Heisenberg's Uncertainty Principle: Three Faces, Two Roles
Year: 2006
Type: preprint
Abstract: A review is given of precise formulations of three conceptually distinct but related manifestations of Heisenberg's Uncertainty Principle. This principle appears in the form of trade-off inequalities: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. The uncertainty principle is often described as expressing a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that apart from this negative role, the full content of the uncertainty principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can indeed be reconciled if an appropriate trade-off is accepted. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.
Source: arXiv (Cornell University)
Authors: Paul Busch, Teiko Heinonen, Pekka Lahti
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W16765545