The Challenge from General Relativity
The synthesis between the tenets of quantum physics and those of general relativity has remained an unsolved problem for over sixty years. The early discussions between Einstein and Bohr on physical reality may well be seen as an omen forshadowing the difficulties encountered. Local quantum physics as described in the previous chapters accepts space-time, including its causal structure, as a given arena in which physics is staged. One may say that the space-time coordinates, tied to a reference system established by an observer, are classical quantities belonging to the observer side of the Heisenberg cut. The global structure of space-time is needed for the commutation relations between observables, in particular for the causal commutativity at (arbitrarily large) space-like separations. The local metric structure is needed in the formulation of dynamical laws in quantum field theory. Translation invariance is necessary for the definition of energy-momentum which, in turn, is central for the formulation of stability and nuclearity. Now, if we wish to include gravity and understand it as a modification of the metric field depending on the matter distribution and hence on the prevailing physical state, we can distinguish three levels.
KeywordsBlack Hole Tangent Space Minkowski Space Local Definiteness Spinorial Charge
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