Detecting Interference Pattern Changes in LIGO Measurement

[pixel]

As the length distortion due to a gravitational wave as it passes by Earth is on the order of the dimension of an atom, or << a wavelength of light, can someone describe in a general sort of way what measurement steps are employed to detect such small changes in an interference pattern? It would seem that there would be so many environmental effects that could produce changes of similar or greater magnitude and the signal would be buried in a lot of noise.

Also, as there are two LIGO facilities, is some kind of correlation from both sites used to verify the signal?

 

[Orodruin]

As the length distortion due to a gravitational wave as it passes by Earth is on the order of the dimension of an atom

This is incorrect. Just like metric expansion is not about a speed but instead abouta rate, the distortion is not about a length distortion but about a strain. The distortion of a size of about 1/1000 of a proton is the change in the 4 km long arms of the experiments. The strain of the signal was about 1e-21.

Also, as there are two LIGO facilities, is some kind of correlation from both sites used to verify the signal?

Of course, this was one of the main reasons (if not the reason) for building two.

 

[pixel]

The distortion of a size of about 1/1000 of a proton is the change in the 4 km long arms of the experiments.

Not sure what you're getting at here, but the small change in the arms of the interferometer is what I'm asking about. What is done to allow phase shift measurements so small, and how do they discriminate against environmental effects, e.g. thermal fluctuations, that would seem to overwhelm the measurement of such small signals?

 

[Orodruin]

Not sure what you're getting at here, but the small change in the arms of the interferometer is what I'm asking about. What is done to allow phase shift measurements so small, and how do they discriminate against environmental effects, e.g. thermal fluctuations, that would seem to overwhelm the measurement of such small signals?

What I am saying is that this

As the length distortion due to a gravitational wave as it passes by Earth is on the order of the dimension of an atom,

has no meaning. The distortion of one of LIGO's arms is not inherent of the gravitational wave, but also depends on the arm length. You cannot say that a gravitational wave gives a distortion of a fraction of a proton sixe without specifying what objects gets that distortion. The Earth itself is three orders of magnitude larger and therefore would experience a distortion three order of magnitude larger.

The mirrors in LIGO are suspended in intricate suspension systems which significantly reduces outside influence.

 

[pixel]

Okay, but you yourself said "The distortion of a size of about 1/1000 of a proton is the change in the 4 km long arms of the experiments." So if we can just agree that the expected change in path length inside the interferometer due to the gravitational wave is very, very small, can someone address my original question? Once they attempted to null the interferometer, it would seem there would be non-zero signals due to environmental factors such as thermal fluctuations, minor movements of the Earth's crust, maybe even someone slamming a door in the building, whose amplitudes are >> the expected gravitational wave signal. I'm simply asking about the signal processing that is done. Any reference would be appreciated.

 

[nsaspook]

https://losc.ligo.org/s/events/GW150914/GW150914_tutorial.html
This was posted on one of the LIGO threads earlier.

 

[Drakkith]

As some interesting info on noise: The extra signal (interference) generated by the slamming of a door, a nearby train, or other things isn't noise. It's just extra signal that can be accounted for and (mostly) removed. We do this all the time in astrophotography when processing images. The problem with noise arises because those extra signals themselves have noise that can't be removed. The larger the amplitude of the interfering signal, the larger the noise of that interference, and once the noise, not the amplitude, overwhelms the signal you actually want, you're toast. Hence the reason for the extreme measures taken to reduce the interference from other sources.

 

[bahamagreen]

The amplitude of the signal and that of the noise are both fundamentally distances, right? That is, the signal and noise amplitudes are proxy representations of distances.

The whole thing about the reflection mirrors moving about 1/1000 of a proton diameter...

I must ask; since the reflection of light comprises an absorption by and subsequent emission from a respectively lower and higher energy level electron in an atom or molecule in the substance of the mirror's surface where those emission origins are different with respect to the path length (and spread many orders greater than the proton), how can the measure be 1/1000 of the proton? In effect, an absorption and emission distance from the "front" and the "back" of the atom would be huge and random compared to the proton. Also, the individual atoms involved might not all be in the same plane perpendicular to the path length (some might be behind others).

I must also ask about HUP regarding this fine a measure... can one measure 1/1000 proton diameter? I think the H atom has a typical uncertainty of COM of about 6 atomic diameters; that is also huge with respect to a proton diameter.

 

[Drakkith]

I must also ask about HUP regarding this fine a measure... can one measure 1/1000 proton diameter? I think the H atom has a typical uncertainty of COM of about 6 atomic diameters; that is also huge with respect to a proton diameter.

I believe the light takes about 75 round trips down the arms before being measured. Still a tiny distance to measure though.

 

[pixel]

As some interesting info on noise: The extra signal (interference) generated by the slamming of a door, a nearby train, or other things isn't noise. It's just extra signal that can be accounted for and (mostly) removed. We do this all the time in astrophotography when processing images. The problem with noise arises because those extra signals themselves have noise that can't be removed.

I know what you're getting at here, but don't quite agree. A camera for instance has a dark level - that is not noise, it's the random fluctuation around that level that's the noise; the level itself can be subtracted away. But the slamming of a door near LIGO is noise as it is random.

Anyhow, I found some general discussion about the steps taken to make the measurement here: http://www.ligo.org/science/GW-IFO.php

 

[pixel]

bahamagreen: Interesting post. I was questioning the effect of more mundane environmental factors, but you make some good points. I look forward to the replies.

 

[pixel]

I must ask; since the reflection of light comprises an absorption by and subsequent emission from a respectively lower and higher energy level electron in an atom or molecule in the substance of the mirror's surface where those emission origins are different with respect to the path length (and spread many orders greater than the proton), how can the measure be 1/1000 of the proton?

We can stick to geometrical optics and ask the same question because mirrors are not polished that precisely. The variation of path length just due to where the light hits the mirrors in their multiple bounces >> the required precision in path length measurement.

 

[pixel]

Wondering why no one has addressed the points raised in the last few posts esp. by bahamagreen that address fundamental questions about the ability of LIGO to measure gravitational waves?

 

[spacejunkie]

I must also ask about HUP regarding this fine a measure... can one measure 1/1000 proton diameter? I think the H atom has a typical uncertainty of COM of about 6 atomic diameters; that is also huge with respect to a proton diameter.

LIGO uses the HUP to increase the sensitivity of the receiver by creating squeezed vacuum states. Here is a page from the LIGO website about it.

http://ligo.org/science/Publication-SqueezedVacuum/index.php

 

[Leo.Ki]

I was just reading about squeezing on this paper: https://dcc.ligo.org/public/0089/P1200041/019/P1200041_v19.pdf
It triggered a question though: With all the 90° reflections that the laser goes through before entering the arms (see fig 1 on pg 6), isn't the phase compromised?

 

[Truecrimson]

Actually advanced LIGO was not using squeezed state injection at the time of detection nor right now according to someone in the team. Color me surprised.
https://www.reddit.com/r/IAmA/comme..._ligo_scientific_collaboration_and_we/czxq8rq

 

[spacejunkie]

Actually advanced LIGO was not using squeezed state injection at the time of detection nor right now according to someone in the team. Color me surprised.
https://www.reddit.com/r/IAmA/comme..._ligo_scientific_collaboration_and_we/czxq8rq

That is a surprise. Here in Australia the AIGO people were talking as if it had been implemented. It is good news though. It means an increase in sensitivity is still possible if the technical problems can be overcome.