Universal Mass Scaling Via A Logarithmic Exponent

This paper presents an empirical mass-scaling relation that spans approximately 120 orders of magnitude, connecting the quantum scale to the cosmological scale. By introducing a dimensionless logarithmic exponent ($x$) and a scaling constant ($S_{\Phi}$), we demonstrate that the masses of elementary particles, planetary bodies, stars, and black holes follow a singular linear regularity when plotted logarithmically.

Key Highlights:

• Universal Formula: Proposes the relation $M(x) = \frac{4\pi}{3} \alpha^x S_{\Phi} m_P$, where $m_P$ is the Planck mass.

• Mass Clusters: Identification of distinct "plateaus" in the distribution of exponent $x$, suggesting organized regimes of matter (Quantum, Planetary, Stellar, and Galactic).

• Cosmological Connection: The scaling constant $S_{\Phi} \approx 1.48 \times 10^{58}$ is shown to align with the $10^{122}$ vacuum energy density discrepancy (the Cosmological Constant Problem).

• Bridging the Gap: The study successfully integrates biological entities (viruses, humans) and intermediate objects into the scaling map, maintaining strict linearity across all tested scales.

Methodology:

The work is intentionally empirical, focusing on pattern recognition and numerical consistency across standard reference masses from the Particle Data Group and astrophysical catalogs. It serves as a foundational "scaling map" for future theoretical investigations into the entropic or informational nature of mass distribution.

Mass Scaling, Empirical Physics, Planck Mass, Cosmological Constant Problem, Logarithmic Scaling, Theoretical Physics, Black Hole Mass, Particle Physics