The textbook projection postulate of quantum mechanics stands in tension with the symmetries of relativistic spacetime: it is stated as an update applied at a single instant to the entire composite state, which presupposes a preferred simultaneity surface, and its description of the distant partner of an entangled pair invites the reading that measurement physically changes that partner. We argue that this tension arises from one removable ingredient of the axiom, and we make precise what that ingredient is and is not. Separating the postulate into three logically independent claims—definite-outcome realization, Born-rule probability, and a globally-timed projection—we show that the third can be replaced by a locally triggered rule: branch selection upon completed local decoherence, in the einselected pointer basis (Postulate M). The measurement operator itself is not modified: the update at a site A is of the local form PiA⊗IB under both the standard postulate and Postulate M, and the two rules yield identical post-measurement states and probabilities, the standard rule being recovered as the vanishing-decoherence-time limit. Postulate M is therefore a reinterpretation of standard quantum mechanics rather than a modification of it; what it changes is the trigger of the update, from a global instant to a local decoherence event, so that the axiom can be stated without reference to any foliation. Parameter independence holds exactly, as it does in the standard theory; the final branch structure and joint outcome statistics are foliation-independent; and the exchange symmetry of the entangled pair is respected. We illustrate the framework in the Einstein–Podolsky–Rosen (EPR) scenario with one and with both particles coupled to local spin environments. The Born-rule probabilities in the pointer basis are exactly conserved throughout decoherence, while the maximal CHSH (Clauser–Horne–Shimony–Holt) value, obtained from the Horodecki criterion, is Smax=2\( \sqrt{1+|z(t)|^2 } \) in terms of the decoherence factor z(t), interpolating between the Tsirelson bound and the classical bound; this corrects the constant-\( 2\sqrt{2} \) claim of Ref. [10]. The single symmetry that quantum mechanics does break, outcome independence, is located entirely in the nonseparability of the global state, never in the measurement operator: it transmits no signal and selects no frame. The single-outcome question—which branch is realized—is left open.
The textbook projection postulate of quantum mechanics stands in tension with the symmetries of relativistic spacetime: it is stated as an update applied at a single instant to the entire composite state, which presupposes a preferred simultaneity surface, and its description of the distant partner of an entangled pair invites the reading that measurement physically changes that partner. We argue that this tension arises from one removable ingredient of the axiom, and we make precise what that ingredient is and is not. Separating the postulate into three logically independent claims—definite-outcome realization, Born-rule probability, and a globally-timed projection—we show that the third can be replaced by a locally triggered rule: branch selection upon completed local decoherence, in the einselected pointer basis (Postulate M). The measurement operator itself is not modified: the update at a site A is of the local form PiA⊗IB under both the standard postulate and Postulate M, and the two rules yield identical post-measurement states and probabilities, the standard rule being recovered as the vanishing-decoherence-time limit. Postulate M is therefore a reinterpretation of standard quantum mechanics rather than a modification of it; what it changes is the trigger of the update, from a global instant to a local decoherence event, so that the axiom can be stated without reference to any foliation. Parameter independence holds exactly, as it does in the standard theory; the final branch structure and joint outcome statistics are foliation-independent; and the exchange symmetry of the entangled pair is respected. We illustrate the framework in the Einstein–Podolsky–Rosen (EPR) scenario with one and with both particles coupled to local spin environments. The Born-rule probabilities in the pointer basis are exactly conserved throughout decoherence, while the maximal CHSH (Clauser–Horne–Shimony–Holt) value, obtained from the Horodecki criterion, is Smax=2( \sqrt{1+|z(t)|^2 } ) in terms of the decoherence factor z(t), interpolating between the Tsirelson bound and the classical bound; this corrects the constant-( 2\sqrt{2} ) claim of Ref. [10]. The single symmetry that quantum mechanics does break, outcome independence, is located entirely in the nonseparability of the global state, never in the measurement operator: it transmits no signal and selects no frame. The single-outcome question—which branch is realized—is left open.
