[Paper Review] Localization, CP-symmetry and neutrino signals of the Dirac matter

A. Makhlin|arXiv (Cornell University)|May 15, 2010

Quantum chaos and dynamical systems10 references3 citations

TL;DR

This paper proposes that the Dirac field's intrinsic polarization structure dynamically generates spacetime geometry, explaining matter localization, mass, and CP-violation through local time slowdown and Lorentz contraction. It identifies neutrinos as signals from abrupt creation/decay of localized objects and reinterprets the vacuum as a uniform Dirac field with preserved light-cone invariance, offering a classical foundation for charge asymmetry and CP-violation via broken Poincaré invariance.

ABSTRACT

The connection between the Dirac field as the field of matter and the spacetime metric is discussed within the framework of classical field theory. Polarization structure of the Dirac field is shown to be rich enough to determine the spacetime metric locally and to explain the emergence of observed matter as localized waveforms. The localization of the waveforms is explained as the result of the local time slowdown and the Lorentz contraction as a dynamic re-shaping of the waveforms in the course of their acceleration. A definition of mass as a limiting curvature of the spinor-induced metric is proposed. A view of the vacuum as a uniformly distributed unit invariant density of the Dirac field with an explicitly preserved invariance of the light cone is brought forward. Qualitative explanation of the observed charge asymmetry as the consequence of the dynamics of localization is given. The origin of the CP-violation is associated with the loss of the Poincare invariance due to localization. Neutrinos are identified with the signals emitted in the abrupt processes of creation or decay of localized objects and the concept of the Majorana neutrino is revisited. The wave equation for the classical pion field is derived from the Dirac equation. Its connection with stresses, mass and charge fluxes in localized waveforms of the Dirac field is traced. Some implications of the finite size of colliding objects for high-energy processes are discussed. A possible difference between the lifetimes and gyromagnetic ratios for positive and negative charges is predicted. A hypothesis that known internal degrees of freedom are the local spacetime (angular) coordinates that have no precise counterparts in Riemannian geometry is proposed.

Motivation & Objective

• To explain the origin of matter localization, finite size, and mass from the classical Dirac field without relying on quantum field theory.
• To resolve the observed charge asymmetry (protons vs. electrons) by linking it to dynamic localization effects in the Dirac field.
• To provide a classical mechanism for CP-violation through the loss of Poincaré invariance due to localization.
• To reinterpret the vacuum as a uniform Dirac field with unit invariant density, replacing the Dirac sea with a geometrically consistent structure.
• To derive the pion field equation from the Dirac equation and connect it to stress, mass, and charge fluxes in localized waveforms.

Proposed method

• Uses bilinear forms of the Dirac field to construct a tetrad of orthogonal Lorentz unit vectors, which define a Riemannian metric via integrability conditions tied to the Dirac equation.
• Applies Fock's formalism for differential calculus of the Dirac field in curved spacetime, extending it beyond standard treatments to include non-holonomic structures.
• Analyzes differential identities derived from the Dirac equation to assess their tensorial nature and independence from coordinate systems, particularly focusing on energy-momentum conservation.
• Introduces a tetrad-based Hamiltonian formulation where angular momentum-like operators (L_A, L_3) mix spinor components and break standard separation of variables unless specific field conditions (e.g., ℵ_r = 0) are met.
• Employs a radial-angular separation ansatz for the Dirac spinor, assuming specific angular functions (Y_k,m, Z_k,m) that satisfy coupled differential equations involving Λ± operators.
• Derives the classical pion field equation from the Dirac equation and traces its connection to mass and charge fluxes in localized waveforms.

Experimental results

Research questions

• RQ1 How can the Dirac field's polarization structure dynamically generate spacetime geometry and explain the localization of matter?
• RQ2 What is the origin of mass in this framework, and how is it related to curvature of the spinor-induced metric?
• RQ3 How does the localization process lead to observable charge asymmetry between protons and electrons?
• RQ4 What is the mechanism behind CP-violation in this classical field-theoretic model?
• RQ5 How do neutrinos emerge as signals from abrupt creation or decay of localized objects, and what does this imply for the Majorana neutrino concept?

Key findings

• The Dirac field's invariant density locally determines the spacetime metric, with time slowdown in high-density regions explaining matter localization and mass as limiting curvature.
• Charge asymmetry arises dynamically from the time-slowing effect of localization, which breaks the physical equivalence of positive and negative charges.
• CP-violation originates from the loss of Poincaré invariance due to localization, not from a fundamental asymmetry in the field equations.
• Neutrinos are identified as signals emitted during abrupt creation or decay of localized waveforms, suggesting a classical origin for neutrino emission.
• The classical pion field equation is derived from the Dirac equation, with its dynamics linked to stress, mass, and charge fluxes in localized waveforms.
• A predicted difference in lifetimes and gyromagnetic ratios between positively and negatively charged particles is proposed based on the asymmetric localization mechanism.