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
Symmetry in quantum mechanics There are rotational matrices for each spin quantum number. Evaluating the exponential for a given "z"-projection spin quantum number "s" gives a (2"s" + 1)-dimensional spin matrix. This can be used to define a spinor as a column vector of 2"s" + 1 components which transforms to a rotated coordinate system according to the spin matrix at a fixed point in space. For the simplest non-trivial case of "s" = 1/2, the spin operator is given by where the Pauli matrices in the standard representation are: The total angular momentum operator is the sum of the orbital and spin and