Is the idea of replacing classical geodesics in spactime with quantal Bohmian trajectories correct ?

Question

I have been reading the paper https://arxiv.org/abs/1404.3093 and https://arxiv.org/abs/1311.6539. What are the implications of using Bohmian mechanics in quantum gravity research like this one ? What happens with locality & lorentz invariance ?

Comments

Its a minority approach unlikely to be successful. Bohmian mechanics cannot even produce QED, about which much more is known than about quantum gravity.

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Why do you say Bohmian mechanics cannot reproduce QED? Here is first reference I could find that in fact explains why it does work: https://arxiv.org/abs/0707.3487

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@RubenVerresen: That paper is about the free electromagnetic field only (no deterministic dynamical system is given for the interacting case).

Moreover, its proposed beables are incompatible with the beables in Bohmian mechanics of particles. But beables in Bell's sense cannot depend on the model chosen to describe reality. Thus the model given in the paper is not Bohmian mechanics.

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See also this for a critical review of the first in the media overhyped paper.

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@ArnoldNeumaier: it does in fact describe the interacting case. Why do you say it does not? The abstract mentions that Bohm did it for the free electromagnetic field, maybe that is what gave you the idea that this paper was only for the free case? In fact it extends Bohm's suggestion to the interacting case. As for the objection that the beables are not the same as in other cases: that's like saying QFT is not consistent with QM because it talks about fields rather than particles? I think that's just the point: that to extend Bohmian mechanics from QM to QFT that one needs to change the beables accordingly. (If the question is then 'how one can derive the QM limit', that is a separate issue, which is just as subtle for the usual 'limit of QFT to QM').

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@RubenVerresen: Thanks for your correction. I retract my claim that it is only about the free case that I got in a first superficial reading. Instead, it is only about an approximation of QED where space is replaced by a finite lattice, and Lorentz invariance therefore lost. See my answer for details.

Answer 1

The mentioned works of Ali and Das is certainly not quantum gravity; it could be at best understood as a variant of semiclassical gravity. That is, gravity is totally non-quantized in any way, but is coupled to a somehow quantum field.

This work has received disproportionate attention from the public. In fact, the only physical model which could perhaps be described by it is a non-interacting Bose-Einstein condensate at zero temperature generating the initial cosmology. This narrow applicability of the investigations of Ali and Das is, I would dare say, somewhat unethically hidden in the chain of their papers. Naturally, journalists did not see through this and went to derive bold claims from the investigations.

If instead we are thinking about a usual ensemble of particles in thermodynamical equilibrium, we see no reason why they should behave according to a single pilot wave, a single wave-function. Particles start to share a single wave function only in the process called Bose-Einstein condensation. However, even simple short-range interaction of the particles breaks the nice "free" behaviour of the shared wave-function.

Furthermore, every theoretical physicist knows that a quantum ensemble at cosmological temperatures and densities is mostly very well described by a classical thermodynamical equilibrium, i.e. no quantum effects enter directly into the evolution of the cosmological fluid (apart from reaction rates determining chemical potentials etc.). Once we are approaching a cosmological singularity, strong interaction kicks in way before Heisenberg's uncertainty principle could bother us. We need to know how a quark-gluon plasma behaves, we need to know what happens at the GUT scale (-> inflation?), and finally the quantum-gravity scale (-> inflation???).

In light of these actual physical concerns the work of Ali and Das might be a nice toy model of some kind of semiclassical-gravity setup but is not really relevant to either actual physical cosmology or quantum gravity.

Answer 2

Both papers are about quantum theory in a classical curved background geometry, hence say nothing about quantum field theory, and hence nothing about locality.

Until someone is able to reconcile renormalization with Bohmian mechanics, the latter says nothing of interest about quantum field theory.

Bohmian mechanics cannot even produce QED, about which much more is known than about quantum gravity.

For QED, the paper https://arxiv.org/abs/0707.3487 mentioned by @RubenVerresen displays the problems with the Bohmian approach in quantum field theory. The authors propose a naive dynamics for the wave function in (23), then state immediately that the dynamics is not well-defined, and then go on to state wrong claims about what Symanzik nd Luescher showed. The same problems appear for their proposed equilibrium density in (24). They say the problems go away when one makes the number of degrees of freedom finite (which is true), but they remain silent about the fact that the problems reapppear when one tries to take the continuum limit.

Without the continuum limit one doesn't have Lorentz invariance (as they note), but then one only has a finite lattice approximation of QED. One doesn't have QED, which is the theory defined in the continuum by Lorentz covariance and minimal coupling.