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Physics World

Is quantum tunnelling faster than the speed of light?

Jon Andreas Støvneng, E. H. Hauge

Published Nov 1, 1993• 4 citations
Publisher

Abstract

The time taken for a single photon to tunnel through a potential energy barrier has been measured for the first time. Surprisingly, perhaps, the photon appears to tunnel through the barrier faster than an identical photon travelling through free space. However, closer scrutiny shows that this apparently superluminal velocity is not in conflict with the theory of relativity.

DOI
10.1088/2058-7058/6/11/23

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Superluminal velocities do exist in tunneling. In theories don’t. Why? Because physicists think the speed of light in spacetime is the absolute speed limit. The superluminal velocity cannot be explained within the spacetime model. How to explain the superluminal velocity during tunneling? Supposing more spaces and more times. The superluminal, tunneling particle travels in barrier. The barrier is an object from our viewpoint. But the particle uses this barrier as space. Studying the tunneling, there are many spaces. Every space has its own time unit and unit space distance. The law of speed limit remains true in every space. The speed of light is the speed limit in every space, but from our viewpoint the same particle travels at different velocities in different spaces. It can be summarized in one sentence: A step in the country of giants is longer than in the country of dwarves. The paper is an excerpt out of the book entitled “19 false axioms of physics”.

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Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.

Physica Scripta•Jan 1, 1998•18 citations
The time taken for a single photon to tunnel through a potential energy barrier has been measured for the first time. Surprisingly, perhaps, the photon appears to tunnel through the barrier faster than an identical photon travelling through free space. However, closer scrutiny shows that this apparently superluminal velocity is not in conflict with the theory of relativity.
Experiments done with single photons in the early 1990's produced a surprising result: that single photons pass through a photonic tunnel barrier with a group velocity faster than the vacuum speed of light. This result has stimulated intense discussions related to causality, the speed of information transfer, the nature of barrier tunneling and the meaning of group velocity. The superluminality of tunneling photons is now textbook material, although the authors note that controversy still remains. Another paradoxical result, known as the Hartman effect, is that the tunneling time of the photons becomes independent of barrier length in the limit of opaque barriers. In this paper we examine the meaning of group velocity in the context of barrier tunneling. We ask whether a single tunneling photon can be described by a group velocity and whether the short group delays imply superluminal group velocity. We resolve the paradox of the Hartman effect and show that the predicted and measured group delays are not transit times but photon lifetimes.
Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric down-conversion light source, which produced correlated, but random, emissions of photon pairs. The two photons of a given pair were emitted in slightly different directions so that one photon passed through the tunnel barrier, while the other photon passed through the vacuum. The time delay for the tunneling photon relative to its twin was measured by adjusting the path length difference between the two photons in a Hong-Ou-Mandel interferometer, in order to achieve coincidence detection. We found that the photon transit time through the barrier was smaller than the twin photon’s transit time through an equal distance in vacuum, indicating that the process of tunneling in quantum mechanics is superluminal. Various conflicting theories of tunneling times are compared with experiment.
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric down-conversion light source, which produced correlated, but random, emissions of photon pairs. The two photons of a given pair were emitted in slightly different directions so that one photon passed through the tunnel barrier, while the other photon passed through the vacuum. The time delay for the tunneling photon relative to its twin was measured by adjusting the path length difference between the two photons in a Hong-Ou-Mandel interferometer, in order to achieve coincidence detection. We found that the photon transit time through the barrier was smaller than the twin photon’s transit time through an equal distance in vacuum, indicating that the process of tunneling in quantum mechanics is superluminal. Various conflicting theories of tunneling times are compared with experiment. An introduction to an introduction Tunneling, the quantum mechanical process by which a particle can penetrate a classically forbidden region of space, is one of the most mysterious phenomena of quantum mechanics. Yet it is one of the most basic and important processes in Nature, without which we could not even exist, for tunneling is involved in the very first step of the nuclear reaction, p + p → d + e + νe, which powers the Sun, the source of energy for life on the Earth. ∗ On appointment as a Miller Research Professor in the Miller Institute for Basic Research
Superluminal velocities do exist in tunneling. In theories don’t. Why? Because physicists think the speed of light in spacetime is the absolute speed limit. The superluminal velocity cannot be explained within the spacetime model. How to explain the superluminal velocity during tunneling? Supposing more spaces and more times. The superluminal, tunneling particle travels in barrier. The barrier is an object from our viewpoint. But the particle uses this barrier as space. Studying the tunneling, there are many spaces. Every space has its own time unit and unit space distance. The law of speed limit remains true in every space. The speed of light is the speed limit in every space, but from our viewpoint the same particle travels at different velocities in different spaces. It can be summarized in one sentence: A step in the country of giants is longer than in the country of dwarves. The paper is an excerpt out of the book entitled “19 false axioms of physics”.
Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.