The Unified Energy Formula

 The Unified Energy Formula

Starting with $E=m{c}^2$:

1. Substitute mass as frequency: $m=f\cdot {\text{Hz}}_{\text{kg}}$

   $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">Hz</span>}}_{\text{<span style="background-color: white;">kg</span>}}<span\; style="background-color:\; white;">\cdot </span>{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">h</span>}\mathrm{<span\; style="background-color:\; white;">f</span>}$$

   (Since ${\text{Hz}}_{\text{kg}}\cdot c^2=h$)
   
   

2. Substitute frequency as temperature: $f=T\cdot {\text{K}}_{\text{Hz}}$

   $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">h</span>}\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">h</span>}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">K</span>}}_{\text{<span style="background-color: white;">Hz</span>}}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}$$

   (Since $h\cdot {\text{K}}_{\text{Hz}}=k$)
   
   

Final Unification:

$$\boxed{{\displaystyle \mathrm{<span\; style="background-color:\; white;">\backslash E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">h</span>}\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}}}$$

Same energy, different perspectives.

• $c,h,k$ are just unit converters.

• In natural units ($c=h=k=1$):

  $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">T</span>}$$

Physics is united at its core.

Natural Unit Scaling
This is a simple process

Define base units:
1 meter = 1 light-second (sets c=1 m/s)
1 Kelvin = 1 Hz
1 kg       = 1 Hz

Resulting natural equivalences:
1 K = 1 Hz = 1 kg = 1 J

Constants naturally become:
c  = 1 m/s
c² = 1 m²/s²
h  = 1 J/Hz
k  = 1 J/K

No hand wave needed.
It is just that simple.