The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical (...) general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity. (shrink)

In November of 1925 Born, Heisenberg and Jordan wrote an article together in which they demonstrated that Einstein's energy fluctuation formula could be derived from quantum mechanics. They remark that the equations are subject to reinterpretation. Specifically, the states of radiation oscillators can be reinterpreted as numbers of quanta of radiation. They also connected this latter idea up with Bose-Einstein statistics. Heisenberg wrote to Pauli that it was Jordan who contributed the idea of reinterpreting the terms. This was the first (...) step toward quantum field theory. In August of the following year Dirac derived Einstein's A and B coefficients for induced transitions between states but on the assumption that the electromagnetic field could be treated classically (Dirac 1927). In 1927 Dirac lay the mathematical foundations for quantum electrodynamics. Early that year he combined quantum mechanics, special relativity, and radiation theory in treating the electromagnetic field as if it were an infinite collection of oscillators. (shrink)