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Space Science

Universe's Curvature Measured? 161

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. "
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Universe's Curvature Measured?

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  • by Anomalous Canard ( 137695 ) on Wednesday April 26, 2000 @08:55AM (#1108908)
    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
  • We miss the most important information:

    Is the curvature positive, negative or null ?

    Are we leaving in an Euclidian space or not? , that is the question !

  • This may be some thing ,to actually get a realistic handle on the size of it all,but it may be a little premature.(I have to go read the article first.)
  • If I remember correctly the universe is supposedly saddle shaped... hence the curvature of the universe being a measurable thing...

    What I've never understood is what is meant by that... does all the universe's matter (planets, stars, etc) fit into a saddle shape? If so, is there any particular reason why?
  • From what I can tell, essentially flat space is within the experimental error.

    Anyway - you are certainly living in a curved space, as demonstrated by the fact that gravity is doing a nice job of holding you in your seat.

  • I mean our universe is so damn boring, as they say in the article :

    "This provides evidence for a euclidean geometry of the Universe."

    Those scientists ain't funny. Now i have to revise all that i have been taught in school about geomertry. Had the universe been curved positively or negatively, we could have said "Forget all that you know, come and join us in our non-zero curved universe" !

    I want to change universe !

    Anybody has a non-zero curved universe to sell ?

  • This paper suggests that space could well be flat. The way to think about the saddle-shaped business is probably to think about more local properties that you could in principle measure from the comfort of your own room. If space were negatively curved you could draw a triangle in your room and the angles in it would add up to less than 180 degrees. Trying to think about how things fit into curved space will only give you a headache :)
  • According to the BBC Synopsis [bbc.co.uk], "one of cosmology's greatest questions by revealing that the Universe is 'flat'." Does this mean that if one flies in a spaceship far enough, they can "fall" off the end of the universe? Should we send a "Columbus" probe out to find out? (c:
  • by mackga ( 990 )
    26/34/38 - easy!
  • Curvature it a good thing. Just as long as she's not all flabby. mmmmm curvature.
  • For those of you who have read Brian Greene's excellent book The Elegant Universe [wordsworth.com], or have other sufficiently advanced physics background, do you know if this "curvature" extends into some or all of the 6 micro spatial dimensions?

    Want to work at Transmeta? MicronPC? Hedgefund.net? AT&T?

  • Never mind the curvature of the universe. Check out the curvature on Miss Universe [missuniverse.com]. Awooooooga!
  • The curvature of the universe in scientific terms is:
    "Somewhat curvy"
    To laymen, the translation is:
    "Quite wobbly."
    I'll bet the shape they're seeing out there is really just a turtle shell. If the looked up a little the might get an impression of four large elephants.
  • It's not better or worse than Heaven, Hell, or anything else out there it's just different, and that's why it's so good :)
  • For those of you who are interested in Cosmology stuff of this type, I highly recommend reading "Wrinkles in Time" by George Smoot. It outlines his many years long quest to validate the big bang theory, included antenna arrays in the Antartic, high altitude balloons, and ultimately a satellite launch. It covers the politics and drama of government funded research as well as the science itself. It is a few years old (1994) but still a very enjoyable and worthwhile read.

    Thad

  • by rangek ( 16645 ) on Wednesday April 26, 2000 @09:20AM (#1108923)

    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.

  • by Anonymous Coward

    If I remember correctly the universe is supposedly saddle shaped...[snip]...If so, is there any particular reason why?

    Well, God's ass has to go somewhere.

  • The term flat applies to the way the universe will continue to expand. Flat refers to a slowing of the rate to 0. the universe will never stop expanding but the rate will go to 0. As opposed to a constantly expanding or eventualy contracting universe.
  • 26/34/38 - easy!

    Ugh. I like 36/24/36 better myself. But to each his/her own I suppose.

  • Saying the Universe is "saddle shaped", "flat", and "curved" are primarily theoretical right now. When we use these terms, the picture that springs to mind is some two-dimensional surface in a three dimensional space. However, our Universe has (roughly) four dimensions. (Well, some theories have more, but they're all more than three.)

    What we really mean by this is that the equations describing the "shape" of the Universe are analogous to the equations that describe flat, curved, and saddle-shaped 2D surfaces in 3D space. It's a relationship like the one between a circle and a sphere, or a square and a cube: there are some strong similarities, but the two are quite distinct. The bottom line is, the Universe follows non-Euclidean geometry (ie. geometry not discovered by the math God Euclid). For more info, I suggest books for the layperson on General Relativity. (Or, if you are so inclined, a full GR test like "Gravitation" by Misner, Thorne, and Wheeler.)
  • The BBC article is misleading. You cannot prove that the universe is flat. All that has been done was to put finer and finer constraints on how close to zero the curvature is. So now we have a greater confidence in the flatness than the universe, compared to before!

    This just leads to the more interesting question. Why is the universe flat? After all, the visible matter (stars, galaxies and nebulae) constitute only 1% of the required amount of mass to keep the universe flat. What is the condidate for the other dark matter? (We know that there must be lots of dark matter around from rates of rotations of galaxies). This is a very controversial topic and worth lots of man-hours of work in cosmology. Whatever the candidate is, it should also explain why the universe is so flat.

  • There I was, all intrigued to see whether the cosmological constant was about to bite the dust and finally lay Einstein's "greatest mistake" to rest, and all they've found is that the universe is flat within 12%. Oh well - have to wait for the next set of results. I'm still rooting for Omega_m to be 1 just so that the universe is old enough to hold its oldest constituents ;-)

    Cheers,

    Toby Haynes

  • by Anonymous Coward on Wednesday April 26, 2000 @09:27AM (#1108930)
    I'd advise Slashdot readers to look at the Cosmology [ucla.edu] and Relativity [corepower.com] FAQs, since they probably answer a lot of questions people are tempted to ask.
  • Does this mean that if one flies in a spaceship far enough, they can "fall" off the end of the universe?
    Don't be silly. There's no gravity at the end of the universe. Didn't you see the sign?

    Should we send a "Columbus" probe out to find out?

