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dcl
2008-Mar-23, 12:30 AM
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.

JimJast
2008-Apr-11, 12:25 PM
[...] 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.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.

dcl
2008-Apr-12, 01:00 AM
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.

undidly
2008-Apr-12, 01:58 AM
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.

Vanamonde
2008-Apr-12, 08:53 AM
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.

dcl
2008-Apr-12, 06:22 PM
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.

Cougar
2008-Apr-12, 10:03 PM
This theory posits the universe as having suddenly come into existence at a single point somewhere in space a long way back in time...

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.


...this initial creation event occurred some 13.7 billion years ago.

"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.


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.

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

dcl
2008-Apr-13, 01:48 AM
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.

undidly
2008-Apr-13, 01:20 PM
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.

Bogie
2008-Apr-13, 01:56 PM
...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.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.

dcl
2008-Apr-13, 06:04 PM
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.

Bogie
2008-Apr-13, 06:49 PM
You said, "Gravity has a cause. If we knew the cause, ---" We DO know the cause. See my second paragraph above, starting with "Undidly:".Hmm. So you are saying that the cause of gravity is:
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.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.


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.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?

dcl
2008-Apr-13, 09:02 PM
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.

dcl
2008-Apr-13, 09:23 PM
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.

tommac
2008-Apr-14, 07:08 PM
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.





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.

EvilEye
2008-Apr-14, 09:23 PM
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.

agingjb
2008-Apr-14, 09:32 PM
S3 is "parallelisable"; make of that what you will.

dcl
2008-Apr-14, 09:51 PM
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.

undidly
2008-Apr-16, 01:09 AM
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 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.
Reply With Quote>>>>>>>>>>>

I already thought there was a small mix up.

The funfair centrifuge is just an analogy.In the real 3D universe everything is just waves and eddies in/on the 3D surface,mostly just in 3D but gravity is at right angles to these 3 directions and is the gradient of the slope around a mass.
Why would mass cause a dip in the 3D surface?.

Objects are not 4D squashed into 3D.Objects are made of 3D.

A shadow is as thick as the distance from the shadow side of an object to the surface on which the shadow is cast.A shadow not only has thickness,
it has volume.Normal geometry is sufficient to work out the volume,H*W*D.

Check out the shadow with a probe.It goes all the way from the object to the
surface.Some would say it even passes through the probe.Check this with a smaller probe behind the first probe.The shadow is still there.

Bogie
2008-Apr-16, 01:18 AM
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.Don't get me wrong, your description of what we know about the effect of gravity is nearly perfect. But the effect of gravity and the cause are not the same.

Per your description, gravity is:
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.
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.
The equations are based on a form of mathematics called "tensor calculus" and are notoriously difficult to derive and to solve for specific cases.
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.
The presence of mass causes the distortion.

If I remove that purely mathematical statements from your explanations above we get:

The presence of massive bodies distorts spacetime in their vicinity.
This distortion in turn distorts the world lines of other bodies in the vicinity of the body causing the distortion.
The presence of mass causes the distortion.

Nothing in your explanation says how mass distorts spacetime.

We agree that the presence of mass causes gravity. You describe the effect of gravity as a distortion of spacetime. I am asking how mass distorts spacetime? Is spacetime actually something physical or some form of energy (http://www.jb.man.ac.uk/news/binary/) that is distorted by mass? There is an active search for the cause, possible gravitational waves that draw energy from mass to cause gravity. It is possible that your description of the effect of gravity will be found to be caused by the "graviton", the missing particle in the Particle Model (http://particleadventure.org/frameless/chart.html).

I hope this helps.

dcl
2008-Apr-16, 06:31 AM
Thank you, undidly and Bogle, for your comments. I'll respond to each of you in turn. In an effort to keep it clear to what I am responding, l'll first quote the paragraph to which I'm responding, starting each sentence on a new line with a short indentation, and then present my response, if any, on that sentence, starting on the next line with an longer indentation.

undidly:

The funfair centrifuge is just an analogy.
In the real 3D universe everything is just waves and eddies in/on the 3D surface,mostly just in 3D but gravity is at right angles to these 3 directions
and is the gradient of the slope around a mass.
I do not understand what you are trying to say. Surfaces in a 3D domain are not waves and eddies and are two-dimensional, not three-dimensional.
Gravity is toward the center of the astronomical body on the surface of whiich is the object is casting a shadow.
Why would mass cause a dip in the 3D surface?
I do not understand what you are trying to say. What dip? Surfaces are two-dimensional.
Objects are not 4D squashed into 3D.
I do not understand what you are trying to say..
Objects are made of 3D.
I do not understand what you are trying to say unless you are trying to say that objects in a three-dimensional space are three-dimensional, which is
true.
A shadow is as thick as the distance from the shadow side of an object to the surface on which the shadow is cast.A shadow not only has thickness, it has
volume.Normal geometry is sufficient to work out the volume,H*W*D.
You seem to be defining a shadow as the three-dimensional space between an object casting a shadow and the shadow itself. That is not the usual
definition of a shadow. It you want to define it that way, you need to say so.
Check out the shadow with a probe.It goes all the way from the object to the surface.Some would say it even passes through the probe.Check this with a
smaller probe behind the first probe.The shadow is still there.
The same comment on the last sentence also applies to this one. I'd like to be able to respond to the questions you have in mind, but it's not clear to
me what they are. I suggsst that you try to state them more clearly.

Bogle: I have no problem with anything you said. Mostly, it was a reiteration of what I said. Toward the end, you asked questions to which I can respond, so I'll start there. I'll respond in the same way in which I responded to Undidly's statement.

I am asking how mass distorts spacetime?
The Einstein field equations describe how mass distorts spacetime. They don't explain how it does it. All we can do is observe that it happens and
describe it. There's a lot we don't know about why things happen.
Is spacetime actually something physical or some form of energy that is distorted by mass?
Spacetime is physical. It is not a form of energy. The structure of spacetime is distorted by the presencer of mass. It is stretched and bent. Empty
space isn't merely nothing. Recent findings that the expansion of the universe is expanding are interpreted as evidence that spacetime itself contains
energy. That same energy may be what caused inflation during the first moments in the Big Bang and was apparently rleased when a phase change
occurred in the nature of space itself, somewhat analogous to when occasionally happens when water in a microwave oven is superheated well above its
boiling point and a slight disturbance suddenly causes the whole mass to explode into superheated steam.
There is an active search for the cause, possible gravitational waves that draw energy from mass to cause gravity. It is possible that your description of
the effect of gravity will be found to be caused by the "graviton", the missing particle in the Particle Model.
I'm not aware that there is an active search for the explanation for why the presence of matter causes spacetime to become distorted. I'm not saying
there is no such search; I'm merely not aware of any. Gravitational waves certainly do draw energy from the motion of mass. Stationary mass does not
produce gravitational waves. Mass that is merely moving at constant speed produces gravitational waves in a way analgous to the way a ship produces
waves or a supersonic aircraft produces shock waves that we hear as sonic booms. The hypothetical graviton would be the "carrier" of "gravitational
force", which itself is f fiction since there is no such force, which is a weird statement in itself because use "gravity" is one of the four basic forces that
are said to "freeze out" during breakdown of "grand unificaation" during the early stages of the Big Bang. What you said about the graviton is ocnsistent
with current thinking. The graviton isn't the only missing particle: There's also the Higgs boson. which is believed to relsponsible for matter having mass
and which the Large Hadron Collider at Cern is expected to find this year.

dcl
2008-Apr-16, 07:05 AM
Thank you, undidly and Bogle, for your comments. I'll respond to each of you in turn. I'll respond sentence by sentence with each labeled to indiccate who said it.

undidly: The funfair centrifuge is just an analogy. In the real 3D universe everything is just waves and eddies in/on the 3D surface,mostly just in 3D but gravity is at right angles to these 3 directions and is the gradient of the slope around a mass.

dcl: I do not understand what you are trying to say. Surfaces in a 3D domain are not waves and eddies and are two-dimensional, not three-dimensional. Gravity is toward the center of the astronomical body on the surface of whiich is the object is casting a shadow.

undidly: Why would mass cause a dip in the 3D surface?

dcl: I do nott understand what you are trying to say. What dip? Surfaces are two-dimensional.

undidly: Objects are not 4D squashed into 3D.

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

undidly: Objects are made of 3D.

dcl: I do not understand what you are trying to say unless you are trying to say that objects in a three-dimensional space are three-dimensional, which is true.

undidly:: A shadow is as thick as the distance from the shadow side of an object to the surface on which the shadow is cast.A shadow not only has thickness, it has volume.Normal geometry is sufficient to work out the volume,H*W*D.

dcl: You seem to be defining a shadow as the three-dimensional space between an object casting a shadow and the shadow itself. That is not the usual definition of a shadow. It you want to define it that way, you need to say so.

undidly: Check out the shadow with a probe.It goes all the way from the object to the surface.Some would say it even passes through the probe.Check this with a smaller probe behind the first probe.The shadow is still there.

dcl: The same comment on the last sentence also applies to this one. I'd like to be able to respond to the questions you have in mind, but it's not clear to me what they are. I suggsst that you try to state them more clearly.

