# I LIGO and light speed constancy

1. Jun 2, 2017

### ewq

From LIGO website re how gravity waves are measured: "The arrival times change because when the arms of the interferometer change lengths, so too do the distances the light waves travel before exiting the interferometer. What gravitational waves do not change, however, is the speed of light. This means that a wave of light that happens to be in a longer arm during a gravitational wave has to travel farther before exiting, so it takes longer to leave than the beam that was in the shorter arm."

So does this not mean that the light speed is actually NOT constant? Will you be not measuring different speed of light when there is a gravity wave and different when there isnt?

2. Jun 2, 2017

### Staff: Mentor

First, a caution: the "speed of light" here means the coordinate speed of light, and that depends on your choice of coordinates. The standard coordinates that are used for analysis of LIGO experiments are such that the coordinate speed of light does not change during the passage of the gravitational wave; all that changes is the lengths of the interferometer arms. But one could also choose coordinates where the coordinate speed of light did change.

That said, in order to actually measure the speed of light, you would divide the distance a light beam covers by the time it takes. What the LIGO website is describing are changes in the distance (lengths of the interferometer arms) and time (round-trip travel time of the light beams in each arm) that happen exactly in concert so that the speed of light doesn't change. What changes at the detector is the relative travel times along each arm; that is what causes the interference fringes that are measured and give information about the gravitational wave. But this change in travel times is due to the changes in the arm lengths, not to any change in the speed of light.

3. Jun 2, 2017

### timmdeeg

No, the light speed is invariant. The light travel time depends on the actual length of the arm (which changes periodically). In case the arm is longer, the light travel time is longer. That's what they measure.

4. Jun 2, 2017

### ewq

OK say im in a tunnel, 10 my local units long. There is no gravity wave and i measure round trip of light to be 5 seconds.
Now comes the gravity wave and stretches the tunnel- I still measure it to be 10 units long because my ruler scales along with the tunnel length, but now I measure light took 6 seconds for the round trip, hence i get different speed?

Or are you saying that the gravity wave affects my clock as well? If i am watching the clock located in the "stretched" space will it seem to run slower than mine from the "unstretched" space?

5. Jun 2, 2017

### Staff: Mentor

The ruler doesn't scale. That is the point. Tidal gravity actually measurably deforms objects.

6. Jun 2, 2017

### Staff: Mentor

No, the gravity wave doesn't stretch the tunnel; it only stretches the distance between the light source/detector at one end of the tunnel, and a mirror at the other end, both of which are hung in such a way that they can move freely in the appropriate plane. In other words, they move relative to the tunnel (and to a ruler inscribed in the tunnel).

(More precisely, the gravity wave stretches the tunnel and its associated ruler so much less than it stretches the distance between the light source and the mirror, that we can consider the stretch of the tunnel to be negligible. This is because the tunnel and the ruler are constrained by internal forces between their atoms, which resist the stretch due to the changing tidal gravity of the wave. The distance from light source/detector to mirror is not so constrained, hence it can stretch freely due to the wave.)

This might be somewhat misleading, since what is actually "deformed" in this case is a distance in free space, not the size of a single object. See above.

7. Jun 2, 2017

### ewq

what? gravity wave affects the tunnel but not my tape measure?

of course it does, gravity wave or not i will always measure the tunnel to be 10 units long

8. Jun 2, 2017

### ewq

This would still mean i measure dofferent light speed with wave present and when not present?

Also does the wave affect my clock or not?

9. Jun 2, 2017

### Staff: Mentor

No. The distance along the tunnel/ruler that the light has to travel changes; so does the time it takes to travel. The two change exactly in sync to keep the speed of light, measured by the ruler along the tunnel, the same.

No.

10. Jun 2, 2017

### ewq

ok- let me see if i understand you:
my physical ruler and tunnel length stretch just a little. distance between free floating mirror and emitter stretches much more. thats the reason why im able to notice length increase even from within "stretched frame".
my clock is unaffected

is this what you are saying?

11. Jun 2, 2017

### pervect

Staff Emeritus
There are multiple ways of describing the situation.

What needs to be decided straight off to answer the question in terms of rulers is to decide what rulers measure and how they work. Either rulers change their length when a gravitational wave passes, or they don't. They can't do both if one wants a self-consistent explanation. One has to decide which definition applies, and have a shared understanding between the explainor and the explainee.

If one regard a ruler as something made out of something physically rigid (to the extent that's possible - nothing is perfectly rigid), one can regard rulers as not changing length ever, and gravitational waves won't change their length either. This is consistent with the SI defintion of the ruler, where one regards rulers as having a constant light round-trip travel time, and the speed of light being a defined physical constant.

Using this line of reasoning, one concludes from the fact that the ruler measures an increase in the distance between the test masses that the test masses must actually move due to the gravitational wave.

I frequently find people who do not seem to realize that the test masses to which the mirrors of the interferometer are mounted are designed to be able to move freely. The test masses are suspended in such a manner as to allow them to move freely (in two dimensions at least, the masses are supported by pendulii to support them against gravity so they can't move in the direciton in which they are suspended). This freedom to move is part of the design of LIGO.

