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After emphasizing that it remains an open question whether one should try to quantize gravity theory (which would mean gravitational force is propagated by a graviton particle), we nevertheless ask whether a limit can be set on the rest mass (₆) of the "graviton. " By recalling that gravitational force is clearly exerted over large distances in systems of galaxies and is not eliminated by a graviton-mass Yukawa cutoff, we find a limit. So, although it is not known if the graviton exists, one can still say that its rest mass is less than 2 10^-62 g.
Goldhaber et al. (Fri,) studied this question.