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You can think of the spatial geometry of the universe in one of three ways; a sphere, a flat sheet or shaped like an infinitely large saddle. In all cases there is no center.

If it is finite and spherical, how can it not have a centre?

Pete, as you rightly point out, the surface of a sphere has no central point. You also point out that this is an analogy and not a physical representation of the space. Would I be right in thinking that in order to apply this analogy to physical, 3D, space, the sphere would actually have to be a 4D hypersphere?

Pete, as you rightly point out, the surface of a sphere has no central point. You also point out that this is an analogy and not a physical representation of the space. Would I be right in thinking that in order to apply this analogy to physical, 3D, space, the sphere would actually have to be a 4D hypersphere? If so, this is where I run into difficulty. I cannot visualise a hypersphere, much less its 3D surface. As a result, useful though the analogy is in some respects, it fails me when I try to connect the dots to apply it to our Universe. I end up seeing a spherical (3D) Universe bounded by a (2D) surface.

Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre?

Quote from: Ron Maxwell on 13/08/2013 17:59:29Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre?Shape of the visible universe: spherical, 3 dimensional.Radius: About 13 billion lightyears.Center: EARTH.We don't know how big the unseen portion of the Universe is, and don't have a good idea to its form and shape. But, the visible portion is roughly a sphere with Earth at the center.

Quote from: Ron Maxwell on 13/08/2013 17:59:29Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre? But, the visible portion is roughly a sphere with Earth at the center.

Shape of the visible universe: spherical, 3 dimensional.Radius: About 13 billion lightyears.Center: EARTH

No joke--the Earth is very close to the center of the OBSERVABLE universe.

When I first tried to comprehend the topology of the universe as a potentially finite but non-bounded volume, I found it helped to think of the old arcade game of ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN, where whatever disappeared off the screen in one direction, reappeared on the opposite side, moving in the same direction - a finite but unbounded 2D surface.

With (hopefully) the intelligence to follow the arguments but not the education to understand the Maths, I go a bit lost with some of this. If the Big Bang theory is correct then surely the universe cannot be infinite.

Is Pmb correct that if it is infinite, it must always have been so?

The replies here seem to suggest the universe (or cosmos) is located on the edge of an expanding shape whether a sphere or not. I had imagined, wrongly it seems, that it was of a 3D form.

It's like the analogy to a balloon. Is the space within akin to the universe or is it the balloon?

Quote from: Ron Maxwell on 12/01/2015 04:04:29Is Pmb correct that if it is infinite, it must always have been so?Yes. But he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.

Quote from: JohnDuffield on 12/01/2015 19:54:14Quote from: Ron Maxwell on 12/01/2015 04:04:29Is Pmb correct that if it is infinite, it must always have been so?Yes. But he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand. I disagree.

Quote from: dlorde on 12/01/2015 12:58:44When I first tried to comprehend the topology of the universe as a potentially finite but non-bounded volume, I found it helped to think of the old arcade game of ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN, where whatever disappeared off the screen in one direction, reappeared on the opposite side, moving in the same direction - a finite but unbounded 2D surface.Right. It had the topology of a cylinder.

Here's something interesting. The space around a cosmic string is flat. The geometry is that of a cone.

Quote from: JohnDuffield on 12/01/2015 19:54:14... he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand. I disagree.

... he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.

I don't think that having an infinite universe would preclude expansion. Using JohnDuffield's logic, wouldn't the energy pressure also "cancel out" if the universe were finite and unbounded?

but the Universe isn't expanding into anything--it's just expanding. The space within it is growing.

I don't know how good an analogy gas pressure is to "energy pressure" (but if there is a reference that explains why it is a good analogy, please direct me there--I would rather be wrong now and right later!)

jeffreyH, what is your definition of infinity?

OK John define the pressure gradient of a black hole. Do it with mathematics and not mumbo jumbo.

jeffreyH, what is your definition of infinity? Is not the result of subtracting any number still infinity? How then can you get back to a 'big bang'?

As I understand it, there's no clear evidence to rule out the infinite hypothesis, so it must remain on the table (unless some new analysis has ruled it out).

Quote from: dlorde on 14/01/2015 10:45:13As I understand it, there's no clear evidence to rule out the infinite hypothesis, so it must remain on the table (unless some new analysis has ruled it out).I think the clear evidence that rules it out is the universe is expanding. An infinite universe can't expand because at every location the spatial pressure is counterbalanced on all sides. What surprises me is that people dismiss that, even though the stress-energy tensor has an energy-pressure diagonal. They don't say what's that all about? even when they've got a physics PhD.

And they never seem to notice that there's one hell of a problem reconciling big bang cosmology with a universe that's always been infinite.

Or that saying a flat universe is infinite is a total non-sequitur. Or that the infinite universe is just a turtles all the way down non-answer.

If the universe has mass, then there is a center of the total mass.

An infinite universe can't expand because at every location the spatial pressure is counterbalanced on all sides.

Quote from: jcccIf the universe has mass, then there is a center of the total mass.No. That is incorrect. Not only is it wrong but there is no justification in any sense for it to be right. That this is so follows from the fact that an infinitely large universe does not have a finite total mass. Consider an infinitely large sheet which has a uniform mass density. Such a sheet wouldn't have a center of mass.

Quote from: CliffordKShape of the visible universe: spherical, 3 dimensional.Radius: About 13 billion lightyears.Center: EARTHI assume this is a joke?

Quote from: jeffreyH on 13/01/2015 05:05:19OK John define the pressure gradient of a black hole. Do it with mathematics and not mumbo jumbo. Jeffrey: broadly speaking the pressure is proportional to the ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN where Kevin Brown says it's one of two alternative interpretations. He doesn't favour it, but I think it's right. Here's a depiction:

What do you want to bet Pete?

Quote from: jcccWhat do you want to bet Pete?I don't make bets on principle. State your argument and I'll show you where your error is.

I bet there is a center of the mass of the universe. Just for a dollar.