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Scientists are talking about our universe not being the only universe, but even if that is true, how can we prove the existence of multiverse? We are being 'confined' in this universe and there is no way we can know what is happening outside, right?

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By definition we'll never be able to observe other universes directly, because if we could they'd be in our universe.

However suppose (for example) string/M theory does get developed into a theory that is easily testable, and suppose we find that all the predictions string theory makes about our universe are experimentally found to be true. That means we'd be pretty convinced that string/M theory was the right theory to describe physics. If this hypothetical development of string theory still predicted a multiverse then we'd be inclined to believe in on the grounds the theory gets everything else right.

It's not unprecedented for a theory to predict things we can never observe. For example we cannot see what is behind the event horizon of a black hole (at least, not without jumping in :-). However we believe what General Relativity tells us about the interior of a black hole because it gives the correct results for everything that we can observe. The multiverse idea is a lot more extreme than the interior of a black hole, but you can see how we could be persuaded that it does exist.

I suppose for completeness I should mention that some scientists have suggested different universes may collide, and we could see evidence of the collision. See this Science Daily article for a introduction to this idea. I'm not sure how seriously this idea is taken.

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This is not a great answer. The interior of a black hole is only predicted to the extent you can get information about the interior out, and positivism forbids you from talking about unobservable things. –  Ron Maimon Jun 19 '12 at 16:09
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I'm no physicist, and this is not quite proof. If you haven't seen it already, please check out Everett's many worlds interpetation Scroll down to the paragraph on interpreting wavefunction collapse.

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This is probably the worst (yet technically not false (or true)) response one could give. It's bad because the person asked how we could prove the multiverse exists and the many worlds interpretation has it as an assumption! Even if the many worlds theory were correct you couldn't use it to prove one of it's assumptions! –  tachyonicbrane Jun 20 '12 at 4:54
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