How Can Interferometer Detect G-Waves?

[Peter Wilson]

I asked this question in another thread, and was not satisfied with the answer, so I'm posing it here in the Q&A section.

Interferometers measure a phase-change between two beams of light that take different paths. This phase-change is interpreted as a change in distance, with the implicit assumption that the wavelength of light does not change.

I.e. a phase change of 360 degrees is interpreted as a change in distance of 1 wavelength of the light used. For example, in high-precision measurements of thermal coefficient of expansion, an interferometer will be attached to a metal rod of a known length. The the rod is heated by a known amount, say 10 degrees. The interferometer measures the phase change in the length of the path between the ends of the rod. The phase change is interpreted as a chnage in length of the rod, under the implicit assumption that the wavelength of light does not change with temperature. In other words, the measurement rests on the assumption that the "measuring stick," the wavelength of light, does not change with temperature, that which is being measured.

The interferometer used in the Gravity Wave Detector works on the same principle--and same underlying assumption. This is the question.

According to GR, does the wavelength of light not stretch or compress in exact proportion to the expansion/compression of space? How can an interferometer yield anything but a null result? If a gravity wave passes perpendicular to one arm, and lengthens it by 1 part per zillion, will the wavelength of light along that arm not also increase by 1 part in a zillion?

This will yield zero phase change, i.e. a null result, like the Michelson-Morley experiment. So far, a null result is all the interferometer G-wave detectors have offered up.

But how can it be otherwise? How can a measuring stick be used to measure G-waves, when the meareuing stick itelf expands and contracts in the same proportion as that which is being measured?

[cmsavage]

The period of the gravity wave is much longer than the time it takes for the light to be emitted, travel down and back the arms, and be detected again. That is, each photon sees very little change in the distance during its lifetime, so its wavelength does not change much.

Regardless, the wavelength does not matter. Send a pulse down the arms and if they arrive back at the same time, the arms are the same length. Send a pulse a moment later (say, when the gravitational wave has reached its "peak") and if they do not arrive back at the same time, the path lengths must have changed. It does not matter if you sent additional pulses between those two sets (or even different numbers of additional pulses along the different arms), the fact that the pulses no longer match up means the arm lengths have changed. Think of the pulses as the peaks in the EM wave, then you can see this applies to frequencies/wavelengths. Since the speed of light is constant, the travel time changes regardless of if the frequency of light also changes.

[Peter Wilson]

Hmmm...Thanks. I'm not sure I buy that, but I'll chew on it

[selden]

Peter,

You asked

How can a measuring stick be used to measure G-waves, when the meareuing stick itelf expands and contracts in the same proportion as that which is being measured?

But the point is that, according to GR, distances actually vary within the affected volume, so photons have to travel for a different amount of time between the mirrors, so their interference patterns will change.

[crosscountry]

aren't the photons also effected by the gravity waves?


seems to me we're trying to detect something where the detector and the detectee are being changed exactly the same. If I grow an inch and you grow an inch then we're still the same height relatively.

I understand the concept, perpendicular arms will not be the same length if hit by a gravity wave. But how do we know that it will change the length anyway?

and again, isn't the photon changed in the same way?

[Tensor]

seems to me we're trying to detect something where the detector and the detectee are being changed exactly the same. If I grow an inch and you grow an inch then we're still the same height relatively.

But, if we compare our heights and find we are exactly the same height, then one of us grows buy some amount and the other growns by a different amount, and then we are compared, there will be a difference, right? We may not know how much each of us grew, but we can find the difference that each of us grew.

I understand the concept, perpendicular arms will not be the same length if hit by a gravity wave. But how do we know that it will change the length anyway?

That is the prediction of GR. The nature of Gravity Waves is such that the length of one of the arms should lengthen, while the other one doesn't. That's why this is a test of all gravitational theories. If Gravity waves are dected, those theories that don't predict gravitational waves will be discarded. For those that do predict waves, detection will contrain the theories.

and again, isn't the photon changed in the same way?

But the photons in each of the arms is changed by a different amount. That difference is what is detected. It's not the actual amount of change that is dectected, but the difference in the amount of change.

