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arXiv:1412.7200

On the Superluminal Quantum Tunneling and "Causality Violation"

Moses Fayngold

Published Dec 22, 2014• 2 citations
arXivHTMLPDF

Abstract

This is an analysis of some aspects of an old but still controversial topic, superluminal quantum tunneling. Some features of quantum tunneling described in literature, such as definition of the tunneling time and a frequency range of a signal, are discussed. The argument is presented that claim of superluminal signaling allegedly observed in frustrated internal reflection experiment was based on the wrong interpretation of the tunneling process. A thought experiment similar to that in the Tolman paradox is discussed. It shows that a new factor, attenuation, comes in the interplay between tunneled signals and macroscopic causality.

DOI
10.48550/arxiv.1412.7200

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This is an analysis of some aspects of an old but still controversial topic, superluminal quantum tunneling. Some features of quantum tunneling described in literature, such as definition of the tunneling time and a frequency range of a signal, are discussed. The argument is presented that claim of superluminal signaling allegedly observed in frustrated internal reflection experiment was based on the wrong interpretation of the tunneling process. A thought experiment similar to that in the Tolman paradox is discussed. It shows that a new factor, attenuation, comes in the interplay between tunneled signals and macroscopic causality.
A potential causality paradox in quantum mechanics involving the measurement of a correlated system of two atoms that have moved far apart is constructed along the lines of a classical causality paradox involving the exchange of superluminal signals between distant observers. It is shown that the quantum measurement example does not lead to a paradox, but that the results have implications for the interpretation of quantum mechanics. The thought experiments presented have been used in undergraduate courses in special relativity and quantum mechanics.
Tunnelling processes are thought to proceed via virtual waves due to observed superluminal (faster than light) signal speeds. Some assume such speeds must violate causality. These assumptions contradict, for instance, superluminally tunnelled music and optical tunnelling couplers applied in fiber communication. Recently tunnelling barriers were conjectured to be cavities, wherein the tunnelled output signal is not causally related with the input. The tests described here resolve that tunnelling waves are virtual, propagations are superluminal, and causality is preserved.
Since 1992 experimental evidence of superluminal (faster than light, FTL) signals are causing much excitement in the physical community and in the media. Superluminal signal velocity and zero time tunneling was first observed in an analog tunneling experiment with microwaves. Recently, the conjectured zero time of electron was claimed to be observed in ionizing helium. The FTL signal velocity was reproduced with infrared light and with various tunneling barriers in several laboratories worldwide. Remarkable, it was shown that the tunneling time is a universal quantity for elastic and for electromagnetic fields. Many theoretical physicists predicted this FTL nature of the tunneling process. However, even with this background many members of the physics community did not accept the superluminal signal velocity interpretation of the experimental results and they also ignored the universal tunneling time. The predicted and measured zero tunneling time was taken as a fantastic nonsense. A brief explanation of the misleading theoretical approaches against FTL signals due to the tunneling process is presented eventually.
It is shown that the transferring of light signal faster-than-c can take place exclusively as the instantaneous quantum tunneling. Its extent (space size of instanton) must be inversely relative to lack of energy till nearest stable or resonant state. ''Superluminality'' leads to nonlocality ''in small'', in a near field zone, and can be described by 4-vector AμA_μAμ​, the E\mathbf{E}E and H\mathbf{H}H fields remain local. These assertions are proven, independently, in the frameworks of general field theory and by the theory of time duration of scattering, with taking into account the entropy growing. They are correlated with peculiarities of tunneling and frustrated total reflection. The results correspond to the Wigner formulation of causality: ''The scattered wave cannot escape a scatterer before the initial wave reaches it'' and are conformed to experimental data on superluminal transferring.
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.