Now, it's also perfectly consistent to regard physical rulers as stretching, which to my mind somewhat defeats the whole purpose of having a ruler in the first place, and is also not consistent with the SI definitions. You'd think that such explanations would not be popular, or at least people would mention that they're not using the standard SI defintions when presenting this sort of epxlanation, but this turns out not to be the case. There's nothing actually wrong with these explanations , however, if they are interpreted and understood correctly. Frequently, though, they cause more confusion than they prevent - in my opinoin, at least.

12. Jun 2, 2017

### Staff: Mentor

In principle, they will, because the internal forces between the atoms can't respond instantaneously to the tidal gravity changes in the wave. But in practice we won't be able to measure any stretching at all. That's why the source/detector and mirrors in LIGO have to be so carefully hung and isolated from the tunnel: if they were just mounted to the tunnel, the detector would never detect a signal.

If you define the "stretched frame" as being the length measured by the ruler, yes, it's the difference between the behavior of the ruler and the behavior of the source/detector and mirrors that explains why the detector detects a signal.

However, you should be aware that this "explanation" depends on defining the "frame" the way you have. There are other ways to define a "frame" (i.e., a system of coordinates). They all make the same prediction for what the detector detects, but they don't all give the same "explanation" for why.

13. Jun 2, 2017

### ewq

not sure what was the goal of this post?
the reality behind physical units of measurement is not arbitrary and subject to our consensus, gravity waves either stretch them or not, lets try and stay focused

14. Jun 2, 2017

### Staff: Mentor

The SI unit of time, the second, and the SI unit of distance, the meter, are completely arbitrary and are not only subject to consensus, they are the product of a committee. It is hard to imagine something more subject to consensus than the output of a committee.

15. Jun 2, 2017

### ewq

I thought that the sole point of intricate suspension was to isolate the mirrors from external disturbances (seismic, thermal etc), didnt occur to me that it also allows it to move independently from the ceiling. So in essence the mirror is a pendulum and the grav. wave will "swing" it as it passes?
Kind of like as if there was an additional weak gravitational force acting horizontally- it wouldnt affect the walls and the ceiling of the tunnel much but it would skew the chandelier a little bit?

OK, on to the next point- why arent the clocks affected by grav wave? Isnt a gravity wave an oscillating curvature of spacetime i.e. gravity potential?

16. Jun 2, 2017

### Staff: Mentor

Sort of, yes. The motion is so small that it can be treated as being solely in the horizontal plane.

No. The concept of "gravitational force" (and "gravitational potential", see below) is only meaningful in a static spacetime, and spacetime while the gravitational wave is passing is not static. The gravitational wave is time-varying tidal gravity.

"Skew" in an oscillating fashion.

Yes.

No. Spacetime curvature is tidal gravity, not "gravitational potential". As noted above, "gravitational potential" is only a meaningful concept in a static spacetime, and spacetime while the gravitational wave is passing is not static.

17. Jun 2, 2017

### Staff: Mentor

You are right. My comment might have been relevant for a Weber bar type of gravitational wave detector, but not so relevant for an interferometer.

18. Jun 2, 2017

### ewq

no matter- why wouldnt tidal gravity affect my clock? dont say that sinusoidal effect averages out to zero because the same argument could be used for distance

19. Jun 2, 2017

### Staff: Mentor

Does the tidal gravity of the Moon on the Earth affect Earth clocks?

Tidal gravity--at least, the kind we're talking about here--is purely spatial. It stretches and squeezes things spatially. It doesn't do anything to time.

20. Jun 2, 2017

### ewq

of course it does, but point taken -negligible when compared to what it does to oceans...

21. Jun 2, 2017

### Staff: Mentor

It does? How? What is your basis for this?

22. Jun 3, 2017

### ewq

every gravitational field has effect on clocks? dont know the exact math but i remember i read somewhere that time dilation on earth because of moons influence is about 1 sec per 200000 yrs

23. Jun 3, 2017

### Paul Colby

Don't know if this helps but LIGO spent a huge amount of effort designing the mirror supports which hold the mirrors. The goal of these mirror supports is to provide a near frictionless support for the mirrors along an axis parallel to local gravity and along the optical beam. The reason for this is so the mirrors that define the interferometer arm for all intents and purposes may be treated as inertial (or in free fall). The only exception to this is the radiation pressure the light beams exert on the mirrors which is central to the measurement as a whole. I bring this up because the interaction of GW with actual material like meter sticks etc is quite complex and in LIGOs case not germane.

24. Jun 3, 2017

### RockyMarciano

Exactly and it is maybe worth recalling here why this is so since you were remarking the time-varying nature of tidal gravity in a previous post and it might confuse some saying at the same time that it only affects the space part. This comes from the fact that with the linearized metric used to approximate the far source effect of GWs a gauge condition(de Donder gauge) is required to solve the EFE linearized equations so that a wave equation is obtained $\Box h_{\mu\nu}=0$, now given this condition its solutions only affect the space components and not the time components. So mathematically it is clear enough.

One could just maybe find odd that the wavelength of the laser light is affected by the GW but not its frequency while c is constant, but this is necessary if one wishes to use the interferometer as a clock.

25. Jun 3, 2017

### Staff: Mentor

A "gravitational field" is not the same thing as tidal gravity. See below.

I haven't checked the math but that sounds roughly correct; but the "Moon's influence" here is not its tidal gravity. It's the gravitational potential due to the Moon. They're different things.