A measurable quantity derived from experimental data that can be used to infer properties of a physical system.In physics, an observable is a measurable quantity that can be derived from experimental data and used to infer properties of a physical system. Observables are the bridge between theoretical models and empirical reality: they are the specific numbers that experiments can extract, such as particle masses, decay rates, cross-sections, or energy spectra. In quantum mechanics, observables correspond to Hermitian operators whose eigenvalues represent possible measurement outcomes.
The concept of observables in quantum mechanics was formalized in the 1920s by Werner Heisenberg and others, who emphasized that physical theories should be built around quantities that are in principle measurable.
An observable is defined operationally: it must have a clear prescription for how to measure it from raw experimental signals. For example, the mass of a particle is not directly measured but is reconstructed from the momenta and energies of its decay products using conservation laws. The theoretical prediction for an observable typically involves calculating expectation values or transition probabilities from a model, which can then be compared with the measured value to validate or falsify the theory.
Observables are used in particle physics to identify new particles (e.g., the Higgs boson via its decay products), in astrophysics to infer the composition of distant objects from spectra, and in condensed matter physics to characterize phase transitions.
In quantum mechanics, not all observables can be measured simultaneously with arbitrary precision—this is the essence of the Heisenberg uncertainty principle, which pairs observables like position and momentum.
| C(t) | variable | Normalized autocorrelation function of observable A — correlation function |
| A(t) | variable | Value of observable A at time t — observable varies |
| A(0) | variable | Value of observable A at initial time — observable varies |
| ⟨...⟩ | operator | Averages the product over a statistical ensemble of initial conditions — ensemble average |



