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arXiv:quant-ph/0104045 · Physical Review A

Discrete time in quantum mechanics

Stanley A. Bruce

Published Jun 12, 2001• 4 citations
arXivHTMLPDF

Abstract

The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation.
DOI
10.1103/physreva.64.014103

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Three cases of wave propagation involving possible superluminal speeds are discussed. The picture that emerges is that the actual propagation velocity of the wave front never exceeds the speed of light in vacuum. However, once the wave front has reached some distant point in space, then propagation may actually seem to take place along this wave with superluminal speed, yet involving no conflict with special relativity. Quantum entanglement – Einstein’s “spooky action at a distance” – is one famous, and now experimentally verified example of propagation at such apparent superluminal speed, but which is here explained within the framework of special relativity. This then at the same time also leads to a deeper understanding of the limitation of the recently proposed clock-hypothesis in special relativity, and also provides an illustration of the mechanism involved in wave-particle duality.