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One's conceptual model might indeed attempt to adhere to a strict
"actio-in-distans" mechanism, whereby a cause might produce a distant
effect (perhaps with a time delay) without any thing travelling between
the two locations. Note that this is conceptual modeling, where one man's
weirdity might be another's loverly.
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.