How can LIGO see gravitational waves, if in GRT the light is stretched along with the space?

3r33300. How can LIGO register gravitational waves if they stretch the light along with the space between the mirrors? 3r33333. 3r33333. 3r33490. Image credit: 3r3324. www.ligo.caltech.edu

[/i] 3r33333. 3r33490. 3r33333. 3r33490. This question certainly arises when there is a conversation about the detection of gravitational waves (GW). Usually the argument is as follows: we know that there is gravitational redshift i.e. gravity stretches wavelengths. It is reasonable to assume that in LIGO the light will also stretch, and the wavelengths that we use as a “ruler” to measure the distance between the mirrors will stretch to the same extent as the distance itself. How, then, can an interferometer be used to measure gravitational waves? 3r33333. 3r33490. 3r33333. 3r33490. Imagine the possible answers to it:

3r33490. 3r33333. 3r33490.

3r33490. 3r340. GWs do not affect the light, so the question does not make sense. 3r33479. 3r33490. 3r340. GW stretch the wavelength of light, but very weakly, so that we do not notice. 3r33479. 3r33490. 3r340. It does not matter, the principle of detection is not sensitive to wavelength. 3r33479. 3r33490. 3r340. Detectors actually do not work. 3r33479. 3r33490.

3r33333. 3r33490. joint detection of HBs and flashes of light 3r33386. from the merger of neutron stars. In LIGO, they saw the GW, triangulated the area in the sky where they came from, and told the telescopes: “Look there!”. Those looked, and saw a flash of a kilon exactly where indicated from LIGO. So there is no doubt that it works. Let's see exactly how. 3r33333. 3r33490. 3r33333. 3r33490. 3r33333. 2. What is LIGO anyway? 3r33333. 3r33333. 3r33490. The Virgo detector is a European detector, one of three detectors that have seen gravitational waves. [/i] * Image credit: 3r3324. www.ligo.caltech.edu ** * 3r33333. 3r33490. 3r33333. 3r33490. A gravitational wave, arising from the merging of massive objects (for example, two black holes), propagates in space-time as a small perturbation of its curvature. This leads to the fact that the distances between objects change slightly when the wave passes through them (more precisely, the very definition of the distance changes). In LIGO, the two arms of the Michelson interferometer with a length of 4 km change by ~ 10 [sup] -18 3r395. m, and the detector is able to catch this change. An important point: if the GW stretches one interferometer arm, the second arm will be compressed proportionally (ideally; this follows from the quadrupole nature of the GW and the presence of two polarizations in them). 3r33333. 3r33490. 3r33333. 3r33490. On Habré already have 3r3-3100. Good article about the device LIGO

, so let's move on to the answer to the question posed at the beginning of the article. 3r33333. 3r33490. 3r33333. 3r33490. 3r33333. 3. The concept of measurement 3r33332. 3r33333. 3r33490. 3r31-10. 3r3111. 3r33112. 3r3113. 3r3114.

3r33333. 3r33490. * An animation that demonstrates the principle of operation of the 3r3326 detector. 3r33333. 3r33490. 3r33333. 3r33490. First, consider an example that will help you understand the basic principle of the detector. 3r33333. 3r33490. This detector works with continuous light - the laser constantly pumps resonators into LIGO with light, and photodiodes constantly record the presence /absence of a signal. But for example, let's simplify the scheme: suppose we have a photon source that simultaneously sends photons in two directions, there they are reflected from the mirrors, and return to the photon detector (in our case, the beam divider), as shown in the illustration below. 3r33333. 3r33490. 3r33333. 3r33490. 3r33132. 3r33333. 3r33490. 3r33333. 3r33490. If two mirrors are at an equal distance from the photon source, two photons will return to the detector at the same time (as in the figure above). If GW stretches one shoulder at3r3141.and compresses the other to3r3141., then one photon will come before the other at3r3144.c, as in the picture above. This is very small, of course, and it would be impossible to measure directly, but we measure it a little differently. I just wanted to demonstrate the main message of this post: 3r33490. 3r33333. 3r33490. 3r33300. The detector is not a ruler, but aclock. 3r33333. 3r33490. 3r33333. 4. Detailed explanation of3r33333. 3r33490. Let us now consider the Michelson interferometer, in which they shine with a continuous laser, the beam is divided equally in the beam divider, reflected from the final mirrors and, returning back to the beam divider, interferes. 3r33333. 3r33490. 3r33333. 3r33490. 3r3162. 3r33333. 3r33490. 3r33333. 3r33490. For simplicity, we assume that the GW is a “step” - instantly changes the metric by a small value3r3168.. By the words “change of metric” we mean that the definition of distance changes somewhat, i.e. all distances increase (or decrease) in 3r33278. 3r3171.time. If we consider the distance between the beam divider and the final mirror3r3174., when the metric changes, it will increase by3r33177.so3r33180.. 3r33333. 3r33490. 3r33333. 3r33490. [i] Note: it is important that the representation of the GW “step” is only useful for viewing on the fingers, in reality it is necessary to consider the GW as a wave with a certain length. * 3r33333. 3r33490. 3r33333. 3r33490. Consider what happens to the light at that moment. 3r33333. 3r33490. 3r33333. 3r33490. 3r3196. 3r33333. 3r33490.

