# Thread: The shape of our universe..

1. I just watched a program on documentary channel, where this guy who hardly knew anything bout maths was gettin taught bout prime numbers and other such stuff..
They got to a question where the teacher was like "If you get this question right, you'll get \$1million bux" I thought that was a simple question to answer...

Well I'll tell you their answer first, they said it was like a 4D donut. (I won't bother explaining what a 4D donut is like but I guess a lot of you have heard or something like it..)

My simple answer would of been endless for a universe, or a near sphere shape for the end of the material universe.

I don't see how they could come up with anything else, in the donut you could reach the "end" of the universe and if you pass that point you'll end up on the other side of the universe and you could pretty much travel till you reach the point where you left off on your journey...

Where on mine you could reach the end of the material universe which is most likely material which has been thrown further out into space by a recent supernova or even further if your counting how far light as traveled since the first star was born (which would still be traveling today.. at the speed of light).
If you could pass that then you'll reach a part of the universe which has nothing and will go on forever in deep darkness.

I think I should of gotten that million dollars.. What are your thoughts?

2.

3. I think you are confusing the absence of any material thing with the absence of space-time. Most people do. It is confusing.

Welcome to the forum.

4. The doughnut shape, called a torus I believe, is the 3-dimensional analogue of 4-dimensional, negatively curved space/time, just like a sphere is the 3D analogue of positively curved space/time and a flat sheet is the 3D analogue of flat space/time.
The positively curved is finite but unbounded while the flat and negatively curved are infinite and unbounded.
Another 3D example of negative curvature is a saddle, which is equivalent to a section of the inner part of a doughnut.
Simple geometric properties. In negative curvature the sum of the angles of a triangle are less than 180 degrees, for flat, or Eucledian, they add to exactly 180, and for positive curvature they add to more than 180 degrees.

You cannot visualise the actual 4-dimensional shapes but you can easily describe them with math. We can hoever visualise in 3 or less dimensions. For example, how would the 2-dimensional inhabitants on a flat sheet of paper visualise a pencil?
Intersect the pencil with the sheet of paper (poke it through) and you get a 2-dimensional circle, ie a cross-section of the pencil. But the pencil's length is in a dimension that the paper's inhabitants cannot visualise. That is the same problem we have with 4D space/time.

5. The hypersphere (a 4D sphere) works best for an expanding universe. The 4D doughnut shape would have anomalies that we would be able to see.

6. Originally Posted by xspike
I just watched a program on documentary channel, where this guy who hardly knew anything bout maths was gettin taught bout prime numbers and other such stuff..
They got to a question where the teacher was like "If you get this question right, you'll get \$1million bux" I thought that was a simple question to answer...

Well I'll tell you their answer first, they said it was like a 4D donut. (I won't bother explaining what a 4D donut is like but I guess a lot of you have heard or something like it..)

My simple answer would of been endless for a universe, or a near sphere shape for the end of the material universe.

I don't see how they could come up with anything else, in the donut you could reach the "end" of the universe and if you pass that point you'll end up on the other side of the universe and you could pretty much travel till you reach the point where you left off on your journey...

Where on mine you could reach the end of the material universe which is most likely material which has been thrown further out into space by a recent supernova or even further if your counting how far light as traveled since the first star was born (which would still be traveling today.. at the speed of light).
If you could pass that then you'll reach a part of the universe which has nothing and will go on forever in deep darkness.

I think I should of gotten that million dollars.. What are your thoughts?
The topology of the universe is inknown.

This is an open question and NOBODY kinows the aanswer.

7. Originally Posted by Cyberia
The hypersphere (a 4D sphere) works best for an expanding universe. The 4D doughnut shape would have anomalies that we would be able to see.
Whatever the answer is it is not a 4D anything.

The question of the shape of the universe is itself based on some idealizations and then on general relativity.

Recall that in general relativity what we have is a curved 4-dimensional Lorentzian manifold in which the very notions of space and time are intertwined. Space and time are purely local. There is no global notion of time and no global notion of space either. But cosmology needs some sort of global notions for both space and time nevertheless.

What is observed is that on the largest scales, and only on the largest scales, the universe seems to be the sane at all places and in all directions. This is called homogeneity and isotropy. The assumption that the universe is homogeneous and isotropic is called the "cosmological principle".

