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In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics , an observable is a real -valued "function" on the set of all possible system states, e.g., position and momentum .
Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals.
The observable universe is a spherical region of the universe consisting of all matter that can be observed from Earth; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion.
For an observable , the expectation value given a quantum state is A = tr ( A ρ ) . {\displaystyle \langle A\rangle =\operatorname {tr} (A\rho ).} A density operator that is a rank-1 projection is known as a pure quantum state, and all quantum states that are not pure are designated mixed .
Quality of life is a latent variable which cannot be measured directly so observable variables are used to infer quality of life. Observable variables to measure quality of life include wealth, employment, environment, physical and mental health, education, recreation and leisure time, and social belonging.
Such an observable is itself a self-sufficient CSCO. However, if some of the eigenvalues of are degenerate (such as having degenerate energy levels), then the above result no longer holds. In such a case, we need to distinguish between the eigenfunctions corresponding to the same eigenvalue.
In physics, the observer effect is the disturbance of an observed system by the act of observation. [1] [2] This is often the result of utilising instruments that, by necessity, alter the state of what they measure in some manner.
The distinction between "observable" and "unobservable" is similar to Immanuel Kant's distinction between noumena and phenomena.Noumena are the things-in-themselves, i.e., raw things in their necessarily unknowable state, [3] before they pass through the formalizing apparatus of the senses and the mind in order to become perceived objects, which he refers to as "phenomena".