Contexts of type 1: Given the state of a system at \(t\) and the forces and constraints to which it is subject, there is an equation, ‘Schrödinger’s equation’, that gives the state at any other time \(U \ket{v_t} \rightarrow \ket{v_{t'}}\).[8]  The important properties of \(U\) for our purposes are that it is deterministic, which is to say that it takes the state of a system at one time into a unique state at any other, it is unitary, which means that it is an automorphism of the Hilbert space on which it acts (i.e., a mapping of that space onto itself that preserves the linear space structure and inner product), and it is linear, which is to say that if it takes a state \(\ket{A}\) onto the state \(\ket{A'}\), and it takes the state \(\ket{B}\) onto the state \(\ket{B'}\), then it takes any state of the form \(\alpha \ket{A} + \beta \ket{B}\) onto the state \(\alpha \ket{A'} + \beta \ket{B'}\).