The Wheeler - DeWitt Quantum Geometrodynamics: its fundamental problems and tendencies of their resolution

TL;DR

This paper critically examines the fundamental issues in Wheeler-DeWitt quantum geometrodynamics, analyzing its origins, flaws like the problem of time, and recent developments in the field.

Contribution

It provides a detailed analysis of the foundational problems in Wheeler-DeWitt theory and discusses new approaches that have emerged in recent years.

Findings

Identifies key flaws such as the problem of time and Hilbert space issues.

Analyzes the origins of these problems from Dirac's Hamiltonian dynamics.

Reviews recent tendencies and approaches in quantum geometrodynamics.

Abstract

The paper is devoted to fundamental problems of the Wheeler - DeWitt quantum geometrodynamics, which was the first attempt to apply quantum principles to the Universe as a whole. Our purpose is to find out the origin of these problems and follow up their consequences. We start from Dirac generalized Hamiltonian dynamics as a cornerstone on which the Wheeler - DeWitt theory is based. We remind the main statements of the famous DeWitt's paper of 1967 and discuss the flaws of the theory: the well-known problem of time, the problem of Hilbert space and others. In the concluding part of the paper we consider new tendencies and approaches to quantum geometrodynamics appeared in the last decade.