The Wavefunction and Primitive Ontology

Quantum mechanics is empirically the best-confirmed theory we have and gives no agreed answer to the question this section asks. Its central object is the wavefunction $\psi$, and what category $\psi$ falls under — object, property, law, or bookkeeping device — is disputed among people who agree about every prediction.

This makes it the section's best case study, and the source of its most important negative result.

What kind of thing is $\psi$?

The wavefunction of an $N$-particle system is a complex-valued function not on three-dimensional space but on configuration space, of $3N$ dimensions:

$$\psi :{\mathbb{R}}^{3N}\times \mathbb{R}\to \mathbb{C}$$

That is the origin of the problem. If $\psi$ is a physical field, it is a field on a $3N$-dimensional space, and for the universe $N$ is enormous. Either the fundamental space of the world has that many dimensions, or $\psi$ is not the sort of thing that lives in space at all.

Wavefunction realism

Wavefunction realism (Albert, Ney, Loewer) takes the first horn. The fundamental physical space is the high-dimensional configuration space; the universal wavefunction is a genuine field on it; and three-dimensional space, along with everything in it, is emergent — a useful pattern in the dynamics of the fundamental field.

The position is admirably direct: it reads the ontology off the formalism without reinterpretation. Its costs are correspondingly high. The manifest world of three-dimensional objects becomes derivative in a strong sense, and the account must explain why the emergent structure has three dimensions and why our experience tracks it. Critics — Maudlin especially — object that a theory whose fundamental description makes no contact with the arrangement of matter in space cannot explain measurement outcomes, which are facts about pointers in rooms.

Primitive ontology

The rival programme (Allori, Goldstein, Zanghì, Tumulka) insists that a physical theory must posit local beables: entities in ordinary three-dimensional space whose arrangement constitutes the observable world. The wavefunction is then not an object but something nomological — a law-like entity that governs the beables, more akin to the Hamiltonian than to a field.

Each interpretation supplies its own primitive ontology:

The advantage is that measurement outcomes are straightforwardly facts about the beables, and the high dimensionality of $\psi$ is no more troubling than the high dimensionality of a classical Hamiltonian, which nobody took to describe a space. The Bohmian version is developed at length in the book's page on Bohmian mechanics, whose section on primitive versus nomological ontology is the natural companion to this one.

The cost is that $\psi$'s nomological status is uncomfortable: it is contingent, time-dependent, and initial-condition-like, where laws are usually none of these.

Is $\psi$ ontic or epistemic?

A prior question. If $\psi$ merely encodes our information about a system, its dimensionality is no more puzzling than that of a classical probability distribution, and the whole problem dissolves.

The PBR theorem (Pusey, Barrett, Rudolph) constrains this. Under an assumption of preparation independence — that systems prepared independently have independent physical states — no model in which $\psi$ represents mere information can reproduce quantum predictions. Distinct wavefunctions must correspond to distinct physical states. This does not force any particular realism about $\psi$, and epistemic views survive by denying preparation independence or by rejecting the underlying model framework, but it substantially raises the cost of the deflationary option.

Everettian emergence

Everettian quantum mechanics takes the wavefunction as the whole story, with no collapse and no additional beables. The ontological interest is what it says about ordinary objects.

Wallace's answer uses Dennett's criterion of real patterns: a pattern is real if positing it affords a substantial predictive and explanatory gain over describing the underlying data directly. Tables, cats, and branches are such patterns in the universal wavefunction — robustly projectible structures picked out by decoherence, neither fundamental constituents nor illusions.

This is a fourth position on ordinary objects, and it does not fit the standard three-way taxonomy. It is not eliminativism, since the table is real; not permissivism, since not every arrangement makes a pattern; and not conservatism, since reality is a matter of degree and explanatory utility rather than of joining the fundamental inventory. It is functionalism about macroscopic objects, motivated by physics rather than by intuition — and it deserves to be on the menu in the mereology debate, where it currently is not. See the book's survey of interpretations.

The negative result

Set the three programmes side by side. Bohmian mechanics, GRW, and Everett are empirically equivalent — no experiment yet performed or currently proposed distinguishes them — and their inventories are wildly different:

One theory posits particles; another denies them and posits discrete events; a third posits neither and treats the manifest world as pattern. All agree on every prediction.

This is the strongest argument in the section that physics constrains ontology without determining it. It is not a sceptical claim about our access to a determinate fact; it is the observation that the empirical content of our best theory is compatible with radically different answers to "what is there?", so that choosing among them must appeal to considerations — parsimony, explanatory depth, locality, compatibility with relativity — that are not themselves empirical.

Two qualifications keep this from being a counsel of despair. The equivalence may be temporary: GRW predicts deviations from linear evolution that experiments continue to bound, and if collapse is detected the question is settled empirically. And the theories are not on a par in every respect: Bohmian mechanics has known difficulties with relativity, Everett with probability, GRW with tails. Underdetermination is not equal support.

Where this sits

This page belongs to the inventory question, and it is the case where the question is asked of our most fundamental theory and returns three answers.

The moral is the one the section's treatment of method must accommodate. A naturalised ontology says: accept the best theory, read off the commitments. Here the best theory is agreed, and the commitments are not — because a physical theory is a formalism plus a story about what it describes, and the formalism does not come with the story attached. Supplying the story is philosophical work, guided by the physics and not dictated by it. That is the same conclusion the space-and-time section reaches from its own material, in the method page there.