Uncertainty principle and uncertainty relations

Foundations of Physics 15 (9):925-944 (1985)

Authors
Jos Uffink
University of Minnesota
Abstract
It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments
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DOI 10.1007/BF00739034
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Four-Space Formulation of Dirac's Equation.A. B. Evans - 1990 - Foundations of Physics 20 (3):309-335.
Uncertainty in Prediction and in Inference.Jan Hilgevoord & Jos Uffink - 1991 - Foundations of Physics 21 (3):323-341.
Uncertainty in Bohr's Response to the Heisenberg Microscope.Scott Tanona - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (3):483-507.

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