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Taking quantisation seriously: a farewell to waves

Geoff Beck

TL;DR

This paper challenges the wave-centric view of quantum interference by showing that the de Broglie wavelength is not a covariant length and cannot serve as a simultaneous spatial structure. It proposes a Duane-style model in which apparent waviness emerges from quantised momentum exchanges with periodic scatterers, deriving the double-slit momentum distribution at the scattering point and unifying phenomena across the Kapitza-Dirac effect, Bragg diffraction, ultrafast electron diffraction, and polarisable-molecule diffraction. Momentum is argued to be fixed by local interactions and conserved per event, with coherence and wavefront overlap playing no fundamental role. The work emphasizes symmetry, Bloch-type periodicity, and Gouy phase as supporting pillars, offering a realist, interaction-based account of diffraction and interference that aligns with quantum formalism while downplaying the necessity of wave-like explanations.

Abstract

The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of Landé and Lévy-Leblond to demonstrate that de Broglie wavelengths are not relativistically covariant as simultaneous spatial structures, making wave properties an unviable explanation of apparent interference. We then explore whether modern experiments vindicate an alternative view: that apparent waviness in diffraction and interference scenarios emerges as a consequence of quantised interactions between particles. Such a view has historically received very little attention, despite being the exact modern explanation of both the Kapitza-Dirac effect and ultrafast electron diffraction. We then study a photon orbital angular momentum realisation of the double slit to show that quantised exchanges can mimic interference. Finally, we demonstrate that the quantum formalism demands that particle momentum is determined at the point of scattering, contravening wave-based explanations of quantum interference.

Taking quantisation seriously: a farewell to waves

TL;DR

This paper challenges the wave-centric view of quantum interference by showing that the de Broglie wavelength is not a covariant length and cannot serve as a simultaneous spatial structure. It proposes a Duane-style model in which apparent waviness emerges from quantised momentum exchanges with periodic scatterers, deriving the double-slit momentum distribution at the scattering point and unifying phenomena across the Kapitza-Dirac effect, Bragg diffraction, ultrafast electron diffraction, and polarisable-molecule diffraction. Momentum is argued to be fixed by local interactions and conserved per event, with coherence and wavefront overlap playing no fundamental role. The work emphasizes symmetry, Bloch-type periodicity, and Gouy phase as supporting pillars, offering a realist, interaction-based account of diffraction and interference that aligns with quantum formalism while downplaying the necessity of wave-like explanations.

Abstract

The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of Landé and Lévy-Leblond to demonstrate that de Broglie wavelengths are not relativistically covariant as simultaneous spatial structures, making wave properties an unviable explanation of apparent interference. We then explore whether modern experiments vindicate an alternative view: that apparent waviness in diffraction and interference scenarios emerges as a consequence of quantised interactions between particles. Such a view has historically received very little attention, despite being the exact modern explanation of both the Kapitza-Dirac effect and ultrafast electron diffraction. We then study a photon orbital angular momentum realisation of the double slit to show that quantised exchanges can mimic interference. Finally, we demonstrate that the quantum formalism demands that particle momentum is determined at the point of scattering, contravening wave-based explanations of quantum interference.

Paper Structure

This paper contains 22 sections, 17 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Contribution to the literature
  3. Paper structure
  4. The problem of wavelengths
  5. The Kapitza-Dirac effect
  6. Diffraction by material gratings
  7. Quantisation of momentum
  8. Bloch's theorem and the Mössbauer effect
  9. Does this conflict with the uncertainty principle?
  10. Evidence supporting Duane's model
  11. Bragg diffraction
  12. Ultrafast electron diffraction
  13. Diffraction of polarisable molecules
  14. Coherence
  15. Momentum conservation
  16. ...and 7 more sections

Figures (1)

  • Figure 1: OAM spectrum from angular double slit when $\alpha = \pi$, $\beta = \frac{\pi}{3}$ plotted as a bar graph. The line plot shows a linear double-slit momentum distribution in $\tilde{p}$ when $\frac{\Delta_y}{\sigma} = 3$ and $f = 1$.