Universe may be curved, not flat(nature.com)
nature.com
Universe may be curved, not flat
http://www.nature.com/news/universe-may-be-curved-not-flat-1.13776
8 comments
Someday in the future children will be taught in history class how in the 21st century people though the universe was flat. And they will laugh.
That's not really a fair way to present the situation. It isn't 'In the 21st century people couldn't imagine the universe could be curved, how terribly quaint!'.
Rather, it's more like 'In the 21st century the best data available from CMB anisotropies was that Ω was approximately 1 (or a tiny bit more), with Ω=1 being inside the confidence interval, so most cosmologists used a model where Ω=1. Later, better data showed that the true value of Ω was actually very slightly less than 1, so cosmologists started using the new, slightly more precise value.'
The fact that there's a change in the words you can use to describe the universe at Ω=1 ('open' at Ω<1, 'flat' at Ω=1, 'closed' at Ω>1), and the latest update happens to have crossed that line (so makes for good headlines), doesn't change that this is just another case of science slowly homing in on a true value.
Rather, it's more like 'In the 21st century the best data available from CMB anisotropies was that Ω was approximately 1 (or a tiny bit more), with Ω=1 being inside the confidence interval, so most cosmologists used a model where Ω=1. Later, better data showed that the true value of Ω was actually very slightly less than 1, so cosmologists started using the new, slightly more precise value.'
The fact that there's a change in the words you can use to describe the universe at Ω=1 ('open' at Ω<1, 'flat' at Ω=1, 'closed' at Ω>1), and the latest update happens to have crossed that line (so makes for good headlines), doesn't change that this is just another case of science slowly homing in on a true value.
This reminds me of a letter from Einstein (EDIT: It was Isaac Asimov) where he points out that saying the earth is flat is a pretty good approximation of the curvature of the earth.
It's also worth pointing out that educated people have known the earth is round since the classical period.
It's also worth pointing out that educated people have known the earth is round since the classical period.
It was Isaac Asimov I believe.
http://chem.tufts.edu/answersinscience/relativityofwrong.htm
http://chem.tufts.edu/answersinscience/relativityofwrong.htm
TIL that Asimov supported the notion of "nearly right", which is good enough as long as you tried really hard and could explain how you got to your incorrect answer.
"Nearly right" is good enough, providing it's within the accuracy you need for any particular job.
I suppose that depends on how the question is asked. Taking a question that has a yes or no answer with one of them being correct and changing the parameters so that nearly right is good enough doesn't seem proper to me.
The idea that medieval people thought the world was flat is entirely unfair, but still popular.
You may find this essay by Isaac Asimov interesting: "The Relativity of Wrong" [1]
1: http://chem.tufts.edu/answersinscience/relativityofwrong.htm
1: http://chem.tufts.edu/answersinscience/relativityofwrong.htm
Don't you laugh. Flat Earth still has a following today.
http://en.wikipedia.org/wiki/Flat_Earth_Society
http://en.wikipedia.org/wiki/Flat_Earth_Society
Time to start a Flat Universe society.
So, the next question is, what animal is saddled with our universe, and who is riding it. Perhaps it's The Foe from Pohl's Gateway series? :)
It's turtles all the way down.
It's clearly a gigantic whale holding an umbrella (well, that reference may be to cryptic for people who don't read French or didn't read the awesome Le Génie des Alpages comic book by F'murrr).
A monkey, clearly. http://en.wikipedia.org/wiki/Monkey_saddle
This result is consistent with what one would expect because of the geometric effect of the recently discovered Dark Energy. A saddle-shaped overall curvature is consistent with a universe accelerated by Dark Energy.
A saddle-shaped overall curvature is consistent with a universe accelerated by Dark Energy.
I wonder about this. As I understand it, the de Sitter spacetime (which would describe a universe containing dark energy and nothing else) has positive spacetime curvature, but admits all three types of spatial slicings: closed (positive spatial curvature, like a sphere), flat, and open (negative spatial curvature, like a saddle). Wouldn't that mean that any spatial curvature we observe could be consistent with the presence of dark energy?
I wonder about this. As I understand it, the de Sitter spacetime (which would describe a universe containing dark energy and nothing else) has positive spacetime curvature, but admits all three types of spatial slicings: closed (positive spatial curvature, like a sphere), flat, and open (negative spatial curvature, like a saddle). Wouldn't that mean that any spatial curvature we observe could be consistent with the presence of dark energy?
We need to distinguish between the curvature of a specific location versus the curvature of the universe as a whole.
As I understand it, for a universe that's being uniformly accelerated, by for example dark energy, its overall curvature should be negative. In the absence of dark energy, and for a universe whose masses possess escape velocity (no more and no less), the classic zero-energy assumption of modern Big Bang models, the overall curvature is zero (i.e. flat). For a universe that has less than escape velocity and will recollapse, an idea that has now been pretty much abandoned, the curvature is positive.
The escape-velocity zero-curvature universe has an interesting property -- it has zero net energy, i.e. gravitational potential energy is exactly balanced by kinetic energy. This means the universe can appear spontaneously, like quantum virtual particle do, but on a larger scale.
