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 results in "more vacuum" - doesn't it? > > > > As far as I know, even without the many worlds I would think the > probability that a (new) cosmos > appears is non null ... Cooling the expanding universe is probably not > enough to prevent the UD, > unless you can justify why all the cosmos are little and somehow > disconnected. You will be > obliged to justify some irreversible erasing of information, which cannot > exist with QM. > > It seems to me you make a lot of ad hoc hypotheses for justifying an > unlikely reality. > It is also hard for me to imagine comp true without RA. Actually RA is the > only part > of comp which is hard for me to conceive being false (but that could be > a personal limitation of course). > Anyway, I am looking for an explanation of the origin of the physical laws > so I will > not take your assumption number one. (But that is a question of goal). > > You seem also to forget that if there are many worlds, even just > sequentially, there cannot be > arbitrary large in time. If they are the UD will be executed integrally and > "real" physics must be > reduced to sum on computational histories (and then with occam or the > filmed graph argument) > we don't have to posit a physical reality. > > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ >