and then point out that using your axes the line extends $\sqrt{2}/2$ centimeters in the x direction but also $\sqrt{2}/2$ centimeters in the y direction. But of course it's the same line; we've just chosen different but equally arbitrary ways of dividing it into x and y components. The spacetime distortion the LIGO people measured is analogous to the length of the line; how much of that is space distortion and how much is time distortion is just a matter of how we draw our space and time axes.

(Note that I did say that this analogy is dangerously simplistic. The mathematical object that describes distortion of spacetime is more complicated than a one-centimeter line and the geometry of curved spacetime is more complicated than the flat two-dimensional surface of a sheet of paper)

 

[pervect]

Summary: Has/Can gravity wave time distortions be measured to any degree of accuracy as does LISA measures space distortions? If not, why not?

Has/Can gravity wave time distortions be measured to any degree of accuracy as does LISA measures space distortions? If not, why not?

To talk about the time distortion of gravitational waves, we'd need to be able to separate time from space. This is essentially observer dependent in both special and general relativity. So we'd need more specifics to answer the question.

My main concerns would be threefold, one is that the concept of "time distortion" is observer and coordinate dependent, so it depends on the details of how we separate time from space.

The second concern I have is that we share a common notion of "time distortion". The later point is particularly problematic, in that I rather suspect we do not share a common definition of the somehwhat ambigious and popularized term "time distortion". Unfortunately, if we're not sharing a common definition, then any exact answer will be misleading.

The third concern is that it's been long enough that I might be making an error here.

I *think* it's possible to choose coordinates (harmonic coordinates) so that what I'd call the time distortions would vanish. What I mean by "no time distortion" is that proper time of the harmonic observers is equal to the coordinate time for said observers. Unfortunately, I could be mis-remebering something. The other two points still apply - that we share a common definition of the problem, and that the remarks only apply to one particular coordinate system, which is convenient for calculations but is most likely not the one that one would intuitively pick. The fact that one can make it vanish by the correct coordinate choices is interesting, but that doesn't mean that it necessarily always vanishes.

 

[PeterDonis]

I *think* it's possible to choose coordinates (harmonic coordinates) so that what I'd call the time distortions would vanish. What I mean by "no time distortion" is that proper time of the harmonic observers is equal to the coordinate time for said observers.

AFAIK the standard coordinates in which, for example, LIGO is analyzed meet this requirement. In these coordinates, the observed interference fringes at the detector when a gravitational wave passes are entirely explained by "space distortion".