Reframing Fundamental Constants: A New Perspective on Energy, Wavelength, and Relativity

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." - Max Planck

Abstract: This paper introduces a novel framework for understanding fundamental constants, especially Planck's constant (h), as an encoding of simpler physical relationships. By reinterpreting constants as products of unit systems, we demonstrate a fresh perspective on the linkage between energy, wavelength, and relativistic effects. This approach suggests that complexities in quantum mechanics and relativity may stem more from unit choices than from fundamental mysteries in nature.

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1. Introduction

The relationship between quantum mechanics and relativity has traditionally relied on a series of fundamental constants, notably Planck’s constant (h). This paper suggests that many constants, including h, may be understood as unit-derived quantities encoding simpler, fundamental relationships. This approach demystifies physical constants and offers a new perspective on the connection between energy, wavelength, and time dilation, paving the way for a geometric interpretation of quantum and relativistic phenomena.

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2. Simple Encoding Using Division and Multiplication

Before discussing physical constants, we introduce a basic encoding-decoding method that shows how division by a constant (c) creates an encoded value that can be reversed simply by multiplication, obscuring the original values.

2.1 Encoding Process

Using an arbitrary value (1234567), we encode it with a constant $c$:

$$h = \frac{1234567}{c}$$

where:

• 1234567 is the original number,
• $c$ is the chosen constant (e.g., 3 for simplicity),
• $h$ is the result of the division.

Calculation:

$$h = \frac{1234567}{3} = 411522.3333\ldots$$

2.2 Decoding Process

To retrieve the original number:

$$\text{Original number}=h\times c=411522.3333\dots \times 3=1234567$$

2.3 Observations

The encoded value $h$ appears independent of the original number, providing a simple form of reversible "hiding." This example will guide our discussion of constants like $h$ and $c$, illustrating that these may encode more basic relationships.

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3. Demystifying Planck’s Constant

3.1 The Relationship $h = \frac{K}{c}$

We hypothesize that Planck's constant $h$ can be expressed as a relationship between another constant $K$ and the speed of light $c$:

$$h=\frac{K}{\mathrm{c}}$$

where $K$ is a constant with units of energy times length, implying that $h$ encodes a unit-derived relationship rather than a standalone fundamental constant.

3.2 Defining $K$ as a Unit Scaling Factor

Using $\times 10^{-25}$ J m and $c$ m/s, we show:

$$h = (1.98644568 × 10−25 J m) / (299,792,458 m/s)h = 6.62607015 × 10−34 J s$$

By redefining $K=1$ J m, we could change our units such that $h$ and K become unit artifacts rather than fundamental mysteries.

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4. Redefining Units to Expose the Fundamental Relationship

You may be tempted to think that h was not fundamental, but K was the fundamental relationship, but this is not true either. K itself is simply a scaling factor for the way we define our units for m and energy. We can do a thought experiment to show this is true.

4.1 Setting $K=1$ J·m as a Thought Experiment

Defining $K$ as 1 J·m, we redefine the speed of light and the meter:

$$\frac{\mathrm{c=K/h<br><br>Which\; makes\; the\; value\; for\; speed\; of\; light\; huge\; and\; the\; unit\; for\; meter\; very\; small.\; This\; does\; not\; actually\; change\; the\; speed\; of\; light,\; just\; the\; units\; that\; measure\; it. \; These\; values\; would\; be\; unworkable\; in\; day\; to\; day\; use,\; but\; they\; are\; a\; valid\; way\; to\; look\; at\; them\; as\; a\; thought\; experiment\; that\; is\; mathematically\; sound.<br>}}{}$$

In these new units:

4.2 Energy as the Inverse of Wavelength

This unit choice clarifies that energy ($E$) relates directly to the inverse of wavelength ($\lambda$):

$$E=\frac{1\text{J}\text{m/}}{\mathrm{\lambda }}$$

$$\frac{\mathrm{<br>or\; more\; generally}}{}$$

This reveals that the energy-wavelength relationship is fundamentally a geometric property, with $h$ and $c$ merely scaling factors based on the units we’ve chosen.  So we can replace hc with just K with the understanding that K is just unit scaling, it is not special or fundamental in any way.

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5. Linking Wavelength and Time Dilation in Relativity

5.1 Wavelength as a Measure of Time Dilation

In this framework, the wavelength of a particle can reflect time dilation. Particles with shorter wavelengths (higher energy) experience different time dilation effects, linking energy to relativistic effects. The shortening of the wavelength is the effect of time dilation on that length. And different observers will see this wavelength differently from their frame of reference.  

5.2 Energy as a Reflection of Time Dilation

This perspective allows us to interpret energy not just as a scalar quantity, but as a geometric factor related to time dilation, offering a bridge between quantum and relativistic descriptions. Because the wavelength depends on your point of view the energy will can depending on how you observe it.

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6. Unification of Key Concepts

This framework enables a unified view of:

• Wave-Particle Duality in quantum mechanics,
• Energy-Frequency Relation as a geometric feature,
• Time Dilation and Length Contraction as direct consequences of relative motion,
• Mass-Energy Equivalence through curvature, reinterpreting mass and gravity as manifestations of spacetime geometry.

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7. Conclusion

Our reinterpretation of physical constants suggests that many aspects of quantum mechanics and relativity might be reflections of the unit systems and measurement choices rather than intrinsic properties of nature. By exposing the geometric relationship between energy and wavelength, this approach encourages a simplified and unified view of quantum and relativistic phenomena, potentially transforming our understanding of physical constants as byproducts of measurement rather than fundamental mysteries.