Einstein’s dream of an accomplished unified field theory?

During the last part of the 20th century, string theory was presented as a unifying theory of physics foundations. The string theory did not meet expectations. This is why we are of the opinion that the scientific community must reconsider what includes elementary forces and particles.

Since the first days of general relativity, leading physicists, such as Albert Einstein and Erwin Schrödinger, have tried to unify the theory of gravitation and electromagnetism. Many attempts were made during the 20th century, including by Hermann Weyl.

Finally, it seems that we have found a unified framework to adapt to the theory of electricity and magnetism within a purely geometric theory. This means that the electromagnetic and gravitational forces are both manifestations of undulations and curvatures in the geometry of space-time.

Dreams of a unified field theory

Einstein’s objective was to explain electromagnetism as a geometric property of four-dimensional space-time. He continued this work until his death in 1955. The work was not completed. Arthur Eddington, Theodor Kaluza and others also highlighted their theories on how to unify gravity and electromagnetism, but none of these theories have been universally accepted.

Schrödinger, the father of quantum mechanics, highlighted his unified theory on the ground in the 1940s, but without success. Many different approaches have been proposed, including five -dimensional theories and theories based on asymmetrical measures.

A new perspective, the new non -linear Maxwell equations

In our approach, the electrical load and the electric currents, as well as the electromagnetic forces, are considered as purely geometric and immanent properties of space-time itself, and not as external objects. This approach was supported by the late physicist John Wheeler, in his vision of geometrodynamics. It turns out that the four-dimensional electromagnetic potential is really a constitutive element of the metric tensor of space-time.

Using an approach to the calculation of variations, we proposed an aesthetically attractive geometric formulation of electromagnetism. When the variation in metric tensor is optimized using functional derivatives, the necessary optimality conditions give a new non -linear generalization of the Maxwell equations. Our work is published in the Journal of Physics: series of conferences.

In the classic electromagnetism theory, Maxwell equations governing electric and magnetic fields are linear partial differential equations. In our approach, optimal measures must be harmonic, which gives non -linear field equations for electromagnetic potentials and Maxwell equations as a special linear case. The field equations then give the correct dynamics for the electromagnetic field.

A generalization of geometry solves the enigma

When Albert Einstein formulated his theory of gravity, he used mathematics known under the name of pseudo-Riennian differential geometry. We have noted in our research that pseudo-Riennian geometry is not general enough for a purely geometric theory of electromagnetism. A more general differential geometry was necessary.

A purely local geometry was invented in 1918 by the famous German mathematician Weyl. We took the ideas of Weyl and combined them with our previous research on this subject, and the puzzle seemed to open up. In a Weyl geometry, lengths are local properties of space-time, it therefore conforms to the principles of the theory of relativity.

We discovered that Weyl’s geometry allowed us to inspect the local compression of space-time. The same results are produced in our research using the so-called geometric algebra. Geometric algebra and Weyl geometry therefore also seem to be usable to formulate a geometric theory of electromagnetism.

Electric load as local space-time compression

We have discovered that in addition to the new non-linear field equations, the electrical load is linked to the local divergence or the compression of space-time. The accusation is therefore an area, which has its own laws of movement.

The familiar law of the force of the Lorentz force governing forces on the loaded particles is a condition for the test particle to move on geodesy, as in general relativity. This functionality completes the geometric description of electromagnetism.

Conclusions

Our results indicate that light and all electromagnetic radiation are really oscillations of space-time itself. In terms of older theories of “ether”, it seems that Einstein was right when he concluded that “ether” is space-time. The electrical load is a local compression of space-time and the forces on the electrical loads correspond to the movement on the shortest paths, that is to say on geodesy.

We believe that a sufficiently complete geometric theory of electromagnetism is now available for new research. In addition, the assumption of fluctuations of space-time in the metric tensor on the Planck scale leads to an electromagnetic field fluctuating random in the void.

The model predicts random fluctuations in the electromagnetic field at the Planck scales and therefore the creation and annihilation of load on a planck scale due to the random covariant divergence of electromagnetic potential with four potentials. Finally, our theory predicts “the forces” acting on loads even without electromagnetic field, that is to say that it explains and predicts the Aharonov-Bohm effect.

This story is part of Science X Dialog, where researchers can report the results of their published research articles. Visit this page for more information on the Science X dialog box and how to participate.

Jussi Lindgren works at the Ministry of Finland of Finance, and he holds a D.SC. Diploma from Aalto University in Applied Mathematics.

Andras Kovacs works in the exafuse start-up, in the role of research on energy based on applied physics. He studied physics at Columbia University.

Jukka Liukkonen holds a doctorate in applied physics, and he works full time at the Nuclear and Radiation Safety Authority, Stuk, Vantaa, Finland.