Quantum Relativity Theory

Relativity theory was in fact as comprehensive and as logically complete as a purely macroscopic theory, had any right to be.Dirac's wave equation was the first connecting link gives only a partial idea of its importance. It was a challenge to those who specialised in relativity theory. Dirac's object was to obtain a form of equation which should be invariance and convariance.

Relativity Theory and Quantum Theory

All other classical theories are completely compatible with the general theory of relativity. Even if the details of the coupling of a classical field ( Maxwell field, Dirac field, neutrina field, Klein Gordon field) to the metric field are not always free of arbitrariness and cannot yet be experimentally tested with sufficient accuracy, no doubt exists as to the inner consistency of the procedure.

The many other interactions between the building blocks of matter can only be described with the aid of quantum theory. A unification of relativity theory and quantum theory has not yet been achieved. The limits of this more or less undisturbed coexistence of quantum theory and relativity theory.

Fundamentals of Quantum Relativity Theory

Quantum theory presupposes a Minkowski space of infinite extent of both in its fandamental commutation rules, which are formulated explicitly using the group of motion of the space (the Lorentz group), and in detailed  technical issues like expansion in plane waves, asymptomatic behaviour at infinity or the formulation of conservation laws.

Relativity theory shows that the space is a Riemannian space. The idea of relativity theory is that the properties of the space are properties of the interaction of the matter and can be measured out by material test bodies and leads to contradictions with the metric in very small regions of space.

If the dimensions are so small that atoms or elementary particles should be taken as test objects, then their location is no longer so precisely defined  that one can really speak of a measurement, even be it only in a gedanken experiemnt. Possible three geometry and its topological properties, and can be described by a point in superspace.  How one couples in nonmetric fields, how man is to interpret the wave function of the universe and how measurement process and observers are to be described is unclear.

The mass less particles of this field, analogous to the photons of the electromagnetic field, have spin 2. By restricting consideration to source free weak fields, the real problems have been swept under the carpet.