The standard measurement postulate of quantum mechanics stipulates an instantaneous, non-local update of the global wavefunction upon measurement of an entangled subsystem. This postulate has been a persistent source of foundational tension, both with the locality structure of relativistic physics and with the dynamical character of the decoherence program. We separate the measurement postulate into three logically independent claims: definite outcome realization, Born-rule probability assignment, and instantaneous projection for the global wavefunction. We argue that the third claim can be eliminated at the axiomatic level and propose a modified measurement postulate, Postulate M, that replaces it. Under Postulate M, a single pointer outcome is realized locally when environmental decoherence has einselected a pointer basis at the measurement site; the corresponding selection acts on the global wavefunction as a conditional restriction to a branch rather than as a physical operation on spacelike-separated regions. We show that Postulate M recovers the standard measurement postulate as a limiting idealization for vanishing decoherence time, derives Lüders’ rule for sequential measurements, and yields no-signaling as an automatic structural consequence — not only at the level of measurement statistics but at the level of physical states themselves. Two explicit illustrations in the EPR scenario — with one and with both particles coupled to local spin environments — demonstrate the framework concretely and exhibit its frame-independent, manifestly local character. The framework is built on standard decoherence theory, compatible with multiple candidate mechanisms for single-outcome realization including gravitationally-induced collapse proposals, and naturally situated within a ψ-ontic reading of the quantum state. It represents, we argue, a reformulation of quantum mechanics as a local, state-realist theory — preserving Einstein’s aspiration for an objective physical world in the only form consistent with the empirical content of quantum mechanics, namely realism about the wavefunction rather than about pre-measurement observable values.
A recently proposed local measurement axiom (Postulate M) replaces the instantaneous global projection of textbook quantum mechanics with branch selection triggered by completed local decoherence, while a companion ψ-ontic analysis identifies continuous spontaneous localization (CSL) as a concrete local mechanism for the selection itself. Here we test this two-stage account quantitatively in the Einstein–Podolsky–Rosen (EPR) scenario. We integrate the nonlinear CSL stochastic Schrödinger equation for an entangled spin pair in which one particle couples to a local spin bath with random couplings, bath self-dynamics, and intra-bath interactions, while the noise field and collapse operator act only at the measurement site. Analytically, we derive an exact law for the maximal Clauser–Horne–Shimony–Holt (CHSH) value under local decoherence, Smax(t)=21+sin2(2θ)∣z(t)∣2, with z(t) the decoherence factor and θ the entanglement angle: the CHSH excess over the classical bound is consumed, never the measurement-basis probabilities, which are exactly conserved. We further show that the selection stage is governed by an exact martingale: the branch weight obeys a scalar Itô equation whose derivation requires only the orthogonality of the branches—supplied by the spin structure, not by the environment—so the Born rule emerges as an absorption probability irrespective of the residual bath coherence. Numerically, the law holds to machine precision (∼ 10−15) for all three bath classes, including interacting environments, and through finite-size recurrences; stochastic trajectories confirm Born statistics to within sampling error, with all realizations fully resolved. The ensemble-averaged reduced state of the distant particle is invariant under the local collapse-operator axis and rate—parameter independence as a structural theorem, verified to machine precision in the unitary sector—and branch amplitudes are invariant across all environmental initial conditions and dynamics (∼ 10−11), confirming that outcome randomness is not of environmental origin. In the symmetric configuration, with independent noises at both wings, the two local noises provably drive a single global branch martingale at the summed rate: selection is one joint event whose absorbing states are the correlated branches—mismatched outcomes are dynamically excluded (zero events in 300 realizations, against ∼ 25% each for a product-state control)—the joint statistics are invariant under swapping which wing completes first (93% vs 9% orderings, distributions equal within sampling error), and sampled outcomes reproduce the singlet’s measurement correlation E(β) = − cos β—with β the angle between Alice’s and Bob’s measurement axes—including a CHSH value |S| = 2.710±0.073, consistent with the Tsirelson bound 2√2 within sampling errors. Decoherence and local stochastic selection jointly reproduce the empirical content of quantum measurement in the EPR scenario with no nonlocal dynamical element: the only nonclassical resource is the nonseparability of the initial state. Nonlocal projection is thus dispensable not only axiomatically and ontologically but operationally.
