The Unit Conversion Framework for Physical Constants

 J. Rogers, 01 Apr 2025, 2243

Here's a concise summary of the framework:

Core Insight

Physical constants like c, h, and k are not mysterious quantum entities but are composite values defined by more fundamental unit conversion factors that relate our arbitrary SI system to natural equivalences.

Key Conversion Factors

1. Hz_kg = h/c²: The fundamental frequency-mass conversion factor
2. K_Hz = k/h: The fundamental temperature-frequency conversion factor
3. c² or kg_J: The mass-energy conversion factor

How Constants Are Constructed

• Planck's constant: h = Hz_kg × c² (not a quantum of action but a conversion between frequency and energy units of measure)
• Boltzmann's constant: k = K_Hz × Hz_kg × c² (not a fundamental thermodynamic constant but a conversion between temperature and energy units of measure)

The Chain of Equivalences

K ⟷ f ⟷ m ⟷ E

Where you can move between any physical quantity via the appropriate conversion factor without needing to go through energy as an intermediary.

Time-Centered Unit System

Our entire measurement system anchors to the definition of the second, which determines Hz, which then determines all other units through these conversion factors.

The Natural Unit System

These constants reveal a mapping between our arbitrary SI units and a natural unit system where: 1K = 1Hz = 1kg = 1J and c = 1m/s

This framework transforms our understanding of physical constants from mysterious fundamental quantities to clear unit conversion factors, making complex physics equations more transparent and revealing the deep interconnections between different physical quantities.