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.
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.
Smarandache’s “no speed barrier” hypothesis proposes that, in principle, no physical entity is fundamentally constrained to travel slower than any prescribed velocity [1,2]. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Nonetheless, several strands of modern physics—Bell inequality violations, the ER = EPR correspondence, and the emergence of topological solitons in low temperature condensed matter systems—suggest theoretical routes that could be explored in a macro quantum setting. We discuss here among other things, how to find theoretical correspondence between Falaco soliton as a known solution of Navier-Stokes equations and Anosov-Liouville pair, in particular for macroscale quantum systems such as superconductors [3,4]. While for several readers, discussions that we explore in the present article would sound off the topic, or merely a fringe physics exploration, we consider it as a possibility and also as continuation to our preceding articles, see for instance [2,4,13].
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).
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).
Abstract This is a review of studies of quantum tunneling, which is described by the one-dimensional Schrödinger equation, and electromagnetic tunneling, where “superluminal” velocities and times of tunneling are considered. Integral and integrodifferential equations have been presented to describe tunneling. According to these equations, superluminal motion is impossible. The paradoxical Hartman effect has been discussed and explained. It has been shown that the velocity of passage of a particle in a beam through a barrier in the case of steady-state and time-dependent quantum tunneling is equal to the velocity of its incidence on the barrier and quasiphotons inside any layer of matter carry the energy always at a subluminal velocity. However, the tunneling time of a single particle or a photon is meaningless.
The present article is dedicated to Robert N. Boyd, PhD, with whom we have discussed several exotic subjects in physics, including interstellar travel, med beds for future medicine, and the Pleiadian council. While we appreciate and admire his vast experience and involvement in several high-profile experiments, we respectfully disagree with his use of the Rodin coil with a special design to shrink the traveling time needed to traverse galaxies through the concept of folded space. We previously argued for a connection between the Navier-Stokes and Schrödinger equations, then used standard tunneling time theory [1, 2]. Here, we propose an alternative interpretation of the Hartman effect in tunneling, suggesting that it represents the multivaluedness of solutions to the Schrödinger equation. This implies that an electron or entity can exist in two places simultaneously, explaining how an entity can seemingly appear on the other side of a tunnel almost instantaneously upon initiating a quantum tunneling experiment. While counterintuitive, this interpretation aligns with Schrödinger's initial ideas. This phenomenon could be detected through near-field effects, such as a spin supercurrent detector in low-temperature physics experiments.
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”.