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Brian Greene in this TED talk about possible multiverse, claims tomwards the end (At around 18:00 mark) this statement. 'Because the expansion is speeding up, in the very far future, those galaxies will rush away so fast, we wont be able to see them, not because of technological limitations, but because of the law of physics.'

This seems to me against the basic premise of relativity, namely that two objects are moving so fast away from each other that their relative speed is greater than that of light. Can anybody explain whether he really meant what I understood, and if not what he really meant.

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+1 Very interesting question as "breaking" the c speed limit would violate the very same laws that make his statement possible. – Argus Jun 21 '12 at 23:22
You might be interested in the answers to the related question – John Rennie Jun 22 '12 at 8:18

In the General Theory of Relativity, spacetime is locally that of Special Relativity. In other words, the relative speed of material objects in the local "neighborhood" must be less than c.

However, there is no upper limit on the metric expansion of space. Indeed, two material objects may both be at rest with respect to the cosmic microwave background but, due to the expanding metric, the "distance" between the objects can be increasing at a rate faster than c.

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This may be slightly confusing. Is the space between galaxies inflating or are the outer boundaries of space itself inflating? – Argus Jun 21 '12 at 23:40
There are no outer boundaries of space, i.e., there isn't a larger structure that space is expanding "into". See the Wikipedia article "Metric Expansion of Space". – Alfred Centauri Jun 21 '12 at 23:46

He means that the stars will fall into our cosmological horizon. This is like a black hole horizon, except surrounding us, and in our current understanding, the accelerating expansion of the universe means that the cosmological horizon will only expand to a finite area and then stop. When it stops, everything far away from us will be sucked into this cosmological horizon and disappear from view.

I prefer to state it this way, because this is a picture which is consistent with staying in a single causal patch, and it is consistent with holographic principle and with logical positivism. There is no need to postulate anything beyond what we can see, and the cosmological horizon is the boundary of what we can see.

In the far, far future, if string theory is to be believed, and if our current understanding of deSitter spaces is accurate, our universe will decay into another vacuum state which doesn't have a cosmological horizon. This will be a catastrophic event, destroying all the matter in our universe starting from some nucleation bubble of the new universe.

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In simple terms, stars and galaxies are not moving through space faster than the speed of light, which would violate current laws of physics. It is space itself which is expanding faster than the speed of light, carrying the stars with it. Thus, no law of physics is violated.

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Let's abandon phrases like "moving through space". – Johannes Dec 15 '12 at 2:14

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