LAUSR

The Wheeler–DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler–DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrodinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler–DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler–DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference f...