--- In ontheoriginofspecies@y..., jsk33 <no_reply@y...> wrote:
>
> I'm way over my head here, but are you disputing that the universe
> does NOT appear to be becoming increasingly disordered over time and
> that I might expect Hawking's broken coffee cup to self repair
> (become ordered)in time but without the reversal of entropy he
> referenced as a criterion? I had thought that indications implied a
> highly ordered (and more simplistic) initial state for the universe
> which state deteriorated as the universe aged. I do agree that at
> this stage order can result from randomness and understand there is
> no discernable "law" which forbids such association as you reference.
> Otherwise the probabilities associated with randomness would be as
> limited as they are with order. However, it would seem that such
> associations (order from randomness) are, for want of better
> terminology, coincidental, and in themselves transient.

I think it's important to distinguish the time arrow and entropy from
our perceptions about disorder. For Hawking's one broken coffee cup, I
could give several examples of the time arrow creating what we humans
would consider order. For an example consider stellar nuclear fusion.
Proto-stars begin as "disordered" clouds of hydrogen gas, which
coalesce under gravity into a dense ball that eventually becomes dense
enough and hot enough to begin nuclear fusion. As fusion occurs,
hydrogen nuclei are fused into helium nuclei and eventually nuclei of
heavier elements. The time arrow is always in the direction of
assembly of heavier nuclei - a mass of iron will not "disorder" into a
ball of hydrogen gas.

As another example, consider two glasses of solutions: one of sodium
carbonate (washing soda); the other of calcium chloride (road salt).
If the two are mixed, the solution becomes cloudy as a white,
crystalline precipitate - calcium carbonate (calcite) - forms. In this
case, we've gone from free ions on solution to a crysalline lattice out
of solution. Order from disorder along the time arrow.

So, what do these examples have in common, and what do they have to do
with entropy and disorder and broken coffee cups? Well, the best
description of the 2nd Law is that the number of possible interactions
between things increases with the time arrow. Why does nuclear fusion
produce ever heavier elements: because a lone proton can only interact
with electrons through the electrostatic force, whereas a proton in a
compound nucleus can also interact with neutrons and other protons
through the weak force, the strong force, and various other
interactions. Similarly, the calcium ions in solution can hydrogen
bond with several water molecules, but in the carbonate lattice there
are a host of stronger interactions that are entropically more
favorable.

Hawkings uses the coffee cup to illustrate the existence of the time
arrow, not to argue that the universe is disintegrating. I'd read that
astronomers see the universe as more clumpy now than it was in the
past, rather than vice versa.