# Particles Associated With Gravitational Waves

I've been reading about linearized GR and the study of gravitational waves, and an odd thought popped into my head. According to wave-particle duality (admittedly, usually used in quantum mechanics!), particles can act like waves, and waves can act like particles. My logic was that, therefore, there should be a particle associated with a gravitational wave. There is one thing, though, that might interfere with this: gravitational waves are plane waves, not longitudinal waves - which is how we describe, for example, photons. But my original question still stands: Is there a particle associated with a gravitational wave? If not, why not? If so, is there a separate mathematical structure associated with it (aside from the metric for the wave)?

FYI: Nope, I'm not talking about gravitons. I know those are completely different and unrelated (and, at the moment, hypothetical).

Let's look theoretically to your question. Let's introduce linearized GR and then let's derive the wave equations. It is exactly the second Bianchi equation for the Weyl tensor. We want to associate some particle to the gravity wave (only for linearized gravity limit). For associating we must do at least two things:

1) Show that equation for hypothetical particle coincides with the equation for the Weyl tensor.

2) Show that theory of interaction of corresponding field of this particle with matter respects the equivalence principle.

It can be shown, that theory for massless free particle with helicity 2 are completely equal to the free generalized GR. Also, in the infrared limit the lorentz-invariance and existence of nontrivial scattering processes requires equivalence principle (i.e., the coupling constants of interaction with different kinds of fundamental fields).

So we may conclude that in a case of linearized gravity we may represent the gravitational waves as gravitons. But corresponding theory has many hard problems, of course.

If there was a quantum theory of gravity (which there isn't) then it would include a graviton as the elementary particle associated with gravity, in the same way that the photon is associated with the electromagnetic field (as CuriousMind says).

An electromagnetic wave in vacuum is transverse - both the electric and magnetic fields are vectors that are at right angles to the direction of propagation. In Quantum Field Theory this is somehow connected to the fact that the photon has spin 1.

A gravitational wave is a tensor wave - the disturbance is in the metric, which is a tensor. One can loosely say it is transverse for the following reason: There is a theorem that says that a spherically symmetric body (for example a symmetric collapsing star) does not generate gravitational waves - because all the movements of matter are radial, and this in the same direction as the putative outgoing wave. The tensor nature means the graviton must have spin 2.

In Quantum Electrodynamics (QED) one or more virtual photons are exchanged between two particles that interact electromagnetically. (I suppose this picture strictly only applies in the perturbation theory approach, in which Feynman diagrams are used.)

In Quantum Gravity Theory (if it existed) one or more virtual gravitons would be exchanged between particles interacting gravitationally. The photon and the graviton are both massless. This is related to the fact that both are long range forces, with an inverse square dependence, with no exponential drop-off with distance.

In QED real photons (observable light) are created when charges accelerate. In Quantum Gravity Theory (if it existed) real gravitons are created when mass (or pressure or stress) accelerates.

The particle nature of gravitational radiation would be difficult to observe experimentally, because it is almost impossible to think of processes that would create gravitons of 1 electron-volt of energy or more - the energy that is easy to measure as it corresponds to chemical reactions, the photoelectric effect, and such-like. Hope this helps, @HDE.

• I have to say, I knew just about everything you stated. But I appreciate the answer. – HDE 226868 Aug 13 '14 at 21:01
• I think by "plane waves", the OP means that the waves are tensors with components perpendicular to the direction of travel, requiring a quadrupole moment to be generated. – Jerry Schirmer Aug 13 '14 at 21:25
• Yep, @JerrySchirmer is right. I should have been more detailed. – HDE 226868 Aug 13 '14 at 22:27