Wigner's friend and continuous time evolution of the state of a closed system and the probabilistic, discontinuous collapse of the state of a system upon measurement. Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox. The thought experiment posits a friend of Wigner in a laboratory and lets him perform a quantum measurement on a physical system (this could be a spin system or also Schrödinger's cat). This system is assumed to be in a superposition of two distinct states, say, state 0 and state 1 (or "dead" and "alive", in the
Expectation value (quantum mechanics) general case, its spectrum will neither be entirely discrete nor entirely continuous. Still, one can write formula_1 in a spectral decomposition, with a projector-valued measure formula_30. For the expectation value of formula_1 in a pure state formula_48, this means which may be seen as a common generalization of formulas (2) and (4) above. In non-relativistic theories of finitely many particles (quantum mechanics, in the strict sense), the states considered are generally normal. However, in other areas of quantum theory, also non-normal states are in use: They appear, for example. in the form of KMS states in quantum statistical mechanics of