# 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

## 1 Answer

No, LIGO is not detecting individual gravitons. It is detecting fairly powerful gravitational waves made of vast numbers of gravitons. Although the waves that reach the Earth carry a significant amount of power per unit area, they cause only a miniscule deformation of spacetime, changing the length of LIGO’s arms by something like one-ten-thousandth of the diameter of a proton. Although they have a tiny effect, you should not think of them as weak.

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.

LIGO is detecting “classical” gravitational waves, as described by General Relativity, and tells us nothing about gravitons. Their likely existence remains a reasonable theoretical assumption, based on quantum wave-particle duality observed for other fundamental interactions. If LIGO eventually detects astronomical events that cannot be explained by GR, then it may some day give us insights into quantum gravity, but it won’t do so by detecting individual gravitons.

• Great answer. So even though the waves are weak the number of gravitons is still so huge that it can be treated classically. I guess you could say that you need a huge amount of energy to stretch the fabric of space-time. So even a "weak" gravitational wave is very strong! Nice comparison with moonlight too. – zooby Nov 2 '18 at 21:46
• 10^28 sounds a lot, but in a square meter of metal layer there might be 10^20 atoms. So every second, about 10^8 gravitons passes though or near each atom. Well, I guess that is still a lot. But in a m^3 of matter there is about 10^30 atoms and there will be about 10^20 gravitons at any instant. So at any instant only 1 in 10^10 atoms in a m^3 block will be next to a graviton. – zooby Nov 2 '18 at 22:05