The theory of gravity can be looked at in two ways: The old fashioned Newtonian gravity, where the potential is proportional to the rest mass of the particles,
$$V=\frac{{G}_{N}{m}_{1}{m}_{2}}{r}.$$ | (7.4) |
We ﬁnd that ${G}_{N}{m}_{p}^{2}\u2215\hslash c$ is dimensionless, and takes on the value
$${G}_{N}{m}_{p}^{2}\u2215\hslash c=5.9046486\times 1{0}^{-39}.$$ | (7.5) |
There are two more levels to look at gravity. One of those is Einstein’s theory of gravity, which in the low-energy small-mass limit reduces to Newton’s theory. This is still a classical theory, of a classical gravitational ﬁeld.
The quantum theory, where we re-express the ﬁeld in their quanta has proven to be a very tough stumbling block – When one tries to generalise the approach taken for QED, every expression is inﬁnite, and one needs to deﬁne an inﬁnite number of diﬀerent inﬁnite constants. This is not deemed to be acceptable – i.e., it doesn’t deﬁne a theory. Such a model is called unrenormalisable. We may return to the problem of quantum gravity later, time permitting.