13 Results Found

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic...

We present a quaternion representation of quantum mechanics that allows its ontological interpretation. The correspondence between classical and quaternion quantum equations permits one to consider the universe (vacuum) as an ideal elastic solid. Ele...

We develop a comparative synthesis of quantum-information geometry beyond complex numbers, with emphasis on what different algebraic frameworks contribute to information-processing structure rather than on their formal novelty alone. The organizing i...

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation o...

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. $\tilde{\psi }=(\frac{i}{c}{\psi }_0,\overrightarrow{\psi })$ , represents a state of a particle with orbital angular momentum, $L=3$...

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and gen...

There are a total of 64 possible multiplication rules that can be defined starting with the generalized imaginary units first introduced by Hamilton. Of these sixty-four choices, only eight lead to non-commutative division algebras: two are associate...

We extend our description of the electron’s quaternion spin (Q–spin) as a geometric rotor. This follows from incorporating both the symmetric polarization and the antisymmetric coherence into the theory. Polarization is observed only thro...

Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan’s mathematical expression of this situation. Recent studies using specia...

An abstract set of one-dimensional (spinor-type) elements randomly oriented on a plane is introduced as a basic subgeometric object. Endowing the set with the binary operations of multiplication and invertible addition sequentially yields a specific...

On October 16th 1843, the prominent Irish mathematician Sir William Rowan Hamilton, in an inspired act of vandalism, carved his famous $i^2=j^2=k^2=ijk=-1$ on the Brougham Bridge in Dublin, thus starting a major clash of ideas with the potential to...

This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jor...

The Heegaard splitting of $SU(2)$ is a particularly useful representation for quantum phases of spin j-representation arising in the mapping $S_1\to S_3$, which can be related to $(2j,2)$ torus knots in Hilbert space. We...