Revealing the True Nature of the Fine Structure Constant Through Unit Analysis

Introduction

In this framework, we’ve taken a step back to reevaluate the relationships between physical constants by breaking them down into fundamental scaling parameters. This allows us to reveal underlying simplicity and natural relationships that are often obscured by the conventions of human-defined units like meters, kilograms, and seconds. This paper describes applying these simplification steps of isolating the units, replacing constants and simplying shows the true nature of the fine structure constant as elemetal charge squared divided by Planck's charge squared.

1. Starting Point We began with a framework that breaks down fundamental constants into scaling parameters:

h = α³β/c    (Planck's constant)
G = α³/β     (Gravitational constant)
k = α³β/γ    (Boltzmann constant)
ε₀ = δ²/(α³β) (Vacuum permittivity)

Where:

• α ≈ 1.53844×10⁻⁶ m (length scaling) ( different alpha here)
• β ≈ 5.45551×10⁻⁸ kg (mass scaling)
• γ ≈ 1.438776877504×10⁻² K⁻¹ (temperature scaling)
• δ ≈ 1.32621132205611221308×10⁻¹⁸ C (charge scaling)

2. Key Discovery We had previously found that Planck's charge simplifies beautifully to:

Planck charge = δ√2

3. Analyzing the Fine Structure Constant We started with the traditional expression:

α = e²/4 * pi * epsilon_0 * h_bar * c
α = e²/4 * pi * δ²/(α³β) * α³β/c/(2 *pi) * c
α = e²/δ²2

But focusing on just the charge relationship:

α = e²/(δ√2)²

4. Unit Analysis Revelation Looking at the units carefully:

• e (elementary charge) is actually just a pure count (1.602176634×10⁻¹⁹), like the mole
• Planck charge (δ√2 ) is our fundamental charge unit
• Therefore α is just comparing these two charge quantities squared

5. Final Understanding The fine structure constant α ≈ 1/137 is simply:

α = (elementary charge)²/(Planck charge)²

This shows that the fine structure constant, rather than being a mysterious number combining e,  epsilon, pi, ℏ, and c, is actually just expressing how the quantum of charge (e) relates to the fundamental Planck charge unit. The traditional formula obscures this simple relationship by introducing human unit conventions.

This insight emerged from:

1. Breaking down constants into fundamental scaling parameters
2. Recognizing that charge, like the mole, is fundamentally just a count
3. Seeing how the unit scalings cancel out to reveal the pure relationship

The seeming complexity of α = e²/(4pi epsilon_0 h_bar c) has been reduced to a simple ratio of two natural charge units squared and divided by each other, giving us deeper insight into why the fine structure constant has its particular value and what it truly represents in nature.

This demonstrates the power of properly separating unit scaling contributions from fundamental physical relationships.

Appendix A - Program showing the math works. 

Calculated alpha: 0.007297352565816502

Standard alpha:   0.0072973525693

Absolute difference: 3.4834982121090263e-12

Relative error: 0.0000000477%

# Constants

delta = 1.32621132205611221308e-18  # Your given z value (C·m)

e = 1.602176634e-19  # Elementary charge (Coulombs)

# Calculate α using your formula

def calculate_alpha(z, e):

    alpha = e**2 / (2 * z**2)

    return alpha

# Compute the fine-structure constant

calculated_alpha = calculate_alpha(delta, e)

standard_alpha = 0.0072973525693  # Standard value of α

# Compare results

difference = abs(calculated_alpha - standard_alpha)

relative_error = (difference / standard_alpha) * 100

# Display the results

print(f"Calculated alpha: {calculated_alpha}")

print(f"Standard alpha: {standard_alpha}")

print(f"Absolute difference: {difference}")

print(f"Relative error: {relative_error:.10f}%")