In 1964, John Bell wrote down an inequality any local hidden-variables theory of quantum mechanics must satisfy. Eighteen years later, Alain Aspect's team confirmed experimentally that the inequality is violated in the actual world. Bell's theorem, together with the experiments, rules out local hidden-variable accounts satisfying the theorem's auxiliary assumptions, including the relevant independence conditions. It does not by itself select one metaphysical interpretation of quantum mechanics. That was one door. Everett's 1957 proposal had already opened another: the quantum state never collapses but branches, with each measurement partitioning reality into decoherent branches, each of which contains a copy of the measuring apparatus and the measurer. And in the relativistic extension of quantum mechanics, as Doreen Fraser and David Baker pressed across the 2000s, the particle concept itself loses its frame-invariant referent. Three results. Three places where a piece of the classical metaphysical picture has had to give ground to the mathematics.

The contemporary literature on these three loci is well-developed. On Bell non-locality: Maudlin's *Quantum Non-Locality and Relativity* (3rd ed. 2011) gives the most sustained metaphysical analysis; Wallace's *The Emergent Multiverse* (2012) develops the Everettian alternative frame. On Everettian branching: Wallace 2012 stands as the systematic contemporary defense; Saunders, Barrett, Kent and Wallace's *Many Worlds?* (2010) is the standard anthology; Albert (*Quantum Mechanics and Experience*, 1992) and Maudlin (*Philosophy of Physics: Quantum Theory*, 2019) press the major objections. On QFT: Fraser (2008) and Baker (2009) give the philosophical case against Fock-space particle ontology; Wallace ('In Defense of Naiveté,' 2006) and Ruetsche (*Interpreting Quantum Theories*, 2011) develop field-interpretive alternatives. The structural reply does not enter these debates as a rival position. It accepts the most demanding reading of each result and asks what the structural roles look like once that reading is incorporated.

The challenges so far in [§4.3](<4.3 Physics and Mind.md>) have come from philosophy of mind and philosophy of mathematics. This final cluster comes from physics itself. Three questions press the account from contemporary physics: one from Bell's result on correlations, one from Everett's branching, one from QFT's treatment of the particle concept. Bell non-locality appears to threaten Space's relational non-identity: distant regions are correlated in ways no local structural description admits. Everett multiplies worlds in a way that appears to threaten Substance's persistence and Time's unique directed succession. QFT appears to remove the thing Substance was meant to name: particles, as well-defined countable objects, do not survive the relativistic formalism. If any of these is taken at face value, the Necessity of Nature of [§2.8.5](<2.8.5 Necessity of Nature.md>), supported by the Triconditional Identity of [§2.6.10](<2.6.10 Triconditional Identity.md>) (the result that Time, Space, and Substance, the bearers of the three structural Conditions Temporality, Spatiality, and Physicality, must be co-instantiated for any concrete existent), faces a counterexample from physics: the kind of counterexample a metaphysical argument has to address directly.

*First.* Bell non-locality holds that quantum correlations between spatially separated outcomes outrun local hidden-variable accounts. Bell (1964) proved a limit on correlations between spatially separated measurement outcomes that any local hidden-variables theory must respect. Experimental violations of that limit, Aspect et al. (1982), followed by the loophole-free experiments of the 2010s (Hensen et al. 2015; Giustina et al. 2015), establish that quantum correlations outrun local common causes. Maudlin (*Quantum Non-Locality and Relativity*, 3rd ed. 2011) has pressed the philosophical consequence with the most clarity: the world, on the best reading of the evidence, contains non-local dependencies between spatially separated events. If Space guarantees relational non-identity (if distinct positions are ontologically distinct loci) Bell's result seems to show that distinctness is weaker than the argument requires. The outcomes display correlations incompatible with local hidden-variable factorization, while the no-signalling structure prevents their use for superluminal communication. Describing this as instantaneous causal influence would add an interpretation the experiments alone do not establish.

