SCIENCE (said in a deep, meaningfully spooky voice)

[Ekona]

So if the universe is flat, then it has an edge, correct? Which I'm assuming to be the furthest point that matter has travelled since the Big Bang.

So how is that possible if matter would have been flung across three axis? Surely everything we know about matter and physics leads us to believe that the universe cannot be flat?





If none of that makes sense, you will now understand why I have kept out of this thread until now

[Tinlad]

Flatness doesn't imply an edge.

Another way to think about flatness is to consider what happens if you hold two lasers parallel to each other and turn them on. In a flat spacetime geometry, the two laser beams are forever parallel: they never converge or diverge. In a universe with positive curvature, the beams converge. With negative curvature, they diverge.

So if spacetime is flat, there you could have an infinite universe without an edge. This is unlikely.

But! There are other geometries for the universe that allow for a flat spacetime without edges or infinities. The most likely is a torus (doughnut). The surface of a torus is 'flat' - parallel lines never meet. But there are no edges either - if you keep travelling in one direction you just end up back where you started!

So the universe is probably flat, with spacetime bounded into a torus shape.

I realise this is probably not a great explanation. I'll try and do better if you want! Because I love this shit.

[Ekona]

Ah, okay, the doughnut thing is a great way to explain it, ta

Although I then get very confused as clearly things cannot be travelling straight if they then bend to meet up with each other again...

[Tinlad]

This image might help:

The gridlines on the surface on the torus are x,y coordinates in space. Follow any line and you're travelling in a straight line in our familiar x,y coordinate system, but you eventually end up back where you started due to the toroidal shape. Pick any two adjacent lines and follow them: they never converge or diverge (the lines don't cross), so it's a flat spacetime.

This is a 2D/3D analogy for a 3D/4D reality - which is why it's difficult to imagine!

[Polito45]

I realise this is probably not a great explanation. I'll try and do better if you want! Because I love this shit.

Au contraire mon ami - you explain it extremely well.

I may be a bit thick (shut up! ) but I find I need to "feel" something in my bones before I can understand it.
I've read one book on relativity 7 times in an effort to comprehend on a human level what "spacetime" actually means in reality.
I'm getting there, I rekcon 40 or so more times will be the charm.

Anyway, could it be that spacetime appears flat because the actual universe (as opposed to the observable universe) is of such an enormous size?
I mean the way say Britain for example appears flat on the surface of the earth when you're walking around on it because the earth is so big,
but the same landmass stretched over the moon would be more obviously curved.

I've read that conservative estimates for the rate of expansion of the universe during the first fractions of a second of the rapid phase of expansion after the big bang would mean that what the observable universe is to the actual universe would be like what a grain of sand is to the observable universe.
My maths is truly terrible but the conservative figure I remember seeing was something like a factor of whatever the number was to a power of 10 - but the expansion rate could have been as much as to a power of 90.

So could the universe just be so big that spacetime appears flat to us?

[Tinlad]

I've spent days thinking about this one, and how best to answer it.

I think the answer is 'unlikely', for the following reason:

The experimental value we have for the density parameter, Ω, (which is our measure of curvature) is based upon measurements of the composition of the observable universe in terms of matter, dark matter and dark energy. This data comes from measurements of the cosmic microwave background (CMB) by probes like NASA's WMAP.

You could say "But that's only the observable universe! How do we know the rest of it is the same?".

The CMB is a snapshot of the observable universe following the period of exponential expansion (10^78 times increase in volume!) just after the Big Bang. This period of inflation was so rapid that it left different areas of the universe causally disconnected from each other: two regions can be so far apart, and the expansion of the space between them so fast, that light from one region will never reach the other!

I realise that this only seems to reinforce the problem, not help to solve it.

But let's go back to before the inflation. The universe was much smaller. We expect that matter, DM and DE are homogeneously distributed; all the theory for how it came to be in the first place implies that this should be the case. So when inflation happens, what we end up with is a universe that is homogeneous and isotropic (essentially the same wherever you are). The uniformity of the CMB, and the motions and distributions of galaxies don't give any indications that there is anything happening on a larger scale.

So we've no reason to believe that we would measure anything different if we could look on a larger scale. But I guess another question is: if it's causally disconnected from us anyway, does it even matter?

[Polito45]

Yes, I understand the idea of regions of the universe being causally disconnected from each other because nothing, no signal of any kind can ever travel between them and that galaxies can be traveling away from each other at faster than the speed of light - but that's not just because of their intrinsic rate of speed, it's also because of the rate of expansion of spacetime between them.

My problem with the idea of spacetime being flat is that spherical seems to be the default shape for all other conglomerations of matter within the universe. Where matter is effected by gravity the most economical shape is - a ball. Stars are round, planets are round, moons are round etc.

The CMB data shows that the distribution of matter in the early universe was extremely even, so surely that means that it was even in every direction?
I guess I hate the idea of the universe being flat because I can't get my head around that. I'd rather believe that the universe is a very, very large ball and it's just so big that when we look around us at the puny bit that we can see - it appears flat.