# Can LIGO be explained in terms of gravitons?

If electromagnetic waves from a star are so faint, all that can be detected are single photons on a photographic plate.

For the LIGO experiment, the gravitational waves were so weak, I would have guessed that only single gravitons would interact with the experiment.

What in my naivety, I would expect is that instead of the whole apparatus growing or shrinking by a small amount, only parts of it would grow or shrink in a stochastic manner. And that what one would observe would be that some photons would take longer or slower to reach the end but some would just behave as if there was no wave at all.

Clearly, I have something wrong. How then could LIGO be explained in a graviton picture of things? Assuming the gravitational wave quanta are gravitons. Or on the other hand does LIGO disprove the existence of gravitons?

• I'm not really sure what you mean in your 3rd paragraph. But surely, LIGO does not disprove the existence of gravitons; it rather verifies an aspect of it. See physics.stackexchange.com/q/235603/133418 – Avantgarde Nov 1 '18 at 20:09
• For the LIGO experiment, the gravity waves were so weak, I would have guessed that only single gravitons would interact with the experiment. No, people have done estimates showing that no foreseeable technology could ever detect individual gravitons. What LIGO is detecting is a coherent state composed of a very large number of gravitons. – Ben Crowell Nov 1 '18 at 21:19
• @Ben. Exactly. But how many gravitons? If the star is so far away, wouldn't the gravitons have diluted? I see the G. Smith has done the calculations. – zooby Nov 2 '18 at 21:41

The power per unit area in a monochromatic gravitational wave is $$c^3h^2f^2/8G$$ where $$c$$ is the speed of light, $$h$$ is the dimensionless RMS amplitude of the gravitational wave, $$f$$ is the frequency of the wave, and $$G$$ is Newton’s gravitational constant. (See eqn. (62) in https://www.sif.it/static/SIF/resources/public/files/va2017/Sutton1.pdf.)
For GW150914, the first wave detected by LIGO, $$h$$ was about $$10^{-21}$$ (meaning that the length of the LIGO arms oscillated by about one part in $$10^{21}$$) and $$f$$ was about 200 Hz. Putting in these numbers gives about 2 milliwatts per square meter. This is roughly the same flux as in moonlight during a full moon... not a huge flux, but a classical-scale one.
Each graviton in a 200 Hz wave carries only $$1.3\times10^{-31}$$ joules. (Multiply the frequency by Planck’s constant.) So, at Earth, the wave consisted of $$1.5\times10^{28}$$ gravitons per second passing through each square meter perpendicular to the line from the merging black holes to Earth.