Bogle: I have no problem with anything you said. Mostly, it was a reiteration of what I said.

dcl: Toward the end, you asked questions to which I can respond, so I'll start there. I'll respond in the same way in which I responded to Undidly's statement.

Bogle: I am asking how mass distorts spacetime?

dcl: The Einstein field equations describe how mass distorts spacetime. They don't explain how it does it. All we can do is observe that it happens and describe it. There's a lot we don't know about why things happen.

Bogle: Is spacetime actually something physical or some form of energy that is distorted by mass?

dcl: Spacetime is physical. It is not a form of energy. The structure of spacetime is distorted by the presencer of mass. It is stretched and bent. Empty space isn't merely nothing. Recent findings that the expansion of the universe is expanding are interpreted as evidence that spacetime itself contains energy. That same energy may be what caused inflation during the first moments in the Big Bang and was apparently released.when a phase change occurred in the nature of space itself., somewhat analogous to when occasionally happens when water in a microwave oven is superheated well above its boiling point and a slight disturbance suddenly causes the whole mass to explode into superheated steam.

Bogle: These is an active search for the cause, possible gravitational waves that draw energy from mass to use gravity. It is possible that your description of the effect of gravity will be found to be caused by the "graviton", the missing particle in the Particle Model.

dcl: I'm not aware that there is an active search for the explanation for why the presence of matter causes spacetime to become distorted. I'm not saying there is no such search; I'm merely not aware of any. Gravitational waves certainly do draw energy from the motion of mass. Stationary mass does not produce gravitational waves. Mass that is merely moving at constant speed produces gravitational waves in a way analgous to the way a ship produces waves or a supersonic aircraft produces shock waves that we hear as sonic booms. The hypothetical graviton would be the "carrier" of "gravitational force", which itself is f fiction since there is no such force, which is a weird statement in itself because because "gravity" is one of the four basic forces that are said to "freeze out" during breakdown of "grand unificaation" during the early stages of the Big Bang. Whatt you said about the graviton is ocnsistent with current thinking. The graviton isn't the only missing particle: There's also the Higgs boson, which is believed to relsponsible for matter having mass and which the Large Hadron Collider at Cern is expected to find this year.

agingjb
2008-Apr-16, 07:42 AM
S3, a four-dimensional hypersphere, is special as a topological object. It is "parallelisable", and I hope that there is a topologist around who can explain this properly.

This does mean that families of great circles can be placed on S3 so that they do not intersect; this is unlike the surface of a sphere, S2, where any two distinct great circles must intersect. I don't know whether this has relevance to the apparent flatness of space on the large scale.

(And BTW the this doesn't happen with any higher dimensional hyperspheres, with the exception of S7.)

dcl
2008-Apr-16, 04:08 PM
Thank you, agingjb, for your comment. It appears to me that you are conversant with the science of topology. I am only vaguely aware that there is such a discipline, and would like to know more. I gather from what you said that standard nomenclature in topology defines S3 as the three-dimensional "surface" of the four-dimensional analog of the three-dimensional sphere whose surface and volume under the same scheme would be designated as S2 and V3, respectively and that the substance of your message is that parallel lines do not intersect in the S3 space comprising the "surface" of a 4D hypersphere. I do not find that surprising because my intuitive expectation is that such lines would be analogous to lines of constant latitude on earth, would be circles lying in parallel planes both in a plane parallel to a great circle through the center of the hypersphere analogous to the equatorial plane on earth.

On the other hand, I would expect that circles equivalent to great circles on earth would intersect. I would be interested in your view on this. It seems to me that there may bes a problem with regarding concentric circles as parallel lines even though they remain equidistant along their entire lengths.

In seeking understanding of your references to S3. I found Internet site

http://www.geocities.com/aletawcox/Sunset.htm

that seems to lend credence to my conjecture as to the meaning of S3 as the term in topology for the three-dimensional "surface" of a four-dimensional hypersphere. It appears to me that I would benefit from studying that reference.

agingjb
2008-Apr-17, 08:06 AM
Yes, the hypersphere S3 is the "surface" of a four dimensional "volume". I'm not a topologist, but such reading as I've done does suggest that the space we can see could be a very small part of something with that topological structure (there are other possibilities). Whether that is significant is another question, that I couldn't begin to answer.

As for the special nature of S3, again I have no idea whether it's anything more than a mathematical curiosity.

dcl
2008-Apr-17, 05:09 PM
Thank you, agingjb, for your comments. My response follows:

You seem knowledgeable on he subject under discussion, so it's a pleasure to discuss it with you. I agree that the geometry of the universe MAY resemble that of the four-dimensional hypersphere for which I have argued but that there are other possibilities. I'm following the Occam's Razor approach in tentatively adopting the least complicated geometry that seems to fit the observational data. Others have argued for more esoteric models and, for all I know, one of them may be right. But as for doughnuts, dodecahedrons, 3-tori, etc., they seem to me to fail the Occam's Razor test rather miserably. It appears that the microwave background radiation, apparently having arisen from hydrogen nuclei capturing electrons 13.7 billion years ago, came from the most distant part of the Universe that we can see now and that the universal expansion has been carrying the source of that radiation away from us ever since at such a rate that that source is now 78 billion light years from us, making that the radius of the currently observable universe. In view of the fact that WMAP has thus far not been able to detect any curvature in the enclosed space, we can confidently say that the Universe is very much larger than this, but we have no idea how much larger. It seems to me that it cannot be infinite since the rate of expansion has presumably been finite throughout a finite period of time.

Steve Limpus
2008-Apr-17, 10:21 PM
Hi DCL

Just a minor correction (and I only point it out because I was confused myself as to the various figures one sees quoted, until I checked it out thoroughly).

Scientists currently consider that the CMBR was emitted 13.7 billion years ago (380,000 years after the Big Bang), when the surface of last scattering was roughly 40 million light years away (or less roughly 42 million light years away in some literature). The photons travelled 13.7 billion light years to reach earth, and the co-moving distance to the surface of last scattering is now 46 billon light years away. The diameter of the observeable universe is hence 92 billion light years.

The red-shift of the CMBR is said to be z=1100, and I've seen it reported that this infers that the observable universe is hence 1100 times larger now, than it was then. Since this is consistent with the most reliable figures reported otherwise, I assume that this is a straight-forward mathematical ratio, but, since I'm not mathematically trained (just a cosmology 'enthusiast') you'd be best to have this confirmed by someone more qualified.

The 'surface of last scattering' can be considered as the inner surface of an expanding sphere of space from which the CMBR was emitted when electrons and protons combined to form hydrogen atoms and allowed photons to travel freely through space.

I like the image here (http://www.astronomycafe.net/qadir/q2191.html).

You can think of the CMBR in terms of look back distance (we see it 13.7 billion light years away, expanding by one light year every year) or in terms of its comoving distance (the distance it has been carried by the expanding universe).

I have no scientific justification for the following: but I also favour the concept of the universe being a hyper-sphere, albeit very large. One can see how nature favours circles, spheres and globes; so it just feels like that is how things should be.

78 billion light years is a term that came, I think, from a paper into examination of the CMBR for clues to the possible complex topology of a 'compact' universe, that was widely mis-reorted. It's also interesting to note no clues were found. You might find this thread (http://www.bautforum.com/questions-answers/71556-center-universe.html) interesting, where the paper is discussed in some detail.

dcl
2008-Apr-18, 03:35 AM
Thank you, Steve Limpus, for your comment. My response follows:

Can you cite the source of your statement that the distance of the surface of last scattering is now 46 billion light years?. The diameter of the observeable universe is hence 92 billion light years." The distance to the surface of last scattering is for all practical purposes that to the source of the CMBR. The only figure I have seen for the current distance of the source of the CMBR is the 78 billion light years cited by Dr. Gay in Podcast 79 and for which she cited no source. I merely cited her figure, assuming it to be valid.

A measured value of 1100 for the cosmological red shift of the CMBR would imply that the radius of the universe is in fact 1100 times what it was when the CMBR that we are measuring now was emitted. The numerical value for a cosmological red shift is merely the ratio of the red-shifted wavelength to the intrinsic wave length less 1, and for a red shift said to have a value of 1100, the "less 1" can be ignored.

Your definition of "surface of last scattering" is correct.

The very last sentence in the text in the item that you referenced via hypertext made a slight error: Space has an additional attribute that the text overlooked: It also has dark energy, which, unlike dark matter, is regarded as a property of space itself as opposed to something that space contains.

