Tuesday, June 23, 2009

More on the Egg Problem

The Egg Problem

Continuing some thoughts:

1. One might argue: since every splattered egg presumably arose from a whole pristine egg, there are exactly as many splattered egg states as there are whole pristine egg states. True, as long as the only degrees of freedom are egg parts; but in the splattering, information is lost in sound and heat and so on, and that is what causes the huge number of initial splattered egg states that do not evolve into whole pristine eggs compared to those that do.

2. There is the old problem - how likely is it that all the molecules of air will find themselves in the half of the room that you are not in and you are at risk of suffocation? Since a room may have 10^28 molecules, the probability is (1/2)^(10^28).

Suppose the probability of a splattered egg turning into a whole pristine egg is similar. That is, one part in 1,000,....(10^27 zeroes, roughly).
The age of the universe in seconds is 1,000,....(17 zeroes roughly).
The volume of the visible universe in cubic seconds is 1,000,... (85 zeroes,roughly).
Large as these numbers are, they are absolutely dwarfed by (the denominator in) the probability (1 followed by 10^27 zeroes). Even if each cubic centimeter of the universe tried to randomly assemble an egg once each second, it would still take essentially 10^27 universes to produce an egg.

Well, our universe found a more efficient way. Briefly, it has life processes running off the free energy gradient between stars and outer space. You can think of it as heat engines, if you like, that do work, in the ways Carnot sought to quantify. Our earth alone has produced a gazillion eggs, and our universe maybe a great many more. The thermodynamic sort of randomness is not the fastest way to get things done. Our existence means there are more powerful self-organizational principles at work. It may also be that these principles, while perhaps most strongly visible in the workings of matter on the atomic scale and above, have their analogs at all scales of the universe. Establishing that would be a more fundamental discovery, in my opinion, then the sterile multiverse.