Investigation of Superluminal Motion of Free Spin-half Particles in Spacetime

Abstract

The possibility of free spin-1/2 particles (also called Dirac particles) superluminal motion in spacetime, is investigated. The universal cover of the entire Lorentz group L consists of S L (2, C) and the spinor map so that to obtain a relativistically invariant description of the state of an electron, one looks to the representations of S L (2, C) , that is, to the 2-valued representation of L, known as spinors. We restrict our approach to realistic one-particle systems along with the "positive energy" and utilize the free Dirac waves propagating in the z−direction. The Dirac wave function ψ (x, t) is considered as a "classical field" and the corresponding wave equation is derived from a Lagrange function. Using the symmetrized Dirac Lagrange density, it is observed that variation in spin angular momentum (in the light cone) leads to causality violation, whereas variation in orbital angular momentum does not. Consequently, it is shown that the expectation value of the relative translational velocity component of the spinning free electron exceeds light speed.

Superluminal Hydrogen Atom in a Constant Magnetic Field in (3+1)-dimensional Spacetime (II)

“…This also means that the general expression of the generalized variation transformation (as derived in [16], Section 3 ) of the free spin-1/2 field, is applicable to the planar Dirachydrogen field. The variations, for intrinsic spin, orbital, and generalized angular momenta are all linear along the z−axis and their corresponding transformations are velocity transformations [16]. We will now seek the solution of the Dirachydrogen plane wave equation and subsequently evaluate the velocity of the field.…”

“…In particular, in our restriction to constant magnetic field where variation of the action with respect to the field potential Aµ is practically null, and since the binding energy −e 2 /r and the field additional energy |e|H (2n + 1 + σ) terms remain constants of motion, one can check and find that the results obtained from second quantization of the Dirac-hydrogen field coincide with those of the free Dirac spin-1/2 field. These common results include notably the mirage of causality violation, the removal of which is achieved by superluminal field velocity prescription [16]. This also means that the general expression of the generalized variation transformation (as derived in [16], Section 3 ) of the free spin-1/2 field, is applicable to the planar Dirachydrogen field.…”

“…These common results include notably the mirage of causality violation, the removal of which is achieved by superluminal field velocity prescription [16]. This also means that the general expression of the generalized variation transformation (as derived in [16], Section 3 ) of the free spin-1/2 field, is applicable to the planar Dirachydrogen field. The variations, for intrinsic spin, orbital, and generalized angular momenta are all linear along the z−axis and their corresponding transformations are velocity transformations [16].…”

“…Consider the hydrogen atom with a single electron orbiting the dense and fixed nucleus with spin, in a radius r ( i.e., spin-orbit coupling), in the context of relativistic quantum theory using the Dirac equation. We restrict ourselves to realistic one-particle systems with positive energy , and waves propagating in the z−direction [16]. In this limit, with no essential lost of generality, the hydrogen atom is considered as one-body problem.…”

“…is the positive energy of the system required in order for the single-particle aspect to hold [16], and the factor N is a normalization constant obtained as…”