kort@hounx.UUCP (B.KORT) (01/17/86)
Ken, thanks for your thoughtful rejoinder to my followup on the "wave equation/many worlds" posting. I think you make a good point and I want to see if I have it clearly. Let me start with an abstract of your response: > Summary: QM is not quantified ignorance. > > In article <501@hounx.UUCP> kort@hounx.UUCP (B.KORT) writes: > > >Perhaps my level of understanding is a bit naive, but don't > >the wave equations encode our state of knowledge (uncertainty) > >about the state of affairs prior to measurement? Also, don't > >we have the basic problem that measurement involves interacting > >with the thing being measured ... ? When the probability wave > >collapses ... aren't we simply experiencing a quantum jump in > >our state of knowledge? ... > > >If this view is sound, then the wave equation is not so much > >a description of what's "out there" as it is a description of > >"what we know" about that which is "out there." > > > > -- Barry Kort > > ...ihnp4!houxm!hounx!kort > > Well said, but I don't think it's true. > > Consider a lone free particle. In general, we don't know where it is, > so we invent a wave function to give the probabilities of it being > here or there. But in the real world, this wave function does not behave > as if it described a distribution of hypothetical positions of a classical > particle. Instead: > > 1. It's evolution in time is entirely self-determined. There > is no "velocity" that can be specified independently of position. > > 2. The values of the wave function are complex numbers who's > squared magnitudes are the aforementioned probabilities. As > the wavefunction evolves, it can destructively interfere with > itself. > > If quantum mechanics did nothing but quantify our ignorance about what > we are looking at, how would it explain, say, the discrete energy levels > of atoms? > > Ken Rimey > rimey@dali.berkeley.edu > ucbvax!rimey > If I understand point 1, your saying that there is a constraint relating position and velocity. I agree. The constraint is that velocity is defined as the time derivative of position. So your first point is that the components of the particle's state vector are not independent, but functionally related in a particular way. Your second point is more interesting (and more subtle); I hope I can interpret it correctly. I note that in the simple Bohr Model of the atom, the discrete orbits of the electrons correspond to closed paths comprised of an integral number of wavelengths of the electron's wave equation. More generally, one can contemplate "orbits" which deviate from simple shapes. Imagine a frictionless roller coaster, given an initial position and velocity. Assume I design a complex track, carefully banked at every curve. The track could, principle meander all over the countryside, never closing on itself. The total energy of the roller coaster (kinetic plus potential) would remain constant. The height speed, and position along the track evolve according to deterministic equations. If I close the track on itself, when the roller coaster returns to the starting point, it must have the same velocity as the initial velocity. Note that the track itself had to be designed (banked and curved) so that at every point force of the cars on the track remained normal to the tangent plane of the track. For a given track, there would be an even integral number of starting states (perhaps exactly 2: forward and backward) that the roller coaster could take. If an observer came along, and didn't know the starting conditions, couldn't he encode his state of knowledge (uncertainty as to position/velocity as a function of time) as a wave equation, just like the electron? To extend the analogy even further, couldn't we introduce forks in the track sytem at arbitrary positions, giving us a "many tracks" network. The tiniest outside force (say a puff of wind) would "determine" whether the roller coaster veered left or right at any given fork. Now the observer's state of knowledge has to encode the uncertainty due to the myriad forking paths. About all he has left is knowledge of the total system energy, and the realization that for every possible instantaneous state of the roller coaster, there is a computable probability that the roller coaster will return to exactly that same instantaeous state after an elapsed time, t. For very small t, the probability is zero. There is a minimum time, say t sub 1, which is the first possible time for the roller coaster to make a circuit. In general, there is a sequence of possible instants when the roller coaster could return, depending on the number of forks in the "many tracks" scenario. In the steady state limit, the initial conditions are washed out, and we just have a probability function that no longer depends on time. I hope my roller coaster analogy is helpful, and not so contrived that it hides any essential subtleties in the more sophisticated models of particle motion. My present bottom line, Ken, is that I still fail to see just how the wave function is *more* than an encoding of our imperfect knowledge of the state of affairs of the particle. Can you help me see the point that I'm missing in order to appreciate the reality of the wave? --Barry Kort