Unveiling the Physics Unit Coordinate System: A Framework of Universal Clarity

 J. Rogers, SE Ohio, 09 Apr 2025, 1811

We are excited to announce the Physics Unit Coordinate System, a revolutionary framework that transforms how physical constants and measurement systems are understood. By leveraging coordinate scaling principles, this system redefines the relationships between fundamental units like mass, length, charge, and temperature, revealing physics' intrinsic simplicity in elegant interconnections.

The github project is here: 

https://github.com/BuckRogers1965/Physics-Unit-Coordinate-System

This project introduces the idea with a python data set for both constants and the periodic table.  These data sets aim to be a comprehensive data about each of the entries in these two data sets.  

In the examples folder of the project are two main examples.

examples/physics_unit_coordinate_scaling.py

In this program you can select one of the configured unit scalings by uncommenting one of them and commenting the others.  The current choices are si, imperial, natural, atomic, and galactic.  The last one is just a placeholder for now. atomic scales to natural units and then further scales the masses to atomic ratios of the electron mass. 

When you run the program it will scale all the constants by the given set of unit scalings.  You can also choose to display data using different command line options, use -h with the command to see the options.

examples/print_periodic_table.py

This program works similarly to the first program in the choices of unit scaling and its own set of help units. and it then will convert the units of the periodic table data.  It is still a work in progress with the options, but I hope to soon have it working as well as the first program does.   

We have also added a module to simplify formulas by breaking out the constants c, h, and k as modular unit scaling factors.  This is the same principles, applied directly to our SI unit system to allow us to understand how c, h, and k are just doing unit scaling between equivalent but differently scaled units of measure.

Modular_Unit_Scaling_Framework

Breaking Boundaries: The Key Insight

One of the central breakthroughs is the idea of scaling mass by Hz_kg—the conversion factor between frequency (Hz) and mass (kg). In SI, this ratio is defined as ${\text{Hz}}_{\text{kg}}=\frac{c^2}{h}\backslash text\{Hz\}\_\backslash text\{kg\}\; =\; \backslash frac\{c^2\}\{h\}$, connecting the speed of light ($cc$) and Planck’s constant ($hh$) through Einstein's $E=m{c}^{2}E=mc^2$ and Planck’s $E=hfE=hf$. You can entirely define h as the ratio of two unit scalings: h = Hz_kg c^2.

What Does This Mean?

In this framework:

• Frequency [Hz] = $\frac{c^2}{h}\text{[Hz/kg]}\backslash frac\{c^2\}\{h\}\; \backslash ,\; \backslash text\{[Hz/kg]\}$ * Mass [kg]

• If we define a new unit of mass, $m_{N}m\_N$, such that $1m_N=\frac{h}{c^2}\text{kg}1\; m\_N\; =\; \backslash frac\{h\}\{c^2\}\; \backslash ,\; \backslash text\{kg\}$, then:

  • A mass of $1m_{N}1\; m\_N$ would correspond to 1 Hz of frequency.

  • A mass of $X{m}_{N}X\; m\_N$ would correspond to $X\text{Hz}X\; \backslash ,\; \backslash text\{Hz\}$.

In this unified system, mass and frequency scale linearly with each other, with the conversion factor between them defined as 1 by design. The Xm_n becomes a simple coordinate scaling in a single unit system that defines all unit systems. This ties the specific scaling of mass in any unit system directly to the underlying reality of physics.

Natural Units: A Foundation of Simplicity

This insight challenges traditional interpretations of natural units, emphasizing that they are not about changing physical constants like $cc$, $hh$, or $kk$. These constants represent real, immutable relationships. Natural units are entirely about redefining unit systems to simplify these relationships.

By choosing units like $m_{N}m\_N$, we transform constants into coordinate mappings within the unified Physics Unit Coordinate System. This reveals the deeper linear relationship between mass and frequency, eliminating the arbitrary barriers imposed by specific unit systems.

Real-World Implications

This framework has far-reaching applications:

• Unified Mass Coordinates: The $m_{N}m\_N$ unit scales mass seamlessly across all unit systems, providing clarity in contexts where 1 kg equals 1 Hz at 1 second, yielding $m_N=7.372497323812708\times {10}^{-51}\text{kg}m\_N\; =\; 7.372497323812708\; \backslash times\; 10^\{-51\}\; \backslash ,\; \backslash text\{kg\}$.

• Simplified Physics: Constants like $hh$ and $cc$ become elegant bridges between units rather than standalone complexities.

• Empowered Research: With clearer mappings between units, researchers can more effectively connect theoretical physics to practical measurements.

Join the Movement

The Physics Unit Coordinate System is more than a conceptual framework—it’s a tool to unify scientific inquiry under a single, cohesive lens. By scaling $kgkg$ by $H{z}_{\text{kg}}Hz\_\backslash text\{kg\}$, as well as other human unit choices, we unveil the profound simplicity of physics and empower researchers, educators, and enthusiasts to explore the universe with new clarity.

Let’s bridge the gap between unit systems and universal truths—together.