In the table of the Particle Data Group on gauge and Higgs bosons the following appears:
graviton J = 2
Mass m < 7 × 10−32 eV
How do they come up with this figure?
I am not a physicist so I will gladly accept any explanation down to and including a Just-So one.
In general relativity gravity is described geometrically by the metric tensor field on spacetime, this is completely different to how other forces are described and is one of the main barriers to quantum gravity. One way round this is to break the metric tensor down into a ‘background metric’ + ‘gravitational field’ which means you now have a reasonably standard classical field defined on spacetime which you can quantitize (not that there aren’t difficulties encountered when you try to do this). The resulting gravitational field is a massless spin-2 self-interacting field.
Now it could be argued that a very small graviton mass could in fact approximate a massless field, so we must allow for that possibility and there are various ways of putting an upper bound on the graviton’s mass. One argument is that if the graviton did have mass, then it’s Compton wavelength must be greater than the size of the visible Universe, otherwise the effects of graviton mass would be discernible the the large scale structure of the Universe. This provides the lowest upper bounds on graviton and is where the figure quoted above comes from.
The mass limit comes from assuming a particular form for the gravitational potential that allows for a massive or massless force carrier and looking for evidence of non-zero mass in gravitational lensing data. Gravitational lensing is the distortion of images of objects in the background by the presence of massive objects in the foreground. In this case the data used are “weak lensing” data, where it is more of a statistical approach to the distortions of images of a whole background field from typically multiple foreground objects rather than a more optics-like object+lens setup. The authors have looked for deviations from the expected statistical behavior in the lensing data. As an aside, larger distances between the gravitational sources and the deflected light rays will have the most information on possible graviton mass, and this naturally puts one in the weak field regime, so one doesn’t need to do any real heavy lifting with general relativity.
(You might have come across this already, but since I’m a fan of people poking around the PDG: You’ve linked to a summary table in the OP, and these are thin on background. The particle listings section gives the same info but with references and brief discussions on the values reported.)
That might be the current best bound, but you can get pretty good bounds on the graviton mass from measuring the gravitational force law in any system. If the graviton had a mass, then the gravitational force would not fall off as 1/r[sup]2[/sup], but according to some other formula (presumably something resembling the Yukawa form). Even just trivial observations like “the Solar System hasn’t fallen apart yet” are enough to show that the graviton is far less massive than any known-massive particle.
*It’s time to try
Defining Gravitons
I think I’ll try
Defining gravitons
And I can’t put it down!
…
…
…
I’m now setting limits
'cause the matrices say they’re true
Some things I cannot change
But till I try, I’ll never know!
Too long I’ve been afraid of
Losing Quantities never found
Well if that’s secure knowledge
It comes at much too high a cost
I’d sooner try
Defining gravitons
Kiss me goodbye
I’m defining Gravitons
And you can’t put me down!*
– with apologies to Stephen Schwartz, Gregory Maguire,
and everyone associated with Wicked.
Reported. To, I don’t know, move it into its own thread? Maybe in MPSIMS?