*At the time of arrival of the GW, the wavelength of the light is stretched relative to the initial wavelength (translucent curves). NB: the wavelength is shown comparable to the length of the arm for clarity, in fact, the laser wavelength is about 1 micron, and the arm length is 4 km.*3r33333. 3r33490. 3r33333. 3r33490. If the mirror before stretching was a node of a standing wave, it will remain in the same place after stretching, as shown in the picture above. Why? The theory of relativity requires this: since there is no dedicated independent system of rest, the node has no choice but to remain where it was relative to the surface of the mirror. That is, the wavelength increases in

times, as expected at the beginning of the article, by analogy with the gravitational redshift. 3r33333. 3r33490. 3r33333. 3r33490. So it turns out that the light still stretched along with the detector, and we can not register the signal? 3r33333. 3r33490. 3r33333. 3r33490. And yet we can! 3r33333. 3r33490. 3r33333. 3r33490.

observed on the beam splitter, and the time 3r-3278.

:

3r33490.

3r33333. 3r33490. 3r33333. 3r33490. It can be shown (eg 3r33252. Here 3r33386. Or 3r33254. Here 3r-3386.) That if the wavelength of the GW is much greater than the arm length of the interferometer, the natural frequency remains almost unchanged. And the delay time will depend on the distance between the mirrors: 3r3333371. 3r33490.

3r33333. 3r33490. Accordingly, upon arrival at the beam splitter, the phase of the light will have a delay depending on the size of the metric 3r-3278.

. In the other shoulder, everything will be the same with the accuracy of the sign before r3r3278.

- because this shoulder will not stretch, but shrink. As a result, on the beam splitter, the phase difference between the two shoulders will be 3r3333371. 3r33490.

3r33333. 3r33490. From this equation, by the way, it is obvious why the detector has such a long arm - the longer the L is compared to the wavelength, the more sensitive the detector. Next-generation detectors, such as Einstein Telescope or Cosmic Explorer will be even longer - from 10 to 40 km. 3r33333. 3r33490. 3r33333. 3r33490.

*I note that in reality, GW is not a “step”, it is a wave with a wavelength much greater than the length of the shoulder, so during the time that one “node” of the light wave travels back and forth, it can be neglected by stretching. Therefore, the first moment of "stretching" the light from the consideration "on the fingers" is actually virtually absent.*3r33333. 3r33490. 3r33333. 3r33490. So, the conclusion. The correct answer to the question at the beginning of the article: both 2 and 3 - gravitational waves act on light a little differently than the distance between the mirrors, but this does not matter, because in any case we measure not the wavelength, but the phase delay. In other words,

3r33490. 3r33300. The gravitational-wave detector works like a clock, not like a ruler. 3r33333. 3r33333. 3r33490. 3r33333. 3r33490. 3r33333. 5. Conclusion 3r33332. 3r33333. 3r33490. It is important to emphasize that the gravitational wave affects the wavelength of light differently than the distance between the mirrors. This is due primarily to the fact that the period of GW is much longer than the time it takes for the light to travel back and forth. The shoulder of the interferometer continues to stretch over time, following the period of the GW, and the light comes all the time "new" from the laser. 3r33333. 3r33490. 3r33333. 3r33490. In addition, in the real detector there are additional mirrors that create several resonators, which effectively increase the length of the shoulder. However, this does not affect the basic idea. 3r33333. 3r33490. 3r33333. 3r33490. So we can really observe gravitational waves, and no conspiracy! 3r33333. 3r33490. 3r33320. 3r33333. 3r33490.

*Image credit: 3r3324. www.ligo.caltech.edu*

3r33333. 3r33490. 3r33333. 3r33490. 3r33333. 6. News LIGO

3r33333. 3r33490. As a postscript, a little about what is happening in LIGO now. The second cycle of O2 observations brought not only 3r33333. observation of neutron star fusion 3r33386. and the first joint 3r33337. observation of GW by three detectors 3r33386. , including Virgo, but also many other events. In the very near future, the results of data analysis will be published, and the data itself will become open and available for analysis. 3r33333. 3r33490. 3r33333. 3r33490. LIGO is now completing numerous updates, among which is the installation of 3r33343. compressed light

and a more powerful laser, which will increase the sensitivity of the detector several times and allow you to observe much more events (with a good deal - on an event per week). 3r33333. 3r33490. 3r33333. 3r33490. At the beginning of next year, a new O3 observation cycle will begin. 3r33333. 3r33490. 3r33333. 3r33490. 3r33333. 3r33354. Literature [/b] 3r33356.[1]P.Saulson “If the waves are stretched by gravitational waves to detect gravitational waves?” . 3r33333. 3r33490.[2]V. Faraoni, A common misconception about the LIGO detectors of gravitational waves Gen. Relativ. Gravit. 3? 677 (2007). 3r33333. 3r33490.[3]L. S. Finn, Response of interferometric gravitational wave detectors Phys. Rev. D 7? 022002 (2009). 3r33333. 3r33490.[4]S. A. Hughes, Gravitational Waves from Merging Compact Binaries Annu. Rev. Astron. Astrophys. 4? 107 (2009). 3r33333. 3r33490.

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3r37474. Laboratory of quantum optics: personal experience and many photos

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3r37474. Another about LIGO (option in the comments)

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