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Journal of Quantum Information Science

Compatibility of Quantum Entanglement with the Special Theory of Relativity

Burke Ritchie

Published Jan 1, 2014• 0 citations
Publisher

Abstract

The Einstein-Podolsky-Rosen paradox is resolved dynamically by using spin-dependent quantum trajectories inferred from Dirac’s equation for a relativistic electron. The theory provides a practical computational methodology for studying entanglement versus disentanglement for realistic Hamiltonians.
DOI
10.4236/jqis.2014.42009

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Recent experimental results have shown a violation of Bell’s inequalities, which are a mathematical formulation of Einstein-Podolsky-Rosen (EPR) paradox. The violation leads to the conclusion that there are no local hidden variable theories that underlie quantum mechanics. However, the Bell’s inequalities do not rule out the possibility to construct non-local hidden variable theories that comply with quantum mechanics, in particular, a theory of special and general relativity that permits an instantaneous transmission of interaction. In this work we show that a special relativity with a Euclidean metric that allows not only local interactions but also interactions that can be transmitted instantaneously can be constructed and, furthermore, such special relativity can also be generalised to formulate a general theory of relativity that leads to the same experimental results as Einstein theory of general relativity. We also show that it is possible to formulate Dirac-like relativistic wave equations in this Euclidean relativity with either real mass or imaginary mass, which suggests that the proper mass of a quantum particle may be defined in terms of a differential operator that is associated with a spacetime substructure of the particle.
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I n the early 20th century, the groundbreaking theories of quantum mechanics and special relativity emerged at roughly the same time.At first, both theories appeared to be entirely incompatible with each other.While the quantum equations written out by Erwin Schrödinger and Wolfgang Pauli dealt with the behaviours of electrons, atoms, and molecules moving at speeds encountered in classical physics, the rules of special relativity first imagined by Albert Einstein described the behaviour of matter moving at close to the speed of light.Initially, this apparent clash of theories presented a crisis in physics.However, in the late 1920s, further theoretical work carried out by physicists including Paul Dirac, Oskar Klein, and Walter Gordon culminated in a new set of equations, which proved definitively that quantum mechanics and special relativity are compatible with each other after all. An educational challengeYet with this groundbreaking discovery came an entirely new problem.In adding a new layer of complexity to the equations of non-relativistic quantum mechanics, the more complete theories of relativistic
This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.