A New Constant: K_kg — Converting Temperature to Mass

J. Rogers, SE Ohio, 09 Mar 2025, 0519

Abstract

This report introduces a new fundamental constant, ${\text{K}}_{\text{kg}}$,  which directly converts temperature ($T$) to mass ($m$). This constant is derived from a modular scaling framework that unifies mass, frequency, and temperature into a single, coherent system. The existence of ${\text{K}}_{\text{kg}}$ is supported by the well-established relationships $E=kT$ (temperature to energy) and $E=m{c}^2$ (energy to mass), but it makes the implicit connection between temperature and mass explicit and modular. This report explores the derivation, significance, and implications of ${\text{K}}_{\text{kg}}$ for theoretical and experimental physics.

K_kg = 1.53617919e-40 kg/K

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1. Introduction

The laws of physics are built on fundamental constants that define the relationships between physical quantities. Constants like Planck’s constant ($h$), the Boltzmann constant ($k$), and the speed of light ($c$) are cornerstones of modern physics. However, the relationship between temperature and mass has remained implicit, relying on intermediate steps involving energy. This report introduces a new constant, ${\text{K}}_{\text{kg}}$, which directly connects temperature to mass, completing a unified framework for scaling between mass, frequency, and temperature.

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2. Isolating the factor of ${\text{K}}_{\text{kg}}$

2.1 Existing Relationships

The relationship between temperature and mass can be derived from two well-known equations:

1. Temperature to Energy:

   $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">,</span>$$

   where $k$ is the Boltzmann constant and $T$ is temperature.

2. 
   

3. Energy to Mass:

   $$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">,</span>$$

   where $m$ is mass and $c$ is the speed of light.

Combining these equations gives the implicit relationship between temperature and mass:

$$\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

2.2 Introducing ${\text{K}}_{\text{kg}}$

To make this relationship explicit, we define a new constant, ${\text{K}}_{\text{kg}}$, as:

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

This allows us to write the temperature-to-mass conversion as:

$$\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">K</span>}}_{\text{<span style="background-color: white;">kg</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

2.3 Connection to Modular Scaling Factors

The new constant ${\text{K}}_{\text{kg}}$ is part of a larger modular scaling framework that includes:

• ${\text{Hz}}_{\text{kg}}$: Converts frequency ($f$) to mass ($m$).

• ${\text{K}}_{\text{Hz}}$: Converts temperature ($T$) to frequency ($f$).

The relationship between these constants is:

$${\text{<span style="background-color: white;">K</span>}}_{\text{<span style="background-color: white;">kg</span>}}<span\; style="background-color:\; white;">=</span>{\text{<span style="background-color: white;">K</span>}}_{\text{<span style="background-color: white;">Hz</span>}}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">Hz</span>}}_{\text{<span style="background-color: white;">kg</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

This completes the triad of scaling factors, allowing seamless conversion between mass, frequency, and temperature.

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3. Significance of ${\text{K}}_{\text{kg}}$

3.1 Modularity and Clarity

The introduction of ${\text{K}}_{\text{kg}}$ modularizes the relationship between temperature and mass, making it explicit and easy to use. This simplifies calculations and provides a clearer understanding of the physics.

3.2 Unification of Scaling Factors

${\text{K}}_{\text{kg}}$

Kkg​ completes the set of scaling factors in the framework, allowing for a unified treatment of mass, frequency, and temperature. This provides a coherent, modular system for understanding physical laws.

3.3 New Theoretical Tools

${\text{K}}_{\text{kg}}$

Kkg​ provides a new tool for analyzing systems where temperature and mass are directly related. This could lead to new theoretical models and predictions in areas like thermodynamics, particle physics, and cosmology.

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4. Implications for Physics

4.1 Experimental Verification

While the relationship $m=\frac{kT}{c^2}$ is already well-established, the explicit representation of ${\text{K}}_{\text{kg}}$ could inspire new experiments to explore the direct relationship between temperature and mass. High-precision measurements of thermal systems could be used to test the validity of ${\text{K}}_{\text{kg}}$.

4.2 Applications in Thermodynamics

${\text{K}}_{\text{kg}}$

Kkg​ could be used to analyze systems where temperature and mass are directly related, such as in blackbody radiation or particle physics. For example, it could provide new insights into the thermal properties of particles or the mass-energy equivalence in thermal systems.

4.3 Teaching and Communication

The explicit representation of ${\text{K}}_{\text{kg}}$ makes the relationship between temperature and mass more intuitive and easier to understand. This could revolutionize how these concepts are taught and communicated.

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5. Conclusion

The introduction of ${\text{K}}_{\text{kg}}$ is a completes the trio of new individual scaling units isolated from the constants. It makes the implicit relationship between temperature and mass explicit and modular, providing a clearer and more intuitive understanding of the physics. 

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6. Future Work

1. 
   

2. Experimental Testing:

   • Design experiments to measure the direct relationship between temperature and mass using ${\text{K}}_{\text{kg}}$.

3. Theoretical Development:

   • Explore the implications of ${\text{K}}_{\text{kg}}$ in areas like thermodynamics, particle physics, and cosmology.

4. Educational Outreach:

   • Develop teaching materials to introduce ${\text{K}}_{\text{kg}}$ and the modular scaling framework to students and researchers.

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References

• Einstein, A. (1905). "On the Electrodynamics of Moving Bodies." Annalen der Physik.

• Planck, M. (1901). "On the Law of Distribution of Energy in the Normal Spectrum." Annalen der Physik.

• Boltzmann, L. (1877). "On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium." Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften.