A New Approach to Quantum Gravity

We quantise General Relativity for a class of energy-momentum-stress tensors. 1. The new method of quantisation 1.1 THE GENESIS OF A CURVED SPACETIME It has been generally believed that QED does not allow a classical spin for the particle described. However, it has now been shown that QED permits the spin of the particle to behave like a four-vector (Bell et al. 2000a&b). This was done by mapping the Dirac and photon equation into a new form, the versatile form, ( D – i e A ) Φ = Φ M, (1) where e is the charge on the electron. This permits the application of QED as a quantum version of General Relativity. We will study one particular sort of curved spacetime here which we will use as the building block for all the others. In this section we discuss its extrinsic description and relationship to the versatile Dirac and photon equations. We define the curvature in terms of co-ordinate systems. We shall call the original flat spacetime that applies to equation (1) the spacetime of the Large observer. We may co-ordinate the x1, x2 and x0, x3 planes of the Large observer with polar co-ordinates, r1, θ1, and r2, θ2, where we have x1 = r1 sin ( θ1 ), x2 = r1 cos ( θ1 ), x0 = r0 sin ( θ0 ), x3 = r0 cos ( θ0 ) and s1' = r1 θ1, s0' = r0 θ0, (2) and s1', s0' are the arcs corresponding to r1, r0 and θ1, θ0. We introduce two further observers who we shall call the Medium observer and the Small observer. We give