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" <marchal.domain.name.hidden>
To: <everything-list.domain.name.hidden>
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/
>
Received on Tue Jul 20 2004 - 11:15:51 PDT