Free Republic
Browse · Search
News/Activism
Topics · Post Article

Skip to comments.

A Small Spherical Universe after All?
spacedaily.com ^ | 21 Dec 01 | several mathematicians

Posted on 12/21/2001 8:40:31 AM PST by RightWhale

http://www.spacedaily.com/news/cosmology-01f.html

A Small Spherical Universe after All?

Paris - Dec 19, 2001

What is the shape of space? Is it finite or infinite? Is it connected, has it "edges", "holes" or "handles"? This cosmic mystery, which has puzzled cosmologists for more than two thousands years, has recently been enlightened by a breakthrough in a new field of research: cosmic topology.

An international team involving researchers from France, the United States and Brazil recently filled a major gap in the field. They propose surprising universe models in which space, spherical yet much smaller than the observable universe, generates an optical illusion on a cosmic scale (topological lens effet).

Einstein's general relativity theory teaches us that space can have a positive, zero or negative constant curvature on the large scale, the sign of the curvature depending on the total density of matter and energy. The celebrated big bang models follow, depicting a universe starting from an initial singularity and expanding forever or not. However, Einstein's theory does not tell us whether the volume of space is finite or infinite, or what its overall topology is.

Fortunately, high redshift surveys of astronomical sources and accurate maps of the cosmic microwave background radiation are beginning to hint at the shape of the spatial universe, or at least limit the wide range of possibilities.

As a consequence, cosmic topology has gained an increased interest, as evidenced by the special session "Geometry and Topology of the Universe" organized by the American Mathematical Society during its 2001 meeting held last October in Williamstown, Mass.

Three French cosmologists were invited to present to an audience of mathematicians, physicists and astronomers the statistical method they recently devised for detecting space topology: cosmic crystallography .

Cosmic Crystallography
Cosmic crystallography looks at the 3-dimensional observed distribution of high redshift sources (e.g. galaxy clusters, quasars) in order to discover repeating patterns in their distribution, much like the repeating patterns of atoms observed in crystals. They showed that "pair separation histograms" are in most cases able to detect a multi- connected topology of space, in the form of spikes clearly standing out above the noise distribution as expected in the simply-connected case. The researchers have particularly studied small universe models, which explain the billions of visible galaxies are repeating images of a smaller number of actual galaxies.

The two pictures below visualize the "topological lens effect" generated by a multi-connected shape of space, and the way the topology can be determined by the pair separation histogram method.

Spherical Lensing
Until recently, the search for the shape of space had focused on big bang models with flat or negatively curved spatial sections. Recently however, a combination of astronomical (type I supernovae) and cosmological (temperature anisotropies of the cosmic background radiation) observations seem to indicate that the expansion of the universe is accelerating, and constrain the value of space curvature in a range which marginally favors a positively curved (i.e. spherical) model. As a consequence, spherical spaceforms have come back to the forefront of cosmology.

In their latest work, to be published in Classical and Quantum Gravity, the authors and their Brazilian and American collaborators fill a gap in the cosmic topology literature by investigating the full properties of spherical universes. The simplest case is the celebrated hypersphere, which is finite yet with no boundary.

Actually there are an infinite number of spherical spaceforms, including the lens spaces and the fascinating Poincaré space. The Poincaré space is represented by a dodecahedron whose opposite faces are pairwise identified, and has volume 120 times smaller than the hypersphere. If cosmic space has such a shape, an extraordinary "spherical lens" is generated, with images of cosmic souces repeating according to the Poincaré space's 120-fold "crystal structure".

The authors give the construction and complete classification of all 3-dimensional spherical spaces, and discuss which topologies are likely to be detectable by crystallographic methods. They predict the shape of the pair separation histogram and they check their prediction by computer simulations.

The Future of Cosmic Topology
Experimental projects related to cosmic crystallographic methods and to the detection of correlated pairs of circles in the cosmic background radiation are currently underway. Presently, the data are not good enough to provide firm conclusions about the topology of the Universe. Fortunately breakthroughs are expected in the coming decade: high redshift surveys of galaxies will be completed, and high angular resolution maps of the cosmic radiation temperature will be provided by the MAP and Planck Surveyor satellite missions. The new data will provide clues to the shape of the Universe we live in, a question that puzzles not only cosmologists, but also philosophers and artists.

The authors are Jean-Pierre Luminet (DARC/LUTH, Observatoire de Paris, France), Roland Lehoucq (Service d’Astrophysique, CEA Saclay, France), Jean-Philippe Uzan (Laboratoire de Physique Théorique, Orsay, France), Evelise Gausmann (Université de Sao Paulo, Brésil) et Jeffrey Weeks (Canton, USA).


