Source
Chen (2018; Philosophy Compass 2019), LIT-204, read in full in NOTE-175. Belot (2011), LIT-100, pp. 7–9, read in full in NOTE-110. Allori (2021), LIT-200, read in full in NOTE-154.
What was actually shown
The map (Chen §§3–5). Realist readings of the universal wave function in non-relativistic quantum mechanics fall into ontological readings (high-dimensional field, multi-field on 3-space, spacetime state realism, Hilbert-space vector), nomological readings and a sui generis reading. Which is open depends on the solution to the measurement problem and on whether fundamental space is high- or low-dimensional (Table 1, asserted, with one cell inconsistent with the text).
The strong nomological reading. ψ has the status of the classical Hamiltonian: it generates the motion and suffers no back-reaction (Dürr, Goldstein and Zanghì; Goldstein and Teufel). Belot shows what it costs in current theory (pp. 7–9): time-indexed law-propositions, and grades of necessity, ψ being “more like an initial condition” than the Schrödinger equation. He ranks them: time-indexing is “the more daunting obstacle”; grades of necessity are tolerable on Lange-style accounts. Both Belot and Chen point to quantum gravity, where Wheeler–DeWitt ĤΨ = 0 (Chen eq. 11) would make the universal state time-independent. Chen notes that whether it holds is open, and that the arrow of time would need revision (fn. 24). Chen’s own variant takes a simple initial mixed state and gives up purity and time-independence of the generator.
The weak nomological reading (Chen §4.2). ψ is a variable of the Humean best system: it need only be the simplest of the competitors, not time-independent or unique. The objection that trajectories carry far less information than ψ is answered by the agreement physicists reach on ψ from pointer facts. The reading has been defended only within extended Humeanism. Chen reports the objection that it is “too cheap”: the same move would banish classical electromagnetic fields (fn. 28).
The functionalist variant (Allori). ψ is whatever plays its empirical, nomological and explanatory roles; it is “an ingredient in the law, rather than a law itself”, one of several possible realizers, as a potential is up to a constant (§§3.2–3.4). An ingredient may be time-dependent and non-unique, so Belot’s and Maudlin’s objections lose their grip. NOTE-154 places the view in Chen’s weak cell, which Allori’s own fn. 46 aligns with Esfeld’s and Bhogal and Perry’s Humeanism.
What could have come out otherwise. One of the readings could have answered both costs: a time-independent universal state already in hand, or a criterion separating ingredients of the law from material posits. None supplies either.
What this does not say
- That ψ is nomological, or is not. Chen’s survey weighs no verdict and says the list may not be exhaustive (§6). Belot’s own conclusion is “inconclusive” (§3).
- That Allori answers the too-cheap objection. She cites Chen (2019) and does not address it. Her reply to objection 4 (p. 20) embraces classical fields as bookkeeping devices whose explanatory force belongs to the law, which is the case the objection treats as a reductio (NOTE-154). Her text is also inconsistent on whether ψ is nomological (pp. 11, 20–21).
- That the functionalist view bypasses PBR. The bypass is asserted (fn. 32) by calling the ontic/epistemic dichotomy false; PBR is not engaged in its own terms (THEORY-605, THEORY-586).
- That the configuration-space problem disappears. Allori asserts it “never arises” (p. 17) and then lets configuration space re-enter through nonlocal nomological facts (objection 5).
- That Table 1 is reliable cell by cell. Ten cells are ”?”, and the Sm cell for the strong reading contradicts §4.1 (NOTE-175).
Connections
- The dispositional reading, Belot’s other option, fails his particle-in-a-box case (THEORY-635); Dorato’s event-based dispositions are THEORY-656.
- Gao’s ψ-ontic particle ontology (LIT-121) rejects both the nomological and configuration-space readings (THEORY-630).
- Poltorak (LIT-164) uses these readings to separate ontic from causal status (THEORY-485).
- The Hilbert-space option is Carroll’s programme (LIT-123).