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.
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.
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.
The phenomenon of quantum tunneling challenges classical intuitions about particle behavior and offers profound insights into the nature of quantum entities. This article examines tunneling through the lens of an effect predicted by Thomas E. Hartman in 1962: the tunneling time-delay becomes independent of the barrier width as the latter increases, implying superluminal effective velocities that appear to conflict with relativistic constraints. Exploiting the inherent symmetries of transmitted and reflected time-delays, our analysis shows that a tunneling particle, like its reflected counterpart, completely avoids the barrier region. However, since it can be detected on the transmitted side of the barrier, the only logical conclusion is that the classical notion of spatiality is violated during the tunneling process. In other words, quantum tunneling and the associated Hartman effect strongly support the idea that quantum non-locality should be interpreted as quantum non-spatiality. The latter, according to the conceptuality interpretation of quantum mechanics, expresses the conceptual-like nature of quantum entities, which during measurement transition from an abstract state to a maximally concrete one, in full compatibility with the Hartman effect.
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).
Quantum tunneling conventionally invokes "energy borrowing" via Heisenberg uncertainty and exhibits the Hartman effect (barrier-independent traversal time). Both are conceptual paradoxes. We demonstrate the particle doesn't traverse the barrier in physical space. Tunneling results from zero-distance projection along an invariant coherence axis (Axis 4.5), orthogonal to the material density gradient. Key mechanism: When coherence is maintained (phase locking), spatial topology folds along the coherence axis. Effective distance D_eff = L·sin(φ). Perfect alignment (φ→0) yields D_eff→0—the particle bypasses metric interval L via rotational displacement. Energy conservation preserved: Transition occurs along isopotential geodesic (W=0, "Yanieva Rail"). Transmission coefficient T is geometric projection factor, not survival probability. Attenuation reflects angular deviation maintaining coherence—signal rotated out of observable plane, not lost. Hartman effect necessary consequence: topological distance zero implies instantaneous traversal without relativity violation. The "mystery" is observing 3D rotation from 1D perspective.
Quantum Tunneling. Redefining Time from Quantum Tunneling to Cosmic InflationA Paradigm Shift in How We Conceptualize Physical RealityWhat if time isn't what we think it is? What if phenomena as diverse as quantum tunneling, cosmic inflation, and cosmological redshift share a common origin—not in exotic fields or unseen dimensions, but in how reality records its own history? This work presents a radical ontological framework where time is not fundamental. Instead, it emerges as a measure of geometric reconfiguration events of spacetime quanta (p-gluons). The key parameter is frame generation rate (Ẋ)—the rate at which the universe "takes snapshots" of itself. Core Discovery: The Ẋ PrincipleLocal frame generation rate Ẋ depends on geometry: under extreme compression (early universe, quantum barriers), Ẋ → 0. This doesn't mean time stops—it means the historical record becomes extremely sparse. Observable phenomena are reconstruction artifacts of this varying temporal resolution. Three Revolutions in One Framework1. Quantum Tunneling ReimaginedTunnel particles don't "disappear" or "jump." They simply undergo processes faster than our observational time resolution (Ẋ_M) can sample. The "tunneling event" is an aliasing artifact—we only register the input and output states, missing the continuous ontological evolution in between. The Hartman effect, lack of in-barrier trajectories, and sudden detection all find natural explanations without modifying Schrödinger's equation. 2. Cosmology Without an InflatonInflation wasn't a physical expansion. It was a change in recording resolution as the early universe transitioned from near-zero Ẋ (geometric compression) to finite Ẋ. The Big Bang? Not the beginning of time, but the first frame of an epoch where frame generation became dense enough to reconstruct cosmological history. Horizon and flatness problems dissolve naturally. 3. Redshift as a Historical ArchiveRedshift doesn't measure galaxy recession. It measures how much faster we generate time now compared to when the photon was emitted (1+z = Ẋ_present/Ẋ_emission). The Hubble constant becomes a measure of the universe's growing capacity to generate frames. What This Work Offers✅ Unified Interpretation: One mechanism (varying Ẋ) explains quantum and cosmological phenomena✅ No New Physics: Doesn't modify Schrödinger or Einstein equations—changes only their interpretation✅ Falsifiable: Makes clear empirical predictions about tunneling time saturation and CMB structure✅ Paradox Resolution: Addresses the black hole information problem, measurement problem, and beginning of time without extra dimensions or multiverses✅ Philosophical Coherence: Presents reality as a sequence of geometric frames—time as history, not flow For Whom Is This?Physicists tired of interpretative patches seeking unified foundations Philosophers of science exploring the relationship between mathematics, observation, and reality Cosmologists questioning inflationary paradigm assumptions Quantum foundations researchers looking beyond Copenhagen, Bohm, and Many-Worlds Interdisciplinary thinkers at the intersection of information theory, geometry, and physics This work doesn't ask you to agree. It asks you to reconsider what time might be. It demonstrates that empirical data can support multiple coherent narratives—and that sometimes the most revolutionary step isn't adding complexity, but redefining the simplest elements. Download to explore a universe where time is not a river, but a film reel with variable frame rate—and where we are just learning to read the projector's settings.
In this work, we present a study of the intriguing Hartman Effect, through two approaches. The first one is a relativistic approach of quantum theory using the Dirac equation, and the second one is a geometrodynamic approach using Bohmian mechanics. Therefore, we first developed a mathematical model from the Dirac equation in an alternative representation, which allowed us to deduce a group (or tunneling) time as the sum of the residence times inside the potential barrier for particles with spin up and spin down, and the self-interaction time between the incident and reflected wave functions of the spin-up particles. In other words, we obtained a model that allows us to observe the influence of spin on the tunneling time, in the absence of an external magnetic field, which offers a less satisfactory explanation of the Hartman Effect in terms of group time. Subsequently, through a geometrodynamic approach of Bohmian mechanics, we constructed a general solution for the problem of scattering of incident particles on a constant potential barrier under the hypothesis that such particles undergo quantum tunneling along geodesic trajectories in an Alcubierre-type spacetime. Consequently, from the solution, we determined the mathematical expressions for the quantum potential, momentum, position, and tunneling time in terms of the spacetime geometry. That is, we obtained a mathematical model that allows us to explain the Hartman Effect as a consequence of the spacetime distortion generated by the quantum potential inside the barrier.