    It's already been done. Columbus 1 was launched in 1978 as part of NASA's top secret "Top Secret" programme. It used a quantum tetryon drive to transport itself instantly to Zeta Reticuli, where it claimed the planet in the name of the Earth. It then spent the next twenty years slaughtering the native population and replacing it with Earthmen and women. The new population has a lot of wacky ideas that they're trying to foist on the rest of the universe, like the freedom to bear tactical nuclear weapons and a literal interpretation of Lord of the Rings.
  • A "remnant" of the Big Bang is something that hasn't interacted with a lot since the Big Bang. These photons in the microwave background just stay out there, while other collections of particles (like the Earth) have changed dramatically. The only thing that really affects the background is the size of the Universe, and there's no direct interaction involved there.

  • This is confirmation at a universal scale of the matter/energy equivalence. i.e. the entire energy of the universe exactly is balanced by the force of gravity.

    If this is true then:

    There REALLY is missing "dark matter" at least 70 percent of the universe is unknown to us.

    The "heat death" ( entropy increasing )of the Universe is going to be our/its final fate. ( Unless that dark matter has some exotic properties we don't know about, which at this point would not suprise me )

    And apparently there is such thing as a "Free Lunch" ( as in beer ). We don't have to pay back the Big Bang with a Big Crunch.

    I kinda was hoping for alternating Bangs and Crunches, it allows one to imagine perhaps existing again in another iteration.

    A Universe that lasts forever and dies an entropy death kind of does not allow that.

    How depressing...

  • six times nine is 54. six times seven is 42.
  • by Anonymous Coward
    These curvature results need not apply to the compactified spatial dimensions of string theory; those dimensions could be either curved or flat.
  • by Anonymous Coward
    Huh! I don't particularly like my universe flat, thank-you-very-much! I much prefer a smooth, roundish spheroid, with just a touch of fur - very much like a peach. Yes, yes!

    Or, perhaps a bit of the bubbly, eh, eh? I mean, WHO would drink flat bubbly, now? Can you tell me THAT? Well, then, why should I accept a universe made up of flat space? After all, I've paid GOOD money here, so I expect to get what I paid for, and I most CERTAINLY did not pay for flat space!

  • by spiralx ( 97066 ) on Wednesday April 26, 2000 @09:36AM (#1108937)

    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.

  • So is that why you rarely ever see the Enterprise fly over / dive under an enemy to evade fire? Cause they'll hit the edge? ;-)

    The Divine Creatrix in a Mortal Shell that stays Crunchy in Milk
  • In this months discover, 'Big Bang' somethin something. They talk about the new satellite that will be going into far orbit around the moon which will be doing lots of studies. One such study is to find out of the universe is finite or not, and what the topology is based off of the primordial acoustics still floating around in the ether. I read in a previous slashdotters post about the piece of paper. Just as a piece of paper can be flat, you can turn it into a doughnut and now you have a finite idea. The scientists/mathmaticians interviewed said that the universe might be so large that the shape will not be definable because we can't see enough of it.

    Just some more interesting reading for the bin, no matter what catagory/field we choose, we're all just guessing apes. I find it interesting to hear this years theories and projections.

    Keep'n it real,
    -Malachi

  • The thing that you are failing to realize is that gravity would have the effect of attraction regardless of the type of curvature of space. If the curature of space is indeed flat as it apears to be, the universe is likely to expand forever.
  • I think what this article implies is that the findings from studying the dispersion of CMB radiation is that it has an asymptotic dispersion towards 0...this implies that the universe will decreasingly expand until it reaches 0 expansion (in the year of our lord infinite)

    This implies dark matter, of some guessed-at percent, but also confirms most of our geometric approximations based upon euclidean space to be more or less exact. This 'discovery' doesnt seem to me to be that...amazing, to me its like a taxonomation of current theory; a worthwhile proof of current theory no doubt. but this isnt saying anything amazing to me, the debate about the curvature of the universe has always been presented to me in misunderstood, vague generalizations...

    maybe i just dont get what they are talking about though.
  • by captainmikee ( 178594 ) on Wednesday April 26, 2000 @09:43AM (#1108942) Homepage
    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.

    From what I remember of astronomy class, the curvature depends on the second derivative of the spatial dimensions over time:

    1. If it's negative, the universe is "spherical" (that might be the wrong word) and it will eventually collapse back to a point in a "big crunch."
    2. If it's zero, the universe is flat, and it will expand asymptotically towards some maximum size.
    3. If it's greater than zero, the universe is "hyperbolic" (saddle-shaped?) and will expand without limit forever.
  • by Alexey Goldin ( 5545 ) on Wednesday April 26, 2000 @09:43AM (#1108943)
    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.
  • by spiralx ( 97066 ) on Wednesday April 26, 2000 @09:46AM (#1108944)

    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 /. :)

  • Even if space-time is flat across the entire universe, it is curved when there is a large amount of matter involved. This has been observed by astronomical observation, where light from distant objects is distorted by closer objects. So if space is flat, it is a pimpled surface, rather than smooth.


    Gonzo
  • What I meant was that I thought that if space was flat locally rather than over the universe as a whole, you have no net gravitational force. Hence although space may be flat when considered on universe-scales the space we are living in is certainly curved.

    But then I'm no general relativity expert :)

  • Yes, I am selling a non-zero curved universe on Geekswap.com, starting price a low US $0.50!
    Here it is [geekswap.com]


    Don't criticise someone who is attempting to use free software for not using enough free software.
  • Sure, it's impossible for us to visualise it...

    Some of us with 6th dimensional sensory organs have no problem `seeing' this.

    Hehehe. Puny humans.

    Bad Mojo [rps.net]
  • Yes, but God uses base 13.


    Don't criticise someone who is attempting to use free software for not using enough free software.
  • by Robert Link ( 42853 ) on Wednesday April 26, 2000 @09:56AM (#1108950) Homepage
    First, the dependence on omega_m goes oppositely to what you suggest. Smaller omega_m -> older universe. Second, a flat cosmology and a nonzero lambda are not mutually exclusive; the condition for flatness is that Omega(matter) + Omega(cosmological constant) = 1. In fact, their preliminary result (based on the test flight data) seems to favor a flat cosmology of the large-lambda variety (Omega(lambda) = 0.75). That's not too much of a surprise, since both timescale arguments and Hubble diagrams from Type Ia supernovae point toward the same thing. The difference seems to be that this result excludes Omega(lambda) = 0 much more strongly than previous results.


    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

  • mmmmmmm........ urban legends...
  • A group of scientists have released data that they claim proves that the world is indeed flat, countering a theory that our planet is a sphere.

    One of the scientists involved in developing the project explains how it worked: "We had this really big balloon...the damn thing was huge, and we let it go in antartica. It flew up and away exactly as predicted."

