Breaking the Circular Definition: The Kilogram and Kelvin Units Self-Referential Trap

The Key Insight

1. We keep using Kelvin (K) and kilograms (kg) because they're practical for human-scale measurements.

2. We recognize that these units are rescaled versions of natural units, where 1 K ≡ 1 Hz ≡ 1 kg in a fundamental sense.

3. The "constants" $h$ and $k_B$ are just the conversion factors between our rescaled SI units and the natural scaling.

This doesn't require abandoning SI—it just means interpreting the constants as unit system correction factors rather than fundamental physics.

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1. Natural Units vs. SI Units: The Scaling Mismatch

In a natural unit system (e.g., Planck units, or a frequency-based system):

• 1 natural unit of frequency (Hzₙ)
  = 1 natural unit of mass (kgₙ)
  = 1 natural unit of temperature (Kₙ).
  
  

But in SI units, we have:

• 1 Hz (SI) = 1 Hzₙ (by definition, since we keep the second the same).

• 1 kg (SI) = α kgₙ, where α is a huge scaling factor (~10⁵⁰).

• 1 K (SI) = β Kₙ, where β is a tiny scaling factor (~10⁻¹¹).
  
  

The "constants" $h$ and $k_B$ encode these rescalings:

• $h$ bridges Hz (natural) ↔ kg (rescaled).

• $k_B$ bridges Hz (natural) ↔ K (rescaled).

The problem is we do not recognize that this is all the constants are doing, so we have assumed they are physical truths of the universe instead of just a circular definition of the kg, meter, and kelvin units of measure against their own definition. Because we measured h and k and c, we believe they are universal truths, but we measured them against a scale we humans devised. The so-called "fundamental constants" h and k_B are not laws of nature - they are conversion factors between human units of measure that are each scaled wildly differently.

The Reality:

1. Constants as Unit Translators

   • h converts between frequency (Hz) and energy (J), only because we measure quantum systems in macroscopic, classical units

   • k_B converts between temperature (K) and energy (J), only because we defined temperature separately from energy
     
     

2. The Circular Trap

   • We first defined kg, meter, and Kelvin arbitrarily (based on water, Earth's size, etc.) each with a wildly different unit scaling.

   • Then we discovered quantum mechanics and statistical physics required bridges between these mismatched units.

   • Now we've locked ourselves into a system where we define units using these same conversion factors, creating a self-referential loop
     
     

3. The Measurement Illusion

   • When we "measure" these constants, we're really just calibrating our artificial units against each other.  There are so many K in a Hz, there are so many Hz in a kg, there are so many kg in an energy unit. 

   • The numbers aren't fundamental - they're artifacts of our chosen reference points (like calibrating rulers made of different materials)
     
     

The Key Insight:
These constants don't represent deep physical truths, but rather the historical baggage of how we chose to build our measurement systems. In a human defined unit system where our kg, meter, and K unit scales are all scaled identically , they would all equal 1 but still carry the units needed to track units in the math.

Why This Matters:
By recognizing this, we:

• Remove false mystique around these numbers

• Focus on the real physics (relationships between quantities)

• Understand why natural units work so well (they eliminate these artificial conversions)

The Bottom Line:
h and k_B aren't laws of the universe - they're just the difference in scale between units in our measurement system. The fundamental truths are in the dimensionless relationships they connect.

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2. The Constants as Scaling Factors

(a) Planck's Constant ($h$)

$$\mathrm{<span>h</span>}<span>=</span>\mathrm{<span>6.626</span>}<span>\times </span>\mathrm{<span>1</span>}{\mathrm{<span>0</span>}}^{<span>-</span>\mathrm{<span>34</span>}}\text{<span>\hspace{0.17em}</span>}\text{<span>J</span>}<span>\cdot </span>\text{<span>s</span>}$$

• 
  What it really means:
  $$\mathrm{<span>1</span>}\text{<span>\hspace{0.17em}</span>}\text{<span>kg (SI)</span>}<span>=</span><span>(</span>\frac{{\mathrm{<span>c</span>}}^{\mathrm{<span>2</span>}}}{\mathrm{<span>h</span>}}<span>)</span>\text{<span>\hspace{0.17em}</span>}\text{<span>Hz</span>}<span>\approx </span>\mathrm{<span>1.36</span>}<span>\times </span>\mathrm{<span>1</span>}{\mathrm{<span>0</span>}}^{\mathrm{<span>50</span>}}\text{<span>\hspace{0.17em}</span>}\text{<span>Hz</span>}\mathrm{<span>.</span>}$$
• 
  

• This is the rescaling factor between our arbitrary kg and the natural mass unit (Hz).

• 
  

(b) Boltzmann's Constant ($k_B$)

$${\mathrm{<span>k</span>}}_{\mathrm{<span>B</span>}}<span>=</span>\mathrm{<span>1.381</span>}<span>\times </span>\mathrm{<span>1</span>}{\mathrm{<span>0</span>}}^{<span>-</span>\mathrm{<span>23</span>}}\text{<span>\hspace{0.17em}</span>}\text{<span>J/K</span>}$$

• What it really means:

  $$\mathrm{<span>1</span>}\text{<span>\hspace{0.17em}</span>}\text{<span>K (SI)</span>}<span>=</span><span>(</span>\frac{\mathrm{<span>h</span>}}{{\mathrm{<span>k</span>}}_{\mathrm{<span>B</span>}}}<span>)</span>\text{<span>\hspace{0.17em}</span>}\text{<span>Hz</span>}<span>\approx </span>\mathrm{<span>4.8</span>}<span>\times </span>\mathrm{<span>1</span>}{\mathrm{<span>0</span>}}^{<span>-</span>\mathrm{<span>11</span>}}\text{<span>\hspace{0.17em}</span>}\text{<span>Hz</span>}\mathrm{<span>.</span>}$$
• 
  

• This is the rescaling factor between our arbitrary K and the natural temperature unit (Hz).

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3. Practical Implications

• We don’t change SI units—we just understand that they’re rescaled.

• The "fundamental" constants are just conversion factors between our human-scale units and natural scaling.  

• They are not fundamental truths, they just exist to scale our units from natural units to the SI unit system of measurement for meter, kg, and K unit scales. 

• c,h,k are completely arbitrary and are just the different from a natural unit system of measurement where 1K = 1Hz = 1kg = 1J  and 1 meter =1 light second and the current definition of our SI unit system.

• Equations simplify in natural units because the rescaling is absorbed into the units themselves.

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4. Why This Perspective Matters

• Demystifies constants: $h$ and $k_B$ aren’t "magic"—they’re just bridges between unit systems.

• Clarifies physics: The underlying relationships (e.g., $E=hf$, $E=k_{B}T$) are what’s fundamental, not the constants’ values.

• Maintains practicality: We keep using kg and K for everyday work, but theorists can work in natural units.

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5. Final Summary

• Natural units unify mass, temperature, and frequency (1 Hzₙ = 1 kgₙ = 1 Kₙ).

• SI units rescale these for human convenience, requiring $h$ and $k_B$ to convert back.

• The constants aren’t fundamental—they’re artifacts of our unit choices.

TL;DR:

• Keep using kg and K, but recognize they’re rescaled from natural units.

• $h$ and $k_B$ are just the conversion factors—they’re not laws of nature, just unit system glue.

• The real physics is in the relationships, not the constants’ numerical values.

This is the cleanest way to reconcile practical measurements with fundamental physics.