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Time and Quantum Gravity

William George Unruh

Published Jan 1, 1988• 1 citation
OpenAlex

Abstract

The role of time in the interpretation of quantum mechanics and quantum gravity are analyzed, and changes to the form of quantum gravity to make it interpretable are suggested.

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The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

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Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must forget time, and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.
Interpretation is not the only way to explain a theory's success, form and features, and nor is it the only way to solve problems we see with a theory. This can also be done by giving a reductive explanation of the theory, by reference to a newer, more accurate, and/or more fundamental theory. We are seeking a theory of quantum gravity, a more fundamental theory than both quantum mechanics and general relativity, yet, while this theory is supposed to explain general relativity, it's not typically been thought to be necessary, or able, to explain quantum mechanics -- a task instead assigned to interpretation. Here, I question why this is. I also present a new way of assessing the various interpretations of quantum mechanics, in terms of their heuristic and unificatory potential in helping us find a more fundamental theory.
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.