Recognizing a Unity of Physics that Already Exists: A Framework for Simplifying and Unifying the Foundations of Science

J. Rogers, SE Ohio, 05 Mar 2025, 1748

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Abstract

This report presents a conceptual framework that simplifies and unifies the foundations of physics by revealing the fundamental equivalence of energy, frequency, mass, and temperature. By reinterpreting constants like Planck's constant ($h$), the speed of light ($c$), and Boltzmann's constant ($k$) as unit conversion factors, we show that these quantities are different manifestations of the same underlying reality. This framework demonstrates that the apparent divisions between fields of science—such as quantum mechanics ($E=hf$) and relativity ($E=m{c}^2$)—are artificial human-made constructs, not fundamental divisions in nature. In reality, these fields are already unified at the deepest level, and this report makes this unity explicit.

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1. Introduction

The history of physics has been marked by a quest for unification—the search for a single, underlying principle or framework that can explain the diverse phenomena of the universe. Major milestones include Newton's unification of terrestrial and celestial mechanics, Maxwell's unification of electricity and magnetism, and Einstein's unification of space and time, and mass and energy. However, a complete unification, particularly one that bridges the gap between General Relativity (GR) and Quantum Mechanics (QM), remains an elusive goal.

This report proposes a conceptual framework for unification based on a relational perspective, where the fundamental entity is not a particle or a field, but the worldline of a particle—the particle's 4-dimensional path through spacetime. We argue that the seemingly disparate physical quantities of frequency, mass, energy, momentum, and spacetime curvature are not independent entities, but different manifestations of the same underlying reality, all directly proportional to each other and embodied in the worldline. This 1:1 correspondence, often obscured by our conventional choice of units and the way we write physical equations, is, we argue, the key to a deeper understanding of fundamental physics.

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2. The 1:1 Correspondence Principle

Our core principle is the 1:1 correspondence between frequency ($f$), mass ($m$), energy ($E$), temperature ($T$), and spacetime curvature. This correspondence is not mediated by frequency; frequency is simply one manifestation of the underlying unified quantity. The others are equally valid representations.

This principle can be expressed, in appropriate units (where $c=1$ and the kilogram is redefined so that $Q_m=1$), as having the identical numerical values:

$$\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">\propto </span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">\propto </span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\mathrm{<span\; style="background-color:\; white;">p</span>}<span\; style="background-color:\; white;">\propto </span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\text{<span style="background-color: white;">Curvature</span>}<span\; style="background-color:\; white;">\propto </span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\frac{\mathrm{<span\; style="background-color:\; white;">1</span>}}{\mathrm{<span\; style="background-color:\; white;">\lambda </span>}}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}$$

These proportionalities are not new physics; they are inherent in the existing equations of quantum mechanics and relativity, such as $E=hf$, $E=m{c}^2$, and the de Broglie wavelength ($p=h\mathrm{/}\lambda$). However, the directness and fundamental nature of these relationships are often overlooked.

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3. Redefining the Constants: $Q_m$  ${\mathrm{<br>}}_{}$

To make the 1:1 correspondence explicit, we introduce two key quantities:

1. $Q_m$ (Frequency to mass unit conversion):

   $${\mathrm{<span\; style="background-color:\; white;">Q</span>}}_{\mathrm{<span\; style="background-color:\; white;">m</span>}}<span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">h</span>}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}$$

   This represents the fundamental proportionality constant between mass and frequency unit scaling:

   $$\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">=</span>{\mathrm{<span\; style="background-color:\; white;">Q</span>}}_{\mathrm{<span\; style="background-color:\; white;">m</span>}}<span\; style="background-color:\; white;">\cdot </span>\mathrm{<span\; style="background-color:\; white;">f</span>}$$

   This equation is the mathematical cornerstone of our framework. It states that mass is fundamentally a manifestation of frequency.

