I LIGO Discovery - A question about space-time properties

[Milan Vojnovic]

A question from a physics laymen to those more advanced: if eLIGO detects gravitational waves by the difference to the combined laser wavelengths (a difference to the destructive interference pattern following curvature of space-time in each individual pathway), how is it that the lasers themselves are not exposed to a stretching of time, rather than spatial lengthening alone, since EM waves are, too, subject to gravitational waves? Would this not cause the pattern to remain the same if there really is a gravitational wave? Thank you for your time.

 

[scientific601]

A very good question. I was thinking the same thing but am having trouble formulating good search keywords to possibly find relevant discussions on the internet.

If gravitational waves / ripples are a temporary cyclical expansion and contraction of space observed in a relatively local region, wouldn't all phenomena in that region be equally affected? It's not the physical lengths of the 4 km laser paths that are measurably changing but rather their encompassing space density.

You just can't measure variations if you are wholly enveloped in a frame-of-reference changing environment.

At least that's how I understand gravitational waves. Therefore I'm having trouble understanding how they can detect anything at all.

 

[phyzguy]

I think most of us who have thought about LIGO have asked this question. In fact, it is on the FAQ list at the LIGO website, which also links to another website which gives a more detailed answer. See below:

http://www.ligo.org/science/faq.php#mirror-distance

http://stuver.blogspot.co.uk/2012/09/q-if-light-is-stretchedcompressed-by-gw.html

 

[Ontophobe]

The paths along which the light waves travel do experience the stretching and contracting, and if c weren't constant for all inertial reference frames, the light itself would experience this, too, and we'd never detect anything. But c is constant, whether in the presence or absence of g-waves. G-waves can't cause c to speed up or slow down but they can cause the paths that light follows to stretch and contract. Does that help? I honestly can't tell if that answers your question. My bad :)

 

[Maxila]

...if eLIGO detects gravitational waves by the difference to the combined laser wavelengths (a difference to the destructive interference pattern following curvature of space-time in each individual pathway... Would this not cause the pattern to remain the same if there really is a gravitational wave?

If you don't read the link (thank you phyzguy), it was the time difference that caused them to see the split beam go out of sync (they used the light beams as a clock and the stretching or compression of space by the gravity wave caused the arrival times to go out of sync).

 

[scientific601]

So in the elongated or compressed pathways, do the subatomic particles out of which they are constructed undergo growth and shrinkage, along with their inter-particle distances? Or at least along one axis? The electron orbits become elongated? It doesn't make sense to me. If light speed is constant independent of matter-affected G waves, then light just isn't part of space-time at all. It's "outside" of it?

I suppose if light were affected by space expansion we wouldn't have red-shift. But we do.

 

[Maxila]

So in the elongated or compressed pathways, do the subatomic particles out of which they are constructed undergo growth and shrinkage, along with their inter-particle distances? Or at least along one axis? The electron orbits become elongated?

That can be a tricky question without more contexts but I’ll take a stab at it. If the space-time dynamics for a place in space uniformly change then the particle is defined by the new dynamics and hasn’t changed in shape or size according to those dynamics.

If light speed is constant independent of matter-affected G waves, then light just isn't part of space-time at all. It's "outside" of it?

Light is very much a part of space-time, it’s a constant for the space-time it travels. In other words, if you observe light from a position close to the surface of a black hole, relative to how you observe distance and time it’s still c, if another observer is a great distance from your position (and the gravitational field) to them your time is slowed and they will see time and distance differently than you, yet c will remain constant to their view of time and distance.

 

[Milan Vojnovic]

Thank you for all your replies. I have read the articles you provided that explain the light as more of a clock, rather than ruler; and that red and blue shift effects following a gravitational wave cause the arrival times to differ. But I was more interested in the effect gravitational waves have on time dilation and compression and their influence on the readings: if time in the reference of the light is affected along with its space, would that not have also an influence on the readings of their arrival time from our reference point? Specifically, if one arm is stretched in space but also in time, would that not mean that while it appears longer to us, in the reference of the stretched arm, time sped up relative to us, and upon return would match the other arm's arrival time, in which the distance was compressed, while time slowed down - thus, both equaling out at the measurement stage? Thank you.

