Bain: Three Principles of Quantum Gravity in the Condensed Matter Approach

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Abstract: Research on quantum gravity (QG) has historically relied on appeals to guiding principles. This essay frames three such principles within the context of the condensed matter approach to QG. I first identify two distinct versions of this approach, and then consider the extent to which the principles of asymptotic safety, relative locality, and holography are supported by these versions. The general hope is that a focus on distinct versions of a single approach may provide insight into the conceptual and foundational significance of these principles.

2013-09-29 9:34:16: Two Principles of Quantum Gravity in the Condensed Matter Approach

This is restricted from 3 principles for the sake of time.

2013-09-29 9:36:13: Two questions: why guiding principles in qg.

empirical guidance is unavailable.

Why these two? Little on asymptotic safety and relative locality.

2013-09-29 9:37:47: Asymptotic safety:

GR as QFT non-renormalizable. So might think non-fundamental effective theory.

But Weinberg thinks safety might allow it to be fundamental after all.

Question arises: what is fundamental theory,

2013-09-29 9:39:16: Relative locality: theory of QG must entail relativity of point-coincidences. b/c momentum obeys non-linear composition law a la non-linear SR law of velocity combination.

2013-09-29 9:40:22: Relevant to condensed matter bc topological invariants play role both there and in relative locality considerations.

2013-09-29 9:42:45: Condensed matter approach to QG:

Mode decomposition of action, integrate out high energy modes, absorb changes into redefined parameters. If successful, find a fixed point for these transformations.

Can stop just at integrating out of high energy modes. This corresponds to EFT.

2013-09-29 9:45:06


2013-09-29 9:45:27: Goal of Condensed Matter approach:

construct EFT that mimics GR and Standard Model

Version A: spontaneous broken symmetries and universality. E.g. Volovik model.

Version B: characterized instead by “topological order”. E.g. Zhang and Hu: 4-d fractional quantum Hall Fluid (FQH).

Vary in the kinds of order that are relevant.

2013-09-29 9:48:14: Asymptotic safety: QG must scale towards UV fixed point with a finite number of UV-irrelevant coupling. I.e. decreases toward high energy (fixed point).

finite # of UV-irrelevant couplings.

infinite # of UV-relevant couplings.

2013-09-29 9:51:09: Claim: EFTs in in both versions of CM approach should aspire to be ASTs.

So aspire toward two fixed points: IR for “high energy” condensate. UV fixed point associated with QCD/GR sector.

But may not be consistent to consider an EFT as an AST.

For AST = fundamental theory to all orders. EFT = theory restricted to a gvien energy scale, beyond which new physics arises.

2013-09-29 9:52:08: Questions from Huggett about how QCD and GR can share a UV fixed point. Butterfield concurs. Bain agrees there’s an issue here.

2013-09-29 9:54:58: Suppose this: EFT and high-energy theory may not need to be related by approximation, but rather emergence. Then perhaps consistent to claim that an AST can emerge in the form of an EFT of a fundamental condensate.

One route: via failure of law-like deducibility (novelty); with ontological distinctness; and ontological dependence. (micro-physicalism from second two)

2013-09-29 9:58:02: Moving on to relative locality: (Amelino-Camelia et al. 2011)

Idea: due to curvature of momentum space. Can see this by comparing the phase spaces of special relativity and GR . Momentum space flat. But for theories with relative locality momentum space curved. Suggestion is that this should happen in QG, because perhaps of non-commutative geometry. Also corrections to relativistic particle dynamics.

2013-09-29 15:03:49: Relation to condensed matter approach: CM systems may have analogues to the physics of relative locality.

Both CM versions encode aspect of EFTs in aspects of parameter space topology. Can be related to p-space curvature.

First version: (1) encode low-energy dynamics  in p-space. (2) Stability of low-energy dynamics. (3) Relate topological invariant to p-space curvature.

Second version: (1) encode internal order of condensate in ground state degeneracy (GSD). (2) Demonstrate stability of GSD. (3) Relate GSD to p-space curvature.

2013-09-29 15:04:42: So now we have relative locality and asymptotic safety connected to the CM approach to quantum gravity.

2013-09-29 15:05:34: Oriti asks whether there is a relation to actual non-commutativity of geometry. Bain says not that he’s aware.

2013-09-29 15:10:00: Motivating phase space realism:

Descriptions of systems in terms of energy and momentum more fundamental that spatiotemporal properties. (Amelino-Camelia especially.)

Analogy between relativity of simultaneity and relativity of locality. Latter explained by invariant phase space interval with observer-dependent slicing of phase space.

2 concerns with latter motivation: doesn’t tell us phase space absolute features more fundamental than decomposed bits; global vs local quantity distinction rather than absolute vs relative quantities.

At most uphold momentum space realism rather than phase space realism.

2013-09-29 15:11:08: Questions have been raised about appropriateness both of asymptotic safety and relativity of locality.

2013-09-29 15:17:26: Question about why relativity of locality: Baker thinks bad for a theory. Advocates see observations of momentum stuff as more fundamental. Butterfield thinks claims applies to classical stuff as well. Darboux’s theorem seems relevant here. Bain says worth thinking about.

Oriti offers motivations: worries about lorentz invariance from fundamental length might lead to attempt to deform the invariance – and that can be done with momentum space curvature; also in simple qg models, can couple point particles to gravity – end up with curved momentum space. These realize relative locality. Bain adds that reason you think you observe locality properties is because the momentum is very low. So only seem like position measurements.

Huggett returns to asymptotic safety concerns about why should have same fixed points in GR and QCD. Latter is gaussian, but GR’s should not be. Bain’s concerns orthogonal to this question.

2013-09-29 15:21:22: Question from Oriti: asymptotic safety people don’t suggest that safety leads to fundamentality. Huggett says he and Weingard argued same thing before. Consensus seems to be that safety does not lead to fundamentality. Butterfield objects that QCD fundamental from perspective that excludes gravity. Fundamental is to be taken wrt to the perspective of the analysis.


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