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Uncertainty Posted March 3, 2002 Hello, you're listening to Mostly Mozart on CJLY in Nelson 93.5fm, Kootenay Coop Radio. My name is Tom Clegg. Mostly Mozart is sponsored by Tom Clegg, local and imported barmenins. Like you, I watched a film last week called "The Man Who Wasn't There." There was a lawyer in this film, whose name I don't remember, who spent a lot of time talking about a German physicist, whose name he didn't remember. Apparently this physicist had shown -- had even written it out in numbers -- that the closer you look, the less you know. This statement of Heisenberg's uncertainty principle, is only slightly more silly than what Heisenberg actually discovered. The uncertainty principle puts a limit on how precisely you can measure something. At first, as everybody knows, the closer you look, the more detailed information you get. For example, if you measure the distance between two particles, the precision of your answer depends on the distance between the marks on your ruler. If you want a better measurement, you have to use a better ruler. One reason you might want a precise measurement of the distance between two particles, is so that you can predict what's going to happen to them in the future. If you could measure the exact positions of all of the particles in a closed system, and their exact speeds and masses, and the strengths of all of the force fields as well, then you could use the laws of physics to predict exactly what was going to happen next. Predicting the future is a very valuable skill, if your prediction is correct; and if your prediction is incorrect, then you've found a flaw in the laws of physics, which can also be a very satisfying thing to do. The problem discovered by Heisenberg, is that beyond a certain level of precision, the more precisely you measure the position of a particle, the less precisely you are able to measure its momentum. No matter what clever scheme you use to measure these things, if you multiply the imprecision in one measurement by the imprecision in the other measurement, that product never gets smaller than a certain fixed number, called Planck's constant. The way the fictional lawyer put it was that the closer you look, the less you know. It would be more accurate to say that the closer you look at one thing, the less you know about the other thing. This interpretation would have worked pretty well in the Cohen Brothers film; although I think Hollywood has an upper limit of complexity, which might well have been exceeded if they had done it that way. That is almost all I want to say about the uncertainty principle, but I'd like to make a connection between that principle and the basic counterintuitive statement of quantum physics. Remember, the only time you're likely to come up against the uncertainty principle is when you're measuring the position and momentum of a particle in order to predict what's going to happen to it. The upshot of quantum physics is that particles are not like that. On a very small scale, they don't act like familiar particles like billiard balls and raisins. A particle doesn't have a position; it has a certain likelihood of being in one position, but it's always possible that it is somewhere else instead. And if you like Richard Feynman's analysis, like many physicists, you'd say that particles don't take direct paths from point A to point B; they take all of the infinite number of possible paths between A to B. The likelihood that you will see the particle pass through a given point C, corresponds to how many of all the possible paths from A to B, happen to pass through C. Fortunately, the bigger the particles get, and the further away you stand, the more closely quantum behaviour approximates classical physics. Billiard balls and raisins also exhibit quantum behaviour, but Planck's constant is sufficiently small, that you are unlikely to see a billiard ball take any path from A to B, besides the obvious one. And if you swallow a raisin, it will probably end up in your stomach. You're listening to Mostly Mozart on Kootenay Coop Radio, CJLY 93.5 fm in Nelson BC. I'd like to remind you that you can read this, and lots of other Mostly Mozart episodes, on the internet at http://mozart.fiction.org. If you'd like to suggest a topic for a future episode, you can reach me at tom@fiction.org or you can phone me in the studio on Sunday afternoon at country code 1, 250-352-3706. |