 

[phyzguy]

Gravitational waves are usually understood by approximating the metric as a flat space Minkowski metric (usually called η) plus a small perturbation (usually called h), then inserting this into the Einstein Field Equations and solving the resulting linearized equations. When this is done (see for example this Wikipedia article), the perturbation h contains only changes to the space part of the metric, so there are no changes to the time components. So we can interpret the passing of the GW as periodically stretching and compressing space while time passes unchanged.

 

[Milan Vojnovic]

I see, thank you for your insights. If time relativity is not a factor in that setting, then the calculations make sense to me now.

 

[mfb]

So in the elongated or compressed pathways, do the subatomic particles out of which they are constructed undergo growth and shrinkage, along with their inter-particle distances? Or at least along one axis? The electron orbits become elongated?

Electrons are bound so tightly that gravitational waves cannot change the size of atoms in any relevant way. The effect is not completely zero but tens of orders of magnitude too weak to be of any relevance.

 

[phyzguy]

I see, thank you for your insights. If time relativity is not a factor in that setting, then the calculations make sense to me now.

You're welcome. Glad I could help.

 

[ewq]

"So we can interpret the passing of the GW as periodically stretching and compressing space while time passes unchanged."

So "deformation" of spacetime is really just the deformation in space while time is unaffected? It affects matter but not time? Which would imply that you cannot detect any changes in length as your ruler (whatever it is) expands or contracts along with spacetime but you can detect the difference in time?

If so this would invalidate the constancy of the speed of light as now you would measure that light takes more / less time to travel the same distance?

 

[mfb]

So "deformation" of spacetime is really just the deformation in space while time is unaffected? It affects matter but not time? Which would imply that you cannot detect any changes in length as your ruler (whatever it is) expands or contracts along with spacetime but you can detect the difference in time?

You cannot use a regular ruler. You can use light as ruler. A very, very stiff ruler would work as well in theory.

If so this would invalidate the constancy of the speed of light as now you would measure that light takes more / less time to travel the same distance?

The distance does change, the speed of the light does not.

 

[ewq]

Doesnt make any difference what the ruler is, a stick or a laser it follows the deformation of spacetime. The point is you are unable to measure the change in length due to spacetime distortion.

So say your spacetime is undistorted and your arm of interferometer is 300000 km long. You measure that light takes 1s to travel that path.

Then gravity wave pases and stretches your 300000km, you canot notice it because of above and you still measure 300000km.
But because light travels at the same speed as in the first measurement you find it takes more timethan 1s to travel your measured 300000. Calculate the speed of light and its different from c now?

something is not right here

 

[mfb]

something is not right here

Your assumption that the length does not change is wrong. And you do measure the difference.

 

[ewq]

Your assumption that the length does not change is wrong. And you do measure the difference.

How do you measure a difference in length? Ligo is set up only to measure interference pattern due to time delay of the signal?

 

[phyzguy]

But because light travels at the same speed as in the first measurement you find it takes more time than 1s to travel your measured 300000. Calculate the speed of light and its different from c now?

Instead you should say, " But because light travels at the same speed as in the first measurement you find it takes more time than 1s to travel the stretched distance. Knowing that the speed of light is constant, you conclude that the distance between the ends of your interferometer has increased."

This is how LIGO works. As the gravitational wave stretches and compresses the arms of the interferometer, the wave crests of the laser light (which travel at a constant speed) arrive slightly sooner or slightly later, shifting the interference signal.

 

[mfb]

How do you measure a difference in length? Ligo is set up only to measure interference pattern due to time delay of the signal?

You answered your own question. The time delay comes from the changed distance.

 

[ewq]

In response to physguy:

In that case time ticks differently in "stretched" and "unstretched" reference frame which contradicts what you said in previous post.
You just can't have two space and time coordinate systems where c and time is constant and lenghts are different.

And second, how can the constancy of c be taken as the very premise of the experiment? How do we know we would measure same speed of light in "deformed" spacetime as measured from "undeformed" reference frame? Has any experiment ever tested this? Or have we just blindly taken Einsteins postulate for inertial reference frames?

 

[phyzguy]

In response to physguy:

In that case time ticks differently in "stretched" and "unstretched" reference frame which contradicts what you said in previous post.
You just can't have two space and time coordinate systems where c and time is constant and lenghts are different.

No. Your mistake is when you assume that the fact that your non-rigid ruler reads the same that this means that the length is unchanged. The length changes. The speed of light is constant. So it takes a different length of time for light to traverse the changed length.