TOPICS: Culture/Society; Extended News; News/Current Events
KEYWORDS:
Navigation: use the links below to view more comments.
first 1-5051-100101-150151-200201-203 next last
a question that puzzles not only cosmologists, but also philosophers and artists

And FReepers who want to know, demand to know what is going on.

1 posted on 12/21/2001 8:40:32 AM PST by RightWhale
[ Post Reply | Private Reply | View Replies]

Comment #2 Removed by Moderator

To: RightWhale
The simplest case is the celebrated hypersphere, which is finite yet with no boundary.

My brain hurts.

3 posted on 12/21/2001 8:47:35 AM PST by Maceman
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale
This probably explains why, when I drive aimlessly and lost around a town I'm not familiar with, I always pass the same intersection a number of times.
4 posted on 12/21/2001 8:48:47 AM PST by My2Cents
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale
I think that within 50 years that scientists will discover that the universe is sitting on the back of a big turtle after all.
5 posted on 12/21/2001 8:49:18 AM PST by Arkinsaw
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale;Physicist
Is this just a pack of Pernod-crazed Frenchmen????

Remember, a topologist is a guy who can't tell the difference between a cup of coffee and a doughnut!

6 posted on 12/21/2001 8:51:46 AM PST by headsonpikes
[ Post Reply | Private Reply | To 1 | View Replies]

To: KayEyeDoubleDee
The authors give the construction and complete classification of all 3-dimensional spherical spaces

Uhh, if this were true, they'd each pocket $200,000.

7 posted on 12/21/2001 8:58:19 AM PST by SlickWillard
[ Post Reply | Private Reply | To 1 | View Replies]

To: Maceman
My brain hurts.

Such articles can be used to re-inflate long-unused math lobes in the brain. I find the process sometimes painful.

The hypothesis that our universe as we see it is actually a much smaller one than we have assumed, --seen multiple times--, is gaining popularity. At the same time, it is only a small step in the direction of my own hypothesis, that the entire universe is a single particle seen hyper-multiple times.

8 posted on 12/21/2001 9:02:53 AM PST by RightWhale
[ Post Reply | Private Reply | To 3 | View Replies]

To: RightWhale
"They propose surprising universe models in which space, spherical yet much smaller than the observable universe, generates an optical illusion on a cosmic scale (topological lens effect)."

So it seems the use of light to measure time/distance is actually an illusion and isn't really accurate. I've always wondered how if time comes to a standstill at C (the speed of light), why scientists would equate time measurement with the distance to stars when time is never consistant - but seems time is relevant only to one's position in the universe.

9 posted on 12/21/2001 9:08:50 AM PST by azhenfud
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale
Nice work if you can get it.

Number: Invention or Discovery?

10 posted on 12/21/2001 9:14:45 AM PST by onedoug
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale
The hypothesis that our universe as we see it is actually a much smaller one than we have assumed, --seen multiple times--, is gaining popularity. At the same time, it is only a small step in the direction of my own hypothesis, that the entire universe is a single particle seen hyper-multiple times.

It's the part about being finite with no boundaries that gives me brain cramps.

11 posted on 12/21/2001 9:16:14 AM PST by Maceman
[ Post Reply | Private Reply | To 8 | View Replies]

To: RightWhale
. They propose surprising universe models in which space, spherical yet much smaller than the observable universe, generates an optical illusion on a cosmic scale (topological lens effet).

Why bother creating a massively huge universe when a small one with perfectly-aligned mirrors at each end will do?

12 posted on 12/21/2001 9:17:16 AM PST by CubicleGuy
[ Post Reply | Private Reply | To 1 | View Replies]

To: headsonpikes
Is this just a pack of Pernod-crazed Frenchmen????

Remember, a topologist is a guy who can't tell the difference between a cup of coffee and a doughnut!

You've gotten them confused with proctocolygist.

13 posted on 12/21/2001 9:21:31 AM PST by packrat01
[ Post Reply | Private Reply | To 6 | View Replies]

To: RightWhale
Mobius strip?
14 posted on 12/21/2001 9:22:01 AM PST by packrat01
[ Post Reply | Private Reply | To 1 | View Replies]

To: Maceman
>The simplest case is the celebrated hypersphere, which is finite yet with no boundary.

My brain hurts.


