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 18-Jul-2004, 04:11 #2 Vadi   Join Date: Apr 2004 Location: Austria Posts: 446 The universe has no finite radius.
 18-Jul-2004, 04:20 #3 K.I.L.E.R Retarded moron   Join Date: Jun 2002 Location: Australia, Melbourne Posts: 2,949 But the contents inside are finite? __________________ I eat coffee.
 18-Jul-2004, 04:26 #4 Vadi   Join Date: Apr 2004 Location: Austria Posts: 446 I don't know. There ain't an upper limit of density though?
 18-Jul-2004, 09:24 #5 Fred Member   Join Date: Feb 2002 Posts: 207 Ok, theres a few problems here.. One, the universe we see is by definition causally connected to us, what we don't see could be infinite. Two, the big bang has no epicentre, it happens everywhere. Now, the question is good, take 2 parts of the visible universe in different directions and ask yourself, were they causally connected in the past? Answer, on average yes, b/c we see an extraordinary homogeneity in the night sky (by experiment the CMB is what you look at), so much so that it was a problem for the usual FRW universe of general relativity. Things were too even, and this is what is known as the horizon problem. This was more or less solved by inflation theory. Here spacetime inflates exponentially so to speak, and if you solve the equations, you will see that everything will have had time to settle in thermal equilibrium more or less. Then the universe pops out of inflation, and we are left with a nice smooth isotropic and homogenous universe governed by the usual friedmann equations. One source of confusion that I think you might be struggling over is exactly what you mean by 'causally connected', and what you use as a clock. This is a little less simple than using Euclidean geometry, you need full General relativity to deal with it appropriately.
 19-Jul-2004, 01:52 #6 g__day Senior Member   Join Date: Jun 2002 Location: Sydney Australia Posts: 575 fred - thanks Few scientists view the Universe as infinite (I can't name any credible ones) The big bang of course happened everywhere, (past tense) because that is all there was. Its epi-centre can not be detected but still exists (to conserve laws of energy, mass and momentum) is the distinction you need to understand. We - nor anyone else - can detect where it was if it is outside our Hubble Sphere (apparently the term specifically used to describe how far light / gravity or any other force can travel over the age of the universe). So yes spacetime unfolded and to the layperson scientists say is centre is undectable, or there remains an unfindable centre - or the question can't be answered ... but the technically more correct answer is it should still exist but our physics can't hope to find it - we are Hubble sphere bound. Parts of the visible sky - in opposite directions - were casually connected and may still so be. But receding parts that are slightly beyond what is visible to us in opposite directions definitely aren't casually connected. Your comments on COBE and background radiation and homogenity are correct. Your statements linking inflation to the observed distributions of background radiation are also correct, although irrelevant to the statement at hand. Casually connected is simply putting together two facts - 1) forces can not instantenously transmit, they travel at lightspeed at best and 2) during inflation the Universe unfolded 50,000 times faster than lightspeed until the laws of relativity took over - around 10 ^ -34 seconds after the big bang. So anything outside our Hubble Sphere can't interact with us and because of inflation most of the Universe is outside our - or any other - Hubble Sphere. Time from a relativity POV doesn't enter this framework of analysis. Thanks for you points!
 19-Jul-2004, 04:50 #7 Vadi   Join Date: Apr 2004 Location: Austria Posts: 446 I meant that the universe has no boundaries so the can't be an epicentre. Also quantum pyhsics smear it out. And parts of the universe can be causally connected through wormholes; in both directons since black holes seem to let information escape them.
 19-Jul-2004, 07:50 #8 g__day Senior Member   Join Date: Jun 2002 Location: Sydney Australia Posts: 575 The Universe may well have boundaries. The wormhole connectedness pitch is so theoretically incomplete it has only the vaguest of frameworks - it can't even tell the typology of other dimensions so far. We can speak more reliabiliy about heaven then wormholes at the moment!
 19-Jul-2004, 09:47 #9 Diplo Senior Member   Join Date: Apr 2004 Location: UK Posts: 1,474 g__day, are you talking about the universe being causally connected or casually connected? You use both and they imply different things to me (a relative layman in these things).
