Coexistence Positive and Negative-Energy States in the Dirac Equation with One Electron

[7 Essential] This paper marks a theoretical milestone in the 0-Sphere electron model program, offering a new interpretation of the negative-energy states in the Dirac equation—a central puzzle in quantum mechanics. Instead of the conventional particle–antiparticle picture, it proposes that positive and negative energy states can coexist within a single electron through the internal dynamics of two spinor particles. Building on the geometric and thermal potential energy framework introduced in A Model of an Electron Including Two Perfect Black Bodies (DOI: 10.5281/zenodo.16759284), the study reframes Dirac’s original concern. It replaces the standard view—Ψ⁽⁺⁾ for particles and Ψ⁽⁻⁾ for antiparticles—with a unified single-electron model where both components correspond to two distinct spinor particles (Te1 and Te2) within one electron. Note that in earlier works these internal components were referred to as spinors (Te1 and Te2), while from 2024 onward they have been consistently described as kernel A and kernel B in subsequent publications. A central innovation is the substitution of conventional momentum p with virtual photon momentum p_γ*. This quantity can take positive or negative values depending on the oscillation phase of thermal energy exchange between the two spinors. This reframing explains negative-energy states without invoking positrons or time-reversal, instead attributing them to the directional flow of thermal radiation and absorption cycles. This is the first systematic attempt to unify Dirac equation solutions with an internal-structure electron model. It establishes groundwork for exploring how quantum field theory phenomena could emerge from deterministic geometric processes. This paper serves as the logical foundation for a subsequently submitted work, Redefining Electron Spin and Anomalous Magnetic Moment Through Harmonic Oscillation and Lorentz Contraction (DOI: 10.5281/zenodo.16871305), which provides predictions that electron Zitterbewegung oscillates at approximately 4% of the speed of light. While some mathematical refinements remain, the work opens a new path for interpreting fundamental equations through internal electron dynamics rather than particle–antiparticle dualism. Relation to Previous Works: 0-Sphere Model — DOI: 10.5281/zenodo.16759284 Anomalous Magnetic Moment via Lorentz Contraction — DOI: 10.5281/zenodo.16871305 Community: Satoshi-Hanamura-Papers