In the responses to my previous post, Cristi Stoica provided some very useful references that, for now, I am going to classify as “Rainich unification” since I needed something for the title of this post. What caught my eye was the following from the abstract of a paper by Misner and Wheeler from 1957:
Maxwell’s equations then reduce, as shown thirty years ago by Rainich, to a simple statement connecting the Ricci curvature and its rate of change. In contrast to unified field theories, one then secures from the standard theory of Maxwell and Einstein an already unified field theory. (Misner, C.W. and J.A. Wheeler (1957). “Classical physics as geometry”. Ann. Phy. 2: 525-603.)
Some related work was done by Penrose and Rindler in the 1980s but not much seems to have come of it. Whatever happened to this approach? Why was it dropped? What are its inherent flaws?