Stathis Papaioannou <stathisp.domain.name.hidden> writes:
> On 01/06/07, "Hal Finney" <hal.domain.name.hidden> wrote:
> > The reference to Susskind is a paper we discussed here back
> > in Aug 2002, Disturbing Implications of a Cosmological Constant,
> > http://arxiv.org/abs/hep-th/0208013 . The authors argued that in current
> > cosmological models the universe dies a heat death and falls into a steady
> > state of exponential expansion which goes on forever. In that state,
> > quantum gravity fluctuations will eventually cause macroscopic objects
> > to appear. This is extremely rare but still with infinite time to work
> > with, every object will appear an infinite number of times. That includes
> > disembodied brains, the so-called Boltzmann brains, as well as planets and
> > whole universes. But the smaller objects are vastly more common, hence it
> > is most likely that our experiences are due to us being a Boltzmann brain.
>
> It isn't generally the case that given a non-zero probability of an event E
> occurring per trial (or per unit time period), then as the number of trials
> n approaches infinity the probability of E occurring approaches 1. For
> example, if Pr(E) = 1/2^n, then even though Pr(E) is always non-zero, the
> probability of ~E as n->inf is given by the infinite product of (1-1/2^n),
> which converges to approximately 0.288788, not zero. So if the exponential
> expansion is associated with a continuous decrease in the probability that
> an event of interest will occur during a unit time period, that event may
> still never occur given infinite time, even though at no point can the event
> be said to be impossible.
Right, but apparently the physics doesn't work this way. The papers
just seem to take the size of the necessary object in Planck units and
say the probability of it popping into existence is 1/e^size. This is
constant and therefore it will happen an infinite number of times.
> > This has a few bad implications; one is that our perceptions should end
> > and not continue (but they do continue) and another is that brains would
> > be just as likely to (falsely) remember chaotic universes as lawful ones
> > (but we only remember lawful ones). So this model is not considered
> > consistent with our experiences.
>
> Another possibility is that Boltzmann Brains arising out of chaos are the
> observer moments which associate to produce the first person appearance of
> continuity of consciousness and an orderly universe. Binding together
> observer moments thus generated is no more difficult than binding together
> observer moments generated in other multiverse theories.
So how would this explain why we see an orderly universe? I think we
would have to say that Boltzmann brains that remember an orderly universe
are substantially smaller (take up fewer Planck units) than those that
remember chaotic ones.
I considered this possibility but I couldn't come up with a good
justification. Now, keep in mind that the Boltzmann brain does not have
to literally be a brain, with lobes and neurotransmitters and blood;
it could be any equivalent computational system. Chances are that true
"Boltzmann brains" would be small solid-state computers that happen to
hold programs that are conscious. Shrinking the brain even a little
increases its probability of existence tremendously.
(I am assuming that probability makes sense even though we are speaking of
events that happen a countably infinite number of times; both Boltzmann
brains and whole universes like ours will appear infinitely often in
the de Sitter state, but the smaller systems will be far more frequent.
I assume that this means that we would be more likely to experience
being the small systems then the big ones, even though both happen an
infinite number of times.)
So to explain the lawfulness we would have to argue that Boltzmann brains
that remember lawful universes can be designed to be smaller than those
that remember chaotic universes, as well as slightly lawless flying-rabbit
universes. It's not completely implausible that the greater simplicity
of a lawful universe would allow the memory store of the Boltzmann
brain to be made smaller, as it would allow clever coding techniques to
compress the data. However one would think that memories of universes
even simpler than our own would then be that much more likely, as would
memories of shorter lifetimes and other possibilities to simplify and
shrink the device. This explanation doesn't really seem to work.
Hal
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Received on Fri Jun 01 2007 - 17:26:04 PDT