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Emergent spacetime and empirical (in)coherence
Nick Huggett, Christian Wuthrich
TL;DR
Quantum-gravity theories that deny fundamental spacetime face a problem of empirical coherence because observations appear to require localized entities. The paper surveys such theories and sketches how local beables may emerge, while examining whether formal derivations establish their physical salience. It concludes that empirical agreement can support both the theory and the salience of derived structures, although the relationship between fundamental and emergent structures remains conceptually constrained.
Problem
The central problem is how theories without fundamental spacetime can account for observable local beables and retain empirical coherence.
Method
The paper surveys quantum-gravity theories with non-spatiotemporal fundamental ontologies and examines their strategies for deriving spacetime and local beables.
Results
The survey finds that local beables can be available even when spacetime is not fundamental, including through dualities and algebraic representations producing phenomenal local beables.
Takeaways & Limitations
Quantitative agreement between derived structures and observed local-beable properties can provide evidence for both the theory and the physical salience of the derivation.
Takeaways & Limitations
The relationship between fundamental and derived structures is not captured by ordinary composition because physical salience is inherently spatiotemporal.
Abstract
from arXiv · showhide
Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities can't be smaller than the derived (since relative size is a spatiotemporal notion) and so can't 'compose' them in any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively.
1 Local beables and empirical coherence
Empirical science presupposes local beables—real entities associated with spacetime regions—yet theories denying fundamental spacetime lack an obvious route to observable entities. The paper frames this as a threat of empirical incoherence and motivates examining how emergent spacetime could address it.
- Local beables: Empirical science presupposes local beables: real entities whose degrees of freedom are associated with open spacetime regions.Bell’s locality condition is weak and does not directly constrain interactions or their propagation.
- Local beables: Local beables constitute the material content of the universe and, unlike merely existing entities, exist somewhere.
- Empirical coherence: Theories without fundamental spacetime preclude fundamental local beables, leaving no obvious strategy for identifying the observable local beables.This creates an empirical-significance problem beyond merely finding a way to test the theory.
- Empirical coherence: A theory is empirically incoherent when its truth undermines our empirical justification for believing it true.For spacetime-denying theories, the concern is that observations of local beables would lack the entities the theory fundamentally permits.
- Empirical coherence: Deriving familiar spacetime and locality is presented as the only escape from the threat that spacetime-denying theories undermine the status of observations.The paper extends Healey’s concern about absent time to the broader problem of absent spacetime in quantum gravity.
2 Theories without spacetime
Theories without fundamental spacetime differ substantially in how their basic structures depart from ordinary spacetime, but several offer routes to recovering localization and empirical coherence. The survey contrasts discrete lattices, causal sets, loop quantum gravity, string dualities, and non-commutative geometries.
- 2.1 Lattice spacetime: Discrete geometry may be fundamental or derived, and its physical significance lies in geometric discreteness such as a shortest length, not ultraviolet finiteness alone.Causal set theory postulates this discreteness, whereas loop quantum gravity arguably derives it from the theory’s axioms.
- 2.1 Lattice spacetime: Discrete spatiotemporal lattices can preserve empirical localization by placing local beables at individual nodes or across simply connected sets of adjacent nodes.The emergence of a smooth continuum remains a challenge, but lattice discreteness alone need not undermine empirical coherence.
- 2.2 Non-metrical lattices: Causal set theory replaces ordinary spatiotemporal relations with a discrete causal ordering lacking fundamental metrics, durations, spacelike structure, and familiar locality.Its fundamental relation is therefore better understood as sui generis causal rather than strictly spatiotemporal.
- 2.2 Non-metrical lattices: Recovering relativistic spacetime from causal sets requires substantial additional work because almost all kinematically admissible causal sets lack well-behaved relativistic continuum limits.This makes the emergence problem more demanding than in the simple lattice case.
- 2.3 Loop quantum gravity: Loop quantum gravity complicates localization because quantum superpositions frustrate locality criteria and adjacency in spin networks need not match proximity in emerging spacetime.The relation between spin networks and relativistic spacetime remains unresolved and is described as the hardest problem facing loop quantum gravity.
- 2.3 Loop quantum gravity: Recovering relativistic spacetimes from loop-quantum-gravity spin networks is necessary to explain general relativity’s empirical success while treating it as false and replaceable.If this recovery succeeds, the authors state that loop quantum gravity’s threat of empirical incoherence is thereby averted.
- 2.4 String dualities: String dualities make the radius of the string’s space representationally surplus, while a dual representation can match phenomenal spacetime and recover local observables.The two dual theories assign reciprocal radii and are physically equivalent, so no possible observation selects between them.
- 2.5 Non-commutative geometries: Non-commutative geometry lacks a manifold and point-values fundamentally, yet its algebraic structure can be mapped into entities resembling local beables.The approach generalizes commutative geometry by deforming coordinate multiplication while retaining the mathematical apparatus needed for Lagrangian physics.
3 Empirical coherence revisited
The paper argues that omitting fundamental spacetime does not automatically make a theory empirically incoherent. Empirical success, theory-relative notions of physical salience, and formal derivations of spacetime structures provide ways to address the challenge.
- 3 Empirical coherence revisited: The authors conclude that no general argument shows that theories without fundamental spacetime must fail to derive local beables or become empirically incoherent.They contrast causal sets, where local beables are not readily identifiable, with string theory, where dualities may leave them available.
- 3 Empirical coherence revisited: The central challenge is whether a formal derivation of local-beable-like structures can establish their physical reality rather than merely reproduce spacetime quantities.The concern is especially acute when the fundamental ontology lacks spacetime and ordinary notions of composition or parthood.
- 3 Empirical coherence revisited: Physical salience is theory-dependent, so applying spatiotemporal standards from ordinary theories to theories without fundamental spacetime improperly biases the assessment.The authors therefore reject an a priori conceptual barrier and emphasize studying particular theories and their derivations.
- 3 Empirical coherence revisited: The paper proposes assessing physical salience from above: successful quantitative agreement with observed local-beable properties supports both the theory and the derivation’s physical significance.On this view, empirical success guides judgments of salience rather than a prior definition being used to validate derivations.
- 3 Empirical coherence revisited: A Lewis-inspired strategy defines non-spatiotemporal entities through a theory whose derived formal structures functionally represent phenomenal spacetime quantities.If the entities exist and uniquely satisfy the relevant theoretical description, the emergent spacetime structure is built into their characterization.
- 3 Empirical coherence revisited: The paper extends this inquiry beyond individual derivations, arguing that conceptual analysis of empirical significance must proceed alongside formal developments through theory fragments, toy models, and false theories.This parallel work connects empirical spacetime to promising structures before a complete formalism is available.