San José State University |
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applet-magic.com Thayer Watkins Silicon Valley & Tornado Alley USA |
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Equation and the Copenhagen Interpretation Thereof |
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There is a very simple theorems to the effect that the time-averaged field generated by a spherically symmetric particle executing a periodic circuit is the same as would be generated by a static particle composed of the charge of the moving particle distributed throughout its path in proportion to the time-spent at the various locations of its path. Observed effects are necessarily time-averaged. Thus at a sufficiently high frequency the effect of the circulating particle is is indistinguishable from that of the equivalent static distributed charge particle. At a macro level this means that the gravitational effect of a rapidly rotating fan is the same as that of the static blurred disk the fan appears to be.
Thus if the time-indendent Schrödinger equation is used to provide a description of the system which picture will it describe? Will it be the dynamic picture of the particle executing a periodic path or will it be the picture of a static particle distributed over the periodic path? Since the equation being used is time-independent the picture is obviously that of the static distributed particle. In terms of the example used above, it is the blurred disk rather than the rotating fan.
The Copenhagen Interpretation has chosen to interpret this picture not of the particle's charge distributed over the path but instead the probability distribution of the particle. But the probability distribution is just the time-spent probability distribution. There is no reference to the physical reality of the particle. In terms of the fan example, the blurriness of the disk does not mean that the fan blade has no physical reality, as the Copenhagen Interpretation would allege.
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