[Paper Review] Quaternionic quantum interferometry

Asher Peres|ArXiv.org|May 16, 1996

Quantum Mechanics and Applications10 references3 citations

TL;DR

This paper proposes a universal algebraic relationship among coherent cross sections in three-scatterer systems under standard complex quantum mechanics. If experimentally violated, such a violation would imply either quaternionic quantum amplitudes or failure of the superposition principle, with potential tests in neutron interferometry, K_S-meson regeneration, and proton-proton scattering.

ABSTRACT

If scattering amplitudes are ordinary complex numbers (not quaternions) there is a universal algebraic relationship between the six coherent cross sections of any three scatterers (taken singly and pairwise). A violation of this relationship would indicate either that scattering amplitudes are quaternions, or that the superposition principle fails. Some possible experimental tests involve neutron interferometry, K_S-meson regeneration, and low energy proton-proton scattering.

Motivation & Objective

• To establish a universal algebraic constraint on coherent cross sections in three-scatterer systems under standard complex quantum theory.
• To identify experimental signatures that could distinguish complex quantum mechanics from quaternionic extensions.
• To propose testable predictions in established quantum systems like neutron interferometers and K_S-mesons.
• To explore the implications of non-complex scattering amplitudes on the superposition principle.
• To provide a framework for experimental validation of alternative quantum formalisms using existing interferometric setups.

Proposed method

• Derives a universal algebraic relation among six coherent cross sections (single and pairwise scatterings) of three scatterers.
• Assumes scattering amplitudes are complex numbers, leading to a constraint that must hold under standard quantum mechanics.
• Analyzes the mathematical structure of scattering amplitudes in a three-body system using unitary evolution and superposition.
• Identifies that any deviation from the derived algebraic relation would signal non-complex amplitudes or breakdown of superposition.
• Proposes specific physical systems—neutron interferometry, K_S-meson regeneration, and low-energy proton-proton scattering—as viable testing grounds.
• Uses standard quantum mechanical formalism to derive the expected cross-section relations, contrasting them with hypothetical quaternionic extensions.

Experimental results

Research questions

• RQ1 What universal algebraic constraint exists among the coherent cross sections of three scatterers in standard complex quantum mechanics?
• RQ2 How would a violation of this constraint signal the existence of quaternionic scattering amplitudes?
• RQ3 In what physical systems can this constraint be experimentally tested?
• RQ4 What would a failure of the superposition principle imply in this context?
• RQ5 Can existing interferometric experiments detect deviations from the complex quantum prediction?

Key findings

• A universal algebraic relationship exists between the six coherent cross sections of any three scatterers, assuming complex amplitudes.
• Any experimental violation of this relationship would imply either that scattering amplitudes are quaternions or that the superposition principle fails.
• Neutron interferometry is a viable experimental platform for testing the predicted constraint.
• K_S-meson regeneration experiments offer a second potential testbed for detecting deviations.
• Low-energy proton-proton scattering provides a third experimental avenue for probing the constraint.
• The derived constraint is independent of specific dynamics and holds universally under standard quantum theory with complex amplitudes.