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.

Foundational Issues in Group Field Theory

“…There have been several proposals for how to interpret these timeless superpositions of geometries as something from which our intuitive picture of a time evolution could be recovered, but they all face important conceptual and technical challenges that make them not convincing from my point of view. I refer the reader to [37][38][39][40][41] for some introductions and criticisms of the proposed resolutions of the problem of time. In the case of canonical approaches to GFT, and especially in the cosmological models inspired by it, the way the problem of time is dealt with is by means of a relational strategy.…”

“…I refer the reader to [41] where I develop these points in more detail and to [37][38][39][40] and references therein for other critical views. Studying the GFT case allows highlighting some of the general worries one may have with relational resolutions, besides some specific issues that appear in the GFT context.…”

“…For instance, instead of having x, y, z one has x, y, t. In this case it is perfectly fine to deparametrize and interpret this wavefunction as a state for x, y evolving in t. But when the model one is considering is not defined on such an expanded configuration space, one cannot apply the same reasoning. I expand on this distinction on [41]. 40 I refer the reader to [42][43][44] for critical discussions of radical versions of relationalism motivated by quantum gravity and which aim to eliminate time from our theories.…”

“…I expand on this distinction on [41]. 40 I refer the reader to [42][43][44] for critical discussions of radical versions of relationalism motivated by quantum gravity and which aim to eliminate time from our theories.…”

“…In cosmological applications of GFT 41 , the states considered are restricted to condensate states, which present certain symmetries that allow to avoid the above problems and a relational dynamics can be defined. For the rest of states it seems that the case of GFT is not different from the one of other theories with a problem of time: once we consider realistic situations with some variety of variables involved, it becomes hard to define a relational dynamics in a way that allows to formally overcome the problem of time.…”