At the limit of weak static fields , general relativity becomes Newtonian gravity with a potential field that falls off as inverse distance , rather than a theory of Yukawa-type fields with finite range .
General relativity also predicts that the speed of disturbances of its waves is c , the vacuum light speed , and is non-dispersive .

For these reasons , the graviton , the boson for general relativity , can be considered to be massless .
Massive gravitons , however , are features of some alternatives to general relativity .
This has motivated experiments and observations that , so far , have been consistent with the zero mass graviton of general relativity , but further tests will be valuable .

A basis for new tests may be the high sensitivity gravitational wave experiments that are now being performed , and the higher sensitivity experiments that are being planned .
In these experiments it should be feasible to detect low levels of dispersion due to nonzero graviton mass .
One of the most promising techniques for such a detection may be the pulsar timing program that is sensitive to nano-Hertz gravitational waves .

Here we present some details of such a detection scheme .
The pulsar timing response to a gravitational wave background with the massive graviton is calculated , and the algorithm to detect the massive graviton is presented .
We conclude that , with 90 \% probability , massles gravitons can be distinguished from gravitons heavier than 3 \times 10 ^ { -22 } eV ( Compton wave length \lambda _ { g } = 4.1 \times 10 ^ { 12 } km ) , if biweekly observation of 60 pulsars are performed for 5 years with pulsar RMS timing accuracy of 100 ns .
If 60 pulsars are observed for 10 years with the same accuracy , the detectible graviton mass is reduced to 5 \times 10 ^ { -23 } eV ( \lambda _ { g } = 2.5 \times 10 ^ { 13 } km ) ; for 5-year observations of 100 or 300 pulsars , the sensitivity is respectively 2.5 \times 10 ^ { -22 } ( \lambda _ { g } = 5.0 \times 10 ^ { 12 } km ) and 10 ^ { -22 } eV ( \lambda _ { g } = 1.2 \times 10 ^ { 13 } km ) .
Finally , a 10-year observation of 300 pulsars with 100 ns timing accuracy would probe graviton masses down to 3 \times 10 ^ { -23 } eV ( \lambda _ { g } = 4.1 \times 10 ^ { 13 } km ) .