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mental invalid

for all my nizzies who love space and the cosmos....

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from october 9 Nature mag

 

Cosmology: The shape of the Universe

 

GEORGE F. R. ELLIS

 

George F. R. Ellis is in the Department of Mathematics, University of Cape Town, Rondebosch 7700, Cape Town, South Africa.

e-mail: ellis@maths.uct.ac.za

 

An analysis of astronomical data suggests not only that the Universe is finite, but also that it has a specific, rather rigid topology. If confirmed, this is a major discovery about the nature of the Universe.

 

What shape is space? On page 593 of this issue, Luminet et al.1 suggest that the topology of the Universe may be a 'Poincaré dodecahedral space' — as illustrated on this week's cover. And this is no idle abstraction: Luminet et al. show that this topology, unlike many others, is supported by data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), published earlier this year2.

 

In thinking about the large-scale shape of the Universe, three interlinked questions must be confronted. First, what is its spatial curvature? There are three possible answers. Three-dimensional sections of space-time may be 'flat' — in such space sections, parallel lines stay the same distance apart and never meet (as in Euclidean space). Or the space sections may be 'negatively curved', such that parallel lines diverge from one another and never meet (the three-dimensional analogue of a Lobachevsky space). Finally, they may be 'positively curved', such that parallel lines converge and eventually intersect (the three-dimensional analogue of the surface of a sphere). The particular case that exists depends on how well the amount of matter in the Universe, coupled with the driving force of dark energy, balances the Universe's kinetic energy of expansion. This is usually expressed in terms of the normalized density parameter Omega0, which is unity for flat space sections; for positive spatial curvature, Omega0 is greater than one.

 

The second question is whether the Universe is 'open' or 'closed' — that is, is it spatially infinite, containing an infinite amount of matter, or is it spatially finite, containing a finite amount of matter? Positively curved space sections are necessarily closed, but the converse does not necessarily follow: both flat and negatively curved space sections can be finite if their connectivity is more complicated than in Euclidean space, meaning that their topology is quite unusual3, 4 (for example, in a flat toroidal space, as you exit right you enter left, and space is finite). So the third issue is, what is the large-scale topology of the Universe?

 

It is worth noting that none of these features is determined by the Einstein gravitational field equations, which are differential equations that govern local, rather than global, properties of space-time5. Topology and curvature seem to be fixed by the initial conditions at the start of the Universe that have since determined its dynamical evolution. To investigate the topology and curvature of the Universe, we must use astronomical observations; from observed values of the energy densities and the expansion rate in the Universe, the curvature can be deduced using Einstein's field equations.

 

If the Universe is closed, and has a small enough diameter, we may be able to see right round it because photons can traverse the whole Universe — Luminet et al.1 illustrate this point well with the image of an insect crawling around the surface of a cylinder (Fig. 2 on page 593). If this is so, we may be able to identify multiple images of the same structure but in different directions in the sky4, 6, or see an effect on the statistics of clustering of galaxies4. Furthermore, the existence of such a 'small universe' should be detectable through its influence on that Rosetta Stone of present-day cosmology, the cosmic microwave background (CMB) radiation7, 8.

 

The CMB is the relic radiation of the Big Bang, and the very slight changes in its temperature across the sky record the density fluctuations that existed at a certain point in the early history of the Universe. Data on these anisotropies2, 9 from WMAP and other sources suggest that the density parameter Omega0 has the value 1.02 0.02. This is compatible with flat space sections. Further data might move the value of Omega0 towards or even below unity. But taking the present data at their face value, the conclusion is that the Universe is spatially closed and hence has finite space sections. This tentatively answers two of the three questions mentioned above.

 

But there is a further intriguing feature in the data. The so-called power spectrum of anisotropies (Fig. 1) shows a distinctive set of peaks when the anisotropy is compared between regions of sky separated by small angles. But on large angular scales (for regions typically more than 60° apart), there is a strange loss of power that does not fit with the expectations of standard cosmological models (in particular, there is less power in the quadrupole than expected). Some have proposed that this can be attributed to as yet undiscovered laws of physics at work in the early Universe10.

