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Saturday, 25 August 2007

Boltzmann Brains - Problem? What Problem?

(You might want to read this post first... or you may not)

Don Page probably gets more headlines for his "ladies and gentlemen, the universe will shortly be ending so please finish up your drinks and put the paper bags provided earlier over your heads..." announcements ( as in "Is Our Universe Likely to Decay within 20 Billion Years"), but James Hartle and Mark Srednicki have a saner approach.

To recap (very loosely) the story so far.

We are not special, we are typical - if we're not, how can our observations be typical of the universe, how can we know anything, doesn't our very existence tell us something about the universe? (Copernican Principle, Anthropic Principles)

Sometime soon (soon in the cosmological sense of umptillion years being a lot less than an infinite number of years) the universe will be crawling with Boltzmann Brains just popping into existence, making an observation or (or two?) and pushing off again into the vacuum, without so much as a "by your leave".

And then we will be utterly insignificant in the grand scheme of things, and hence not typical at all and can't possibly be learning anything sensible about the universe.

But, since clearly we are significant and know loads of stuff (and Stuff, I hasten to add), it follows that we can't be about to be invaded by Boltzmann Brains and hence that the universe will end shortly because that's the only way to stop them taking over.

[It would spoil the story to admit that there are other ways to deal with them pesky Brains... but there are, e.g. ..."Repelling the Invasion of the Boltzmann Brains" by S Carlip]

(And may I add as an aside how very short-sighted some physicists can be - even if they do have a way with catchy titles for their papers? What about some preventative measures? Surely it's not too late to take action! A Department of Home World/Galaxy/Universe Defense for example, the e-petition I mentioned in the previous post? Oh, what I wouldn't give to hear Dubya pronounce "These Bolts-men folk are un-American! We must fight their statistical evil!")

The argument up for ridicule is basically: if we are to remain typical we need to pull the plug quickly (or get cloning) - before we become atypical.

Of course it's complete tosh, the fundamental problem being "What do you mean by Typical?" and here Hartle and Srednicki have done a far better job than I ever could in their paper Are We Typical?.

I was going to waffle on about the fact that at least one observer (e.g. the first) has to be atypical, and that "being" is entirely different from "being randomly selected from a population of observers", and that since we see time as having an arrow ["Time flies like an arrow; fruit flies like a banana"] we should perhaps, at best, think of ourselves as typical observers of the now - Temporal Typicality as an eternal assumption probably leading to a Steady State theory (which seems unlikely).

Hartle & Srednicki's paper says it all very clearly and only needs the tiniest bit of maths (in the form of Bayesian Probability) to follow. They basically say that there is no basis other than prejudice (ideas that one likes or dislikes because they lead somewhere interesting) in the selection of the prior probabilities used in the Bayesian calculations; by all means assume what you like, but be clear about it and recognise that the choice is not scientific.

They also deal neatly with the whole Typicality thing: we are typical of what? Of things weighing between 10kg and 100kg? Of things with ten toes? And point out how silly assumptions can lead to equally silly conclusions.

Read it. It's worth it.

Conclusion: so what? Even if the universe will shortly be hosting The Great Boltzmann Brain Ball it doesn't affect us at all.

So, unless Boltzmann Brains are improbably more probable than they would seem to be a priori (in which case I suspect we have a different kind of problem) there's nothing to worry about.

Phew! I can sleep soundly now.

Ugh! What was that grey squishy thing I just sat on?

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