And second, how can the constancy of c be taken as the very premise of the experiment? How do we know we would measure same speed of light in "deformed" spacetime as measured from "undeformed" reference frame? Has any experiment ever tested this? Or have we just blindly taken Einsteins postulate for inertial reference frames?

By definition a postulate is something that we accept without proof and reason from there. The constancy of the speed of light is a fundamental part of special and general relativity. The fact that these theories have passed every experimental test gives us confidence that the postulate is sound.

 

[jerromyjon]

Or have we just blindly taken Einsteins postulate for inertial reference frames?

Ever heard of 100 scientists against Einstein?
Criticism of the theory of relativity

 

[pervect]

I think the discussion is in danger of wandering off into a philosphical dead-end. So in an effort to try and stay more in touch with the scientific method and away from philosophy, let's use an operational approach to what we might actually measure via a thought experiment.

Suppose we have a gravitational wave interacting with two, free floating test masses in an inertial frame. The actual situation on the Earth is/was more complicated, we'll avoid the complications of how we compensate for the Earth not being an inertial frame, and instead focus on an easier to analyze idealized experiment carried out far away from any perturbing masses.

So, we've got two free-floating test masses (and because they're test masses, we assume that their gravity is negligible), and two rulers. One ruler is based on the current SI standard, another ruler is based on the old platinum bar standard.

For more details, see for instance http://www.nist.gov/pml/wmd/metric/length.cfm

The definition of the meter (m), which is the international unit of length, was once defined by a physical artifact - two marks inscribes on a bar of platinum-iridium. Today, the meter (m) is defined in terms of constant of nature: the length of the path traveled by the light in vacuum during a time interval of 1/299, 792, 458 of a second.

What happens when the gravity wave passes?

The free-floating masses move as measured by the both rulers so that the distance between the test masses as measured by both sorts of ruler varies. The amount of movement is essentially the same within experimental accuracy, as one might expect the "new" standard based on the light standard behaves almost identically to the old standard based on the platinum bar.

I said "almost the same". Why not exactly the same? The short answer is that neither the light-based ruler or the platinum bar ruler is perfectly rigid, but it turns out that the platinum bar based ruler is less rigid than the light based ruler, and we can operationally view the passage of the gravity wave as exerting a perturbing tidal force on both the test masses AND the rulers.

The theoretical notion of "perfectly rigid" that I'm using to judge both rulers is called "Born Rigidity". This may be of some interest, but it would be too much of a digression to go off on a tangent and explain any more details than this.

The important thing to realize is that the two test masses are moving relative to either sort of ruler, and that within experimental error (certainly parts per thousand, probably parts per million) the two results agree.

Let me add that there is absolutely nothing wrong with viewing the gravity wave as a metric pertubation, and that's in fact how it's reported by the Ligo group. The question becomes as to what the physical significance and interpretation of this metric pertubation is, and the answer I'm suggesting to this question of physical sigificance is that one looks at the Riemann curvature tensor , which in lay terms can be regarded as being equivalent to the hopefully familiar notion of a tidal force, or tidal gravity.

 

[mfb]

The platinum ruler has to be short for that experiment. Speed of sound in platinum is about 3 km/s, with 100 Hz this corresponds to 30 meters. The ruler has to be much shorter to reach equilibrium while the wave is passing. If the gravitational wave has a constant frequency of 100 Hz, a 30 meter platinum ruler would even start resonating.

 

[RockyMarciano]

The length changes. The speed of light is constant. So it takes a different length of time for light to traverse the changed length.

Wait, when you say that the length changes, are you including the wavelength of the light? If you do I'm not sure this reasoning would lead to a constant c. If the wavelength of the laser changes you are either also changing the frequency in the same amount , by the constancy of c, in which case you wouldn't be able to use the interferometer as a clock and measure the time difference, or if the frequency remains unaltered the formula that relates frequency and wavelength of light through a constant c no longer works.

 

[mfb]

The light that "sees" the maximal amplitude does not even exist when the arms get stretched. Its wavelength cannot be altered by that.
Also, different wavelengths from the two arms and the corresponding time delay would lead to the same detectable effect.

 

[RockyMarciano]

The light that "sees" the maximal amplitude does not even exist when the arms get stretched. Its wavelength cannot be altered by that.

I don't know what you mean, can you explain? I'm following the classical reference by Saulson given by aLIGO on this issue (AJP, 65 6 501-505) that explicitly says the wavelength is altered by a passing GW.

