Is the Wheeler–DeWitt equation more fundamental than the Schrödinger equation?

2019

Gravit. Cosmol.

The paper is devoted to some of the difficulties which the Wheeler -DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the Universe through a path integral and the illegality of asymptotic boundary conditions in quantum gravity, the derivation of the Wheeler -DeWitt equation from the path integral and the equivalence of the Dirac quantization scheme with other approaches, the problem of definition of physical states in quantum gravity, possible realizations of the Everett concept of "relative states". The problems are rarely discussed in the literature. They are related with the guiding idea that quantum theory of gravity must gauge invariant. It will lead to the question if it is possible to achieve this goal in a mathematically consistent way.Universe. But it contradicts to the fact that a solution to the Wheeler -DeWitt equation does not depend on time and, therefore, the probability distribution determined by the wave function must be true at every moment of the Universe existence. Thus, if the probability distribution predicted that geometries with small values of the scale factor are more feasible, the Universe would have had no chance to become macroscopic. Otherwise, if the probability distribution predicted that large values of the scale factor are more probable, it would mean just the statement of the fact that our Universe is macroscopic, but it would not tell us anything about the early stage of its existence. If so, the Wheeler -DeWitt theory can hardly add something to our understanding of the beginning of the Universe.But the analogy with quantum mechanics goes even further. In fact, some authors state that spacetime does not exist in quantum gravity. For instance, Kiefer [5] wrote:"In classical canonical gravity, a spacetime can be represented as a 'trajectory' in configuration space -the space of all three-metrics. . . Since no trajectories exist anymore in quantum theory, no spacetime exists at the most fundamental, and therefore also no time coordinates to parameterize any trajectory."The same idea one can find in the book by Rovelli [6]:". . . in quantum gravity the notion of spacetime disappears in the same manner in which the notion of trajectory disappears in the quantum theory of a particle." However, the structure of spacetime plays a significant role in general relativity. Do we really need to reject it when quantizing gravity? Rovelli [7] called the Wheeler -DeWitt equation "a strange equation, full of nasty features", but, in spite of all this, it is "a milestone in the development of general relativity". What gives us confidence that this equation is fundamental? How can we be so sure that it expresses gauge invariance of quantum gravity? The Wheeler -DeWitt equation is the result of application of the Dirac quantization scheme [8,9] to gravitational theory.Dirac just postulated that after quantization any constraint must become a condition on a state vector. But this post...

Section: Discussionmentioning

confidence: 99%

Wave Function of the Universe, Path Integrals and Gauge Invariance

2019

Gravit. Cosmol.

“…Accordingly, I consider the Dirac conjecture as a postulate, the validity of which is questionable. This point is important for the soundness of the extended phase space approach and discussed in details in [30,48].…”

Section: The Extended Phase Space Approach To Quantum Gravitymentioning

confidence: 98%

“…According to the idea of Wheeler [29], the wave function of the Universe is determined on superspace of all possible three-space geometries and corresponding matter fields configurations. The wave function of the Universe is a solution to the Wheeler-DeWitt equation, which is considered as more fundamental than the Schrödinger equation in most approaches to quantum gravity (see [30] in this connection). As a consequence, the wave function does not depend on time.…”

Section: Destruction Of Spacetime In Quantum Gravitymentioning

confidence: 99%

Is the Copenhagen Interpretation Inapplicable to Quantum Cosmology?

2020

Universe

Self Cite

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.

“…In Section 2 I shall remind what grounds we have to consider the Schrödinger equation as more fundamental than the Wheeler -DeWitt equation in quantum gravity and what are the main features of the extended phase space approach (this question is discussed in details in [12]). In Section 3 an outline of a cosmological scenario will be given that can be proposed in the framework of this approach.…”

Section: Introductionmentioning

confidence: 99%

On the meaning of the wave function of the Universe

2019

Int. J. Mod. Phys. D

Self Cite

The meaning of the wave function of the Universe was actively discussed in 1980s. In most works on quantum cosmology it is accepted that the wave function is a probability amplitude for the Universe to have some space geometry, or to be found in some point of the Wheeler superspace. It seems that the wave function gives maximally objective description compatible with quantum theory. However, the probability distribution does not depend on time and does not take into account the existing of our macroscopic evolving Universe. What we wish to know is how quantum processes in the Early Universe determined the state of the present Universe in which we are able to observe macroscopic consequences of these quantum processes. As an alternative to the Wheeler -DeWitt quantum geometrodynamics we consider the picture that can be obtained in the extended phase space approach to quantization of gravity. The wave function in this approach describes different states of the Universe which correspond to different stages of its evolution.