[Ken G]

Think about this. There is an ignorable degree of freedom embedded in reality, which has to do with size. If everything grows by a factor of 2, and time slows down accordingly to keep the speed of light the same, there would be no way for us to tell the difference. If there's no way to tell the difference, then there is no difference. So your question is, why don't gravity waves do the same thing? If they did, they would do nothing-- they wouldn't exist. There'd be no need for a theory that does nothing. So we know that the theory of gravity waves must describe a different kind of effect. It is an effect that changes distances in a way that is measurable, because time applies the same way to both directions, and the speed of light is the same in both directions, so if the distances are relatively different, there will be a relative change in time too. That's what is measured.

[crosscountry]

Think about this. There is an ignorable degree of freedom embedded in reality, which has to do with size. If everything grows by a factor of 2, and time slows down accordingly to keep the speed of light the same, there would be no way for us to tell the difference. If there's no way to tell the difference, then there is no difference. So your question is, why don't gravity waves do the same thing? If they did, they would do nothing-- they wouldn't exist. There'd be no need for a theory that does nothing. So we know that the theory of gravity waves must describe a different kind of effect. It is an effect that changes distances in a way that is measurable, because time applies the same way to both directions, and the speed of light is the same in both directions, so if the distances are relatively different, there will be a relative change in time too. That's what is measured.

I guess that's what I was asking. I ask that because even though I've studied (just a little) gravity waves they are still unresolveable to me.

But, if we compare our heights and find we are exactly the same height, then one of us grows buy some amount and the other growns by a different amount, and then we are compared, there will be a difference, right? We may not know how much each of us grew, but we can find the difference that each of us grew.

But if as Ken says the detector changes with the one who grows some height then we still measure the same. It's not possible to keep the detector seperated from the experiment.

That is the prediction of GR. The nature of Gravity Waves is such that the length of one of the arms should lengthen, while the other one doesn't. That's why this is a test of all gravitational theories. If Gravity waves are dected, those theories that don't predict gravitational waves will be discarded. For those that do predict waves, detection will contrain the theories.

It's worthy, you're right, to try. How long should we go without detection?

But the photons in each of the arms is changed by a different amount. That difference is what is detected. It's not the actual amount of change that is dectected, but the difference in the amount of change.

What I've studied shows that if gravity waves do exist they affect the physical world so minutely it is nearly impossible to detect. Even a nearby pulsar, which is supposed to create quite a lot of gravity waves, would barely be within the order of magnitude of our greatest detectors.

[Tensor]

But if as Ken says the detector changes with the one who grows some height then we still measure the same.

You are confusing the detector with the different legs. A laser light beam is split and sent down the different legs. It each beam makes several trips down and back up the legs (bounced off of mirrors). The beams are then brought back together and compared at the dectector. If a wave has gone by, the beams will be different (due to traveling different amounts) and that difference is what is detected at the detector. It doesn't matter that one of the legs has been stretched the same amount as the beam in that leg. I think you getting too caught up in thinking that they are directly measuring the change in the legs. They're not, they're measuring the difference in the changes between the legs.

It's not possible to keep the detector seperated from the experiment.

Before the beams are split, any effects the wave produces will be same on both split beams. Once brought back together, at the detector, the beams will again be affected by the wave by the same amount. Neither of these has any effect on the measurement. It is while the beams are split and in the different legs that each beam will change by a different amount. It is that difference that is detected when the beams are brought back together.

[crosscountry]

interferometry right? I get that part. it seems to me the photon will move accordingly when the wave passes to ofset the new length. Even that, don't these waves come by at the speed of gravity/light? if so the effect would/could go by before the photon was able to reflect - thus no measureable change.

[Peter Wilson]

Think about this. There is an ignorable degree of freedom embedded in reality, which has to do with size. If everything grows by a factor of 2, and time slows down accordingly to keep the speed of light the same, there would be no way for us to tell the difference. If there's no way to tell the difference, then there is no difference. So your question is, why don't gravity waves do the same thing? If they did, they would do nothing-- they wouldn't exist. There'd be no need for a theory that does nothing. So we know that the theory of gravity waves must describe a different kind of effect. It is an effect that changes distances in a way that is measurable, because time applies the same way to both directions, and the speed of light is the same in both directions, so if the distances are relatively different, there will be a relative change in time too. That's what is measured.

