The Unnecessary ‘Collapse of the Wave Function’

Abstract

‘The collapse of the wave function’ was first introduced as an explanatory concept by Heisenberg. Then it was ‘formalized’ by von Neumann, in his book Mathematical Foundations of Quantum Mechanics . Essentially, this concept says that at the moment of measurement the superposition probability amplitude collapses to a single quantum state. In quantum interference and quantum entanglement, it is found that this hypothetical reduction to a single quantum state is an unnecessary intermediate step that provides no further information to the experimentalist. Indeed, in quantum interference the measurement sequence goes from superposition probability amplitude to multiplication of this superposition probability amplitude with its complex conjugate which yields the probability distribution, in short: https://www.w3.org/1998/Math/MathML" display="inline"> 〈 d | s 〉 → 〈 d | s 〉 〈 d | s 〉 ∗ . A hypothetical ‘collapse of the wave function’ adds an unobservable, unmeasurable, intermediate step that in the case of N -slit quantum interference would lead to the prediction of an erroneous probability distribution. Indeed, https://www.w3.org/1998/Math/MathML" display="inline"> 〈 d | s 〉 → 〈 d | s 〉 〈 d | s 〉 ∗ represents a direct and clear mathematical expansion . The same is the case in quantum entanglement.