Sunday, June 6, 2010

Lazy Nature, Lazy God

Is nature lazy? It certainly is slow. Look how long it took for life as we know it to evolve.

The ancient Greek philosopher-scientists knew that light was lazy. They showed that when light is reflected from a surface the angle of reflection is equal to the angle of incidence. Whatever the speed of light was, this reflection rule resulted in the shortest, and therefore the fastest, path between a source of light, an observer, and a reflective surface between them. Light takes the shortest path.

In the era historians refer to as the Enlightenment, this came to be called the principle of least action.

Nature has a number of definitions; when I write Nature, I mean the Universe or totality of things, including the principles that cause it to exist and determine the specifics of existence. Primitive people take the ancient idea of a god (tree, rock, ghost, or human) and try to amplify that up until they have a God that created and rules over, or at least within, Nature. Whether you believe in God or Nature, the physics experiments come out the same.

So the principle of least action implies that God is lazy too. God's laziness makes the universe predictable.

You can make a lot out of this simple principle, which applies to solid physical objects as well a light and energy fields. To understand this, unfortunately, the path of least effort leads through the quicksand of something called the calculus of variations. And of course, most people in the world need to start working or fighting or begging before they even get to regular calculus in school. On the other hand, if you do happen to study calculus and then the calculus of variations, you can get anything you want in the world. You will be able to see deeper and further than other humans, and make of it what you will.

With your math magic, you are now ready to do Lagrangian dynamics, among other things. You can see where Newton's Laws come from: a lazy, symmetrical universe (designed by a lazy God). And using only the principle of laziness, you can work out Schrodinger's equation (for the motion of a non-relativistic particle in a potential field) [Byron & Fuller, Mathematics of Classical and Quantum Physics, p. 71]. Thus you have the key to quantum physics. In retrospect it is surprising no one came up with it before Erwin Schrodinger.

Which brings up another important point: Chance. Or probability, if you like the more modern formalism. Many Romans worshipped Chance, or Fortuna (Tyche to the Greeks). In addition to the chance events of human lives, the practice of gambling was already well-developed. Dice pre-exist recorded history, as did other methods of casting lots or determining oracles. The minor Christian god Jesus Christ may have been an incarnation of chance, as it was written in the Bible (King James translation), Mark 15:24, "And when they had crucified him, they parted his garments, casting lots upon them, what every man should take." [Alternate versions found in Matthew 27:25, where this is attributed to fulfilling a Jewish prophecy; Luke 23:34; and John 23:24]

The role of probability in quantum physics, and in particular the Uncertainty Theorem, has led to a lot of guru-driven nonsense spouted in the popular arena of wishful thinking. There is probability in quantum physics, which is to say in Nature, but it is of a type. We say things like "the probability of finding an electron within this space-time region in our experiment is 40%." It sounds like "there is a 40% chance of rain today." But if an experiment where the equations create a 40% expectation is run a few hundred times and the electron is only found 37% of the time, what physicists do is alter their equations. Afterwards it looks like they got the 37% figure from theory, but in fact they got it from practice and molded their theory to their results. See Inward Bound by Abraham Pais for numerous historical examples.

Asking where an electron is in space-time relative to an atomic nucleus is actually simply asking a bad question, although strangely it is fine to ask where the same electron is traversing a vacuum tube. Chance in quantum land is probably best seen in radioactive decay, where it is clearly a result of a probabilistic decay mechanism, not of observational or prediction problems.

The principle of least action leads to quantum probability equations. So in some sense the rules of probability in quantum phyics are themselves predictable. Just as we cannot be sure what any throw of the dice may bring, but we can predict the outcome of large numbers of throws using the rules of probability.

In classical physics, laziness appears to be exact (assuming you know exactly everything about your system), or too pick an exact shortest path. In quantum physics the mask of exactness is removed, but the laziness of Nature is still the rule.

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