Simple explanation of the Boltzmann Brain paradox

[Graeme M]

Mods: I am not sure if this is a Physics question or more appropriate for Cosmology.

I read a short discussion (on another forum) about the Boltzmann Brain paradox. I did a little further reading on the web but most explanations were a bit too deep (read: over my head). I wonder if someone could offer a reasonably simple layman's explanation?

My understanding from what I have read is that a universe should tend to exist in a state of high entropy, however the universe we observe has a relatively low entropy and arose from a time of maximal low entropy. This could occur as a statistical fluctuation - that is that over time, an eternal universe would most of the time be in a state of high entropy but fluctuations within that state could give rise to local regions of low entropy.

However, the most likely of such fluctuations would overwhelmingly be smaller than the observed universe - that is, it is more likely that we would see a single galaxy, a solar system or even more likely a single brain. The ordered universe we do observe is exceedingly unlikely.

If that's the idea, I don't quite see why it's a paradox? Surely any possible state must occur at some time no matter how rare. Why is it strange (paradoxical) to be in that particular state?

I also read about the anthropic principle, and although I read about the strong and weak forms of this and the various takes on that, I generally understood it to say that "the universe is in the ordered state that we observe because we exist as observers to see this order". Or put another way, although it is unlikely to be in this state, the fact that we are here to observe is evidence that it has occurred and is real.

The idea of the Boltzmann Brain Paradox appears to say "the universe in the ordered state we observe is highly unlikely, and thus is most likely not real".

All of which boils down to "the universe appears of a form that is most unlikely, but that in itself is evidence that is real. Or not real."

Clearly I have misunderstood one or the other (or both) of these ideas. Can anyone (simply) set me straight?

 

[marcus]

Here's a simple online discussion:
http://physics.about.com/od/thermodynamics/f/BoltzmannBrains.htm

I'll try to give an even simpler account. Bo-Brn is something made up and used in the context of an argument about (1) second law (2) "arrow of time" in cosmology

For me the paradox is resolved when one realizes that the concept of entropy IS NOT ABSOLUTE but is observer dependent. It depends on the observer's coarsegraining map. I think the most plausible picture of cosmology is the one beginning to emerge in papers like Cai and Wilson-Ewing's "LambdaCDM bounce". You get a free PDF if you simply google that phrase "LambdaCDM bounce"

In that context it is no puzzle that the universe's expansion apparently began with a state of very low entropy. Very low entropy (as judged by observers in the expanding phase) is just what one might expect from a standard LCDM cosmos collapse and rebound.
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However to many people (especially some time ago, perhaps not so many now) it seemed like a great puzzle that the U expansion began with very low entropy.
Imagine that the U exists in a state of equilibrium and that regions with low entropy can only occur via statistically rare random fluctuations.

that seems at first to explain the arrow of time. our observable universe arose by accident out of a vast entropic boredom and began with low entropy and has been running by 2nd law back down to equilibrium.

Then a critic counters that by saying Consider which is more likely:
A. You did not exist one second ago, Your brain and your memories of your past life and all you learned in school and what the chair feels like on your bottom are all FAKE memories and sensations produced by a random fluctuation. The universe you think is there isn't real, what's real is your brain and the impressions in it, caused by a local random fluctuation.
B. the universe is not illusory but is instead real and was produced by a random fluctuation (necessarily involving a great deal more matter and energy).

The critic argues that A is much more likely because it takes relatively little randomness to gather a brain's worth of atoms into a structure with the required fake memories and fake awareness---that is only a small momentary production of negative entropy, a minor reversal of the 2nd law flow.

whereas it is enormously more improbable that a random fluctuation would produce a whole universe in a state of extremely low entropy (as at start of expansion)
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So I am saying that the "Boltzmann brain paradox" can be understood as a STAGE IN A CONVERSATION between two people who have made a lot of conventional assumptions---and who maybe do not understand the concept of entropy (and the second law) very well.
They think that entropy is ABSOLUTE and they are very puzzled by the fact that the U seems to have started expanding in a state of very low entropy (what appears to be a "clean slate" so to speak).
They have no clear idea of what could have preceded the start of expansion and they cannot imagine how anything could have, because it would need to have been even lower entropy! (Because they think entropy is absolute, existing even in the absence of any observer or any coarsegraining map, and always increases somehow, even when it is not defined.) So this boggles them and they encounter paradoxes.