# B How to measure Gravitational waves

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1. Nov 1, 2017

### Number 42

Why are clocks not used to measure gravity waves?

Spacetime wriggle and time must also vary. It is possible to measure time very accurately and with a high resolution. Så why not use clocks to detect gravity waves?

2. Nov 1, 2017

Staff Emeritus
What exactly do you intend to time?
How good a clock do you need?
How do you compare two clocks far away from each other?

3. Nov 1, 2017

### Ibix

Not necessarily. Gravitational waves (not gravity waves - that's a kind of surface wave on water) can affect the spatial part of the metric only. I don't think they can ever affect the time part of the metric only.

4. Nov 1, 2017

### Staff: Mentor

In appropriately chosen coordinates, yes. Those coordinates (the transverse-traceless gauge) are the ones standardly used to analyze gravitational wave detectors like LIGO, but it's worth keeping in mind that it's still a choice of coordinates.

That's correct; to state it more precisely, there is no possible choice of coordinates for which a GW only affects $g_{00}$ and not any other metric coefficient.

5. Nov 1, 2017

### vanhees71

One should emphasize however that the deformation of LIGO's arms due to the gravitational wave is of coarse gauge independent since it's a real physical effect of gravity. The choice of coordinates is completely arbitrary. Any choice will lead to the same outcome of the measurable physics, including the deformation of LIGO's arms and the change of the interference pattern of the laser light finally measured.

6. Nov 1, 2017

### Ibix

Understood. But whatever you choose to mean by "time" shouldn't there be a way to pick a gravitational wave so that it doesn't have any component in the time-like direction?

7. Nov 1, 2017

### vanhees71

You need to define some physical quantity to get a sensible answer to the question about the physical meaning of a particular solution of Einstein's equations (here gravitational waves in the usual approximation of the linearized theory). That's analogous to the solutions of Maxwell's equations in terms of the potentials. The potentials have no physical meaning a priori, but you have to calculate physically measurable quantities (like the electromagnetic field components) or evaluate how particles move in the so defined electromagnetic field (which of course also only depends on the field components but not the potentials). For sure, any "gauge dependent" quantity in gauge theories is not directly physically interpretable but you have to use gauge independent measureable quantities to get physics sense from it.

8. Nov 1, 2017

### Staff: Mentor

For weak (i.e., linear) gravitational waves, yes, they are purely transverse, so you can always choose coordinates (the transverse traceless ones) that express all of the spacetime curvature due to the waves as purely spatial. But of course that choice will be different for different waves (i.e., waves going in different directions).

9. Nov 1, 2017

### Ibix

Right. So doesn't that answer why you wouldn't use clocks to detect gravitational waves? There are a whole family of waves you just can't detect without sensors in relative motion.

10. Nov 1, 2017

### Staff: Mentor

I would say it shows why you can't use a set of clocks all at rest relative to each other to detect gravitational waves. (The OP's question probably had the part I put in italics as an unstated assumption, but it's still an assumption.)

11. Nov 2, 2017

### Number 42

I would think that the clocks should be spaced so that some are far enough away to be in different part of the wave. Say 1/4 of a wavelength.
Clocks close together will ofcourse not show any difference.
Transmitting the clock signal would not be a problem , but are clockes accurate enough?

12. Nov 2, 2017

### timmdeeg

Lets assume LIGO's mirrors carry synchronized clocks. Aren't they no more synchronous in case a GW passes by?

13. Nov 2, 2017

Staff Emeritus
I repeat:

What exactly do you intend to time?
How good a clock do you need?
How do you compare two clocks far away from each other?

14. Nov 2, 2017

### Staff: Mentor

This is not something you can just assume. You have to describe what "synchronized" means and how it will be accomplished. (For example, Google "Einstein clock synchronization".)

15. Nov 2, 2017

### pervect

Staff Emeritus
Yes. On a practical note, one can define clock synchronization is to choose some coordinates. With defined coordinates, clocks can be defined as synchronized if they have the same time coordinate. But in general, the results will depend on one's choice of coordinates.

