Entangled qubits are interconnected at any separation. Quantum mechanics represents the interconnection by one unfactorizable entangled state. A measurement at one station collapses the entangled state and fixes the state assigned to the other qubit, depending on the outcome. Interpreted as physics, the entangled state and wavefunction collapse conflict with Einstein's separability and locality. We resolve the conflict by Corpuscular Quantum Mechanics, which replaces the entangled state with source constraints and reproduces the quantum joint probabilities exactly. Each qubit leaves the source carrying one of two definite states and an unshared random variable. An extended Born rule assigns a generally complex coefficient to the transition from the source-assigned state to the recorded outcome, using only what the qubit carries and the locally chosen measurement direction. Averaging products of the coefficients over the source ensemble returns the joint probabilities. Nothing is fitted. An exact identity maps the amplitudes of any pure n-qubit state to the source constraints. We prove the random variables admit a positive distribution meeting the constraints. The identity yields the joint probabilities of the Bell, Greenberger-Horne-Zeilinger, Eberhard, W, Hardy, and Dicke states for arbitrary directions. The resolution requires no action at a distance, no collapse, and no outcomes for unperformed measurements. The one change is that the event-level quantity is a transition coefficient, not a probability. Bell's theorem therefore does not apply. Quantum mechanics is thus one recipe for computing the correlations, and the entangled state is a feature of the recipe, not of nature.
Entangled qubits are interconnected at any separation. Quantum mechanics represents the interconnection by one unfactorizable entangled state. A measurement at one station collapses the entangled state and fixes the state assigned to the other qubit, depending on the outcome. Interpreted as physics, the entangled state and wavefunction collapse conflict with Einstein's separability and locality. We resolve the conflict by Corpuscular Quantum Mechanics, which replaces the entangled state with source constraints and reproduces the quantum joint probabilities exactly. Each qubit leaves the source carrying one of two definite states and an unshared random variable. An extended Born rule assigns a generally complex coefficient to the transition from the source-assigned state to the recorded outcome, using only what the qubit carries and the locally chosen measurement direction. Averaging products of the coefficients over the source ensemble returns the joint probabilities. Nothing is fitted. An exact identity maps the amplitudes of any pure n-qubit state to the source constraints. We prove the random variables admit a positive distribution meeting the constraints. The identity yields the joint probabilities of the Bell, Greenberger-Horne-Zeilinger, Eberhard, W, Hardy, and Dicke states for arbitrary directions. The resolution requires no action at a distance, no collapse, and no outcomes for unperformed measurements. The one change is that the event-level quantity is a transition coefficient, not a probability. Bell's theorem therefore does not apply. Quantum mechanics is thus one recipe for computing the correlations, and the entangled state is a feature of the recipe, not of nature.
We propose a corpuscular framework in which qubits possess individually defined states and single-event probabilities, based on an extension of the Born rule to single events. The extended rule provides a dynamical account of measurement at the single-event level. It reproduces quantum-mechanical joint probabilities through constraints on admissible joint states, replacing factorization over shared variables and relaxing the measurement-independence assumption underlying Bell-type analyses while maintaining independence of the source and measurement settings. Correlations arise from constraints imposed by the preparation and measurement configurations, without invoking dynamical non-local influence. The framework applies to arbitrary entangled states, including Bell, Greenberger-Horne-Zeilinger, and W states. Interference emerges as a statistical effect of indivisible corpuscles where visibility diminishes after sequential beam splitting, providing an experimental test distinguishing it from standard quantum mechanics.
The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.
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 Probability is distinguished into two kinds: physical and epistemic, also, but less accurately, called objective and subjective. Simple postulates are given for physical probability, the only novel one being a locality condition. Translated into no-collapse quantum mechanics, without hidden variables, the postulates imply that the elements in any equiamplitude expansion of the quantum state are equiprobable. Such expansions therefore provide ensembles of microstates that can be used to define probabilities in the manner of frequentism, in von Mises’ sense (where the probability of P is the frequency of occurrence of P in a suitable ensemble). The result is the Born rule. Since satisfying our postulates, and in particular the locality condition (meaning no action-at-a-distance), these probabilities for no-collapse quantum mechanics are perfectly local, even though they violate Bell inequalities. The latter can be traced to a violation of outcome independence, used to derive the inequalities. But in no-collapse theory it is not a locality condition; it is a criterion for entanglement, not locality.
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. A major family of derivations is based on envariance, a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Further, we demonstrate envariance in a purely local quantum system, showing its independence from relativistic causality.
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.