I fully endorse the following slightly modified version of dang58103's statement "The center of the universe is a point in a four-dimensional space that we, along with the rest of the universe, are constantly moving away from" at the beginning of the thread that you cited. Much of the remainder of that thread strikes me as a mixture of uninformed juvenile speculation and gibberish.

Steve Limpus
2008-Apr-18, 06:36 AM
Can you cite the source of your statement that the distance of the surface of last scattering is now 46 billion light years?. The diameter of the observeable universe is hence 92 billion light years."

http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf


Currently observable light that has been travelling towards us since the beginning of the universe was emitted from comoving positions that are now 46Glyr from us.

http://www.spaceandtechnology.com/universe_size.htm


The comoving distance from the Earth to the edge of the visible universe (also called cosmic light horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction. This defines the comoving radius of the observable universe. The observable universe is thus a sphere with a diameter of 28-29 billion parsecs (9294 billion light-years). Since space is roughly flat, this size corresponds to a comoving volume of about 3.5610^80 cubic meters.

For example, the cosmic microwave background radiation that we see right now was emitted about 13.7 billion years ago by matter that has, in the intervening time, condensed into galaxies. Those galaxies are now about 46 billion light-years from us, but at the time the light was emitted, that matter was only about 40 million light-years away from the matter that would eventually become the Earth.

http://en.citizendium.org/wiki/Universe#Size


The observable (or visible) universe, consisting of all locations that could have affected us since the Big Bang given the finite speed of light, is certainly finite. The comoving distance to the edge of the visible universe is about 46.5 billion light years in all directions from the earth; thus the visible universe may be thought of as a perfect sphere with the Earth at its center and a diameter of about 93 billion light years.

http://www.deepastronomy.com/hubble-deep-field.html


I've recently read a paper in the Physical Review Letters (2004) which uses WMAP data to put some size constraints on the size of the universe. According to the paper, the universe is probably no smaller than 46.5 billion light years. http://arxiv.org/abs/astro-ph/0310233

http://home.earthlink.net/~mrob/pub/math/numbers-16.html


Current estimate of the distance to the edge of the visible universe, in light years (in Planck units it is a much more impressive 8.021060). The matter that produced the cosmic background radiation, emitted 13.7 billion years ago, has subsequently traveled away from us (while forming into galaxies) and is now about 46.5 billion light years from us. This is a "comoving distance".

http://www.reference.com/search?q=observable%20universe


The comoving distance from the Earth to the edge of the visible universe (also called cosmic light horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction. This defines the comoving radius of the observable universe. The observable universe is thus a sphere with a diameter of 28-29 billion parsecs (9294 billion light-years).

http://www.symmetrymagazine.org/cms/?pid=1000303


The universe is expanding at the same time light travels through it. So by the time light from the cosmic microwave background reaches us, it has been travelling for approximately 13.7 billion years but the point of origin is now much further away. The distance (more specifically, the co-moving radial distance) is actually about 14,000 Megaparsecs, or about 46 billion light years. You can check this for yourself: visit www.astro.ucla.edu/~wright/CosmoCalc.html and plug in z=1100 for the redshift to the cosmic microwave background.

http://en.wikipedia.org/wiki/Observable_universe


The comoving distance from the Earth to the edge of the visible universe (also called cosmic light horizon) is about 14 billion parsecs (46 billion light-years) in any direction.[4] This defines a lower limit on the comoving radius of the observable universe, although as noted in the introduction, it's expected that the visible universe is somewhat smaller than the observable universe since we only see light from the cosmic microwave background radiation that was emitted after the time of recombination, giving us the spherical surface of last scattering (gravitational waves could theoretically allow us to observe events that occurred earlier than the time of recombination, from regions of space outside this sphere). The visible universe is thus a sphere with a diameter of about 28 billion parsecs (about 92 billion light-years).

Many secondary sources have reported a wide variety of incorrect figures for the size of the visible universe (including) 78 billion light-years. This is a lower bound for the size of the whole universe, based on the estimated current distance between points that we can see on opposite sides of the cosmic microwave background radiation, so this figure represents the diameter of the sphere formed by the CMBR. If the whole universe is smaller than this sphere, then light has had time to circumnavigate it since the big bang, producing multiple images of distant points in the CMBR, which would show up as patterns of repeating circles.[10] Cornish et al looked for such an effect at scales of up to 24 gigaparsecs (78 billion light years) and failed to find it, and suggested that if they could extend their search to all possible orientations, they would then "be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter". The authors also estimated that with "lower noise and higher resolution CMB maps (from WMAP's extended mission and from Planck), we will be able to search for smaller circles and extend the limit to ~28 Gpc."[2] This estimate of the maximum diameter of the CMBR sphere that will be visible in planned experiments corresponds to a radius of 14 gigaparsecs, the same number given in the previous section.

