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, \( S_{\max}(t)=2\sqrt{1+\sin^{2}(2\theta)\,|z(t)|^{2}} \), 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.
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, ( S_{\max}(t)=2\sqrt{1+\sin^{2}(2\theta),|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.
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=21+∣z(t)∣2 in terms of the decoherence factor z(t), interpolating between the Tsirelson bound and the classical bound; this corrects the constant-22 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.
Local branch selection—a frame-independent postulate under which environmental decoherence einselects a branch structure and a local stochastic process realizes one branch with Born probability—has so far been implemented with continuous spontaneous localization (CSL), whose noise is phenomenological. Here we determine which physical noises can play this role. First we prove a kernel-universality theorem: for any set of commuting Hermitian collapse operators driven by Gaussian noises with an arbitrary positive-semidefinite correlation kernel C, the einselected branch weights are exact martingales, so absorption occurs with Born probability for every kernel; the kernel controls only the selection rate Γ=ΔTCΔ, where Δ is the vector of branch eigenvalue differences. For the Diósi–Penrose (DP) kernel G/ℏ∣x−x′∣ acting on mass densities, the rate is Γ=2EG/ℏ, with EG the gravitational self-energy of the branch mass-density difference: Penrose's collapse criterion emerges as the nondegeneracy condition of the Born martingale, and gravitationally induced collapse becomes a parameter-free physical implementation of the selection postulate, with τsel∼3×10−16s for a milligram pointer. Second, we prove a no-selection theorem: noise coupled as a random Hamiltonian (classical stochastic spacetime fluctuations included) leaves every branch weight exactly constant along every realization while dephasing the ensemble—decoherence without selection—so classical metric-fluctuation dephasing cannot implement the postulate; selection requires measurement-type (norm-changing) noise. Third, for the symmetric EPR configuration we show that gravitational noise cross-correlation between the wings preserves no-signaling exactly (the cross terms of the correlated-kernel Lindblad dissipator vanish under the local partial trace), shifts only the selection rate, and is of relative size ∼Rδ2/L3≈4×10−9 at one-meter separation; a common-mode stall at perfect correlation is exhibited and verified numerically. Stochastic simulations confirm Born statistics across kernels to sampling precision, machine-zero weight drift for random-unitary noise, and the rate law across the full correlation range. The results upgrade the selection postulate from “CSL-compatible” to “gravitationally implementable,” identify exactly which proposed mechanisms can and cannot supply its randomness, and inherit the active experimental program constraining the DP model.
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.
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.
The Einstein-Podolsky-Rosen (EPR) paradox challenges the completeness of quantum mechanics under the assumptions of separability and locality, while Bell's theorem and its loophole-free experimental confirmations rule out local hidden variables and establish that entangled correlations are nonlocal yet no-signaling. This paper formulates, within the spacetime-quantum unified-field theory, a self-contained resolution of the paradox. Starting from the six axioms of the theory, we model the entangled pair as two local excitations of the single global spacetime-quantum field, a coherent superposition of discrete spacetime quanta (Axiom 1). We show that the EPR elements of reality are not attributes of the separated subsystems but properties of the global coherent configuration established within the common past light cone, so that EPR's tacit separability premise fails in this ontology (Axioms 1 and 5). Measurement is identified as a strictly local energy exchange (Axioms 2 and 5) whose influence propagates at most at the speed of light by the local hyperbolic master equation (Axiom 3), and we prove, by the invariance of the reduced density matrix, that no signaling is possible. The Bell correlations are reproduced as a consistency condition inherited from the standard-model sector (Axiom 4), with the Tsirelson bound 2√2 following from the no-signaling structure. Complete derivations of the correlation function, the Clauser-Horne-Shimony-Holt inequality and its violation, the no-signaling theorem, the local measurement model, and the coherence-entanglement relation are provided in the appendices.
Quantum mechanics, despite its extraordinary success in describing microscopic phenomena, continues to raise foundational questions concerning measurement, nonlocality, and the nature of physical reality. These issues are exemplified by the Einstein-Podolsky-Rosen (EPR) paradox and the Bell inequality, which contrast quantum correlations with classical notions of locality and realism. In this work, we critically examine the assumptions underlying Bell’s theorem in light of the incompatible and contextual nature of quantum observables. We show that Bell’s constraint on simultaneous definite values for incompatible observables, together with the assumption of hidden variables, is not applicable to quantum mechanics itself, which is inherently nonclassical and contextual. When measurement is modeled as a local system-environment interaction within the framework of quantum decoherence, the resulting dynamics remain entirely local and unitary in the EPR scenario. Decoherence naturally selects pointer states and suppresses interference, giving rise to the appearance of wavefunction collapse consistent with quantum predictions. Importantly, the Bell correlations obtained in this framework reproduce the standard quantum results and are independent of both system-bath and inter-bath interactions, which affect only the rate of decoherence. Our analysis suggests that, in the EPR scenario, quantum mechanics can be both local and realistic when the wavefunction is treated as an ontic description of reality within the decoherence framework, offering a potential route toward a locally realistic quantum theory aligned with Einstein’s vision. This work contributes to a more rigorous foundation for quantum mechanics, providing insights that can accelerate progress in quantum computing and nanoenergy harvesting.