It is not the gravity waves that concern me. I am convinced "beyond a reasonable doubt" that gravity waves exist. My question is detecting them with interferometer. For example, we know from theory and experiment that the wavelength of light increases or decrease as you go up or down in a gravitational field. But can you detect this by putting interferometer on an elevator? I don't think so. With the whole appartus going up and down, everything will change in same, relative proportion.

Regarding the distance and wavelength changing but the speed of light being the same, let us try another thought experiment: the mirrors on each arm of the interferometer are 1 exactly zillion wavelengths apart. A gravitational wave from a supernova, which should have low frequency and thus long wavelength, happens to line up with one arm, and as it passes the instrument, the wave increases the distance between mirrors by 1 wavelength, or 1 part per zillion (ppz). The wavelength of the light also increases by 1 ppz, so there is no phase-change at the detector, but the time-of-travel has also increased by 1 ppz, which should be detectable as a relative change in time...except, the gravitational wave as it passes causes my clock to run 1 ppt slow, so my measurement of the round-trip time between mirros is the same

[Tensor]

Regarding the distance and wavelength changing but the speed of light being the same, let us try another thought experiment: the mirrors on each arm of the interferometer are 1 exactly zillion wavelengths apart. A gravitational wave from a supernova, which should have low frequency and thus long wavelength, happens to line up with one arm, and as it passes the instrument, the wave increases the distance between mirrors by 1 wavelength, or 1 part per zillion (ppz). The wavelength of the light also increases by 1 ppz, so there is no phase-change at the detector, but the time-of-travel has also increased by 1 ppz, which should be detectable as a relative change in time...except, the gravitational wave as it passes causes my clock to run 1 ppt slow, so my measurement of the round-trip time between mirros is the same

Let's see if we can help you work it out yourself. You've described one leg, now describe what happens in the other leg, the one that doesn't change it's length (actually, the length of other leg shrinks, I may have been keeping it too simple in trying to describe it to you).

[Tensor]

interferometry right? I get that part. it seems to me the photon will move accordingly when the wave passes to ofset the new length.

But the main thing is that the offset will be different for each of the legs, that is what detected

Even that, don't these waves come by at the speed of gravity/light? if so the effect would/could go by before the photon was able to reflect - thus no measureable change.

For LIGO, you are talking about waves with legths from 10's of Kilometers to the diameter of the earth. There is plenty of time, even moving at c, for the wave to cause a change in the length.

[crosscountry]

It is not the gravity waves that concern me. I am convinced "beyond a reasonable doubt" that gravity waves exist. My question is detecting them with interferometer. For example, we know from theory and experiment that the wavelength of light increases or decrease as you go up or down in a gravitational field. But can you detect this by putting interferometer on an elevator? I don't think so. With the whole appartus going up and down, everything will change in same, relative proportion.

Regarding the distance and wavelength changing but the speed of light being the same, let us try another thought experiment: the mirrors on each arm of the interferometer are 1 exactly zillion wavelengths apart. A gravitational wave from a supernova, which should have low frequency and thus long wavelength, happens to line up with one arm, and as it passes the instrument, the wave increases the distance between mirrors by 1 wavelength, or 1 part per zillion (ppz). The wavelength of the light also increases by 1 ppz, so there is no phase-change at the detector, but the time-of-travel has also increased by 1 ppz, which should be detectable as a relative change in time...except, the gravitational wave as it passes causes my clock to run 1 ppt slow, so my measurement of the round-trip time between mirros is the same

You have caught the essence of my questions.

[crosscountry]

But the main thing is that the offset will be different for each of the legs, that is what detected



For LIGO, you are talking about waves with legths from 10's of Kilometers to the diameter of the earth. There is plenty of time, even moving at c, for the wave to cause a change in the length.

isn't there enough time also for the change to end and the length be the same as before.