"Because there is a law such as gravity, the universe can and will create itself from nothing ... Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist." — Stephen Hawking in "The Grand Design".
I'm not qualified to say what a negative curvature might do to that pretty spontaneous-creation picture. It's a nice model, and it offers an answer to the question "where did all this come from?"
As I understand it, for a universe that's being uniformly accelerated, by for example dark energy, its overall curvature should be negative. In the absence of dark energy, and for a universe whose masses possess escape velocity (no more and no less), the classic zero-energy assumption of modern Big Bang models, the overall curvature is zero (i.e. flat). For a universe that has less than escape velocity and will recollapse, an idea that has now been pretty much abandoned, the curvature is positive.
The escape-velocity zero-curvature universe has an interesting property -- it has zero net energy, i.e. gravitational potential energy is exactly balanced by kinetic energy. This means the universe can appear spontaneously, like quantum virtual particle do, but on a larger scale.
"Because there is a law such as gravity, the universe can and will create itself from nothing ... Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist." — Stephen Hawking in "The Grand Design".
I'm not qualified to say what a negative curvature might do to that pretty spontaneous-creation picture. It's a nice model, and it offers an answer to the question "where did all this come from?"
As I understand it, for a universe that's being uniformly accelerated, by for example dark energy, its overall curvature should be negative.
By "overall curvature", do you mean spacetime curvature, or the curvature of a spatial slice?
As I said in my previous post, the de Sitter spacetime, which is the model for a universe that is being uniformly accelerated, has uniform positive spacetime curvature. These Wikipedia links give a good overview (of course Wikipedia is not always reliable, but these pages appear to be consistent with what I read in other more knowledgeable sources such as GR textbooks):
http://en.wikipedia.org/wiki/De_Sitter_universe
http://en.wikipedia.org/wiki/De_Sitter_space
The spacetime curvature scalar R is 4 Lambda, where Lambda is the (positive) cosmological constant.
The second Wikipedia link also describes the different possible spatial slicings of de Sitter spacetime; as I noted previously, slicings exist with all three types of spatial curvature (positive, zero, and negative).
However, it is true that the slicing with negative curvature is the one that's used in the standard cosmological models of a universe that is dark energy dominated; that's the FLRW model with exponential expansion that's discussed in the first Wikipedia link. So if that specifically is what you were referring to by negative "overall curvature", then I agree; but I would specify that it's overall negative spatial curvature, and that that model assumes a particular spatial slicing which is not the only possible one.
By "overall curvature", do you mean spacetime curvature, or the curvature of a spatial slice?
As I said in my previous post, the de Sitter spacetime, which is the model for a universe that is being uniformly accelerated, has uniform positive spacetime curvature. These Wikipedia links give a good overview (of course Wikipedia is not always reliable, but these pages appear to be consistent with what I read in other more knowledgeable sources such as GR textbooks):
http://en.wikipedia.org/wiki/De_Sitter_universe
http://en.wikipedia.org/wiki/De_Sitter_space
The spacetime curvature scalar R is 4 Lambda, where Lambda is the (positive) cosmological constant.
The second Wikipedia link also describes the different possible spatial slicings of de Sitter spacetime; as I noted previously, slicings exist with all three types of spatial curvature (positive, zero, and negative).
However, it is true that the slicing with negative curvature is the one that's used in the standard cosmological models of a universe that is dark energy dominated; that's the FLRW model with exponential expansion that's discussed in the first Wikipedia link. So if that specifically is what you were referring to by negative "overall curvature", then I agree; but I would specify that it's overall negative spatial curvature, and that that model assumes a particular spatial slicing which is not the only possible one.
> By "overall curvature", do you mean spacetime curvature, or the curvature of a spatial slice?
I'm referring to the overall spacetime curvature shared by the universe as a whole.
> ... and that that model assumes a particular spatial slicing which is not the only possible one.
Sorry, out of my depth.
I'm referring to the overall spacetime curvature shared by the universe as a whole.
> ... and that that model assumes a particular spatial slicing which is not the only possible one.
Sorry, out of my depth.
I'm referring to the overall spacetime curvature shared by the universe as a whole.
Then that's positive, not negative, for a spacetime dominated by dark energy. The curvature that is negative is the curvature of the spatial slices in the model used in cosmology for a dark energy dominated universe--more precisely, in the model referred to in the article as being suggested by the new data.
Then that's positive, not negative, for a spacetime dominated by dark energy. The curvature that is negative is the curvature of the spatial slices in the model used in cosmology for a dark energy dominated universe--more precisely, in the model referred to in the article as being suggested by the new data.
http://www.youtube.com/watch?v=wdJyafSBCb0 Howard Bloom's "Big Bagel" theory hand waves an entire scheme for everything. Pretty interesting.
The geometry of (the surface of) a torus is actually flat, not curved! This is quite unintuitive.
How do torus and saddle fit together?
Putin on a Ritz[1] comes to mind
[1]http://putintheritzon.ytmnd.com/
[1]http://putintheritzon.ytmnd.com/
> This means that if large triangles could be ‘drawn’ in space, their internal angles would add up to less than 180 degrees.
