Uncertainty principle (redirected from Heisenberg's uncertainty principle)

uncertainty principle, physical principle, enunciated by Werner Heisenberg in 1927, that places an absolute, theoretical limit on the combined accuracy of certain pairs of simultaneous, related measurements. The accuracy of a measurement is given by the uncertainty in the result; if the measurement is exact, the uncertainty is zero. According to the uncertainty principle, the mathematical product of the combined uncertainties of simultaneous measurements of position and momentum in a given direction cannot be less than Planck's constant h divided by 4π. The principle also limits the accuracies of simultaneous measurements of energy and of the time required to make the energy measurement. The value of Planck's constant is extremely small, so that the effect of the limitations imposed by the uncertainty principle are not noticeable on the large scale of ordinary measurements; however, on the scale of atoms and elementary particles the effect of the uncertainty principle is very important. Because of the uncertainties existing at this level, a picture of the submicroscopic world emerges as one of statistical probabilities rather than measurable certainties. On the large scale it is still possible to speak of causality in a framework described in terms of space and time; on the atomic scale this is not possible. Such a description would require exact measurements of such quantities as position, speed, energy, and time, and these quantities cannot be measured exactly because of the uncertainty principle. It does not limit the accuracy of single measurements, of nonsimultaneous measurements, or of simultaneous measurements of pairs of quantities other than those specifically restricted by the principle. Even so, its restrictions are sufficient to prevent scientists from being able to make absolute predictions about future states of the system being studied. The uncertainty principle has been elevated by some thinkers to the status of a philosophical principle, called the principle of indeterminacy, which has been taken by some to limit causality in general. See quantum theory.

Bibliography

See W. Heisenberg, The Physical Principles of the Quantum Theory (tr. 1949); D. Lindley, Uncertainty (2007).

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uncertainty principle

 or Heisenberg uncertainty principle or indeterminacy principle

Principle that states that the position and velocity of an object cannot both be measured exactly at the same time, and that the concepts of exact position and exact velocity together have no meaning in nature. Articulated by Werner Heisenberg in 1927, it applies only at the small scales of atoms and subatomic particles and is not noticeable for macroscopic objects, such as moving vehicles. Any attempt to measure the velocity of a subatomic particle precisely will displace the particle in an unpredictable way, thus invalidating any simultaneous measurement of its position. This displacement is a result of the wave nature of particles (see wave-particle duality). The principle also applies to other related pairs of variables, such as energy and time.

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Uncertainty principle

A fundamental principle of quantum mechanics, which asserts that it is not possible to know both the position and momentum of an object with arbitrary accuracy. This contrasts with classical physics, where the position and momentum of an object can both be known exactly. In quantum mechanics, this is no longer possible, even in principle. More precisely, the indeterminacy or uncertainty principle, derived by W. Heisenberg, asserts that the product of Δx and Δp—measures of indeterminacy of a coordinate and of momentum along that coordinate—must satisfy inequality (1).

(1) 

The Planck constant, h ≃ 6.63 × 10^-34 joule-second, is very small, which makes inequality (1) unimportant for the measurements that are carried out in everyday life. Nevertheless, the consequences of the inequality are critically important for the interactions between the elementary constituents of matter, and are reflected in many of the properties of matter that are ordinarily taken for granted. For example, the density of solids and liquids is set to a large degree by the uncertainty principle, because the sizes of atoms are determined with decisive help of inequality (1).

In classical physics, simultaneous knowledge of position and momentum can be used to predict the future trajectory of a particle. Quantum indeterminacy and the limitations it imposes force such classical notions of causality to be abandoned.

Another well-known example of indeterminacy involves energy and time, as given by inequality (2).

(2) 

Physically, its origins are somewhat different from those of inequality (1). Inequality (2) relates, for example, lifetimes of unstable states with the widths of their lines. See Linewidth

In quantum physics, relations similar to inequalities (1) and (2) hold for pairs of many other quantities. They demonstrate that the acquisition of the information about a quantum object cannot be usually achieved without altering its state. Much of the strangeness of quantum physics can be traced to this impossibility of separating the information about the state from the state itself. See Quantum mechanics