Once More Into The Breach
Prompted by a new paper by Brian Greene et. al., Lumo once more takes on the Second Law of Thermodynamics and its implications for the early universe. The whole long dicussion is quite fascinating, not least because it looks to me like Lubos is struggling not only against Greene but with his own uncertainties - acting, that is, exactly like a good physicist ought to.
Here is the part that got my attention. First Greene et al.
The status of [Boltzmann's H-theorem] is less settled than often claimed, because it requires the so-called 'molecular chaos' assumption, doubts about whose applicability have not been firmly laid to rest.
This is precisely where my own doubts arise, but Lubos has an answer. Once again, the argument looks pretty good - until I back off and start wondering if it's not just begging the question. In the traditional sense of assuming that which is to be proven. It seems OK in a hand wavy kind of way, but I sure wish he could show a logical proof, with all assumptions explicit.
So the central problem of the arrow of time consists in finding a justification for the so-called past hypothesis - the assumption that the universe had low entropy at early times.
Greene, like Penrose and (maybe) Sean Carroll, wants to find some cosmological reason why the universe has to start in a state of low entropy. Lubos doesn't like this, but he seems to have deleted an earlier version in which he compared this (favorably) to wondering why an elephant doesn't have 486 legs and (unfavorably) to speculations about why the fine structure constant is what it is.
Of course there are good biological reasons why elephants didn't evolve with as many legs as a millipede, and there may well be consistent physical theories in which the fine structure constant is other than it is. It seems similarly reasonable to me to speculate that there might be some more "fundamental" or "natural" reason for the universe to have started in the special state that it apparently did start in.
Lumo can't help going off the rails a bit:
While it's manifest that the authors of similar papers are bothered by the very validity of the second law and they would indeed like the entropy to be higher in the past...
Jeez Lumo, why do you have to spoil a really good discussion by saying something lame like this. Nobody "wants" the entropy to be higher in the past, and Greene et. al. aren't bothered by the validity of the second law. What they are trying to do, perhaps quite unsuccessfully, is come up with a principle that explains the initial state in terms of some simple mathematical idea - that's a lot of what cosmology is about. That observations and the second law imply that the initial state was of low entropy is uncontroversial, but it's not an explanation, any more than saying that an elephant has four legs explains why it has four legs.
Perhaps there is no possible explanation, but it seems silly to deny the possibility that there might be such out of hand. On the other hand, it is perfectly sensible to critique a suggested explanation, as Lubos has here.