I wonder if this could somehow be done with the voyager 1 and 2, although I imagine this would involve setting the two voyagers up to look for each other - something that may well be many orders of magnitude outside what is possible, though they still seem to be able to contact us.
Also it may not be a large enough distance, but I'd guess its the largest available to us that we could actually test.
I wonder if this could somehow be done with the voyager 1 and 2, although I imagine this would involve setting the two voyagers up to look for each other - something that may well be many orders of magnitude outside what is possible, though they still seem to be able to contact us.
Also it may not be a large enough distance, but I'd guess its the largest available to us that we could actually test.
i imagine the problem is finding an area of space that's smooth enough to make the measurement accurately. the distribution of mass within would need to be very uniform and "average" (mass curves space; what you're trying to find here is the average curvature). so it would need to be a very large area (since matter in the universe is clumped into galaxies and the like - you want a region so large that those clumps are averaged out).
since the voyagers are only separated by a scale similar to the size of the solar system, and we're talking of sizes much larger than the separation of galaxies (or superclusters), the answer is no (unfortunately) (and of course, at those scales, you have the practical problem of light having a finite speed, so your experiment would take a long time!).
in fact, that's why this comes from cmb (cosmic microwave background) measurements. because those give you, in effect, measurements across the largest chunk of universe observable.
having said all that, measuring changes in curvature is an easier problem. and that's what gravitational wave detectors try to do. and i am pretty sure there have been proposals to do that with satellites (measuring (changes in) distances to each other with lasers).
since the voyagers are only separated by a scale similar to the size of the solar system, and we're talking of sizes much larger than the separation of galaxies (or superclusters), the answer is no (unfortunately) (and of course, at those scales, you have the practical problem of light having a finite speed, so your experiment would take a long time!).
in fact, that's why this comes from cmb (cosmic microwave background) measurements. because those give you, in effect, measurements across the largest chunk of universe observable.
having said all that, measuring changes in curvature is an easier problem. and that's what gravitational wave detectors try to do. and i am pretty sure there have been proposals to do that with satellites (measuring (changes in) distances to each other with lasers).
It's not the drawing of them in space that's the issue. Remember, you're in space right now in addition to being on the earth.
The issue is in making the measurement. The 180 degree problem is really complex.
The issue is in making the measurement. The 180 degree problem is really complex.
I'm not saying it's easy to send three probes to the edge of the solar system, but how come measuring the angles is hard? (Granted you cannot do it with the Voyager probes).
Also does anyone know what total interior angles you'd have to measure, ie. would be it ~179° or ~179.99999999°?
Also does anyone know what total interior angles you'd have to measure, ie. would be it ~179° or ~179.99999999°?
> But this version of inflation cannot account for the Universe’s lopsidedness except as a statistical fluke — similar to, for example, a fair coin that happens to come up heads many more times than tails over 1,000 flips.
So, does this mean p = .001 for this result? Does the result hold if we choose a different way to partition the sky into two connected regions?
So, does this mean p = .001 for this result? Does the result hold if we choose a different way to partition the sky into two connected regions?
my reading of that section is that they're just trying to illustrate what statistical error is. i don't think there's any real meaning to the 1000 value.
[edit] but googling for "statistical significance planck anisotropy" turned up http://arxiv.org/abs/1303.5083 which says "3 sigma" which is about 0.3% (p=0.003). so it's close.
[edit2] whoa. but you've got the right answer with the wrong maths. if you toss the same side of the coin 10 times in a row, that's p=0.001 (1/2^10 = 1/1024). getting the same side 1000 times in a row is much, much less likely.
ps since the result is basically (if i understand right) "one side of the universe is slightly different from the other" then it depends on how you choose the halves. if you divided things "at right angles" to what gives the signal, you wouldn't see anything at all. not sure if that is what you meant by partitioning (mathematically they use something like a 3d fourier transform - spherical harmonics - and this is a significant deviation from zero for the lowest frequency component).
[edit] but googling for "statistical significance planck anisotropy" turned up http://arxiv.org/abs/1303.5083 which says "3 sigma" which is about 0.3% (p=0.003). so it's close.
[edit2] whoa. but you've got the right answer with the wrong maths. if you toss the same side of the coin 10 times in a row, that's p=0.001 (1/2^10 = 1/1024). getting the same side 1000 times in a row is much, much less likely.
ps since the result is basically (if i understand right) "one side of the universe is slightly different from the other" then it depends on how you choose the halves. if you divided things "at right angles" to what gives the signal, you wouldn't see anything at all. not sure if that is what you meant by partitioning (mathematically they use something like a 3d fourier transform - spherical harmonics - and this is a significant deviation from zero for the lowest frequency component).
Lawrence Krauss talks about the physics of the curvature of space and why the current consensus is that it's flat. I found this Youtube to be really helpful in understanding something of the subject:
http://www.youtube.com/watch?v=Z0HqZxXZK7c
http://www.youtube.com/watch?v=Z0HqZxXZK7c
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