This work continues the framework developed in Ref. [1], in which time is treated relationally as the +1 evolution parameter associated with the dimensional configuration space of a physical phenomenon, and quantum-mechanical structure is proposed to emerge from the information-preserving dimensional recording of a higher-dimensional wave field. Here we extend that construction beyond the single-system description and investigate whether additional central elements of quantum mechanics can arise without being introduced as independent quantum postulates. We first clarify the recording process in terms of physically distinguishable equivalence classes of parent configurations and show how changes of the parent field can produce effective measurement-induced state updating in the reduced description. For independently preparable systems, preservation of local linear superposition leads to bilinear composition and, subject to completeness of the accessible composite state space, to Hilbert-space tensor products. Joint interactions then generate nonfactorizable reduced states, providing a structural origin for entanglement before any probabilistic interpretation is introduced. We subsequently derive the Born probability rule from the geometry of orthogonal reduced alternatives together with unitary invariance, noncontextual consistency, continuity, normalization, and additive coarse-graining. The resulting probability structure is compared with the independent robustness-based reconstruction of De Raedt, Katsnelson, and Michielsen [2]. Using the derived composite structure and probability rule, Bell–CHSH correlations are obtained from generic interaction-generated pure entangled states without assuming a singlet state or Pauli spin operators, while operational no-signalling is preserved. Finally, we explore a possible geometric extension toward internal gauge symmetries: aligned three-dimensional, tilted three-dimensional, and fully four-dimensional parent-field deformations lead respectively to one, two, and three component complex internal representations, suggesting U(1), SU(2), and SU(3) type symmetry structures. Unlike approaches that take the quantum formalism as their starting point, or reconstruction programs based primarily on operational or informational axioms, the present framework seeks a concrete physical mechanism from which these structures emerge together. The fact that a single modification in the dimensional role of time, combined with information-preserving reduction, consistently generates multiple otherwise independent features of quantum theory makes this possibility physically significant even before genuinely new empirical predictions are established.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems there is no “state of B” to be affected by measurement at A. The reduced density matrix of a subsystem, while operationally useful, is not ontologically real for non-factorizable states. Measurement is a local dynamical process — concretely modeled by continuous spontaneous localization (CSL) — that destroys one local wavefunction component at the measurement site. The global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle’s reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. We show that this framework is consistent with no-signaling, with the contextuality required by the Kochen–Specker and GHZ theorems, and with the local measurement axiom (Postulate M) proposed in a companion paper. Bell’s theorem does not force nonlocality upon our framework because it presupposes outcome determinism — the assignment of definite values to observables prior to measurement — which several quantum mechanical theorems and our ψ-ontic ontology explicitly deny. Decoherence, which is ubiquitous in nature, provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems, there is no "state of B" to be affected by measurement at A. Measurement is a local dynamical process-concretely modeled by continuous spontaneous localization-that destroys one local wavefunction component at the measurement site; the global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle's reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. The framework satisfies no-signaling and embraces the contextuality required by the Kochen-Specker and GHZ theorems. We are explicit about its relation to Bell's theorem: Bell local causality (factorizability) fails, as it must in any empirically adequate theory, but the failure is confined to outcome independence and is identified with the nonseparability of the global ontic state, while parameter independence-and with it the locality of the dynamics-holds exactly. Decoherence provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.
Abstract Standard quantum mechanics asks us to live with two laws of time. The first is the continuous, linear, unitary evolution of the Schrödinger equation. The second is the discontinuous, non-unitary reduction that appears when a measurement yields one result rather than many. We have learned to use this double description with remarkable success, yet the success of the practice does not remove the tension in the principle. This paper proposes a conditional framework, Record-Gated Martingale Collapse (R-MC), for a narrower and sharper question: how can a state that has branched through ordinary unitary interaction among a system, an apparatus, and an environment settle into a single recorded outcome without adding an external projection rule? The framework begins where ordinary dynamics leaves us: unitary branching and decoherence. It then adds three elements. First, a non-selective record gate opens the collapse mechanism only after inter-branch overlap has weakened and a sufficiently independent environmental record has accumulated. Second, the collapse rate is amplified by the effective number of independent recording channels, not by the raw number of environmental degrees of freedom. Third, an uncontrollable objective seed generates the stochastic path along which branch weights move. Under quantum non-demolition (QND) conditions these weights are bounded martingales that diffusively localize toward a single branch, and Born-rule weights follow from conservation of their mean rather than from a postulated projection. We separate this gradual convergence from the operational recording time, and we distinguish a safe external form, in which the gate depends on local environmental variables and the ensemble mean closes into a linear Lindblad equation, from a more ambitious internal form that requires operational locality of the gate and locality of the apparatus pointers. A distinctive prediction, record-threshold collapse delay, states that two environments with comparable decoherence may nevertheless yield different outcome times if they differ in their capacity for independent, amplifiable recording.