Sunday, March 23, 2025

Unification Through Radical Simplification: A New Framework Based on Fundamental Constants

 J. Rogers, SE Ohio, 23 Mar 2025, 1748

Abstract

The quest for unification in physics has traditionally relied on complex frameworks such as string theory, extra dimensions, and new particles. In this paper, we present a radically simplified approach to unification by re-examining the role of fundamental constants—c (speed of light), h (Planck’s constant), and k (Boltzmann’s constant)—as unit scaling factors. We show that these constants encode the precise scaling needed to unify mass, energy, frequency, and temperature, revealing a deep interconnectedness in the laws of physics. This framework achieves unification without invoking speculative new dimensions or particles, offering a testable and elegant alternative to traditional approaches.

1. Introduction

The unification of physical laws has been a central goal of theoretical physics since the early 20th century. While significant progress has been made—such as the unification of electricity and magnetism into electromagnetism and the unification of electromagnetism with the weak force into the electroweak force—the integration of gravity and quantum mechanics remains elusive. Traditional approaches, such as string theory and quantum gravity, often rely on speculative ideas like extra dimensions or new particles at untestable energy scales.

In this paper, we propose a radically simplified framework for unification by focusing on the fundamental constants ch, and k. We demonstrate that these constants are not merely arbitrary numbers but encode the unit scaling factors needed to transition from human-defined SI units to natural units. By recognizing the equivalence of mass, energy, frequency, and temperature through these constants, we reveal a deep unity in the laws of physics that does not require new dimensions or particles.


2. The Role of Fundamental Constants as Unit Scaling Factors

2.1. The Speed of Light (c)

The speed of light c is traditionally understood as the maximum speed at which information can travel. However, it also serves as a unit scaling factor, converting between space (meters) and time (seconds). By setting c=1, we redefine the meter such that 1meter=1light-second. This rescaling unifies space and time, as described by special relativity, and reveals the equivalence of mass and energy through E=mc2.

2.2. Planck’s Constant (h)

Planck’s constant h relates energy to frequency via E=hf. By setting h=1, we redefine the kilogram such that 1kg=1Hz. This rescaling unifies mass and frequency, revealing the wave-particle duality of matter and energy as described by quantum mechanics.

2.3. Boltzmann’s Constant (k)

Boltzmann’s constant k relates energy to temperature via E=kT. By setting k=1, we redefine the kelvin such that 1K=1Hz. This rescaling unifies temperature and frequency, revealing the deep connection between thermodynamics and quantum mechanics.

2.4. Difference between natural units and current SI units defines the value of the constant. 

The fact that constants are the exact ratio between the meter, kg, and K unit scaling and their current definitions in the SI system of unit measure exactly determines their value. Frequency is not central, it just so happens that frequency is in the same units of measure they would have in natural units for Hz. 

3. Unification Through Equivalence

3.1. Mass, Energy, Frequency, and Temperature

The constants ch, and k encode the scaling factors needed to unify mass, energy, frequency, and temperature. By setting c=h=k=1, we establish the following equivalences:

  • E=mc2 (mass-energy equivalence),

  • E=hf (energy-frequency equivalence),

  • E=kT (energy-temperature equivalence).

  • E ~ m ~ f ~ T are all equivalences to each other by the transitive property. 

These equivalences reveal that mass, energy, frequency, and temperature are different facets of the same underlying reality, interconnected through the constants ch, and k.


3.2. Momentum, Curvature, and the Worldline

By this law of transitivity, the unification extends to other physical quantities, such as momentum (p), curvature, and the worldline ({E/c,px,py,pz}). For example:

  • Momentum is related to energy via E2=(pc)2+(mc2)2,

  • Curvature is related to mass/energy, inertia, gravity, experience of time,  via general relativity,

  • The worldline combines energy and momentum into a single geometric object.

These relationships demonstrate that the unification achieved through ch, and k is not limited to mass, energy, frequency, and temperature but extends to all physical quantities.

4. Implications for Theoretical Physics

4.1. Simplification of Physical Laws

By using natural units and recognizing the equivalence of different quantities, we can simplify physical equations and focus on the underlying physics. For example:

  • The equivalence E=mc2=hf=kT eliminates the need for explicit conversion factors,

  • The worldline {E/c,px,py,pz} provides a unified description of energy and momentum in spacetime.

4.2. Testable Predictions

Because this framework is grounded in known physics, it leads to testable predictions. For example:

  • The equivalence of temperature and frequency could be tested in systems where thermal and quantum effects are both significant,

  • The unification of mass and frequency could be explored in experiments involving wave-particle duality.

4.3. A New Paradigm for Unification

This framework suggests that unification might be achieved by focusing on the relationships between units and constants, rather than on forces, particles, or dimensions. This represents a new paradigm in theoretical physics, one that emphasizes simplicity and elegance.

