Auwvax.349 net.misc utzoo!decvax!harpo!uwvax!doug Tue May 4 20:08:48 1982 polarizers and the quantum watched pot I think the answer to -------> |/- (> is If the light is incident on the first filter with an intensity of I, then the light which passes through the middle filter leaves with an intensity of I * cos^2 (45) and the light which leaves the right-most filter has an intensity of I * cos^4 (45). ------------------------------------------------------------ Anyway, what's *really* interesting here is an extension to this problem. Notice that cos^4 (45) is greater than cos^2 (45) (for any angles you're ever going to see in this problem). That is, the intensity of light passing through the whole collection of filters is GREATER than the intensity of light which passed through just the middle one. This means the presence of the middle filter actually "helped restore" things to the initial state, if you look at it in a certain way. Of course, I'm ignoring simple attenuation of light through the substance of the polarizer. The reason I mention it, is it reminds me of an article I read a year or so ago in the American Journal of Physics. It purports to relate this sort of classical phenomena to the quantum mechanical principle that "the closer you watch a state, the less it changes". As a matter of fact, in the limit where you *continously* watch a state, the state never changes. For example, if you could continously watch a certain unstable nuclide it would never decay (certainly a change of state). By the way, the description of the classical experiment was this: Suppose you had a rectangular tube containing some optically active liquid. | | | | <------L--------> If the tube has length L, and the liquid is optically active, then linearly polarized light, say vertical, which passed through it would emerge at a polarization of some angle theta from the vertical: ----> | | | | / | | | <------L--------> (polarizer) A vertical polarizer positioned at the right side could be used to measure theta by seeing what fraction of the intial intensity of light gets through it. Using the sort of analysis above, we can see that a SECOND vertical polarizer placed half-way through the tube would mean that a GREATER intensity of light would emerge from the far right polarizer than had the second polarizer not been there. A third polarizer would mean even more. And so on, and so on. Obviously in the limit of an infinite number of infinitely thin vertical polarizers throughout the whole liquid, the exact same intensity of light would emerge finally as intially was incident on the liquid. The mathematics of closely watched quantum states is very analagous. The quantum mechanical state of a system changes with time, however it changes less when more measurements are made of it. The quantum mechanical watched pot never boils. ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.