Non-locality refines Space's specification without dissolving it. Bell's inequality is a constraint on what kinds of correlations are possible between spacelike-separated outcomes; it is not a denial that spacelike-separated outcomes are distinct. The correlation presupposes the distinction: Alice's measurement and Bob's measurement are two measurements, at two locations, with two outcomes, and the correlation Bell quantifies is the relation between those two. What Bell rules out is a specific metaphysical picture: local hidden-variable determination. What survives is a richer structural picture in which non-identity is preserved but the relations binding non-identical positions exceed signal-bounded causation. Maudlin's own preferred reading (non-locality as a fundamental relational feature of the world) is Space specified at higher resolution, not Space refuted. The argument has never required that all spatial relations be mediated sub-luminally. It has required that distinct positions be distinct. Non-locality leaves that requirement intact and tells us what else is true at its level. A sharper version of the worry does not stop at the correlations. If the entanglement-geometry program in quantum gravity is right — if spatial separation is itself emergent from entanglement structure, as the ER=EPR conjecture and allied approaches propose — then Spatiality is pressed one level below distinctness: the reply above secures that the outcomes are two, not that the spatial gap between them is fundamental. The structural answer runs parallel to the emergent-time handling at the QFT locus below. The S-role never required that spatial extension be fundamental, only that real differentiation be realized; a proposal on which space emerges from entanglement must still ground an order of real differences, and the role then attaches to whatever grounds the emergence — entanglement structure included, which is itself a structure of distinct, differently related relata. Whether any emergent-spacetime program succeeds is a live physical question, an alignment matter for the framework rather than something this survey derives; what no such program can deliver is differentiation from no differences at all.

*Second.* Everettian branching holds that the quantum state never collapses but forks into decoherent branches at every measurement. The Everett interpretation (Everett 1957; Wallace, *The Emergent Multiverse*, 2012) holds that the quantum state never collapses. Measurement interactions branch the universal wave function into decoherent branches, each containing a copy of the measurement and a copy of the observer. On Wallace's mature development, branching is continuous and ubiquitous, the branches are real, and the classical world is one branch's-eye view of a structure larger than any single branch. Time's unique directed succession appears to split. Substance's persistence appears to fork. The Triune architecture, specified at the level of a single temporal-spatial-substantial flow, appears to meet a physics in which that flow is one trajectory among indefinitely many.

The Everettian picture, at its clearest, does not dissolve Time and Substance. It multiplies them. Each branch instantiates the structural roles. Branching itself requires what any differentiating operation requires: distinct outcomes (Space), distinct directions of succession within each branch (Time), and the maintenance of causal capacity within each branch (Substance). On a realist Everettian reading, the universal wave function and its decoherent branch structure are taken as physically real. Whether branches are exact ontological loci or emergent, approximate patterns is part of the interpretation and should not be settled by the structural vocabulary alone. The argument's claim that existence requires T, S, and Φ (Temporality, Spatiality, and Physicality) is satisfied within every branch. That there are many branches speaks to the scale of the structural commitment, not its nature. The Everettian owes the argument one answer: does the universal wave function, considered as the whole of reality, itself instantiate the structural architecture the argument requires? For T and S, it does. Unitary evolution and decoherence supply an ordered dynamical structure, while decoherent branch-patterns become distinguishable for practical purposes. Whether the universal state supplies the Φ-role as a persisting physical entity or only as mathematical state structure depends on the ontology adopted. Everett multiplies the domain across which the architecture is instantiated without replacing the architecture itself.

A qualification on dialectical scope is owed before proceeding. The preceding reply works on Wallace’s (2012) mature Everettianism, granting the branching structure and showing that it instantiates T, S, and Φ. Maudlin’s own position is not Everettian; he is among the interpretation’s most sustained critics. His principal objections concern branch individuation (the formalism provides no physical criterion for individuating branches, leaving the probability calculus without a derivable foundation), the Born-rule problem (recovering the Born-rule probabilities from branching ratios requires a notion of branch weight that cannot be derived from the wavefunction alone without circularity), and the absence of primitive ontology (Everettianism specifies a formalism without saying what physically exists in spacetime — the universal wavefunction is not itself local, and no catalogue of local beables is provided). These objections press whether Everettianism should be granted in the first place, not whether, granted, it preserves the structural roles. The structural argument is therefore not adjudicating between Maudlin and Wallace. What it establishes is scope-neutral: whatever interpretation of quantum mechanics is adopted, Everettian branching, Bohmian mechanics (whose particle trajectories are paradigm local beables instantiating S, Φ, and T directly), GRW collapse theories (whose flash or matter-density ontologies similarly supply local Φ-realizers), or algebraic approaches, the structural roles must be satisfied by whatever the interpretation countenances as its primitive ontology. Maudlin’s local-beable insistence is, from this vantage, a demand that the Φ-role be explicitly realized by something in spacetime; the structural argument agrees, and adds that every serious candidate for that something satisfies the role.

