Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.
Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.
We have studied how relativistic causality limits on the generalization of quantum probability assignment, which can give more nonlocal (superquantum) correlations than quantum correlations. We have shown that 'no causal order' condition between two spacelike separate events is stronger than no faster-than-light-signaling condition as the requirement of relativistic causality. Using no causal order condition we have proved that Born rule is the only probability assignment to quantum measurement on an arbitrary entangled quantum state described by the Hilbert space language, consistent with relativistic causality. We have also shown that all superquantum correlations, which preserve relativistic causality, can be understood as hypothetical correlations given by applying modified quantum probability assignments to quantum measurements on a Bell state.
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the situation that two spacelike separate parties Alice and Bob share an entangled two qubit system. We have modified the quantum probability rule as small as possible such that the first local measurements are governed by the usual Born rule and the second measurement by the modified quantum probability rule. We have shown that only the maximally entangled states can have higher nonlocality than the quantum upper bound while satisfying the no-signaling condition. This fact could be a partial explanation for why the nonlocality of the quantum theory is limited. As a by-product we have found the systematic way to obtain a variety of nonlocal boxes.
According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of a non-local box . The concept has been introduced from the principle of non-locality, which satisfies relativistic causality. In this paper, we show that a correlation leading to the non-local box can be derived consistently if we release one of major axioms in quantum mechanics, Born’s rule . This allows us to obtain a theory that in one end of the spectrum agrees with the classical probability and in the other end agrees with the theory of non-local causality. At the same time, we argue that the correlation lies in a space with special mathematical constraints such that a physical realization of the correlation through a probability measure is not possible in one direction of its limit, but is possible in the other limit.
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.
This preprint clarifies a persistent category error in the interpretation of quantum mechanics and relativity by explicitly distinguishing propagation from correlation. Relativistic constraints, including the finite speed of light, apply to the transmission of energy, matter, and information through spacetime. Quantum mechanics, by contrast, permits nonlocal correlations between entangled systems that do not involve transmission, motion, or signal propagation. The apparent instantaneity of quantum effects therefore reflects the revelation of pre-existing correlation structure rather than superluminal dynamics. By maintaining this separation, the preprint shows that the finite speed of light and quantum nonlocality are not in conflict. Light is limited in speed because it propagates; quantum correlations have no speed because nothing propagates. This framing resolves common misconceptions surrounding entanglement, nonlocality, and causality without introducing hidden structures, preferred frames, or violations of relativistic invariance. The work is intended as a conceptual clarification and falsifiable interpretive framework, not a modification of quantum theory or relativity. Keywords quantum correlation nonlocality entanglement speed of light relativity causality non-signaling propagation vs correlation foundations of quantum mechanics conceptual clarification
It is shown that quantum mechanics is, like thermodynamics, a phenomenological theory i.e., not a causal theory, ( not because it is a statistical theory - statistical theories with caused probability distributions can be regarded as causal) but because pure states, i.e., probability distributions of measurement values, cannot inhere in elementary particles and therefore cannot change when their world tubes intersect and hence they cannot be regarded as interacting causally. By a causal theory is meant a theory that specifies the changes in time of the states of causally interacting entities in its domain. The areas in quantum mechanics in which causal interactions are relevant include, though not explicitly, measurement and therefore the Born rule, and, explicitly, the unitary Schrodinger time development of states. The Born rule probabilities are shown to to refer not to conjoint superpositions of eigenstates but to classical mixtures of mutually exclusive eigenvalues and the Schrodinger time development of states is shown to refer to the time development of the states of non-causally interacting elementary particles and hence cannot be regarded as as a causal time development equation, appearances to the contrary notwithstanding. The recognition that quantum mechanics is not a causal theory but a phenomenological theory like thermodynamics does not affect the way it is employed to calculate an predict and hence preserves its empirical success but it does allow a typically simple phenomenological theory explanation of entanglement and other apparently non-local phenomena.