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I read an article about possibility of existence of multiverse and came up with a conflicting view with one of the sentences written in the article which goes as follows:

"If space-time goes on forever, then it must start repeating at some point, because there are a finite number of ways particles can be arranged in space and time."

What does this mean? What does it mean to say when it hints that it must start repeating at some point? Also, where are these multiverses enclosed within? If they are expanding at such a rate, is the container in which they are enclosed also expanding?

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If the universe is infinite there is obviously an infinite number of ways of arranging the matter within it, so there is no requirement for the universe to repeat at large scales. What the article is suggesting is more subtle than this.

Suppose we take a finite volume. This could be as small as you, or as large as the observable universe, but in both cases there is a finite number of ways of arranging the matter in a finite volume. The reason there is only a finite number of ways is that we assume separations smaller than the Planck length can't be distinguished. So our finite volume is made up of a large but finite number of Planck volumes, and there is only a finite way of arranging the matter between this finite number of Planck volumes. Depending on how you do the calculation the number of ways of arranging the matter in the observable universe is around $2^{10^{118}}$.

So if you assume the universe is completely random then the probability of a randomly selected volume the size of the observable universe looking just like ours is 1 in $2^{10^{118}}$. This is obviously very unlikely, but in an infinite universe there are an infinite number of observable universe sized volumes, so somewhere there will be an exact replica of our observable universe. In fact there will be an infinite number of such exact replicas.

None of this has anything to do mith multiple universes. The argument above is just that there must be repeating regions within our universe.

John Rennie
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