Freethought & Rationalism Archive

Gauge Boson · 11-16-2002, 12:04 PM

Quote:

eh
Nothing is excessive in an infinite universe. Even in standard BB cosmology, the prediction for a flat universe is that the cosmos is infinite - and has been from the very beginning. Tell me why time would make any difference in an open universe.

Not necessarily. It is possible for the universe to be flat, appear infinite, and be finite. For example, it could be perfectly flat, but wrapped up in a toroidal shape (with a 4-dimensional surface in non-Euclidean space, but that is perfectly acceptable). More complicated topologies are possible, but they allow for a finite, flat universe. Even an open universe can be finite with the right topology. Searches of the CMBR are currently underway to look for evidence of this. (1) You are right, however, that time makes no difference for an open universe as opposed to a flat one.

Quote:

eh
We would only be able to know the age of our visible universe, created from the inflation.

Correction: we only currently know this (approximately). We could very well discover whether the whole universe has infinite age or not from indirect evidence. NASA's MAP sattelite is currently making some such observations and the ESA's Planck sattelite is scheduled to do the same.

Quote:

luvluv
Not really. I'll get some literature in front of me for next time, but there are several A.C.'s which ALONE have random probabilities in the trillions. I'll have specifics next time.

You are making the baseless assumption (it is actually contradicted by evidence) that our current theories of fundamental physics require no modification. We currently have 19 free parameters; a theory of quantum gravity, which we have no idea what it will look like, could have only one. Some physicists have suggested that a final Theory of Everything may even have no free parameters, leaving no room for the anthropic coincidences. Currently, M-theory predicts that there be only one coupling constant or parameter: the string (or membrane) tension. The others would all be derived from this and two vacuum constants. (2)

Setting that aside for a moment, there are two serious flaws with your argument. First, you are saying that what is the case is so unlikely it must be divinely created. A good analogy would be a game of poker. Say you get dealt a royal flush. Would you calculate the infintessimal odds and conclude that it is so unlikely that you would be dealt that hand by chance that it must have involved divine intervention? I sure hope not. Calculating the odds after the fact is typically meaningless. The chance that what is the case is the case is always 100%.
Second, the odds are only very tiny if you restrict yourself to universes that humans could arise in. Victor J. Stenger, a physicist at the University of Hawaii, found that:

Quote:

Victor J. Stenger
"The fine-tuning argument assumes only one form of life is possible. But many different forms of life might still be possible with different laws and constants of physics. The main requirement seems to be that stars live long enough to produce the elements needed for life and allow time for the complex, nonlinear systems we call life to evolve. I have made some calculations in which I randomly vary the values of the physical constants by many orders of magnitude and look at the universes that would exist under those circumstances. I find that almost all combinations lead to universes, albeit some strange ones, with stars that live a billion years or more. Life of some kind would be likely in most of these possible universes."(3)

Finally, we know that, because we are here, the constants must be in the range permitting that, no matter how unlikely. All we can say about the anthopic coincidences is that the constants are as they are - for whatever reason - because if they were any different, we would not be here to observe the universe (though someone probably would). This is a more relevant way of looking at the problem of calculating odds after the fact.

(1) "Is Space Finite?" Scientific American, vol.12, no.2, Y02: Cosmology special edition. Luminet, Jean-Pierre; Starkman, Glenn D.; Weeks, Jeffrey R.
(2) "alpha: A Constant that is Not a Constant?" Fiorentini, G. and Ricci, B. <a href="http://www.arXiv.org/abs/astro-ph/0207390" target="_blank">Available on the arXiv e-print archive</a>.
(3)"Has Science Found God?" Free Inquiry, vol.19, no.1, Winter, 1998. Stenger, Victor J.

eh · 11-17-2002, 08:40 AM

Quote:

Originally posted by Gauge Boson:
Not necessarily. It is possible for the universe to be flat, appear infinite, and be finite. For example, it could be perfectly flat, but wrapped up in a toroidal shape (with a 4-dimensional surface in non-Euclidean space, but that is perfectly acceptable). More complicated topologies are possible, but they allow for a finite, flat universe. Even an open universe can be finite with the right topology. Searches of the CMBR are currently underway to look for evidence of this. (1) You are right, however, that time makes no difference for an open universe as opposed to a flat one.

Hmmm, now that you mention it, I do recall reading that in Sci American. But wouldn't a universe with the shape of a donut have constant curvature like a sphere would?

Gauge Boson · 11-17-2002, 10:15 AM

WARNING: LONG POST

Quote:

Originally posted by eh:

Hmmm, now that you mention it, I do recall reading that in Sci American. But wouldn't a universe with the shape of a donut have constant curvature like a sphere would?

Only in Euclidean space. It is impossible in Euclidean space for a something with flat or hyperbolic curvature to be finite. But there is nothing that requires the universe to be embedded in any higher-dimensional space, let alone a Euclidean one. Don't try constructing the examples they give, only crudely visualize them. None of the 2-dimensional examples they use can be exist in Euclidean-3 space.