    The scientists waited and waited, but the balloon never returned. "Yeah, if the world wasn't flat, the balloon would've gonna around it and come back by now. We've only been here 3 weeks, but that's because we're using a superclock, instead of a nondescript desktop clock, with which we would've had to wait 6 months." said the project leader.

    Scientists are thorougly excited by this new data, because now they have the task of finding a suitible replacement for all of the "globes" that fill the world's schools and households. One excited professor exclaimed "We might even get to rewrite textbooks. Do you have any idea how fun it is to write textbooks?"

  • by spiralx ( 97066 )

    I've read the book and done some research into superstrings, and the answer is no. The micro dimesions called for by superstring theory are curved, but in their own separate dimensions rather than in the 4 macroscopic dimensions of "normal" spacetime. The current thinking is that these microscopic dimensions form what is mathematically known as a Calibi-Yau space, which is next to impossible to visualise without being a 6-dimension being, whereas current cosmological evidence says that the macroscopic dimensions are flat. The two have distinct curvature due to their differences in size.

  • Of course, it is fine to attempt to measure the curvature of the universe, but as Douglas Adams has stated in one of the Hitchhiker's Guide to the Galaxy novels (sorry, can't remember which one right now), the universe isn't really curved, but is, in fact, bent.
  • by Anonymous Coward on Wednesday April 26, 2000 @10:06AM (#1108957)
    Sorry for the negative tone of this post, but many of your points are quite wrong:

    (1) Inflation does not demand a zero cosmological constant, it only predicts a flat universe. And as soon as measurments started to come out conclusivly showing that there was not enough matter in the universe to make it flat without a cosmological constant (Sne IA, baryon mass fraction in massive clusters, weak gravitational lensing in the field), inflation stoped even a flat universe (it's an evolving theory...:)

    (2) You are correct that current mass estimates will not close the universe and that it will expand forever -- but that only means it has negative curvature if the cosmological constant is zero. Flat universe (boomerang result) + low mass universe = positive cosmological constant.

    (3) The power spectrum measured by boomerang directly rules out cosmological defects as a source of dark matter. Microlensing searches in the galactic halo place very low constraints on the mass of "black hole" type dark matter. Also big bang nucleosysthes + light element abundance measurements totally rule out the possibility of such black holes being made of baryons -- so they would have to be made of dark matter anyway, thus they are not a good solution to the dark matter problem (read that as: dark matter is not black holes)
  • by Snard ( 61584 ) <mike...shawaluk@@@gmail...com> on Wednesday April 26, 2000 @10:10AM (#1108960) Homepage
    "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
  • The flat universe implied by these measurements is of the Omega~0.3, Lambda~0.7 variety. If the results are valid, that means that most, if not all of the matter in the universe is observable through its gravitational effects, albeit not directly through emitted radiation.


    Also, the nonzero cosmological constant invalidates the BBC journalist's claim that the universe will coast to a stop at very large times. As the universe expands the matter density drops, and so a positive cosmological constant will drive the universe into exponential expansion when the matter density becomes negligible. That's assuming, of course, that the cosmological constant really is constant, which is the case in the standard cosmological models. One can imagine (and there are compelling theoretical reasons to believe) that if lambda is nonzero, then it is also nonconstant.


    Finally, regarding the heat death of the universe, see the article by Adams and Laughlin in the August 1998 issue of Sky and Telescope. Apparently there will still be interesting phenomena in the universe, even after the last of the stars burn out.


    -rpl

  • And apparently there is such thing as a "Free Lunch" ( as in beer ). We don't have to pay back the Big Bang with a Big Crunch.

    The thing about this is that the Universe is a "free lunch". The positive energy of the Universe from all of its matter in whatever form is exactly balanced out by the negative energy from the potential energy of the gravitational force, and so the net energy of the Universe is zero.

    Since the Universe has a net energy of zero, from the time-energy uncertainty relation h-bar >= E * t then the Universe could have been created from nothing and still exist forever without violating quantum mechanical principles. So in that repsect it truly is a "free lunch" and the question of its end is irrelevant.

  • by algae ( 2196 ) on Wednesday April 26, 2000 @10:17AM (#1108964)
    You forgot:

    - Revolves around Hemos
    - 1 0wN 7h3 un1v3r53!!!

  • As far as I can remember (and I'm too lazy to find my cosmology lecture notes), inflation was originally proposed by Alan Guth, then Linde sorted out some of the maths to make it work properly . . .

    Doh! My poor memory there :) Yes, Guth did come up with the first idea and Linde then worked on it. Linde also came up with the idea of "chaotic inflation" whereby there is a kind of underlying "meta-Universe" in which chaotic effects constantly cause inflation to occur within small parts of it. Due to the speed of inflation preventing information from travelling outside of a given area, inhabitents of each inflated area would perceive that area as being the whole "Universe", just as we do.

    More importantly, inflation theory *does* predict a flat universe, but this isn't necessarily the same as one with zero cosmological constant.

    No, but IIRC current experimental constraints upon the cosmological constants place it as being no greater than 10^-120, which is a very small number indeed. Hence even if there is a cosmological constant, it's effects will be minimal and a flat universe will be equivalent to a matter density of omega = 1.

    Anyway, sorry for the errors, it's been over a year since I studied relativity, and you know how easy it is to forget the little things :)

  • There are three basic types of geometry: Euclidean which has triangles whose angles sum to 180 degrees, saddle shaped whose triange angles sum to less than 180 degrees, and spherical whose triangle angles sum to greater than 180 degrees. Saying that the universe has a 'saddle shape' means that the spacetime geometry has a negative curvature. This is not something that you can really see directly in the universe, much like an ant on a sphere has only indirect methods of determining that he is on a finite unbounded 2-space.
  • by Gaber ( 157796 ) on Wednesday April 26, 2000 @10:32AM (#1108968)
    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/ [rice.edu].
  • huh? IIRC positive curvature is synclastic [everything2.com], while negative curvature is anticlastic [everything2.com]. You've got it backwards.
  • The Universe ate my balls.

    At least that was his response to me trying to explain this story. I thought it appropriate.

    --
  • Feel free to shoot me down, as it's been too many years since I was a hardcore physics geek. The curvature of our 4-D universe is often compared to a two-dimensional sheet, which could be flat, spherical, or saddle-shaped. What if the two-dimensional sheet is actually 2.4 dimensional - ie, it has fractal qualities? Does it make sense to measure the curvature of a fractal surface? Does the measurement depend on the scale that is being measured? What would the effect on cosmological theories be?

