Unwinding unit definitions from constants.

We are systematically unwinding the unit definitions from physical constants by isolating the contributions of each fundamental unit (e.g., $\text{kg}$, $\text{m}$, $\text{s}$) embedded within the constants. This process involves expressing the constants solely in terms of their units and then solving for the contributions of those units directly. By doing so, we demonstrate that the constants can be reconstructed precisely from their unit relationships alone. Any unaccounted for ratio that is left over after the units are accounted for is the actual real dimensionless constant buried inside the constant. 

The program that does this is part of an effort where we are deconstructing h, G, and now just about all constants by looking at unit definitions.  You can find it here:

https://github.com/BuckRogers1965/RedefineUnitsForPlancksConstant/blob/main/define_const_from_units.py

Here’s how my approach can be summarized:

1. Analyze the Dimensional Structure:

   • Start by identifying the unit structure of the constants (e.g., $hc$ and $G$).
   • Represent the constants in terms of their fundamental units (e.g., $\text{kg}$, $\text{m}$, $\text{s}$).
   • Notice that hc and G have the same exact units except that kg is in the numerator in one and in the denominator in the other. 
   • The inversion of $\text{kg}$ between $hc$ ($\text{m}^3 \cdot \text{kg}/\text{s}^2$) and $G$ ($\text{m}^3 / (\text{kg} \cdot \text{s}^2)$) revealed an anchor point to hack the unit system.

2. Solve for Unit Contributions:

• By isolating the contribution of $\text{kg}$, we could balance the contributions of $\text{m}$ and $\text{s}$, essentially "solving" the system of equations hidden within these constants.
• Set up a system of equations derived from the definitions of multiple constants.
• Solve for the numerical contribution of each unit ($\text{kg}, \text{m}, \text{s}$) using these relationships. 
• Start by saying that hc/kg = G * kg, solve for kg. Replace kg with the value.
• Solve for m, replace m in the equation.  
• Solve for s, replace s and kg in the original formula, and solve for m for the last time. 
• Solve for c, see what scaling is wrong, scale m to fix c, push that scaling into G and hc, these are a ratio in these formulas that is not accounted for by the units. 
• Continue solving each constant, finding ratios that are not accounted for by the unit scaling.  

This is the basic framework where I show how I create the constants from their units: 

As you can see I recreate the speed of light with m/s and sigma by just defining the the units as a variable with the power it has in the units of the constant.  In the sigma,  that number is the moles. I already updated the formula to say mol in the program in git hub.   

This is the comparison between the calculated and known values:

 

What is left to do is to add as may constants as possible to this framework and start looking for patterns.  This is just day one of this project, there is a long way to go to validate this approach and we have so much to learn. 

When you encounter a new unit you have not seen before, replace the values you have seen before, and solve for the new unknown.  Just introduce constants with just one new constant at a time.