Quote:

"Is the Universe Finite?"
One problem with this conclusion (that the universe is infinite) is that the universe could be spherical yet so large that the observable part seems Euclidean, just as a small patch of the earth�s surface looks flat. A broader issue, however, is that relativity is a purely local theory. It predicts the curvature of each small volume of space � its geometry � based on the matter and energy it contains. Neither relativity nor standard cosmological observations say anything about how those volumes fit together to give the universe its overall shape�its topology. The three plausible cosmic geometries are consistent with many different topologies. For example, relativity would describe both a torus (a doughnutlike shape) and a plane with the same equations, even though the torus is finite and the plane is infinite. Determining the topology requires some physical understanding beyond relativity. The usual assumption is that the universe is, like a plane, �simply connected,� which means there is only one direct path for light to travel from a source to an observer. A simply connected Euclidean or hyperbolic universe would indeed be infinite. But the universe might instead be �multiply connected,� like a torus, in which case there would be many different paths. An observer would see multiple images of each galaxy and could easily misinterpret them as distinct galaxies in an endless space, much as a visitor to a mirrored room has the illusion of seeing a huge crowd. (Here it goes on to discuss Mach's principle of inertia). Mach inferred that the amount of inertia a body experiences is directly proportional to the amount of matter in the universe. An infinite universe would cause infinite inertia... In addition to Mach's principle, there is preliminary work in quantum cosmology, which attempts to describe how the universe emerged spontaneously from the void. Some such theories (e.g., the Wave Function Theory of the Universe) predict that a low-volume universe is more probable than a high-volume universe. An infinite universe would have zero probability of coming into existence...
(Some stuff about how Riemann discovered a finite, unbounded universe is possible if it is the surface of a hypersphere). One might still ask what is outside the universe. But this question supposes that the ultimate physical reality must be a Euclidean space of some dimension... Nature, however, need not cling to such a notion...
Schwarzschild�s example illustrates how one can mentally construct a torus from Euclidean space. In two dimensions, begin with a square and identify opposite sides as the same � as is done in many video games, such as the venerable Asteroids, in which a spaceship going off the right side of the screen reappears on the left side. Apart from the interconnections between sides, the space is as it was before. All the familiar rules of Euclidean geometry hold. At first glance, the space looks infinite to those who live within it, because there is no limit to how far they can see. Without traveling around the universe and reencountering the same objects, the ship could not tell that it is in a torus. In three dimensions, one begins with a cubical block of space and glues together opposite faces to produce a 3-torus.
The Euclidean 2-torus, apart from some sugar glazing, is topologically equivalent to the surface of a doughnut. Unfortunately, the Euclidean torus cannot sit in our three-dimensional Euclidean space. Doughnuts may do so because they have been bent into a spherical geometry around the outside and a hyperbolic geometry around the hole. Without this curvature, doughnuts could not be viewed from the outside...
Of all the issues in cosmic topology, perhaps the most difficult to grasp is how a hyperbolic space can be finite. For simplicity, first consider a two-dimensional universe. Mimic the construction of a 2-torus, but begin with a hyperbolic (generally saddle-shaped) surface instead. Cut out a regular octagon (in hyperbolic space, these have different angles than in Euclidean space) and identify opposite pairs of edges, so that anything leaving the octagon across one edge returns at the opposite edge. Alternatively, one could devise an octagonal Asteroids screen. This is a multiply connected universe, topologically equivalent to a two-holed pretzel. An observer at the center of the octagon sees the nearest images of himself or herself in eight different directions. The illusion is that of an infinite hyperbolic space, even though this universe is really finite. Similar constructions are possible in three dimensions, although they are harder to visualize.

[ November 17, 2002: Message edited by: Gauge Boson ]

Gauge Boson · 11-17-2002, 11:03 AM

Quote:

Originally posted by luvluv:
Are reffering to is the notion scientists promoted to explain the uniformity of the cosmic background radiation? That the universe expanded much faster than normal for some unknown reason and then slowed down just as inexplicably? If that is what you mean by inflationary, I'm pretty sure Ross does not accept that.

Aside from the claim that inflation is 'inexplicable', what you mentioned is by definition inflation (temporary rapid expansion of the universe). So you are saying that he does accept inflation, but he does not accept inflation. Thanks for clearing this up, eh. Also, there are several possible causes for the inflationary epoch. One that has been getting a lot of attention lately because of recent observations is that the cosmological constant (a misnomer because it is not constant, but the name is retained for historical reasons) was very large then (1). What would cause this cosmological constant? The most likely explanation is that it comes from some form of "dark energy" (which has additional evidence pointing toward it (1, 2, 3) ) that arises from vacuum energy, the negative energy that "empty" space has from particle-antiparticle pairs briefly popping into and out of existance (1, 2, 3). These "virtual particles" may sound ridiculous, but their existence agrees with experiment to nine decimal places (2). A slight variation of the cosmological constant you may have heard of is called "Quintessence" (1, 2). Inflation is far from inexplicable; we have observed a mild version of it occurring now (1, 2, 3, 4).

(1) "The Quintessential Universe", Scientific American, vol. 12, no. 2: Cosmology special issue. Ostriker, Jeremiah P. and Steinhardt, Paul J.
(2) "Cosmological Antigravity", Scientific American, vol. 12, no. 2: Cosmology special issue. Krauss, Lawrence M.
(3) "Why Cosmologists Believe the Universe is Accelerating." Turner, Michael S. <a href="http://www.arxiv.org/abs/astro-ph/9904049" target="_blank">Available online at the arXiv e-print archive</a>.
(4) "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant", the Astronomical Journal, June, 1998. Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter; Clocchiatti, Alejandro; Diercks, Alan; Garnavich, Peter M.; Gilliland, Ron L.; Hogan, Craig J.; Jha, Saurabh; Kirshner, Robert P.; Leibundgut, B.; Phillips, M.M.; Riess, David; Schmidt, Brian P.; Schommer, Robert A.; Smith, R. Chris; Spyromilio, J.; Stubbs, Christopher; Suntzeff, Nicholas B.; Tonry, John. <a href="http://www.arxiv.org/abs/astro-ph/9805201" target="_blank">Available online at the arXiv e-print archive</a>.

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