It is said there is no central point to the universe. It all started inflating 14 bya and that elides the concept of a center.

I get that there isn't a centerpoint in the sense of the point of an explosion, with velocity taking everything away from that point. Space is inflating rather than objects rushing away.

But isn't there an outer edge to the expansion? A sort of surface of an expanding balloon?

Aren't there points in the universe where if you look one way, you see the void, you look 180 degrees opposite, you see beau-coup galaxies?

Suppose you have a "cube" with opposite faces identified, i.e. a 3D torus.



Where is the centre? Where is the boundary?

Am I to take from this that the universe should be thought of as a surface rather than a volume or something?

I can see how if the universe is a surface, then a center is arbitrary. But how is that right?

My mind insists the universe is an expanding sphere, not the surface of a cube.

Proceeding...

If two quanta of light (our points) are the maximum distance of any points in the universe, they are both on the boundary (though it be expanding).

A point equal distant of these two is the center.

The example I gave is 3D and has volume. It's not the surface of the cube, it's the whole cube but with opposite surfaces identified.

The 2D version is a square with opposite edges identified. Like in a video game where if you go up through the top you come out through the opposite place on the bottom. The game is taking place in a 2D torus, i.e. the surface of a doughnut.



Think of the cube example as a 3D version of this.

Just Google e.g. 3D Asteroids and play that to get the idea. (I'd link one, but I don't know which are safe, and I'm no good at getting them to work anyway.) Must be a bunch of games which take place in a 3D torus.

Op made me think of this image that Krauss uses



Top two images show expansion left to right.
The following two images show that no matter what two corresponding points you choose, all the other points look like they are moving away and the ones twice as far are moving faster and so on.

No, all the galaxies are like spots on the surface of a balloon, and you can only look at the surface, you can't look inside the balloon or away from the balloon. The surface of the balloon itself already represents all 3 spatial dimensions, unlike an actual balloon whose surface only represents 2 dimensions (latitude and longitude). If you could look inside or away from the balloon, that would be a 4th dimension, but it's not necessary for that 4th dimension to actually exist. IOW, space doesn't have to be expanding "into" anything as a balloon expands into space. It's just expanding. That is, galaxies that are far enough apart are getting even farther apart over time.

There are other issues with the balloon analogy. One is that it suggests space is curved outward and back on itself. The actual universe is flat over large distances as far as we can see, and we don't observe that it curves back on itself, though it's possible that it could outside our observable universe. There is no evidence that it acts like asteroids where you go out one side and pop back in the other side. So it's more like a very large balloon that's flat as far as we can see, or you could think of it as a flat rubber sheet, possibly infinitely large, but still stretching to cause galaxies to get farther apart. Another issue is that the big bang shouldn't be thought of as happening at the center of the balloon. Nothing inside the balloon has any meaning. Instead, light from the big bang can be seen coming from every direction.

In that case we are the center of the universe. Jumpin' Jehovah! Case closed.

No really, my head just exploded a little bit, or expanded if you will

So there's something very funky and unintuitive about the nature of space and I'm probably not going to get it.

Can you describe an aha! moment where you got it?

Bruce, how can space be "flat," as you say, but the expanding universe not have a leading-edge boundary? If we see nothing but galaxies anywhere we look, that suggests to me some sort of curving back.

And is it forbidden to think of the universe from a metadistance, like it is one universe that popped into existence and is expanding, among many others to be seen from a god's eye?

I've decided to take the balloon analogy a step further. The universe behaves like a giant, extremely soft, balloon(like a balloon that has lost most of it's air). The balloon is so big that on the small scale it is flat and behaves like the rubber mat analogy for gravity. Small gravitational forces bend the surface of the balloon but do not change the overall shape of the balloon. Large gravitational forces on the other hand have a direct affect on the shape of the balloon. The balloon has to stretch to balance the pressure. So, the expansion of the universe is a direct result of matter/gravity becoming more concentrated on the smaller scale. The expansion of the universe and dark energy are just the air in the balloon. The transmission of information from other places on the balloon are limited by the speed of light. Since the observable universe expands based on the r^3 the expansion is accelerating.

That is the universe in my head.

It may just be a simplified reality that my brain can understand but the model does produce some interesting relationships between the amount of observable gravity and the expansion rate.

To me, the universe is more than the matter (of all types) in it.

So, in the universe I'm thinking of, there are no boundaries to IT, just to the matter that's in it, and of course, that matter is expanding outward at this point.

To me, the universe itself is infinite, and the Big Bang happened in IT. But, that could be wrong, I'm sure.

Anyhow, from the standpoint of an infinite universe, there wouldn't be a center. And, of course, there would likely be more than one Big Bang if you consider a Big Bang as being matter related and not universe related.

My head exploded once.

Space isn't flat. It is flat enough though.

Yes. Or, rather, there is no way to think of it in a reasonable way from an outside the universe sort of position. From such a point of view it would look like a ham on rye with a dab of mustard that is oozing out of one of the corners due to bad deli workmanship or something else entirely. I'm quite certain of that. Most likely the "something else entirely" thing, of course.