[Ken G]

The wavelength of the light also increases by 1 ppz, so there is no phase-change at the detector, but the time-of-travel has also increased by 1 ppz, which should be detectable as a relative change in time...except, the gravitational wave as it passes causes my clock to run 1 ppt slow, so my measurement of the round-trip time between mirros is the same

But this is just it-- there's only one clock, one rate of time, not two for the two different legs.

[Tensor]

isn't there enough time also for the change to end and the length be the same as before.

I hesitate, only because it could very well be that you are not understanding this becuase of the way I am describing it. But to your question, yes, there would be time for each of the legs to stretch, return to zero and then shrink several times as the waves pass (there shouldn't be just one GW, there should be a train of them). Basically, as the waves pass, the legs continually change their lengths, the interference pattern would be constantly changing.

[Ken G]

And to add to that last point, note that the rate of stretching has nothing to do with the speed of light. That is set by the frequency of the source. So if it is two neutron stars in close orbit, then the frequency of the orbit is the frequency of the wave, is the frequency of the stretching. Think of it as a "ringing" effect. The only thing the speed of light affects is the wavelength, but that means we need a long rod to sample an appreciable fraction of a wavelength. (Again, think in terms of the physical size of the source, that controls the wavelength).

[Peter Wilson]

Let's see if we can help you work it out yourself. You've described one leg, now describe what happens in the other leg, the one that doesn't change it's length (actually, the length of other leg shrinks, I may have been keeping it too simple in trying to describe it to you).

Well, that does make sense...except the part about the other leg shrinking while the one expands. But I'll quit while ahead, thanks

[crosscountry]

I hesitate, only because it could very well be that you are not understanding this becuase of the way I am describing it. But to your question, yes, there would be time for each of the legs to stretch, return to zero and then shrink several times as the waves pass (there shouldn't be just one GW, there should be a train of them). Basically, as the waves pass, the legs continually change their lengths, the interference pattern would be constantly changing.

Thanks. I guess I am just focusing on the difficulty to 'see' these gravitational waves. From what I understand our best sensors might be of the right magnitude to detect the strongest G-waves. Of course it takes old science to make new science. We can get better.


Hey, why don't we have 3D detectors? It is too hard to make an isolated structure that deep? I guess so. That makes detection even more difficult.

[selden]

They don't have to be in exactly the same location:
detectors parallel to the surface of the Earth in the US and in Eastern Europe could be at right angles to one another.

[Nereid]

They don't have to be in exactly the same location:
detectors parallel to the surface of the Earth in the US and in Eastern Europe could be at right angles to one another.

This is one (but only one) reason why it would be sooooo much better to have four detectors, well-separated on the Earth's surface, with the fourth a looong way from the plane defined by the other three.

Or, to put it crudely, there should be a LIGO in Australia (the US, Japan, Germany, and Italy are not enough).

[crosscountry]

They don't have to be in exactly the same location:
detectors parallel to the surface of the Earth in the US and in Eastern Europe could be at right angles to one another.

then they wouldn't be interferometers would they?

[selden]

The idea is that different sets of interferometers at different longitudes would be sensitive to gravitational waves that have different polarizations than the waves detectable at other longitudes, not that the different sites would act interferometrically with one another over those distances.

[AGN Fuel]

Well, that does make sense...except the part about the other leg shrinking while the one expands. But I'll quit while ahead, thanks

My understanding is that a beam of coherent light is split and the two light paths sent at 90 degrees to each other. They are then reflected back and recombined at a detector.

If a gravitational wave passes the apparatus, the deformation caused by the wave will cause one beam path to increase while the orthoganal path will decrease*. At recombination, this deformation causes the beams to be out of phase.

So the important point is not how long the light takes up and down the one leg of the apparatus, but rather how long it takes in comparison to the same beam sent on an othagonal path.

(*What would happen if the deformation in both directions was exactly half a wavelength each way?!)

[crosscountry]

The idea is that different sets of interferometers at different longitudes would be sensitive to gravitational waves that have different polarizations than the waves detectable at other longitudes, not that the different sites would act interferometrically with one another over those distances.

I'm probably misunderstanding what you mean. Don't the perpendicular arms of the interferometer have to be connected at a common point? that's what makes them interferometers right? that they share a split single beam of light?