A New View on the Uncertainty Principle
Upon close examination Heisenberg’s microscope argument is found to depend on a relation between two quite distinct concepts of uncertainty. The first is an uncertainty in what can be predicted. The second is related to the notion of resolving power and is an uncertainty in what can be inferred (retrodiction). Quantitative measures of both kinds of uncertainties are introduced and discussed. The standard deviation is criticized as a measure of uncertainty. The usual uncertainty relations connect two uncertainties of the first kind. Uncertainties of the first and second kinds are also related by an uncertainty relation; this relation provides a general basis for the microscope argument. This new kind of uncertainty relation also allows for an adequate formulation of the uncertainty principle for line width and lifetime.
Bohr’s argument with respect to the double slit problem, which is based on the uncertainty principle, is analysed and is found to depend on two uncertainties of the second kind. No corresponding uncertainty relation is known to exist; nevertheless, the validity of Bohr’s conclusion can be established in a direct way.
KeywordsWave Packet Interference Pattern Uncertainty Relation Point Spread Function Uncertainty Principle
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