Interferometry relies on the change in the phase of two orthogonal light beams reflected back to the source point. Assume there is an interferometer at the equator, one mirror is planted 1 mile due north and another mirror is planted 1 mile due east. Every 6 hours the axis of the east mirror-interferometer experiences a tidal effect and its length should increase. Michaelson and Morley would not have detected this because their mirrors were planted on the same piece of granite which could not expand and contract. But the mirrors in the LIGO interferometer should detect this. Do they?
Asked
Active
Viewed 196 times
2
-
Are you asking if the LIGO interferometers detect changes in Earth's tidal field? And by "a tidal effect" do you mean ANY change in the Earth's gravitational field? – Daddy Kropotkin Dec 13 '20 at 14:59
2 Answers
1
In the LIGO interferometers, there are various sources of noise. As the saying goes, "one person's source of noise is another person's signal!" So there are geophysicists who study seismic and atmospheric waves and there's whole fields of study on these things that are very interesting and rich. Gravitational wave detectors treat those signals as a type of noise, since they're interested in pulling out a gravitational wave signal that originates extra-terrestrially.
That said, there are numerous sources of noise among the vibrations that LIGO detects. Indeed, the only reason LIGO has detected gravitational waves is due to the immense engineering/analysis efforts accomplished over the last 50 years. Here is a complete guide to LIGO noise cancellation and signal extraction.
Now to answer your question: the LIGO interferometers are certainly sensitive to seismic waves of all sorts, the image below of theoretical noise curves in the LIGO detector shows lots of sources of noise and you can clearly see the seismic wall (brown curve) at $\sim 10$ Hz (and the advantage of space-based observatories is that they do not have this wall of noise!). LIGO is also sensitive to changes in the tidal field of the Earth due to the propagation of the seismic waves themselves, this is called "Newtonian Noise" or "gravity gradients," which is the green curve in the figure. All these sources of noise are accounted for in data analysis, and future engineering goal is to have real-time feedback systems so the seismic and Newtonian noises can be cancelled out of the data in real-time.
[Image credit]
A experimental noise spectrum for the LIGO detector looks more like this:
. [Image credit]
Lastly, the Michelson-Morley experiment was too small to be able to be sensitive to the gravity gradients. LIGO detector arms are $\sim 4$km long, while the Michelson-Morley apparatus was $\sim 10$m. Modern Michelson-Morley type experiments have pushed the sensitivity to levels comparable to LIGO, e.g. here and here, however, due to advances in quantum optics and other things.
Daddy Kropotkin
- 2,731
-
Thank you for showing me the complexity into which my question waded. I noticed that you interpreted my question as asking about noise. Certainly vibrations in the mirrors would cause strain noise.And the scale is measured in hertz. But I am thinking about the meters that the earth stretches due to the gravity of the sun and the moon. The equatorial axis of the interferometer should stretch much more than the axis pointing north. I am not asking about changes in the earth's gravity either. I simply asking about the changing distance of the mirrors that happens every 6 hours. – aquagremlin Dec 14 '20 at 02:00
-
Oh. WELL, what makes you think the effect of moon's gravity on Earth is on the order of "meters"?? It is miniscule, far smaller than the curves shown above, since the Earth-moon system is ~20 million time less massive than a binary black hole. The moon's gravity is strong enough to effect the tides. The bulge of the Earth at its equator is due to the Earth's rotation, not due to gravity. – Daddy Kropotkin Dec 14 '20 at 12:06
-
More importantly, the frequency of the Earth-Moon system is far too low for LIGO to detect, i.e. it's below the seismic wall I discussed above. "the Moon’s orbital period is 27 days; the period of the gravitational waves generated by its orbital motion around the Earth is 13.5 days. LIGO is only sensitive to gravitational waves with periods between about 0.02 seconds and 0.001 seconds. The gravitational waves from the Earth-Moon system would be well outside the range of periods LIGO can detect." https://astronomy.com/magazine/ask-astro/2016/06/gravitational-waves – Daddy Kropotkin Dec 14 '20 at 12:07
