Abstract
It is generally accepted that the Copenhagen interpretation is inapplicable to quantum cosmology, by contrast with the many worlds interpretation. I shall demonstrate that the two basic principles of the Copenhagen interpretation, the principle of wholeness and the principle of complementarity, do make sense in quantum gravity, since we can judge about quantum gravitational processes in the very early Universe by their vestiges in our macroscopic Universe. I shall present the extended phase space approach to quantum gravity and show that it can be interpreted in the spirit of the Everett’s “relative states” formulation, while there is no contradiction between the “relative states” formulation and the mentioned basic principles of the Copenhagen interpretation.
Highlights
There exists an opinion that the Copenhagen interpretation of quantum theory is inapplicable to quantum cosmology, and the many worlds interpretation would probably be the only interpretation that is appropriate for this case
In [1], one can read: “. . . the wave function collapse postulated by the Copenhagen interpretation is dynamically ridiculous, and this interpretation is difficult if not impossible to apply in quantum cosmology.”
If someone insists on the Copenhagen interpretation, at least in its present form, she or he must assume that quantum theory is not universal, that quantum cosmology does not make any sense at all and that we are stuck.”
Summary
There exists an opinion that the Copenhagen interpretation of quantum theory is inapplicable to quantum cosmology, and the many worlds interpretation would probably be the only interpretation that is appropriate for this case. A wave function will depend on spacetime geometry, like in the Wheeler–DeWitt quantum geometrodynamics, and on a reference frame with respect to which this geometry is studied This outcome is just a strict mathematical consequence of the mentioned feature of gravity, it may seem to be rather strange for those who believe that quantum gravity must be a gauge invariant theory not depending on the choice of a reference frame and the state of the observer. I mean that the spacetime structure determined by the lapse and shift functions plays no role in the Wheeler–DeWitt theory It seems to be natural from the point of view of the requirement of its gauge invariance, but it leads to the question: is the theory we try to quantize general relativity? It seems to be natural from the point of view of the requirement of its gauge invariance, but it leads to the question: is the theory we try to quantize general relativity? Section 6 is entirely devoted to the extended phase space approach to quantization of gravity and its interpretation
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