Superluminal Motion of free spin-half particles in Spacetime

  Emmanuel D.K. Gazoya  Summary: As is well known in science, there are two main procedures to reaching scientific realities ...

Global Journal of Science and Frontier Research


Emmanuel D.K. Gazoya 

Global Journal of Science Frontier Research

Summary: As is well known in science, there are two main procedures to reaching scientific realities of nature: theoretical investigation and experimental approach. In a situation whereby there arise critics and controversies concerning results obtained using one of these methods, the remaining other can be summoned to rescue, in confirming or invalidating the findings. Our work can be regarded as an attempted theoretical counterpart of the non-conclusive CERN experiments on the superluminal neutrino results of 2008 and 2012.
The universal existential problem of particles capable of superluminal motion continues to be a subject of great interest and controversies among scientists, for decades. The actual physical theory of the universe, that is, Special/General Relativity, by its relativistic principles, demonstrates the impossibility of superluminal entities. Yet, Quantum theory of the electron (or other subatomic particles) with spin, producing angular momentum, offers a favorable prospect, but this is not a realistic system. Therefore, the relationship between mass/energy, space, and time has to be revisited, in another formalism.

In the general survey of the various branches of knowledge at our disposal, obviously, a joint-theory of Relativity and Quantum Field Theory (with the related topics thereof) is sought as an essential tool for our examination of this problem. This involves Lorentz transformations and group theoretical notions and relations.
The result of this work could lead to the solution of two vital problems confronting humanity at present, namely, the problematic of energy and the question of the TIME FACTOR in interstellar and intergalactic mechanically manned space exploration


In order to link the subatomic (nonrealistic) spin phenomenon to reality (that is, physical rotation process), we determine a mathematical relationship between spin and spatial rotation. It is first shown that there exists an isomorphism between the special linear group SL(2;C) unto the Lorentz group SO(1;3). In particular, the unitary subgroup SU (2) is isomorphic to the special Lorentz group SO+ (1;3) via the spinor map, which is an action of the special linear group, SL(2;C) on the space of Hermitian complex matrices, H. It is then established that the spin transformations of the 3-dimensional real space correspond precisely to spatial rotations of angle 2k pi; with k = 1,2,...[For more detail, see Gazoya et. al (Journal of Ghana Science Association, Vol.16 No.1, June, 2015)].
For a realistic one-particle system theory, in the restriction to “positive energy” only and considering waves propagating in the z-direction, the Dirac field is subject to second quantization, and Noether’s theorem (resulting in conservation laws and their applications) together with Ehrenfest theorems are applied. This time, we go beyond the usual method of obtaining subluminal and luminal velocities of particles with half-integer spin (where the unsymmetrized Dirac Lagrange density is used, in literature), by employing the symmetrized Lagrangian. There, it is observed that
  • variations in intrinsic spin and orbital angular momenta are linear dependence along the z-axis,
  • orbital variation is relativistically concordant,
  • intrinsic spin variation is Lorentz violating (or violate causality).
Contrary to the traditional attitude of regarding causality violation as a paradox which seals scientific unfolding, we rather “dare” to treasure (or secure) this unusual occurrence as a catalyst to uncover the hidden superluminal dimension of the free spin-half field, in the following two stages of calculations, and an explanatory diagrammatic representation.
(A) The expectation value of :
  • the relative linear velocity component produced under variation in intrinsic spin angular momentum is found to be quantized and exceeding the speed of light,
  • the relative linear velocity component due to variation in orbital angular momentum is found to be subluminal. Next, it is understood that the generalized transformation of the field is a composition of the two intrinsic spin and orbital variations transformations.
As a result, the expectation value of the generalized linear velocity component of the free spin-half field is determined and found to be quantized and superluminal. For detailed information, see [Gazoya et. al (doi:10.5539/jmr.v7n4p12)].

(B) Since spacetime is curved, each “local” system of rectangular coordinate axes (so far used in Euclidean geometry, with its Newton’s theory of universal absolute space and time, and pseudo-Euclidean geometry of flat spacetime) could be thought of as an orthogonal intersection of two great circles (longitude and latitude), at the infinity scale. The linear motion, in spacetime, of a superluminal particle departing from the origin along any of these great circles (longitudinal, for example) will be circular from one hemisphere to the other; so that when the particle (under ‘excessive’ speed) is found in the other hemisphere, its (temporal) component will appear negative on the “local” picture of the coordinate axes. This is one way we may comprehend the change to negative temporal component of variation in spin angular momentum, leading to “apparent” backward in time motion in the light cone. Thus, in reality, there is no backward in time scenario, and the resulting causality violation may be regarded as just a mirage [see Gazoya et. al (DOI: 10.9734/BJAST/2016/26498), and Fig. 0.1, below].

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Finally, we have shown, theoretically, in the limit of a kinematically permissible medium with absence of dispersion, that the superluminal motion of free fermions could be a reliable dynamical system, in conformity with one of nature’s basic laws of conservation of energy. This disproves the persistent speculation which anticipates fast energy loss that would bring this kind of systems to instant collapse in their dynamical evolution. Detailed information can be found at [https.// (F), Vol.16, Issue 5, Version 1.0, Year 2016(35-48)].

Short Biography: I completed the studies of Bachelor of Science in Mathematics, Master of Philosophy in Mathematics, and the Philosophy Doctorate in Mathematical Physics in 2006, 2011, and 2016, respectively. Passionate of space travel, I have been a private aviation student pilot, initially. I embrace a carrier of research scientist and lecturer, presently working on superluminal particles. I have so far published four articles on this project:
  • THE ONE-PARAMETER SUBGROUP OF ROTATIONS GENERATED BY SPIN TRANSFORMATIONS IN THREE-DIMENSIONAL REAL SPACE. Gazoya et. al (JGSA_Vol.16, No.1, June 2015, p.120), published by Journal of Ghana Science Association.
  • INVESTIGATION OF SUPERLUMINAL MOTION OF FREE SPIN-HALF PARTICLES IN SPACETIME. Gazoya et. al (doi:10.5539/jmr.v7n4p12), published by Journal of Mathematics Research. Canadian Center of Science and Education.
  • SUPERLUMINAL MOTION OF FREE SPIN-HALF PARTICLES IN A FIBER BUNDLE FORMALISM. Gazoya et. al (DOI: 10.9734/BJAST/2016/26498), published by British Journal of Applied Sciences & Technology. SCIENCEDOMAIN international.
  • EFFECT OF CHERENKOV RADIATION ON SUPERLUMINAL FREE SPIN-HALF PARTICLES MOTION IN SPACETIME. (https.// (F), Vol.16, Issue 5, Version 1.0, Year 2016, pp.35-48), published by Global Journal of Science Research Frontier. 
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Superluminal Motion of free spin-half particles in Spacetime
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