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Universe's Curvature Measured?
jmobiusmaximus writes "Right next to the wormhole site on the BBC News page is an article about the results of the Boomerang project in Antarctica. This resulted in a new map of the 2.7K cosmic microwave background radiation, which is thought to be a remnant of the energy released in the Big Bang. The BBC News synopsis isn't bad, and has some links that will answer most "WTF?" questions. For those of you who have taken a little bit of physics, the original Nature article is better. This could have a large impact on our understanding of the universe's evolution and will probably be the source of much debate in the near future.
"
My Ideal universe:
- Has Flat Curvature
- Has Positive Curvature
- Has Negative Curvature
I'm all for Positive Curviture. Yeah, Baby!
Anomalous: inconsistent with or deviating from what is usual, normal, or expected
Anomalous: deviating from what is usual, normal, or expected
Canard: a false or unfounded repor
Want to work at Transmeta? MicronPC? Hedgefund.net? AT&T?
Can your IM do this?
The problem here is that they are talking about the curvature of four dimensional space time. One way for us to visualize this is to pare things down to a two dimensional sheet. Imagine teh universe is a plastic sheet lying on the floor. The sheet can be flat, having zero curvature (because the second derivative of the sheet "height" is zero), or it can be curved. If it has negative curvature everywhere, it could be something like a sphere. A saddle on the other hand has positive curvature. That is, the second derivative is positive somewhere.
All of this seems kinda wacky when applied to four dimensions. We can't visualize four dimensions easily, let alone what thier geometry looks like. And that is really the point here. On a flat surface (universe), normal Euclidean geometry holds. E.g., two parallel line never intersect, the sum of the interior angles of a triangle is 180, etc. On a curved surface (universe), this is not true. Draw a triangle on a deflated ballon (the flat universe) and then blow it up. The sum of the interior angles increases.
Pretty neat, huh? And that is some of the reasons they are looking into this.
I'd advise Slashdot readers to look at the Cosmology and Relativity FAQs, since they probably answer a lot of questions people are tempted to ask.
Since inflation theory (originally proposed by Linde in 1985 IIRC) predicts (well, demands might be a better term) that the cosmological constant be equal to zero, this is a victory for this theory, albeit one that practically everyone involved in cosmology expected a long time ago. But the question still remains, why is the Universe flat?
According to our current estimates of the density of matter in the Universe, the curvature of the Universe should be negative (producing a hyperbolic, "saddle"-like shape), producing a Universe where expansion continues forever and the Universe eventually dies from "heat death" as thermal equilibrium is acheived throughout the entire Universe.
But this measured value is out by a factor of 100 from the necessary value for the Universe to be flat (referred to as omega by cosmologists). Where is the missing 99% of the mass of the Universe? The point of this study is that the data is inconsistent with a lot of the more "exotic" models of this missing mass - topological defects, WIMPs and so on. But the data is consistent with the so-called "cold dark matter" models, which includes things like black holes which could be everywhere but are too dark for us to see.
Of course this is just one study, and the whole question is still open in a scientific sense. But this does provide some good evidence for inflationary theory as well as some additional data for cosmologists working on where the "missing mass" of the Universe is.
Let me chime in as a member of competing team (http://topweb.gsfc.nasa.gov) that did not make it on time to get all the credit.
This is the great result, comparable only to discovery of microwave background radiation in 1965 and first detection of CMBR anisotropy by COBE in 1992. It tells us much more then flatness of the Universe. From the results of this and followup experiments (ours will be somewhat more precise when we finally do it) it will be possible to find how much of the matter in the universe is barionic (composed of protons, neutrons and electrons) as opposed to stuff we have no idea about, which is probably contains up to 90-95% of the mass of the Universe. It will be possible to measure often mentioned energy of vacuum (do not count on using it --- not only it is low, it is also unextractable). Boomerang already a strong evidence in favor of inflation --- a strange theory, describing how most of matter in the universe was created from nothing, just because its positive rest energy was compensated by negative gravitational energy, so that total energy of the flat universe was and remains zero (this is how you create the whole Universe from nothing without violating the law of energy conservation). Future experiments will tell us more about how inflation happened and what kinds of fields and particles are responcible for it. We definetly will learn new things about fields and particles at energies far above what can be achieved in accelerators.
We live in interesting times.
