Dirac's æther in curved spacetime

2003

We propose a new formulation for the AEther of Dirac based on a lagrangian approach. We analyse how the presence of a particular self-interaction term in the lagrangian lead us to a description of the aether as being a medium with conductivity which is governed by macroscopic Maxwell equations with a polarization tensor M αβ depending on the vector potential. These results are then applied to the analysis of the amplification of the primordial magnetic induction in a curved background of Friedmann's geometry.

Physical Review D

We consider configurations consisting of a gravitating nonlinear spinor field ψ, with a nonlinearity of the type λðψψÞ 2 , minimally coupled to Maxwell and Proca fields through the coupling constants Q M [U(1) electric charge] and Q P , respectively. In order to ensure spherical symmetry of the configurations, we use two spin-1=2 fields having opposite spins. By means of numerical computations, we find families of equilibrium configurations with a positive Arnowitt-Deser-Misner (ADM) mass described by regular zeronode asymptotically flat solutions for static Maxwell and Proca fields and for stationary spinor fields. For the case of the Maxwell field, it is shown that, with increasing charge Q M , the masses of the objects increase and diverge as the charge tends to a critical value. For negative values of the coupling constant λ, we demonstrate that, by choosing physically reasonable values of this constant, it is possible to obtain configurations with masses comparable to the Chandrasekhar mass and with effective radii of the order of kilometers. It enables us to speak of an astrophysical interpretation of such systems, regarding them as charged Dirac stars. In turn, for the system with the Proca field, it is shown that the mass of the configurations also grows with increasing both jλj and the coupling constant Q P . Although in this case the numerical calculations do not allow us to make a definite conclusion about the possibility of obtaining masses comparable to the Chandrasekhar mass for physically reasonable values of λ, one may expect that such masses can be obtained for certain values of free parameters of the system under consideration.

Journal of Physics: Conference Series, 2016

Anais da Academia Brasileira de Ciências, 2004

We search for an amplification mechanism of the seed cosmic magnetic induction by studying a new version of the Dirac's æther in a curved cosmological background. We find that the variation of the scale factor R(t) with cosmic time brings to the magnetic field the desired effect of amplification, that we call geometric amplification.

The geometric properties of General Relativity are reconsidered as a particular nonlin- ear interaction of fields on a flat background where the perceived geometry and coordi- nates are “physical” entities that are interpolated by a patchwork of observable bodies with a nonintuitive relationship to the underlying fields. This more general notion of gauge in physics opens an important door to put all fields on a similar standing but requires a careful reconsideration of tensors in physics and the conventional wisdom surrounding them. The meaning of the flat background and the induced conserved quantities are discussed and contrasted with the “observable” positive definite energy and probability density in terms of the induced physical coordinates. In this context, the Dirac matrices are promoted to dynamic proto-gravity fields and the keeper of “phys- ical metric” information. Independent sister fields to the wavefunctions are utilized in a bilinear rather than a quadratic lagrangian in these fields. This construction greatly enlarges the gauge group so that now proving causal evolution, relative to the physical metric, for the gauge invariant functions of the fields requires both the stress-energy conservation and probability current conservation laws. Through a Higgs-like coupling term the proto-gravity fields generate a well defined physical metric structure and gives the usual distinguishing of gravity from electromagnetism at low energies relative to the Higgs-like coupling. The flat background induces a full set of conservation laws but results in the need to distinguish these quantities from those observed by recording devices and observers constructed from the fields.

General Relativity and Gravitation, 2016

In this work we take a formal approach to the problem of decoupling Proca equations in curved space-times. We use Newman-Penrose (NP) twospinor formalism to represent the Proca vector by one complex and two real scalars. We show that a decoupled second order differential equation for one of the real scalars can be derived if and only if the background space-time admits a covariantly constant null vector. Thus, the background space-time must be a pp-wave vacuum. We evaluate the separability of Proca, Maxwell and Dirac equations on the resulting pp-wave background.

arXiv (Cornell University), 2007

This paper is a continuation of my earlier paper (Nyambuya 2007a) in which the equivalent of the Dirac Equation in curved spacetime is derived. This equation has been developed mainly to account in a natural way for the observed anomalous gyromagnetic ratio of fermions and the suggestions is that particles including the Electron, which is thought to be a point particle, do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. In this reading, I investigate four symmetries of this equation, Lorentz invariance, charge conjugation (C), time (T) and space (P) reversal symmetries. I show that this equation is Lorentz invariant, obeys C invariance symmetry and violates T and P symmetry but is TP &, PT invariant. These symmetries show that anti-particles have positive mass and energy but a negative rest mass and the opposite sign in electronic charge. A suggestion is made that the rest mass of a particle must be related to the electronic charge of that particle. The equivalent Klein-Gordon and Schrodinger equation in curved spacetime are discussed. It is shown that these equations imply Bosons and atoms naturally must have a spin-orbit interaction when immersed in an ambient magnetic field. As currently understood, these equations can not account for spin-orbit interaction in a natural way.

arXiv: Quantum Physics, 2019

The main objective of this work is to present an implementation of the Dirac equation, coupled to classical gravitational and $U(1)$ background fields, in $2+1$ dimensions in a waveguide array. We study the Dirac equation in such backgrounds, make some assumptions on the metric and the vector potential and argue that the restrictions allow for a wide array of physical spacetimes, such as all vacuum solutions of Einstein's field equations and all static spacetimes. Next, we develop a method that allows one to implement the Dirac equation in such a setting in a coupled waveguide array. Lastly, as an example of possible applications, we devise a thought experiment to observe the gravitational Aharonov-Bohm effect and briefly discuss its implementation in the proposed waveguide setup.

×ØÖ Øº I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, two of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Muon -despite their acute similarities -exhibit an asymmetry in their mass is possible. The Mourn is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible.

arXiv (Cornell University), 2007

This paper is a continuation of my earlier paper (Nyambuya 2007a) in which the equivalent of the Dirac Equation in curved spacetime is derived. This equation has been developed mainly to account in a natural way for the observed anomalous gyromagnetic ratio of fermions and the suggestions is that particles including the Electron, which is thought to be a point particle, do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. In this reading, I investigate four symmetries of this equation, Lorentz invariance, charge conjugation (C), time (T) and space (P) reversal symmetries. I show that this equation is Lorentz invariant, obeys C invariance symmetry and violates T and P symmetry but is TP &, PT invariant. These symmetries show that anti-particles have positive mass and energy but a negative rest mass and the opposite sign in electronic charge. A suggestion is made that the rest mass of a particle must be related to the electronic charge of that particle. The equivalent Klein-Gordon and Schrodinger equation in curved spacetime are discussed. It is shown that these equations imply Bosons and atoms naturally must have a spin-orbit interaction when immersed in an ambient magnetic field. As currently understood, these equations can not account for spin-orbit interaction in a natural way.