# What does it mean for a graviton to have mass?

Astronomical observations of the kinematics of galaxies, especially the galaxy rotation problem and modified Newtonian dynamics, might point toward gravitons having non-zero mass.

But what does it mean for a graviton, the particle itself being the carrier of gravity force occuring between all massive objects to have mass? Does that mean that two gravitons actually could be attracted towards each other through other gravitons? In this case assuming in finite space amount of gravitons is finite there would be no gravitons left to be force carriers of other gravitons.

To explain my reasoning:

Let there are 3 gravitons in the area.

Suppose gravitons $g_1$ and $g_2$ are participating in gravity. They can only do it using other gravitons. Well, let they do it using only one graviton $g_3$. But then why would not $g_3$ participate in gravity with $g_1$ and $g_2$ themselves? In this sense the idea of massive graviton seems self-refuting.

Is there any model allowing massive gravitons which handles this issue and do physicists really assume the idea of massive gravitons to be plausible?

In the classical limit:

$$V(r) \propto G \frac 1 r e^{-r/m}$$

so in the limit $m\rightarrow 0$, $V(r)\rightarrow$ Newton.

Meanwhile, gravitons (like photons) are their own anti-particle, so their number isn't conserved.

Regarding a quantum field theory of massive gravitons: why not? The massless one doesn't work anyway.

• Do massive gravitons work in QFT? And I was assuming analogy with photons: they do not have charge therefore not "shooting" any particles anywhere. – user168013 Aug 26 '18 at 2:45
• Massive gravitons would imply a limited range and that gravitational waves fly slower than light. So no gravity after a certain distance. No? Unclear though how this would help the galaxy rotation. – safesphere Aug 26 '18 at 3:07
• @safesphere, well, in absolute vacuum these gravitons, more precisely a single graviton, still would fly arbitrarily long. The issue with galaxy rotation is that angular speed almost does not reduce with radius which makes a galaxy a solid body. However, solidity in (almost?) all matter is created by electromagnetism. – user168013 Aug 26 '18 at 3:19
• @rus9384 This is incorrect. Garvitons do not mediate the gravitational force, virtual gravitons do. So it is irrelevant how long real gravitons fly, they are not the source of gravity of the body that emitted them. There is a principal difference between a wave and a field. A wave consists of real particles (photons, gravitons, etc.). A field "consists" of virtual particles (that are not real meaning do not exist in reality). For example, there is a big difference between a field of a magnet (electromagnetic field) and a beam of light (electromagnetic wave). – safesphere Aug 26 '18 at 3:29
• The Kaluza Klein model has massive gravitons in addition to the mass zero spin 2 lowest order graviton. – anna v Aug 26 '18 at 7:53