This is aesthetically pleasing, as nature seems to strive for harmony, efficiency and simplicity. Electric current seems to be a re-balancing object, which transports charge in order to keep the spacetime manifold Ricci-flat. Moreover, electric charge relates to some compressibility properties of spacetime. Tensions in spacetime manifest themselves as electric and magnetic fields. It means that the material world always corresponds to some geometric structures of spacetime. Our research strongly supports this kind of natural philosophy. John Wheeler, the famous physicist, put forward the idea that all of the material world is constructed from the geometry of the spacetime. On the other hand, this means that general relativity is a generalized theory of nonlinear electromagnetism. 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. 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. Electric and magnetic fields represent certain local tensions or twists in the spacetime fabric. In a way, spacetime itself is therefore the aether. In particular, our research shows how electromagnetism is an inherent property of spacetime itself. 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. Test particles follow what are called geodesics-the shortest paths in the spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. The metric tensor also thus determines the curvature properties of spacetime. The metric tensor of spacetime tells us how lengths determine in spacetime. Indeed, it becomes clear that Maxwell's equations hide inside the Einstein field equations of general relativity. Therefore, we thought that perhaps we are talking about the same governing equation, which could describe both electromagnetism and gravitation. Both equations are ultimately of second order, if seen properly. 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. The equations relate the electromagnetic field to currents and charges. Maxwell's equations are the key linear partial differential equations that describe classical electromagnetism. Maxwell's equations and general relativity-what are these all about? So what is the mutual relationship of electromagnetism and gravitation? We provide one possible explanation to the riddle. The Serbian inventor Nikola Tesla thought that electromagnetism contains essentially everything in our universe. The brilliant mathematician Hermann Weyl had especially interesting theories in this regard. Many eminent mathematical physicists have tried to understand electromagnetism directly as a consequence of general relativity. General relativity explains that energy and mass tell the spacetime how to curve and spacetime tells masses how to move. On the other hand, the theory of gravitation is rather well understood. 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. In the 19th century, scholars thought that electromagnetic waves must propagate in some sort of elusive medium, which was called aether. 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.Įlectromagnetism has always been a subtle phenomenon.
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