You can lookup your question here: Why does a flat universe imply an infinite universe]? When K < 0 the universe is infinite per definition. However, present empirical observations are that k =1. This means that our global geometry is flat. There are two forms that have a flat geometry: an infinite flat plane, or a torus (think about computer games where an object disappears at the higher border of the screen, appears at the lower. Same for left and right) The error you make is thinking that the fact that the distances between galaxies globally increase, proves that the universe as a whole is expanding in something else. Your logic is based on everyday objects in the universe, but you cannot treat the universe itself in such a way. You cannot do else than believing what the equations of general relativity tell us. And if the math is too complex for you, you just cannot do else than believe what cosmologists tell you: that the universe seems to be flat, and that it is improbable that it has the form of a torus: until now nobody has seen our galaxy billions of light years away through a telescope.GdB said, No. First I would not call my posting an analysis: it was more of a statement. And nowhere I implied that ‘infinite space has always existed’, on the contrary.This is what you said (quote from wiki)"suggest that the Universe is infinite in extent with a finite age"And this makes the problem easier to solve? It suggests that our universe is already infinite, something which is being debated by the scientific community.
But do any of the "finite" universal shapes rule out a larger permittive condition which accommodates these closed universes and especially a multiverse?You are thinking too much about a torus with a 2-D surface in 3-D space. So you think about our universe as a 3-D space in 4-D space. But AFAIK we live in a 3-D space with an additional time dimension. Do not forget: gravity is not the curvature of space, but of spacetime. General Relativity uses internal attributes of spacetime only, e.g. that in curved spacetime angles of a triangle do not add up o 180 degrees. But this does not mean there is something outside this spacetime, in a higher dimension. It are the analogies with flat planes, surfaces of spheres or tori in our 3-D space that seduce you in thinking there must be something outside. Same for the multiverse. Under this heading go very different concepts of 'other universes'. To imagine them as e.g. spherical universes in a much wider space in which they all expand, is again just some analogy. E.g. it does not apply to the multiple universes as they form in the many worlds interpretation in quantum mechanics.
But do any of the "finite" universal shapes rule out a larger permittive condition which accommodates these closed universes and especially a multiverse?You are thinking too much about a torus with a 2-D surface in 3-D space. So you think about our universe as a 3-D space in 4-D space. But AFAIK we live in a 3-D space with an additional time dimension. Do not forget: gravity is not the curvature of space, but of spacetime. General Relativity uses internal attributes of spacetime only, e.g. that in curved spacetime angles of a triangle do not add up o 180 degrees. But this does not mean there is something outside this spacetime, in a higher dimension. It are the analogies with flat planes, surfaces of spheres or tori in our 3-D space that seduce you in thinking there must be something outside. Same for the multiverse. Under this heading go very different concepts of 'other universes'. To imagine them as e.g. spherical universes in a much wider space in which they all expand, is again just some analogy. E.g. it does not apply to the multiple universes as they form in the many worlds interpretation in quantum mechanics. I stipulate that that my knowledge of cosmology is limited and this is not intended to be an argument but a probing. But according to CDT (causal dynamical triangulation) itself can curve spacetime as is demonstrated in fractals.
I stipulate that that my knowledge of cosmology is limited and this is not intended to be an argument but a probing.OK, I try to be kind...
But according to CDT (causal dynamical triangulation) itself can curve spacetime as is demonstrated in fractals.I think there is a word missing: what is 'itself' referring too? So I do not understand what you are trying to say here. I even doubt you understand it yourself... CDT at the moment is just one hypothesis about how General Relativity and quantum mechanics can be reconciled. It is not proven. Why are you so desperately looking for some first principle? Are you missing God, after his passing away?
CDT at the moment is just one hypothesis about how General Relativity and quantum mechanics can be reconciled. It is not proven.CDT at least seems based on scientific principles, unlike the many worlds interpretation of quantum mechanics which is pure fantasy.
