It is possible to construct the non-euclidean geometry of space-time from the
information carried by neutral particles. Points are identified with the
quantal events in which photons or neutrinos are created and annihilated, and
represented by the relativistic density matrices of particles immediately
after creation or before annihilation. From these, matrices representing
subspaces in any number of dimensions are constructed, and the metric and
curvature tensors are derived by an elementary algebraic method; these are
similar in all respects to those of Riemannian geometry. The algebraic method
is extended to obtain solutions of Einstein’s gravitational field
equations for empty space, with a cosmological term. General relativity and
quantum theory are unified by the quantal embedding of non-euclidean
space-time, and the derivation of a generalisation, consistent with
Einstein"s equations, of the special relativistic wave equations of
particles of any spin within representations of SO(3) ⊗ SO(4; 2). There
are some novel results concerning the dependence of the scale of space-time on
properties of the particles by means of which it is observed, and the gauge
groups associated with gravitation.
Quantum Theory of Gravitation
