# Measuring Distance with Time

Revolution
Joined: 17 Jun 05
Posts: 11
Credit: 14,349
RAC: 0
Topic 189509

I'm a relative (relativistic?) newcomer to Einstein@home but have been processing for seti@home since its inception.

I have some basic concerns about the science of the LIGO method of detecting Gravity Waves and thought I'd post here.

After having read the (layman) LIGO science doc explaining the process it seems fair to assume that variations in gravity fields of distant objects should be detectable by some method. Obviously we live inside a rather deep gravity well which for all intents and purposes is reasonably stable. At least I weighed the same yesterday as I do today.

The LIGO system therefore is looking to detect gravity waves (variations in gravity?) by measuring the distance between two points four kilometers apart and by using two detectors at right angles hope to see a phase change between distance. Note that facilities using long arms and short arms can null out local gravity disturbances or seismic activity.

So my main concern is the use of measuring distance using time. As I see it, variations in curved space-time are as a result of a variations in gravity. Wouldnt the time vary in harmony with space?
If a laser burst (say a one microsecond pulse) is timed across an 8 klm distance (2 x 4klm) and takes 26uS to traverse the distance wouldnt the time taken be altered by a gravity wave resulting in a null value in perceived distance?

I look forward to someone clarifying this.

Chipper Q
Joined: 20 Feb 05
Posts: 1,540
Credit: 708,571
RAC: 0

### Measuring Distance with Time

Take a quick look at this animation of how LISA will “directly detect” gravitational waves (click the “directly detect” link on this NASA website to open the applet of the animation).

If that doesn't help, I believe it's thoroughly covered in this web-based course from Caltech.

Quote:

So my main concern is the use of measuring distance using time. As I see it, variations in curved space-time are as a result of a variations in gravity. Wouldnt the time vary in harmony with space?

I think the 'harmony' you're concerned about occurs in the “near zone” (near a gravitational wave source, relative to the mass and physical size of the source), but at greater distances from the source, in the “local wave zone”, it becomes less a concern, and the question becomes, “what is the nature of the component realization of the equation of geodesic deviation?”

MarkF
Joined: 12 Apr 05
Posts: 393
Credit: 1,516,715
RAC: 0

### The effect of a gravity wave

The effect of a gravity wave on the propogation of laser beam is to create weak side band signals. If fl is the frequency of the light and fg the frequency of the gravity wave then first order side bands are fl-fg and fl+fg. These side band signals are so weak compared to the main beam that the effect on the interference pattern can be ignored.

Ben Owen
Joined: 21 Dec 04
Posts: 117
Credit: 65,916,710
RAC: 3,643

### Revolution, This question,

Revolution,

This question, or another version of it, is actually quite common. I think it's because those of us who work on gravitational waves explain it in two ways and forget to mention the link between them.

The usual version I hear goes something like: Yesterday you said that LIGO has a couple of 4km arms and that a gravitational wave makes the arm length change a little bit. Today you said that the gravitational wave shows up as a little bit of a change in the frequency of the laser light because the definition of time is changing. But if c is constant, the wavelength of the light must be changing too. If the wavelength and the arm length change in the same way, how can you tell?

The answer is that yesterday I gave an answer that was true in one frame of reference, and today I gave one that was true in another. You can pick a frame where the arm length changes and the wavelength does not. You can pick another frame where the arm length does not change and the wavelength does. You can pick another, in between, where both change by half as much; and so on. You can't pick one where both change in harmony. What is actually being measured is basically the number of wavelengths that fit into an arm, and that changes in the same way in all frames.

What's behind the answer is the principle of relativity itself: Fundamental physical observables are the same in any frame of reference (coordinate system), so you can use any frame you like and switch at will. Those of us who have been doing it for a while often don't explain it because it's become second nature to us and we forget that it's not obvious.

Hope this helps,
Ben

Revolution
Joined: 17 Jun 05
Posts: 11
Credit: 14,349
RAC: 0

WOW!

I'm a CATV production test tech and work with RF and laser optics in the 1310 and 1550 nm wavelengths here in Australia. I understand what you're saying in that post.
The effect then of the gravity wave is as Mark said

Quote:
to create weak side band signals

due to the phase change.
I guess that you compare the emitted laser with the returned laser and result in a "difference" signal equal to the wavelength of the gravity wave.
I'm curious about the effect of the gravity wave on a fixed mass at a known point. For instance LISA will use a small polished cube as the reflective mass.
Does any Gravity Wave detector have to use a single mass as the detector reference?
As I work with optical fiber and shooting 10mW lasers down long fibers is how many people get their television, could the same principle be used with a straight line optical fiber and achieve the same thing as LIGO or even LISA?
If I used a 100klm length of optical fiber would I see a phase change between the emitted laser and the returned laser?
Could I in fact then use 100 x 1klms up and back and see 100 x the phase change I would see in a 1 Klm run?