CDT at least seems based on scientific principles, unlike the many worlds interpretation of quantum mechanics which is pure fantasy.I nearly do not know anything about CDT, but it seems at least that it makes some empirical predictions that might be tested. However I would not say that the many worlds interpretation of quantum mechanics is pure fantasy: the empirical predictions it makes are correct. But they are not better than the Copenhagen interpretation (ain't that not the 'shut up and calculate' approach?). The many worlds interpretation just tries to keep determinism upright (as the wave function is strictly deterministic). It does that at the cost of a pretty extreme metaphysics. On the other side, personally I think that the idea that the 'wave function collapses' is just another metaphysical monstrosity, which leads to funny philosophies about living and/or dead cats... I see much more in the decoherence] approach, as it has no special role for consciousness, not many worlds, and also not some magical Bohmian quantum potential (sorry, Write4U).
I see much more in the decoherence] approach, as it has no special role for consciousness, not many worlds, and also not some magical Bohmian quantum potential (sorry, Write4U).Agree 100% on the decoherence hypothesis. If it works decoherence will pave the way for quantum computers. The many worlds postulate predicts nothing, explains nothing, and is not testable.
CDT at least seems based on scientific principles, unlike the many worlds interpretation of quantum mechanics which is pure fantasy.I nearly do not know anything about CDT, but it seems at least that it makes some empirical predictions that might be tested. However I would not say that the many worlds interpretation of quantum mechanics is pure fantasy: the empirical predictions it makes are correct. But they are not better than the Copenhagen interpretation (ain't that not the 'shut up and calculate' approach?). The many worlds interpretation just tries to keep determinism upright (as the wave function is strictly deterministic). It does that at the cost of a pretty extreme metaphysics. On the other side, personally I think that the idea that the 'wave function collapses' is just another metaphysical monstrosity, which leads to funny philosophies about living and/or dead cats... I see much more in the decoherence] approach, as it has no special role for consciousness, not many worlds, and also not some magical Bohmian quantum potential (sorry, Write4U). I also agree on the concept of *decoherence*. Seems to me that can this can be simply demonstrated in the result of wave-interferences. The beauty of triangulation is its very simplicity. A triangle is the smallest possible *plane* and if applied 3 dimensionally, it results in dodecahedrons which is another proposed configuration of a finite universe. CDT goes much deeper and in the abstract is causal to the "unfolding" (by a process of dynamical iteration) of spacetime itself. http://images.iop.org/objects/phw/news/thumb/7/10/5/polygon.jpg
Jean-Pierre Luminet of the Observatoire de Paris and colleagues believe that the finite size of the universe itself is responsible for this behaviour. Moreover, they show that the predictions of a model in which space consists of 12 curved pentagons joined together in a sphere agrees with the WMAP observations (figure 2). Their ‘small’, closed universe should be about 30 billion light years across.http://physicsworld.com/cws/article/news/2003/oct/08/is-the-universe-a-dodecahedron Visualize a soccer ball., Curved and joined pentagons resulting in a perfectly round sphere. Moreover, the illustration suggests an inherent spiral function. The main point which makes this concept so attractive is that it is background independent and is compatible with both GR and QM.. And notice the natural spirality of this configuration. The Fibonacci Sequence can be found everywhere we look. Just a little afterthought: Is it possible that Pi may be an important (causal) aspect in CDT? A transcendental number which can never reach it's full potential?
The many worlds postulate predicts nothing, explains nothing, and is not testable.You seem to be quite irritated about the the many worlds interpretation. ;-) I tend to agree with you, however, there is quite a bunch of physicists who somehow take it serious. And it seems that the idea of decoherence arose under MWI adepts... Some of them even believe that, at least in principle, empirical tests would be possible (well, at least according to Wikipedia]...)
Write4U,
Such speculations are high above my head, so I haven’t much to say. As once said before: it is fascinating stuff, but we, science amateurs, can just wait and see which theory will float above in a few years. I do not think it is very useful to anticipate some outcome, just while it feels good.
Understanding established Quantum Mechanics and Relativity is already difficult enough…
The many worlds postulate predicts nothing, explains nothing, and is not testable.You seem to be quite irritated about the the many worlds interpretation. ;-) I tend to agree with you, however, there is quite a bunch of physicists who somehow take it serious. And it seems that the idea of decoherence arose under MWI adepts... Some of them even believe that, at least in principle, empirical tests would be possible (well, at least according to Wikipedia]...) Yes, the MWI irritates me. See the Objections section of the wikipedia page you linked for some of the many reasons. The Many Worlds Interpretation is bad science and bad philosophy that relies on special pleadings for its justification.