Russell Standish <lists.domain.name.hidden> writes:
> I came across a reference to Boltzmann brains in a recent issue of New
> Scientist.
Coincidentally (or not) I was reading all about this last night, from
the fqxi.org web site Max Tegmark mentioned a few weeks ago. The new
blog entry by Anthony Aguirre discusses this issue and some related ones
regarding multiverses, the Doomsday paradox, etc. I ended up reading
several papers by Don Page and others.
> The piece, quoted in full is:
>
> Spikes in space-time
>
> There is another way to think about why our universe began in a highly
> ordered or "low entropy" state. In 2002, a group of physicists led by
> Leonard Susskind at Stanford University in California proposed that
> entities capable of observing the universe could arise via random
> thermal fluctuations, as opposed to the big bang, galaxy formation and
> evolution. This idea has been explored by others, including Don Page
> at the University of Alberta in Edmonton, Canada. Some researchers
> argue that under certain conditions, self-aware entities in the form
> of disembodied spikes in space-time - "Boltzmann brains" - are more
> likely to emerge than complex life forms.
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.
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.
Hal Finney
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Received on Thu May 31 2007 - 18:48:09 PDT