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Gravity and levity
In article , Ulf Torkelsson
wrote: The formula you gave, GM/(c^2 r), would give hints on how big a cosmological glob might become, as it should set a limit as GR forces grow strong. This is rather the length scale at which the curvature of space-time becomes significant. If we use the critical density of the universe 1.88e-26 kg/m3, then this lenght scale becomes of order r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly which is about the size of the observable universe. There is one interesting consequence of this observation: Suppose, for a start that the universe is made up by a series of globs, each limited in size by the GR estimate GM/(c^2 r). Then this formula would also act on the globs attracting to each other. It means that no matter what the glob density is, the universe cannot be homogenous. So this perhaps suggest that in such a case there should be another force "levity" that counteracts gravity. This might be a an Einstein cosmological constant or something or some other force. But this force should be so that in the very large of the universe, the estimate GM/(c^2 r) is properly counteracted. The interesting thing is that one ends up on a similar picture if one want to explain the expansion of lit matter, if one wants to settle for an older universe that is not created merely by a Big Bang. I find this reasoning interesting, because I felt formerly sceptical over the idea that GR should be augmented with some cosmological constant or "levity" force. But perhaps this should be so. Hans Aberg |
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Gravity and levity
Hans Aberg wrote:
In article , Ulf Torkelsson wrote: This is rather the length scale at which the curvature of space-time becomes significant. If we use the critical density of the universe 1.88e-26 kg/m3, then this lenght scale becomes of order r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly which is about the size of the observable universe. There is one interesting consequence of this observation: Suppose, for a start that the universe is made up by a series of globs, each limited in size by the GR estimate GM/(c^2 r). Then this formula would also act on the globs attracting to each other. It means that no matter what the glob density is, the universe cannot be homogenous. So this perhaps suggest that in such a case there should be another force "levity" that counteracts gravity. This might be a an Einstein cosmological constant or something or some other force. But this force should be so that in the very large of the universe, the estimate GM/(c^2 r) is properly counteracted. In the last paragraph here you reason the same way as Einstein did when he introduced his cosmological constant. Gravity is always attractive, so in order to get a static universe he was forced to introduce the cosmological constant to counteract gravity on large distance scales. If you do not assume that the universe is static the cosmological constant is no longer necessary, and we can for instance get an expanding universe in which the expansion is gradually slowing down due to the effect of gravity. If we keep the cosmological constant, but allow the universe to change over time, it turns out that the static solution is unstable, and any perturbation will either cause it to contract or expand. The interesting thing here is that the expansion can eventually become exponential if we do have a cosmological constant. Ulf Torkelsson [Mod. note: quoted text trimmed -- mjh] |
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Gravity and levity
Hans Aberg wrote:
In article , Ulf Torkelsson wrote: This is rather the length scale at which the curvature of space-time becomes significant. If we use the critical density of the universe 1.88e-26 kg/m3, then this lenght scale becomes of order r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly which is about the size of the observable universe. There is one interesting consequence of this observation: Suppose, for a start that the universe is made up by a series of globs, each limited in size by the GR estimate GM/(c^2 r). Then this formula would also act on the globs attracting to each other. It means that no matter what the glob density is, the universe cannot be homogenous. So this perhaps suggest that in such a case there should be another force "levity" that counteracts gravity. This might be a an Einstein cosmological constant or something or some other force. But this force should be so that in the very large of the universe, the estimate GM/(c^2 r) is properly counteracted. In the last paragraph here you reason the same way as Einstein did when he introduced his cosmological constant. Gravity is always attractive, so in order to get a static universe he was forced to introduce the cosmological constant to counteract gravity on large distance scales. If you do not assume that the universe is static the cosmological constant is no longer necessary, and we can for instance get an expanding universe in which the expansion is gradually slowing down due to the effect of gravity. If we keep the cosmological constant, but allow the universe to change over time, it turns out that the static solution is unstable, and any perturbation will either cause it to contract or expand. The interesting thing here is that the expansion can eventually become exponential if we do have a cosmological constant. Ulf Torkelsson [Mod. note: quoted text trimmed -- mjh] |
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