On the Collapse of the Wave-Function
It ought to guarantee that measurements always have outcomes (that is: it ought to guarantee that there can never by any such thing in the world as a superposition of ‘measuring that A is true’ and ‘measuring that B is true’).
It ought to preserve the familiar statistical connections between the outcomes of those measurements and the wave-functions of the measured systems just prior to those measurements (that is: it ought to guarantee that a measurement of non-degenerate observable 0 on a system in the state | ψ> yields the result o’ with probability |<ψ|φ>|, where 0|φ>=o’|φ>).
It ought to be consistent with everything which Is experimentally known to be true of the dynamics of physical systems (for example: it ought to be consistent with the fact that isolated microscopic physical system’s have never yet been observed not to behave in accordance with linear quantum-mechanical equations of motion; that such systems, in other words, have never yet been observed to undergo collapses).
KeywordsBrain State Schrodinger Equation Measured Particle Macroscopic Change Occurrent Belief
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- 1).Of course, measurements need not have outcomes until they’re over, until a recording exists in the measuring-device! So, if (i) is to be a meaningful physical requirement of a satisfactory theory of the collapse, then something is going to have to be said about what a recording is.. It will be best (it will make our argument as strong and as general as possible, as the reader will presently see) to be very conservative about that here; so no change in the physical state of a measuring-device will be called a recording here unless that change is macroscopic, irreversible, and visible to the unaided eye of a human experimenter.Google Scholar
- 2).J.S. Bell, “Are There Quantum Jumps?” in “Speakable and Unspeakable in Quantum mechanics Cambridge University Press (1988).Google Scholar
- 4).See also P. Pearle “Combining Stochastic Dynamical State-Vector Reduction with Spontaneous Localization” to be published in Phys. Rev. A.Google Scholar
- 5).Unless, of course, the initial wave-function of the particle is an eigenfunction of σ Z. We shall be interested in cases where it isn’t.Google Scholar
- 6).Actually, the first thing that gets correlated to the z-spin in an arrangement like this is the momentum, or something approximating the momentum, of the measured particle; but that momentum (since the initial wave-function of the particle is taken to be reasonably well localized) quickly (before the particle hits the screen) get translated into a position, which can be ‘read-off from the screen.Google Scholar
- 7).Whatever it is that that (macroscopic) turns out to mean. Let it mean anything you like.Google Scholar