So cosmologists make the assumption that the cosmological principle is valid and then apply general relativity to model the large-scale structure of the universe. The assumption of homogeneity and isotropy results in solutions (not explicit closed form solutions but a categorization of possibilities) of the Einstein field equations that permit a decomposition of 4-dimensional spacetime as a 1-parameter foliation of 3-dimensional space-like hyperspaces of constant curvature. That parameter serves as a surrogate for "time. The question of the shape is then a question as to the topology of the hypersurfaces, which are what one calls "space", which is 3-dimensional.

And the answer is that absolutely no one knows the answer.

It is not even known whether space is compact (closed) or non-compact (open).

8. I dont see how the universe goes out for infinity if its currently expanding

how does something that already continues without stopping, expand, it just doesnt make sense to me :?

9. Originally Posted by james43
I dont see how the universe goes out for infinity if its currently expanding

how does something that already continues without stopping, expand, it just doesnt make sense to me :?
Expansion has nothing to do with being finite or infinite.

If you can imagine an infinite sheet of rubber being stretched you can imagine an infinite universe expanding. Or just think of what happens if you look through a variable power binocular and reduce the magnification -- things appear to spread appart.

10. Having just finished 'Cycles of Time' by Penrose - the current thoughts are that the universe is sort of bell shaped with the last bit of the 'bell' flaring off to infinity.

No 'big crunch' is needed as in the latter stages, the universe will be composed of
photons and gravitons. Nothing will have any mass and the universe will become
'conformally invariant' which mathematically is a valid state from which the next
big bang can occur thus the universe cycles through aeon after aeaon indefinately.

I had to read the book twice - I'm not too hot on the calculus

11. DrRocket. I admire the certainty with which you speak even if I don't agree with what you say.

Ignoring the nonsense about time being the fourth dimension (from maths and the Dr Who TV programme), if the universe has just 3 physical dimensions then we can trace the big bang back to it's origin by simply following everything backwards over time. All very large things are spherical as it is the most gravity efficient shape so why should not the universe be?

How would expansion work in a 3D universe? Here's how it works in a 4D universe (on which our universe is the 3D skin on a 4D hypersphere): Imagine a number of 10 feet long needles (10 meters say for those who like metric). They are joined at their points and face outwards in various directions. You now have a balloon six feet across with represents the universe at time A. Where these needles penetrate the balloon is where there are galaxies.

Now at time B, the balloon is 12 feet across but the needles all still penetrate the balloon in exactly the same place. The galaxies have not moved but the distances between them has grown. At time C, the balloon is now 18 feet across and the galaxies are much further apart, but all in exactly the same position with the needles still held steady and penetrating them exactly as before.

The universe is anything but smooth.

http://www.atlasoftheuniverse.com/superc.html

It is full of huge voids, walls of galaxies, and so on. These in some cases go back to the very earliest times in our universe, and to say that tiny perturbations in the BB expansion produced them just does not work because in expansion there is no bias. Flip a coin ten times and it is possible that you will have ten heads or ten tails or anything in between. Flip it a million or billion times and you will get about 50% heads and 50% tails. So with expansion and it's contents. They would balance out without any need for inflation.

The universe is open as in if the universe was much smaller than it originally was and expansion was less powerful than it now is and that did not stop the universe from expanding, it is not going to happen when the universe is far, far bigger. It's like having an ever faster expanding solar system and you ask at 5 billion miles across if it will shrink when it did not do so at 1 billion miles in diameter.

12. Originally Posted by james43
I dont see how the universe goes out for infinity if its currently expanding

how does something that already continues without stopping, expand, it just doesnt make sense to me :?
Indeed, you are getting something for nothing, if you have ever increasing dark energy with a universe going to ever higher energy levels.

There is also the problem that if something expands, it should become less energetic as in a gas cooling down as it expands. This could be explained by the temperature dropping from near infinite to 2.7K, but this happened at the earliest times in the universe when it was still very tiny, and the universe has expanded zillions of times since then and the temperatures at the earliest times are the same as now for space away from any star's heat.

