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International Journal of Physics

Apparent Superluminal Speeds in Evanescent Fields, Quantum Tunnelling and Quantum Entanglement

Arne Bergström

Published Jan 24, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.12691/ijp-3-1-7

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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.
There have been many recent theoretical and experimental reports on the propagation of light pulses at speeds exceeding the speed of light in vacuum ccc within media with anomalous dispersion, either opaque or with gain. Superluminal propagation has also been reported within vacuum, in the case of inhomogeneous pulses. In this paper we show that the observations of superluminal and non-causal propagation of evanescent pulses under the conditions of frustrated internal reflection are only apparent, and that they can be simply explained employing an explicitly (sub)luminal causal theory. However, the usual one-dimensional approach to the analysis of pulse propagation has to be abandoned and the spatial extent of the incoming pulse along the directions normal to the propagation direction has to be accounted for to correctly interpret the propagation speed of these evanescent waves. We illustrate our theory with animations of the time development of a pulse built upon the Huygen's construction.
The quantum mechanical tunneling effect was theoretically described in the first half of the last century, which witnessed the rise of quantum theory and groundbreaking experimental results in nuclear physics. A similar tunneling effect also takes place in the case of EM waves. The wave account (in the case of evanescent waves), the quantum-mechanical formalism, as well as the electrodynamical one, revealed a phenomenon that is counterintuitive and possibly even inconsistent with the special relativity theory paradigm. In the quantum formalism, the time of wave propagation within a photonic barrier is expressed as an imaginary number, which can be interpreted as the zero speed of propagation. In the nineties, scientists offered further experimental proofs of the theory; in experimental systems constructed for testing EM-waves tunneling, superluminal speed of propagation has been recorded. In the article, I introduce the problem of photon tunneling in the experimental context of the possibility of nonlocal wave propagation and superluminal transmission of information.
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.
The widespread belief, that energy and signal velocities are bounded by the speed of light in vacuum has been challenged in recent years by observations of superluminal propagation of classical evanescent modes in tunneling time experiments. These experiments thus provide a frame for testing the limits of transport velocities physically achievable. Obvious and hidden time-scales involved in tunneling time experiments are discussed focussing on optical tunneling in frustrated total internal reflection. A suggestion for a direct test of the energy transport velocity—also of interest in future hyper-fast space travel—is presented. Related questions touching our current understanding of some fundamental concepts in physics are addressed.