I mean is it somewhat science or is it purely sci-fi?
Do you mean more dimensions in our universe or other universes with a different number of dimensions?
yes, our universe itself acording to m-theory is 11 dimensional
Both...string theorists say both is true, that our brane is 11 dimensions but it is also just one "slice", so to speak.
Both are certainly possible, though any talk about separate universes is pointless. Separate universes would, by definition, have no impact on ours, so we can only speculate about them. As for extra spatial dimensions in our universe, let's wait until it's actually observed before we jump to any conclusions. I'm not well versed in string theory, but I do know that it hasn't produced any successful predictions yet.
What is the definition of a dimension and the definition of a universe? If we answer unambiguously these questions we can probably proceed to find answers to the original question.
Also as SpaceTiger mentioned, if we cannot have any interaction with other universes then it is pointless to discuss about them.
Well string theorists say that gravity might "leak" into other universes, I mean these "higher dimensions" and "other universes" are said to come right out of the String Theory equations, but of course it is all just scientific equations and there is no evidence, but it is still scientific, right?
I would say this makes them part of our universe, by my definition, but ramollari is absolutely right that we need to agree on a definition of "universe".
Even if these other universes are extremely different from ours?
When somebody tells you that out universe is extremely energetic (as the quantum theorists do today), you should ask yourself why things like gravitation, cosmological expansion, etc are so fine-tuned. Then after you've managed to convince yourself that this can be true, you might want to ask yourself what our universe would look like if gravity or any other force can "leak" into another universe.
If gravity and the cosmological constant have been fine-tuned for 13.7 Billion years so that the univese has not collapsed or exploded, there's got to be one heck of a damping factor in play if we can strip gravitational energy out of our universe and give it to another one without causing the immediate collapse or explosion of the other.
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