nLab uncertainty principle

Idea

In quantum mechanics, the uncertainty principle states that the best possible experimental uncertainties of expectation values of a pair of quantum observables whose commutator is a non-vanishing multiple of the identity operator are complementary: To the extent that the uncertainty in one observable shrinks, the uncertainy in the other observable has to grow. In particular it is impossible to know both observables jointly with certainty.

(But see Uffink & Hilgevoord 1985 for a more careful statement of the situation.)

Related concepts

• matrix mechanics

• quantum observables

• commutator

• uncertainty of fluxes

References

Most textbooks listed at quantum mechanics have a section on the uncertainty relation.

The uncertainty principle goes back to and is often named after:

• Werner Heisenberg: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik 43 (1927) 172–198 [doi:10.1007/BF01397280, pdf]

  (where it is announced as equation (1) and established as equation (6))

with English translation (or something close) in

• The actual content of quantum theoretical kinematics and mechanics, NASA Technical Memorandum NAS 1.15:77379 (1983) [pdf, pdf]

See also:

• Wikipedia: Uncertainty principle

Careful discussion of subtleties:

• J. B. M. Uffink, J. Hilgevoord: Uncertainty principle and uncertainty relations, Foundations of Physics 15 (1985) 925–944 [doi:10.1007/BF00739034]