Toward unification: the dimensionless equation of motion

TL;DR

This paper derives a dimensionless equation of motion unifying gravitational and electrostatic forces, suggesting fundamental constants are transformation factors rather than intrinsic properties of nature.

Contribution

It introduces a dimensionless form of the equation of motion that eliminates fundamental constants, proposing they are human-defined transformation factors.

Findings

Equation becomes dimensionless with only ratios of physical quantities.

Fundamental constants may be transformation constants between artificial and natural quantities.

Implication that physical constants are not intrinsic but related to measurement conventions.

Abstract

We demonstrate that if masses and charges figuring in the equation of motion including both Newton gravitational and Coulomb electrostatic force laws are divided by mass and charge, respectively, which are derived using the relations contaning only the fundamental physical and mathematical constants (like relations defining the Planck's mass, length, and time), then the gravitational constant and permitivity of vacuum can be eliminated from the equation. In addition, the equation becomes dimensionless containing only the ratios of distances, velocities, masses, and electric charges. The ratios of masses and charges can further be replaced with the ratios of wave-lengths or frequencies. The corresponding equation of motion implies that the fundamental physical constants as the gravitational constant, permitivity of vacuum, and Planck constant are, likely, mere the transformation constants between artificial quantities as mass and electric charge, which were established by man to communicate some concerning things and events in every-day life, and natural physical quantities as wave-length or frequency of oscillations of waving space-time.