Through observation with the world's largest telescopes, It has been established that aside from small random deviations among the motions of individual galaxies, all galaxies appear to be receding from our location in the universe at speeds that increase in direct proportion to their distances from us. This observation has given rise to the concept of the Expanding Universe, now widely accepted among cosmologists. Attempts to explain these observations have given rise to what is now popularly known as the Big Bang theory of the origin of the universe.

This theory posits the universe as having suddenly come into existence at a single point somewhere in space a long way back in time and as having been expanding since then into the universe in which we find ourselves today. Modern physics has enabled cosmologists to run the picture backward in time to see how it seems to have all started. In this picture, we extrapolate current observational data back to a time when the entire universe was compressed into an almost inconceivably hot speck of pure energy. Via data extracted from an orbiting satellite called WMAP, standing for "Wilkinson Microwave Anisotropy Probe", it has proven possible to extract convincing evidence that this initial creation event occurred some 13.7 billion years ago. Only theologians suggest how this creation event might have come about.

In the following, I offer a description of the present SHAPE of the universe that seems consistent with observation. There is not and probably never will be any way to prove or disprove its validity.

The universe appears to be so vast that we can see only a tiny porton of it even with the largest telescopes that can ever be built. The part we see now appears to be homogeneous and isotropic. Homogeneous means essentially the same as viewed from anywhere in the universe. Isotropic means essentially the same no matter the direction from which it is viewed from anywhere in the universe. This also means that we do not envisage the universe as having a boundary beyond which there is nothing.

This raises two questions: (1) How can the universe have been expanding at only a finite rate of speed and for only a finite period of time without there being a boundary beyond which there is nothing? (2) In what direction in the night sky to look to see the point from which the universe burst into existence?

To understand what appears to be the only plausible answer to these questions, it helps to resort to analogy. Our universe appears to be three-dimensional. That is, at any point in space, there are just three directions: forward and backward, left and right, up and down relative to the direction in which you are facing. Suppose that instead of being three-dimensional, our universe were only two-dimensional, like the surface of a sphere, with the only directions being forward and backward, right and left, but no up and down. All objects in such a universe would be two- instead of three-dimensional. The earth would occupy a circular area on the surface of that sphere with no thickness whatever. We would exist as much smaller two-dimensional objects on the edge of the disk. Without mechanical aids, we could move only backward and forward along the edge of the disk. With aircraft, we could move only as far away from the edge of the disk as there existed air to support us. With spacecraft, we could leave the disk altogether and visit other worlds, also disk-shaped like the earth. With tunneling equipment, we could burrow slightly toward the center of the disk-shaped earth. But we could move neither toward nor away from the center of the sphere. We would, in fact, have great difficulty in even perceiving the possibility of there even being such a direction.

With two-dimensional telescopes, we could see that the universe contains all of the objects that we have found in our actual three-dimensional universe, but we would find them to be two-dimensional. We could also use the telescopes to discover that our two-dimensional universe was expanding because all galaxies seen through our telescopes would be seen as moving away from our own location. It would be very difficult for the inhabitants of our disk-shaped world to conceive of the possibility that our universe is merely the surface of an expanding sphere. They would tend to think that they lived on a flat infinitely large surface.

The second of the above lquestions was: In what direction must we look in the night sky to see the point from whichi the expansion of the universe began? The above analogs should lead us to the conclusion that the direction to that point is not anywhere in the night sky but in a direction in which we cannot point. It must correspond to the center of the sphere in the two-dimensional universe on the surface of the three-dimensional balloon. Inhabitants of that universe would not be able to look in the direction of the center of the sphere. They might learn that the center of their universe is at right angles to any direction in which they can look. through analogoius reasoning, we must conclude that the center of our universe is in a direction in which we cannot point and that that it is at right angles to any direction in which we can point. It is at the center of curvature of the three-dimensional "surface" of the four-dimensional hypersphere that comprises our universe.