    I realize that posting this question here probably makes as much sense as asking comp sci questions on alt.physics.geeks, but interesting answers to interesting questions are often forthcoming.
  • by doop ( 57132 ) on Wednesday April 26, 2000 @10:46AM (#1108973)
    Sort of :-) I believe the canonical explanation involves ants, and runs something like this:


    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.

  • I often read about the universe's expansion being described as like points on a balloon being blown up, and there was no point that the universe expanded away from.
    However a balloon is manifestly curved.
    How does this stay consistent with the result that the universe is flat?
  • by Anonymous Coward
    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.
    Certain mathematicians also call it a straight line too. I think that it is a very appropriate term. There are two ways in which you can define a geodesic: you can say that it's the "shortest path between two points", or you can say that it's "a straight path between two points". In the latter case, "straight" means "parallel transports its own tangent vector" where "parallel transport" is defined using a connection placed on the space. When the connection is metric-compatible (as in general relativity) the two definitions are compatible. Both definitions are consistent with the Euclidean notion of a "straight line". I see no problem in calling a geodesic a "straight line" because using the only meaningful definition of straight -- the one defined by the connection -- a geodesic really is straight.
    Except that it was phrased in an exceedingly accurate way that boils down to sixteen smaller equations.
    Ten, actually; the number of independent components of a 4x4 symmetric matrix.
    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.
    Actually, it doesn't in any way imply that. The "curvature" you've written is the Einstein curvature, and the vanishing of Einstein curvature implies the vanishing of Ricci curvature. However, there can still be nonvanishing Weyl curvature and hence nonvanishing overall (Riemann) curvature. There are LOTS of important vacuum solutions of Einstein's equation (even with zero cosmological constant) that have nonzero curvature, such as the Schwarzschild and Kerr black hole solutions, gravitational wave in empty space solutions, etc.
    Now, Einstein wasn't sure of this for various reasons, and changed the equations to read: (curvature) = (const) * (amount of matter) + (another constant)
    He changed the equations for reasons other than not being sure about empty space implying zero curvature. Rather, he changed them to admit static solutions since at the time he didn't think the universe was expanding (or contracting).
    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.
    Well, some of it, at least...
    What the article suggests (as far as I can gather), is that, to a not huge degree of accuracy, this constant is zero.
    No, it suggests that the mean curvature of space is zero. There is other evidence that still remains that suggests that the cosmological constant is not zero.

    As for your book recommendations, they're good. For more solid texts that are more advanced than Rindler but easier than MTW, try some combination of Schutz or d'Inverno or Martin. Something at the level of Rindler would be Ellis and Williams.

  • Then what happens to the "place" that used to be there when one forms? How about the "places" where one has expanded (if in fact they do that) into?

    Hey Rob, Thanks for that tarball!
  • A good book to read for those interested in this topic is "Wrinkles in Time" by, I think, George Smoot. It describes in novel form his work with Cobe (one of these background radiation imaging research project). He carries the story through working with Nasa, launching weatherballoons, even to antarctica. The novel is interspersed with well described information about the theories behind background radiation, the origins of the universe, and what the images they discovered really mean.

    I recomend it.
  • This theory is based on the idea that since the universe is curved, nothing can ever travel in a truley 'straight' line, and by observing the current path of anything, we can calculate the overal curvature of the universe. There are, however, many problems with this theory leading it to be highly disputed. 1) In order to measure the true curvature of an object, you can't be on the same path as that object. So the only way to measure the universal curvature of a particle in space would be to step outside of space. 2) The theory also assumes that the universe has a constant curvature throughout it. There is no evidence anywhere for or against this. All that this 'evidence' would ever show is what the curvature of the universe is in the immediate vicinity of our galaxy. 3) you can't measure anything without effecting your results. 4) There is no way to dispute the fact that at least part of the curvature of space around us is to be contributed to the mass of objects we can or can not see. Therefore, measuring the curvature of the space around us ONLY measures the curvature of the space around us and not the entire universe
    --
    ICQ#: 7012329 | AIM NICK: CW0LVES
  • Try another analogy, since the one you gave is flawed (as you noticed). One which matches better is the "baking cake with raisins," in which the raisins all get farther apart as the cake raises during baking.

    Of course, the flaw in this one is that the raising cake is expanding into the same 3-space you're measuring raisin separation in... while the with the expanding universe it's actually space itself which is expanding.

    Analogies seem to have these problems, I guess -- which is why physicists use mathematics, not analogies, to describe the universe [unless they're this John Dobson guy ;) ].

    ---

  • Hi, spiralx,

    I've seen you on a lot of the topics I browse, so I assume we have similar interests. Please understand that I don't mean to be obnoxious when I say this, but it is my understanding that there is no mathematical requirement for a Calibi-Yau space to have a specific curvature (positive negative or zero)

    Instead of saying that "The two have distinct curvature due to their differences in size", wouldn't it be more accurate (and enlightening) to consider that the two have different sizes due to their curvature?

    A (terribly) gross analogy: a 'garden hose' of infinite length is an non-bounded two dimensional surface embedded in a three dimensional space. The difference between the nature of its [infinite, essentially zero curvature] length and its [finite, positive curvature) circumference can be seen as a function of the curvature. Less curvature = larger diameter hose; a much lower curvature would be like a subway tunnel, much closer to flat locally, but of identical global geometry.

    [Sorry for mixing the r=1/kappa definition of curvature where it doesn't quite fit. All readers actively involved in the large-scale warping of space, please cover your eyes -- no, not while you're.... >GLURP ]
    _____________
  • Okay then smartass, let's hear you explain how homophobia leads to porn. I'm waiting...


    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • ...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).

    Correct me if I'm wrong, but I believe it isn't precisely zero.

    A small initial mass on the order of a few kilograms spontaneously generated by a quantum fluctuation, created a small universe (the big bang) in which inflation could then take place. Admittedly, this small mass would be dwarfed by the quantum uncertainty which relates to the presently much larger mass of the universe.