Please feel free to tell me I'm an idiot ;-)

Thanks

Robert.

MarkF
Joined: 12 Apr 05
Posts: 393
Credit: 1,516,715
RAC: 0

### RE: could the same

Quote:
could the same principle be used with a straight line optical fiber and achieve the same thing as LIGO or even LISA?

Yes if your fiber was perfect. But as good modern fiber optics are there is nothing like a good hard vacum for consitency.

I don't think Ben and I were talking about the same thing. I was talking about how the laser beam is affected by gravity waves, without regard to the end points. I think Ben was talking about various ways to describe the behavour of the end points.

Chipper Q
Joined: 20 Feb 05
Posts: 1,540
Credit: 708,571
RAC: 0

### RE: Yes if your fiber was

Message 13920 in response to message 13919

Quote:

Yes if your fiber was perfect. But as good modern fiber optics are there is nothing like a good hard vacum for consitency.

If the diameter of the fiber was made very small (~nanometers), and the fiber was curved in a radius that very nearly exceeded its critical angle, would a propagating GW alter the critical angel of the fiber (at all, or) enough to detect a change in an optical signal in the fiber?

Chipper Q
Joined: 20 Feb 05
Posts: 1,540
Credit: 708,571
RAC: 0

### RE: Yes if your fiber was

Message 13921 in response to message 13919

Quote:

Yes if your fiber was perfect. But as good modern fiber optics are there is nothing like a good hard vacum for consitency.

I'm sorry if it seems like there's “hard vacuum” between my ears --
As I continue learning, I'm finding no shortage of models and theories trying to combine GR with QM, and so I was wondering if there's a generally preferred way to think of empty space?
The question (I've seen expressed elsewhere ) may also be phrased, “what energy and circumstance is provably required to create such a state of matter-free space?”
Do stray particles in the arm of a LIGO detector affect the interferometry that much?

MarkF
Joined: 12 Apr 05
Posts: 393
Credit: 1,516,715
RAC: 0

### RE: If the diameter of the

Quote:
If the diameter of the fiber was made very small (~nanometers), and the fiber was curved in a radius that very nearly exceeded its critical angle, would a propagating GW alter the critical angel of the fiber (at all, or) enough to detect a change in an optical signal in the fiber?

An interesting idea. I believe something similar was attempted to build small gyroscopes.
I have never modeled the system you discribe so I can't say what the overall effect would be. If the stability and consitency of fiber optic cables were high enough and the dispersion low enough I think the folks at LIGO would have taken advantage of it and saved them selves the all the headaches of pump down and bake out.

Revolution
Joined: 17 Jun 05
Posts: 11
Credit: 14,349
RAC: 0

### Could we be seeing Amateur GW

Could we be seeing Amateur GW Astronomers one day?
GW telescopes (in as much as a dish antenna is a "telescope") could be engineered using new methods of construction to allow both a good sensitivity of detection and physically smaller size.
In the lectures I've watched, G waves have to conform to the same laws that EM waves do. One could think therefore of steady state gravity as keeps us here on the Earth as "DC" and close GW sources like the Moon and Sun as "AC".

Obviously a great start for Amateur GW Astronomers would be to detect those strong GW sources and use them as a benchmark for improvement.
Having not read through the whole site here I'm not sure if this kind of idea has been thought of. Luckily I do have a few semiconductor lasers/detectors and reels of optic fiber.
Please dont think I'm taking anything away from the amazing work thats been done at LIGO etc. I am intruiged to think others could achieve "science@home".

Chipper Q
Joined: 20 Feb 05
Posts: 1,540
Credit: 708,571
RAC: 0

### RE: RE: If the diameter

Message 13924 in response to message 13922

Quote:
Quote:
If the diameter of the fiber was made very small (~nanometers), and the fiber was curved in a radius that very nearly exceeded its critical angle, would a propagating GW alter the critical angel of the fiber (at all, or) enough to detect a change in an optical signal in the fiber?

An interesting idea. I believe something similar was attempted to build small gyroscopes.
I have never modeled the system you discribe so I can't say what the overall effect would be. If the stability and consitency of fiber optic cables were high enough and the dispersion low enough I think the folks at LIGO would have taken advantage of it and saved them selves the all the headaches of pump down and bake out.

I was actually thinking along the lines of a couple types of carbon nanotubes: 1 type for the optics, and a 2nd type for maintaining stability of the “fiber”. (The 2nd type might provide feedback as well.) As you point out, stability and dispersion factors are key (and bulk fiber hence may not qualify)...