Re: All possible worlds in a single world cosmology?
Stathis Papaioannou writes: > On 18 July 2004 Hal Finney wrote: > > We had some discussion a while back about a paper which proposed some > > similar ideas, http://xxx.lanl.gov/abs/hep-th/0208013, Disturbing > > implications of a cosmological constant. If you want to look in the > > archives, the thread was called "Doomsday-like argument in cosmology" > > and was in August 2002... > > Yes, I know there are all sorts of twists on the standard models in > cosmology out there, most of them controversial. But what I am looking at is > the "worst case scenario" for many world theories: no "Big Crunch", no > Tipler Omega Point, no daughter universes from black holes, no God, just a > finite universe expanding and cooling forever. Right, that's the same thing as that paper assumed. And it should be noted that this is basically the standard model of cosmology at present. > In a zillion years from now, > the universe will be a zillion light years across, almost all the "stable" > matter will have decayed, and the temperature will be extremely close to > absolute zero. My understanding is that even in this bleak scenario, > standard, non-controversial physics does not exclude the possibility that > new matter/energy will arise out of the vacuum. In the MWI of QM, this > possibility MUST be realised in some parallel universe, albeit one of very > low measure if the new matter is something like the event "P" I defined in > my original post, an exact copy of our solar system complete with conscious > inhabitants. In a non-MW interpretation of QM, P is possible but > fantastically unlikely. If the probability of P occuring in a unit time > period remains constant, or increases, with time, then - remember, we still > have eternity ahead even though a zillion years have already passed - P will > certainly occur. If this probability falls with time, P may or may not > occur, depending on the equation. Can anyone write down the equation showing > how Pr(P) evolves as a function of time in the above situation? The paper did in fact deal implicitly with this question. As I wrote, in effect they seemed to take as given that the probability was constant. As you have noted, this implies that all possible universes would appear eventually. This is what produced the "disturbing implications" of their title. Hal
Re: All possible worlds in a single world cosmology?
On 18 July 2004 Hal Finney wrote: QUOTE- We had some discussion a while back about a paper which proposed some similar ideas, http://xxx.lanl.gov/abs/hep-th/0208013, Disturbing implications of a cosmological constant. If you want to look in the archives, the thread was called "Doomsday-like argument in cosmology" and was in August 2002... ...I still wonder about the physical assumptions that treat the de Sitter state as a steady state. That little coordinate transform seemed pretty fishy to me. -ENDQUOTE Yes, I know there are all sorts of twists on the standard models in cosmology out there, most of them controversial. But what I am looking at is the "worst case scenario" for many world theories: no "Big Crunch", no Tipler Omega Point, no daughter universes from black holes, no God, just a finite universe expanding and cooling forever. In a zillion years from now, the universe will be a zillion light years across, almost all the "stable" matter will have decayed, and the temperature will be extremely close to absolute zero. My understanding is that even in this bleak scenario, standard, non-controversial physics does not exclude the possibility that new matter/energy will arise out of the vacuum. In the MWI of QM, this possibility MUST be realised in some parallel universe, albeit one of very low measure if the new matter is something like the event "P" I defined in my original post, an exact copy of our solar system complete with conscious inhabitants. In a non-MW interpretation of QM, P is possible but fantastically unlikely. If the probability of P occuring in a unit time period remains constant, or increases, with time, then - remember, we still have eternity ahead even though a zillion years have already passed - P will certainly occur. If this probability falls with time, P may or may not occur, depending on the equation. Can anyone write down the equation showing how Pr(P) evolves as a function of time in the above situation? Stathis Papaioannou _ SEEK: Now with over 50,000 dream jobs! Click here: http://ninemsn.seek.com.au?hotmail
Re: All possible worlds in a single world cosmology?
