Re: All possible worlds in a single world cosmology?
In reply to posts by Hal Finney and Bruno Marchal-- Hal: I found the paper you referred to, and it certainly has some very interesting ideas, for example the idea that the arrow of time is actually an anthropic artefact. I admit that I have much reading to do if I am to understand the paper properly, but I am not sure what I was proposing - that all possible worlds will at some stage exist - is the same thing as the Poincare recurrences discussed in this paper. It possible that only a subset of possible events (everything that has occurred so far, and then some) will cycle endlessly, and if so, as Nietzche commented, that'll suck (or words to that effect). I probably gave the wrong example when I proposed as my unlikely event the formation of an exact copy of our solar system and its inhabitants in far future interstellar space; much more interesting would be a rather different copy, where you would be resurrected with intact personality and memories of your past life, with enhanced intelligence and physical abilities, and a whole new civilization with scientific wonders, intelligent aliens, and things so strange that no-one today has even imagined them, all to explore. Of course, you will also experience burning in hellfire as the flipside to this happy state, but who was it that said it was better to burn than to disappear? Bruno: I agree that my four assumptions are dubious, but I chose them, for the sake of argument, as being (a) most inimical towards Many Worlds theories, (b) closest to what most people would think of as common sense, and (c) least controversial/ most conservative in the scientific community. I do think they are internally consistent, even if they are completely wrong. I do not understand your comment that by saying the universe is unique, finite, expanding and cooling forever, it is contradictory to allow that my example of an unlikely event will occur as time approaches infinity. The increase in entropy and cooling which go with the model I suggested are average trends over time. It is possible within this long term decline to have pockets of order/ decreasing entropy, both in classical statistical mechanics and quantum mechanics. It is a mathematical fact, independent of the actual physics, that given enough time (and eternity is certainly enough time), any event that is possible, however close to zero its probability per unit time, will occur with probability arbitrarily close to 1. What rather surprised me, however, is the fact that the last statement is only true in general if the probability per unit time stays constant or increases with increasing time; if it decreases, limiting towards zero as time approaches infinity, then it is possible that this event, which still always has non-zero probability per unit time, may never actually occur. For example, if Pr(P)=1/(t^2), as t goes from 2 to infinity, the cumulative probability that P will occur at some point is 1/2. Stathis Papaioannou _ Protect your inbox from harmful viruses with new ninemsn Premium. Go to http://ninemsn.com.au/premium/landing.asp?banner=emailtagreferrer=hotmail
Re: All possible worlds in a single world cosmology?
It all depends what do we deem: POSSIBLE. According to what conditions, belief, circumstances? If we accept the here and now as the world, Stathis #1 may be right. John Mikes - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, July 20, 2004 4:03 AM Subject: Re: All possible worlds in a single world cosmology? At 20:46 17/07/04 +1000, Stathis Papaioannou wrote: 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; I don't know if this is true, false or meaningless. It fits with common (aristotelian) sense. From a motivation point of view I cannot take the existence of the universe for granted because it is such an existence, or the appearance of such an existence, that I would like having an explanation for. If we assume comp, and if 1 is true the UDA alone shows that the physical universe whatever it is exactly must be little in the sense of being unable to run the universal dovetailer. I call that the Delahaye move. But the filmed graph argument shows that this move does not really work unless you drop out the Arithmetical Realist part of COMP. 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; OK, you take COMP without RA. Then your physical universe is necessarily little in space and time. But then it cannot leads to your sequential many worlds. 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; If that cooling is enough to prevent a UD to run forever, it confirms what I was saying. So you are coherent indeed. 3, or something similar follows from 1 and 2. 4. Some single world interpretation of quantum mechanics is correct. Obviously, from 1 and 2 too. 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. Then you need a *very* big unique little universe! That seems to me rather ad hoc (but still coherent). 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). Is that not in contradiction with the cooling? What does mean a going to infinity if the universe is little. Are you positing a external finite time with an internal infinite time? 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. I see. You want an infinite cooling but suspect this would not prevent unlikely events to occur if the 3-time is infinite. As you say such computation can be hard, but I don't see anything inconsistent with such events except that it makes your universe enough big for a DU to proceed and this jeopardizes your COMP hyp, even without Arithmetical Realism RA (giving that this UD will be physically concrete and then UDA will go through. 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
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