 

Luminet et al.1, however, suggest it is because we live in a universe with positively curved space sections and non-standard topology. The smaller-than-usual diameter of the Universe means that there is a maximum length scale that fits into it — and consequently there is a loss of power in the CMB spectrum on scales that are larger than this maximum7. The authors propose that the spatial sections of the Universe are dodecahedral sections of a space of positive curvature, fitted together to make finite three-dimensional spaces. This topology accounts for the WMAP data better than do standard models1.

 

Can this proposal be confirmed? Yes indeed. First, Luminet and colleagues' model suggests that Omega0 = 1.013, and future observations will produce data that should pin down the value of Omega0 to this level of accuracy (the current value from WMAP is accurate only to 2%). Second, a remarkable paper by Cornish et al.11 showed that, however complex the spatial topology, in a small universe there will be circles of identical temperature fluctuations in the CMB sky that could be identified from data on the CMB anisotropies. Luminet et al. determine what those circles would be in their model. Future analyses of WMAP data — and of data from its successor, the Planck satellite, to be launched in 2007 — should be able to verify whether the circles are there or not.

 

In many models of the Universe, it is assumed that spatial homogeneity extends outside our visual horizon for ever. However, in the case of chaotic inflation12, 13 — a variant of the inflationary model for an exponential expansion that occurred in the wake of the Big Bang — the Universe is very inhomogeneous on scales much larger than we can observe, and we are in one expanding bubble in the middle of innumerable other, similar ones. But if Luminet et al. are correct, chaotic inflation is ruled out: there is only one expanding universe bubble, and we can see almost all the way round it.

 

In 1917, Einstein14 proposed that spatially closed universes are advantageous because that would remove the problem of boundary conditions at infinity15. A small universe in which we have seen most of what exists is even more advantageous6; indeed, strictly speaking, they are the only universes in which we can predict the astronomical future — the return of Halley's comet, for example — because only in them do we have access to all the data needed to make such predictions. The WMAP data, as interpreted by Luminet et al.1, suggest that we might indeed live in such a small closed universe.

 

------------------

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Guest PHYNE

[i got flicks of the lunar eclipse the other night.....pretty dope shit to see......................

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Guest WebsterUno

I was watching TDC

the other night. They

had this thing about

the satelite Ulyssess.

The one that was on its

way to Saturn. It was

pretty interesting.

I was toggling between

that, and some show about

Subways on another

Discovery Channel.

Ahh...the wonders of satellite TV!

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saw this in a record store on monday and it dropped me on my head....

 

From Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan, Random House, 1994)

 

 

Earth (the dot in the middle) as seen from 3.7 billion miles away by the Voyager 1 spacecraft, on 6/6/1990.

 

 

 

... Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there - on a mote of dust suspended in a sunbeam.

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light.

 

Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

 

The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.

 

It has been said that astronomy is a humbling and character building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we've ever known.

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Guest Pilau Hands
Originally posted by OPEN_PIEHOLE

nizzies? wiggers suck!!

it's a joke...

put your pants back on

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cooool stuff guys.

 

Just a thought..if space is actually finite, then what would be surrounding this space? If space is a soccer ball, is it just floating in nothing, and if so, then this nothing actually is something. Perplexing....

 

Thoughts?

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Guest imported_El Mamerro

Sagan fucking crushes...

 

Where's the picture?!?

 

As far as other laymen books, not sure, haven't been able lately to drop back into the full-on physics mode I was into a few years ago... I got distracted by mathematics and AI type-stuff for a while, and am now taking a break from smart reading and eating up $8 action paperback bestsellers. I should hop back into it as soon as I find a good one on M-Theory that picks up where "The Elegant Universe" left off.

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This is copyrighted..... I have mailed myself the original. So, not that

anyone would care enough, but I've never seen this theory anywhere.

Someday I'll scan/post the paper I drew the pictures on..

 

 

1) Big bang theory. All matter was the size of a single point and instantly

spanned out millions of lightyears across the galaxy.