It's not hard to understand. The notion is that space is curved, kind of like the outer edge of a ring. The outer edge of a ring is finite, but you can go along it forever and never hit a boundary -- you just eventually end up right back where you started. Thus you have a finite spance with no boundaries, and from a two dimensional perspective it could be seen as infinite, because it can be traversed indefinitely.

Expand that to a three-dimensional curve, wheren you can start at one point in the universe, travel and after some indeterminable time you end up right back where you started. That's also what would create the illusion of a massive universe -- you keep looking and you keep seeing more "stuff" but as you go further you're really just looking at the same thing over and over again.

Now just try to picture it in your head. I'll try it...

...okay, now my brain hurts.
15 posted on 12/21/2001 9:22:05 AM PST by Dimensio
[ Post Reply | Private Reply | To 3 | View Replies]

To: RightWhale
>At the same time, it is only a small step in the direction of my own hypothesis, that the entire universe is a single particle seen hyper-multiple times.

Does any of this mean that if a pretty girl in a short skirt is standing behind me, then I can see up her skirt by looking forward and up? (Didn't the Nazis do research along these lines during WWII?)

Mark W.
;-)

16 posted on 12/21/2001 9:22:08 AM PST by MarkWar
[ Post Reply | Private Reply | To 8 | View Replies]

To: RightWhale
The hypothesis that our universe as we see it is actually a much smaller one than we have assumed, --seen multiple times--, is gaining popularity. At the same time, it is only a small step in the direction of my own hypothesis, that the entire universe is a single particle seen hyper-multiple times.

And that's almost identical to my own personal hypothesis, except you left out the part where it revolves around me.
17 posted on 12/21/2001 9:23:28 AM PST by Dimensio
[ Post Reply | Private Reply | To 8 | View Replies]

To: headsonpikes
Remember, a topologist is a guy who can't tell the difference between a cup of coffee and a doughnut!

BWAAA-HAAAA-HAAA!

Guess the fact I found that so funny means I'm a nerd after all! Sheesh!
18 posted on 12/21/2001 9:25:35 AM PST by GodBlessRonaldReagan
[ Post Reply | Private Reply | To 6 | View Replies]

To: headsonpikes
That's because there is no difference. Hey, I read the story that proved it.
19 posted on 12/21/2001 9:26:48 AM PST by techcor
[ Post Reply | Private Reply | To 6 | View Replies]

To: packrat01
"You've gotten them confused with proctocolygists."

Aren't those the guys who handle who-sits-where at diplomatic luncheons?

20 posted on 12/21/2001 9:27:56 AM PST by headsonpikes
[ Post Reply | Private Reply | To 13 | View Replies]

To: Dimensio
So that means that with a powerful enough telescope my wife can answer the Question:"Does my butt* look big in these?" without my input. ;-)

*It doesn't. She has a very nice derriere.

21 posted on 12/21/2001 9:28:47 AM PST by Dead Corpse
[ Post Reply | Private Reply | To 15 | View Replies]

To: RightWhale
And FReepers who want to know, demand to know...

Inquiring minds want to know.

22 posted on 12/21/2001 9:29:36 AM PST by MaeWest
[ Post Reply | Private Reply | To 1 | View Replies]

To: RightWhale
"...the entire universe is a single particle seen hyper-multiple times."

The 'mote in God's eye' hypothesis, hmmmm?

23 posted on 12/21/2001 9:30:03 AM PST by headsonpikes
[ Post Reply | Private Reply | To 8 | View Replies]

To: Dimensio
I guess this means if we have a powerful enough telescope, we should be able to see if we are comming or going.
24 posted on 12/21/2001 9:31:59 AM PST by Gadsden1st
[ Post Reply | Private Reply | To 17 | View Replies]

To: GodBlessRonaldReagan
A nerd wouldn't laugh!

Knowledge is power. ;^)

25 posted on 12/21/2001 9:34:08 AM PST by headsonpikes
[ Post Reply | Private Reply | To 18 | View Replies]

To: headsonpikes
Ooooh! Good 'un!
26 posted on 12/21/2001 9:34:55 AM PST by GodBlessRonaldReagan
[ Post Reply | Private Reply | To 25 | View Replies]

To: RightWhale
I am suddenly feeling somewhat confined.
27 posted on 12/21/2001 9:35:44 AM PST by KC Burke
[ Post Reply | Private Reply | To 1 | View Replies]

To: Maceman
Unfortunately, if you go to the archived paper in postscript format, you may find several charts do not display completely; and on top of that I had to reboot to clear memory afterwards. You may be able to fill in the gaps in the paper or you may wish to contact Mr. Luminet directly.

