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.
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.
>
> > Because they depend on
> > fluctuations of particles, Boltzmann brains would be more common in
> > regions of high entropy than low entropy. If the universe had started
> > out in a state of high entropy, it would be more likely to be
> > populated by Boltzmann brains than life forms like us, which suggests
> > that the entropy of our early universe had to be low. As a low-entropy
> > initial state is unlikely, though, this also implies that there are a
> > huge number of other universes out there that are unsuitable for us.
>
> I don't think this reasoning makes sense, for two reasons. First, even
> though the universe did apparently start out in a low-entropy state,
> hence giving an opportunity for non-Boltzmann (ie not disembodied)
> brains like ours to form, still as argued above eventually it gets into
> a high-entropy state and you then still have the problem of an infinite
> number of Boltzmann brains. The choice then is between a universe that
> starts high-entropy and has only Boltzmann brains, and one that starts
> low-entropy and has a finite number of "normal" brains and an infinite
> number of Boltzmann brains. It's not clear that the latter choice really
> explains and justifies why we are non-Boltzmann.
>
> Second, even if so, as it says these ideas are usually applied in the
> context of multiverse theories, so there would be an infinite number of
> universes, some starting in low entropy and some in high entropy states.
> Again we would have an infinite number of Boltzmann brains in the
> multiverse compared with only a finite number of non-Boltzmann brains,
> so we haven't really explained why we find ourselves in one of the
> universes which has normal non-Boltzmann brains.
>
> I would suggest two ways out of the dilemma. The first is from physics.
> One of the things I learned in my reading last night is that this
> model of an infinite expanding universe may not actually work. This
> so-called de Sitter state does not have a consistent quantum explanation.
> The theory suggests that the de Sitter state may be inherently unstable
> and will somehow decay, perhaps by tunnelling into another vacuum state.
> This could happen fast enough that the total expected number of Boltzmann
> brains is finite, potentially resolving the paradox.
>
> The other is from our measure-based reasoning. For various reasons we
> might argue that the measure of brains existing in the extremely far
> future is less than that of brains existing today. Such brains are much
> smaller spatially in comparison to the universe as a whole than our brains
> are today, for one thing, so perhaps they deserve a lesser share of the
> universe's total measure. Also, the amount of information to specify
> the location of such a brain in terms of Planck moments since the Big
> Bang would be vastly greater than for brains like ours existing in the
> relative youth of the universe. A measure concept related to information
> might therefore reduce the measure of such brains to insignificance.
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.
--
Stathis Papaioannou
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Received on Fri Jun 01 2007 - 06:41:47 PDT