- #1
MTd2
Gold Member
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Let me be more rephrase what I wrote, to not sound rediculous as usualy I am. Loll's universe seems to mimick some futures of our universe, but I just can't see anywhere how a QFT can be defined over that space.
To begin with, the space we observe in this universe is not a single one, but an ensamble of spaces. One could say alright, since a sum-over-some parameters is what we always we expect from a quantum theory, but not in this case. In this situation, it doesn't end alright, because in some cases, the hausdorff dimension does not even converge to a value that is close to a unit, rather, you get "extreme" fractional numbers, like 2.5, 1.5. You can see that on this Article ( http://arxiv.org/PS_cache/hep-th/pdf/0404/0404156v4.pdf ) page 7, where the number of dimensions shows a continue convergence going from 0 to 4, depending on the V of a sample cell of that universe.
In the end, the best we'd get would be a highly amorphous, say fractal if you like, pseudo latice, in which we wouldn't get define a local continuous neighborhood, not even if we took a sample size N going to infinity. In such regimes of extreme fraction dimensions, I can't see how one could even locate a particle in space, because we wouldn't know if there is space, say universe, defined at that given place (supose we consider that space embeded in a higher dimensional space, so that we can define points even though they are not define at the original place). Much less we would be able to talke about the measure of fields, because the space would be really bad defined, highly irregular, between any 2 points of this universe.
Something else that I can´t see working, it is how mass could ever emerge from that. Usualy in the crazy theories around, mass has a relation with geometry and/or geometry. We expect a high curvature if we get close enough of a particle, but in that case, if you get close to anything, the dimenion number goes decreases. At a particle we wouldn't see anything, but a hole (dimension 0)! How you can define mass, or anything else, if you have a
hole. This is the universe, not a semiconductor. There's nothing outside it.
Maybe this is a toymodel, but if they don't put something else on that, I can't see how you could progress with that...
To begin with, the space we observe in this universe is not a single one, but an ensamble of spaces. One could say alright, since a sum-over-some parameters is what we always we expect from a quantum theory, but not in this case. In this situation, it doesn't end alright, because in some cases, the hausdorff dimension does not even converge to a value that is close to a unit, rather, you get "extreme" fractional numbers, like 2.5, 1.5. You can see that on this Article ( http://arxiv.org/PS_cache/hep-th/pdf/0404/0404156v4.pdf ) page 7, where the number of dimensions shows a continue convergence going from 0 to 4, depending on the V of a sample cell of that universe.
In the end, the best we'd get would be a highly amorphous, say fractal if you like, pseudo latice, in which we wouldn't get define a local continuous neighborhood, not even if we took a sample size N going to infinity. In such regimes of extreme fraction dimensions, I can't see how one could even locate a particle in space, because we wouldn't know if there is space, say universe, defined at that given place (supose we consider that space embeded in a higher dimensional space, so that we can define points even though they are not define at the original place). Much less we would be able to talke about the measure of fields, because the space would be really bad defined, highly irregular, between any 2 points of this universe.
Something else that I can´t see working, it is how mass could ever emerge from that. Usualy in the crazy theories around, mass has a relation with geometry and/or geometry. We expect a high curvature if we get close enough of a particle, but in that case, if you get close to anything, the dimenion number goes decreases. At a particle we wouldn't see anything, but a hole (dimension 0)! How you can define mass, or anything else, if you have a
hole. This is the universe, not a semiconductor. There's nothing outside it.
Maybe this is a toymodel, but if they don't put something else on that, I can't see how you could progress with that...