 

[mfb]

See the previous posts. The length changes happened on a timescale of milliseconds, the light just needs microseconds to go through the tunnel.
The recycling mirrors make the analysis a bit more complex, but the idea stays the same.

 

[RockyMarciano]

See the previous posts.

Wich ones specifically, I didn't find any relevant to what you are saying(#24 maybe?)

The length changes happened on a timescale of milliseconds, the light just needs microseconds to go through the tunnel.

I don't see how this is relevant. The GW has the same speed as the light. What you mention about the frequency of the arms length change only affects the interferometer's sensitivity to the GW's frequency in terms of the maximal amplitude detectable. What's relevant here is the laser light's frequency and any change or absence of change in light's frequency must be correlated with a change in wavelength if c is constant. That's the relevant quantity when considering the differential time of flight of the laser in the arms.
I'm still not clear on whether you are saying that the GW affects the laser wavelength when traversing the interferometer at light speed or not(or that it doesn't matter if it does or not). Could you clarify? Thanks.

 

[mfb]

Wich ones specifically, I didn't find any relevant to what you are saying(#24 maybe?)

Sorry, must have been one of the other LIGO threads. We have so many of them.

The GW has the same speed as the light.

The (relevant) motion of light is orthogonal to the direction of the gravitational wave.

The wavelength changes for light that moves in the arms while the waves changes the length of the arms, sure.

 

[RockyMarciano]

The (relevant) motion of light is orthogonal to the direction of the gravitational wave.

I'm afraid I can't relate this sentence to what I wrote in #25.
I think I understand that you referred above(when mentioning the different scales of microseconds to miliseconds, and "The light that "sees" the maximal amplitude") to the effect of the GW frequency on the amplitude detected from the phase shift at the photodetector, which certainly can never cancel the amplitude at such low GW frequencies, so certainly the arms stretching is measured, that is understood, a much higher frequency of GWs would be needed to achieve such amplitude cancelling you correctly discard.

But what I was saying in reply to phyzguy post has nothing to do with the above. I was simply explaining that if the wavelength of a light wave is altered so is its frequency/period and this change of frequency must be accounted for when using the interferometer as a clock to detect phase shift build-up between the arms as it delays or rushes time of flight by laser light in the arms in proportion to any shrinking/stretching in the arms.

Compare it to the case with interferometer phase shift build-up in response to other causes different from GWs like seismic vibrations, where there is obviously no change of wavelength/frequency of the laser light from spacetime ripples.

 

[PeterDonis]

how can the constancy of c be taken as the very premise of the experiment?

That isn't the premise. The premise is that light travels on null worldlines. "Constancy of c" in the sense of a constant coordinate speed of light only follows from that premise if you choose appropriate coordinates. The standard coordinates that are used to analyze LIGO are such coordinates. But you could choose coordinates in which the coordinate speed of light was not constant.

What you can't do is make the actual observed result change by changing coordinates. The actual observed result is that the passage of a gravitational wave causes interference fringes in the LIGO detector. The fundamental reason for that is that the gravitational wave changes the geometry of spacetime as it passes (more precisely, the change in spacetime geometry is the gravitational wave), and the change is different in the different arms. The difference in the spacetime geometry in the different arms causes the laser beams to not be precisely in phase when they return after a round trip, so interference is produced.

All of these different ordinary language descriptions in terms of "distance changing", "time changing", "speed of light changing", "wavelength of light changing", "frequency of light changing", are not different possible explanations of the above results that are in competition with each other. They are just different ways of translating the fundamental reason I just gave--different changing spacetime geometry in the different arms--into terms that seem more intuitive to people. They are different ways of trying to describe the same underlying reality. So much of the argument over how to interpret LIGO is not an argument over the actual physics at all; it's an argument over which ordinary language descriptions people prefer.

The ordinary language description that says "the speed of light stays the same, but the arm lengths change differently, so the round-trip travel time of the light changes" is the one that seems to work best for the people who are actually working on LIGO, so that's the one you see in the stuff they write. That ordinary language description is also backed up by a detailed mathematical model, based on linearized GR in the TT gauge, which correctly predicts observations. That doesn't necessarily make other ordinary language descriptions wrong. It does, however, mean that if you want to use a different ordinary language description, it's not enough to just say you don't like the standard one; you need to have your own detailed mathematical model, based on some different choice of coordinates in which your ordinary language description makes sense, that also correctly predicts observations. This is not in principle impossible, but it's certainly not easy, and AFAIK nobody has done it.