ThinkerEmeritus wrote:You know, I think that discussions of measurement theory would be a lot more productive if everyone agreed on some term other than "wave function collapse" for the information gained by a measurement. The term, even though it is almost always used, is misleading. Wave functions are governed by the Schroedinger equation and they don't suddenly change just because we know something. "State collapse" would be a much better term.
Oh but they do. At least, you'll be hard pressed to find a well accepted theory or interpretation in which they do not collapse in the sense of a sudden discontinuous change in the wave function. To see what is odd in a continuous evolution theory, consider electrons passing through two slits and forming a diffraction pattern on a mesh of detectors at the far end. In the Copenhagen interpretation, the electron's wave function collapses and it ends up stuck in a ccd cell or bound to a phosphor or otherwise interacting with one particular detector. Now suppose we claim that quantum electrodynamic interactions between the electron and the detector somehow causes the wave function to continuously deform into the known end state. Poof, no wave function collapse, everything is fine, Schrodinger's equation to the rescue!
But when does this deformation start to occur? This continuous deformation has some speed no? In order for this electron to find and reshape itself to one specific detector, it must start changing before it reaches the detector
. And if the detector is moving, it has to change according to how the detector mesh will be aligned before
it gets there. The fact that it somehow shrinks down far enough to interact with and potentially push around a tightly bound particle is exactly why this is normally an example of wave particle duality.
Now I think Feynman-Wheeler advanced potentials are just dandy and probably have a place in quantum electrodynamics, but you might be amazed at how hard it is to convince people to accept the loss of microscopic causality that comes with them.
Certainly the measurement process can be described by the Schroedinger equation if we know enough. We usually don't, and we approximate the result by going ahead and doing something not specified in detail and saying "this time the spin was up," and the next time maybe "this time the spin was down." The process of determining that the spin was "down" or "up" in a given case may be complicated theoretically so that we can't tell what happened to change the wave function.
Certainly this statement that "the measurement process can be described by the Schroedinger equation if we know enough." is not well accepted by many quantum physicists. In fact, claiming such a thing has oft been considered to be a sign of crack-pottery. Furthermore, they bring us back to a point made above. Because of the "entanglement at a distance" inherent in spin correlation and other experiments any
such theory would be non-local. As in, violates Bell's-inequality-and-means-that-photons-and-electrons-know-where-they-are-going-before-they-get-there-and-doesn't-that-make-mincemeat-of-free-will non-local.