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arXiv:gr-qc/9611029 · Classical and Quantum Gravity

Comments on the quantum potential approach to a class of quantum cosmological models

J. Acácio de Barros, Nelson Pinto-Neto

Published Jul 1, 1997• 3 citations
arXivHTMLPDF

Abstract

In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the representation in which we want to express the physical results. This is particularly important when canonical transformations that mix momenta and coordinates are present. This implies that some of the results obtained by B aut and Kowalski-Glikman are incorrect.

DOI
10.1088/0264-9381/14/7/030

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In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the representation in which we want to express the physical results. This is particularly important when canonical transformations that mix momenta and coordinates are present. This implies that some of the results obtained by B aut and Kowalski-Glikman are incorrect.
In this paper we discuss the quantum potential approach of Bohm in the context of a quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe into a set of equations describing the time evolution of the universe. Following Ashtekar et al we make use of a quantum canonical transformation to cast a class of a quantum cosmological models into a simple form in which they can be solved explicitly, and then we use the solutions to recover the time evolution.
We argue that the Copenhagen interpretation of quantum mechanics cannot be applied to quantum cosmology. Among the alternative interpretations, we choose to apply the Bohm-de Broglie interpretation of quantum mechanics to canonical quantum cosmology. For minisuperspace models, we show that there is no problem of time in this interpretation, and that quantum effects can avoid the initial singularity, create inflation and isotropize the Universe. For the general case, it is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures.
Philosophers of science have not paid much attention to recent developments in quantum cosmology. This fact is surprising, since quantum cosmology is replete with conceptual issues involving (e.g.) the fundamental nature of time and space, the interpretation of quantum mechanics, and the ultimate meaning of probability. One notable exception, Quentin Smith, has recently examined the Hartle-Hawking (1983) proposal. Trying to make sense of the view, he resorts to an instrumentalist picture, which treats the proposal as merely a heuristic device for the algorithm responsible for predictions. While we do not examine Smith's account here, we would like to contrast it with the model presented in this note, in which a fully realistic interpretation of quantum cosmology is developed. Recently there has been a resurgence of interest in the de Broglie-Bohm causal interpretation of quantum mechanics.
If You feel that scientific theories should reveal facts about the world, you will, of course, be profoundly dissatisfied with quantum mechanics! For, as it is generally interpreted, the formalism is a tool for making predictions about outcomes of possible experiments and nothing more. Quantum mechanics has nothing to say about the nature of the physical processes that bring about the very experimental results that it predicts, yet it is supposed to be the whole story of the phenomena it speaks of (i.e. it is supposed to be "complete").