Steve Limpus
2008-Apr-18, 06:39 AM
dcl,

I was rather hoping you would find my posts in the thread I linked to interesting or useful. We were faced with the problem of conflicting popular press reports, so went to the source of those articles quoting 78 Glyrs: a series of papers by Neil Cornish. We found the figure related to the lower bound of a multiply connected manifold, of the sort that would allow one to 'see around the universe to the back of your head'. The figure does not refer to the radius, nor the diameter, of the observeable universe:


I've had another crack at these two articles:

http://arxiv.org/PS_cache/astro-ph/p.../0604616v1.pdf

My bold.


"The full sky search for back-to-back and almost backto-
back matching circles was performed in Ref. [4], and
it is apparent in Figures 3 and 4 of that paper that no
statistically significant matches were found.
A simulation of the CMB has been produced [4] that
includes all relevant physics, using model parameters that
give a good match to the real CMB power spectrum, but
with a non-trivial topology built in. This 3-torus universe
with a fundamental domain that fits inside the sphere of
the CMB is used to test the search codes. The results of
the back-to-back search on the simulated 3-torus universe
indeed show peaks in the matching statistic, indicating
matched circle pairs (Ref. [4], Figure 1). The fact that
the results of the same back-to-back and nearly back-toback
searches of theWMAP data show no such peaks can
be used to place a lower limit on the size of our Universe."


"The null result of the search for matching circles in
the CMB indicates that the fundamental domain of the
Universe must be at least on order the size of the surface
of last scatter. The fact that the false positive line intersects
the maximum peaks expected for the matching
statistic at α = 20◦ means that the fundamental domain
must be big enough such that only circles smaller than
20◦ could be produced by intersections of copies of the
CMB. This, along with the best fit values for the other
cosmological parameters, places a lower bound on the size
of the Universe at 24 Gpc."

"There are a couple of techniques that can be applied
in an attempt to extend this bound beyond 24 Gpc (or
possibly detect the topology of the Universe, lurking just
below the current false positive threshold)."

"The previous limit of 24 Gpc [4] can be extended by about
10% using filtering of theWMAP power spectrum. A full
search with optimal filtering is now underway."

...and this one, which in part addresses confusion around this figure of 78 or 156 billion light years being the size of the universe, and the diameter of the observable universe or particle horizon, and the surface of last scattering:

http://en.wikipedia.org/wiki/Observable_universe#Size


"The comoving distance from the Earth to the edge of the visible universe (also called cosmic light horizon) is about 14 billion parsecs (46 billion light-years) in any direction. [Here they cite Lineweaver and Davis - my note.] This defines a lower limit on the comoving radius of the observable universe, although as noted in the introduction, it's expected that the visible universe is somewhat smaller than the observable universe since we only see light from the cosmic microwave background radiation that was emitted after the time of recombination, giving us the spherical surface of last scattering (gravitational waves could theoretically allow us to observe events that occurred earlier than the time of recombination, from regions of space outside this sphere). The visible universe [to be internally consistent this should read observable universe - the 'visible' universe is smaller - my note] is thus a sphere with a diameter of about 28 billion parsecs (about 92 billion light-years)."

Edit: Even this is a little ambiguous - if you search wikipedia for 'cosmic light horizon' which they infer is the same as 'visible' universe, it simply links back to 'observable' universe. I'm taking the view they mean the particle horizon, the distance a particle could in theory have travelled since t=0, is 92 Gly; and the surface of last scattering something less. If anyone has info to the contrary, please chip in.

"78 billion light-years... is a lower bound for the size of the whole universe, based on the estimated current distance between points that we can see on opposite sides of the cosmic microwave background radiation, so this figure represents the diameter of the sphere formed by the CMBR. If the whole universe is smaller than this sphere, then light has had time to circumnavigate it since the big bang, producing multiple images of distant points in the CMBR, which would show up as patterns of repeating circles.[10] Cornish et al looked for such an effect at scales of up to 24 gigaparsecs (78 billion light years) and failed to find it, and suggested that if they could extend their search to all possible orientations, they would then "be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter". The authors also estimated that with "lower noise and higher resolution CMB maps (from WMAP's extended mission and from Planck), we will be able to search for smaller circles and extend the limit to ~28 Gpc."

