A friend asked about the geometry of the universe, and Rob Sheldon replied, saying News could quote him:
Understanding curvature
On a positive curvature surface, the sum of the interior angles of a triangle > 180.
On a negative curvature surface, the sum of the interior angles of a triangle < 180.
On a flat surface, e.g., a sheet of paper, the sum of the interior angles of a triangle = 180.
Now a small triangle drawn with ball point pen on a sufficiently large balloon will look flat, the angles add up to 180. But if the triangle is made bigger and bigger, the angle sums start to get more and more obviously different, so if you draw from the north pole to the equator, and then 90 degrees of latitude along the equator, and then back to the north pole, you will have drawn a triangle with 3 right angles = 270 degrees. So in order to determine the curvature of the universe, one needs to use distant objects—quasars and galaxies and suchlike, to determine the angles.
When one does this, the universe appears remarkably flat. It takes a lot of effort to find any curvature at all, and certainly it is difficult to get good agreement between different types of measurement.
What curvature implies
Philosophically, of course, a “closed” universe that collapses back down to itself solves the problem of infinite time, and so one would like it to have positive curvature to avoid infinities. Negative curvature suggests an “open” universe that will expand forever, ending “not with a bang, but a whimper”, and gives a feeling of the infinite emptiness of existence. I’m not really sure what a “flat” universe portends, perhaps a feeling of driving the speed limit across Kansas.
Most astronomers (e.g. experimentalists) find that the universe is flat, though there are some arguments as to why it should have a very, very slight negative curvature. The Nobel prize was awarded 2 years ago for a claim that some observed supernovae are further away than the flat universe predicts, and therefore the expansion rate is accelerating. Of course, this claim requires a model to predict what the expansion rate was at various epochs in the past, and that model has all sorts of assumptions. Personally, I think the Nobel Prize was a big mistake. But it shows that experimentally it is really difficult to find absolute distances between galaxies and quasars, so that most of our models are only weakly supported by data.
But even if we all agree that the universe is flat, we still don’t know what is causing it to be so flat. That is, gravity is always attractive, so it will make a positive curvature universe, collapsing down to a point, unless something else were counterbalancing it. The Big Bang is outward kinetic energy, and that gives a negative curvature. So in computing the sum of gravitational and kinetic energy, which one wins? Well, we can measure the expansion rate—the red shift of distant galaxies—and we can measure the number of stars in the volume from here to a distant galaxy to compare the gravitational attraction to the Big Bang explosion rate. According to these calculations, only about 10% of the mass needed to balance the kinetic energy is visible, is in stars. We can add in red dwarfs, dust and molecular clouds, and we get up to about 30%. But roughly 70% of the necessary mass to “flatten” the universe is invisible, is unaccounted for.
Conclusions
a) In the present epoch, as in right now, the universe is experimentally as flat as can be measured—the “fine-tuned Big Bang” problem.
b) About 70% of the matter that is needed to make it flat is unobserved—the “Dark Matter” problem.
c) There is some controversial data that the universe is becoming negatively curved in the next epoch. The unknown cause of this “anti-gravity” is called the “Dark Energy” problem.
d) “Inflation” is not occurring now, but is a strong “negative curvature” term from a previous epoch that presumably solves problem (a).
But it introduces a whole new set of “Fine-Tuning” parameters into the model which are even more contingent than the ones it was meant to replace! Inflation also interacts with (c) in ways that cause trouble. Nor does it explain (b) at all. So by and large, I would ignore “inflation” as a solution for anything, since it merely “solves” one problem by introducing a dozen more.
BTW, the hope that the search for the Higgs boson would reveal novel physics needed by the “inflaton”-field were dashed, making inflation a fast-receding threshold of confirmation.
Advice on books
If you stick to observational astronomy books, they will all talk about a flat universe.
Cosmologists tend to be faddish thrill-seekers, and will tell you anything. The past 30 years of publishing has been particularly brutal, with nearly every cosmological model having a shelf-life in single digits. The “flat” cosmology is almost apophatically defined—as one cosmology after another is denied. Perhaps there is something religious about cosmology that prevents the “flat” universe from being acceptable theology.
See also:
Big Bang exterminator wanted, will train
Copernicus, you are not going to believe who is using your name. Or how.
As if the multiverse wasn’t bizarre enough …meet Many Worlds
Note: Yes, that’s Mars up there beside “Now a small triangle …” Useful as any sphere for picturing the cosmology.
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Thanks News and Dr. Sheldon!
Of Note:
Refutation Of Oscillating Universe – Michael Strauss PhD. – video:
http://www.metacafe.com/watch/4323673
Evidence For Flat Universe – Boomerang Project
http://www.lbl.gov/Science-Art.....-flat.html
http://www.lbl.gov/Science-Art.....megal3.gif
I agree Obama shouldn’t have gotten the Nobel Peach prize. Oh wait, you were referring to Perlmutter, Riess and Schmidt’s discovery of Dark Energy. 🙂
Bummer to some extent if you’re right. The day I met Dr. Riess was a very happy day for me since it was the first time I ever got to shake hands with a Nobel Prize winner in physics.
I have rather strong opinions that I’ve shared at UD regarding the redshift of quasars particularly since there is absence of apparent time dilation in their blinking “clocks” the more red shifted they are. This suggests quasar redshift is :
1. possibly mistinterpreted from spectral data (Varshni)
2. or the redshift is possibly intrinsic
3. both
I’m trying to get more info on LB 8956 and other quasars showing proper motion and thus only a few hundred light years form Earth….
