Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier

Abstract

This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study's results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.

Evanescent waves and superluminal behavior of matter

“…This process occurs thanks to the interaction between the particle and barrier: the higher the barrier, the greater the probability that the particle passes into a tachyonic state. This conclusion is consistent with the fact that the Hartman effect is particularly favored by sufficiently large barriers [17,23]. In fact, in this situation the probability of interaction between the particle and barrier increases, which is precisely the condition necessary to obtain a superluminal state.…”

“…This effect has been experimentally verified in optics [21] and cosmology [22]. On the other hand, in particle physics the Hartman effect has been extensively investigated but has not yet been supported by experimental evidence [23][24][25]. However, experimental confirmation could come from neutrino physics (specifically superluminality and flavor oscillations) [26].…”

Evanescent Waves and Superluminal Behavior of Matter

“…This process occurs thanks to the interaction between the particle and the barrier: the more high the barrier is the greater the probability that the particle passes into a tachyonic state. This conclusion is consistent with the fact that the Hartman effect is particularly favoured by sufficiently large barriers [17,23]; in this situation, in fact, the probability of interaction between the particle and the barrier increases, which is precisely the condition necessary to obtain a superluminal state.…”

“…As usual the temporal part of the evanescent wave may be omitted. If we denote with 0 the point where the barrier begins, which length is , in the space where < 0 the total spinor is given by the linear combination between the incident wave and the part of the wave that is reflected and does not penetrate the barrier [23]:…”

“…In optics this effect has been experimentally verified [21] as well as in cosmology [22]. In particle physics, on the other hand, the Hartman effect has been extensively investigated but has not yet been supported by experimental evidences [23][24][25]. However, experimental confirmations could come from neutrino physics (superluminality and flavor oscillation) [26].…”