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March 27, 2009

Comments

Even if the hypothesis of a low-entropy origin of the universe was proved false, this would not invalidate thermodynamics or the 2nd Law. So clearly it is incorrect to say that thermodynamics somehow "depends" on the Past Hypothesis or that it is somehow "scandalous" that the cosmological implications of the 2nd Law are not explained in textbooks.

It almost seems like people are iterating through all possible misunderstandings, suggesting I should have just ended the post with all possible disclaimers. :)

Phil, I said statistical mechanics was bad at predicting the past, not thermodynamics; it gets teakettles wrong too.

Scent, we know how to calculate the future, so calculating the past would be just as easy if the same approach applied.

James, Scent is right about records.

mjgeddes, tim is right; high entropy states can be very simply indicated.

Robin, this is false, weakly so in the first case[1], strongly so in the second. Please read what I write.

[1]Unless you have, for example, the definitive explanation on whether the universe is open or closed, etc. You are confusing local, gravity-free cases with global, non-gravity free cases. Iow, don't extrapolate from a gas enclosed inside a jar.

Robin:

Sean, the "past hypothesis" seems to me more of restatement of our failure than an actual solution. And I'd be more comfortable accepting it if I saw some formal calculations showing what it implied; the hand-waving makes me nervous.

The low-entropy-past hypothesis is neither a full solution nor a restatement of our failure; it is a partial explanation. It is like starting with the question "Why is this room hot?" and getting the answer "because there is a thermostat connected to a heating device, which produces heat until the room is brought to a certain temperature". Sure, this explanation prompts the question "why is the thermostat set so high?", but that doesn't mean the explanation is just a useless restatement of the question.

In comparing the low-entropy-past hypothesis to the fictional "life appeared even though it seems unlikely" law, you ignore the substantial predictive power of the former.

You've got to be very careful how to set up the boundary conditions, even in a very simplified classical regime. For example, any collection of particles assembled in a finite volume of space, no matter how large, and allowed to expand outward for whatever length of time you care to specify into a vacuum of infinite space will be in a condition of 'low entropy' in comparison to later times. It's also not very difficult to define conditions so that the total energy of the universe is zero. Thus, a localized 'quantum fluctuation' in infinite space and time would under these conditions quite nicely start out in a condition of 'low' entropy and propagate forward in time into the infinite future in a very natural way.

I'm not endorsing this simplified model at all, btw. Just pointing out that reasoning by analogy to a more familiar situation can lead to apparently nonsensical results.

@Tim Tyler: I follow that, but it doesn't matter: obviously the concisely-describable high entropy states are a tiny fraction of their total number, so it's *still* justified to assign a non-negligible prior to a low-entropy state if you're using Solomonoff induction.

Stuart, yes I recall Penrose's flat past hypothesis; is it still considered viable?

Hard to tell. It is very speculative, and Penrose is reaching the end of his career, and some people are clearly humouring him... But there is some weak evidence supporting it, and it does appear to be testable.

And the mathematics appear correct - in the absence of the Ricci tensor, the slow, infinite, cold end of the universe is indistinguishable from the fast burning expansion of the big bang...

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