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I have been reading several papers on massive gravity. All of them have equations that involve the square of the graviton mass, rather than graviton mass itself. See for example, equations 43 and 44 in

https://arxiv.org/abs/1505.00743

or de Rham's review of massive gravity in https://arxiv.org/abs/1401.4173 .

This makes me wonder if a graviton has a negative mass. Such negative mass gravitons will still obey these equations (because the square of a negative number is a positive number, just like the square of a positive number).

Can anyone in this forum give any reason why gravitons cannot have a negative mass? Of course, general relativity (GR) is compatible only with gravitons having a zero mass. But massive gravity theories are a modification of general relativity. So the question of massive gravitons contradicting GR does not arise.

Qmechanic
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doctorsundar
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3 Answers3

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You are partially correct. Gravitons are considered to be massless. It is because gravitational force propagates with the speed of light and you need to be massless to reach such speeds.

But here is the interesting thing:

Some dude tried to put some negative mass in the Unvierse and tested the hypothesis that resulted in some paradoxes. Read up on "runaway phenomenon".

There is another hypothesis that antimatter may have negative (gravitational) mass. This would indeed violate the principle of equivalence since chunks of antimatter (eg, antiparticles produced in an accelerator) still have positive energy.

Since General Theory of Relativity is not the theory of matter, there is no reason why we could not introduce, in principle, matter with negative mass. People did try that but the problem with such a theory was not due to the equivalence principle, but due to the fact that such negative mass states would have lower energy than empty Minkowski space, so the vacuum itself would be unstable.

In massive gravity theory, gravitational waves obey equations where they travel at a speed lower than the speed of light. Food for thought: if we happen to observe a gravitational wave at the exact same time as we visibly see it, then we would know that they travel at the same speed but if we observe something different, then we have something to work with. I am sure some Noble Prize aspirants are probably working on that theory.

LostCause
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A particle with a negative mass (meaning, a mass lower than the energy of the vacuum) would be disastrous. The vacuum would be unstable to decay into a state with an arbitrary number of negative mass particles balanced with positive kinetic energy.

The reason that the mass squared parameter appears in the action, instead of the mass, is so that the dispersion relation of the free theory on a flat background has the form $\omega^2=k^2+m^2$, so that when you quantize the free theory and find modes with $E=\omega$ and $k=p$, particle excitations associated with each mode obey the energy-momentum relationship for a free particle in special relativity $$ E^2 = p^2 + m^2 $$ Physical excitations have positive energy (relative to the vacuum) and correspond to the positive square root of this equation. This is common to how all relativistic theories are formulated, and is not special to massive gravity.

Andrew
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The universe could be full of negative mass particles that cause dark matter and dark energy, see http://arxiv.org/abs/1712.07962

The graviton mass could then be negative.

Richard Foreman
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