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arXiv:2508.20788

A predictive solution of the EPR paradox

Henryk Gzyl

Published Aug 28, 2025• 0 citations
arXivHTMLPDF

Abstract

In this work, we examine the paradox proposed by Einstein, Podolsky, and Rosen (EPR). They argued that since one may know the exact momentum of a particle without measurement and subsequently measure its position, a contradiction with the Heisenberg uncertainty principle arises. We demonstrate that there is no paradox by two equivalent approaches: first, by computing the quantum conditional expectation to make predictions after a measurement; and second, using the von Neumann post-measurement state. We establish the equivalence between these two methods. In both cases the predictor is an operator valued function of the observables being measured. This ensures that no violation of the Heisenberg uncertainty principle occurs.

DOI
10.48550/arxiv.2508.20788

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In this work, we examine the paradox proposed by Einstein, Podolsky, and Rosen (EPR). They argued that since one may know the exact momentum of a particle without measurement and subsequently measure its position, a contradiction with the Heisenberg uncertainty principle arises. We demonstrate that there is no paradox by two equivalent approaches: first, by computing the quantum conditional expectation to make predictions after a measurement; and second, using the von Neumann post-measurement state. We establish the equivalence between these two methods. In both cases the predictor is an operator valued function of the observables being measured. This ensures that no violation of the Heisenberg uncertainty principle occurs.
The famous EPR paradox shows that if we describe quantum particles in the usual way -- by their wave functions -- then we get the following seeming contradiction. If we entangle the states of the two particles, then move them far away from each other, and measure the state of the first particle, then the state of the second particle immediately changes -- which contradicts to special relativity, according to which such immediate-action-at-a-distance is not possible. It is known that, from the physical viewpoint, this is not a real paradox: if we measure any property of the second particle, the results will not change whether we perform the measurement on the first particle or not. What the above argument shows is that the usual wave function description of a quantum state does not always adequately describe the corresponding physics. In this paper, we propose a new, more physically adequate description of a quantum state, a description in which there is no EPR paradox: measurements performed at the first particle does not change the state of the remote second one.
The EPR paradox appears when measurement results of some properties of two distantly entangled particles are correlated in a way that cannot be explained classically, and apparently violate locality. The resolution of the paradox depends on one’s interpretation of quantum mechanics. Explanations from quantum mechanics remain commonplace today, but they fail to explain the EPR (Einstein, Podolsky and Rosen) paradox totally in a way than can be accepted by the whole community. Here, we present a simple resolution to this paradox in which the uncertainty in the energy of the two-particle system is reduced by its lack of interaction during the journey so that the uncertainty in time becomes greater than the time they have been separating. Consequently, the present and past become indistinguishable because when we measure an observable in the system its value is the same as if the two particle were still together or very close. It is also argued that the destruction of information as the present and past become identical should release heat by Landauer’s principle, and this might make this proposal testable.
Experiments have reported the entanglement of two spatially separated macroscopic atomic ensembles at room temperature (Krauter et al 2011 Phys. Rev. Lett. 107 080503; Julsgaard et al 2001 Nature 413 400). We show how an Einstein–Podolsky–Rosen (EPR) paradox is realizable with this experiment. Our proposed test involves violation of an inferred Heisenberg uncertainty principle, which is a sufficient condition for an EPR paradox. This is a stronger test of nonlocality than entanglement. Our proposal would enable the first definitive confirmation of quantum EPR paradox correlations between two macroscopic objects at room temperature. This is a necessary intermediate step towards a nonlocal experiment with causal measurement separations. As well as having fundamental significance, the realization of an atomic EPR paradox could provide a resource for novel applications in quantum technology.
We first consider the Einstein-Podolsky-Rosen (EPR) paradox for the system of two particles with spin 1/2 with entangled spins in first-quantized quantum mechanics (QM). If measurement is governed by wavefunction collapse, then gedanken experiments show that a number of fundamental principles including conservation of angular momentum and the Heisenberg uncertainty principle can be violated. We conclude that the collapse of the spin part of the wavefunction cannot happen and therefore an EPR paradox does not arise for this system. QM unitarity alone is sufficient to rule out "spooky" action at a distance. The absence of spin wavefunction collapse leads to several interesting conclusions about how measurement works in QM: When wavefunction collapse does not happen, (i) a signal from a macroscopic measuring device indicating that a system is in a state S does not necessarily mean that it is or was in S and (ii) the uncertainty in QM at the microscopic level is transmitted to uncertainty in signals for the macroscopic measuring device. We derive two general results on how quantum measurement works and illustrate them in a spin-1/2 measurement. In contrast to first-quantized QM, in quantum field theory we are unable to fully rule out the possibility of wavefunction collapse. However, when we insist on unitarity (thereby excluding the possibility of wavefunction collapse) and additionally take into account in the wavefunction all degrees of freedom involved in the measurement (including those of the equipment, experimentalists, etc.), a consistant acceptable understanding of the Bell-inequality-type experiments involving entangled photon polarizations emerges including the absence of an EPR paradox. The ability of an experimentalist to be aware of his perceptions but unable to be conscious of other components of a generalized Schrodinger Cat plays a role in resolving the Measurement Problem.
Quantum mechanics allows for multiple predictions for the outcome of an EPR experiment. The correct calculation must be used, guided by the physical conditions of the experiment. The quantum joint prediction for EPR correlation is derived and shown to involve a single sampling. The solution for separated measurement, where there are two private samplings, is then developed using orthodox quantum mechanics with Luders' rule for state projection on measurement. The separated solution is shown to duplicate the predictions of the quantum joint solution. However, it is shown that this solution requires superluminal transmission of information and therefore it is physically impossible. Alternative predictions respecting special relativity are developed using both Von Neumann projection and null projection (no projection at all). Conditions for the proper application of state projection rules are considered and Luders' rule is identified as the primary culprit in the EPR paradox. It cannot be applied to EPR.
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.