A proposal for the solution of the paradox of the double-slit experiment

Gerrit Coddens (1)

1 LSI - Laboratoire des Solides Irradiés - Irradiated Solids Laboratory

We propose a solution for this paradox within the framework of our reconstruction of quantum mechanics (QM), based on the geometrical meaning of spinors. We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby the particles yield information about the set-up rather than an experiment whereby the set-up yields information about the behaviour of the particles. The probabilities of QM are conditional, whereby the conditions are defined by the macroscopic measuring device. They are therefore not uniquely defined by the interaction probabilities in the point of the interaction. When a particle interacts incoherently with the set-up the answer to the question through which slit they have moved is experimentally decidable. When it interacts coherently the answer to that question is experimentally undecidable. We show that the expression $\psi_{3}= \psi_{1} + \psi_{2}$ for the wave function of the double-slit experiment is numerically correct, but logically flawed. It has to be replaced in the interference region by the logically correct expression $\psi'_{1} + \psi'_{2}$, which has the same numerical value as $\psi_{1} + \psi_{2}$, such that $\psi'_{1}+\psi'_{2} = \psi_{1} + \psi_{2}$, but with $\psi'_{1} = e^{\imath \pi/4 } (\psi_{1} +\psi_{2})/\sqrt{2} \neq \psi_{1}$ and $\psi'_{2} = e^{-\imath \pi/4 } (\psi_{1} +\psi_{2})/\sqrt{2} \,\neq \psi_{2}$. Here $\psi'_{1}$ and $\psi'_{2}$ are the correct (but experimentally unknowable) contributions from the slits to the total wave function $\psi_{3} = \psi'_{1} + \psi'_{2}$. We have then $p = |\psi'_{1} + \psi'_{2}|^{2} = |\psi'_{1}|^{2} + |\psi'_{2}|^{2} = p'_{1}+p'_{2} $ such that the paradox that quantum mechanics would not follow the traditional rules of probability calculus for mutually exclusive events disappears.

Mots clés: Foundations of Quantum Mechanics; Group Theory; Relativistic Wave Equations; Interference

Domaines: Physique mathématique [math-ph]

Gerrit Coddens. A proposal for the solution of the paradox of the double-slit experiment. 2021. ⟨cea-01383609v7⟩