Reassessing the problem of time of quantum gravity

Abstract

In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn't lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don't work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn't lead to a meaningful quantum theory. Finally, I comment that this has an impact on the foundations of different approaches to quantum gravity.

To be published in General Relativity and Gravitation

References in corpus (3)

• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• No Time for Time from No-Time
• Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity

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• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• Against Radical Relationalism: in Defense of the Ordinal Structure of Time
• Does Quantum Cosmology Predict the Age of the Universe?
• Quantum Cosmology and the Age of the Universe
• Gauge and Metaphysics of Spacetime