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In the context of:
"How can you have a "long-range" force at all, given that special
relativity and basic notions of causality require everything to be
local in space and time?"
The argument goes like this: If A were to cause B via some
nonlocal interaction, i.e. separated by a spacelike interval
in some frame, then in some other frame the effect would
occur before the cause ... violating the most basic notions
of causality.
Sure, you can define such a distance, and you can have
object A separated by object B by such a distance ... but
then A cannot be the cause of B, nor vice versa.
The language of cause-and-effect is tricky; (to put it mildly)To me, any system of separated events, be it within or outside of the light cone, is nonlocal - simply because it resides in an extended region of spacetime. But these are purely terminological issues. A really interesting question is: How does the model with the intermediate virtual particles kicking A and B away from each other explain the attraction between A and B?
...we can avoid
some of that by saying event A can send /information/ to
any point in its forward light-cone, and not otherwise,
i.e. not to the past, and not to any point at a
spacelike separation.