1. Short "Derivations" of Key Formula of Modern Physics
W. J. Wilson
Department of Physics & Engineering
University of Central Oklahoma
Edmond, OK 73034
Web:

2. Outline
World’s Shortest Derivation of the Lorentz Transformation of SR
“Derivation” of Bohr Quantization Condition,
“Derivation” of Maxwell-Boltzmann Distribution
“Derivation” of Fermi-Dirac Distribution

3. World’s Shortest Derivation of the Lorentz Transformation
We assume that in the previous lecture one has developed the time dilation
And the Lorentz contraction formulae in the usual way
Where

4. In O Frame, x’ (Length measure by O’) is Lorentz contractedv
v t x’ x x’ x
In O Frame, x’ (Length measure by O’) is Lorentz contracted
So, solving for x’

5. In O’ Frame, x is Lorentz contractedy’ y v
v t’ x’ x x’ x
In O’ Frame, x is Lorentz contracted
But as we just showed So
Solve this for t’

6. Solve this for t’
But
Thus, the Lorentz Transformation: So

7. “Derivation” of Bohr Quantization

8. “Derivation” of Bohr Quantization

9. “Derivation” of Boltzmann Factor

10. For ideal gas
Isothermal (Exponential) Atmosphere:

11. But So
But the probability of finding a particle should be proportional to the density, so …