Related papers: A predictive solution of the EPR paradox

A predictive solution of the EPR paradox

URL: http://arxiv.org/abs/2508.20788v1
Date: Thu, 28 Aug 2025 13:53:03 GMT
Title: A predictive solution of the EPR paradox
Authors: Henryk Gzyl,
Abstract summary: In an eigenstate of the total momentum operator, the standard deviation on the measurement of the position of any of the two particles has to be infinite.<n>We prove, using the basic tenets of quantum measurement theory, that after measurement of the total momentum, the probability density coincides with the (quantum) conditional density given the total momentum.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this work an incorrect argument in EPR's paper is corrected. A predictive approach to further confirm the validity of quantum theory is also proposed. The essence of the detail that EPR missed is that in a state of given total momentum (in their example the total momentum is zero), since the total momentum operator $\hat{\bp}=\hat{\bp}_1+\hat{\bp}_2$ does not commute with any of the position operators $\hat{\bx}_1$ and $\hat{\bx}_2,$ then in an eigenstate of the total momentum operator, the standard deviation on the measurement of the position of any of the two particles has to be infinite. Below we compute the (quantum) conditional expectation of the momentum of any of the particles (say, the first) given the value of a measurement of the total momentum. Since the predictor of the momentum of the particle depends on the total momentum, and the total momentum does not commute with the position operator of any of the particles, the uncertainty principle is not violated, and no contradiction appears. We also prove, using the basic tenets of quantum measurement theory, that after measurement of the total momentum, the probability density (computed as the absolute square of the wave function), coincides with the (quantum) conditional density given the total momentum.

Related papers

A disputable assumption behind the empirical equivalence between pilot-wave theory and standard quantum mechanics [0.0]
We argue that the derivations of absolute uncertainty and the POVM theorem depend upon the questionable assumption that "information is always configurationally grounded"<n>We explain in detail why the offered rationale behind such an assumption is deficient and explore the consequences of having to let go of it.
arXiv Detail & Related papers (2025-08-08T19:28:54Z)
Defining coherent states: why must they be eigenstates of the annihilation operator? [0.0]
We show that coherent states are chosen as the most classical ones by the decoherence process induced by coupling the particle to an environment in the standard Quantum Brownian motion model. We also show that the reason why coherent states are chosen as the most classical ones by the decoherence process induced by coupling the particle to an environment in the standard Quantum Brownian motion model is precisely due to the validity of the two above theorems.
arXiv Detail & Related papers (2024-10-21T20:18:20Z)
Wave Mechanics as Realistic Local Theory without Hidden Variables and Measurement Problem [0.0]
It is shown that the amplitude and phase uniquely determine two fields of the particle's momentum.<n>The Schr"odinger equation can be written as a closed system of local equations for these fields.
arXiv Detail & Related papers (2024-07-05T14:24:33Z)
Measuring the Evolution of Entanglement in Compton Scattering [101.11630543545151]
The behavior of quantum entanglement during scattering is identical to the behavior of initially classically correlated photons up to a constant factor equal to two. Our dedicated experiment with photons confirms these results and explains the "Puzzle of Decoherence" observed recently.
arXiv Detail & Related papers (2024-06-20T14:21:23Z)
Testing trajectory-based determinism via time probability distributions [44.99833362998488]
Bohmian mechanics (BM) has inherited more predictive power than quantum mechanics (QM) We introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We derive probability distributions that are unreachable by QM.
arXiv Detail & Related papers (2024-04-15T11:36:38Z)
A non-hermitean momentum operator for the particle in a box [49.1574468325115]
We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
arXiv Detail & Related papers (2024-03-20T12:51:58Z)
Real-time dynamics of false vacuum decay [49.1574468325115]
We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
arXiv Detail & Related papers (2023-10-06T12:44:48Z)
Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
arXiv Detail & Related papers (2022-07-30T08:07:28Z)
Bouncing Wave Packets, Ehrenfest Theorem, and Uncertainty Relation based upon a new Concept for the Momentum of a Particle in a Box [0.0]
We show that the Ehrenfest theorem is satisfied for all physically admissible boundary conditions. We derive a very simple form of the general Heisenberg-Robertson-Schr"odinger uncertainty relation.
arXiv Detail & Related papers (2022-06-15T13:24:33Z)
Effect of Wigner rotation on estimating unitary-shift parameter of relativistic spin-1/2 particle [21.22196305592545]
We use a specific model of a relativistic spin-1/2 particle described by a gaussian wave function with a spin down in the rest frame. It is shown that estimation accuracy decreases monotonically in the velocity of the observer when the moving observer does not measure the spin degree of freedom.
arXiv Detail & Related papers (2022-04-21T20:26:45Z)
Path integral action in the generalized uncertainty principle framework [0.36832029288386126]
We study the path integral representation of a particle moving in an arbitrary potential using the generalized uncertainty principle (GUP) First we work out the action of the particle in an arbitrary potential and hence find an upper bound to the velocity of a free particle.
arXiv Detail & Related papers (2021-05-10T13:17:37Z)
Quantum mechanics is a calculus for estimation under epistemic restriction [0.0]
We discuss a classically consistent, weakly unbiased, best estimation of the momentum field. The results suggest that quantum wave function is not an objective agent-independent attribute of reality. We then argue that unitary time evolution and wave function collapse in measurement are normative rules for an agent to update her/his estimation.
arXiv Detail & Related papers (2020-05-14T06:43:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.