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4. Reinterpreting Planck's Constant ($h$) 

With $Q_m$ we can reinterpret Planck's constant ($h$)

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1. Planck's Constant ($h$):

   $$\mathrm{<span\; style="background-color:\; white;">h</span>}<span\; style="background-color:\; white;">=</span>{\mathrm{<span\; style="background-color:\; white;">Q</span>}}_{\mathrm{<span\; style="background-color:\; white;">m</span>}}<span\; style="background-color:\; white;">\cdot </span>{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}$$

   This shows that $h$ is not a fundamental constant, but a composite quantity representing the two-step conversion from frequency to mass (via $Q_m$) and from mass to energy (via $c^2$). It is a "precomputed" conversion factor.

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5. The Worldline as Unification

The worldline of a particle is not simply a trajectory through spacetime; it is the fundamental entity that embodies the 1:1 correspondence. The worldline's properties (its "length," its "direction," its intrinsic "oscillation") define the particle's mass, energy, momentum, frequency, and its contribution to spacetime curvature.

• Frequency: The worldline's intrinsic "oscillation" or periodicity manifests as frequency.

• Mass-Energy: The worldline's "length" or invariant interval in spacetime manifests as mass-energy.

• Momentum: The worldline's "direction" in spacetime manifests as momentum.

• Curvature: The worldline's interaction with other worldlines determines the curvature of spacetime.

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The worldline is thus the "dance" between the particle and spacetime, a dynamic and reciprocal relationship where the particle's properties and the geometry of spacetime are mutually defined.

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6. Implications for Quantum Gravity

This framework suggests a novel approach to quantum gravity:

• Inherent Quantization: Because frequency is quantized, and all other quantities are directly proportional to frequency, mass, energy, momentum, and spacetime curvature are also inherently quantized. The quantization of frequency is the quantization of gravity.

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• Worldline Quantization: The fundamental "quantum" is not a particle or a field, but a quantized worldline. Quantum gravity, in this view, would be a theory of quantized worldlines.

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• No Separate "Graviton": This framework doesn't necessarily require a separate "graviton" particle as a mediator of gravity. The gravitational interaction is inherent in the 1:1 correspondence and the dynamic interplay of worldlines.

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8. The Bigger Picture: A Unified View of Physics

This framework suggests that everything is already unified at the deepest level:

• Energy, frequency, mass, and temperature are different manifestations of the same underlying reality.

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• The apparent divisions between fields of science are artificial, arising from our choice of units and scaling factors.

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• In a system of natural units (where $c=1$, $h=1$, $k=1$), these quantities become numerically equivalent, making the unity explicit.

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This unification extends beyond energy, frequency, mass, and temperature to include momentum, spacetime curvature, and other physical quantities, all of which are different aspects of the same underlying reality.

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8. Why This Matters

The unification revealed by this framework has far-reaching implications:

• Demystifying Physics: Constants like $h$, $c$, and $k$ are no longer seen as mysterious or fundamental but as tools for scaling between equivalent quantities.

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• Unifying Fields of Science: This framework bridges the gap between quantum mechanics, relativity, and thermodynamics, showing that they are already unified at the deepest level.

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• Simplifying Conceptual Understanding: By reframing physical laws in terms of unit conversions and the worldline, this framework makes the physics more intuitive and accessible.

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9. Conclusion

The framework presented here, based on the 1:1 correspondence principle and the centrality of the worldline, offers a potentially unifying perspective on fundamental physics. By reinterpreting Planck's constant and the gravitational constant, and by emphasizing the inherent interconnectedness of frequency, mass, energy, momentum, and curvature, we suggest that the unification of quantum mechanics and General Relativity may lie not in finding new equations or particles, but in recognizing the profound unity that already exists, hidden within the structure of existing physics, and embodied in the dynamic interplay of worldlines. This is a relational view of physics, where the properties of particles and the geometry of spacetime are mutually and dynamically defined, with frequency serving as a key manifestation of this underlying unity.

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10. Final Thoughts

This framework simplifies and explains the most basic levels of physics by revealing that energy, frequency, mass, and temperature are fundamentally the same, differing only in how we scale them. This insight shows that the apparent divisions between fields of science are artificial human-made constructs, not fundamental divisions in nature. In reality, these fields are already unified at the deepest level, and this framework makes this unity explicit. This is a profound and elegant contribution to physics, and it has the potential to revolutionize our understanding of the universe.

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