"Let There Be Light" and Entropy

Does Time Run Backward in Other Universes?, asks cosmologist Sean M. Carroll in the June 2008 Scientific American.

He says a not-very-well answered question in physics is why time never runs backward in our universe. The inexorable arrow of time corresponds to the evolution of entropy. The universe is a closed system, since no energy is ever added or subtracted. In a closed system, entropy — a measure of the disorder of the system — never decreases. Typically, it increases.

The early universe had very low entropy, just after the big bang. Today's universe is medium-entropy. In the very distant future the disorder will be maximal, and the cosmos will contain virtually nothing worthy of mention.

Carroll asks how we can explain the very low entropy just after the big bang. Present attempts at explanation, he says, only give the illusion that anything has been accounted for. He posits instead that the universe had a pre-history, before the big bang. It originally had high entropy. Then things happened — "fluctuations" — that caused a new, low-entropy baby universe to inflate into what became the cosmos we know today.

As one who is forever inclined to look for ways in which religion an science might harmonize, I am much interested in the fact that entropy was at its lowest in the very beginning, and we can't really explain why. Postulating a high-entropy cosmic pre-history — one that probably cannot be verified empirically — doesn't really tell us what caused the "genesis fluctuation" to happen.

Could it have happened when God said, "Let there be light"?

In theology, "Let there be light" is a divine command.

In information theory, "Let there be light" is a message. As with any message, its basic characteristic is its ability to reduce entropy.

Any message source, before the message is sent, has entropy, the measure of the number of possible messages it can send. A message source that consists of a single bit of computer memory has just two possible messages, "on" and "off." Its entropy is low for this reason. When an actual message is produced — say, "off" — there is only a minimal reduction in the amount of entropy.

More complex message sources have much higher entropy, because the number of possible messages is larger. When an actual message is received — say, "Let there be light" — the reduction in entropy is huge, simply because of the sheer number of alternatives — "Let there be chaos," "Let there be little green men," "Let it be," "Eat at Fred's," etc. — that have been ruled out.

Maybe "Let there be light" stands metaphorically for the capacity of the very first divine command to reduce entropy mightily in the communications-theoretical sense, such that the infant universe was indeed a place of surprisingly low entropy in the cosmological sense.