They are dealing with 3-dimensional spherical manifolds only, which greatly simplifies the problem. They also mention the conditions where a repeating crystalline structure is detectable.

The thought of Charles Sanders Peirce, American semiotician, that the universe will eventually turn to pure crystalline mind is recalled in this context.

28 posted on 12/21/2001 9:39:40 AM PST by RightWhale
[ Post Reply | Private Reply | To 11 | View Replies]

To: Arkinsaw
But what is the turtle standing on?
29 posted on 12/21/2001 9:40:19 AM PST by Billy_bob_bob
[ Post Reply | Private Reply | To 5 | View Replies]

To: MarkWar
Does any of this mean that if a pretty girl in a short skirt is standing behind me, then I can see up her skirt by looking forward and up?

That's why God invented Cosmic Dust: to obscure your view.

30 posted on 12/21/2001 9:42:07 AM PST by CubicleGuy
[ Post Reply | Private Reply | To 16 | View Replies]

To: packrat01
Mobius strip?

Klein bottle, if it's in three dimensions.
31 posted on 12/21/2001 9:42:30 AM PST by WyldKard
[ Post Reply | Private Reply | To 14 | View Replies]

To: Billy_bob_bob;Arkinsaw
"But what is the turtle standing on?"

15,000,000,000 years worth of turtle dung.

32 posted on 12/21/2001 9:44:40 AM PST by headsonpikes
[ Post Reply | Private Reply | To 29 | View Replies]

To: MarkWar
If it doesn't mean that, then all research grants for physics have been wasted!-)
33 posted on 12/21/2001 9:44:53 AM PST by beowolf
[ Post Reply | Private Reply | To 16 | View Replies]

To: RightWhale
If the universe is not simply connected, wouldn't we see large fluctuations in the cosmic microwave radiation background, owing to the fact that the "opaque" part of the universe would be farther away in some directions than in others?

Prediction: there may be some funny bumps in the distribution of pair-separations of cosmologically distant sources, at least in the small-separation bins, owing to the fact that we often do see multiple images of gravitationally lensed objects.

34 posted on 12/21/2001 9:44:59 AM PST by Physicist
[ Post Reply | Private Reply | To 1 | View Replies]

To: Arkinsaw
The story so far:
In the beginning the Universe was created.

This has made a lot of people very angry and been widely regarded as a bad move.

Many races believe that it was created by some sort of God, though the Jatravartid people of Viltvodle VI believe that the entire Universe was in fact sneezed out of the nose of a being called the Great Green Arkleseizure.

The Jatravartids, who live in perpetual fear of the time they call The Coming of The Great White Handkerchief, are small blue creatures with more than fifty arms each, who are therefore unique in being the only race in history to have invented the aerosol deodorant before the wheel.

However, the Great Green Arkleseizure Theory is not widely accepted outside Viltvodle VI and so, the Universe being the puzzling place it is, other explanations are constantly being sought.

more here... and also a good bit about the restaurant at the end of the universe...

35 posted on 12/21/2001 9:51:42 AM PST by Mr. K
[ Post Reply | Private Reply | To 5 | View Replies]

To: Maceman
Think of it in terms of a democratic congressional budget. That helps.
36 posted on 12/21/2001 9:52:21 AM PST by Arkie2
[ Post Reply | Private Reply | To 11 | View Replies]

To: headsonpikes
OK, but what is the Turtle Dung resting on?
37 posted on 12/21/2001 9:53:14 AM PST by Billy_bob_bob
[ Post Reply | Private Reply | To 32 | View Replies]

To: RightWhale
Unfortunately, if you go to the archived paper in postscript format, you may find several charts do not display completely; and on top of that I had to reboot to clear memory afterwards.

All that means is your computer is smaller than you thought it was. Proves the theory, if you ask me....

38 posted on 12/21/2001 9:56:23 AM PST by r9etb
[ Post Reply | Private Reply | To 28 | View Replies]

To: Billy_bob_bob
"...what is the turtle dung resting on?"

See Physicist's account of 'gravitationally-lensed objects'.