They might, but what is the point? We don't live in 2-D but in a 3-D universe. Those of us who know about 3-D curved spaces (mostly mathematicians) can imagine that the universe is just such a closed curved 3-D space. Once I explained how it works in practice and if someone is interested I might do it again. I don't see many folks interested in this thread though.

I offered my contribution as a replacement for Dr. Gay's doughnut-shaped universe, which appears to be based on a misguided attempt to liken the shape of the universe to that of a modified 3-torus. In the latter, opposite faces of a cube are merely "glued" in the sense in which that word is used in topology. It appears to me that Dr. Gay sought, instead of gluing one pair of faces, to stretch the 3-torus along the normal to one pair of faces, then to bend that normal into a circle to join the faces, thereby producing a doughnut-like figure with a square cross section through the now-circular former normal. I described an analogical two-dimensional universe only as an aid to perception. It makes sense to me to suspect that the three-dimensional world that we experience is actually the three-dimensional "surface" of a four-dimensional hypersphere.

I feel that anyone who bought into Podcast 78 should be interested in this thread.

dcl

>It makes sense to me to suspect that the three-dimensional world that we experience is actually the three-dimensional "surface" of a four-dimensional hypersphere.>

Makes sense to me also.
We would be four dimensional except for the spin of the universe which squashes us
and all matter (flat) into three dimensions because of the centripetal force.This also explains gravity and why all masses accelerate at the same rate in a G field.

The problem with the hypersphere (as elegant as it is), is that over long distances, parallel lines would not remain parallel. The current evidence is the large scale structure of the universe is "flat" - that is to say parallel lines (in ALL directions) stay parallel. That is the evidence for the hypertorus over the hypersphere.

I do not pretend to understand the evidence. Superheroes who eat very scary math for breakfast have found it in the cosmic microwave background radiation. The very weird thang is that for this to be, means that the universe has just the right about of density of matter and energy to one part in sextillion!

Very, very strange and not what anyone expected.

I welcome JimLast's, Undidly's, and Vanamonde's comments. I'll respond to each:

Undidly: I am not aware of any basis for suspecting that the universe is spinning. There are no known phenomena that suggest that. Also, spin would not render an otherwise four-dimensional universe three-dimensional. Gravity is explained not by centripetal force but by the warping of spacetime in the manner described by the general theory of relativity. All masses accelerate at the same rate only within a volume of space in which the spacetime metric is uniform.

Vanamonde: I'm glad that you said that current evidence only indicates, not proves, that the universe is flat. WMAP has thus far been unable to detect any curvature. It is conceivable that it will detect a slight curvature after it has collected more data. Additional data has already refined the age of the universe from 13.7 to 13.73 billion years. It remains conceivable that lines that are parallel locally may converge at cosmological distances.

I am not aware of any valid argument for regarding the shape of the universe as like that of any kind of torus. As far as I am aware, only the three-dimensional "surface" of a four-dimensional hypersphere can model a finite homogeneous and isotropic universe in four dimensions. As for needing to eat very scary math for breakfast in order to understand how the universe can be as close to flat as it seems to be, it's sufficient only to recognize that a hypersphere expanding from a point in a four-dimensional space with a finite initial expansion rate and an always finite expansion rate may asymptotically approach flatness but cannot reach it within a finite time. I'm not so sure that we should not have expected the universe to have become very nearly flat over 13.7 billion years, especially after having started out with an inflation phase.

Not really. We just know that there must have been a very, very dense, hot phase in the early universe that was expanding and cooling rapidly. After three minutes, it was no longer hot enough to make helium out of hydrogen.

"Creation event" is certainly highly charged with religious overtones. Since we know so little about what's going on at t = 10^-44 sec., we can't rule out there was something going on before that..... so "creation event" may not be appropriate.

Scientific theories are not proven. They are supported by observations... or not.

__________________
Everyone is entitled to his own opinion, but not his own facts.

Thank you, Cougar, for your comments. My responses follow:

Are you comfortable with the idea that the original "creation" event (no religious overtones intended) could have occurred simultaneously at points separated by finite distances without violating causality considerations? If so, I would be interested in knowing how you defend your position. I'm willing to be corrected.

