Monday, July 26, 2021

It's all about geometry

Credit: Pixabay/CC0 Public Domain

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions (commonly called forces) in nature, together with the strong interaction, the weak interaction, and gravitation.[1] At high energy, the weak force and electromagnetic force are unified as a single electroweak force.

Researchers are now becoming increasingly convinced that the electroweak force, like gravity, may be a property of spacetime because ...

The electromagnetic force is responsible for practically all phenomena one encounters in daily life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting between the electrically charged atomic nuclei and electrons of the atoms. Electromagnetic forces also explain how these particles carry momentum by their movement. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which result from the intermolecular forces that act between the individual molecules in our bodies and those in the objects. The electromagnetic force is also involved in all forms of chemical phenomena.

The mystery of electromagnetism

Electromagnetism has always been a subtle phenomenon. In the 19th century, scholars thought that electromagnetic waves must propagate in some sort of elusive medium, which was called aether. Later, the aether hypothesis was abandoned, and to this day, the classical theory of electromagnetism does not provide us with a clear answer to the question in which medium electric and magnetic fields propagate in vacuum. On the other hand, the theory of gravitation is rather well understood. General relativity explains that energy and mass tell the spacetime how to curve and spacetime tells masses how to move. Many eminent mathematical physicists have tried to understand electromagnetism directly as a consequence of general relativity. The brilliant mathematician Hermann Weyl had especially interesting theories in this regard. The Serbian inventor Nikola Tesla thought that electromagnetism contains essentially everything in our universe. So what is the mutual relationship of electromagnetism and gravitation? We provide one possible explanation to the riddle.

The link between general relativity and electromagnetism becomes clear by assuming that the so-called four-potential of electromagnetism directly determines the metrical properties of the spacetime. In particular, our research shows how electromagnetism is an inherent property of spacetime itself. In a way, spacetime itself is therefore the aether. Electric and magnetic fields represent certain local tensions or twists in the spacetime fabric. Our research shows that the Lagrangian of electrodynamics is just the Einstein-Hilbert action of general relativity; it reveals how Maxwell's equations of electromagnetism are an optimality condition for the metric of spacetime to be sufficiently flat. As Einstein's theory of general relativity provides that the metric is optimal in a sense, electromagnetism is hidden in the nonlinear differential equations of general relativity. On the other hand, this means that general relativity is a generalized theory of nonlinear electromagnetism.

It's all about geometry 

John Wheeler, the famous physicist, put forward the idea that all of the material world is constructed from the geometry of the spacetime. Our research strongly supports this kind of natural philosophy. It means that the material world always corresponds to some geometric structures of spacetime. Tensions in spacetime manifest themselves as electric and magnetic fields. Moreover, electric charge relates to some compressibility properties of spacetime. Electric current seems to be a re-balancing object, which transports charge in order to keep the spacetime manifold Ricci-flat. This is aesthetically pleasing, as nature seems to strive for harmony, efficiency and simplicity.

The ancient Greeks could relate to this would they not? :)

 

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