Last year Sean wrote a marvelous short on Boltzmann's Brains
A Boltzmann Brain is a self-aware entity that spontaneously appears from a low probability statistical fluctuation to a low entropy state.
A very low probability fluctuation.
We're talking something like a potted plant appearing spontaneously high above a planet's surface, thinking "oh no, not again" and then plummeting to its more probable, energy conserving, high entropy disassembly.
No violation of physical law or cherished symmetries, just a low probability rapid assembly of ordered mass, followed by return to normalcy.
The point, of course, is that while this is a very low probability event, it is finitely probable; so, given large enough a space, exploring its state space for long enough a time, such events will occur.
More interestingly, in the absence of preferred initial conditions predisposed to evolving to interesting states, the probability of us appearing is finite. Which is good.
But the probability of our current state appearing evanescantly - with the illusion of the actual projected past, without actually evolving through the preceding states - is much higher than our entire cosmological history appearing spontaneously. Naively... there may be subtle flaws with the preceding argument.
So, it is much more likely that we popped into existence last thursday and will spontaneously and acausally decay at 3 am this morning, than that we actually existed for however long you imagine you did.
Bother.
Further, it is much more likely still that a flawed copy of our apparent existence should pop spontaneously into being. So somewhere out there, is a "me" all bothered, because the universe is all wrong in detail. Lots of me actually, but only finitely many.
This is inevitable given some suitable simplifying assumptions, given a large enough space, long enough time, and physical laws that are ergodic, and if you can effectively approximate the visible universe as a finite state system (it doesn't actually have to be a finite state system, it is sufficient that it can be well approximated by a finite state system).
Ok... still here?
But, clearly we can conceive of a vastly larger intelligence, which spontaneously assembles as a very unlikely low entropy fluctuation, which is large and coherent enough that it can emulate within its internal state a "visible universe size sub-system". ie it holds within its larger organised internal state and entire copy of the state of the whole of our visible universe for a "long time", it is a full 3+1 copy of our visible, finite universe. If our universe has an infinitely long interesting future, we can agree to terminate the time slicing given some consistent choice of foliation.
This is of course a much less likely fluctuation, but it is still only finitely improbable.
If the universe is holographic, as has been postulated, then this is clearly possible - the state of the universe is finite, or well approximated by a finite system, and its state can, in principle be read from its boundary.
So... it can be wholly encompassed by a larger but finite system which emulates our universe faithfully, and can read the state of our apparent universe.
Since this is possible, it must happen. So somewhere, somewhen, we exist as an illusion imaged by a very large organized and arguably aware entity.
Uh-oh.
But, we are not done yet; because for all such omniscient entities encompassing us within their spontaneously created brains, there are a large number of entities who try to do this small thing, but fail.
There will be a lot of fallible but very large and smart entities who screw up their emulation of our existence. Some might even do so capriciously, to the extent that the concept of volition can apply to such an entity.
Having a bad day? don't worry, it may just be because your current instantiation is being done by a particularly inept, or mean, B-Brain.
But, we are not done yet; because there is still a finite probability that there will be such an instantiation which experiments with refinements - running repeated emulations of our apparent existence, but subtly altering the boundary conditions each time to achieve some sort of idealized perfection - this will of course be attempted for all possible conceivable standards for perfection, since that is merely a small number of additional trials.
So, maybe we do live in the best of all possible worlds?
Aargh.
But, we are not done yet; because each such minimally large enough omniscient entity is still but a (very large) finite state system - so it too can be embedded in a larger, and much less probable, instantation of improbable fluctuation from statistical equilibrium. Not likely, but not infinitely improbable.
Or not.
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So in other words, it's turtles all the way down?
We totally live in a test trial.
I wonder who one would apply to to be on the dev team for Universe 2.0.
We are exploring loopholes in Bell test experiments in a larger setting, I take it?
So you are saying that it is impossible that an infinite universe is a fluctuation as philosophers would like to speculate, but part of it could be. And we still have no way of telling. Bummer.
When theologians in effect discuss Boltzmann's Brains Matrixing the world, I like to point out that they are describing Cosmic Cheaters, showing us one physics and secretly using another. Maybe I should switch to calling them Cheated Cosmoses instead. :-)
One interesting consequence though, is that it seems as hard to always distinguish causality from fluctuation as it is to distinguish pseudorandomness from randomness, given just examples. Perhaps it is a principle of nature.
