This paper presents a pedagogical model, and accompanying R code, of the electron double-slit experiment using the perspective of indivisible stochastic processes. The approach offers an alternative lens on quantum probability and coherence phenomena, emphasizing a statistical rather than purely wave-mechanical interpretation.
We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons. We also show how the concept of undecidability can be used in an intuitive way to make sense of the double-slit experiment and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully deterministic way (following Einstein's conception of reality), while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable (which follows more Bohr's conception of reality). We show that the expression ψ1+ψ2 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 ψ1′+ψ2′, which has the same numerical value as ψ1+ψ2, such that ψ1′+ψ2′=ψ1+ψ2, but with ψ1′=2ψ1+ψ2e4π=ψ1 and ψ2′=2ψ1+ψ2e−4π=ψ2. Here ψ1′ and ψ2′ are the correct contributions from the slits to the total wave function ψ1′+ψ2′. We have then $p = |ψ'_{1} + ψ'_{2}|^{2} = |ψ'_{1}|^{2} + |ψ'_{2}|^{2} = p_{1}+p_{2} $ such that the paradox that quantum mechanics (QM) would not follow the traditional rules of probability calculus disappears.
Abstract One of the greatest mysteries that has puzzled and seemingly hoodwinked our very understanding of nature is the single electron double slit experiment – one that Feynman termed the central mystery of quantum mechanics. At the heart of this mystery is how can an electron that is a physical particle exhibit a wave-like property? We’ve proposed a non-counterintuitive way to explain this phenomenon called the randomly-jumping electron hypothesis, in which the electron randomly “jumps” in discrete succession to specific points only and not others which is what causes the electron to indeed be a classical particle only but is able to produce a wave-like interference pattern. To provide supporting evidence for our hypothesis, we’ve developed a computer program to simulate the single electron double slit experiment by treating the electron as a classical particle while still exhibiting wave-like fringes in agreement with real-world observed data of the single electron double slit experiment performed. Our interpretation does not set out to “solve” the mystery of why an electron can produce a wave-like interference pattern once and for all, however our hypothesis is a monism ontological interpretation that does address some of the crucial debates that have remained unsolved for 100 years since the formulation of quantum mechanics.
This article examines the double-slit experiment from a configurational perspective and compares it with the standard quantum-mechanical, Bohmian, and Many-Worlds interpretations. Rather than focusing on microscopic trajectories or wavefunction collapse, the work argues that the central question posed by the experiment is not “how” individual particles behave, but “why” a stable interference pattern emerges with overwhelming statistical certainty. By framing the experiment in terms of constrained configuration spaces and typicality, the article shows that interference can be understood as an inevitable macroscopic outcome, not a mysterious dynamical process.
The thesis offers an innovative analysis of quantum mechanics. Firstly, it clearly expounds the characteristics of quantum mechanics in measurement and other aspects, and proposes seven criteria for judging scientific nature. Then, it points out that there are some key problems with the orthodox assumptions of quantum mechanics, such as unclear physical mechanisms, lack of rigorous logic, difficulty in falsification, and incomplete main considerations.Regarding the double-slit interference experiment, the thesis conducts a comprehensive derivation and demonstration, proposing a unique interpretation. The traditional view holds that the interference is caused by the wave nature of electrons, while this thesis suggests that it is the periodic fluctuating Coulomb force field in the double-slit slits. A large number of electrons interact with it, undergo regular deflection to form a probability distribution, and then superimpose to produce interference fringes. This interpretation challenges the traditional cognition of the wave nature of microscopic particles in quantum mechanics, prompting us to re-think the basic concepts and experimental interpretations of quantum mechanics from the new perspective of the Coulomb force field, providing new ideas and directions for the study of quantum mechanics.
We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby
one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons.
We also show that the concept of undecidability (like e.g. occurs in G\odel's theorem) can be used in an intuitive way to make sense of the double-slit experiment
and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully
deterministic way, while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable.
It is very important to make a distinction in quantum mechanics
between the determinism of nature (Einstein)
and the decidability of a question within an experimental set-up (Bohr).
The former is about the absolute truth of an answer to a yes or no question, and follows binary logic
(true or false),
the latter about what an experimental set-up
can decide and tell about the truth of that answer, and follows ternary logic (true, false or undecidable).
Binary and ternary logic are incompatible.
The viewpoints of Bohr and Einstein are thus operating on different levels and it is only by confusing these two levels
that these two viewpoints seem to be irreconcilable.
We show that the expression ψ1+ψ2 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 ψ1′+ψ2′, which has the same numerical value as
ψ1+ψ2, such that ψ1′+ψ2′=ψ1+ψ2,
but with ψ1′=2ψ1+ψ2e4π=ψ1 and
ψ2′=2ψ1+ψ2e−4π=ψ2.
Here ψ1′ and ψ2′ are the correct
contributions from the slits to the total wave function ψ1′+ψ2′.
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 (QM) would not follow the traditional rules of probability calculus disappears.
The paradox is rooted in the wrong intuition that ψ1 and ψ2 would be the true physical contributions to
ψ1′+ψ2′=ψ1+ψ2 like in the case of waves in a water tank.
The solution proposed here is not {\em ad hoc} but based on an extensive analysis of the geometrical meaning of spinors within group representation theory
and its application to QM. Working further on the argument one can even show that an interference pattern is the only way to satisfy simultaneously
two conditions: The condition obeying binary logic (in the spirit of Einstein) that the electron has only two mutually exclusive options to get to the detector (viz. going through slit S1 or going through slit S2) and the condition obeying ternary logic (in the spirit of Bohr)
that the question which one of these two options the electron has taken is experimentally undecidable.
A very important element in the analysis is the problem of the non-existence of {\em common} probability distributions for different experimental set-ups.
And this is a recurrent theme in other situations that are felt as paradoxical.
The CHSH inequality used in the experiments of Aspect {\em et al.}
clashes with quantum mechanics because it
is based on the assumption that there would exist a {\em common} probability distribution for the
hidden variables in the different experiments that have to be made to determine the various quantities that intervene in the inequality.
That common probability distribution for measured quantities does not exist is well known from quantum mechanics itself (because the operators that come into play do not commute and therefore do not have common eigenstates, i.e.
common probability amplitudes). But this non-existence of common probability distributions applies also to certain variables in the set-ups of the different experiments and the latter fact
can also be explained by purely classical reasoning.
The aim of the present lecture note is not to propose an alternative formulation of quantum mechanics, but to emphasize that several apparently distinct descriptions of the double-slit experiment may be understood as complementary consequences of a single geometric projection onto the transmission subspace defined by the apertures. Modeling the double slit as a projection onto the two-dimensional transmission subspace spanned by the localized slit modes provides a common mathematical framework for the wave-based, particle-based and information-theoretic descriptions of interference. The formalism starts from an arbitrary incident localized wave packet and naturally reproduces Duane's momentum-selection law, which emerges directly from the geometric transmission condition rather than being introduced as an independent postulate.