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How does something infinite "expand" though? It's not expanding into anything, because it's infinite. I always hear "space itself is expanding" but how does t

How does something infinite "expand" though? It's not expanding into anything, because it's infinite. I always hear "space itself is expanding" but how does that work with topology? When you travel in a given direction you will arrive back where you started? Surely that "shape" or "object" or topology or whatever you want to call it has a volume, relative to something else, or it wouldn't be able to be calculated? As you can tell, I have no idea what I'm talking about but endlessly curious on this subject.

pdonis 3y ago
> How does something infinite "expand" though? Infinite things don't work like our ordinary intuitions expect. > I always hear "space itself is expanding" but how does that work with topology? The topology doesn't change as the universe expands. "Expanding universe" just means that a particular metric (geometry) is imposed on the topology. If you think of the spacetime of the universe as a stack of 3-dimensional spatial slices, "expansion" just means that a given pair of points in space gets further and further apart as you advance from slice to slice into the future. That is perfectly well-defined for infinite slices, even though it's hard to imagine intuitively. The math works just fine. > When you travel in a given direction you will arrive back where you started? No. That would be the case for a spatially finite universe with the topology of a 3-sphere. But our spatially infinite universe has the topology of Euclidean 3-space. > Surely that "shape" or "object" or topology or whatever you want to call it has a volume The spatial 3-volume of the universe is infinite. > relative to something else, or it wouldn't be able to be calculated? Not at all. The universe doesn't need to be embedded in anything else to have a well-defined volume.
photonic54 3y ago
>How does something infinite "expand" though? It's not expanding into anything, because it's infinite. I’ve found it easiest to think of this in one dimension first. Imagine a number line. It’s infinite in both directions, in the sense that you can move along it and never reach an end. Suppose we’re sitting at X=0 and look in the positive direction at X=1. That point is distance 1 away from us. Look the other way at X=-1, and that point is distance 1 away, too. Now let’s multiply the number line by 2. The point that used to be 1 is now 2, and 2 is now 4. 0.5 is now 1. Look in both directions, and it’s still infinite by the same definition; you can travel in either direction and never reach an end. We’re still at X=0 and look in the positive direction. The point that used to be 1 is now distance 2 away. Same with what was previously -1. There’s nothing special about the location at the origin either. If we had originally sat at X=10 and looked at X=11, we’d now be at X=20 and looking at X=22: a distance of 2 away. In this way, every point has an equal claim to being the “center of expansion.” In one dimension, this is equivalent to saying that “space expanded,” it was infinite before, and it’s infinite after expansion.

pdonis 3y ago

> How does something infinite "expand" though? Infinite things don't work like our ordinary intuitions expect. > I always hear "space itself is expanding" but how does that work with topology? The topology doesn't change as the universe expands. "Expanding universe" just means that a particular metric (geometry) is imposed on the topology. If you think of the spacetime of the universe as a stack of 3-dimensional spatial slices, "expansion" just means that a given pair of points in space gets further and further apart as you advance from slice to slice into the future. That is perfectly well-defined for infinite slices, even though it's hard to imagine intuitively. The math works just fine. > When you travel in a given direction you will arrive back where you started? No. That would be the case for a spatially finite universe with the topology of a 3-sphere. But our spatially infinite universe has the topology of Euclidean 3-space. > Surely that "shape" or "object" or topology or whatever you want to call it has a volume The spatial 3-volume of the universe is infinite. > relative to something else, or it wouldn't be able to be calculated? Not at all. The universe doesn't need to be embedded in anything else to have a well-defined volume.

photonic54 3y ago

>How does something infinite "expand" though? It's not expanding into anything, because it's infinite. I’ve found it easiest to think of this in one dimension first. Imagine a number line. It’s infinite in both directions, in the sense that you can move along it and never reach an end. Suppose we’re sitting at X=0 and look in the positive direction at X=1. That point is distance 1 away from us. Look the other way at X=-1, and that point is distance 1 away, too. Now let’s multiply the number line by 2. The point that used to be 1 is now 2, and 2 is now 4. 0.5 is now 1. Look in both directions, and it’s still infinite by the same definition; you can travel in either direction and never reach an end. We’re still at X=0 and look in the positive direction. The point that used to be 1 is now distance 2 away. Same with what was previously -1. There’s nothing special about the location at the origin either. If we had originally sat at X=10 and looked at X=11, we’d now be at X=20 and looking at X=22: a distance of 2 away. In this way, every point has an equal claim to being the “center of expansion.” In one dimension, this is equivalent to saying that “space expanded,” it was infinite before, and it’s infinite after expansion.