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Comment by galaxyLogic | Hacker News Reader

Finally an explanation.

And there's a good metaphor: The surface of Earth has no center. Therefore we can imagine that space similarly has no center if we imagine it having 4 dimensions.

But what proof is there that universe is actually 4-dimensional? Or > 3 dimensional in general?

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In general relativity space-time is a 4-dimensional (3 space + 1 time) surface that itself can expand, contract, or move around. It's perfectly reasonable in GR to have a distance be L at time t, then L+dL at time t+dt. No extra spatial dimensions needed.

The thing is that you don't need to imagine extra dimensions. Th surface of a sphere remains 2-dimensional in this metaphor, even if the actual sphere is 3-dimensional. The Universe is not stretched on anything though, and whatever number of dimesion it exhibits, the stretching relies on them only.

The explanation isn't very satisfying to me. If you expand the surface of a sphere, you're still expanding a 2-manifold in 3 dimensions. When you expand the sphere, you're expanding into the empty part of 3-space.

You can describe any 2d shape using 3 dimensions, just imagine that it's set askew or bent. From the perspective of the inhabitant of such a flatland, it's undetectable and irrelevant. So is it from the perspective of the topology of the shape.

Describing the universe's shape is similarly done from within, so we can't see the outside and don't need any "outside" to see that the Universe is expanding. It's a description of how our 3d world is behaving, seen from within, and not relying on any "outside".

The word "expand" is not describing the exact same physical phenomenon as what we are used to seeing, because when we expand something, we typically cause it from the outside. That's why it can't be satisfying: it's a similar but different thing.

Right so the expansion of our 3-D universe would need to be happening into the 4th or more dimensions for the analogue to make sense. But is that really what they are saying that when cosmologists speak of the expansion of the universe they mean it is expanding to the other 3+ (spatial) dimensions?.

Note the title of the article "What is our Universe Expanding Into? Is it expanding into the 4th spatial dimension?

AIUI, strictly speaking, the universe could be "stretched on something". The manifold could be embedded in a higher dimensional space, like the 2D surface of a balloon being embedded in 3D space. However, the maths is the same whether it's embedded like that (in any of an infinity of possible ways) or the manifold is all there is. My understanding is that physicists assume the latter simply because there's no practical benefit to doing otherwise, rather than because they have any evidence the universe isn't embedded in a higher space.

(I believe this is a different thing to the various higher dimensional cosmological theories that exist - branes and the like - but such things are beyond me.)

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