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Originally Posted by DivineNathicana
Einstein said that instantaneous travel was impossible.
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AFAIK Einstein's point was that it is impossible due to the limits on speed of information, ie
c. So you cannot avoid
c in this discussion.
Instantaneous travel boils down to semantics: what is an "instant". You might be interested in reading something about Goedels Continuum Hypothesis which tries to explain the relation between space, time, and distance:
The Continuum Hypothesis
http://www.ii.com/math/ch/
For something to move from the Sun to the Earth instantaneously, it would actually have to travel faster than light, which spends 8 minutes on the journey (at the speed of c, obviously). So instantaneous travel is the same as travelling back in time.
I think splitting the line of motion into points is needless - macroscopic objects most definitely do NOT move at planck scales. Even when you stand still every single cell in your body is moving somewhere (say you sway slightly back and forth or shiver) and the ground you are standing on is on a rotating globe in orbit around a star in orbit around a galaxy heading towards a galaxy cluster.
Quantum particles show strange behaviour, yes. But they are not observed to move faster than
c (the hypothetical "tachyon" does this but is not yet observed - and Feynman's diagrams show that all particles move backwards in time - theoretically).
Since we do not completely understand what time is, arguments about this have a lot of fallacies. We know more about space than time so maybe we will find that isntant motion is possible. But as for today the only possible instant motion for macroscopic objects would be theoretical wormholes.
