Alena Tensor in unification applications

Abstract Alena Tensor is a recently discovered class of energy-momentum tensors that provides mathematical framework in which, as demonstrated in previous publications, the description of a physical system in curved spacetime and its description in flat spacetime with fields are equivalent. The description of a system with electromagnetic field based on Alena Tensor can be used to reconcile physical descriptions. (1) In curvilinear description, Einstein Field equations were obtained with Cosmological Constant related to the invariant of the electromagnetic field tensor, which can be interpreted as negative pressure of vacuum, filled with electromagnetic field. (2) In classical description for flat spacetime, three densities of four-forces were obtained: electromagnetic, against gravity (counteraction to gravitational free-fall), and the force responsible for the Abraham-Lorentz effect (radiation reaction force). Obtained connection of Einstein tensor with gravity and radiation reaction force, after transition to curvilinear description, excludes black hole singularities. There was obtained Lagrangian density and generalized canonical four-momentum, containing electromagnetic four-potential and a term responsible for the other two forces. In this description charged particles cannot remain at complete rest and should have spin, their energy results from the existence of energy of magnetic moment and the density of this energy is part of the Poynting four-vector. The distribution of charged matter was expressed as polarization-magnetization stress-energy tensor, what may explain why gravity is invisible in QED. 3) In quantum picture, QED Lagrangian density simplification was obtained, and the Dirac, Schrödinger and Klein–Gordon equations may be considered as approximations of the obtained quantum solution. Farther use of Alena Tensor in unification applications was also discussed.