"156 billion light-years [has been widely reported as the size of the universe]. This figure was obtained by doubling 78 billion light-years on the assumption that it is a radius. Since 78 billion light-years is already a diameter, the doubled figure is incorrect [11] [12] [13]."

The way I read this is (only) if the fundamental domain of the universe is smaller than the co-moving diameter of the surface of last scattering (which is less than 92 billion light years), we expect matching circles in the CMBR. We've not found them so far with a margin of error (due to the accuracy of the data/analysis) such that we infer the fundamental domain of the universe is greater than 78 billion light years. The next round of research will have a higher resolution and will set a lower bound of greater than 86 billion light years, if no matching circles are found.

This lower bound for the fundamental domain is necesarily less than the diameter of the surface of last scattering, as otherwise we would not expect matching circles and the experiment would be moot.

The lower bound for the size of the entire universe, should the fundamental domain be larger than the surface of last scattering, remains the co-moving diameter of the observable universe, the particle horizon - 92 billion light years.

BTW, the formula for the particle horizon is here:

http://www-astro.physics.ox.ac.uk/~s...s/formulae.pdf

This was the next post I hoped you might enjoy:


the clincher for me is that if they had decided the lower bound for the fundamental domain was a diameter of 156 Gly - there would be no point to the "full search with optimal filtering". If the fundamental domain is larger than the surface of last scattering, there won't be any matching circles. The only way the paper makes sense to me is if the lower bound is a diameter of 78 Gly.

That bound was set because they didn't detect circles with a diameter greater than twenty degrees. With the optimal filtering they expect to be able to detect circles smaller than twenty degrees and push the lower bound closer to the surface of last scattering, assuming they don't actually find the circles. Once the lower bound diameter equals 92 Gly, this line of enquiry is exhausted as I see it.

I should say I don't understand the detail of what a 'twenty degree circle pair' means, but I'm reasonably confident I've got the gist of it as it applies to this dilemma.

And of course, now the terms 'observable' and 'visible' universe are bothering me with respect to how they are used in the wiki arcticle - I think there is an equally valid argument that they mean the surface of last scattering is a diameter of 96 Gly and the particle horizon somewhat larger. For now I'm running with the other interpretation. It's probably a touch semantic, but these are just the burrs that get under the saddle of my borderline obssesive complusive personality.

(My wife just says I'm mental - what can ya do?)


"A simulation of the CMB has been produced [4] that
includes all relevant physics, using model parameters that
give a good match to the real CMB power spectrum, but
with a non-trivial topology built in. This 3-torus universe
with a fundamental domain that fits inside the sphere of
the CMB is used to test the search codes. ...
.... This, along with the best fit values for the other
cosmological parameters, places a lower bound on the size
of the Universe at 24 Gpc."

That line "The null result of the search for matching circles in the CMB indicates that the fundamental domain of the Universe must be at least on order the size of the surface of last scatter" bothers me too. It doesn't really fit either scenario - one is a fair amount smaller, the other quite a bit a larger, so I don't see where 'on the order of' fits. It would suit what I think they mean about the expected results of the filtered search - but that's not what it says...

And of course, this one:


From Neil Cornish in letters from 2004:

http://www.physics.montana.edu/facul...h/PRL01302.pdf

"Has this search ruled out the possibility that we live in
a finite universe? No, it has only ruled out a broad class of
finite universe models smaller than a characteristic size.
By extending the search to all possible orientations, we
will be able to exclude all topologies out to 24 Gpc.
More directed searches can extend the result for specific
manifolds somewhat beyond 24 Gpc. With lower noise
and higher resolution CMB maps (from the extended
mission of WMAP and from Planck), we will be able to
search for smaller circles and extend the limit to
28 Gpc. If the universe is larger than this, the circle
statistic will not be able to constrain its shape."

Cornish is saying here the 'manifold' is 24 Gpc - I would take that as the entire topological space that is connected and locally Euclidean. In other words the diameter rather than the radius. I think the reason he doesn't use the word 'diameter' is that he is generally talking about a 3torus or other topology and 'diameter' is not the correct terminology. But I'm feeling even more confident he is referring to the entire space.

