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I have recently been working on the Classical Unified Field Theory, and i want to ask, why the Einstein-Maxwell equations does not candidate for a Classical Unified Field Theory, since it incorporates both general relativity and electromagnetism, into a single formalism?

I have seen that people, after the discovery of general relativity, have persued the dream of a unified field theory, in this case in the classical sense. So why ain't this the truth about the Einstein-Maxwell equation?

Also, when this is not true for the EME, could one do unification, in the same way used to discover the Grand Unified Theory in the 1970s, by using groups symmetries at very high temperatures?

\Schreiber