PROTON: INTERNAL PRESSURE AND BULK MODULUS OF THE SHELL

AbstractThis work presents a structural formalization of the fundamental constituents of matter, movingbeyond the conventional probabilistic interpretation by introducing the concept of ExistenceDensity (ρE). The theoretical framework is based on the hypothesis that mass is not an intrinsicscalar attribute, but rather the macroscopic manifestation of a local pressure gradient within theenergy-momentum tensor. Utilizing experimental CODATA values for the proton charge radius, theExistence Pressure (Pv) is analytically derived and quantified at ≈ 0.603 × 10^35 Pa. This valueidentifies the polytropic saturation limit required to confine the baryonic singularity and preventthe adiabatic expansion of its proper volume. Furthermore, a comparative analysis of the leptonicphase is presented, which is characterized by a reduced coercivity (Pv,e ≈ 8.73 × 10^29 Pa). Thedefinition of a topological Existence Barrier allows for the description of structural stability andannihilation inhibition processes as hydrodynamic equilibrium phenomena at high energy density,returning particle physics to the domain of continuum mechanics. Additionally, the Bulk Modulusof the barrier (shell) is calculated through its differential response to the stress conditions of boththe Neutron and the Proton. The obtained results provide a coherent, consistent, and elegant theoreticalfoundation to the experimental evidence from Jefferson Lab, specifically the measurementsby Dr. V. Burkert regarding the internal pressure distribution of the proton.