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 ${K}_{S}$ -meson regeneration.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 ${K}_{S}$-meson regeneration.

Physical Review LettersMar 12, 197993 citations

Proposed Test for Complex versus Quaternion Quantum Theory via Quantum Superdense Coding

Songsong Dai

While complex numbers form the foundational number system of quantum mechanics, the theoretical possibility of higher-dimensional hypercomplex alternatives persists. In this paper, we present a test protocol designed to distinguish between complex and quaternionic quantum mechanics. The protocol is founded upon the quantum superdense coding scheme and functions by detecting the presence of multiple distinct quantum phase gates. We also provide the corresponding quantum circuit required to perform this test.While complex numbers form the foundational number system of quantum mechanics, the theoretical possibility of higher-dimensional hypercomplex alternatives persists. In this paper, we present a test protocol designed to distinguish between complex and quaternionic quantum mechanics. The protocol is founded upon the quantum superdense coding scheme and functions by detecting the presence of multiple distinct quantum phase gates. We also provide the corresponding quantum circuit required to perform this test.

Apr 8, 20260 citations

Remarks on quaternion quantum mechanics

František Jenč

Czechoslovak Journal of PhysicsJul 1, 19663 citations

{K}_{S}

-meson regeneration.