# Could two atomic clocks really be used to detect gravitational waves from a distant source? If so, how?

Three articles report on the recent paper in Phys Rev. D: Flanagan, Éanna É. et al. 2019 Persistent gravitational wave observables: General framework (also ArXiv):

The Live Science article's summary is probably the most simplified. One of the three new proposed effects is explained as follows:

Two atomic clocks placed some distance from each other would experience a gravitational wave differently, including its time-dilation effects: Because time would be slowed more for one clock than the other, subtle differences in their readings after a wave passed might reveal a memory of the wave in the local universe.

Question: Could two atomic clocks really be used to detect gravitational waves from a distant source? If so, how in principle?

I'm not asking if a practical detector could be built today using two atomic clocks. I'm just asking how two atomic clock could do this in principle, as (apparently) Flanagan et al. seem to suggest.

The three effects described in Flanagan et al. are summarized in the Phys.org article as follows:

The researchers identified three observables that show the effects of gravitational waves in a flat region in spacetime that experiences a burst of gravitational waves, after which it returns again to being a flat region. The first observable, "curve deviation," is how much two accelerating observers separate from one another, compared to how observers with the same accelerations would separate from one another in a flat space undisturbed by a gravitational wave.

The second observable, "holonomy," is obtained by transporting information about the linear and angular momentum of a particle along two different curves through the gravitational waves, and comparing the two different results.

The third looks at how gravitational waves affect the relative displacement of two particles when one of the particles has an intrinsic spin.

• I'm not clear on what you're asking. You link to a research paper, as well as several popularizations or press releases which are targeted at an audience with less expertise. Are you (1) asking whether the paper is wrong, or (2) asking for an explanation at some different level? If 1, then do you have some reason to think it's wrong? If 2, then what level do you want? An intermediate level? What intermediate level? Undergrad engineering major? First-year grad student in relativity? – Ben Crowell May 10 at 3:35
• @BenCrowell I think what I am asking is absolutely clear, "Question: Could two atomic clocks really be used to detect gravitational waves from a distant source? If so, how in principle?" but it's the nature and level of the desired answer that can be clarified. I can't access the Phys. Rev. D paper for another few days, but if I could I have a hunch there won't be a paragraph that outright explains how one could use two atomic clocks to detect gravitational waves. Since one summary claims the paper supports this, I'm asking how. – uhoh May 10 at 3:40
• @BenCrowell if however it is fairly clear in the paper how this could be done in principle, then it's possible that a block quote with a bit of an added explanation might be the perfect answer. If it turns out the paper does not support this, and the statement in Live Science turns out to be wrong or ill-informed, then the answer would be pretty straightforward and short. – uhoh May 10 at 3:41
• @BenCrowell but certainly an answer based on original though and other references instead of the linked paper is welcome as well. That's why the phrasing of the question itself does not refer to the linked paper. I don't want to constrain the answer to have to be based on it. – uhoh May 10 at 4:08
• If you substitute one of the clocks with a pulsar that is spinning with a constant frequency, this idea sounds a lot like what they do with Pulsar Timing Arrays. The way I see this (without understanding GR) is that by comparing the arrival times of the regular pulses with a good clock, you observe the distance variations between the pulsar and the radio telescope (basically a sort of Doppler measurement) due to a passing GW. A similar trick can be done by exchanging the time of two clocks via radio. – Bas Swinckels May 15 at 15:18