I agree with your comment about "creation" event. Can you suggest a better word for this context?

I agree that scientific theories are not proven. They are accepted by the scientific community only as long as they are not shown by new information to be invalid.

dcl

>Undidly: I am not aware of any basis for suspecting that the universe is spinning. There are no known phenomena that suggest that. Also, spin would not render an otherwise four-dimensional universe three-dimensional. Gravity is explained not by centripetal force but by the warping of spacetime in the manner described by the general theory of relativity.>

Visit the funfair centrifuge.Stand against the wall.Spin it up to a very high speed.
Now stand up at right angles to the spinning wall.Can't?.You are squashed into two dimensions.
A rubber wall would have dips (warping)where the mass is.Masses roll or slide into each others dips.The masses move together and appear to attract each other.Thats the two dimensional equivalent of gravity.

> All masses accelerate at the same rate only within a volume of space in which the spacetime metric is uniform.>

I mean different masses side by side accelerate at the same rate even though their masses are different.

It is true that a flat universe is one of sextillion other possibilities. But it doesn't have to be that way. Take out the possibilites that are dependant on the coupling of space and time, i.e. GTR solutions that are not flat and all you have left is flat .

But how do we justify eliminating curved space-time?

Gravity has a cause. If we knew the cause we would probably be able to determing the shape. Until then we have math that accounts for observations and predicts the effect of gravity but we have no cause.

When we don't know the answer, there are always sextillion possibilites. When we find out the answer then all but one were wrong. There is just one answer to the real shape of the universe and if it is flat there will be a new set of sextillion possibilites about just what flat means.

Thank you, Undidly and Bogle, for your comments. Following are my responses:

Undidly: You appear to believe that gravitation is caused by motion. It is not. It is fully accounted for by the field equations of Einstein's general theory of relativity. The presence of massive bodies distorts spacetime in their vicinity in a manner described by solutions to the Einstein field equations. This distortion in turn distorts the world lines of other bodies in the vicinity of the body causing the distortion. For example, it causes the planets of the solar system to orbit the sun in approximately elliptical paths.

Bogle: Your statement that "Take out the possibilites that are dependant on the coupling of space and time, i.e. GTR solutions that are not flat and all you have left is flat " is an example of circular reasoning. It is like saying that throwing away all of the items in a collection containing the item you want except the one you want will leave only the item you want, which is really too obvious to be worth mentioning, Would you like to try again to say whatever you were trying to say?

You asked, "How do we justify eliminating curved spacetime? The answer is that we cannot justify it. In fact WMAP measurements have been interpreted as eliminating it. My argument is I suspect that spacetime IS curved but so slightly that we have thus far not been able to detect the curvature.

You said, "Gravity has a cause. If we knew the cause, ---" We DO know the cause. See my second paragraph above, starting with "Undidly:".

Also, you seem to think that compressing a three-dimensional object can make it two-dimensional. Not true. No matter how thin you make a sheet of paper, it's still three-dimensional. A valid example of a two-dimensional object is a shadow: It has no thickness at all.

Hmm. So you are saying that the cause of gravity is:I don't see the cause there. Accounting for the effect of gravity mathematically and describing it as a distortion of spacetime which distorts world lines leads to the question of what causes the distortion. If you are saying that the distortion is caused by the field equations then I'm sure you see the error in your thinking. Equations don't distort space-time.Sorry, I don't follow how from what I said you arrive at a me suggesting that compressing a three-dimensional object can make it two-dimensional?

I'll try again to clarify for you the nature of gravity. First, I'll give you some necessary background. Then I'll try to respond to your specific questions and remarks.

