Finding Space in a Non-Spatial World

What is the relation between space in the manifest image of perceptual experience and in the scientific image of physics? I will argue that we have moved from spatial primitivism (on which space is understood as a primitive conception that we are acquainted with) to spatial functionalism (on which space is picked out by its functional role). I investigate different forms of spatial functionalism on which the relevant roles are experiential (involving effects on our experience) and non-experiential (involving patterns of causal interactions). I draw connections to functionalism in the philosophy of mind, to Cartesian skepticism, and to recent literature on spacetime functionalism and emergent spacetime.

Thinking about Spacetime

Several different quantum gravity research programmes suggest, for various reasons, that spacetime is not part of the fundamental ontology of physics. This gives rise to the problem of empirical coherence, which I frame in terms of entailment: how could a non-spatiotemporal fundamental theory entail spatiotemporal evidence propositions? Solutions to this puzzle can be classified as realist or antirealist, depending on whether or not they posit a non-fundamental spacetime structure grounded in or caused by the fundamental structure. These approaches place different constraints on our everyday concepts of space and time. Applying lessons from the philosophy of mind, I argue that only realism is both conceptually plausible and suitable for addressing the problem at hand. I suggest a role-functionalist version of realism, which is consistent with both grounding and causation, and according to which our everyday concepts reveal something of the true nature of emergent spacetime.

The Measurement Problem for Emergent Spacetime in Loop Quantum Gravity

Any quantum theory of gravity faces the measurement problem. Carlo Rovelli sees his relational interpretation as offering a solution to this problem when applied to his favored loop quantum gravity (LQG). I examine the prospects of Rovelli’s relationalism in LQG. In LQG it is not clear what physical systems there are at a fundamental level with no spacetime. But implementing Rovelli’s relational interpretation in the context of LQG requires an account of interaction and a model of observer systems whose relational states represent determinate outcomes. Even if no such account is forthcoming at a fundamental level in LQG, it might still be available in a limit at which spacetime has emerged. But to use this account effectively to address the measurement problem, it would be necessary to reconcile the observer-relativity of measurement outcomes with a basic norm of scientific objectivity.

IIB matrix model: Emergent spacetime from the master field

We argue that the large-N master field of the Lorentzian IIB matrix model can give the points and metric of a classical spacetime.

A symmetry principle for emergent spacetime

There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay, we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge–gravity duality and explain how their breaking describes features of gravitational theory. Such symmetries imply the existence of nonlocal objects in the gravitational theory — in gauge–gravity duality these are the strings and branes of the bulk theory — giving an alternative way to understand the nonlocality necessary in any ultraviolet completion of gravity.

The cosmological constant of emergent spacetime in the Newtonian approximation

We present a simple quantum-mechanical estimate of the cosmological constant of a Newtonian Universe. We first mimic the dynamics of a Newtonian spacetime by means of a nonrelativistic quantum mechanics for the matter contents of the Universe (baryonic and dark) within a fixed (i.e. nondynamical) Euclidean spacetime. Then we identify an operator that plays, on the matter states, a role analogous to that played by the cosmological constant. Finally, we prove that there exists a quantum state for the matter fields, in which the above-mentioned operator has an expectation value equal to the cosmological constant of the given Newtonian Universe.