 

2) Stars, planets, dust clouds, etc. are formed. Most of the matter and

light are still expanding out into space.

 

3) As stars die, they collapse on themselves and create black holes.

For another myriad of years, they draw in light (which has a mass) and

bits of dust/whatever.

 

4) Our sun will eventually die, as all others do. Hopefully by that time,

we've either learned how to work together as a species and respect our

surroundings, or we die out. No need to pollute the universe with our

self centered bullshit.

 

5) These black holes have enormous amounts of energy and mass inside

them. Eventually, they will begin to draw on each other, as well.

 

6) The gravity escalates to the point where the black holes begin to

accelerate toward each other. As they collide, they gain more and more

mass, and therefore, more gravity.

 

7) If there was any mass in the universe not already swallowed by a

black hole, it is now. The gravity of the black holes has stopped the

expanding of the universe... even that being done by light itself.

 

8) The black holes accellerate toward each other at the speed of light.

As they collide, the mass they hold once again collapses in on itself.

 

9) The super dense matter continues to eat itself, as all of the energy

and mass of the universe condenses into the normally empty space in

atoms. Through this effect, the matter is once again brought down to the

size of a single point.

 

10) The big bang happens once again.

 

 

 

 

The funny part: because all of the mass is at that single point, it must

be uniform in nature. The Big Bang is identical every time it occurs...

 

what this means: The universe, as an event, occurs over and over and

over again as we move through time. I will type this on 12oz an infinite

amount of times, you will read it again and again, and on and on we march.

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Yeah i have heard about that theory that the universe will collapse on itself instead of spreading out for ever. The shit that worries me is that i am going to read this again and have read it before and it will continue on forever. Thank you for granting me this moment of clarity.

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boggling me:

 

if the universe is finite, even in the form of expanding/contracting energy or matter, what lies beyond the limits of the universe.

 

my little brain has always had a difficult time truly comprehending infinity

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Nothing. It's like space, but nothing is there.

 

 

Would would happen if you made a reflective lead box in the middle

of space, and somehow filtered out all of the matter inside that box?

There would be areas inside that box that are truly empty. What's the

difference between that and the outside of the universe?

 

 

i submit to you there isn't diddly squat different.

 

 

 

Here's something for you to ponder: If we somehow find a way to travel

at the speed of light, we would live in a world without time for as long

(strange, right? no time, but our speed is defined with time?) as we were

at that speed. However, if we could travel faster than light, we could

eventually catch up to the light originally shed off by the big bang. Using

this logic, with a big enough telescope, we could watch the big bang

happen from the farthest reaches of space. Hahaha.

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some people believe that there are muliple universes in side a mega universe i guess you can say, just as we are in a globe, earth, and earth is in a galaxy, milky way, and the milky was is in the universe, the universe its self is inside sometihng much larger, but i too wonder what could be on the out most regions of the universe, i always thought that if you traveled in a straing line away from earth that eventually you will come back to it, but i dont beleive the fact that everything will happen as it did again, upon the next big bang, earch may not even be formed, but something more to be worried about in the future rather than the sun inevetibaly going super nova on us is that our galaxy is on a crash course with our sister galaxy, which i dont know the name of, upon collision it will form one new galaxy, most likely destroying everything in both galaxies and starting over from scratch

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Guest imported_El Mamerro

S@T@N, you can stop worrying about copyright issues cause that theory's been around for quite some time now. I can't believe you've never seen it before.

 

As for the lead box thing, even if you filtered out all of the matter in it, it would still be different from what's outside the universe. That space may not have matter, but it does have spatial geometry and dimensions, which amounts for "something". "Space" is something.

 

I don't understand why people get so upset about the finite universe thing, and ask "what is there beyond it?". There simply isn't anything in the world you can use as a reference to visualize this, so why bother? We are used to seeing things fit inside other things, it is impossible to accept that the universe doesn't fit in anything larger than itself. "Nothing" isn't just a vacuum of space, "nothing" is nothing. It is so "nothing", you might as well say "it doesn't exist". Don't sweat it, we will never ever have a concept of what this is like.