This from an even earlier paper, from the time of COBE:

http://arxiv.org/PS_cache/astro-ph/p.../9906401v2.pdf


"Our main focus will be on universes with compact hyperbolic
spatial sections [8] as these are the most appealing
from a theoretical standpoint. However, the growing
body of observational evidence favouring a flat universe
with a cosmological constant [9] prompts us to reconsider
models with three-torus topology. We refer to a model
as being “small” if its comoving spatial volume is less
than the comoving volume enclosed by the particle horizon
(measured in the covering space). The ratio of the
horizon volume to the volume of the space exceeds 500 for
several of the models we looked at. Small universe models
are obtained from the usual FRWmodels by making identifications
between different points in space. These identifications
break global isotropy and homogeneity, but
do not alter the evolution history. There is one caveat to
the last statement: by altering the mode spectrum, the
topological identifications will alter the vacuum structure,
leading to a Casimir-like vacuum energy that could
alter the dynamics. If an effective cosmological constant
could be linked to the universe having non-trivial topology,
we would have a strong motivation for re-considering
flat models."

"Returning to the compact hyperbolic models, we want
to see if the ISW effect ruins the the matched circle
test [2] for non-trivial topology. The matched “circles in
the sky” occur wherever the surface of last scatter selfintersects.
Since the surface of last scatter is a 2-sphere,
the intersections occur along circles. We see two copies
of each circle of intersection, centered at different points
on the sky. The portion of the microwave temperature
coming from the surface of last scatter will be identical
around each circle. However, the ISW contribution will
be uncorrelated.
Taking one realization of the Weeks universe (Figure
6), we find the temperatures around a pair of matched
circles (Figure 7a) and see that the match is poor. However,
the ISWeffect only operates on large angular scales,
so we filter Figure 6 to remove all power below ℓ = 21.
The temperature match for the filtered sky is shown in
Figure 7b. The correlation coefficient [3] increases from
0.29 to 0.92 after filtering out modes with ℓ ≤ 20. The
matched circle pairs will persist until the visible universe
is simply connected, which occurs at around o = 0.95
for most models in the SnapPea census. If we do live in
a small universe, the Microwave Anisotropy Probe will
find matched circles in the sky when it starts collecting
data in 2001".

I think Cornish's papers are consistent that the lower bound he refers to is less than the surface of last scattering.

I regret you found that:


Much of the remainder of that thread strikes me as a mixture of uninformed juvenile speculation and gibberish. :(

Kebsis
2008-Apr-18, 06:41 AM
Hi, I have a question. If it were to turn out that the universe is curved, would it then be possible to use that information to find out how large the universe is? Similiar to how you could be shown a fraction of a circle, and be able to draw out, from the curvature presented, how large the entire circle is.

Steve Limpus
2008-Apr-18, 06:49 AM
Just to show I'm not still grumpy, I also found these interesting sites:

http://www.astro.ubc.ca/people/scott/faq_email.html#universe

http://background.uchicago.edu/~whu/beginners/introduction.html

http://universe-review.ca/F02-cosmicbg.htm#universe

Hope someone else likes 'em. :)

Steve Limpus
2008-Apr-18, 07:00 AM
Hi, I have a question. If it were to turn out that the universe is curved, would it then be possible to use that information to find out how large the universe is? Similiar to how you could be shown a fraction of a circle, and be able to draw out, from the curvature presented, how large the entire circle is.

Hi Kebsis

Scientists tell us their observations are that the universe is flat, within 2%, out to the light horizon, a diameter of 92 billion light years. So if anyone can do the math, that should set a lower bound on the curvature, and therefore the size, of the universe (for whatever curvature or topology you favor).

Sorry I can't do the math for you, I am but a humble motor mechanic... :)

dcl
2008-Apr-18, 07:40 PM
Thank you, Steve Limpus, for your 3/18/2008 6:36 AM and 6:39 AM messages. It's going to take me a while to digest the material you provided, but I intend to do so and will respond to what I find as soon as I can. I never intended to ignore youre contribution.

dcl
2008-Apr-18, 07:40 PM
Thank you, Steve Limpus, for your 3/18/2008 6:36 AM and 6:39 AM messages. It's going to take me a while to digest the material you provided, but I intend to do so and will respond to what I find as soon as I can. I never intended to ignore your contribution.

Steve Limpus
2008-Apr-18, 07:41 PM
digest away dude! :)

dcl
2008-Apr-18, 08:40 PM
Thank you, Steve Limpus, for your two comments. My responses follow:

Thank you for referring me to the multiple Internet references. I can appreciate that it took considerable work on your part to put that list and quoted material together. It'll take me some time to go through them, but I intend to do so in a timely manner Much thanks for your effort.