    I just wanted to point out that the inflationary generation of mass out of negative pressure doesn't account for the origin itself.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Another question is whether the universe is finite or infinite. I think if the curvature is positive (enough), the Universe must be finite (essentially, you look at the surface of a sphere and you make the radius of the sphere become larger and larger: at some point it must decrease because of the positive curvature, and when it goes back to zero your sphere is the entire, finite, universe — sorry for the hand-waving). If the curvature is zero or negative, on the other hand, the Universe can be infinite but it can also be finite (notice that there is no difference between a finite universe and a periodic one). This applies for time as well as space.

    Would you rather live in a finite universe or an infinite one?

  • An easy way to explain this 180 degrees, less than 180 degrees, more than 180 degrees garble is like this: Take a sheet of paper. Draw a right-angled triangle (it doesn't have to be right-angled, but this helps explain the following examples). Add up the angles. 180 degrees. Voila! This is your flat universe. Now, take the Earth. The whole thing. It doesn't have to be the Earth; it could be the sun, or a rubber ball. Pick any two points on the equator. Connect these two lines with a big pencil. Now, remember grade 4, where you were taught all longtitudnal (sp?) lines ended up at one of the poles? Well, take your two points and draw straight north from each of them. Both end up at the north pole! So you will have two 90 degree angles, plus an x degree angle. More than 180! This is a spherical, or closed universe. Now for this last one, let's take that hollow rubber ball, and cut the top half off. We're looking in on a bowl-like shape. Draw a triangle inside. The angles add up to less than 180. This is your saddle, or open universe. This makes sense, if you flatten out the earth or the open bowl. If you do this, your triangles won't really be triangles at all; your flat earth will have pushed in sides, and in the bowl the triangle's sides will stretch outwards. The theory behind the closed (spherical) universe is that, given enough mass, the universe will close in on itself, somewhat in the way in which the Earth is closed on itself. In the open (saddle) universe, there isn't enough mass, so the shape of the universe is that of a parabola (A 'U' type thing, except the sides keep moving outwards instead of being parallel). Lastly, the flat universe has a perfect quantity of mass, meaning its shape is not curved in any way. If you go from the Earth to Pluto, you're going in a perfectly straight line (well, you're really going in a straight line in whatever universe you're in; but remember, like with the triangle sides, if you are in an open or closed universe you would appear to be moving in a curved line to an outsider. This shows how in an open or closed universe, the shortest distance between two points is _not_ a straight line. This shortest distance is called a geodesic. But now I'm off topic.) In an open universe, since it does not have enough mass, the galaxies will continue to fly apart from each other, forever and ever. On the flip side, in a closed universe, eventually the force of attraction between the galaxies will be strong enough to slow down this acceleration, and the galaxies will then move back together into a Big Crunch. And again, lastly, in the flat universe, the mass of the universe is just enough to stop the acceleration apart, but not enough to start bringing it back together. Therefore, it will just stop and be still, and we'll live in a static universe. You can see how important it is, then, that we detect the enigmatic "dark matter". This invisible matter could account for up to 90% of the mass of the universe, and is really the button to whether our universe is open, closed, or flat. There is not enough detected mass in the universe to allow for a closed universe. We need dark matter. You can also see how favourable the closed universe is over the other options. A Big Crunch would give way to another Big Bang (in fact, this is not necessarily the first 'universe'; there could have already been a hundred, or a million, or infinite universes before this), and this would continue. This is the theory of the oscillating universe, and it's really preferrable to believe this as opposed to the thought of the universe going cold and dark forever. I'm personally skeptical of these findings implying a flat universe, as it just seems unlikely to have a _perfect_ amount of matter (well, it's within a range, but it's still rather precise on a universal scale) to allow for a flat universe. I'll keep my eyes open, but what I'd really like conclusive evidence of a closed universe! You don't always get what you like, though. Anyways, I just intended to explain the triangles, but I went way overboard. I guess this is just a topic that interests me! Best wishes, Mark Ferguson
  • Interesting insights. However, I've always wondered why 'dark matter that steadfastly refused to cluster like ordinary matter' would be such a problem. [I understand that it would impact some current theories of galaxy formation, etc. but I'll get to that in a moment]

    First off, 'ordinary matter' may well a minority constituent of the universe (Sure *we* like it, but it's all we've seen)

    We've been modeling galactic dynamics as an attraction-only model, yet I have never seen any discussion of the 'exclusion-type' epiphenomena that we commonly observe on earth. An example would be the manner in which large rocks float (seemingly counterintuitively) to the surface of shaken gravel. (This has many practical applications: they recently reversed avalanche survival procedure to reflect this -- so we're betting lives on it!) Other exclusionary epiphenomena include immiscible droplets (e.g. oil 'excluded' from water by the greater polar attraction between water molecules) and cellular membranes (which are lipid bilayers in aqueous environments)

    If the dark matter interacted more strongly with itself than with 'ordinary matter' then we might expect similar exclusionary epiphenomena... droplets or bubbles of 'ordinary matter' excluded from a sea of dark matter. Given how extremely tenuous matter (of all types) was in space even in the first Billion years, this effect might simply speed the creation of the initial protogalaxies slightly.

    Once excluded, 'ordinary matter' would exhibit the intragalactic dynamics we would otherwise predict from our models. AFAIK, current theories of inter-galaxy dynamics would be unaffected, since they acknowledge 'something's out there' but don't specify how that 'something' would interact with *itself*.

    I agree this is all speculative, but the key is that all interactions between dark matter and ordinary matter are unchanged, it's only the interaction between dark matter and dark matter that is changed. I'd expect this to be detectable through very subtle variations in 'observable matter' (galaxy) dynamics, reflecting the underlying distribution of dark matter, but I don't think experiments/models of sufficient detail exist yet.

    Your comments would be appreciated

    _____________
  • This post is informative and corrects many of the incorrect things people are saying over again and again on this thread. I was going to post my own explanation, but there's not much more to say. If moderators are still around it should be bumped up.

    One minor addition. There are lots and lots of very good cosmologists saying very different things about the implications of these results. The message that this confirms everything that may have been drawn from he press conference is very misleading. Yes, the overall picture is verified. However, several of details are in significant disagreement with the most standard of the standard models. It seems everybody has fit their favorite model to the data, but it will take time (and more data) before we really sort out the true implications.

  • by astrophysics ( 85561 ) on Wednesday April 26, 2000 @01:43PM (#1109010)
    This is similar to recent proposals of Self-Interacting Dark Matter and Repulsive Dark Matter. If you'd like to see details search for either on http://xxx.lanl.gov/find/astro-ph . If you have trouble, good starting points are the papers by (Spergel and Steinhardt) and Goodman for SIDM and RDM, respectively.