 19-Jul-2004, 10:44 #10 Fred Member   Join Date: Feb 2002 Posts: 207 'Few scientists view the Universe as infinite (I can't name any credible ones) ' Again what most people mean when they say 'the universe' is precisely 'the visible universe'. That of course cannot be infinite. This is actually a question of topology, and unfortunately experiment has ruled out a few possibilities (the closed universe with a spherical topology). However, our universe *can* be more or less an infinite plane. This is consistent with a FRW solution that is accelerating (COBE/WMAP). It also could be something that looks like a Torus, with a hyperbolic metric. That would be in principle observable, and things in this picture actually do collapse (by homotopy) to a point. However, if its the simplest case, the flat plane, the Big bang has no point like compactification, and well you're singularity is sitting throughout all points in space, even points infinitely *far* apart (with zero proper length... chew on that for a minute or two). There are other possibilities for topology choice, including some rather complicated nonsimply connected stuff. But most people use Occams razor. "But receding parts that are slightly beyond what is visible to us in opposite directions definitely aren't casually connected" No thats not necessarily true, (though it is on average). One reason could be a nontrivial topology as I pointed out (a Torus for isntance). Another could be a nontrivial local metric describing the patch. btw, the definition of causal connection is not quite that simple in GR, i'll call it horizon distance. it is for the Robertson Walker metric something like d(t) = R(t) integral ( 0--t) c dt'/R(t').. Where R(t) is the scale factor. For an open universe, in the matter era, this will give a completely nontrivial looking distance for causal connection, not at all a euclidean looking thing.
 20-Jul-2004, 00:01 #11 g__day Senior Member   Join Date: Jun 2002 Location: Sydney Australia Posts: 575 Fred can you elaborate on "if its ... the flat plane, the Big bang has no point like compactification, and well you're singularity is sitting throughout all points in space, even points infinitely *far* apart " please, as I read yesterday the latest Cosmic Background Radiation Studies from the South Pole show the predicted polarisation, giving both alot of support for inflation and a flat Universe topology. Scientists believe the sum matter / energy of the Universe from the moment of the Big Bang - if once again concentrated into a localised area to produce gravitational collapse - would give a Black Hole with the equivalent Schwartzschild radius about 40% bigger than we estimate the entire Universe has today. So the fact that the Big Bang didn't implode under that kind of pressure means simply and greater force stopped it. By definition nothing was outside this singularity so the force that created reality must have allowed expansion forces to outpace the propogation of the gravity field that would have stopped things cold in the first pico second. Inflation accounts for this, but as you say it allows very complex possibilities to occur when it comes to the shape or topology of the Universe. So the singularity was likely uniform - but not for too long - inflation ripped that apart and although we see great uniformity possibly this is allowed even with dis-continous connectivity (causality). I ponder how reliable are our estimates of the size and topology of the Universe are given we accept it is much larger than our Hubble Sphere. It leads me to ponder greatly the meaning of a whole Universe that may really be just a giantic series of mainly dis-connected super cluster galaxies. Thinking about the 'edges' of the Universe - well the expression "You can't get there from here" never seemed more relevant!
 21-Jul-2004, 12:54 #12 Fred Member   Join Date: Feb 2002 Posts: 207 " if once again concentrated into a localised area to produce gravitational collapse" The problem here again, is what you mean exactly by 'area'. One of the perpetual confusions, students of mine have when I teach GR, is precisely what mass, energy, length, area, time and volume correspond too exactly. In general, these things have several definitions depending on what you are trying to accomplish, and the level of abstraction. I don't know how much I can help you in this type of forum, i'd really need to explain a little bit about pointset topology, manifolds, etc and giving length a meaning in topology (in fact in general, topologies that give a good meaning to length are a small subset of possibilities). The way I like to think about it physically, is the topology of our universe is fixed, but length and what not will vary depending on the metric and the parameters that are there. So in the case of a flat plane topology, what you see at all moments is still a flat plane, but the way you measure length is shrinking as you approach the physical singularities (where energy blows up). On one hand, its sorta artificial, in the sense that we are sure quantum corrections are going to replace the classical theory at one point, inflation happens sorta by hand in such a regime. Here is an explanation Brian Greene gave me. Consider a number epsilon (which is small) after the big bang. Galaxies and stuff are going to still be seperated topologically in the sense that the corresponding points will be outside balls of radius epsilon. However, the way we measure length via the metric is shrinking to zero. So send a photon out, and you will see that the distance it needs to travel goes to zero. But they are still physically apart. So the big bang (better known as the big stretch) happens throughout the entire topology, even though there is a singularity of the metric, and how you measure physical quantities goes to zero. This whole thing is quite subtle. Consider for instance a closed universe (the big crunch).. Normally we like to think of it as a spherical R^4 type thing. What they usually don't tell you in layman presentations of the subject, is that this too admits a flat plane interpretation topologically. Consider a 3 sphere as an analogy. Remove the north pole, you will see by a smart relabeling of coordinates that you can make flat plane(s) out of the rest of the points. And by another patch, this time with the north pole included, but with the south pole removed, you get the entire information of the topology. But they are distinct physically, even though the sphere is related to two patches of flat planes by a homeomorphism. So we have an indeterminism or an ambiguity at a very fundamental level, only very subtle experiment can distinguish things, and sometimes not even that is possible.

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