Thinking Non Locally: The Atemporal Roots of Particle Physics

Abstract

Developing an approach defined in previous papers a correspondence between elementary particles and elements of a particular set of directed graphs said "glyphs" is made explicit. These can, in turn, be put in correspondence with a particular set of biquaternions. Charge conjugation and weak isospin inversion then become both topological (on glyphs) and algebraic (on biquaternions) symmetries. The formalism describes leptons and quarks, the latter successfully combined into mesons and baryons. The introduction is possible of both a de Sitter interior spacetime of particles and the usual external Minkowski spacetime. The biquaternions can be related to creation and annihilation operators of the corresponding fermionic fields in Quantum Field Theory (QFT). The base states of QFT and their mutual interactions are thus constrained by their common emergence from logically antecedent structures. This result appears relevant for the understanding of the elementary particles spectrum.

The Electron and the Cosmos: From the Universe of Fragmented Objects to the Particle-World

“…The fact that, in a network, the nodes coincide with their relationships identifies a level of minimum complexity that cannot be further reduced and we identify it as that of the "elementary particles". Therefore the nature of elementarity is identified by the irreducibility of the structural complexity of a set of relationships and has nothing to do with the existence of "basic bricks" without internal structure [27]. The same concept can be understood in terms of Peirce's triadic relationship "sign": in a typical relationship as ij = k between quaternion units, j can be assimilated to the Object, i to the Representamen and k to the Interpretant (ie the interaction between i and j which allows to associate the Object j with i).…”

“…Therefore, at this fundamental level dominated by triadicity both the material (triangle) and spacetime (transformations of the sphere that leave the triangle unchanged) degrees of freedom make their appearance. From the perspective of the single positional eigenstate |x contained in the decomposition of |Ψ , the quantum jump from which |Ψ exits can be seen as a cascade of symmetry breakings induced by the (ordinary) interactions involved in that jump [27]. The specific succession of symmetry breakings defines the type of particle of the Standard Model (electron, proton, etc.).…”

“…In other words, it is the process of spatio-temporal localization of the particle that defines the "type" of particle. This process can be represented through a particular graph called "glyph" [27]. All glyphs are subsets of a mother glyph (the "universal oscillator") and can be viewed as its "states".…”

“…All glyphs are subsets of a mother glyph (the "universal oscillator") and can be viewed as its "states". In [27] it is hypothesized that the structure of the localization process, ie the sequence of symmetry breakings involved in a quantum jump, is the following. First of all, the fundamental quaternionic units defined by the oriented three-rectangle are subdivided on the basis of their sign, with the resulting constitution of two conjugated sets of units.…”

“…The construction is completed by assuming, in accordance with an old micro-causality argument discussed by Caldirola [28], that (x, t) is the tangency point of a de Sitter space of radius cθ (with θ ≤ θ 0 ) on the usual spacetime and that the positions of centers of charge are enclosed (confined) within the projection of this space on spacetime. This leads [11,27] to the usual systematics of elementary particles and their subdivision into leptons, mesons and baryons, according to the Standard Model (with the bonus of an ab initio condition of confinement of quarks and gluons). This representation is completely a-dynamical and synchronic, since a connection is involved between an a-temporal layer of physical reality and the usual temporal domain.…”