BTW, read http://www.astro.ucla.edu/~wright/cosmolog.htm --- it is a good introduction to cosmology.
The problem here is that they are talking about the curvature of four dimensional space time.
Why is this a problem? Sure, it's impossible for us to visualise it, but mathematically it's no problem at all for anyone armed with the relevant techniques. The fourth dimension is a concept that's a century old, and has invaded the Western world's thinking in many ways. Just think of Picasso - a lot of his pictures were attempts to visualise things from the perspective of a 4-dimensional being.
Anyway, with the current superstring theories of physics there are a lot more than 4 dimensions - there are 10, 11 or 26 dimensions in this case depending on whether you're talking about basic superstrings, hetoric superstrings or M-theory. And again, these are impossible to visualise but easy to deal with mathematically.
And yeah, it's all very neat, and I'm just glad that physics is comprehensible enough that we can even attempt to understand it, let alone so that we can argue about it in places like /. :)
What I found most interesting, however, was the discrepancy between their estimates of Omega(baryon) = 0.05 and Omega(matter) = 0.31 (again, based on the test flight data). That means that their result requires Omega(non-baryonic) of 0.26. That is, if this result is correct there is definitely not just dark matter, but 'exotic' dark matter (WIMPs, primordial black holes, or other strange stuff) out there. Again, that's not too surprising, since primordial nucleosynthesis arguments place rather severe restrictions on how much baryonic matter there can be in the universe. Still, this gives yet another independent argument for dark matter. What's more, the amount of dark matter required is close to what is implied by galactic dynamics, which means that you have enough to explain galaxy rotation curves, but you don't have any embarrassing intergalactic dark matter. It would be a problem if there were a lot of dark matter that steadfastly refused to cluster like ordinary matter.
At the end of the day, this result looks huge. If it is borne out, then it will go a long way toward settling the question of cosmography. Then the question becomes, what to do with lambda. A nonzero cosmological constant really doesn't make any sense from a theoretical standpoint, and it brings back all of the fine-tuning problems that inflationary scenarios were supposed to rid us of in the first place. The cosmological question of the next decade will be, "What does this nonzero cosmological constant mean, and why are both it and omega so close in magnitude?" The so-called 'quintessence' models look promising in this regard. At any rate, the ball is pretty firmly back in the theorists' court.
-rpl
"This has not, however, stopped their earnings from pushing back the boundaries of pure hypermathematics, and their chief research accountant has recently been appointed Professor of Neomathematics at the University of Maximegalon, in recognition of both his General and his Special Theories of Disaster Area Tax Returns, in which he proves that the whole fabric of the space-time continuum is not merely curved, it is in fact totally bent."
-- "The Restaurant at the End of the Universe" - Douglas Adams
- Mike
Others have already pointed out the error in the earlier post - the surface of a sphere is an example of a surface with positive curvature, not negative curvature. For discussion (and a Java applet - yay) of a surface with negative curvature (in this case, hyperbolic geometry), try http://math.rice.edu/~joel/NonEuclid/.
Draw two dots on a piece of paper. The path between the two dots with the shortest length (ie, the path in which you will expend the least ink or graphite drawing), is a "straight line". Now, draw two dots on an orange (say, at the North Pole and somewhere on the Equator), with a magic marker or something. The shortest path on the surface of the orange between those two points is some part of a great circle - part of the meridian running down from the pole to the other point. Most of the time, the path you've drawn on the orange looks curved to you, and you can imagine drilling a hole through the orange which would connect the two points as the crow flies. This is because you live (pretty much) in 3-dimensional Euclidean space.
But imagine a tiny ant or microbe on the surface of the orange - in the same way that the Earth looks flat to us, the orange would look flat to the ant. If you put some ant food (say, a drop of sugar or something) on the equator of the orange, and drop a hungry ant at the North pole, then the ant will take the shortest path it can to the food, which is along a meridian. This path looks like a straight line to the (2d) ant, but like a curve to (3d) us.
Mathematicians have a special name for a curve which takes the shortest route between two points - they call it a "geodesic". Certain theoretical physicists irritatingly call it a straight line, which can be confusing, because it's almost always not a straight line in the Euclidean sense.
