The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science)

by Roger Penrose

Regarding ψ as describing the ‘reality’ of the world, we have none of this indeterminism that is supposed to be a feature inherent in quantum theory – so long as ψ is governed by the deterministic Schrödinger evolution. Let us call this the evolution process U. However, whenever we ‘make a measurement’, magnifying quantum effects to the classical level, we change the rules. Now we do not use U, but instead adopt the completely different procedure, which I refer to as R, of forming the squared moduli of quantum amplitudes to obtain classical probabilities!4 It is the procedure R, and only R, that introduces uncertainties and probabilities into quantum theory. The deterministic process U seems to be the part of quantum theory of main concern to working physicists; yet philosophers are more intrigued by the non-deterministic state-vector reduction R (or, as it is sometimes graphically described: collapse of the wavefunction). Whether we regard R as simply a change in the ‘knowledge’ available about a system, or whether we take it (as I do) to be something ‘real’, we are indeed provided with two completely different mathematical ways in which the state-vector of a physical system is described as changing with time. For U is totally deterministic, whereas R is a probabilistic law; U maintains quantum complex superposition, but R grossly violates it; U acts in a continuous way, but R is blatantly discontinuous. According to the standard procedures of quantum mechanics there is n...

Reason for uncertainties qm