Do gravitational waves distort time?

[Danijel Gorupec]

As a gravitational wave passes though a constellation of precise clocks, would it be possible, at least in theory, to detect its passage by measuring time difference between clocks? If so, is it harder to make such measurements than to measure spatial distortions?

[Genady]

In the approximation of week gravitational waves, the spacetime metric is perturbed only in the two-dimensional plane perpendicular to the wave propagation.

[swansont]

29 minutes ago, Danijel Gorupec said:

As a gravitational wave passes though a constellation of precise clocks, would it be possible, at least in theory, to detect its passage by measuring time difference between clocks? 

In principle, yes, if you have an array on the scale of the GW wavelength

https://arxiv.org/abs/1501.00996

[Danijel Gorupec]

3 hours ago, Genady said:

In the approximation of week gravitational waves, the spacetime metric is perturbed only in the two-dimensional plane perpendicular to the wave propagation.

I was indeed interested in weak gravitational waves... I would be surprised if the theory only predicts disturbances in spatial dimensions, and not the time dimension. Because I am under impression that the theory treats space and time on more or leas equal footing.

Anyway, I am now thinking about what you said, if gravitational waves indeed can cause only (or predominantly) spatial disturbance, can then there exist a different type of gravitational wave that only (or predominantly) causes time disturbance?

 

@swansont Thinks for the link.

[Genady]

1 hour ago, Danijel Gorupec said:

I was indeed interested in weak gravitational waves... I would be surprised if the theory only predicts disturbances in spatial dimensions, and not the time dimension. Because I am under impression that the theory treats space and time on more or leas equal footing.

Anyway, I am now thinking about what you said, if gravitational waves indeed can cause only (or predominantly) spatial disturbance, can then there exist a different type of gravitational wave that only (or predominantly) causes time disturbance?

 

@swansont Thinks for the link.

Yes, what is spatial and what is temporal depends on frame of reference. In the approximation that I refer to, the frame of reference is fixed in such a way that the gravitational waves are small perturbations in flat Minkowski spacetime which move along, say, x-axis. Then, they cause length contractions and expansions in the y- and z-axes.

Edited December 26, 2023 by Genady

[Genady]

I've looked at the derivation again. In simple terms, it boils down to the fact that gravitational waves are transverse waves in spacetime. So, in coordinates where they move along t- and x-axes, they perturb the metric in the orthogonal y- and z-axes.

[Danijel Gorupec]

On 12/30/2023 at 4:44 PM, Genady said:

I've looked at the derivation again. In simple terms, it boils down to the fact that gravitational waves are transverse waves in spacetime. So, in coordinates where they move along t- and x-axes, they perturb the metric in the orthogonal y- and z-axes.

The derivation you are mentioning... is it considering some sort of plane gravitational waves, or more general? As I understand you, you are also talking about near-observer perturbations?  Otoh, the array of clocks, I was mentioning, is distributed.

[Genady]

30 minutes ago, Danijel Gorupec said:

is it considering some sort of plane gravitational waves

Yes.

 

30 minutes ago, Danijel Gorupec said:

near-observer perturbations?

Yes.

It is a linearized GR approximation.

Edited January 1 by Genady

[Boltzmannbrain]

Yes, I would definitely think that the detector would read a dilation of time.  A precise clock should breifly slow *slightly* as the wave passes.

 

A gravitational wave comes from the acceleration of mass.  This would seem to mean that a gravitational wave would cause a very brief moment of gravitational increase and decrease to the detector.  So depending on how strong the wave is, it would be just like a mass existing for a brief period and then disappearinas at the detector.  And I would think that this must cause a brief time dilation as well.

A question I find interesting is what is the trough of a gravitational wave?  If the crest is a brief pull with time dilation, is the trough a push with time "expansion"?  Is it a sort of moment of anti gravity or dark energy? 

I am very much open to critique by anyone if what I said is nonsense.  

[Markus Hanke]

On 12/26/2023 at 4:32 PM, Danijel Gorupec said:

As a gravitational wave passes though a constellation of precise clocks, would it be possible, at least in theory, to detect its passage by measuring time difference between clocks?

Yes, this is possible; this is in fact one of the standard ways to (in principle) build GW detectors:

https://arxiv.org/abs/1501.00996

You need an extended array of clocks for this, since what you are measuring is the dilation between clocks at different positions within a passing GW wavefront.

On 12/26/2023 at 4:32 PM, Danijel Gorupec said:

If so, is it harder to make such measurements than to measure spatial distortions?

Let’s just say it’s equally hard

You’d need an extended array of very precise and perfectly synchronised atomic clocks. This is doable at least in principle with current technology.

[Genady]

8 hours ago, Markus Hanke said:

https://arxiv.org/abs/1501.00996

Quote

The standard time-dilation effect for a clock at some distance from a black hole, would be modulated by the periodic change in this distance due to the orbital motion in a binary black hole system.

Do I understand correctly that they do not talk about measuring time dilation due to a passing gravitational wave but rather about changes in the background time dilation due to a motion of the sources of that time dilation?