Stathis - > I would have guessed > that as the universe expands, chemical and nuclear reactions are less likely > to occur, in the same way as chemical reaction rates are proportional to the > concentration the reagents. On the other hand, it is not clear to me how > more exotic processes such as spontaneous appearance of particles out of the > vacuum are affected by the expansion, which after all results in "more > vacuum" - doesn't it? We had some discussion a while back about a paper which proposed some similar ideas, http://xxx.lanl.gov/abs/hep-th/0208013, Disturbing implications of a cosmological constant. If you want to look in the archives, the thread was called "Doomsday-like argument in cosmology" and was in August 2002. According to this paper, if there is a cosmological constant then the expansion of the universe will accelerate and eventually reach what is called a de Sitter state, where it is expanding exponentially. However the authors suggest that we could simply imagine our yardsticks also expanding exponentially, and the universe would then be in a steady state. In a steady state universe, fluctuations such as you describe will occur and all possible universes will eventually exist, in fact they will come into existence an infinite number of times. Now, I never really understood the physics involved here. I tried to learn about de Sitter universes and the data I got was somewhat contradictory. Some writers suggested that the mass density was zero in such a universe. It certainly seems odd to suggest that the yardsticks can expand without realizing that this would cause particles to appear to contract, presumably with physical implications similar to the questions you raise. However the authors were physicists and supposedly know their stuff. So maybe it is true that even in our current cosmological models, random fluctuations will be able to bring future universes into existence. The point of this paper was that in that case, since such universes occur an infinite number of times, it is infinitely unlikely that we should find ourselves in the first one, the "original" universe which is evolving from the Big Bang and just transitioning into the de Sitter expansion. Hence, on anthropic principles, this is a contradiction. One might propose to resolve it by suggesting that in fact we don't live in the primordial universe, but are in one of the fluctuations. However this doesn't work, because fluctuation universes are overwhelmingly likely to look very different from our universe. The chance that an observer in a fluctuation universe would see a past that was consistent with a Big Bang is essentially zero. So again, the anthropic principle seems to indicate that our observations are inconsistent. We can't both observe a universe with an infinite number of (eventual) observers, and see ourselves in such a unique position. I still wonder about the physical assumptions that treat the de Sitter state as a steady state. That little coordinate transform seemed pretty fishy to me. I don't know if this paper ever got peer reviewed but I'd take it a lot more seriously if or when that happens. Hal Finney
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Hi everyone! I have been a fan of this list for some time, reading the archive. I am an attorney with no educational background in science, so I probably will mostly keep my mouth shut and continue to read. With that said, I do have a great deal of interest in these topics, and have read a number of books and papers on the subject matter. Given my background, my approach is often more logical and philosophical than science based. I look forward to further enlightening discussion! Danny Mayes
All possible worlds in a single world cosmology?
I have been wondering about the possibility that all possible worlds exist, but sequentially rather than simultaneously, under a conservative cosmology with assumptions as follows: 1. There exists one, and only one, real, physical universe; 2. While it is possible to simulate any subset of this universe, including conscious beings, with a computer program, this program must be implemented on a physical computer, or on a virtual machine (or series of such) which is itself implemented on a physical computer; 3. The universe has a finite age and is comprised of a finite amount of matter/space/energy, but it is expanding and cooling and will continue to do so forever; 4. Some single world interpretation of quantum mechanics is correct. My understanding is that the above assumptions, which I have deliberately chosen as being contrary to many of the ideas discussed on the Everything List, still allow for the possibility of fantastically unlikely events, such as the spontaneous formation of an exact and stable copy of our solar system from the random motion of particles in interstellar space, or from vacuum fluctuations posited by the Uncertainty Principle. Let p(t) = probability that an event P will occur somewhere in the universe during the next year, t years from the present. The probability that P will NOT occur at some time between the present (t=0) and (t=a+1) is then given by the product: [1-p(0)]*[1-p(1)]*[1-p(2)]...*[1-p(a)] As a-> infinity this becomes an infinite product, representing the probability that P will NEVER occur. It is easy to see that this infinite product diverges to zero in the special case where p(t) is constant for all t; in other words, that P, however unlikely, will definitely occur at some point in the future if the probability that it occurs during a unit time period remains constant over time. The same conclusion applies if p(t) increases with increasing t: the infinite product diverges to zero, more quickly than in the case of constant p(t). Things get more difficult, however, if p(t) decreases over time. A Google search for "infinite product" brought up some very complicated expressions for even rather simple p(t), and it is by no means obvious (to me, anyway) whether the product will converge or diverge. Now, my question is, what happens to p(t) over time? I would have guessed that as the universe expands, chemical and nuclear reactions are less likely to occur, in the same way as chemical reaction rates are proportional to the concentration the reagents. On the other hand, it is not clear to me how more exotic processes such as spontaneous appearance of particles out of the vacuum are affected by the expansion, which after all results in "more vacuum" - doesn't it? I'm sure the above is a gross oversimplification - I'm not a physicist - but I would welcome people's thoughts on it. Stathis Papaioannou _ Find love today with ninemsn personals. Click here: http://ninemsn.match.com?referrer=hotmailtagline
