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 Posted: Wed Jul 26, 2006 10:34 am
I remember reading some time ago an example of how systems tend to states with the lowest posible energy. The example given was of a rubber band stretched out accross the surface of an orange. Since the rubber band will keep itself in as short and therefore low energy configuration as it can it seeks out the shortest path on the orange which makes it naturally find its way to a great circle. I have come to be rather fond of the phrase because it seems so random to say "just like an orange and a rubber band" when someone is talking about least energy or stable states. So the question is this, could the universe be, at least in part, as flat as it is because that is a least energy state for it so is the universe like an orange and a rubber band? It would make sense if the universe were to seek a flat state as a least space configuration. I don't know the math behind it well enough to be sure but it seems like if we were going to give ourselves a little bit of leeway and embed the different geometries of gtr within a euclidean space that the one which would take up the fewest dimensions would be the flat one. occams razor favors simplicity but then often times nature favors it too making complex states have higher energy requirements than simple ones.
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Posted: Fri Aug 04, 2006 2:28 pm
The thing is, though, that the universe isn't flat. As far as we know it's round. It also seems pointless to talk about the universe finding lowest energy. Because the universe is the universe onto itself. It has a certain amount of energy, and there is no energy transfer between universe and sorrounding, because, well, there is no sorrounding. The universe comes with a set mass and energy, which can interchange (as you are probably aware of) at any time.
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Posted: Fri Aug 04, 2006 6:49 pm
poweroutage The thing is, though, that the universe isn't flat. As far as we know it's round. It also seems pointless to talk about the universe finding lowest energy. Because the universe is the universe onto itself. It has a certain amount of energy, and there is no energy transfer between universe and sorrounding, because, well, there is no sorrounding. The universe comes with a set mass and energy, which can interchange (as you are probably aware of) at any time. When I say flat I mean that the universe overall has an essentially euclidean geometry. Sure gravity wells shmush it up some here and there but when you look at the whole picture it has neither a positive nor negative curve to it. It looks as though the density of the universe is just about right to make the equations of gtr come out with something that looks for all the world like R^3. The only problem is that the amount of mass that we see in the universe doesn't look like it is enough to make the equations of gtr pump out such a geometry. With as little mass as we have the universe should actually be quite negatively curved. That is one of the reasons we are pretty sure there is a bunch of dark matter out there. The question I am asking is if perhaps a certain favorabilitity of a flat state, in terms of stability or what have you, might contribute towards this extra mass without actually being a mass at all but rather simply When I say lowest energy state I don't mean that the universe lowers its overall energy but I mean that it reaches a state in which its energy distribution is the smallest a.k.a. equilibrium.
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Posted: Fri Aug 04, 2006 9:26 pm
I'm having a hard time understading what it is that you intend to ask or what exactly you mean by that analogy. There is no reason in either thermodynamics or general relativity as to why the universe is flat; at the most, a trend toward uniformity will mean that the universe will have a constant curvature on the large scale, rather than specifically zero (flatness). On the very large scale, flatness cannot be explained by simple energy trends. In fact, energy distribution will tend away from uniformity rather than toward it.
For now, I'll simply make some broad qualitative generalizations. For 'typical' systems, equilibrium and higher entropy states can be associated with dispersion--e.g., gas particles starting out confined to a small space will expand, and cool down when they radiate away energy (positive heat capacity). The trend is toward uniformity. For a gravitationally-dominated systems, things are a bit different. The highest-entropy states the most compact, up to to the Bekenstein limit of a black hole, and the system will heat up when radiating away energy (negative heat capacity). The trend is reversed. Gravitationally dominated systems will become more and more clumped, and thus have an increasingly uneven energy distribution, rather than a uniform one.
All of that is really just a theoretical way of making the simple-minded observation that `gravity pulls matter together and it doesn't stop pulling'. To explain flatness, one needs a much more complicated mechanism, e.g., inflation.
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Posted: Wed Aug 09, 2006 12:27 am
Lets suppose that the parralell universes interpretation of quantum mechanics is true and let us further suppose that these universes influence each other gravitationally. Close to the big bang huge variations in density could have occurred in these dimensions one right next to the other. So that we have a highly negatively curved universe close to a positively curved one and so on with a more or less random distribution of curvatures for any particular region of space in the different universes. It makes sense to me that the gravitational interactions of these universes would have an averaging effect on each other which would tend to cause flatness. The reason I didn't propose this effect before was because I think it is bull-plop. although I haven't done any calculations it seems to me that the universes which would influence each other the most strongly gravitationally would be the ones which have similar histories in which case the influences from the other universes would average out to nill. I thought I would mention this possible mechanism though because it kind of illustrates what I mean when I say that a universe that tends to a universe with the most uniform energy distribution might also tend to flatness.
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