*Third.* The QFT particle-concept problem holds that the relativistic formalism dispenses with frame-invariant particles. Quantum field theory in its relativistic form dispenses with the classical particle concept. Fraser ("The Fate of 'Particles' in Quantum Field Theories with Interactions," 2008) and Baker ("Against Field Interpretations of Quantum Field Theory," 2009) develop the philosophical consequences. In interacting relativistic QFT there is no Fock-space particle description invariant across frames, no particle-number operator that commutes with the full Hamiltonian, no countable thing whose identity persists across the field's evolution. Particles, as well-defined individuals, do not survive the mathematics. What survives, depending on interpretation, is a structure of fields, algebraic observables, excitations, state-transition constraints, or some more austere QFT ontology. If Substance was meant to name particle-persistents, QFT has removed its referent.

Substance was never specified as particle-persistence. Substance is defined at [§1.4.3](<1.4.3 Substance.md>) as the maintenance of causal capacity across transitions, leaving open what realizes the maintenance. Particles were one candidate: the nineteenth-century candidate, inherited by the early twentieth. Fields are another. The reply does not simply trade particles for fields as if field ontology were uncontested. Whether the preferred interpretation speaks in terms of fields, local algebras, excitations, gauge-invariant structures, or state-transition constraints, the structural point is the same: the formalism preserves determinate capacities across transitions. There are states or observables that can differ, rules or constraints governing their transformations, and stable relations across which those transformations are specified. That is the role Substance plays here. QFT refines the realizer of Substance (perhaps beyond both particles and naïve fields) rather than eliminating the role.

Maudlin’s primitive-ontology insistence bears directly here: an unspecified disjunction of realizers (fields, algebraic states, excitations, gauge-invariant structures) is not yet an ontology, and a role-claim ungrounded in a specified ontology is, on his methodological view, physics-as-decoration. The structural argument’s response is not to choose among the candidates but to explain why the choice can be deferred at this level without losing force. The Φ-role specifies what any acceptable realizer must do: make a determinate physical capacity available to the ordered regime in which a real difference can occur. When the ontology is fundamentally dynamical, that is the maintenance of causal capacity across transitions. When a proposal treats time as emergent, it need not posit a fundamental clock-time; it must instead show how its fundamental constraints or states ground an emergent order in which determinate capacities can be carried and made effective. A proposal that denies any such capacity-and-order story has not yet supplied a realizer of change, rather than having supplied a counterexample to it.

This is a division of roles, not a collapse of Φ into T. T supplies the order of before and after; Φ supplies what can remain determinate and make a difference through that order. The present survey does not decide whether any timeless quantum-gravity program successfully supplies the required emergence account. That is a live physical question, and the framework's use of the role here is abductive rather than a result it certifies in advance. Committing to one realizer would narrow the claim without strengthening it; remaining at the role level preserves the comparison across the live interpretive options. Where Maudlin’s demand is directed at physical theory (QFT owes a primitive ontology) the argument agrees, and defers to that ongoing debate on its own terms.

*What converges.* Each of the three questions finds the physics specifying the structural roles at higher resolution than the classical picture anticipated. Bell's inequality is a constraint on what kinds of correlations are possible between spacelike-separated outcomes, not a denial that the outcomes are distinct; the correlation presupposes the distinction, and non-locality refines Space's non-identity rather than dissolving it. The Everett multiverse multiplies the domain across which the architecture is instantiated without replacing the architecture: every branch instantiates T, S, and Φ, and the universal wave function supplies the ordered, differentiated structure at its own level. QFT refines the realizer of Substance beyond the classical particle concept without eliminating the role: the maintenance of causal capacity across transitions survives the loss of the particle concept. None of the three tells us the roles are dispensable. Physics, pressed to its contemporary frontier, leaves the structural roles intact: each result refines rather than dissolves a Time in which things happen, a Space in which things are distinct, and a Substance whose causal capacity persists across the happening.

Fraser and Baker have pressed the philosophical consequences of interacting quantum field theory that the physics literature more often takes up as technical rather than metaphysical questions. What contemporary physics finds at its frontiers is, on the present reading, the structural architecture itself rather than the classical picture specialists grew up pressing against.


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← [4.3.7 Mathematical Universe Hypothesis](<4.3.7 Mathematical Universe Hypothesis.md>) | [4.3.9 Structural Realism](<4.3.9 Structural Realism.md>) →
