Re: Universes infinite in time
On Wed, Jan 08, 2003 at 04:07:47PM -0800, Hal Finney wrote: > How could we go about modelling a universe like this? A mathematical model should be straightforward. For a computational model, consider a program that takes an infinitely long string as input, which it interprets as the description of a 3d slice of such an infinite 4d universe. The description starts at an arbitrary "center of the universe" and continues in concentric shells. The program computes the future of the universe from the center, reading its input as needed to obtain information about the past lightcone. Now to avoid an actual input that is infinitely long, use a pseudorandom number generator to produce the input to the above program. While the computational model has a fixed beginning and a center, the observers living inside it have no way to tell that. Still it seems a lot less elegant than a mathematical model that has no center or fixed beginning. I think it's another reason to prefer a theory of everything based on all mathematical structures rather than all computations. > Can we rule out > Steinhardt's cosmology on fundamental principles? No, I don't think so. > Are infinite-time > universes of zero measure compared to ones with a fixed beginning? It seems that all computational models must have fixed beginnings, but maybe you can always find one that can't be distinguished from an infinite-time universe from the inside. > It would be interesting if the everything-exists model could be used to > constrain cosmological theorizing in this way. It may be possible, but not in this case, I don't think.
Re: Universes infinite in time
Bruno Marchal wrote: For example they will correctly infer some standard model particle theory from they high level experimentations, but as soon they will build particle accelerator to verify their theories, discrepancies will appear (just because we have not simulate the society-world at such a detailed level. So now those researchers can infer that they are simulated at some different reality level. But this is what we don't want. So let us add a subroutine which observes the researchers, and each time reserachers find (serious) discrepancies, the subroutine freezes the researchers and refines their level of reality. ...and there is another theory which says this has already happened... D. Adams.
Re: Universes infinite in time
At 16:07 -0800 8/01/2003, Hal Finney wrote: The interesting aspect from this list's perspective is how to regard infinite-time cosmologies. Does it make sense to imagine a universe which has had an infinite past? How could we simulate that on a computer, if there were no starting point? We certainly cannot simulate a 3-person infinite past history. But imagine we simulate a society-world of researchers in a computer, and that we would like those researchers never guess anything about our own reality level. Now, the computer is locally finite (i.e. at each time it is finite but it is capable to grow indefinitely) so that those researchers, experimenting their reality, will find little local inconsistencies. For example they will correctly infer some standard model particle theory from they high level experimentations, but as soon they will build particle accelerator to verify their theories, discrepancies will appear (just because we have not simulate the society-world at such a detailed level. So now those researchers can infer that they are simulated at some different reality level. But this is what we don't want. So let us add a subroutine which observes the researchers, and each time reserachers find (serious) discrepancies, the subroutine freezes the researchers and refines their level of reality. Now, it is quite logically possible that the refining need not only to add sub-particles, but need to add past further "past-interactions". So, although that past is generated, little by little, in the 3-future, it will happen that from the 1-perspective of the simulated researchers their stories will look as if they are infinite in their past. Is not UD* like that? Open problem. But quite possible once we distinguish the 1-time of the simulated people and the "3-time" describing the definite steps of the UD in Platonia. Bruno
Re: Universes infinite in time
I wrote: > Paul Steinhardt, one of the original cosmic-inflation theorists and the > man who coined the term "quintessence" has a new theory of cosmology > which is described at http://arxiv.org/abs/astro-ph/020447. Sorry, the correct URL is http://arxiv.org/abs/astro-ph/0204479. Hal
Universes infinite in time
Paul Steinhardt, one of the original cosmic-inflation theorists and the man who coined the term "quintessence" has a new theory of cosmology which is described at http://arxiv.org/abs/astro-ph/020447. The abstract reads, The Cyclic Model is a radical, new cosmological scenario which proposes that the Universe undergoes an endless sequence of epochs which begin with a `big bang' and end in a `big crunch.' When the Universe bounces from contraction to re-expansion, the temperature and density remain finite. The model does not include a period of rapid inflation, yet it reproduces all of the successful predictions of standard big bang and inflationary cosmology. We point out numerous novel elements that have not been used previously which may open the door to further alternative cosmologies. Although the model is motivated by M-theory, branes and extra-dimensions, here we show that the scenario can be described almost entirely in terms of conventional 4d field theory and 4d cosmology. The theory does not actually have a "big crunch" in the traditional sense; rather, after a long period of expansion so that there is less than one particle in each visible segment of the universe, a hidden dimension contracts and suddenly the universe is full of light and energy, and it starts expanding again. There is no inflation as in the regular model, instead the long period of expansion from the previous cycle is what is responsible for the remarkable uniformity that is observed. The interesting aspect from this list's perspective is how to regard infinite-time cosmologies. Does it make sense to imagine a universe which has had an infinite past? How could we simulate that on a computer, if there were no starting point? I think Steinhardt's model also allows for a spatially infinite, flat universe as well. So we have infinities in all directions, temporal as well as spatial. We could avoid the problem by postulating that every cycle in Steinhardt's model is identical, giving the effect of a single universe, but I don't think there is any reason in the theory to suppose that would happen. Rather, each crunch is slightly different, and these small perturbations carry over into unique initial conditions for the next big bang. How could we go about modelling a universe like this? Can we rule out Steinhardt's cosmology on fundamental principles? Are infinite-time universes of zero measure compared to ones with a fixed beginning? It would be interesting if the everything-exists model could be used to constrain cosmological theorizing in this way. Hal Finney
