----- Original Message ----- From: "Ray Ludenia" <[EMAIL PROTECTED]> To: "Killer Bs Discussion" <[email protected]> Sent: Sunday, March 13, 2005 7:09 AM Subject: Re: quantum darwin?
> which is now much clearer to me than before. Sin(x)^2 and cos(x)^2 > refer to probability amplitudes iirc, though why the angle used to > remeasure is 2x momentarily escapes me. Because it fit the data. :-) Let's look at a particle traveling in the z direction, and treat the xy dimentions in polar coordinates. If we measure at 0 degrees and get up, that is the exact same thing as measuring at 180 degrees and getting down. (use yourself as the pointer, with up as your head and down as your feet. If you were standing on your feet and said something was up, and then stood on your head, if it didn't move, it would now be down in your new coordinate system.) >From symmetry, we see that at 90 degrees, (in the y direction) we are equally likely to measure up and down in the y direction after measuring up in the x direction. If we call the angle a, we see that sin(a)^2 and cos(a)^2 do not cut it, because the probability of down is 100% at 90 degrees and 0 % at 180 degrees, after measuring up at 0 degrees. But, sin(a/2)^2 and cos(a/2)^2 do work. So, intermediate values were tried, and they fit. This brings out an important part of science....the idea is to find an explaination that first fits and then predicts observations. When the data do not fit established theories, phenomenology is first used. An example of this is the Bohr atom. Electrons really couldn't orbit the nucleus in a classical manner, Bohr knew that. But, he did have a rough model that explained some of the data. Later, with the Copenhaugen school of physicists, he put together the first real quantum theory. Dan M. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