Strange as it may seem, there is no such thing as a force of gravity! We used to think that the sun exerts a force on a planet. That's what Newton told us, and Kepler's laws of planetary motion describe the shapes of planetary orbits. That all changed in 1916 when Einstein came along with his General Theory of Relativity. This involves what are called the "field equations of general relativity", a set of ten tensor equations whose solutions describe distortions in the shape of spacetime caused by the presence of massive bodies such as the sun. Inputs to these equations are positions and states of motion of massive bodies such as the sun. The equations are based on a form of mathematics called "tensor calculus" and are notoriously difficult to derive and to solve for specific cases. Although I'm a physicist, solving them is far beyond my abilty since I've never had anyneed to learn how to solve them. When applied to the sun, they yield solutions that describe the shape of spacetime in the vicinity of the sun. These solutions can be used to derive "geodesics" for specific masses such as planets initially at specific locations and moving in specific directions with specific speeds in this distorted spacetime. The geodesics describe the paths that other bodies will follow in the neighborhood of the mass causing the distortion of spacetime.

Now I'll respond to your specific questions and remarks:

Question: What causes the distortion?
Answer: The presence of mass causes the distortion. If space were empty, that is, contained no mass, it would be "flat", meaning no distortion. Light rays would always follow straight paths. Hopefully, you are aware that one of the three crucial tests of general relativity was the observed bending of light rays as they pass close to the sun during total solar eclipses. This bending is caused by expansion of space itself close to large masses. The same effect casues the "lensing" of distant galaxies that brings into view objects hidden behind those galaxies so that they would otherwise not be visible to us.

Remark: Equations don't distort space-time.
Response: Equations describe warpage of spacetime, It's presence of mass that causes it. I hope the above description made this clear.

Bogie: Sorry, Bogie, I erroneously attributed to you a remark that I should have attributed to Didly. Sorry.

Didly. Please note that it was to you that I intended to address my remark about three versus two dimensions. Your remark was:

Visit the funfair centrifuge.Stand against the wall.Spin it up to a very high speed.
Now stand up at right angles to the spinning wall.Can't?.You are squashed into two dimensions.
A rubber wall would have dips (warping)where the mass is.Masses roll or slide into each others dips.The
masses move together and appear to attract each other.Thats the two dimensional equivalent of gravity.

My intended response was:

Also, you seem to think that compressing a three-dimensional object can make it two-dimensional. Not
true. No matter how thin you make a sheet of paper, it's still three-dimensional. A valid example of a two-
dimensional object is a shadow: It has no thickness at all.

What I dont get here is that it is possible to draw parallel lines on the surface of a balloon? Do we have proof that there are not any possible ways to draw non parallel lines in 4d space time? In fact I believe that einstein wrote about worm holes which in theory could create non parallel lines.

To have a spin, you have to have a centerpoint (an axis of rotation). The universe by definition is that all points are equal. There is no center AND everywhere is the center. Therefore the universe cannot spin.

S3 is "parallelisable"; make of that what you will.

Thank you, tommac, EvilEye, and agingjb, for your comments. My responses follow.

tommac: Parallel lines CAN be drawn on the surface of a balloon. For example, lines of latitude on the earth are parallel.

It is true that parallel STRAIGHT lines cannot be drawn on the surface of a sphere because only great circles are straight lines, and great circles necessarily intersect. It is true that straight lines on the surface of a balloon necessarily intersect.

I'm not aware that Einstein wrote about worm holes. Other theorists discussing Einstein's general theory of relativity wrote about worm holes. It is easy to create non-parallel lines. Any pair of intersecting lines is nonparallel. For example, every line of constant latitude on earth intersects every line of constant longitude.

EvilEye: You are right in saying there has to be an axis of rotation in order for something to spin.
There are no bases for your other statements. Saying them does not make them true.

agingjb: I do not understand what you are trying to say.

dcl

Bogie: Sorry, Bogie, I erroneously attributed to you a remark that I should have attributed to Didly. Sorry.

Didly. Please note that it was to you that I intended to address my remark about three versus two dimensions. Your remark was:

Visit the funfair centrifuge.Stand against the wall.Spin it up to a very high speed.
Now stand up at right angles to the spinning wall.Can't?.You are squashed into two dimensions.
A rubber wall would have dips (warping)where the mass is.Masses roll or slide into each others dips.The
masses move together and appear to attract each other.Thats the two dimensional equivalent of gravity.

My intended resp