As far as galactic redshift, I don’t know. The apparent time dilation in supernova’s is pretty powerful in favor of the Big Bang but I hold out there might be some explanation for this too. Is it possible something can be moving and redshifting without space having to also expand? Expanding space is a solution to GR, but solutions to an equation of physics doesn’t mean it is right (negative mass gives solutions to Newton’s 2nd law, but it doesn’t mean negative mass is real).
If there is a mechanism for redshifting light that we’re not accounting for, then all bets are off that the Big Bang is even right and that space is expanding. It’s very hard to say. Lot’s of drama over what theory will prevail, and that makes cosmology a fun topic…
@ News
Would Dr. Sheldon be describing Riemannian Geometry in this instance?
Hyperbolic Geometry by chance?
Our good friend, Euclidean Geometry?
So the prevailing concept is to identify the 70% as “dark matter”? It seems like this would amount to something along the lines of the Luminiferous Ether wouldn’t it?
If one day they (science community) could observe dark matter, I could imagine a theory being put forth positing that some of this dark matter was converted into non-dark matter at the Big Bang. Or at the very least converted into the species of sub-atomic matter that enabled the formation of atomic Hydrogen.
If dark matter truly is the “missing” mass, then it would seem to reason that dark matter and non-dark matter would share at base some elemental, sub-atomic particles (Higgs?). Is that the thought in the world of physics today?
Yes. Here is one example of a triangle defined by Riemannian Geometry which you can actually visualize:
http://mathworld.wolfram.com/S.....angle.html
The triangles Dr. Sheldon describes are impossible to visualize since that sort of 3-D curvature is alien to human experience, but the math is similar.
To put my unsolicited two cents in as to ‘what it means’ to live in an exceptionally flat (and round) universe,,,, Since according to multiverse cosmology, in which it is posited we could be living in any shape universe whatsoever, I find it strange that we ‘just so happen’ to live in a universe that is exceptionally round and flat. So since it is unparsimonious to believe that a exceptionally round and flat universe ‘just so happened’ to pop into existence (from some as of yet unidentified random universe generate) for no particular reason at all, then I personally believe God designed the universe along the parameters of pi, using the infinite pi as a sort of a template if you will. In fact, I believe the following equation gives us an overall ‘template of the universe’ if you will.
But to focus on pi for now. The following evidence is very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere which ‘coincidentally’ corresponds to the circle of pi within Euler’s identity and which also ‘coincidentally’ matches a theistic prediction for the shape of the universe:
Moreover, there is now known to be an unexpected ‘flatness’ to the universe that also corresponds to the diameter of pi in Euler’s identity, and which also ‘coincidentally’ matches another theistic prediction in the Bible:
That the fine-tuning of the roundness of the universe is unexpected from a naturalistic perspective is revealed by the fact that naturalists attempted to ‘explain it away’ (tried to explain the homogenity of the Cosmic Background Radiation away) (A. Guth) by postulating a short burst rapid inflation during the initial stages of the Big Bang (to ‘smooth the universe out’), which, as Mr Multiverse, Max Tegmark himself, concedes is a epistemologically self-defeating proposition,
Also of note:
Besides the evidence that Dr. Ross listed for the 1 in 10^120 finely tuned expansion of the universe, this following paper clearly indicates that we do live in universe with a ‘true cosmological constant’. A cosmological constant that is not reducible to a materialistic basis. Thus, the atheistic astrophysicists are at a complete loss to explain why the universe expands in such a finely tuned way, whereas Theists are vindicated once again in their beliefs that the universal constants are truly transcendent!
Here are the verses in the Bible, which were written over 2000 years before the discovery of the finely tuned expansion of the universe by ‘Dark Energy’, that speak of God ‘Stretching out the Heavens’; Job 9:8; Isaiah 40:22; Isaiah 40:24; Isaiah 48:13; Zechariah 12:1; Psalm 104:2; Isaiah 42:5; Isaiah 45:12; Isaiah 51:13; Jeremiah 51:15; Jeremiah 10:12. The following verse is one of my favorites out of the group of verses:
Also of interest is two other places in the universe where ‘unexpected roundness’ is found:
and also this ‘unexpected roundness’:
The delicate balance at which carbon is synthesized in stars is truly a work of art. Fred Hoyle (1915-2001), a famed astrophysicist, is the scientist who established the nucleo-synthesis of heavier elements within stars as mathematically valid in 1946. He is said to have converted from staunch atheism into being a Theist after discovering the precise balance at which carbon is synthesized in stars. Years after Sir Fred discovered the stunning precision with which carbon is synthesized in stars he stated this:
I echo the idea that perhaps we have misinterpreted red shifts. Perhaps the YECs are right about the slowing of light, the initial rapid expansion of the universe with planets and stars fully formed rather than by natural processes, and all we’ve had since is decay.
The shape of the universe depends on the matter + energy density. It is represented by Omega. If Omega = 1, we have Flat universe. Omega less than 1 represents a saddle shaped Open universe and Omega >1 represents Sphere shaped Closed universe.
If we look at the CMBR, we will find that the brightest spots (fluctuations) are close to 1 degree across (with a 0.4% error). This proves our universe is flat. For Open universe, we would have less than 1 degree and for Closed universe, we would have observed > 1 degree.
If we have a flat universe, the value for PI is maximized. If the curvature of the universe is extreme, PI can be as small as exactly 2.0000, depending on the size of the circle.
-Q
Most of the cosmology in this post is incorrect. Cosmology 101 incorrect, not even controversially incorrect. More details here:
http://letterstonature.wordpre.....oductions/