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N-slit interference and ‘the collapse of the wave function’

Francisco Duarte

Published Jul 10, 2026• 0 citations
Publisher

Abstract

It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.

DOI
10.1364/opticaopen.32928824

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It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.
It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.
It is explained that, in an N-slit experimental configuration the so called ‘collapse of the wave function’ is an unnecessary concept. The explanation begins going back to the original words of Heisenberg on the reduction of the wave packet and continues while considering the measurement process in an N-slit interferometer. In this regard, it is articulated that a clean and direct transition from the superposition probability amplitude to the probability distribution is all that is needed. The discussion includes measurable decoherence in the interferometric domain and the Diósi-Penrose hypothesis.
‘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.
A novel approach for measuring wavefunction collapse is proposed which, unlike interferometric measurements, is not affected by decoherence. A mirror of a Michelson interferometer is transferred into a quantum superposition, where the decay of the mirror superposition is measured by the fact that it affects the probability of detecting photons in the interferometer. The experiment can be realised with currently available technology for photon generation and detection and is suitable for testing collapse models, which is shown by calculating the expected outcomes for the gravity-based models of Diósi and Penrose.
Probability and interference According to Feynman, single-particle interference is ‘the only mystery’ of quantum theory (Feynman, Leighton and Sands 1965, ch. 1, p. 1). Feynman considered an experiment in which particles are fired, one at a time, towards a screen with two holes labelled 1 and 2. With both holes open, the distribution P 12 of particles at the backstop displays an oscillatory pattern of bright and dark fringes. If P 1 is the distribution with only hole 1 open, and P 2 is the distribution with only hole 2 open, then experimentally it is found that P 12 ≠ P 1 + P 2 . According to the argument given by Feynman (as well as by many other authors), this result is inexplicable by ‘classical’ reasoning. By his presentation of the two-slit experiment (as well as by his development of the path-integral formulation of quantum theory), Feynman popularised the idea that the usual probability calculus breaks down in the presence of quantum interference, where it is probability amplitudes (and not probabilities themselves) that are to be added. As pointed out by Koopman (1955), and by Ballentine (1986), this argument is mistaken: the probability distributions at the backstop – P 12 , P 1 and P 2 – are conditional probabilities with three distinct conditions (both slits open, one or other slit closed), and probability calculus does not imply any relationship between these. Feynman's argument notwithstanding, standard probability calculus is perfectly consistent with the two-slit experiment.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.