Funny, I was thinking this is the usual order reversed with turtles all the way up instead, ever larger nested Boltzmann's Brains. I hope the philosophers can sort out the implied direction in turtle units. :-)
> with the illusion of the actual projected past
I think this assumption is not necessary.
How many times do you check the consistency of all your memories? And how many times do you check that they agree with reality?
All you (we) have is this one feeling that "everything seems to be alright" in this instant...
It should require much less to reproduce this feeling by chance.
Long ago, David Hume argued against the Argument from Design, even before it had that name. One of his points was that the design we observe couldn't really tell us anything about the purported Designer. For example, what if we were a rough draft? Or, even more horrifying -- what if the Designer were a committee?
Let me refer back to an 1895 paper, which anticpates the notion, and the anthropic principle, by the immortal
Boltzmann, which has recently attracted attention in
the controversy over so-called "Boltzmann Brains":
Boltzmann's original paper (now available as pdf). The reference is
Nature 51, 413 (1895), as tracked down by Alex
Vilenkin. Don Page copied it from a crumbling
leather-bound volume in his local library, and the
copy was scanned in by Andy Albrecht. The discussion
is just a few paragraphs at the very end of a short
paper.
"I will conclude this paper with an idea of my old
assistant, Dr. Schuetz.
"We assume that the whole universe is, and rests
for ever, in thermal equilibrium. The probability that
one (only one) part of the universe is in a certain
state, is the smaller the further this state is from
thermal equilibrium; but this probability is greater,
the greater is the universe itself. If we assume the
universe great enough, we can make the probability of
one relatively small part being in any given state
(however far from the state of thermal equilibrium),
as great as we please. We can also make the
probability great that, though the whole universe is
in thermal equilibrium, our world is in its present
state. It may be said that the world is so far from
thermal equilibrium that we cannot imagine the
improbability of such a state. But can we imagine, on
the other side, how small a part of the whole universe
this world is? Assuming the universe great enough, the
probability that such a small part of it as our world
should be in its present state, is no longer small.
"If this assumption were correct, our world would
return more and more to thermal equilibrium; but
because the whole universe is so great, it might be
probable that at some future time some other world
might deviate as far from thermal equilibrium as our
world does at present. Then the afore-mentioned
H-curve would form a representation of what takes
place in the universe. The summits of the curve would
represent the worlds where visible motion and life
exist."
Interesting - so, when can we see a pilot program for the SciFi channel??
BTW, this vaguely reminds me of J. L. Borges' 'The Library of Babel'
Soon as the Sci-Fi channel script writers discover Olaf Stapledon;
although I think Odd John or Sirius will be done before Star Maker
Hm, universe by committee, as opposed to the inept designer...
must happen, scarily enough, given time enough and ergodicity
Yes, the volume thingie strikes me too. If any anthropic or environmental cosmologists succeeds in making a realistic probability measure over expanding Hubble volumes, it would be so much more probable with an anthropic volume than a BB one.
Still, that we can imagine anything and everything is cool.
HA!
yes, the Boltzmann brains are merely a metaphor for anything. still, i never laughed so hard in my life as when i read the article in the NYT yesterday by Dennis Overbye - good job Dennis - i'd forgotten about Boltman brains!
and to think i've been disturbed and anxious about the current and upcoming presidential election shenanigans!
freaky cosmology always brings me back to earth, especially whenever lay reporters DO cosmology! but Dennis did do a great summary, i thought.
the last few lines in the article are hysterical! (for those who haven't read it yet) --
[Assuming eternal inflation]
"...The main way life emerges [Andrei Linde says] is not by reincarnation but by the creation of new parts of the universe.
'So maybe we don't need to care too much, about Boltzmann brains.'
'If you are reincarnated, why do you care about where you are reincarnated?', he asked. 'It sounds crazy because here we are touching issues we are not supposed to be touching in ordinary science. Can we be reincarnated?'"
"People are not prepared for this discussion," Dr. Linde said.
Far out Dr. Linde! very cool!