The Elasto-Hydrodynamics of the Proton: Absence of Membrane, Barometric Respiration, and Electronic Valve through the E=PV Law

Abstract

The Standard Model of particle physics treats the proton either as an immutable rigid structure or as a blurred cloud of mathematical probabilities, running into insoluble contradictions such as the "proton radius puzzle". Drawing upon the Kenophobia paradigm, this paper demonstrates that the proton is a purely hydrodynamical entity lacking any rigid membrane or skin. Anchored in a fractal universe governed by the principle of Maximum Entropy Production (MEP) and Universal Darwinism, the proton is revealed to be a stationary toroidal vortex composed of 919 $e^+/e^-$ pairs and a single central positron (totaling 1839 electron masses). Its global steric envelope conforms to a Spherical Hill’s Vortex, while its internal hydrodynamics follow a triangular Kelvin-Helmholtz architecture, providing a purely fluid alternative to the illusory "quarks". Through the unified thermodynamic equation: $$E = M_p \cdot c^2 = P_v \cdot V$$ we establish how the steric volume of its Hill sphere dynamically and elastically adapts to variations in vacuum pressure $P_v$. This fluid and fractal model: Resolves the proton radius puzzle recorded at the Paul Scherrer Institute (2010) by explaining the radius contraction from $0.877\text{ fm}$ (electronic spectroscopy) to $0.841\text{ fm}$ (muonic spectroscopy) as a direct barometric compaction ($P_v$ increasing locally from $5.33 \times 10^{34}\text{ Pa}$ to $6.02 \times 10^{34}\text{ Pa}$) caused by the kinetic stress of the heavy muon. Establishes the natural respiration radius at terrestrial rest at $R = 0.981\text{ fm}$ for a baseline pressure of the depleted Plenum of $P_v = 3.8 \times 10^{34}\text{ Pa}$. Finds its direct temporal proof in the recent 500-attosecond delay observed in quantum tunneling (July 2026), which physically measures the time required for this exact barometric respiration and steric adjustment to occur without violating the constancy of the speed of light $c$. Assigns to the peripheral electron the role of a mechanical regulating valve, adjusting its orbit onto the exact interface where internal centrifugal pressure balances the confinement of the Plenum. Builds a direct fractal bridge to black hole astrophysics, modeling Sagittarius A* (Sgr A*) as a polyhedral macro-hadronic core measuring $4088\text{ km}$ in diameter under a critical density of $2.3 \times 10^{17}\text{ kg/m}^3$.