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due to the nature of [my own] thought processes, i cannot simply "not bother; or not sweat it"

 

i guess the accompaniament to that would be that there are no concepts i have not been able to fully wrap my mind around (besides those discussing the finite limitations of the universe)

 

"nothing" is also not good enough an answer for me.

 

i have lots of faith in physics, but as a scientist, i am aware that we are limited by the information and data we have available to us..

all these theories could get blown wide open..

 

i am also intrigues by the possible correlation, at that point of the boundaries of our universe, whether what lies beyond doesn't have some sort of meaning or purpose or substance [beyond the states of matter and the energies and philosophies that we are aware of]

 

i mean, there's lots of tandem repeats in the genetic code..we have no idea why they are there, and lots of genetecists have implied that it is "junk" ..but i have a curiosity about it, i believe our understanidng of it is limited by what we already know about the genetic code, and that those 'non-coding' regions may in fact have a very specific purpose, for example the genetic code of our aura, or maybe our soul..these are farfetched, and unlikely, but intriguing nonetheless..

 

i am goign to get back into physics classes.

i am fascinated by the concept of a unifying theory..and the possibility that by the time a satisfactory one is created, it will encompass not only science, but also philosophy.

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oh well mams, it was just something I was kinda proud of because its

something I figured out that wasn't fed to me. And when I say "figured

out" I'm not asserting it's the absolute truth, just that I was able to give

form to it.

 

Anyway.... as to the argument on the concept of nothingness that

!@#$% can't grasp:

 

It's like being blind. And I dont' mean philosophically, metaphorically

blind, I mean physically, literally blind. You can't explain to a someone

born blind what colors are, or what something looks like, because they

simply have nothing to refer to.. their brain structure just doesn't include

what sight is. Same with being deaf...

 

It's like Gene Wilder in "See No Evil, Hear No Evil", when Richard Pryor

screams in his ear, "HEY, CAN YOU HEAR THIS? AT ALL?" And Gene is

like "Come here... a little closer... I'M DEAF, I CAN'T HEAR ANYTHING"

or something like that. So funny.

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your argument holds nothing.

 

uhhhhh...

 

deaf people can appreciate music.

vibrations and such are felt, and can be interpreted..

 

blind people can have a notion of color based on other senses, such as touch [of temperature, of surface] and sound..

 

i do not believe that my mind is physically incapable of comprehending a space beyond 'nothing'

 

it is more that i do not fully buy that argument, that the universe is indeed finite, with undefined characterisitcs of what lies beyond those borders..

 

i think there is something there.

i also believe that with all the new information accesible, the universe is now a misnomer..

because it is not INfinite (by definition)

in fact, it is bound...so its original definition does not apply

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Re: your argument holds nothing.

 

Originally posted by !@#$%

uhhhhh...

 

deaf people can appreciate music.

vibrations and such are felt, and can be interpreted..

 

blind people can have a notion of color based on other senses, such as touch [of temperature, of surface] and sound..

 

i do not believe that my mind is physically incapable of comprehending a space beyond 'nothing'

 

it is more that i do not fully buy that argument, that the universe is indeed finite, with undefined characterisitcs of what lies beyond those borders..

 

i think there is something there.

i also believe that with all the new information accesible, the universe is now a misnomer..

because it is not INfinite (by definition)

in fact, it is bound...so its original definition does not apply

 

 

 

 

Are you fucking smoking crack? I was giving an example to try to help

you out, not arguing (and I know that's the definition of argument you

were going for.)

 

 

 

So lets disregard the fact that you totally misinterpretted the mood of

what I was saying. You're saying that the can appreciate the vibrations?

Well shit, if I was talking about the sense of touch, that's wonderful.

Fuck, I can feel a train coming, but that doesn't mean I understand what

it sounds like.

 

 

Second: Sorry to shut you down twice, but there while there may be

some feeling linked to colors, blind people don't truly have a sense of

any fucking colors if they're born blind. Unless, of course, you'd like to

show me evidence otherwise.

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