String theory was proposed as a unifying theory of physics foundations in the later half of the 20th century. However, string theory has fallen short of predictions. For this reason, we believe that the scientific community should reevaluate what constitutes elemental particles and forces.
Prominent physicists like Albert Einstein and Erwin Schrödinger have attempted to integrate the theories of electromagnetism and gravity since the early days of general relativity. The 20th century saw numerous attempts, including Hermann Weyl’s.
It appears that we have at last discovered a cohesive framework that allows the theory of electricity and magnetism to be included in a purely geometric theory. This implies that ripples and curvatures in spacetime geometry are the source of both gravitational and electromagnetic forces.
Dreams of a unified field theory
Explaining electromagnetic as a geometric characteristic of four-dimensional spacetime was Einstein’s goal. Until his passing in 1955, he carried on with this effort. The task was not finished. None of the hypotheses proposed by Arthur Eddington, Theodor Kaluza, and others to combine gravity and electromagnetic have gained widespread acceptance.
The father of quantum physics, Schrödinger, attempted, but failed, to propose his unified field theory in the 1940s. A wide range of methods, such as theories based on asymmetric metrics and five-dimensional theories, have been put forth.
A new perspective, new nonlinear Maxwell’s equations
Our method views electromagnetic forces, electric charge, and electric currents as essentially geometrical and inherent characteristics of spacetime itself rather than as some extraneous entities. In his conception of geometrodynamics, the late physicist John Wheeler endorsed this strategy. The metric tensor of spacetime is actually a building block of the four-dimensional electromagnetic potential.
We have proposed an attractive geometric description of electromagnetism using a method from calculus of variations. The required optimality criteria result in a new, nonlinear version of Maxwell’s equations when the variation of the metric tensor is optimized with functional derivatives. The Journal of Physics: Conference Series has published our paper.
Maxwell’s equations for electric and magnetic fields are linear partial differential equations in the classical theory of electromagnetic. Our method requires optimal metrics to be harmonic, resulting in Maxwell’s equations as a specific linear case and nonlinear field equations for the electromagnetic potentials. The proper dynamics for the electromagnetic field are then provided by the field equations.
