A brief overview of my constants framework.

This framework identifies common factors between h and G that allow us to define h and G in terms of these unit scaling factors.  Doing this shows the 1/c that is implicit inside  h and this shows that the energy, momentum and mass are all directly powers of 1/c.

Definitions:
m_P  = sqrt(hc\G)              = 5.455511861334621e-08 kg

s_va = sqrt(hcG)               = 3.641172281610566e-18 m³/s²
G    = (s_va / m_P)            = 6.6743e-11 m³/kg⋅s²
hc   = (s_va * m_P)            = 1.9864458571489286e-25 m³/kg⋅s²

h    = (s_va * m_P)/c          = 6.62607015e-34 kg⋅m²/s

Unit analysis: 
hc   = (s_va * m_P)/c^0 = hc   = 1.9864458571489286e-25 kg⋅m³/s²
E    = (s_va * m_P)/c^1 = h    = 6.62607015e-34 kg⋅m²/s
p    = (s_va * m_P)/c^2 = h/c  = 2.210219094e-42 kg⋅m
m    = (s_va * m_P)/c^3 = h/c² = 7.372497324e-51 kg⋅s

Scaling E, p, and m by frequency brings them to their observed values and units.

Note, that this is not the reduced plank mass and that s_va is the other common factor between hc and G. s_va and m_P have no physical significance, they only exist to bring powers of 1/c into alignment with our values and units for energy, momentum and mass. Think of them as like the scaling factor to convert km to miles.

As we move from the base scaling at c^0 you can observe the units reducing by s/m as the value changes by 1/c each step from hc to E to p to m.  This is why our unit system has the structures and relationships it does between energy, momentum and mass.  Our definition of c requires it. 

This shows that the basis for energy, momentum and mass are geometric projections of a progression of powers of c.  What we missed before because h itself contains an implicit 1/c that obscured this simple relationship.


Mathematically you can see

1/c^n                * unit scaling         = observed value

3.33564095198152e-09 * 1.98644585714892e-25 = 6.6260701500e-34
1.11265005605361e-17 * 1.98644585714892e-25 = 2.210219094e-42
3.71140109219698e-26 * 1.98644585714892e-25 = 7.372497324e-51

h and G in Imperial units

An example of how this framework works is to explore what an imperial units version of this framework would look like:
hc = (s_va * m_P) / c^0 = hc Units: ft³⋅lb/s² E = (s_va * m_P) / c^1 = h Units: ft²⋅lb/s p = (s_va * m_P) / c^2 = h/c Units: ft⋅lb m = (s_va * m_P) / c^3 = h/c² Units: lb⋅s