    This is a big fad right now and lots of people are working very on it quite rapidly. You'll notice all the papers on astro-ph are from the last several months. We'll see whether this is the big break through dark matter has long needed or whether it's just another wacky idea.
  • You're missing my point. I'm asking a simple question here: What happens to the SPACE the singularity formed in? Take the colapse of a star for instance: What happens to the space, and more importantly, the energy and the matter that used to exist there? What happens to things in the new hole's proximity? Is that more clear?

    Hey Rob, Thanks for that tarball!
  • Hey, I've been trying to get a straight answer out of someone about that exact issue for several years now. I always got a different (and incomplete) answer depending on who I spoke to. Your answer puts it all together at last. Thanks!


    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • GLURP

    ROTFLMAO! (I always wanted to know what a large-scale space warping accident sounded like)

    BTW if anybody's interested: this [nature.com] other recent paper about the Boomerang results states explains why the size of the small CMB ripples confirms that inflation must have taken place.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction

  • There can only be two answers to the question of why the universe is flat:

    (i) Some chance combination of initial starting conditions at the big bang which cannot be further explained - this universe just happened to be like that.

    (ii) A universe with a higher degree of curvature would have been unlikely to produce intelligent life either because it would have failed to produce enough baryonic matter or because it would have collapsed too soon for life to evolve, or because it would have cooled down too fast for life to evolve.

    Cosmology is at least more straightforward if you know your Barrow and Tipler ;o)

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • I don't know if that's necessarily true. Whether zero or 10 to the -120th, it may not really matter either in terms of consequences or even from a theoretical standpoint. The universe's starting conditions are de facto inexplicable: they have the values they do simply because that's just the way they happened to come out in our universe. Since I know of no theory in which lambda is the result of other still more fundamental parameters, I think this might be one of those starting conditions that (putting the Cosmological Anthropic Principle aside for a moment) took purely random values.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • I don't think the question is meaningful. The term "dimension" doesn't mean quite the same thing when applied to fractal geometries as it does when applied to spacetimes.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • by Robert Link ( 42853 ) on Wednesday April 26, 2000 @04:25PM (#1109024) Homepage
    Good points, all. First, 'hot' dark matter, that is, matter that has too much energy to remain bound to galaxies, is right out. Hot dark matter impedes the formation of large scale structure.

    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

  • Yeah, what he said. :-)

    This should be moderated up, unlike many other posts that have appeared on this subject. Maybe we should introduce a "blatantly wrong" moderation modifier. :-)

  • Caveat: I haven't actually read the BOOMERANG group's paper, so I probably shouldn't even comment. But what the hell.

    The way many of these groups arrive at their estimate that the universe is "flat" is basically from such power spectrum measurements. Basically, the first peak of that spectrum (at an angular scale of about l=200) implies (to within reasonably small error bars) that we live in a flat universe. (More rigorously, it implies that Omega_k, an effective density term arising from the curvature, is equal to zero.)

    The "power spectrum" does tell you lots of other things, true. But so does the mere fact that the CMB spectrum itself is Planckian -- it's possible to show that energy injection by unknown particle species at early times would alter the spectrum that we see today. It's also possible to constrain lots of other cosmological things, like the redshift at which reionization occurs, by observing the spectrum. This is getting more technical than is really appropriate, so I'll stop -- point is, though, that the result here (and from other similar papers) is actually pretty significant. Doesn't mean there aren't other significant papers to be written. :-)

  • There is more than one solution satisfying a positively curved GR universe with even curvature. One of these would be the solid surface of a hypersphere. Of course the "centre" of the hypersphere doesn't exist in our four-dimensional spacetime. But then, the throat of a wormhole or an "open" black hole doesn't exist in our four-dimensional spacetime either. Even so, it is (as you suggest) fairly unlikely that wormholes or tunnels between rotating blackholes would ever cross each other.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Yes, a pure hot dark matter making up most of \Omega_{crit} (and probably even \Omega_{matter}, at least for current estimates) is ruled out by large scale structure. However, large scale structure is unlikely to rule out a contribution as small as a massive neutrio might provide.

    I don't understand your motivation for feeling that as of yet undiscovered particles are more likely to have short-range potentials with a characteristic scale comperable to that of the other particles we know about.

    Sorry, I used standard model in the context of cosmology, not particle physics. Both exist (at least in the minds of physicists) and are almost certainly connected in some way we don't yet fully understand. By standard model I meant something along the lines of CDM possiblely plus a lambda term.

    While I'd agree that the standard model of particle physics has demonstrated significant predictive power, I can't think of much significant the standard model of cosmology has predicted. If you meant to imply that the standard cosmological models (CDM or LCDM) have "a lot of useful predictive power", then I'd like to be reminded of what they've predicted.

  • A "hole" in spacetime develops when a singularity forms. The hole doesn't "go" anywhere, it's just as if you removed a piece of spacetime. There is literally no space or time where something can exist.

    For a stationary black hole carrying no electrical charge, the singularity has the dimensions of a single point of zero size. You can't traverse this region since you'd need to be stripped down to your component subatomic particles in order to do so. Tidal forces near the singularity would see to that anyway...

    Furthermore, the extreme curvature of spacetime in the vicinity would delay your arrival at the singularity until an infinite amount of time had elapsed in reference frames away from the black hole.

    However, singularities may be formed with different geometry if the black hole is rotating (the usual case for a natural "collapsar" black hole) or if it carries an electric charge. In some such cases there are solutions which represent trajectories through the black hole without annihilation by the singularity.

    There are also solutions to the GR equations which imply that the throat of the black hole may be connected with some other region of spacetime, either in this universe or in another.

    So far as I am aware, these exotic possibilities have not been ruled out on theoretical grounds. Therefore it is possible at least in principle for information and/or matter to be transmitted through a suitable black hole to a remote space and/or time or even to a different universe.

    However the resources required to manipulate a sufficiently large black hole to the required degree (or to build one from scratch) are so enormous that this technology will certainly be beyond our means for a very long time indeed, most likely for ever.

    The universe, for instance, isn't a singularity that "expanded".

    Well...I almost hate to say it but that is indeed pretty much what most "big bang" cosmologists do think the Universe is. In a nutshell: a few kg of matter spontaneously formed out of the void by some process of quantum uncertainty. This event is indeed commonly described as a singularity, BTW, because it forms the t=0 boundary for the universe.

