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) A particularly simple case arises when formula_1 is a projection, and thus has only the eigenvalues 0 and 1. This physically corresponds to a "yes-no" type of experiment. In this case, the expectation value is the probability that the experiment results in "1", and it can be computed as (3) formula_24. In quantum theory, also operators with non-discrete spectrum are in use, such as the position operator formula_25 in quantum mechanics. This operator does not have eigenvalues, but has a completely continuous spectrum. In this case, the vector formula_11 can be written as a complex-valued function formula_27 on the spectrum