I believe the turtle dung is the cosmological 'paired object' of Hitlery's brain. ;^)

39 posted on 12/21/2001 9:58:28 AM PST by headsonpikes
[ Post Reply | Private Reply | To 37 | View Replies]

To: Mr. K
If Douglas Adams were alive today I imagine he would be inspired by the new developments in quantum computing, and would write of the "Quanta" people on some distant planet. It might go something like this:

The Quanta would be a race of people who had so wholly embraced the notion and technology of quantum mechanics that their entire society had become deterministic. Children could sleep late and attend school at the same time, people would tell the truth and lie simuntaneously, you would literally have your cake and eat it too. However, due to their unfortunate infuatuation with democratic processes, they have left every event to be resolved via a voting process, with run-off elections and re-votes for controversial outcomes. Since every outcome in a deterministic universe is, by definition, controversial, the unfortunate result has been a society where every possibility is being embraced simuntaneously while no possible resolution of any possibility is allowed, by law.

Anyway, that's my guess.

40 posted on 12/21/2001 10:00:35 AM PST by Billy_bob_bob
[ Post Reply | Private Reply | To 35 | View Replies]

To: Billy_bob_bob
That's where Gary Condit hid Chandra Levy's body.
41 posted on 12/21/2001 10:00:57 AM PST by Redcloak
[ Post Reply | Private Reply | To 37 | View Replies]

To: Physicist
large fluctuations in the cosmic microwave radiation background

Speaking of which, Spider Robinson points out that until mankind invented refrigeration, nothing in the universe was colder than 2.7 degrees absolute. This is the main impact of the activities of mankind so far.

42 posted on 12/21/2001 10:02:53 AM PST by RightWhale
[ Post Reply | Private Reply | To 34 | View Replies]

To: Billy_bob_bob
But what is the turtle standing on?

It's turtles all the way down. :)

43 posted on 12/21/2001 10:10:29 AM PST by mlo
[ Post Reply | Private Reply | To 29 | View Replies]

To: Billy_bob_bob
Since every outcome in a deterministic universe is, by definition, controversial, the unfortunate result has been a society where every possibility is being embraced simuntaneously while no possible resolution of any possibility is allowed, by law.

Isn't that pretty much what we have here on Earth already?
44 posted on 12/21/2001 10:18:02 AM PST by Dimensio
[ Post Reply | Private Reply | To 40 | View Replies]

To: RightWhale
Spider Robinson points out that until mankind invented refrigeration, nothing in the universe was colder than 2.7 degrees absolute. This is the main impact of the activities of mankind so far.

Nature abhors a vacuum, hence Golobal Warming?...Nah, it's the Sun.;-)

45 posted on 12/21/2001 10:25:42 AM PST by PeaceBeWithYou
[ Post Reply | Private Reply | To 42 | View Replies]

To: Dimensio
Ssssshhh! You're not supposed to notice!
46 posted on 12/21/2001 10:27:42 AM PST by Billy_bob_bob
[ Post Reply | Private Reply | To 44 | View Replies]

To: mlo
Thank You for stealing my line. That woman told Steven Hawking the truth! "Turtles all the way down!"
47 posted on 12/21/2001 10:27:57 AM PST by Conan the Librarian
[ Post Reply | Private Reply | To 43 | View Replies]

To: Maceman
The simplest case is the celebrated hypersphere, which is finite yet with no boundary.

My brain hurts. Naah, it's probably the neck.

Imagine that you are an ant crawling on a surface of a ball. You maintain the same direction and discover that, after awhile, you have reached the same point from which you have started. What would you conclude?

Is the surface finite? Yes, you just reached the starting point.

Does it have a boundary? No. At no time did you encounter where it ends.

Told you it was the neck.

48 posted on 12/21/2001 10:35:16 AM PST by TopQuark
[ Post Reply | Private Reply | To 3 | View Replies]

To: RadioAstronomer; ThinkPlease; PatrickHenry; VadeRetro
cosmo-topological bump

(or should that be "topo-cosmological bump"?)

49 posted on 12/21/2001 10:35:23 AM PST by longshadow
[ Post Reply | Private Reply | To 34 | View Replies]

To: CubicleGuy
Does any of this mean that if a pretty girl in a short skirt is standing behind me, then I can see up her skirt by looking forward and up?

That's why God invented Cosmic Dust: to obscure your view.

And that's why catholic school boys learned to polish their black, patent leather shoes to a mirrorlike glare. To overcome God's will.

50 posted on 12/21/2001 10:40:06 AM PST by Wm Bach
[ Post Reply | Private Reply | To 30 | View Replies]


Navigation: use the links below to view more comments.
first 1-5051-100101-150151-200201-203 next last

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
News/Activism
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson