Thursday, April 02, 2009

Lumo vs. The Volcano

Maybe Lubos *is* the model for Sheldon Cooper. Lumo goes one-on-one against Boltzmann and his eggs (and brains) yet again. He makes a number of correct obsevations, but seems to think he is pointing out things that people like Sean Carroll don't already understand. I'm pretty sure that he is mistaken about that.

He conjures up some postulates to describe Boltzmann brainiacs:

there are infinitely many possible cosmological models

many of them describe the past of our Universe as one that contains an infinite (or nearly infinite) spacetime volume with a nonzero density of matter

in these infinite (or almost infinite) regions, all localized configurations of matter (microstates) such as those of eggs appear (nearly) infinitely many times

on the other hand, the evolution from a tiny, low-entropy Universe appears only a few times

it is thus infinitely (or almost infinitely) more likely that our life was born as a statistical fluctuation, from a Boltzmann egg, or our brain was directly created as a Boltzmann brain

because of this (nearly) infinite discrepancy between the priors, no finite number of arguments or experiments can change the conclusion that we are just a statistical fluctuation that evolved completely randomly

and so on...

Perhaps there are some who believe this, but I doubt that Sean Caroll is one of them. Moreover, says Lubos:

In the very same sense, if you accept the assumption that the high-entropy initial states are exp(10^{120}) times more likely than the low-entropy initial states, all the people who disagree with you, the heretics who believe thermodynamics up to its second law or even beyond ;-), are obliged to find an effectively infinite miracle that beats your effectively infinitely powerful argument.

Except that you're wrong in the very same sense as your Christian colleagues. The nearly infinite factors that you like to talk about do not measure the actual validity of your framework. They only determine how much blinded you are in your defense of your wrong dogmas.

Past and future: symmetries

The hypothesis that the Universe in the distant past should have a higher entropy than the current entropy is simply fundamentally wrong. It contradicts the second law of thermodynamics which holds according to all observations. It contradicts the proper theoretical derivations that are relevant for statistical physics and thermodynamics. Because the entropy increases with time, the entropy in the distant past had to be lower than today, not higher than today. Any retrodiction about the past that ends up with a qualitatively different conclusion is wrong - in the scientific sense.

Is there really any group of people who believe that our present regime of the universe did not begin in a low entropy state? Not many, I guess, if any. However, if you do the usual statistical mechanics and weight all states compatible with the known constraints on the initial macro state equally, then states of sufficiently low energy are very improbable, so it might be nice to have some explanation of why the initial state was such. You can simply note that it evidently was, or you can try to imagine an explanation.

Anthropicists and landscapers have been known to speculate that that a low entropy initial state evolved from some random prior state by means of a spontaneous fluctuation. The problem is that the probability of a whole low entropy universe evolving spontaneously from a fluctuation is extremely low (at least based on known physics and extensive entropy) compared to the probability of some small part of it fluctuating into a very low entropy state - a Boltzmann egg or Brain perhaps. That is the point of the Boltzmann Brain argument, and even though Lubos states this more or less explicitly in his postulates, he doesn't seem to grasp the implications. If you think that the universe evolved from an entropy fluctuation, there doesn't seem to be any known way to avoid things like Boltzmann Brains, which, improbable as they are, appear to be vastly more probable than the whole universe being a fluctuation. Thus you are left with three choices:
(a)Simply stipulate that the universe started in a very low entropy state and don't try to derive this fact from anything else.
(b)Go with the fluctuation theory, but accept that there are probably a lot more Boltzmann Brains and Eggs than whole coherent universes, or
(c)Try to find some other principle that might explain an initially low entropy state.

The trouble with (b) is that it's not really compatible with science - any given mental of physical state is more likely to be a fluctuation than a reality. Lubos gets this point, but he doesn't seem to get that the whole value of (b) is for discrediting the fluctuation theory altogether.