Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

left to itself the quantum state ψ evolves with time according to the Schrödinger equation, this being unitary evolution, a deterministic, basically time-symmetric, continuous process for which I use the letter . However, in order to ascertain what value some observable parameter q might have achieved at some time t, a quite different mathematical process is applied to ψ, referred to as making an observation, or measurement. This is described in terms of a certain operation which is applied to ψ, providing us with a set of possible alternatives ψ1, ψ2, ψ3, ψ4, …, one for each of the possible outcomes q1, q2, q3, q4, … of the chosen parameter q, and with respective probabilities P1, P2, P3, P4, … for these outcomes. This entire set of alternatives, with corresponding probabilities, is determined by and ψ by a specific mathematical procedure. To mirror what actually appears to happen in the physical world, upon measurement, we find that ψ simply jumps to one of the given set of alternatives ψ1, ψ2, ψ3, ψ4 …, say to ψj, where this choice appears to be completely random, but with a probability given by the corresponding Pj. This replacement of ψ by the particular choice ψj that Nature comes up with is referred to as the reduction of the quantum state or the collapse of the wavefunction, for which I use the letter . Following this measurement, which has caused ψ to jump (to ψj), the new wavefunction ψj again proceeds according to until a new measurement is made, and so on.