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?

  • $\begingroup$ What exactly do you mean by "the frequency of the oscillation goes to infinity"? In physics when you take a limit to infinity you don't literally mean that the physical thing represented by your variable is allowed to be infinite - just that it's far too large for you to care about its actual value. $\endgroup$ – Benjamin Hodgson Aug 14 '12 at 22:29
  • $\begingroup$ I mean infinity here in the mathematical sense, not in the practical sense. I mean that if you measure some observable of the wave function at some t0 in experiment A and then measure it at some t0+delta in experiment B (assuming both experiments are identical) that no matter how small delta is you will still get a different value dependant upon the form of the oscillations. However, if delta were exactly 0 then the two experiments would yield identical measurements. But, such a case could never be observed because there is no way to reproduce two experiments with delta=0. $\endgroup$ – mcFreid Aug 14 '12 at 22:56
  • $\begingroup$ Thus, we see what appears to be a probabilistic phenomena. As far as I can tell, such an interpretation is not experimentally provable and therefore not really "physics". But, it is something I just thought about and was curious if anyone had taken the thought further already and perhaps proved/disproved such an interpretation. $\endgroup$ – mcFreid Aug 14 '12 at 22:58
  • $\begingroup$ I think Occam's Razor applies - infinite frequency is not something that has a reasonable definition anywhere else, you can't get new physics from it, and probability distributions are already well-understood mathematical objects. Fun idea though. $\endgroup$ – Benjamin Hodgson Aug 14 '12 at 23:12

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://www.mat.univie.ac.at/~neum/ms/optslides.pdf then implies that the same holds for the quantum description of a photon.


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...

  • 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.

  1. The CCD registers a single photon at a time, each landing on a single pixel of the detector.
  2. 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.

  • $\begingroup$ I don't see how this contradicts an oscillation interpretation. In fact, I'm beginning to wonder if an oscillation with an infinite frequency is in fact a definition of a probability.... $\endgroup$ – mcFreid Aug 14 '12 at 18:16

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