June 14, 2024
Electromagnetism is a property of spacetime itself, study finds
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.

Imagine if we could use strong electromagnetic fields to manipulate the local properties of spacetime—this could have important ramifications in terms of science and engineering.

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.

Maxwell’s equations and general relativity—what are these all about?

Maxwell’s equations are the key linear partial differential equations that describe classical electromagnetism. The equations relate the electromagnetic field to currents and charges. On the other hand, in general relativity, the Einstein field equation is a set of nonlinear partial differential equations describing how the metric of spacetime evolves, given some conditions, such as mass density in the spacetime. Both equations are ultimately of second order, if seen properly.

Therefore, we thought that perhaps we are talking about the same governing equation, which could describe both electromagnetism and gravitation. Indeed, it becomes clear that Maxwell’s equations hide inside the Einstein field equations of general relativity. The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as “force.” In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.

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