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If the universe is infinite, by virtue of chance it means that every possible configuration of matter must exist somewhere (according to this documentary).

Therefore, if we accept that the universe is infinite and it's possible to travel through time and space near-instantaneously, by sheer chance there must be a version of me out there that can do so and that wants to contact me.

Since this has not happened yet, can I conclude that either near-instantaneous travel through time and space is impossible or that the universe isn't infinite?

On a broader scale: given the infinity of the universe, should certain occurences that occur everywhere at the same time not occur always throughout the universe? Or do such occurences simply not exist?

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I suspect most physicists think that near-instantaneous travel through time and space is impossible - the jury is still out on whether the universe is infinite. Can you expand your last paragraph: maybe with an example? As it stands it's not clear what you're asking. – John Rennie Aug 8 '12 at 15:55
What I mean is, if we can prove that the universe is infinite, would that not immediately disprove that near-instantaneous travel through time and space is possible? Because if it were possible, the chance of my doppelganger (or any traveller for that matter) visiting me would be 1 (since there would always be someone doing so in an infinite universe in which such travel would be possible). – Samuel Aug 8 '12 at 16:07
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@Samuel Why would they choose to visit you and not any of your doppelgängers? If "instantaneous spacetime travellers" are scarce enough, the fraction of dopelgängers that are visited by them may also be small. – mmc Aug 8 '12 at 17:02
See this: phys.org/news/2013-01-dont-infinite-scientists.html You don't exist in an infinite number of places, say scientists – Raindrop Jan 27 at 1:48

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Your problem is that you have included some unproven assumptions, namely:

  • The universe is infinite
  • It is possible to travel through space instantaneously
  • It is possible to travel through time instantaneously

But you have assumed that they are the only assumptions in play here.

What about:

  • Your doppelganger doesn't want to meet you
  • This locale is off limits or unpopular
  • Time travel may be popular, but instant space travel may not
  • etc...

In general it is considered that the universe is not infinite, just very very big. Mindbogglingly big.

As regards time travel - the jury is still out, and may be for some time, or until last Tuesday - who knows.

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Well, your second set of assumptions are all covered by the first set: if the universe is infinite there will always be someone who wants to do that (if it's theoretically possible, according to the profs in the doc.). – Samuel Aug 8 '12 at 15:34
Infinite doesn't have to mean everything happens. Infinite is weird like that. Time travel may be a physical impossibility - an infinite universe won't change that. – Rory Alsop Aug 8 '12 at 15:36
"Infinite doesn't have to mean everything happens." Not everything, but if there is a remote chance, it will (i.e. a monkey typing the complete works of shakespeare by chance). Check out the doc. for the rationale behind this. – Samuel Aug 8 '12 at 15:38
"Time travel may be a physical impossibility - an infinite universe won't change that.", I'm sorry but did you read my question? I know that and I clearly stated: "if we accept that the universe is infinite and it's possible to travel through time and space near-instantaneously" – Samuel Aug 8 '12 at 15:41
In addition to my previous comment: en.wikipedia.org/wiki/Infinite_monkey_theorem – Samuel Aug 8 '12 at 16:05
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