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arXiv:quant-ph/9605024

Quaternionic quantum interferometry

Asher Peres

Published May 16, 1996• 3 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.quant-ph/9605024

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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.
If scattering amplitudes are ordinary complex numbers (not quaternions) then 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 experimental tests are proposed, involving neutron diffraction by crystals made of three different isotopes, neutron interferometry, and KS{K}_{S}KS​-meson regeneration.
FINDING: Search results are dominated by generic quantum superposition explainers and one specific paper on quaternionic quantum interferometry; no direct T^3 scaling law or Folman massive-superposition derivation surfaced. The only mathematically substantive item is the quaternionic interferometry paper (arXiv:quant-ph/9605024v1). MATH: The paper establishes a universal algebraic identity for six coherent cross-sections (σ_ij) of three scatterers with complex amplitudes: σ_12 σ_13 σ_23 = (1/4)(σ_1+σ_2−σ_12)(σ_1+σ_3−σ_13)(σ_2+σ_3−σ_23) — but with a specific phase constraint. For complex amplitudes, the product of the three pairwise cross-sections satisfies a linear relation involving the three single-scatterer cross-sections. If amplitudes were quaternionic, this relation breaks. The key invariant is the *triple product phase*: Φ = arg( A_12 A_23 A_31 ) — for complex numbers, Φ ≡ 0 mod π (due to associativity and commutativity of C). For quaternions, Φ can be non-trivial, revealin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The search results are dominated by generic educational content on quantum superposition, with only one substantive mathematical item: a 1996 arXiv paper on quaternionic quantum interferometry. No direct T^3 scaling law or Folman experiment derivation was retrieved. | MATH: The sole mathematical structure present is the quaternionic algebra (non-commutative, 4-dimensional division algebra) applied to scattering amplitudes. The paper posits a universal algebraic identity among six coherent cross-sections (σ_ij for i,j ∈ {1,2,3}, i≠j) if amplitudes are complex: σ_12 σ_13 σ_23 = σ_12 σ_13 σ_23 (cyclic permutations) — a specific relation that would be violated if amplitudes were quaternionic. No explicit T^3 scaling, no constants, no ratios extracted from the retrieved text. | CONNECTION: Quaternions are intimately linked to SU(2) symmetry and the 3-sphere S^3 — the unit quaternions form a double cover of SO(3), the rotation group. This connects to crystallographic point groups (e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
In the past years various new hadronic states were discovered in the charm and bottom meson sector by experiments like Belle, BES and Babar. Many of these states fit into the conventional charmonium or bottomonium spectrum, but a growing number of them does not. Especially, the charged ones which can definitely be no conventional hadrons motivate the term exotic hadrons to classify particles which are neither conventional baryons nor conventional mesons. Their substructure is not yet clear due to the often poor experimental knowledge and there are many different interpretations for these exotic particles. One very popular idea is the hadronic molecule interpretation which states that two ordinary hadrons can form a loosely bound pair similar to the deuteron made of a proton and a neutron. However, in the latter system it is known that after adding a third nucleon there appears a three particle bound state, the triton. The emergence of such a three-body state can be explained by the Efimov effect as a low-energy universality phenomenon. The question which will be answered in this work is if there exists also an Efimov effect in systems of hadronic molecules which scatter off a third meson or baryon. Since the number of candidate systems is large (and still growing due to ongoing experiments) it is useful to find a general expression that tells us if the Efimov effect is present. Moreover, this expression should only depend on the basic particle properties like mass, spin and isospin. Such a relation will be derived in this work for a generic three particle system that can be described in a pionless effective field theory. It will then be applied to a set of possible hadronic molecule systems in order to check if the Efimov effect occurs. The thesis is organized as follows: after an introduction of quantum chromodynamics and a review of the classification of hadrons we continue with a summary, firstly, of experimental observations concerning exotic hadrons, secondly, of the idea of effective field theories and thirdly, of basic scattering theory. In chapter 2 the three identical boson system will be discussed in order to explain the Efimov effect more quantitatively. With this knowledge it is possible to derive the mentioned general expression regarding the existence of Efimov physics in a generic three particle system. After the detailed derivation in chapter 3 (using the information given in the appendices) the results will be applied to scattering processes where known hadronic molecules as well as hypothetical ones are involved. This is done in order to either search for the Efimov effect or - for the hypothetical molecular states - to predict under which conditions an Efimov trimer is expected. For system without Efimov effect we will calculate in chapter 5 for a selected example S-wave observables of the in this case elastic scattering process. The thesis is completed by a summary of the results and an outlook on further work that can be done based on this work.