Mass, Charge and Color Charge as Progressive Manifestations of Energy

Mass, charge and color charge are not mutually independent intrinsic properties of matter. Instead, they are external manifestations and progressive forms of energy emerging at distinct cosmic scales and under different fundamental interactions.

Mass represents the most macroscopic and intuitive manifestation of energy, corresponding to gravitation and inertia. It follows the mass-energy relation E=mc^2 and constitutes the condensed state of energy in low-speed macroscopic regimes. Charge stands for the refined expression of energy under electromagnetic interaction, mediated by electric fields and photons and governed by a unified charge-mass-energy relation. Color charge corresponds to deeper subatomic structures of energy within the strong interaction, carried by quarks and gluons and characterised by three quantum color states; it forms the binding energy that stabilizes atomic nuclei and constitutes the more microscopic, fundamental quantum form of energy.

The three quantities share a single fundamental origin and deepen hierarchically, unified under the essence of energy. Proceeding from mass to charge and then to color charge, energy undergoes continuous progression and differentiation from macroscopic to microscopic scales and from weak to strong interactions, jointly forming the entire foundation of the material world.

Derived from the above hierarchically unified physical insight, the total global energy of a single elementary particle can be decomposed into three parallel intrinsic energy reservoirs, expressed mathematically as:
E = \gamma m c^2 + \frac{e^2}{k_e} + \frac{g_s^2}{k_s}

The three terms correspond respectively to geometric energy carried by mass, charge and color charge, which are mutually independent and non-nested in superposition, fully representing all underlying energy borne by a particle. Mathematically, this formula confirms that mass, charge and color charge are merely differentiated configurations of energy under distinct geometric curvature dimensions, with a unified origin in the intrinsic spacetime geometric energy reservoir.

Differential Verification of the Three-Term Energy Formula via Extremely Compact Distorted Celestial Objects

Extremely compact distorted celestial objects enable targeted testing of the second and third energy terms within the particle total energy formula, clearly distinguishing predictive discrepancies between traditional theoretical frameworks and the present model.

1. Magnetars and Ultra-Magnetized Neutron Stars: Independent Verification of the Charge Topological Energy Term \boldsymbol{\dfrac{e^2}{k_e}}

Within traditional astrophysical models, electromagnetic energy is treated solely as interaction potential energy originating from external stellar magnetic fields. The total internal particle energy is approximated exclusively by the relativistic mass-energy term \gamma m c^2, with no account for intrinsic topological energy carried by charge itself. Accordingly, traditional theories yield fixed theoretical upper bounds for magnetar outburst total energy, steady-state radiative luminosity and gravitational redshift offsets.

By contrast, the three-term energy framework posits that dense charged particles across the stellar surface each carry intrinsic charge topological energy, contributing additional electromagnetic geometric energy to the compact magnetized object as a whole. At identical total mass, the total internal energy, outburst release intensity and high-energy photon radiative flux of magnetars will systematically exceed predictions derived from the single mass-energy model.

Model discrimination can be performed against observational total energy of magnetar outbursts recorded by space-based X-ray and gamma-ray telescopes:

- If observed energies are systematically higher than traditional theoretical upper bounds and consistent with elevated predictions from the three-term formula, the hypothesis of independent intrinsic charge topological energy is validated.
- If observational data strictly conform to the classical mass-energy-only model, the assumption of independently existing intrinsic charge energy is falsified.

2. Quark Stars and Cores with Ultra-High-Pressure Quark Matter: Independent Verification of the Color Charge Topological Energy Term \boldsymbol{\dfrac{g_s^2}{k_s}}

In conventional QCD models for compact stars, color charge effects are described only as transient interaction potentials between quarks, with no allowance for permanent intrinsic energy carried by individual quarks. Ordinary neutrons and atomic nuclei exist as color singlets, where color charges mutually cancel with zero net color energy contribution.

Under extreme core pressures within compact stars, color confinement breaks down, producing abundant locally uncompensated color charges. The inclusion of color charge topological energy substantially raises the total internal energy of the stellar system and directly modifies two key observable physical quantities:

- Numerical shifts in the maximum stable mass limit of compact objects (TOV limit);
- Systematic corrections to core cooling evolution rates and critical pressures triggering supernova collapse.

Comparisons between gravitational wave detections, statistical mass measurements of compact stars and X-ray cooling timescale observations can distinguish discrepancies in stellar mass upper bounds and evolutionary curves predicted by classical QCD and the extended model incorporating intrinsic color charge energy, thereby verifying the physical reality of intrinsic color charge topological energy.

Supplementary Rigorous Remarks

1. Algebraic Origin: The quadratic forms of the charge and color charge terms trace back to classical electrostatic self-energy and QCD color Coulomb potential, respectively. This work proposes a novel physical interpretation: the two terms no longer represent derivative interaction energies between particles, but intrinsic energy arising from microscopic spacetime topological distortion induced by each charge, independent of relativistic mass-energy.
2. Theoretical Stage Positioning: This threefold energy decomposition serves as a quantitative expression supporting the accompanying physical intuition. The coupling constants k_e and k_s remain unsolved via analytical derivation and uncalibrated by experiment at present, functioning merely as a mathematical model supporting the overarching framework of “energy as hierarchical manifestations”. Subsequent quantitative constraints can be refined via multi-origin geometric field equations.