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On the road to considering dissertation topics, Feynman (under Wheeler)
tried to construct an electrodynamics based solely on this
actio-in-distans mechanism. I don't have details, but they finally
abandoned the idea. I think (?) one of the difficulties appeared to be
that the advanced solutions to the wave equation had to be taken
seriously, with undesirable conceptual consequences. Perhaps someone
knows more - it is an interesting question.