The Universe is Finite, not Infinite

Dr. Bee addresses the question: Is the Universe Infinite or Finite?

She correctly explains that we do not know. There have been attempts to prove that the universe is finite, but there is no way to prove that it is infinite.

Is the universe really infinite? Or could it close back on itself like a sphere? If it’s infinite, how can it expand? And is it true that there might be copies of you in it? Today I want to explain how much we know about those questions and what the expansion of space has to do with Hilbert's Hotel.

She explains:

3:02 You could ask now, well, if those are all things we measure on the inside, what sense 3:09 does it even make to call this curvature. Couldn’t we just say that spacetime is flat, 3:14 just that these observables have difficult relations that are mediated by some sort of field. 3:20 Indeed, this is a valid interpretation of the maths, that you refuse to give this a geometric 3:26 interpretation and instead just say gravity is determined by some sort of complicated field. 3:32 This is why Steven Weinberg in his book on general relativity famously refused to use a 3:38 geometric interpretation. You don’t need it. And if you don’t need the geometric interpretation, 3:43 why subscribe to it. ...

3:56 That said, most physicists use the geometric interpretation, I believe because it makes it 4:01 easier to visualize things. Either way, the relevant point is that General Relativity is 4:06 entirely about what happens inside of space-time. This also answers the often-asked question, 4:13 if the universe expands, then what does it expand into? The answer is that that’s a meaningless 4:19 question.

I think that it was Poincare, in his very popular 1902 book, Science and Hypothesis, where he made the point that we cannot truly tell whether space is curved. We could just adjust our Physics formulas to account for the curvature. He said flat space was just a convention.

Einstein also had an attitude similar to Weinberg's book. That the geometric interpretation is interesting, but not really essential to the Physics. I was surprised to learn this, as almost everyone credits Einstein with having the geometric interpretation. But he denied it.

Almost everyone else accepts the geometry as being essential to the Physics, and not just a conventional Math interpretation.

Infinities cannot be observed, so mathematical models of spacetime can be finite or infinite, as a matter of convenience. The infinity is physically meaningless.

Here is where she loses me:

9:22 If spacetime is really infinite, then that has the odd consequence that every 9:27 possible configuration of matter appears infinitely many times. That includes you, 9:33 unless you are an impossible configuration of matter, 9:36 in which case, please tell me more about your workout schedule in the comments.

9:41 So in an infinite universe there would be infinitely many copies of you and 9:45 also versions with very small alterations. Somewhat more hair. Somewhat less brain. A 9:52 physics degree or a desire for mathematical self-torture, but then I repeat myself.

9:57 It’s not a new insight. To my best knowledge it was first discussed by George Ellis and 10:02 Graham Brundrit in 1979. George Ellis by the way is one of the people who I 10:07 interviewed about the multiverse for my first book. That an infinitely extended 10:12 universe would have infinitely many copies of each of us is often considered the simplest, 10:18 and least controversial type of multiverse.

She is correct that many astrophysicists accept this multiverse as so self-evident to be not controversial, and yet it is a crazy idea. There are not infinitely copies of each us, and it is almost meaningless to talk about such foolishness. The observable universe is finite, and does not include copies of yourself. Even if the universe were infinite, there is no reason to believe that all possibilities would be replicated indefinitely. You would have to assume that all possible conditions are being recreated infinitely. Any such talk is like theology -- beliefs that are not grounded in science.

She talks about the possibility of the universe being finite and closed, like a torus. Most models have an open spacetime where space has an infinite extent, but there might be only a bounded portion of it with matter in it. The unoccupied space beyond our observation is just a mathematical convenience, with no reality.