Think of the balloon analogy that Bruce gave and imagine that you can only see things that are on the balloon and have no ability (at all, in any way) to look through the balloon or outside the balloon and the only way to get around is by following the surface of the balloon. How far would the farthest point be from you from your point of view? Half the circumference of the balloon, of course. Now picture yourself standing on a different part of the balloon. The furthest point from you would be equal to half the circumference of the balloon. No matter where you stand, it appears as if you are in the middle of everything else.

Really, when it comes down to it, it is no different than how your average teenager thinks of him/herself in relationship to the rest of the world. That might be an easier analogy.

A plane is flat, but it has no boundary. If you had an infinitely large piece of rubber with spots on it, it could still be stretching to cause the spots to become farther apart.

By flat we mean that it obeys regular Euclidean geometry like you learned in high school. That implies that every triangle has angles that sum to 180 degrees, and the ratio of the circumference to the diameter of a circle is pi. That's not true on a surface with curvature. On a surface that curves outward like a sphere, called positive curvature, every triangle has angles that sum to more than 180 degrees, and the ratio of the circumference of a circle to it's diameter is only 2. For example, consider the equator. The diameter of that circle goes over the north pole because that's the shortest distance, and it is half the length of the circumference. On a surface that curves inward like a saddle, called negative curvature, the sum of the angles of a triangle are always less than 180 degrees, and the ratio of the circumference of a circle to its diameter is greater than pi.

All these surfaces are 2-dimensional even though we think of them existing in a 3-dimensional space. These same possibilities for flat, positive curvature, and negative curvature exist for a 3-dimensional space which we can think of as existing within a 4-dimensional space, though it isn't necessary for a 4th spatial dimension to actually exist. That's hard to visualize, which is why we rely on mathematics to think about such things. If you think about taking that flat plane and rolling it up, you get a cylinder that is infinite in one dimension, and finite in another, but it still has flat geometry. If you then join the ends, you get a doughnut shaped thing called a torus, and that's still flat. You needed 3-dimensons to actually make it. If you had 4-dimensions, you could do another step where you join the inner surface of the torus to the outer surface which is hard to visualize, but that's one possibility for a flat but finite universe. There is also a possibility for a universe that has positive curvature, like one shaped like a soccer ball or dodecahedron. There is also a possibility for a universe with negative curvature shaped like a horn.

Note that none of these have a boundary, and there is no center. Curvature can be measured by the density of matter. The fact that we see galaxies in every direction approximately uniformly distributed actually leads to the conclusion that the curvature is constant, and that leads to a model in which there is no boundary.

There are cosmologists who believe there is evidence for each of these possible geometries from the cosmic microwave background radiation. However, we know that our observable universe is flat to within 0.5%. If the curvature is too slight, we may never be able to detect it, and we may never be able to determine which of these geometries the global universe has. We may never know if it's finite or infinite. However, there are clues that we look for that could provide evidence for the various geometries. For example, a finite geometry could produce multiple images of the same galaxies if the light had time to circumnavigate the universe, and a doughnut shaped universe would have different path lengths that light could travel to arrive back at the same place.


Yes, there are such theories of a multiverse. Some even believe there is evidence of that in the cosmic microwave background where dark spots indicate that our universe collided with other universes. But even if there aren't other universes per se, if ours is infinite, then there are effectively infinitely many universes that can never interact with ours because they're expanding away from us faster than the speed of light. In fact, if the universe is truly infinite, there should be universes exactly like ours that formed just by random chance. Max Tegmark has estimated that our closest doppelganger universe would be 10^10^115 light years away. That's more than a googolplex light years.

Correction: Tegmark's estimate was 10^(10^115) meters to next universe (Hubble volume), not light years. He says that's an extremely conservative estimate, and that the nearest copy of you is likely to be much closer than 10^(10^29) meters away. Here's one of his papers where he says things like this that will interest some of you:

"This raises an interesting philosophical point that will
come back and haunt us in Section VB: if there are
indeed many copies of “you” with identical past lives and
memories, you would not be able to compute your own
future even if you had complete knowledge of the entire
state of the cosmos! The reason is that there is no way
for you to determine which of these copies is “you” (they
all feel that they are). Yet their lives will typically begin
to differ eventually, so the best you can do is predict
probabilities for what you will experience from now on.
This kills the traditional notion of determinism."


Here's his website with more papers about other types of parallel universes.

I'm playing with a new visualization. I get how in the horizontal plane along the surface of an expanding balloon, there is no center. So I try to imagine we are also located on another balloon surface perpendicular to the first. The up/down dimension is also a balloon. So whether we look sideways or up, there is no center.

So although locally space is flat and right angles have 90 degrees, at the macro level there is a sense in which the universe must curve. Is that correct?

Maybe the universe is a balloon, but we're on the inside of it.