Friday, May 04, 2007

Boltzmann’s Brain explained

I'd blogged earlier on a Cosmic Variance article about emergent brains in the eternal soup of a senescent universe, but I didn't know the original context of the Boltzmann Brain idea. Another CV article today pointed me to one from last year that filled in the gaps. The Boltzmann Brain comes from a 2004 paper by Albrecht and Sorbo, and it was described in CV last year:
Boltzmann’s Anthropic Brain | Cosmic Variance

...Let’s posit that the universe is typically in thermal equilibrium, with occasional fluctuations down to low-entropy states, and that we live in the midst of one of those fluctuations because that’s the only place hospitable to life. What follows?

The most basic problem has been colorfully labeled “Boltzmann’s Brain” by Albrecht and Sorbo. Remember that the low-entropy fluctuations we are talking about are incredibly rare, and the lower the entropy goes, the rarer they are...
...So if we are explaining our low-entropy universe by appealing to the anthropic criterion that it must be possible for intelligent life to exist, quite a strong prediction follows: we should find ourselves in the minimum possible entropy fluctuation consistent with life’s existence.

And that minimum fluctuation would be “Boltzmann’s Brain.” Out of the background thermal equilibrium, a fluctuation randomly appears that collects some degrees of freedom into the form of a conscious brain, with just enough sensory apparatus to look around and say “Hey! I exist!”, before dissolving back into the equilibrated ooze.

You might object that such a fluctuation is very rare, and indeed it is. But so would be a fluctuation into our whole universe — in fact, quite a bit more rare. The momentary decrease in entropy required to produce such a brain is fantastically less than that required to make our whole universe. Within the infinite ensemble envisioned by Boltzmann, the overwhelming majority of brains will find themselves disembodied and alone, not happily ensconsed in a warm and welcoming universe filled with other souls. (You know, like ours.)

This is the general thrust of argument with which many anthropic claims run into trouble. Our observed universe has something like a hundred billion galaxies with something like a hundred billion stars each. That’s an extremely expansive and profligate universe, if its features are constrained solely by the demand that we exist. Very roughly speaking, anthropic arguments would be more persuasive if our universe was minimally constructed to allow for our existence; e.g. if the vacuum energy were small enough to allow for a single galaxy to arise out of a really rare density fluctuation. Instead we have a hundred billion such galaxies, not to count all of those outside our Hubble radius — an embarassment of riches, really....

Of course there's no end to the anthropic principle, which I tend to think of as an extreme application of Bayes theorem. We can be anthropic ad absurbum, and say that since we live in a rich universe we must exist in a really, really, really big and really, really, rare entropic excursion event.

Or maybe we're a dream of a more modest excursion, which is, after all, more likely.

Hmph. Cosmology is becoming about as satisfying as quantum mechanics.

6 comments:

island said...

Very roughly speaking, anthropic arguments would be more persuasive if our universe was minimally constructed to allow for our existence; e.g. if the vacuum energy were small enough to allow for a single galaxy to arise out of a really rare density fluctuation. Instead we have a hundred billion such galaxies, not to count all of those outside our Hubble radius — an embarassment of riches, really....

if its features are constrained solely by the demand that we exist.


But, they aren't, Gordon, not even close.

http://evolutionarydesign.blogspot.com/2007/02/goldilocks-enigma-again.html

Leave it to theorists to isolate on a couple of about a hundred different anthropic coincidences that are *all, together,* telling you something very important.

Hmph. Cosmology is becoming about as satisfying as quantum mechanics.

And I'll guarantee you, that will remain the case for as long physicists dismiss strong interpretations of the anthropic physics out of hand without justification, and without really knowing anything at all about the anthropic physics.

You can bank on that.

John Gordon said...

Island, I scanned your web site but couldn't figure out where you were going. Are you arguing that the universe is designed for some purpose and that purpose is life like us?

I've heard the argument before, but it's a bit self-referential.

If you're trying to argue for design (creator, designer, hacker, deity, automated universe assembly line) I think you'd get more mileage of out the Fermi Paradox.

Anyway, it's a treacherous argument. Suppose we find that the universe is really tuned for something involving dark matter, and we're basically "mold" growing around the margins ...

island said...

Hi John... everybody calls you, Gordon, right?

Are you arguing that the universe is designed for some purpose and that purpose is life like us?

No, I think that the universe is configured from first principles, exactly as was expected before our normal turbulance driven models failed.

I believe that I have and can re-established for you good reason to think that life is necessarily and specially relevant to the structure mechanism in the same context that John Wheeler and Paul Davies do, but I don't think that observer dependent quantum mechanics is what it is all about.

Hamiltonian mechanics isn’t inherently able to describe dissipative structuring, except by way of the master equation in the Lindblad form. Correct me here if I’m wrong, but this derives that the apparently unexpected value of the cc actually produces a natural harmonic damping mechanism that enables the universe to dissipate energy most uniformly.

So the AP is just an energy conservation law, since energy can’t be conserved if it goes inert before it can do any work

If you're trying to argue for design (creator, designer, hacker, deity, automated universe assembly line) I think you'd get more mileage of out the Fermi Paradox.

No, it's just thermodynamics, but if you had read the article that I'd linked, then you would know why Fermi's "Paradox"... isn't.

Anyway, it's a treacherous argument. Suppose we find that the universe is really tuned for something involving dark matter, and we're basically "mold" growing around the margins ...

Please just entertain this **fact** for a moment, and I can promise you that I can give you valid physics for it that very simply resolves all of the anthropic problems, but also includes a vald theory of quantum gravity, (that I can't even begin to write down):

There is an inherent prediction to any true anthropic cosmological principle, which notes that the anthropic constraint on the forces necessitates a reciprocal connection between the human evolutionary process and the evolution of the universe, meaning that physicsists should be actively searching for a mechanism that enables the universe to “leap/bang” to higher orders of the same basic structure.

In this case, absolute symmetry is the unattainable “goal” of evoltion.

Nobody even knows that this ****OBVIOUSLY SELF-EVIDENT**** prediction falls from this, and there is only one reason why this is true... and it ain't pretty, because unjustified dogma has nothing to do with science.

island said...

Well, I didn't expect that to be the final word, and I hope that I didn't say something to offend or alienate you, Gordon.

John Gordon said...

Hi Island. No, I'm fine. I just don't know much physics. My physics studies ended at the undergrad level 25 years ago, so now I just read popular books. I can't comment on much beyond popular works; I just don't have the mathematical expertise or the scholarship.

island said...

Oh, oops... sorry, I could have been more clear had I known.

I've been accused of making my point a thousand different times in a thousand different places, but I don't believe that I've ever made a single point, since my words typically fall on deaf (willfully ignorant) ears.

I don't usually fail because I'm not understood... ;)

Thanks for your time.