Boltzmann brains
Russell Standish
Scientist. 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. 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.
It seemed to me that a Boltzmann brain was none other than one of our
white rabbits, or at least very closely related. Any thoughts?
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpc...@hpcoders.com.au
Australia http://www.hpcoders.com.au
----------------------------------------------------------------------------
Hal Finney
> 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
Stathis Papaioannou
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.
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
Hal Finney
> On 01/06/07, "Hal Finney" <h...@finney.org> 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
Mohsen Ravanbakhsh
Mohsen Ravanbakhsh,
Stathis Papaioannou
> 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.
My immediate thought on hearing the term was that the Boltzmann Brains are due to fortuitous arrangement of matter in any physical system, such as interstellar clouds of hydrogen, which happens to instantiate a particular Turing machine, but only for a tiny instant before it goes into another arrangement. Thus, not only will smaller systems be more frequent, but briefer systems will be more frequent; it is very unlikely that a large and long-lasting entity like a human brain will appear by chance, but rather more likely that very brief human brain-equivalent snapshots will arise, widely separated in time and space.
This is really very much like saying "every possible observer moment exists", and then trying to define a probability or measure which explains why in fact we tend to experience a certain kind of observer moment.
(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.
--
Stathis Papaioannou
LauLuna
ordered. Is there any room for order in such a tiny thing?
Best
On May 31, 1:51 pm, Russell Standish <l...@hpcoders.com.au> wrote:
> I came across a reference to Boltzmann brains in a recent issue of New
> Scientist. 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. 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.
>
> It seemed to me that a Boltzmann brain was none other than one of our
> white rabbits, or at least very closely related. Any thoughts?
>
> --
>
> ----------------------------------------------------------------------------
> A/Prof Russell Standish Phone 0425 253119 (mobile)
> Mathematics
> UNSW SYDNEY 2052 hpco...@hpcoders.com.au
> Australia http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
Russell Standish
>
> I have never been able to understand how a singularity can be highly
> ordered. Is there any room for order in such a tiny thing?
>
> Best
Highly ordered means small entropy. All you need is a small number of
states, so small things naturally have small entropy, and large things
naturally have high entropy. What's unnatural are large things with
low entropy.
Cheers
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics