This writing has been prepared on the occasion of the 75th birthday of E.C.George Sudarshan, who (besides the originator of the V-A theory for weak-forces, of quantum optics --the quantum representation of coherent light--, of dynamical maps for open quantum systems, of the Zeno effect, etc.) was a pioneer, already in the sisties, also of the theory of the so-called "tachyons". This paper wishes to be a homage to E.C.G.Sudarshan, in connection with the last-mentioned pioneering work of his. After a brief theoretical introduction (based on the standard postulates of Special Relativity, and therefore extending it --or rather non-restricting it-- without any violations: for example, without any violations of the so-called Einstein causality), the main aim of this article is an updated presentation of the status-of-the-art of the "superluminal" experiments. In particular, we devote such a review to the phenomena met in tunneling through quantum (and classical) barriers [e.g., referring to the Genelalized Hartman Effect]; and in connection with the "Localized (nondiffracting) Solutions" of the wave equantions [e.g., of Maxwell equations]: especially of the "X-shaped" ones. The interested reader is provided with an extended Bibliography.
This writing has been prepared on the occasion of the 75th birthday of E.C.George Sudarshan, who (besides the originator of the V-A theory for weak-forces, of quantum optics --the quantum representation of coherent light--, of dynamical maps for open quantum systems, of the Zeno effect, etc.) was a pioneer, already in the sisties, also of the theory of the so-called "tachyons". This paper wishes to be a homage to E.C.G.Sudarshan, in connection with the last-mentioned pioneering work of his. After a brief theoretical introduction (based on the standard postulates of Special Relativity, and therefore extending it --or rather non-restricting it-- without any violations: for example, without any violations of the so-called Einstein causality), the main aim of this article is an updated presentation of the status-of-the-art of the "superluminal" experiments. In particular, we devote such a review to the phenomena met in tunneling through quantum (and classical) barriers [e.g., referring to the Genelalized Hartman Effect]; and in connection with the "Localized (nondiffracting) Solutions" of the wave equantions [e.g., of Maxwell equations]: especially of the "X-shaped" ones. The interested reader is provided with an extended Bibliography.
After a brief theoretical introduction (based on the standard postulates of Special Relativity, and therefore extending it --or rather non-restricting it-- without any violations: in particular without any violations of the so-called Einstein causality), the main aim of this article is an updated presentation of the status-of-the-art of the
superluminal experiments. In particular, we devote such an article to the phenomena met in tunneling through quantum (and classical) barriers [e.g., referring to the Genelalized Hartman Effect]; and in connection with the Localized (nondiffracting) Solutions of the wave equations [e.g., of Maxwell equations]: especially of the X-shaped ones. The interested reader is provided with an extended Bibliography. This paper was written as a homage to E.C.G. Sudarshan, in connection with his pioneering work on the so-called tachyons. Actually, E.C.George Sudarshan, besides the originator of the V-A theory for weak-forces, of quantum optics --the quantum representation of coherent light--, of dynamical maps for open quantum systems, of the Zeno effect, etc., was a pioneer, in the sisties, also of the theory of Tachyons.
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.
In the First Part of this paper [that was submitted for pub. in 1991 and appeared in print in Phys. Reports 214 (1992) 339] we critically review the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection times. Moreover, within conventional QM, we propose a new definition of such durations, on the basis of a recent general formalism of ours. At last, we discuss a surprising result: that QM predicts tunnelling through opaque barriers to take place with Superluminal group-velocities. In the Second Part [that appeared in print later, in J. de Physique-I 5 (1995) 1351] we, e.g., present the results of some numerical calculations (based on our equations) on the penetration and return times during tunnelling INSIDE a rectangular potential barrier, and set forth suitable definitions also of the variances, or dispersions, for the transmission and reflection time-durations. The numerical evaluations confirm that our approach implied, and implies, the existence of Superluminal tunnelling (that we called "Hartman effect"): an effect that in these days is receiving --at Cologne, Berkeley, Florence and Vienna-- indirect, but interesting, experimental verifications. More detailed reviews of the same topics are in the LANL Archive cond-mat/9802126 (and in an Appendix to physics/9712051, where the data are summarized of the experiments that --in four different sectors of physics-- seem to indicate the existence of Superluminal motions).
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 phenomenon of one-dimensional non-resonant tunnelling is analyzed through two or more successive (opaque) potential barriers, separated by intermediate free regions R, just by exploiting the relevant solutions to the Schroedinger equation. The total traversal time has been shown by us to be independent not only of the barrier widths (the so-called ‘Hartman effect’), but also of the R-widths: so that the effective group velocity in the regions R, between two successive barriers, can be regarded as practically infinite. Such a prediction has been theoretically confirmed and generalized (as well as interpreted in terms of ‘super-oscillations’) by Aharonov et al. A recent experiment by Longhi et al. supported the predictions by considering two successive gratings in an optical fibre, that is, by having recourse to two ‘classical barriers’ (which allow simulating the tunnelling, due to the known formal identity between the Schrödinger and the Helmholtz equation).
This book explores the theoretical and philosophical implications of transcending the speed of light limit, building upon Florentin Smarandache's "no speed barrier" hypothesis. This collection of works develops the hypothesis that no physical entity is fundamentally constrained by a speed barrier, suggesting a framework for extending classical and relativistic physics into the realms of Superluminal Physics and Instantaneous Physics. The book’s core technical argument centers on the phenomenon of quantum tunneling and the Hartman effect, where the tunneling time appears independent of barrier width, leading to seemingly superluminal results. The authors propose a novel interpretation of the Hartman effect, suggesting that it is a manifestation of the multivaluedness of solutions to the Schrödinger equation, implying a quantum entity can exist in multiple locations simultaneously and thus appear to tunnel instantaneously. To provide a plausible mechanism for this superluminal effect, the book considers soliton tunnelling, specifically the Falaco soliton, which is presented as a known exact solution to the three-dimensional Navier-Stokes equations and is proposed as a realistic mechanism for quantum tunneling. Ultimately, the research seeks to find a general theory, such as the S-Multispace Theory, that unites physics at subluminal, relativistic, superluminal, and instantaneous speeds. This theoretical path is explored as an alternative for deep space and interstellar travel, moving beyond conventional concepts like the Alcubierre warp drive or wormholes in General Relativity.