If a universe is finite and is not expanding at a speed equal to or greater than c, what happens when light or another form of electromagnetic radiation traveling reaches the boundary?
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3$\begingroup$ "Bounded" and "has a boundary" are distinct concepts. You can have one without the other. $\endgroup$– zibadawa timmyCommented May 16, 2016 at 5:57
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$\begingroup$ That's my thoughts on this as well. The models that I know of for a bounded universe, it's curved in on itself, so light wouldn't reach a boundary but would ultimately travel back to where it started, but that would take a very long time. $\endgroup$– userLTKCommented May 16, 2016 at 7:59
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$\begingroup$ Thanks, zibadwa timmy. For the purposes of my question, does the distinction make a difference? I am not trained at all in astrophysics. $\endgroup$– gwofatlantaCommented May 16, 2016 at 9:42
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$\begingroup$ Thanks, userLTK. Can you point me to a layman's description of the models you refer to? $\endgroup$– gwofatlantaCommented May 16, 2016 at 9:45
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$\begingroup$ @gwofatlanta Yes, it makes a difference, as physical behaviors are linked to the geometry they occur in, and a "boundary" has dimension one lower than the rest of space. I feel like you're not the first person to make this mistake on this site, and some answers were given in an earlier case that addressed the mathematical distinction and some possible physical implications, but I haven't been able to find that Q&A so far. Maybe it got deleted or I'm picking the wrong search items... $\endgroup$– zibadawa timmyCommented May 16, 2016 at 11:41
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2 Answers
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One important concept that has not been mentioned yet is the "cosmological principle." This is the key simplifying idea for our cosmological models, it says that the universe is the same everywhere on the largest scales at a given age, so alien astronomers 50 billion light years from us that also conclude the universe is 13.8 billion years old will be observing pretty much all the same things we are. This principle is not proven by data, but the data is consistent with it, most notably the Hubble law and the homogeneity of the cosmic microwave background. It allows us to understand the past of our own part of the universe by seeing the past of distant parts (a constraint we are stuck with given the speed of light).
So that's why a universe model that is finite in size must curve back on itself-- nothing else would satisfy the cosmological principle. This doesn't mean the principle is true, it means we are not going to part with it unless we have to.
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$\begingroup$ "This principle is not proven by data"... No need to be so modest. No scientific statement can be proven by data (Karl Popper). $\endgroup$ Commented Dec 10, 2016 at 21:18
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This is one of the most essential questions in cosmology. The first gedankenexperiment probably. If the universe were finite what could be at the boundary? If there were some sort of wall, what would be on the other side? Can space just end? What would stop one from pushing past the end? If you extend your arm out past the end does your arm cease to exist? It is because we cannot provide any logically consistent answers to these questions that we accept that there are only two possibilities for the boundaries of the universe: 1) the universe is infinite and has no boundaries or 2) the universe is finite, but bends around and closes in on itself like the surface of a sphere and has no boundaries. That is, there are no boundaries. Alternative 2 then forces one to contemplate that there is at least one more dimension to space then the known 3.
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$\begingroup$ A finite universe with closed curvature does not require another dimension. It may help us to visualize the curvature to embed it in an imagined fourth dimension, but it is not necessary that the fourth dimension actually be there. $\endgroup$– Ken GCommented Dec 8, 2016 at 13:45
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$\begingroup$ @KenG I do agree with you. It is possible that Euclid's postulate for parallel lines is just wrong and the geometry of this universe simply is non-Euclidean. Or, the universe, if non-Euclidean in 3 dimensions, could be Euclidean in some higher dimension. $\endgroup$– eshayaCommented Dec 8, 2016 at 18:08
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$\begingroup$ Yes, I think the question is whether Euclid's parallel postulate is regarded as something that has to be true, so if it doesn't hold in 3 dimensions, there must be higher dimensions to embed those in. Or, if there is no reason why Euclid's parallel postulate needs to be true, then there's also no need to embed what we observe into anything we don't. The embedding can simply be regarded as a conceptual picture, to help a mind that relates to the parallel postulate, deal with a universe that doesn't. On the other hand, the universe does appear to be flat, after all. $\endgroup$– Ken GCommented Dec 10, 2016 at 22:17