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OzOz · 05-01-2004, 03:15 PM

FleaCircus, actually the idea of quantum state collapse on measurement is *not* necessarily what Quantum Mechanics says - it is an interpretation of the mathematical formalism, and one that can be argued against. For me, one of the biggest difficulties with this interpretation is specifying how the wave function collapses - is this effect simultaneous everywhere? Given that there is no absolute simultaneity in Relativity etc...

To me, the best explanation of it all is from "Quantum Mechanics: A Modern Development" (Leslie Ballentine, World Scientific, 1998). He is very thorough in trying to dispell misconceptions about the subject, both mathematical and philosophical. For the meaning of quantum state vectors and the difficulties of collapse, see section 9.3 (The Interpretation of a State Vector).

As I understand it, the view presented in this book is that a quantum state does *not* apply to a single system (like your single electron), but to a (large or infinite) ensemble of similarly prepared systems. The implication would seem to be that the individual particle does have definite values of whatever dynamical quantities you're interested in - it's just that you won't know what they are until you measure them, and when you do, and if you repeat the measurement for a sufficiently large ensemble of similarly prepared systems, you will find your probability distribution emerging - which is the only thing you *can* predict. The most obvious example is the double-slit experiment. Trying it with a normal light source is essentially trying it with gazillions of similar systems at once. Try it with single photons, but repeatedly, and you still get the interference pattern building up.

Something else to note is the dubious assertion that if you measure a particle's position accurate to a small amound dx, then its momentum immediately acquires an uncertainty dp, where dx times dp = h / 2Pi (the supposed content of Heisenberg's Uncertainty Principle). Actually, as Ballentine takes great pains to point out in another part of the book, the mathematical derivation of this result is clearly statistical in nature, which points clearly towards the infinite ensemble interpretation. What the Uncertainty Principle actually says is that if you have a system in a state in which the "uncertainty" (actually, standard deviation) in position is dx and the "uncertainty" in momentum is dp for the whole ensemble of all such systems, then dx times dp = h / 2Pi.

05-01-2004, 03:15 PM	#13 (permalink)
OzOz Psycho Location: Right here, right now.	FleaCircus, actually the idea of quantum state collapse on measurement is not necessarily what Quantum Mechanics says - it is an interpretation of the mathematical formalism, and one that can be argued against. For me, one of the biggest difficulties with this interpretation is specifying how the wave function collapses - is this effect simultaneous everywhere? Given that there is no absolute simultaneity in Relativity etc... To me, the best explanation of it all is from "Quantum Mechanics: A Modern Development" (Leslie Ballentine, World Scientific, 1998). He is very thorough in trying to dispell misconceptions about the subject, both mathematical and philosophical. For the meaning of quantum state vectors and the difficulties of collapse, see section 9.3 (The Interpretation of a State Vector). As I understand it, the view presented in this book is that a quantum state does not apply to a single system (like your single electron), but to a (large or infinite) ensemble of similarly prepared systems. The implication would seem to be that the individual particle does have definite values of whatever dynamical quantities you're interested in - it's just that you won't know what they are until you measure them, and when you do, and if you repeat the measurement for a sufficiently large ensemble of similarly prepared systems, you will find your probability distribution emerging - which is the only thing you can predict. The most obvious example is the double-slit experiment. Trying it with a normal light source is essentially trying it with gazillions of similar systems at once. Try it with single photons, but repeatedly, and you still get the interference pattern building up. Something else to note is the dubious assertion that if you measure a particle's position accurate to a small amound dx, then its momentum immediately acquires an uncertainty dp, where dx times dp = h / 2Pi (the supposed content of Heisenberg's Uncertainty Principle). Actually, as Ballentine takes great pains to point out in another part of the book, the mathematical derivation of this result is clearly statistical in nature, which points clearly towards the infinite ensemble interpretation. What the Uncertainty Principle actually says is that if you have a system in a state in which the "uncertainty" (actually, standard deviation) in position is dx and the "uncertainty" in momentum is dp for the whole ensemble of all such systems, then dx times dp = h / 2Pi. __________________ Maybe you should put some shorts on or something, if you wanna keep fighting evil today.