Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

EPR Correlations of Spin Measurements in Two Moving Inertial Frames

Jakub Rembieliński, Kordian A. Smoliński

Published Apr 26, 2002• 0 citations
OpenAlex

Abstract

The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz covariant quantum mechanics formulated in the absolute synchronization framework. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum mechanical preferred frame.

Related papers

Einstein-Podolsky-Rosen correlations of spin measurements in two moving inertial frames

Jakub Rembieliński, Kordian A. Smoliński

The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.

arXiv:quant-ph/0204155•Physical Review A•Nov 26, 2002•51 citations

Lorentz-covariant quantum mechanics and preferred frame

Paweł Caban, Jakub Rembieliński

In this paper the relativistic quantum mechanics (QM) is considered in the framework of the nonstandard synchronization scheme, which preserves the Poincar\'e covariance but (at least formally) distinguishes an inertial frame. This enables one to avoid the problem with a strong formulation of local causality related to the breaking of Bell's inequalities in QM. Our analysis has been focused mainly on the problem of the existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. This operator is Hermitian and covariant, it has commuting components, and its eigenvectors (localized states) are covariant too. We have found an explicit form of the position operator and demonstrated that it coincides with the Newton-Wigner one in the preferred frame. We have also defined a covariant spin operator and constructed an invariant spin squared operator. Moreover, full algebra of observables consisting of position, four-momentum, and spin operators is manifestly Poincar\'e covariant in this framework. Our results support expectations of other authors [J. S. Bell, in Quantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Oxford University Press, Oxford, 1981), p. 611; P. H. Eberhard, Nuovo Cimento B 46, 392 (1978)] that a consistent formulation of quantum mechanics demands the existence of a preferred frame.

arXiv:quant-ph/9808013•Physical Review A•Jun 1, 1999•46 citations

Spin-momentum correlation in relativistic single particle quantum states

M. A. Jafarizadeha, M. Mahdian

This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and has shown that entanglement decreases with respect to the increasing of observer velocity. Finally, we argue that, Wigner rotation is induced by Lorentz transformations can be realized as controlling operator.

arXiv:1008.0690•Aug 4, 2010•0 citations

SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES

M. A. Jafarizadeh, M. Mahdian

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

International Journal of Quantum Information•Apr 1, 2010•4 citations

Quantum preferred frame: Does it really exist?

Jakub Rembieliński, Kordian A. Smoliński

The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by physicists such as J. S. Bell and D. Bohm. The possibility of the existence of a preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen–type experiment for testing the possible existence of quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists, it is enough to perform an EPR-type experiment with a pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin–one-half or spin-one particles.

arXiv:0910.5324•Europhysics Letters (EPL)•Oct 1, 2009•19 citations

Special relativity, EPR, and the collapse of the wave function

M. Socolovsky

We discuss a paradox which appears in EPR experiments when the collapse of the wave function is analyzed in moving reference frames: the collapse can occur before the actual measurement of the spin component (or polarization) of one of the particles. We show that the paradox can be solved using the instantaneity of the reduction process in all reference frames. Using the same concept, we illustrate with an example the impossibility of defining, in certain circumstances, a covariant state vector in all regions of space-time.

Il Nuovo Cimento B•May 1, 2003•0 citations
The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz covariant quantum mechanics formulated in the absolute synchronization framework. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum mechanical preferred frame.
The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.
In this paper the relativistic quantum mechanics (QM) is considered in the framework of the nonstandard synchronization scheme, which preserves the Poincar\'e covariance but (at least formally) distinguishes an inertial frame. This enables one to avoid the problem with a strong formulation of local causality related to the breaking of Bell's inequalities in QM. Our analysis has been focused mainly on the problem of the existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. This operator is Hermitian and covariant, it has commuting components, and its eigenvectors (localized states) are covariant too. We have found an explicit form of the position operator and demonstrated that it coincides with the Newton-Wigner one in the preferred frame. We have also defined a covariant spin operator and constructed an invariant spin squared operator. Moreover, full algebra of observables consisting of position, four-momentum, and spin operators is manifestly Poincar\'e covariant in this framework. Our results support expectations of other authors [J. S. Bell, in Quantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Oxford University Press, Oxford, 1981), p. 611; P. H. Eberhard, Nuovo Cimento B 46, 392 (1978)] that a consistent formulation of quantum mechanics demands the existence of a preferred frame.
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and has shown that entanglement decreases with respect to the increasing of observer velocity. Finally, we argue that, Wigner rotation is induced by Lorentz transformations can be realized as controlling operator.
This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.
The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by physicists such as J. S. Bell and D. Bohm. The possibility of the existence of a preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen–type experiment for testing the possible existence of quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists, it is enough to perform an EPR-type experiment with a pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin–one-half or spin-one particles.
We discuss a paradox which appears in EPR experiments when the collapse of the wave function is analyzed in moving reference frames: the collapse can occur before the actual measurement of the spin component (or polarization) of one of the particles. We show that the paradox can be solved using the instantaneity of the reduction process in all reference frames. Using the same concept, we illustrate with an example the impossibility of defining, in certain circumstances, a covariant state vector in all regions of space-time.