J. Rogers, SE Ohio, March 9, 2025, 2018
Fundamental constants like Planck’s constant (h) and Boltzmann’s constant (k) are traditionally viewed as intrinsic properties of the universe. However, this paper argues that these constants are not fundamental but rather encoding mechanisms for natural unit scaling factors. By decomposing h and k into their constituent scaling factors – K_Hz, Hz_kg, and kg_J – we reveal a hidden E=mc² pattern embedded within these constants.
This perspective provides a clearer, more unified understanding of the relationships between mass, frequency, temperature, and energy, and demonstrates that these quantities are fundamentally equivalent, differing only in the units we use to describe them. This framework illuminates the deep connection between our human-defined unit systems and the natural scaling of the universe.
1.
For over a century, constants like the speed of light (c), Planck's constant (h), and Boltzmann's constant (k) have been treated as fundamental properties of the universe, bridging seemingly distinct domains of physics such as relativity, quantum mechanics, and thermodynamics. However, this paper proposes a shift in perspective: these constants are not fundamental but rather unit conversion factors that arise because our human-defined units (e.g., kilograms, meters, kelvins) are mismatched with the natural scale of frequency.
By decomposing h and k into their constituent natural unit scaling factors, we reveal a deeper unity in physics and show that mass, frequency, temperature, and energy are fundamentally equivalent, differing only in the units we use to describe them. Furthermore, we demonstrate that the mass-energy equivalence expressed by E=mc² plays a central role in these scaling relationships.
2.
In the natural framework of the universe, physical quantities like mass, frequency, and temperature are fundamentally equivalent, scaling 1:1 with each other. However, our human-defined units (e.g., kilograms, meters, seconds, kelvins) are not aligned with this natural scaling, necessitating the use of constants like c, h, and k to reconcile the differences. These constants can be decomposed into natural unit scaling factors that explicitly account for the mismatched scaling of human-defined units.
2.1
The speed of light encodes the mass-to-energy conversion factor (kg_J):
c² = kg_J
This factor arises because our mass units (kilograms) are mismatched with the natural scale of energy. The kg_J factor has units of J/kg, or m²/s² , which is c².
2.2
Planck's constant encodes the frequency-to-energy conversion factor (Hz_J):
h = Hz_J
This factor arises because our energy units (Joules) are mismatched with the natural scale of frequency.
2.3
Boltzmann's constant encodes the temperature-to-energy conversion factor (K_J):
k = K_J
This factor arises because our temperature units (Kelvin) are mismatched with the natural scale of energy.
It’s important to note that frequency is not inherently more fundamental than other quantities like mass or temperature. In natural units, all these quantities are equally fundamental and scale 1:1 with each other. Frequency is often used as a reference because it aligns with the time scale we use for seconds, which is already normalized to 1 in natural units (s = 1). However, this does not make frequency special—it simply reflects the fact that time is one of the base dimensions in our unit systems.
3.
The constants h and k are not fundamental but composite constants built from individual natural unit scaling factors. By decomposing these constants, we reveal the fundamental unity of physical quantities and the underlying role of mass-energy equivalence.
3.1
Planck's constant can be decomposed as:
h = Hz_kg ⋅ kg_J
Where:
Hz_kg: Converts frequency to mass.
kg_J: Converts mass to energy (kg_J = c²).
This decomposition shows that h is not a fundamental property of the universe but a unit conversion factor that arises because our mass and energy units are mismatched with the natural scale of frequency. The value of h can be thought of as the product of converting frequency to an equivalent mass and then applying the mass-energy equivalence through the kg_J = c² scaling factor.
3.2
Boltzmann's constant can be decomposed as:
k = K_Hz ⋅ Hz_kg ⋅ kg_J
Where:
K_Hz: Converts temperature to frequency.
Hz_kg: Converts frequency to mass.
kg_J: Converts mass to energy (kg_J = c²).
This decomposition shows that k is not a fundamental property of the universe but a unit conversion factor that arises because our temperature, mass, and energy units are mismatched with the natural scale of frequency. Like Planck's constant, Boltzmann's constant also embodies the mass-energy equivalence, but here, temperature is first scaled to a frequency, which is then scaled to a mass, and finally, the mass is scaled to energy via E=mc².
4.
The presence of the kg_J = c² scaling factor in both h and k highlights the central role of the mass-energy equivalence relationship in linking frequency, temperature, and energy. Rogers' framework suggests that h and k and our SI units are fundamentally unified through the inter-convertibility of frequency, mass, temperature, and energy, a unity expressed through E=mc².
4.1
The Hz_kg factor is a scaling factor that allows us to express frequency as a mass-equivalent. Because frequency has units of inverse seconds (s⁻¹) and mass has units of kilograms (kg), Hz_kg must have units of kg⋅s to properly convert between them.
Similarly, K_Hz is a scaling factor that allows us to express temperature as an equivalent frequency. Because temperature has units of Kelvin (K) and frequency has units of inverse seconds (s⁻¹), K_Hz must have units of s⁻¹⋅K⁻¹ to properly convert between them.
5.
The decomposition of h and k into natural unit scaling factors has profound implications for our understanding of physics.
5.1
By isolating the natural unit scaling factors, we reveal that mass, frequency, temperature, and energy are fundamentally equivalent, differing only in the units we use to describe them. This provides a unified understanding of physics, showing that relativity, quantum mechanics, and thermodynamics are not separate domains but different expressions of the same fundamental relationships.
5.2
In a natural unit system, where these scaling factors are set to unity, many equations become simpler and more intuitive. For example, Planck’s Law in natural units becomes:
B(f,T) = 2 f³/ (e^(f/T) - 1)
where f and T are already scaled to unity.
However, when expressed in SI units, Planck's Law requires the scaling factors for frequency and temperature, demonstrating how close this framework is to a true natural unit system:
B(f,T) = 2 f³ Hz_kg / (e^(f/(T K_Hz)) - 1)
Here, f must be scaled by Hz_kg (from natural unit for frequency to kg units) and T must be scaled by K_Hz (from Temperature to the natural units of frequency). The need for only these two simple specific scaling factors highlights that this framework is just one small step away from achieving a fully natural unit system. Setting these 2 factors to unity would put the entire formula into natural units.
5.3
This framework shows that constants like h, k, and c are not fundamental properties of the universe but unit conversion factors that arise from our choice of units. The values they carry are the scaling of those units required for natural units. The units they carry highlight the simple unit scaling they are doing from one unit system to another. This demystifies physics and makes it more accessible and intuitive.
6. Conclusion
The constants c, h, and k are not fundamental properties of the universe but encoding mechanisms for the natural unit scaling factors. By decomposing h and k into their constituent scaling factors – K_Hz, Hz_kg, and kg_J – we reveal the critical presence of the E=mc² relationship. These constants arise from the mismatch between human-defined units and the natural scale of frequency. This perspective provides a clearer, more unified understanding of the relationships between mass, frequency, temperature, and energy, and demonstrates that these quantities are fundamentally equivalent, differing only in the units we use to describe them. These relationships are not arbitrary, but rather an expression of the underlying unity of nature that reveals how the human-defined unit system relates to the natural unit system.
This insight has the potential to transform how we teach, communicate, and research physics, making it more accessible, intuitive, and collaborative. It’s a reminder that simplicity and clarity are often the keys to deeper understanding and that preserving the physical meaning of formulas is just as important as their mathematical elegance. This framework also provides a new perspective on the connection between seemingly separate areas of physics by directly linking Relativity, Quantum Mechanics, and Thermodynamics through the E=mc² scaling factor.
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