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Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one the of characteristics of quantum physics. Prior to quantum physics, it was thought that a physical system had a determinate state which (a) uniquely determined all the values of its measurable properties and conversely (b) the values of its measurable properties uniquely determined the state. Albert Einstein may have been the first person to carefully point out the radical effect the new quantum physics would have on our notion of physical state.

Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. For pairs of complementary observables, the dispersions of the corresponding distributions are related by the Heisenberg uncertainty principle.

Indeterminacy in measurement was not an innovation of quantum mechanics, since it had established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the latter half of the eighteenth century, measurement errors were well understood and it was known that they could either reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.

Measurement

An adequate account of quantum indeterminacy, requires a theory of measurement. Many theories have been proposed since the beginning of quantum mecahnics and quantum measurement continues to be an active research area in both theoretical and experimental physics. Possibly the first systematic attempt at a mathematical theory was developed by John von Neumann. The kind of measurements he investigated (discussed in the book Mathematical Foundations of Quantum Mechanics) are now called projective measurements. That theory was based in turn on the theory of projection-valued measures for self-adjoint operators which had been recently developed and the Hilbert space formulation of quantum mechanics.

Incompleteness

Albert Einstein argued that if quantum mechanics is correct, then we necessarily have incomplete information about the physical world. This was one of the conclusions of the EPR thought experiment, which using the formal apparatus of quantum theory, showed that some parts of the classical view of how observation affects nature had to be changed.

Single particle indeterminacy

Quantum uncertainty can be illustrated in terms of a particle with a definitely measured momentum for which there must be a fundamental limit to how precisely its location can be specified. This quantum uncertainty principle can be expressed in terms of other variables, for example, a particle with a definitely measured energy has a fundamental limit to how precisely one can specify how long it will have that energy. The units involved in quantum uncertainty are on the order of Planck's constant (found experimentally to be 6.6 x 10 J·s).

See also

• Quantum indeterminacy in computation
• Quantum mind
• just about any of the quantum mechanics articles

• Quantum mechanics
• Determinism