Clock synchronization is presented as a human choice, and to a large extent it is. However, if one wants decent compatibility with Newtonian phsyics, so one can use most Newtonian formulae, one needs to use something like Fermi normal coordinates and make sure that the region one is analyzing is "small enough". I've seen a lot of posters who deal with the clock synchnoziation issue by ignoring them :(, this almost always leads to confusion in the end.

Conventional wisdom is more along the lines of "don't use coordinate dependent methods at all". This is OK, if one can get the necessary physical intuition that way, but if one is seeking some intuitive insight, using the coordinate methods and the right set of coordinates can be helpful. Contrawise, using the wrong set of coordinates can lead to more confusion.

The biggest problem with using Fermi normal coordinates in this context is converting the GW solution to these coordinates - while the GW has a nice closed form solution in the TT coordinates, attempts to convert them to Fermi Normal coordinates quicly results in a real mess. I do recall vaguely seeing some paper on the topic that talked about this issue and (I believe) they managed to deal with the mess, somehow. BUt I don't know how.

The aproach of "Fermi coordinates are too hard so I'll just use TT coordinates and interpret them in a Newtonian manner is just wrong :(.

16. Nov 4, 2017

### timmdeeg

I've read that but am thinking about a more-straight forward approach to see how the proper time is affected by the so-called ripples in spacetime. The proper time of a free clock in flat spacetime is recorded during the passage of a gravitational wave. The clock frequency shall be much higher than the frequency of the gravitational wave. After the wave has passed by the recorded ticks are compared with the ticks of the clock. Are the recorded ticks slower and faster according to the phase of the gravitational wave?

17. Nov 4, 2017

### Staff: Mentor

What "recorded ticks"? Other than the clock itself, what else is "ticking"?

18. Nov 4, 2017

### timmdeeg

The ticks which have been recorded by the clock during the passage of the GW will then be compared with the ticks of the same clock in flat spacetime however without a GW passing by.

19. Nov 4, 2017

### Staff: Mentor

How would you make such a comparison? Think carefully.

20. Nov 4, 2017

### timmdeeg

I would check if the frequency of the recording is periodically lower and higher than the frequency of the the clock. But how to do this technically, I would have to ask my technician.

21. Nov 4, 2017

### Staff: Mentor

Your technician will tell you that there is no way to make this comparison, because the recording does not tell you at what speed to play it back, relative to the frequency of the ticks you are observing now. You have to have some independent way of telling when you are playing back the recording at "the right speed", and the only such way is to use clocks that are ticking right now. There is no independent standard of time.

22. Nov 5, 2017

### pervect

Staff Emeritus
I think you need to adopt a coordinate system, otherwise all you'll find out is that clocks tick at a constant rate as measured by clocks. That's what clocks do. The idea of clocks changing it's rate requires that one have a coordinate system that one compares the proper time reading of the clock (which doesn't depend on the coordinates) with. At least I can't imagine what else you'd be comparing the clock to. Then we back to asking - what coordinates are you talking about. If you define a set of coordinates, then we just need the metric associated with that set of coordinates, and what you're asking about is basically $g_{00}$ for that specific metric. But that isn't defined until you define the coordinates.

23. Nov 5, 2017

### Ibix

Let’s assume that your recording is a standard CD quality digital one that takes 44k samples per second. If the clock being recorded slows down in some sense, what's going to happen to the clock driving the sampler?

24. Nov 5, 2017

### timmdeeg

Oh, you have been very fast. I've seen your post after having deleted mine, because I started to see my misconception. What I described wasn't "an independent way of telling when you are playing back the recording at "the right speed", as PeterDonis mentioned in #21.
Thanks for taking care.

So would the only reasonable way be to compare the clock rates of the free and the fastened clock by means of Einstein synchronisation?

25. Nov 5, 2017