The electromagnetic field tensor is another second order antisymmetric tensor field, with six components : three for the electric field and another three for the magnetic field.
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Albert Einstein became affiliated with the theory in 1928 during his unsuccessful attempt to match torsion to the electromagnetic field tensor as part of a unified field theory.
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This almost parallels the electromagnetic field tensor ( also denoted ) in quantum electrodynamics, given by the electromagnetic four-potential describing a spin-1 photon;
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Where " F ab " is the electromagnetic field tensor representing the electromagnetic field and " J a " is a four-current representing the sources of the electromagnetic field.
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Another example is the values of the electric and magnetic fields ( given by the electromagnetic field tensor ) and the metric at each point around a charged black hole to determine the motion of a charged particle in such a field.
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The algebraic classification of bivectors given above has an important application in relativistic physics : the electromagnetic field is represented by a skew-symmetric second rank tensor field ( the electromagnetic field tensor ) so we immediately obtain an algebraic classification of electromagnetic fields.
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Finally ( and more technically ), Born Infeld theory can be seen as a covariant generalization of Mie's theory and very close to Einstein's idea of introducing a nonsymmetric metric tensor with the symmetric part corresponding to the usual metric tensor and the antisymmetric to the electromagnetic field tensor.
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The transformation properties of the electromagnetic field tensor, including invariance of electric charge, are then used to transform to the lab frame, and the resulting expression ( again Lorentz force law ) is interpreted in the spirit of Newton's second law, leading to the correct expression for the relativistic-momentum.
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Wheeler was also much intrigued by the fact that the ( nonspinning ) point-mass solution of general relativity, the George Rainich had shown decades earlier that one can obtain the electromagnetic field tensor from the electromagnetic contribution to the stress energy tensor, which in general relativity is directly coupled to spacetime curvature; Wheeler and Misner developed this into the so-called " already-unified field theory " which partially unifies gravitation and electromagnetism, yielding " charge without charge ".
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