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reilly

Science Advisor

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My introduction to QM happened almost 50 years ago, at which point I became fascinated with the issues of interpretation. Nobody then worried much about interpretation, because the heyday of particle and solid state was in full swing by the late 50s -- Schwinger's Radiative Corrections Paper came out in 1949. There was more opportunity for theoreticians than there were theoreticans -- many of us found working with experimentalists fascinating and rewarding -- dealing with Nature face-to-face if you will. QM interpretation was not on the A-list; too many other things to do.

After reading many posts about interpretation, some clear and straight forward, some logically and factually challenged, some that are over the top, I feel comfortable in laying down my views on interpretation, many of which I owe to Sir Rudolf Peierls' writings.

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To be direct: QM probabilities represent states of knowledge, just as classical probabilities do. When I do a measurement, indeed the wave function collapses to provide the knowledge of the particular outcome. The collapse is a physical phenomena, as the brain goes from knowledge of probabilities to knowledge of the outcome.

This approach has many advantages, and requires no mysticism nor methodological hand-waving. And it recognizes that, at the probability level, classical and quantum physics are very similar. That is, probability is probability, whether applied to electrons or football games. Why? The formal measure-theoretic approach is applicable to both flavors of physics. The probabilities at issue are often governed by similar differential equations for the systems probability density. In physics we use the evolution of the density matrix, in classical cases we use some form of a stochastic differential equation. (See An Introdution to Stochastic Processes by M.S. Bartlett. This is a tough book.But, if you can get through it, you'll have a better understanding of why probability is probability -- QM and CM just use different dynamics and assumptions. )

It's relevant to note that classical and quantum meet in Rutherford's experiment. The alpha-nucleus cross section can be computed classically or quantumly (sorry 'bout that) with identical results.

This means, of course, that there are many wave functions, one for each observer if you will. Naturally, when doing a scattering experiiment, all observers will agree on the outcome probabilities. It's crucial at this point to reinforce the almost obvious: the outcome probabilities of the various observers must be the same: they are all observing the same event. And, Einstein is our authority. He says that events are invariant. (I'm assuming all the observers are in the same inertial frame. But unitary transformations are around to help any referehnce frame generalization required.

There's another way to view this interpretation, based in the Shannon-Weiner Theory of Communication(or Information) -- discussed in Bartlett's book --. Roughly speaking, a measurement generates a signal, which ultimately one or more of the experimenters receive. If you push through, you can identify the transmitter and the receiver, the channel(s), the aplphabet, and the error patterns. One of the coolest results is that it is always possible to discern a message from noise -- but it may take a long time. The basics are simple: Shannon, sort of in so many words, uses the law of Large Numbers to average out the errors, which may require lots of repititions.

(I'm fairly convinced that all of physics, at the minimum. can be fully described as a communication system -- nature speaks to us through experiments and observations. What I'm less than clear about, is the value of such an enterprise. if it has not been done, it might well be a great thesis topic for a budding theorist.)

A look at EPR, and then we're done. EPR is probably unparalleled in physics for the amount of nonsense generated, the amount of profoundity generated, and the amount of passion generated. Let's look at EPR from the knowledge perspective. Let's do the simplest experiment-- electrons or photons, each with opposite helicities. and each travelling down a tube toward a detector, which will measure helicities. We'll make a configuration that precludes quick communication between Mr. A, and Ms. B -- there is no chance they can compare notes afer one measurement.

Mr. A finds helicity UP. He knows from appropriate theory, that Ms. B, measuring after Mr. A will measure spin down. he is projecting by means of established theory, that the second measure ment MUST be spin down. (We do this sort of thing all the time.) He knows that a single helicity measurement is sufficient to determine the spin state of the two particle system.

Ms. B knows zip about Mr. A. As far as she is concerned, there's an equal chance for UP or DOWN. However, she does know that if she gets UP, then he got DOWN, and vice versa. Again, this is aplication of fundamental theory.

Everything is local, and there is no need to invoke faster-than-light communication. Also note, that this experiment can be done with numerous classical systems. The difference beteween QM and CM show up when, for example, we measure spin in a direction other than that of the particle's momentum, the outcomes of which are controlled by Clebsch-Gordan coefficients. (The closest classical situation I can imagine is a pair of spinning tops with nutation and precession somehow paired.)

If there is any magic here, it has to do with physics itself. Physics tells Mr. A about things outside his immediate environment, by inference rather than by direct observation. It is our cumulative knowledge that allows Mr. A to transcend space and time with his knowledge.

Regards,

Reilly Atkinson

What about simultaneous measurements with Mr. A and Ms. B? Anybody know anything about this issue?