A budweiser beer (the phase operator)


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R. F. Streater lists Phase, the operator conjugate to the number operator as his http://www.mth.kcl.ac.uk/~streater/lostcauses.html#VIII [Broken].

I have found recently a curious historical report of this cause: hep-th/9304036, and its prottagonists are intriguing as well.
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I found Streater's "Lost Causes" website quite amusing, particularly because I am interested in a number of the topics that he mentions. However, it is good to know that lost causes can be regained http://www.mth.kcl.ac.uk/~streater/regainedcauses.html#III [Broken].

Generally, I agree that most of the things he mentions are not of much use for the purposes they were originally invented for. However, the trick in regaining lost causes is to find new applications for the math, where the foundational issues are not relevant. For example, variants of Bohm's theory has been used by quantum chemists for numerical simulations of molecular dynamics.
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I hate to see the discussion of the phase operator drift off the top page. So I'll stir the pot up a little.

There's a subtle argument for considering phase in quantum mechanics as being a sort of position information. The argument goes as follows:

Since we don't see any Schoredinger cats, we intuitively expect that objects must undergo some sort of reduction in their wave function that reduces them to a position.

Phase is necessary for probability waves to interfere. So without phase we will lose interference.

Naively, we would expect that random reductions of the wave functions by a position operator would destroy phase coherence, and we would expect to see Schroedinger's (or whatever) wave equation fail over long distances. But experiments don't detect these.

If we consider phase as a part of the position data, so that a position operator has to reduce a wave function to a point in space and a phase (rather than just reduce a wave function to a point in space), then random reductions of a wave function will not eliminate phase coherence.

Now if there is a small circular hidden dimension, then you can argue that the phase would correspond to position in that dimension. Then it would be very natural that phase should be included with the rest of the position information.

It's not a complete explanation, but at least it gets us one step closer to avoiding having to believe in a wave particle duality that borders on Zen.


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