Wave Function Statistical Interpretation vs Oscillation Interpretation Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the wave) in the limit that the frequency of the oscillation goes to infinity?
I don't see how any experiment could test such a claim, but can this be proved/disproved on theoretical grounds?
 A: Not the wave function itself. But the resulting probabilistic properties can indeed be interpreted this way.
This is done already classically; for example the stochastic Maxwell equations are derived (in the book on optical coherence by Mandel and Wolf, where these figure very prominently) from the deterministic Maxwell equations by assuming that experimentally unresolved extremely high frequencies (with an essentially contiunous spectrum) make up the stochastic noise.
My lecture http://arnold-neumaier.at/ms/optslides.pdf then implies that the same holds for the quantum description of a photon.
A: Consider the classic two slit experiment (which really is an enormously powerful demonstration often undervalued until you've though about it several times), but let's do two things...


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*Lets use a really good CCD or a multichannel plate for the image plane detector (rather than a white screen or phosphor field or something). The important thing here is that this is a discrete, digital device capable or registering single photons on many small spatial areas.

*Turn the intensity way down so that on average there is only one photon in transit at a time.


Two things become obvious.


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*The CCD registers a single photon at a time, each landing on a single pixel of the detector.

*If we wait long enough we still get the interference pattern.


These results mean that the device is not registering some smear of values for over the whole region, at most it registers a smear over one pixel; and the second one means that it registers on each pixel with a frequency consistent with the probabilistic interpretation.
