X-Message-Number: 14219 From: "John Clark" <> Subject: Identity Of Indiscernibles Date: Tue, 1 Aug 2000 00:25:11 -0400 In #14207 Wrote: > Use common sens Sounds like a fine idea, if it works. >the NY carbon could be included in an apple and the Boston one in coal :-) OK, but to repeat my previous question, if I switched the carbon atom in coal with a carbon in an apple how would things be different? Another example, I cool your two atoms and bring them so close together that their positional uncertainty overlap and a Bose-Einstein condensation is formed, the atoms merge identities. Then I warm things up and I can see two atoms again, at this point what meaning is there to ask which atom is which, even in principle? >[Physics 101 stuff deleted] Waves are at the root of the uncertainty principle. It's more complex than that. The uncertainty is not caused by the wave, it's caused by the thing that's waving. If it were just matter that was waving things could still be as deterministic as a cuckoo clock, but that's not the case. The thing that's waving is the square root of a probability not matter. And being a square root means it can and does have negative terms in it and even imaginary terms, and that means the quantum wave function is not a scalar like simple probability but a vector with an intensity and a direction, and that means you can not just add up 2 independent probabilities to figure the probability both will happen the way we usually do, and that means two very different wave functions can yield the same probabilities, and that means we can't do things the way "common sense" would dictate. And that's why the quantum world is so weird. >So that there is no uncertainty if there is no wave and there is no wave if there is not an >euclidean displacement. I never said you can't know some things exactly, you can know with certainty all the numbers in one of Heisenberg's matrices for a particle, equivalently you can know the quantum wave function of the particle exactly, but neither will let you know the position and velocity exactly, and that's not all, neither will let you know the exact energy of a particle and the exact time it had it either. >I suggest you look at an elementary differential geometry book to >get some familliarity with these concepts. Thanks for the advice but I don't believe I need to do that. John K Clark Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=14219