5. The Historical Oversight: Constants as "Fixed Numbers" vs. Unit Scaling Factors


5.1. The Traditional View of Constants

In the traditional framework, fundamental constants such as ch, and k were treated as empirical values to be measured with increasing precision. Their numerical values were seen as fixed properties of nature, determined by experiment but lacking a deeper conceptual foundation. While these constants were acknowledged as "conversion factors" in equations (e.g., E=mc2E=hfE=kT), this role was often viewed as a mathematical convenience rather than a reflection of a fundamental principle of unit scaling and equivalence.


5.2. The Disconnect from Unit Definitions

Crucially, the traditional view did not explicitly link fundamental constants to the definitions of base units (meter, kilogram, kelvin). Constants were seen as existing "outside" or "alongside" the unit system, rather than being integral to its very foundation. This disconnect led to a missed opportunity to recognize the constants as the key to unifying physical quantities through unit scaling.


5.3. Consequences of the Oversight

The failure to interpret constants as unit scaling factors had several significant consequences:

  • Constants as "Mysterious Numbers": Without the unit scaling interpretation, fundamental constants appeared as arbitrary "magic numbers" with no clear underlying reason for their specific values in SI units.

  • Natural Units as "Just Math": The use of natural units (c=h=k=1) was often presented as a purely mathematical simplification, without connecting it to a fundamental redefinition of units or a deeper understanding of the constants' role.

  • No Motivation for Unit Redefinition: Because constants were not seen as unit scaling factors, there was no strong conceptual motivation to redefine the base units (meter, kilogram, kelvin) based on these constants. The SI system remained anthropocentric and historically based, rather than fundamentally grounded in nature's constants.

  • Obscured Path to Unification: The simple and direct path to unification through unit scaling remained obscured. Physicists pursued unification through complex and speculative means (e.g., extra dimensions, new particles), missing the simpler answer that was "hidden in plain sight" within the constants and units themselves.



6. The New Framework: Constants as Unit Scaling Factors


6.1. Constants as Unit Scaling Factors

In the new framework, fundamental constants ch, and k are explicitly identified as unit scaling factors. Their numerical values in SI units are not arbitrary but are precisely determined by the ratios between SI units and the more natural units implied by setting the constants to 1. For example:

  • c encodes the scaling needed to unify space and time (1meter=1light-second),

  • h encodes the scaling needed to unify mass and frequency (1kg=1Hz),

  • k encodes the scaling needed to unify temperature and frequency (1K=1Hz).


6.2. Constants as Keys to Unit Redefinition

By understanding constants as unit scaling factors, we can use them to redefine the base units in terms of more fundamental quantities (e.g., frequency and time). This leads to a more natural and unified unit system, where:

  • Mass, energy, frequency, and temperature are all equivalent,

  • The distinctions between these quantities arise from human-defined units, not from any intrinsic property of nature.


6.3. A Simpler Path to Unification

This framework provides a simpler and more elegant path to unification than traditional approaches. Instead of invoking speculative new dimensions or particles, it reveals the deep interconnectedness of physical laws through the natural equivalence of mass, energy, frequency, and temperature. This unification is achieved by recognizing the role of constants as unit scaling factors, which has been overlooked in the traditional framework.



7. Implications for the Future of Physics


7.1. A New Paradigm for Unification

The new framework suggests that unification might be achieved by focusing on the relationships between units and constants, rather than on forces, particles, or dimensions. This represents a new paradigm in theoretical physics, one that emphasizes simplicity and elegance.


7.2. Testable Predictions

Because this framework is grounded in known physics, it leads to testable predictions. For example:

  • The equivalence of temperature and frequency could be tested in systems where thermal and quantum effects are both significant,

  • The unification of mass and frequency could be explored in experiments involving wave-particle duality.


7.3. Educational Impact

This perspective could transform how we teach physics, making it easier for students to see the connections between different areas of the subject. By emphasizing the role of constants as unit scaling factors, we can provide a more intuitive and unified understanding of physical laws.



8. Conclusion

The traditional framework's failure to interpret fundamental constants as unit scaling factors led to a missed opportunity to unify physical quantities through a simpler and more elegant approach. By recognizing ch, and k as the keys to unit scaling and redefinition, we reveal a deep interconnectedness in the laws of physics that does not require new dimensions or particles. This framework provides a testable and elegant alternative to traditional approaches, offering new insights into the unification of physical laws.


References

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

  2. Planck, M. (1900). "On the Theory of the Energy Distribution Law of the Normal Spectrum." Annalen der Physik.

  3. 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.

  4. Dirac, P. A. M. (1928). "The Quantum Theory of the Electron." Proceedings of the Royal Society A.

  5. Weinberg, S. (1967). "A Model of Leptons." Physical Review Letters.

No comments:

Post a Comment