-
And see this https://physics.stackexchange.com/questions/412980/does-the-earth-emit-gravitational-waves – Daddy Kropotkin Dec 14 '20 at 12:08
-
it's not just earth -moon, it's earth sun. the tides on our planet are due to earth sun moon tidal effects. even millimeters of stretching add a million times of variation to the distance of the mirror and the source of in the LIGO interferometer that it can resolve. I was hoping for someone who actually worked at LIGO to address how this variation is normalized. Certainly, if a measurement occurs on the order of microseconds, then a calibration followed by measurement could eliminate most of it. – aquagremlin Dec 14 '20 at 16:47
-
whatever the cause of the bulge, even if it's by santa's elves at the core, the changing geometry of the earth is what i am asking about-how that unevenly but slowly changing ellipsoid deformation of the crust (and hence distances of the mirrors to the source) is normalized (eliminated) from the measurement. Most of the references you listed I did come across but they are high frequency variations. – aquagremlin Dec 14 '20 at 16:50
-
i am asking about-how that unevenly but slowly changing ellipsoid deformation of the crust (and hence distances of the mirrors to the source) is normalized (eliminated) from the measurement Yes, this is the gravity gradient (Newtonian noise). – Daddy Kropotkin Dec 14 '20 at 17:35
-
thank you for your persistent attempt to understand my naive question. After reading some papers, like https://iopscience.iop.org/article/10.1088/1742-6596/363/1/012004/pdf , I notice they all refer to noise suppression at >2 hz. Yes I know this is vibration and I am asking about changes that are glacial by comparison. Nevertheless, I marked your answer as correct because you are the only one who attempted to answer. – aquagremlin Dec 15 '20 at 15:22
-
My pleasure! Yes I know this is vibration and I am asking about changes that are glacial by comparison. what do you really mean by this? Because there are seismic disturbances that cause huge vibrations in the LIGO mirrors but those are accounted for in data analysis (i.e. see the LIGO noise extraction paper linked in my answer). The noise/sensitivity plots like I show are usually down to very small sensitivities, i.e. the strain $h \sim 10^{-20}$, since thats where g-waves are expected. But there are certainly louder vibrations, the curves in the plots are really lower bounds. – Daddy Kropotkin Dec 15 '20 at 17:46
-
The noise I am talking about has a frequency of 1 cycle every 12 hours. – aquagremlin Dec 16 '20 at 21:42
-
That's a very low frequency vibration which is far to the left of the plots above, at the lower end of the LISA band actually https://commons.wikimedia.org/wiki/File:LISA_and_eLISA_noise_curves.png – Daddy Kropotkin Dec 16 '20 at 23:37
-
but my point is that it alters the distance from mirror 1 to the source differently than the distance from mirror 2 to the source. If the distances change, then you cannot tell if it was due to a gravity wave or simply the earth's crust flexing under tidal forces. – aquagremlin Dec 17 '20 at 03:14
-
I'm sorry but that is way too oversimplified to be substantive. The whole point of a g-wave detector is that the mirrors are effected by different amounts which are correlated to search for g-waves. A g-wave passing through LIGO detector will stretch or shrink the mirrors just depending on the incidence of the wave, but this is handled in data analysis. YOu should really check out the LIGO noise extraction paper – Daddy Kropotkin Dec 17 '20 at 12:23
-
And as I said before, the LIGO detectors are insensitive to the very low frequency of the vibration you're referring to.... – Daddy Kropotkin Dec 17 '20 at 12:32
1
This exact question was considered in a 1997 LIGO paper by Raab and Fine entitled "The Effect of Earth Tides on LIGO Interferometers". Not only is there the expected semi-diurnal tide (known as the "sectorial" component of the tide) but there is a diurnal ("tesseral") component due to the Sun and Moon not being in the equatorial plane of the Earth.
The resulting length changes in the LIGO arms are very significant compared to the magnitudes of the sought-for gravitational wave events. The biggest tidal amplitudes produce changes on the order of 100 microns.
The effect was then measured in 2006-2007 and reported by Melissinos in "The Effect of the Tides on the LIGO Interferometers". This extract of a two-day period in the observing run clearly shows the diurnal and semi-diurnal components:
Peter Swords
- 136