    As this mass sprang into existence it flew apart, creating spacetime as it did so. But before the void could reclaim its borrowed matter to balance the books, inflation kicked in; the energy released by the expansion of spacetime was condensed into matter and so even if the initial seed was returned, everything else was still created out of nothing by compensating with an increase in negative energy. The net energy content of the universe is therefore zero (and hence there is no violation of the law of conservation of mass/energy).

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • The space is all still there, only it will be curved a little more tightly (since the mass is all compacted down within a fairly small event horizon). The mass/energy is all frozen just inside the event horizon, falling (infinitesimally slowly, from the POV of an outside observer) towards the central singularity. It will reach the singularity at time t=infinity.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Frankly, this whole argument boils down to: if we can't prove the Big Bang theory completely, then we should arbitrarily except this other model here ENTIRELY ON FAITH. Oh, and I'm going to argue something random about sentiency which violates the anthropomorphic principle over and over and over.... There are many plausible theories, each with at least some evidence backing them up, about what this 99% matter is. Probably the neatest is the macroverse theory that's part of superstrings- that most of this mass is actually "leaked" from other dimensions. That may sound wacky, but believe it or not- it's a testable theory (unlike this guys version of steady state). In fact they're going to test it pretty soon...
  • Actually, some new theories suggest that at least one of those "Extra" dimensions might not be as curled up as previously thought- and hence CAN be detected by us. Of course, this is just a new theory about a theory, not anything tangible. But if this is true, it means we could actually start testing some of the predictions of superstring theory, which would be quite neat.
  • I kinda was hoping for alternating Bangs and Crunches, it allows one to imagine perhaps existing again in another iteration.

    A Universe that lasts forever and dies an entropy death kind of does not allow that.

    How depressing...

    It's no problem at all. According to the dominant theories:

    Time is measured only from big bang to big crunch (and even then we're not sure that it keeps flowing forward during the collapse phase). Whatever, all spacetime is destroyed along with the universe at the big crunch. So, supposing an oscillating big bang cosmology: any subsequent big bang starts at time t=0 again, as if it were a replay of the original. Or - more to the point - as if it were concurrent with the original.

    So sequential iterations of the big bang are exactly equivalent to completely unconnected alternate universes or alternate world lines.

    However, the zero net content of the universe must cancel out (almost) exactly at the big crunch and there probably isn't going to be much of a bounce anyway. I therefore doubt that the oscillating universe was ever a realistic model, even if a collapse *was* on the cards.

    Does that mean we don't get more than one go? Absolutely not. The same process of quantum fluctuation that provided our universe with a kickstart can (indeed must) have happened an infinite number of times, often resulting in a big bang.

    All realities that *can* exist *do* exist, at least they do from the point of view of their inhabitants. But to the inhabitants of any specific universe, their universe and any baby universes spawned from it are all there is and all there ever will be. The siblings can never be known.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction

  • Unfortunately, your "humans are dark matter" theory has several serious problems. First, humans give off lots of infared radition (making them at least slightly luminous), and can easily be detected by telescopes (albiet only very crappy ones). Of course, if you mean human beings are floating around in space, then they'd probably be dead, meaning they wouldn't give off any radiation at all..... my god maybe you're right after all. The soylent universe! It's full of... people!
  • Given that, in my lifetime, I won't even get to the nearest star... I don't really care ;)

    In all seriousness though...
    On both a cosmological scale (relativity, black holes.. background radiation.. all that stuff) and a subatomic level (quantum physics) things start to not make sense. I think that kicks ass. It means there is more to be discovered.
  • Is the problem not that it still appears as a straight line to us? I mean, unless we view something on a large enough scale so we can see relativistic effects.. (which is what the cosmic background radiation is just great for? It's easily identifiable, and the largest 'thing' we can observe?)
  • Right. The universe isn't expanding in a radial 3 dimensional pattern.. like an explosion.... everything is just moving away from everything else. So the balloon is a good analogy... of a positively curved universe.
    A flat universe would be like...a giant rubber sheet, being stretched in both directions at once, so that every point on the sheet is moving away from every other point. It would look just like the balloon.. until you looked at things extremely far away...
  • Please understand that I don't mean to be obnoxious when I say this, but it is my understanding that there is no mathematical requirement for a Calibi-Yau space to have a specific curvature (positive negative or zero).

    Looking back at my post I can see how it sort of implies that, but that's not what I meant. Oh well, my poor writing skills are to blame there I suppose. Yes, the "extra" dimensions themselves are compactified into a Calibi-Yau space, but there is no requirement as of yet for that space as a whole to be curved - it is my understanding that there are a very large number of possible Calibi-Yau spaces which can be formed from compactification - selecting the correct one so that the Universe as we see it is produced is one of the major challenges of superstring theory, and one which might have to what for an underlying principle to be discovered.

    Anyway, I was going to E-mail you about this but you don't have an address, so you might not get this. If you do, feel free to mail be about it. Thanks :)

  • So my question is really, "is the nonzero vacuum energy part of the overall-zero energy balance of the Universe (as in the various inflationary theories)? Or does it require some other explanation?"

    Now that is a good question :) IIRC the vacuum energy comes from quantum field theory and the Uncertainty Principle - since any field can be treated as an infinite array of harmonic oscillators and everything can be represented as fields in QFT, you get a non-zero default energy from "empty" space since the lowest energy level of the harmonic oscillator is 1/2 h-bar.

    Alternatively, since virtual particles can be created from nothing via the energy-time uncertainty relation, empty space is constantly seething with these particles, giving it a non-zero energy density again.

    I think these are actually both saying the same thing but in different ways, but the exact details of QFT weren't something I did a lot of at university, so I can't give you a better explanaition. Anyway, yes, the Casimir effect has been proven experimentally, and does seem to be a way to extract the "zero-point" energy of the vacuum, although it is such a minute amount that the size of the plates would have to be very big, or you'd need a lot of them.

    So really, after all that I haven't answered the original question at all have I? Damn :) I think that this is one of those things which might require a deeper understanding of physics than we currently have, incorporating relativistic and quantum mechanical effects as it does. Anyway, feel free to mail me if you want, this topic will die soon...

  • What you seem to be saying is that a Universe *can't* have a positive net mass because the generation of space in which the mass is embedded must always exactly cancel out the mass. If that's really so, then Universe generation has no associated cost whatever. It certainly makes it seem more credible that infinite universes representing all possibilities are created out of the void.