A problem here is that space is said to actually have substance, similar to the Victorians idea of the aether. It can be stretched, curved, whatever. Not just a little but infinitely. The same area of space can be stretched from an atom's width to a galaxy's width, and still remain exactly the same. Others say that new space is being created but this is just an empty idea because it does not tell us how or where the material/energy is coming from.

on another forum I asked what space was and after many, many posts did not get any ideas. Space is whatever is required of it, it seems. However to me space is literally nothing, given reality only by what occupies it, so while occupying no area originally, it has infinite potential.

13. Originally Posted by Cyberia
DrRocket. I admire the certainty with which you speak even if I don't agree with what you say.

Ignoring the nonsense about time being the fourth dimension (from maths and the Dr Who TV programme), if the universe has just 3 physical dimensions then we can trace the big bang back to it's origin by simply following everything backwards over time. All very large things are spherical as it is the most gravity efficient shape so why should not the universe be?

How would expansion work in a 3D universe? Here's how it works in a 4D universe (on which our universe is the 3D skin on a 4D hypersphere): Imagine a number of 10 feet long needles (10 meters say for those who like metric). They are joined at their points and face outwards in various directions. You now have a balloon six feet across with represents the universe at time A. Where these needles penetrate the balloon is where there are galaxies.

Now at time B, the balloon is 12 feet across but the needles all still penetrate the balloon in exactly the same place. The galaxies have not moved but the distances between them has grown. At time C, the balloon is now 18 feet across and the galaxies are much further apart, but all in exactly the same position with the needles still held steady and penetrating them exactly as before.

The universe is anything but smooth.

http://www.atlasoftheuniverse.com/superc.html

It is full of huge voids, walls of galaxies, and so on. These in some cases go back to the very earliest times in our universe, and to say that tiny perturbations in the BB expansion produced them just does not work because in expansion there is no bias. Flip a coin ten times and it is possible that you will have ten heads or ten tails or anything in between. Flip it a million or billion times and you will get about 50% heads and 50% tails. So with expansion and it's contents. They would balance out without any need for inflation.

The universe is open as in if the universe was much smaller than it originally was and expansion was less powerful than it now is and that did not stop the universe from expanding, it is not going to happen when the universe is far, far bigger. It's like having an ever faster expanding solar system and you ask at 5 billion miles across if it will shrink when it did not do so at 1 billion miles in diameter.
Apparently you don't know what in the hell you are talking about -- your post is complete nonsense and contrary to observation and current cosmological models..

You don't know what I was talking about either -- which is what the current best cosmological theory tells us.

I did NOT say that the universe (aka spacetime) is 3-dimensional. According to the best available theory, general relativity, it is in fact a 4-dimensional Lorentzian manifold. If one makes the approximation that is usually made by cosmologists, that spacetime is homogeneous and isotropic then spacetime decomposes as a 1-parameter foliation by 3-dimensional spacelike hypersurfaces. Those hypersurfaces turn out to be of constant curvature.The parameter serves as a SURROGATE for time -- but is not really time as we know it on earth.

You can mathematically model "following things back in time" using that parameter, and that is exactly what Hawking and Penrose did in their singularity theorems to conclude that a big bang is dictated by general relativity.

There is no reason to conclude that the hypersurfaces are spheres. That is possible, but so are other topologies. The current prevailing opinion is that the hypersurfaces are not compact, but no one really knows. Spheres are compact.

To understand the origin of lumpiness (galaxies and such) you need to understand the theory of inflation. It is not confirmed, but a lot of evidence supports it. See for instance The Inflationary Universe by Alan Guth. It in no way contradicts the general relativistic model of the universe as a smooth (i.e. differentiable) manifold.

The fact that you disagree is of zero consequence. Go do some reading and learn the basics.

14. wow

15. Originally Posted by nancy3412
wow
Yes, Dr. Rocket often produces that effect. It comes from a combination of high intellect, great experience and questionable social skills.

16. Originally Posted by Ophiolite
Originally Posted by nancy3412
wow
Yes, Dr. Rocket often produces that effect. It comes from a combination of high intellect, great experience and questionable social skills.
You forgot intent and utter disdain for fools.

17. Originally Posted by DrRocket
You forgot intent and utter disdain for fools.
No. I deliberately omitted them to give you a further moment in the sun.

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