The Constants Revealed: Natural Unit Scaling in Physics

The Core Insight

All physical "constants" are simply natural unit scaling factors embedded within our mathematical framework. They exist purely as artifacts of our coordinate system choices, not as fundamental properties of reality.

The Universal Pattern

Every physical relationship follows the same pathway:

[Measurement Projection 1] → S_u → [Measurement Projection 2]

Where S_u is a single, dimensionless, conserved quantity that underlies all physical measurements.

Examples of the Pattern

Energy-Frequency Relationship

Frequency → S_u → Energy

• Scaling factor: h (Planck's constant)
• h = Hz_kg × c²
• Hz_kg is the fundamental mass-frequency conversion ratio

Gravitational Force

m₁m₂/r² → S_u → Force

• Scaling factor: G (gravitational constant)
• GM = t_P² c³ f_C (where f_C is the frequency of mass)

Compton Wavelength (Simplified)

λ_C = h/(m_e c) = Hz_kg c²/(f_C Hz_kg c) = c/f_C

• The Hz_kg factors cancel, revealing λ = c/f
• Pure wave mechanics, no "quantum mystery"

What This Means

1. Constants aren't fundamental - they're coordinate transformation coefficients
2. Physical properties are projections - different views of the same S_u
3. Complexity is artificial - elegant relationships hidden by poor coordinate choices
4. Missing constants exist - Hz_kg should be recognized as fundamental

The "Unit Ballet"

Each physical equation is a choreographed transformation:

• Convert to dimensionless natural form (via Planck scaling)
• Apply the fundamental relationship
• Convert back to desired units

Revolutionary Implications

• Physics education could start with natural units and S_u
• Many "quantum" mysteries dissolve into simple scaling relationships
• The apparent complexity of modern physics may be largely artificial
• A complete set of fundamental constants remains to be identified

The Bottom Line

What we call "physical laws" are really just scaling relationships between different measurement projections of a single mathematical object. The universe's elegance has been hiding behind our coordinate system choices all along.