Aaanyway. The special theory of relativity showed that you can't treat time and space separately - they are all wrapped up in one another in a way which only really becomes apparent if you have things travelling at high speeds. In a sense, we live in a 4-dimensional mixture of space and time, but we perceive this as 3 space dimensions and 1 time dimension which don't intermix much because you need to travel at an appreciable fraction of 600 million miles per hour to notice anything going on, and very few people ever manage to travel at a millionth of that relative to the planet's surface without ending up a bloody pulp.
So, the special theory of relativity ("SR" to its friends), says we really live in 4 dimensions. The *general* theory of relativity ("GR"), which emerged later, talks about how, in addition to time and space being wrapped up in one another, the presence of matter changes this relationship.
This is where get to spout the physics catchphrases like "Matter tells space how to curve, and space tells matter how to move".
Let's get back to the ants. Say you decide to raise a load of ants who spend their entire lives on a flat rubber sheet - the ants' idea of a straight line (quickest line between ant and food), coincides with our ideas of straight line. Now, drop a marble on to the rubber sheet - if the marble is heavy enough, it will distort the sheet. Drop a cannonball on the sheet, and you get lots of distortion. Put a drop of sugar near the cannonball, where there's lots of distortion, and you'll see the ants travelling along curves again.
Now - generalize this. Imagine a race of four-dimensional beings, who have a 3-dimensional rubber sheet on which they watch some beings who are so tiny, they usually only notice the surface of the sheet.
We are those ants.
(Sort of.)
Now, Einstein's Field equations, which you arrive at after wrestling about with some rather tedious algebra, originally took the form:
(curvature of a bit of space) = (constant) * (amount of matter in it)
Except that it was phrased in an exceedingly accurate way that boils down to sixteen smaller equations. Notice that this kind of implies that if you take away all the matter, or you travel to some region of the universe with very little in it, there's no curvature - "straight lines" are straight lines in the Euclidean sense.
Now, Einstein wasn't sure of this for various reasons, and changed the equations to read:
(curvature) = (const) * (amount of matter) + (another constant)
Where the second constant he threw in is the famous "Cosmological constant", which represents the curvature of space when you take all the matter away. If it was nonzero, it would be like you had a really saggy rubber sheet and hung it up by the corners so it was curved even if you didn't put any weights on it.
What the article suggests (as far as I can gather), is that, to a not huge degree of accuracy, this constant is zero. (Or that something else is going on - see other posts).
(Sort of. It's much, much more complicated than this, and I'm sure I'll get jumped by the local physics mafia, but I hope you get the idea.)
Apologies for the huge post, I hope it was of use to someone. If you want to read more on the subject, go for vol. 2, chapter 42 of the Feynman lectures for a very readable explanation which also involves ants, or if you want something more solid, "Essential Relativity" by Wolfgang Rindler (ISBN 0-387-10090-3) is rather good. Someone else suggested "Gravitation" by Misner, Thorne, and Wheeler, which is good and really comprehensive, but forbiddingly huge.
It's certainly possible that dark matter has some sort of weird interaction characteristics that cause it not to cluster, but it's not what you expect. Particle-particle interactions are typically mediated by short-range forces, while gravity is a long-range force. In dense materials like water and oil the molecular separations are small enough that van der Waals forces and the like dominate gravity. By contrast, in space interparticle separations are large, and so interactions strong enough to separate out the dark matter would be surprising. That's not to say it can't happen (in fact, something very like that scenario happens with phenomena like ambipolar diffusion), but for it to happen on intergalactic length scales would require some creative physics. Moreover, if I recall correctly, field (i.e. away from galaxy clusters) gravitational lensing surveys put some constraints on the existence of dark clusters, so the dark matter would have to interact in such a way that it doesn't cluster at all, not even with itself. Again, one could probably work up a scenario to fit this constraint, but it's not what you expect.
Basically, it comes down to a question of parsimony. It's bad enough that the dark matter has to be nonbaryonic; one would like to stay away from anything that makes it even more exotic. Finding more mass density in the universe than can be accounted for in galaxy clusters would have required lots of new physics, and in some sense it would have undermined confidence in the standard model because when a model starts growing too many patches you start to look for something simpler. Instead the new result bolsters confidence that the standard model is basically on the right track.
I guess the short answer, then, is that nonclustering dark matter is only really "a problem" for the standard model. If the standard model is overthrown it's not the end of the world or anything. However, we like the standard model; we think we understand it pretty well, and it has a lot of useful predictive power. Consequently, most astrophysicists (including this one) would rather see it refined than discarded.
-rpl