The gravitational constant Other fundamental constants are and .

The combination is the only combination of fundamental constants involving G that gives a length, known as the Planck Length. To make this into an energy one can invert it and multiply by to get or . So the so called Planck Mass is . The GUT unification mass was so did not include gravity.

How do we make a quantum theory of gravity?

In analogy with other interactions, a field is equivalent to the exchange of quanta. We postulate that the gravitational field arises through the exchange of gravitons between masses.

Because gravity has a dependence with infinite range like electromagnetism, the graviton must be massless.

The spin of the exchanged particle has a significant effect on the force. Half integer (1/2, 3/2 etc) give no force and also greater that spin 2 give no force. Spin 1 (as for photons) gives rise to a repulsive force between two identical particles i.e electrons repel other electrons. Since gravity is attractive the graviton must have spin 0 or 2. It turns out that the field equations of a massless spin 2 particle are equivalent to the components of 4 dimensional curved spacetime. Therefore we assume the graviton is spin 2.

Gravitons can scatter and interact with each other as well as with ordinary matter.

Unfortunately attempts to calculate scattering cross sections lead to problems such as infinities. It is not easy to construct a consistent renormalizable (i.e. no infinities) quantum theory of gravity.

Two incoming gravitons combine at A to give a third that travels to B before splitting back into a pair. Unfortunately these other diagrams that have to be added lead to infinite cross sections.

It is not easy to construct a consistent renomalizable (i.e. no infinities) quantum theory of gravity.

Supersymmetry helps. The supersymmetric partner of the graviton, the gravitino (spin 3/2) can be used to cancel out some of the infinite loops. Such a theory is called Supergravity. However, there are still problems so although supergravity may be a component of the final theory it is not the fundamental theory of physics.

Information provided by: http://hepwww.ph.qmw.ac.uk