    Consciousness is not what it thinks it is
    Thought exists only as an abstraction
  • Sure, small amounts of hot dark matter are ok, but as you point out, the densities that people talk about for things like massive neutrinos are not enough to make up major portions of Omega. So, while the existence of hot dark matter is not ruled out, it doesn't provide a solution to the dark matter problem. In the context of my post, the point was that if cosmological measurements were to show that Omega(matter) were much greater than what we see in galaxy clusters, you couldn't invoke hot dark matter to make up the difference.


    The reason I expect new particles to have short range interactions is that we (think we) know all the forces available to mediate the interactions between them. Of all of those forces only electromagnetism is a serious contender, and in practice it generally seems to be limited to modest-range magnetic interactions. I'm not saying it can't happen, but absent any evidence to the contrary it is generally wise to assume that new phenomena will resemble old phenomena. The significance of this measurement is that it fails to provide any "evidence to the contrary"; in fact, quite the opposite, it gives reasonably compelling evidence that dark matter, exotic though it may be, behaves much like the other forms of matter we are familiar with.


    Finally, when I referred to the "predictive power of the standard model" I was thinking of particle physics, in the context of invoking some sort of "fifth force" to explain why dark matter is smoothly distributed without being hot. On giving it a little more thought, I don't doubt that one could come up with a way of making nonclustering dark matter while leaving the standard model largely intact, but I think my original conclusion remains valid; viz, that this result obviates the need for much of the physics gymnastics that would have been required to explain nonclustering dark mater. To the extent that our current physics, without substantial modification, explains the behavior of exotic matter as well as the behavior of the more familiar sort, I count that as a win for physics.


    -rpl

  • You are wrong on several points. Taking your points in order:
    1. "You have to step outside of space to measure the curvature of space". This is patently false. The curvature of a manifold can be defined entirely in terms of and measured solely by observing properties within the manifold. In other words, not only do you not have to step outside of a manifold to measure its curvature, there doesn't even have to be an "outside" for you to step into. For instance, you could compute the average curvature of the earth (i.e. the 2D manifold comprising the earth's surface) solely from a table of great-circle distances between cities, without any reference to the earth's 3-space properties like it's diameter.
    2. The assmuption that the curvature of the universe is constant when averaged over large scales is derived from the observation that the matter density is constant when averaged over large scales. All curvature measurements will be averages over some length scale, but in this case the measurement extends far beyond the "immediate vicinity of our galaxy". In fact, CMBR measurements average over the electromagnetically observable universe, which is not much smaller than the entire observable universe. It is true that things may be different on length scales larger than the observable universe. This, in fact, is part and parcel of the inflation scenarios, which predict that the reason the observable universe is flat is because whatever the curvature of the universe before the inflation, inflation expands the universe so much that the curvature over any observable patch (i.e. (light crossing time) The effect on the curvature of the universe of observing the CMBR is so minute that it can safely be neglected.
    3. Again, the CMBR curvature measurements are averages over the observable universe; local perturbations are insignificant. You do, however, have to control for distortions to the CMBR by nearby objects (either through lensing, or through noncosmic emissions), but the Boomerang researchers describe how they do this in their paper.

    In other words, give the researchers a little credit for knowing their business. It's not like they haven't thought of these things and taken them into account to the best of their (or anyone else's) ability. The have gone to great lengths to give the best estimates possible given our current understanding of physics.


    -rpl

  • I guess I don't understand why you beleive you know about all the forces, including those between particles that have never been observed except via their gravitational interactions. For example, before we observed subatomic particles, there was no need for the strong force. (You could argue weak was necessary to explain radioactivity.)

    Certainly seeing the first acoustic peak was comforting. For example, at an IAS get-together today it was generally agreed that it's sharpness almost completely rules out cosmic string models.

    However, there's still a lot of work to be done. From what I understand, the combination of the first peak at l=196 rather than 220 and the amplitude ratio of the two peaks seems to require _at least_ one of the following:

    - Raising \Omega_b h^2 to violate current nucleosynthesis constraints (either the models or the observation of the deuterium abundance. I think most people would be much more willing to give up the mesaurements than the theory, since the theory is very nice and the measurement is rather difficult (measuring a bumb on the wing of a line))

    - Adding a "tilt" to the standard LCDM. (To me this seems rather ad hoc and unmotivated.)

    - Replacing \Lambda with a quintesence.

    - Saying the data is wrong by more than 2 sigma. Several people seemed concerned about their pointing error and calibration (based on Eta Carinae and the dipole rather than Jupiter). So there might be large systematics than they claim.

    Fortunately, other missions will check and improve upon the data.


  • I guess I don't understand why you beleive you know about all the forces, including those between particles that have never been observed except via their gravitational interactions. For example, before we observed subatomic particles, there was no need for the strong force. (You could argue weak was necessary to explain radioactivity.)

    People have done all sorts of extensive tests for "fifth forces", and so far there has not been any convincing evidence for such a force. So, we would have to come up with a fifth force that for some reason affects only intergalactic matter, and not the stuff that stars, planets, and astronomers are made of. Doesn't that seem just a little contrived to you? The situation is not at all analogous to the discovery of the nuclear forces because evidence for those forces manifested as soon as we were able to make sufficiently precise measurements of plain-old everyday matter.


    I haven't had a chance to look over the articles you posted earlier in the discussion. Do any of them even have workable models for a force that would make dark matter avoid clusters without producing dark clusters? Just coming up with such a beast seems a challenging mathematical problem in itself.


    Anyhow, we could add a new force to describe every new particle, but then we wouldn't have very much confidence in our physical theories. We might just as well attribute physical phenomena to invisible faeries or something. The point is that whenever you discover a hitherto unknown phenomenon and you find that it is entirely explainable in terms of previously known physical laws, it's a big win for physics. Naturally, when theory and observation conflict, theory must give way, but the fantastic thing about this measurement is that it seems to indicate that that will not be necessary in this case. I guess what I can't understand is why you don't think this is a Good Thing.


    The other points you make are well-taken, but I don't worry much about factor-of-order-unity discrepancies in a preliminary measurement. Remember that Hubble's original measurement of H0 made the universe to young to contain the earth's oldest rocks. It all got sorted out with time, and this will too. As I said earlier, I think the quintessence theories sound promising, since constant, nonzero lambda really doesn't make any sense theoretically.


    -rpl

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