Main Question or Discussion Point
This may be a silly question, but how do we give a shape to the universe if it is The same from every point we look?
We dont give a shape.This may be a silly question, but how do we give a shape to the universe if it is The same from every point we look?
You could ask the same about the surface of the Earth, assuming it were ideally spherical. Its curvature can be defined by its being a 2D surface embedded in 3D space: i.e. it's the surface of a 3D sphere.This may be a silly question, but how do we give a shape to the universe if it is The same from every point we look?
It's flat on a large scale. But, locally, where there are galaxies, black holes or simply where there are stars or planets you have locally curved spacetime.I get the analogy of the Earth, but as regards to the universe what does flat mean, surly due to gravity and dark matter the universe must be globular, but how can that be flat?
Why it would be globular ? And how can it be globular and flat at the same time ?surly due to gravity and dark matter the universe must be globular, but how can that be flat?
Mathematically it means that curvature is zero, In example a plane is a flat becasue, when you set a triangle, and you measure the angles it gives you ##π##. But in spherical geometry it gives you more then ##π##.but as regards to the universe what does flat mean
But if the universe were a sphere, that would clearly imply a preferred direction and there is zero evidence of such a thing.The universe can have a spherical geomtery or it can be just flat as ours, but If its sphere the R (radius of the sphere) must be so huge that, we observe, the observable universe as flat.
No, it woudn't; there is no preferred direction in a 3-sphere. A 3-sphere is spatially isotropic.if the universe were a sphere, that would clearly imply a preferred direction
That's one of the biggest flaws of such analogies.Using the balloon analogy, what's inside the balloon skin? Is it the Universe from a moment ago?
Not as far as it goes, but in our real universe there are no "gods of mathematics" to tell us whether in fact we could see the same object in all directions if we could see far enough. And we have no evidence that we could. So we have no evidence that your play is describing our actual universe.Do you see any problem with its logic?
No, it is not true. The "point-like start" is an artifact of a particular class of idealized models. It is not a feature of our actual current best-fit model of the universe.Is it not true that the big bang thesis posits a point-like start to our universe
Nope. This argument also fails for the reason I gave above. Even if the "point" is actually a small region, it would have to be a timelike "world tube" (a small bundle of timelike worldlines) for your argument to be valid; but the "tube" occupied by, for example, the region of last scattering is spacelike, not timelike.Here is another neat topological way to convince yourself that the universe must have the topology of S³.
No, it isn't. You're leaving out the time dimension. Our observable universe back to the surface of last scattering is a 4-ball, not a 3-ball. More precisely, it's the past light cone of the Earth at its present point in spacetime, which is a 4-volume bounded by a spacelike surface in the past (the surface of last scattering) and a null cone whose apex is the Earth's present event.First, consider the universe starting with us now, extending out (and backward in time) to the surface S of last scattering (at which CMB was produced). We see this surface isotropically in all directions in microwave light. This is a 3-ball (the interior of a big 2-sphere plus boundary S).
You're not addressing my argument. My argument is not that you need to look at a larger "time slice" around the surface of last scattering. My argument is that your argument requires that the "point" or "region" (you are correct that it doesn't have to be a single spatial point) being looked at is timelike, not spacelike. Since the surface of last scattering is spacelike (as you agree), your argument does not apply to our observations of it.when we view the CMB, we are looking at a very narrow interval on the time axis, so I have treated this surface of last scattering (S) as a purely space-like surface, albeit at a particular time.
The surface of last scattering was a finite time ago, and light travels at a finite speed. That means we are only seeing a finite intersection of our past light cone with the surface of last scattering.Has this claim actually been verified
In other words, S is the surface of last scattering. If that is the case, then we have two 4-balls, separated by a spacelike 3-surface, yes. But you have not shown that that spacelike 3-surface is an ##S^3##. See below.We have a 4-ball bounded by a space-like S containing the (invisible) early universe. and another 4-ball containing the visible universe, also bounded by S.
Yes. But what topology does this 4-manifold have? You are claiming that it has topology ##S^3 \times R##; but you haven't shown that. See below.As before, we merge these two objects by identifying their common boundaries S. We now have a universe with one time dimension (t = 0 to now)
Nope. The construction of an ##S^3## by merging two 3-balls works like this: you have two 3-balls, each with a 2-sphere as a boundary. You identify the two boundaries and "glue" the two 3-balls together at their common boundary; the resulting manifold is then an ##S^3##.and whose spatial context is S³ (positive curvature, not flat).