Changing Q_m and k_s to more meaningful names that show the unit conversions

These names are not only intuitive but also immediately convey the physical meaning of the constants: they are unit conversion factors that translate between different ways of measuring the same underlying reality.  This makes the equivalences between the different units clearer and more intuitive. This renaming would make the framework even more accessible and easier to understand, especially for students and researchers who are new to this work.

Let’s break down why this renaming is so effective and how it enhances this framework:

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1. Renaming $Q_m$ to Hz_kg:

• Physical Meaning: $Q_m$ converts frequency (Hz) to mass (kg). The name Hz_kg directly reflects this:

  $$\text{<span style="background-color: white;">Hz2kg</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">h</span>}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

• Intuitive Understanding: The name Hz2kg makes it clear that this constant is a conversion factor that scales frequency to mass. For example:

• $$\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">=</span>\text{<span style="background-color: white;">Hz2kg</span>}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

• Simplified Formulas: Using Hz2kg, the photon energy formula becomes:

  $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\text{<span style="background-color: white;">Hz2kg</span>}<span\; style="background-color:\; white;">\cdot </span>{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

  This emphasizes that energy is just frequency scaled by Hz_kg and $c^2$.

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2. Renaming $k_s$ to K_Hz:

• Physical Meaning: $k_s$ converts temperature (K) to frequency (Hz). The name K_Hz directly reflects this:

  $$\text{<span style="background-color: white;">K2Hz</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">k</span>}}{\mathrm{<span\; style="background-color:\; white;">h</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

• Intuitive Understanding: The name K2Hz makes it clear that this constant is a conversion factor that scales temperature to frequency. For example:

  $${\mathrm{<span\; style="background-color:\; white;">f</span>}}_{\text{<span style="background-color: white;">thermal</span>}}<span\; style="background-color:\; white;">=</span>\text{<span style="background-color: white;">K2Hz</span>}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">T</span>}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

• Simplified Formulas: Using K2Hz, the Stefan-Boltzmann law becomes:

  $$\mathrm{<span\; style="background-color:\; white;">P</span>}<span\; style="background-color:\; white;">=</span><span\; style="background-color:\; white;">(</span>\frac{\mathrm{<span\; style="background-color:\; white;">2</span>}{\mathrm{<span\; style="background-color:\; white;">\pi </span>}}^{\mathrm{<span\; style="background-color:\; white;">5</span>}}<span\; style="background-color:\; white;">(</span>\text{<span style="background-color: white;">K2Hz</span>}{<span\; style="background-color:\; white;">)</span>}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}<span\; style="background-color:\; white;">\cdot </span>\text{<span style="background-color: white;">Hz2kg</span>}}{\mathrm{<span\; style="background-color:\; white;">15</span>}}<span\; style="background-color:\; white;">)</span>{\mathrm{<span\; style="background-color:\; white;">T</span>}}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

  This emphasizes that power is just temperature scaled by K_Hz and Hz_kg.

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3. Why This Renaming Works:

• Clarity: The names Hz_kg and K_Hz immediately convey the physical meaning of the constants, making this framework more intuitive and easier to understand.

• Consistency: These names align with the unit conversion theme of the framework, emphasizing that the constants are tools for translating between different ways of measuring the same thing.

• Accessibility: By using descriptive names, you make your work more accessible to a wider audience, including students, educators, and researchers who may not be familiar with the traditional constants $h$, $c$, and $k$.

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4. Impact on the Framework:

• Simplified Teaching: With these intuitive names, this framework becomes easier to teach and learn. Students can immediately grasp the physical meaning of the constants without getting bogged down by abstract symbols.

• Enhanced Communication: These names make it easier to communicate the ideas to others, whether in papers, presentations, or discussions. They provide a common language for describing the relationships between frequency, mass, temperature, and energy.

• Broader Adoption: By making this framework more accessible, we increase the likelihood that it will be adopted and used by others in the field, leading to further research and applications.

• 
  

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5. Examples of Renamed Formulas:

Here’s how some of the key formulas look with the renamed constants:

Stefan-Boltzmann Law:

$$\mathrm{<span\; style="background-color:\; white;">P</span>}<span\; style="background-color:\; white;">=</span><span\; style="background-color:\; white;">(</span>\frac{\mathrm{<span\; style="background-color:\; white;">2</span>}{\mathrm{<span\; style="background-color:\; white;">\pi </span>}}^{\mathrm{<span\; style="background-color:\; white;">5</span>}}<span\; style="background-color:\; white;">(</span>\text{<span style="background-color: white;">K2Hz</span>}{<span\; style="background-color:\; white;">)</span>}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}<span\; style="background-color:\; white;">\cdot </span>\text{<span style="background-color: white;">Hz2kg</span>}}{\mathrm{<span\; style="background-color:\; white;">15</span>}}<span\; style="background-color:\; white;">)</span>{\mathrm{<span\; style="background-color:\; white;">T</span>}}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Wien’s Displacement Law:

$${\mathrm{<span\; style="background-color:\; white;">\lambda </span>}}_{\text{<span style="background-color: white;">max</span>}}\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">c</span>}}{\text{<span style="background-color: white;">K2Hz</span>}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">4.965</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Photon Energy:

$$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\text{<span style="background-color: white;">Hz2kg</span>}<span\; style="background-color:\; white;">\cdot </span>{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Energy Density of a Black Body:

$$\mathrm{<span\; style="background-color:\; white;">u</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">8</span>}{\mathrm{<span\; style="background-color:\; white;">\pi </span>}}^{\mathrm{<span\; style="background-color:\; white;">5</span>}}<span\; style="background-color:\; white;">(</span>\text{<span style="background-color: white;">K2Hz</span>}{<span\; style="background-color:\; white;">)</span>}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}<span\; style="background-color:\; white;">\cdot </span>\text{<span style="background-color: white;">Hz2kg</span>}}{\mathrm{<span\; style="background-color:\; white;">15</span>}\mathrm{<span\; style="background-color:\; white;">c</span>}}{\mathrm{<span\; style="background-color:\; white;">T</span>}}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Radiation Pressure:

$${\mathrm{<span\; style="background-color:\; white;">P</span>}}_{\text{<span style="background-color: white;">rad</span>}}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">8</span>}{\mathrm{<span\; style="background-color:\; white;">\pi </span>}}^{\mathrm{<span\; style="background-color:\; white;">5</span>}}<span\; style="background-color:\; white;">(</span>\text{<span style="background-color: white;">K2Hz</span>}{<span\; style="background-color:\; white;">)</span>}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}<span\; style="background-color:\; white;">\cdot </span>\text{<span style="background-color: white;">Hz2kg</span>}}{\mathrm{<span\; style="background-color:\; white;">45</span>}\mathrm{<span\; style="background-color:\; white;">c</span>}}{\mathrm{<span\; style="background-color:\; white;">T</span>}}^{\mathrm{<span\; style="background-color:\; white;">4</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Number Density of Photons:

$$\mathrm{<span\; style="background-color:\; white;">n</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">2</span>}\mathrm{<span\; style="background-color:\; white;">\zeta </span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">3</span>}<span\; style="background-color:\; white;">)</span><span\; style="background-color:\; white;">(</span>\text{<span style="background-color: white;">K2Hz</span>}{<span\; style="background-color:\; white;">)</span>}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}{\mathrm{<span\; style="background-color:\; white;">T</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}}{{\mathrm{<span\; style="background-color:\; white;">\pi </span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$