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The electron double-slit experiment from an ISP perspective

David LeBlond

TL;DR

This work reframes the electron double-slit experiment within an indivisible stochastic process (ISP) framework, offering a probabilistic interpretation of quantum coherence via a fixed configuration space and transition dynamics. By increasing the discretization to $N=2000$ positions and coupling the system to an environmental qubit with behaviors None, Remembers, and Forgets, the model reproduces standard QM phenomena: interference when the qubit is inactive, suppression when it records the path, and revival when it forgets. The authors provide explicit formulas for marginal amplitudes, a path-integral-like kernel, and a finite transition-matrix construction, along with open-source R code to reproduce and explore the ISP predictions. The work suggests that ISP dynamics can capture key quantum features, offering intuitive teaching tools and a path toward self-contained ISP formulations of quantum evolution and interference in more complex settings.

Abstract

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.

The electron double-slit experiment from an ISP perspective

TL;DR

This work reframes the electron double-slit experiment within an indivisible stochastic process (ISP) framework, offering a probabilistic interpretation of quantum coherence via a fixed configuration space and transition dynamics. By increasing the discretization to positions and coupling the system to an environmental qubit with behaviors None, Remembers, and Forgets, the model reproduces standard QM phenomena: interference when the qubit is inactive, suppression when it records the path, and revival when it forgets. The authors provide explicit formulas for marginal amplitudes, a path-integral-like kernel, and a finite transition-matrix construction, along with open-source R code to reproduce and explore the ISP predictions. The work suggests that ISP dynamics can capture key quantum features, offering intuitive teaching tools and a path toward self-contained ISP formulations of quantum evolution and interference in more complex settings.

Abstract

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.

Paper Structure

This paper contains 12 sections, 12 equations, 8 figures, 1 table.

Table of Contents

  1. Background and motivation
  2. Purpose of the present work
  3. Description of the "experimental" set-up
  4. Assumptions about the electrons
  5. Assumptions about the slit wall
  6. Assumptions about the environmental qubit
  7. Assumptions about the screen
  8. Graphical representation of the transition matrix
  9. ISP modeling of the double slit experiment
  10. Results
  11. Discussion and Future Work
  12. Appendix

Figures (8)

  • Figure 1: Double-slit experimental setup. Red arrows indicate one possible electron path.
  • Figure 2: Transition matrix for composite system-qubit configuration states when qubit is inactive (qubit behavior = "None").
  • Figure 3: Transition matrix for composite system-qubit configuration states when qubit detects and "Remembers" the electron's entry slit.
  • Figure 4: Transition matrix for composite system-qubit configuration states when qubit detects but then "Forgets" the electron's entry slit.
  • Figure 5: Graphic displaying the active and inactive states and transitions as a function of qubit behavior. Note: $i'\le N/2\equiv$ lower slit and $i'> N/2\equiv$ upper slit.
  • ...and 3 more figures