Miscellaneous musings from the perspective of a lefty (both senses) atheist with a warped sense of humor.

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Location: Madison, WI, United States

I am a geek, but I do have some redeeming social skills. I love other people's dogs, cats, and kids. Snow sucks, but I'm willing to put up with it just to live in Madison.

Saturday, July 21, 2007

The Theory of Immaculate Precision

I got the following question on a listserv I participate in and took a shot at the answer. I figured it might be worth distributing to a wider audience.

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I would appreciate the advice of anyone with a knowledge of physics.

For some years I've been tantalized by the idea that everything is precise and therefore predictable. Like, from the moment of the Big Bang (or whatever) accurate instruments could have predicted everything from that point on. The instruments could have predicted the rise of Judaism, christianity, all wars, all inventions, all catastrophes, Hiroshima, 9/11, and the exact moment when the first hydrogen bomb busts over the first city. The instruments could have predicted cloud formations a billion years hence and the moment of your and/or my conception, birth and death.

The fact that such an measuring device didn't exist, doesn't exist, and may never exist doesn't alter the hypothesis.

Here are my first two questions: Does every atom have a precise weight and a precise temperature at any given trillionth of a second? Does every nucleus have a precise chemical formation and a precise density? And does every electron move at a precise speed in a precise direction at any given trillionth of a moment?

Two more questions for now: Is this an old theory that I've regurgitated? Am I talking abject nonsense?

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Richard replies:

The so-called "clockwork universe" which you find so intuitively appealing had its greatest vogue following the astronomical discoveries of Brahe, Kepler, Copernicus, Galileo, and Newton. The models they constructed looked for all the world like very big, very predictable mechanisms. The idea that there were precise rules that governed the movement of everything and led to absolute determinism of all future events was extremely appealing to both a certain school of philosophers and some extremely brilliant scientists.

Most notable among the latter was Albert Einstein -- a guy who made quite a rep by showing that Newton's laws needed a bit of tweaking when you're dealing with things that are either very speedy (special relativity) or gigantic (general relativity). But he didn't OVERTHROW Newton's laws, he REFINED them. They were still laws, only now they took more factors into account. Einstein's success at discovering the regularities of the Universe led him to believe that there would ALWAYS be underlying regularities in all physical phenomena, thus his famous phrase "God does not play dice with the Universe." (which some religionists have seized on as a statement about God using gambling as a metaphor, when really it was a statement about predictability using God as a metaphor). Einstein spent the last half of his life looking for those underlying regularities in an effort to come up with a Grand Unified Theory that would explain everything his Theory of Relativity did and more besides.

On the opposite side of the fence from Einstein in this latter endeavor stood the quantum guys, starting with Max Planck and furthered by Paul Dirac but most notably including Neils Bohr. They are the modern-day heirs of Democritus, the Greek philosopher who speculated (in the complete absence of any instrumentation that would let him conduct a serious inquiry) that there was bound to be a smallest unit of any substance (say, copper) that still QUALIFIED as that substance. He reasoned that you could start with a wire and cut it in half. Then you could cut one of the halves in half, and so on. Could you do that indefinitely? He speculated that the answer was no, that eventually you come across the smallest possible unit of copper (or whatever the wire was made of), and that, if you try to cut IT in half, you either cannot do it or you end up with something else. This smallest unit he called an atom. And so do we.

Planck went much further. He speculated that you cannot cut up the very fabric of space and time into infinitesimally smaller and smaller pieces. Sooner or later you come across the smallest unit of space and the smallest unit of time possible, beyond which it is meaningless to speak of further subdivision. These smallest units are named in his honor the Planck length (10^-35 m) and the Planck time (10^-43 s). They are interrelated by the value c, which Einstein would recognize from his famous equation E = mc^2 as the speed of light. It takes light the Planck time to traverse a distance equal to the Planck length.

Just to give you an idea how fantastically small these things are, you spoke of "a trillionth of a second". That would be 10^-12 seconds (a picosecond or 0.1% of a nanosecond) -- a quantity that would include 10,000,000,000,000,000,000,000,000,000,000 Planck time units. At the picosecond level, yes, everything is still pretty much describable in terms of the classical clockwork Universe that we up here in Middle World find so familiar.

Things get progressively stranger as you get smaller and smaller. For example, Werner Heisenberg's Uncertainty Principle says that there's always some error involved in every measurement (invariably, and as a matter of principle, not simply because our tools aren't good enuf or we aren't using them properly) that becomes more and more significant as the things we're trying to measure get smaller and smaller. Finally, down at the quantum level, the amount of error is AT LEAST as large as the things we're measuring. If, for example, you try to measure momentum (the product of mass and velocity, where velocity is a vectored or directional form of speed), you discover that you can either know where a subatomic particle IS but not where or how fast it's going, or you can know its PATH (velocity) without having any idea where it's located on that path. We know that electrons hang out somewhere in the vicinity of atomic nuclei, but we're not exactly sure just WHERE. (Incidentally, you asked "Does every nucleus have a precise chemical formation ...?", and the technical answer to that is no, because nuclei don't experience chemistry per se. Chemistry occurs when the electron cloud around a given nucleus interacts with the electron clouds of naboring atoms. The nuclei play no role in this process.)

You don't have to get all the way down to the Planck scale for quantum effects to kick in. The very computer on which you are reading these words is made possible by quantum tunneling of electrons passing thru (or not, as the case may be) the SEMIconductor materials in your CPU. Not only do quantum effects exist at the scale of subatomic particles, we have learned how to harness them to get work done.

But, as Heisenberg pointed out, there's a limit to how much of this we can get away with, because fundamentally the Universe is chock full of random events. The only reason it SEEMS orderly to us up here in Middle World is because there are a fantastically large number of these teeny-tiny random events occurring all the time, and all the fluctuations average out in a stochastic manner that lets us predict MASS behavior pretty reliably -- SO reliably, in fact, that we use the word "laws" to describe such behavior.

It is this statistical regularity which seduced Einstein -- and many another brilliant person -- into thinking that "It's turtles all the way down.", that is, that the Universe was regular and predictable and followed immutable, built-in laws at every scale we could possible detect, including the very large and the very small. They were wrong.

Quantum Theory is the best-tested theory in physics. It produces results of such fantastic precision that, if you could somehow use quantum principles to measure the distance from New York to LA, you would be off by less than the width of a human hair. And, at bottom, it says that the Universe is fundamentally unmeasurable, because its very most basic phenomena happen randomly and spontaneously.

But don't feel unduly intimidated by all of this. The brilliant physicist Richard Feynman said it best:

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I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will go "down the drain" into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
-- Richard Feynman (1918-1988) American physicist

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