According to GRT, the rate of time (in other words, the speed of light) depends on the gravitational potential of the observer, which undergoes fluctuations during the passage of gravitational waves. There is no way to measure local changes in the tempo of time, since the reference chronometer is also affected.
Thus, for an observer immersed in curved space-time, relative changes in the lengths of the arms of the interferometer, caused by the arrival of gravitational waves, are being completely canceled out by the corresponding deviation of the tempo of time. As a result, the interferometer has no principle ability to register the curvature of space-time.
reply to Ivan: in fact, you are right in observing, that
the space-tine properties of a gravitational wave are more
complicated than popular texts often make one to believe.
In the scientific papers on the propagation of gravitational
waves however, it is clearly shown, that all 10 independent
components of the metrical tensor have to be calculated.
And then one can find out, which combination of these
components are really useful to distinguish between waves
and non-waves. One of the problems is to distinguish between
fluctuations caused by a gravitational wave from those
caused by an unusual coordiate transformation only.
Answering in a simplistic manner, gravitational potential varies with the distance of an object from a central object while gravitational waves are transverse so don't vary radial distance, hence to first order they do not alter the potential at all.
In fact I doubt that the concept of gravitational potential can even be applied to such a wave.
Scientifically speaking, what LIGO did assume is that the observed signal is a result of a single event.
What advanced LIGO aims to do is to search for gravitational wave backgrounds from a variety of sources, and test the assumption of isotropy. Data from Advanced LIGO is also used to check whether the signal is narrow or broad in frequency ranges. They are also performing narrow band GW searches directing towards specific locations in the sky, such as, Scorpius X-1, Supernova 1987 A, and the Galactic Center. What I fail to understand is how an interferometer, which is fixed to earth can be aimed at specific points in the sky, which can of-course be done with a telescope.
Dear Sirs, thank everyone for the comments, and sorry for the offline pause.
to Kåre Olaussen: - In order to get appropriate answer, one needs to express and motivate his own opinion.
to Hans-Jürgen Schmidt: - Indeed, in GRT the metric tensor invariantly defines the complete picture of the gravitational perturbations at the point, both due to the curvature of space, and the possible variation of the gravitational potential. However, I want to draw attention to the problem of metrological nature, when the standard used for measuring the curvature of space-time itself is subject to perturbations of the curvature of space-time, the search for which it is aimed at. The measuring system is immersed in the same space, for measuring the fluctuations of which it is intended. Theoretically, it would be possible to solve this fundamental problem by placing the measuring standard remotely, outside the space whose fluctuations in curvature need to be measured, but there exist no any method of high accuracy measurement with respect to the remote standard ...
to George Dishman: - Speaking about fluctuations of space-time vs fluctuations of gravitational potential, you are right, GW are expected to bring us only space-time ripples, and my example regarding time dilation effect is not appropriate. Time dilation effect is a subject to difference in gravitational potential, and may not relate directly to GW properties. Consider it just a similar case of the measuring standard (the setup) being under the effect of the disturbance which it even can not estimate.
to Biswajoy Brahmachari: - assumptions of the GW source location is not based on a single interferometer data, - they are using only the time delay value between the waveforms arrival at Hanford and Livingston and assumption that GW are moving with the speed of light.
IK: Consider it just a similar case of the measuring standard (the setup) being under the effect of the disturbance which it even can not estimate.
GR does produce non-linear effects because, for example, the energy carried by gravitational waves also contributes to gravity, however the pure equations of GR do account for that. The linear approximations of GW don't but the numerical modelling that LIGO does is not limited to the first order term, in fact they account for effects to fifth or sixth order, look for "5.5PN".
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