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/
