Good questions.
 Quote by jpi
If it is accepted that the four dimensions of general relativity correspond to physical reality, does that imply that physical objects also have a non-zero ( non-infinitesimal ) extent along the time dimension?
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It would help if you thought about this in terms of how we describe things: i.e. we
describe an object by defining an extent in 3D space. Similarly, if we described a length of time to describe it, we would just be describing a duration. That's exactly what you're doing when you ask, "how long is the movie?" With a event it is relatively simple: 'such and such occurred for so long.' With an object it is a little strange, we don't necessarily know how long an object will exist, or how long it has existed.
It comes in handy in particle physics though.
 Quote by jpi
If so, does an object exist, in part, in the future and the past?
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That's more of a philosophical question---how you interpret these things.... but yes, thats definitely accurate to some extent.
 Quote by jpi
If so, does if imply that a photon can "see ahead" enough to be behave appropriately in the two slit experiment?
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No. Not at all. Photons can't 'see' anything---because they don't have a valid reference frame. Additionally, even if they could 'see,' they would no equivalent of actions---because everything would appear to be at the same instant in time and space.... sounds weird because it doesn't work--you can't think in the photons frame.