X-Message-Number: 14218 From: "John Clark" <> Subject: Identity Of Indiscernibles Date: Mon, 31 Jul 2000 23:32:53 -0400 In #14194 Wrote: >How very strange! By his own account, you never know (for example) which >electron is which, so how could you know they switch places--or why would it >even be meaningful to say they switched places??!! It's not meaningful and that's the entire point. You postulate that two apparently different things are really the same and then calculate what the world would have to look like to make that true. If the world really does look that way then you're on to something. As an example I'll quote from my article " Waiting For Zed" at www.extropy.org/eo/articles/zed.htm Let's consider a very simple system with lots of space but only 2 particles in it. P(x) is the probability of finding two particles x distance apart, and we know that probability is the square of the wave function, so P(x) =[F(x)]^2. Now let's EXCHANGE the position of the particles in the system, the distance between them was x1 - x2 = x but is now x2 - x1 = -x. The Identity Of Indiscernibles tells us that because the two particles are the same, no measurable change has been made, no change in probability, so P(x) = P(-x). Probability is just the square of the wave function so [ F(x) ]^2 = [F(-x)]^2 . From this we can tell that the Quantum wave function can be either an even function, F(x) = +F(-x), or an odd function, F(x) = -F(-x). Either type of function would work in our probability equation because the square of minus 1 is equal to the square of plus 1. It turns out both solutions have physical significance, particles with integer spin, bosons, have even wave functions, particles with half integer spin, fermions, have odd wave functions. [...] If we put two fermions like electrons in the same place then the distance between them, x , is zero and because they must follow the laws of odd wave functions, F(0) = -F(0), but the only number that is it's own negative is zero so F(0) =0 . What this means is that the wave function F(x) goes to zero so of course [F(x)]^2 goes to zero, thus the probability of finding two electrons in the same spot is zero, and that is The Pauli Exclusion Principle. Two identical bosons, like photons of light, can sit on top of each other but not so for fermions, The Pauli Exclusion Principle tells us that 2 identical electrons can not be in the same orbit in an atom. If we didn't know that then we wouldn't understand Chemistry, we wouldn't know why matter is rigid and not infinitely compressible, and if we didn't know that atoms are interchangeable we wouldn't understand any of that. >The exclusion principle says, for example, that you can't have two >electrons in the same quantum state in the SAME ATOM. It says the probability of detecting two electrons in the same state in the same place is zero. >if we disregard the phase space coordinates of the atom as a >whole, which is precisely what I argue we cannot do, in general. I never said it's OK to ignore position when dealing in physics, I said position is not useful in conferring identity. John K Clark Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=14218