Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.
Prior to quantum physics, it was thought that
- (a) a physical system had a determinate state which 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. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution.
Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be 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.
Read more about Quantum Indeterminacy: Measurement, Indeterminacy and Incompleteness, Indeterminacy For Mixed States
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