Physics' Best-Kept Secret: The Constants of Nature Are Human Inventions

 J. Rogers, SE Ohio

Introduction: The Paradox of Our Cosmic Ruler

How can the universal laws of physics, which operate with unerring precision across the cosmos, function perfectly using units like the meter and the kilogram—measurements that are completely arbitrary and human-invented? This question points to a fundamental paradox that sits at the heart of physics: our most profound descriptions of reality seem to be built on a foundation of historical accident and human convenience.

This paradox is solved by the "Three Worlds of Physics" framework, which reveals the complexity is not in reality itself, but in the "distorted map" we use to describe it. By separating the universe from our description of it, a clearer picture emerges, revealing that many of the things we thought were fundamental discoveries are, in fact, human inventions.

This article will explore the four most surprising takeaways from this framework—four mind-bending ideas that will change how you think about physical reality.

1. The Constants of Nature Aren't Discoveries—They're Inventions

The most challenging idea comes first: fundamental physical constants like the speed of light (c) and the gravitational constant (G) are not inherent, fundamental numbers of the universe that we discovered. They are inventions. More precisely, they are the necessary mathematical consequences of our decision to describe a unified reality with a fragmented set of tools.

They function as "admissions of our map's flaws." We created a measurement system—the familiar SI chart of meters, kilograms, and seconds—where we incorrectly assumed that Length, Mass, and Time were independent and orthogonal concepts. But reality forced us to see that they are deeply connected. Constants were invented as mathematical "patches" to fix the disconnects our flawed map created. The speed of light, c, is the patch that connects our separate ideas of Length and Time. The gravitational constant, G, is the patch that fixes our incorrect assumption that Mass-Energy is independent of the geometry of Spacetime.

"...physical constants are not fundamental numbers of nature, but rather artifacts of our chosen measurement system—operators that scale and rotate our distorted human measurements to align with an underlying, unified reality."

This is deeply counter-intuitive. We are taught to see constants as unchanging truths etched into the fabric of the cosmos. This new view reframes them as tools we built to correct our own limited perspective.

2. Physical Constants Are a "Translation Key" for Reality

If constants are patches for our flawed map, then they must function as a kind of translation key—a mathematical lens to correct our distorted view of the universe. The formal term for these operators is Planck Jacobians.

Think of our system of SI units as a distorted Mercator map of the globe. A Mercator map is useful for navigation, but it fundamentally misrepresents the planet's geometry, making Greenland look as large as Africa. Our measurement system is similarly useful, but it misrepresents the unified nature of reality by treating concepts like Mass, Length, and Time as separate.

Physical constants are the mathematical formulas that "un-distort" our measurements. They scale and rotate them to align with the true "globe" of physics, where everything is unified.

A concrete example of this is the operation v/c (an object's velocity divided by the speed of light). This isn't just a calculation; it's the physical act of taking a velocity measured on our human-scaled chart (in meters per second) and rotating it into the true, dimensionless velocity that exists in fundamental reality.

This implies that the numerical value of a constant—like c = 299,792,458 m/s—has no fundamental meaning on its own. It is just the specific "correction factor" required for our specific, arbitrary map of meters and seconds. If we had chosen different units, the number for c would be completely different.

3. There Is a Universal Recipe for Creating Any Constant

If constants are inventions, there must be a way to create them. This framework provides a simple, universal, two-step algorithm to construct any physical constant from scratch. They are not found through painstaking experiment; they are "algorithmically generated" to fix our math.

Here is the algorithm, simplified:

• Step 1: Find the Mismatch. Start with a physical law, like Newton's law of gravity (F ∝ m1*m2 / r²). Check if the units on both sides of the equation balance out using our SI system. In this case, they don't. The units for Force ([M][L][T]⁻²) do not match the units for mass squared over distance squared ([M]²[L]⁻²). This mismatch means you need a "dimensional patch"—a constant.
• Step 2: Build the Patch. The required dimensions of the patch become an explicit recipe. For gravity, the patch needs units of [L]³[M]⁻¹[T]⁻² to make the equation work. To build the actual constant, you simply plug in the fundamental "building blocks" of reality—the Planck units (l_P, m_P, t_P)—raised to the powers determined by the recipe.

This reveals a stunning truth: all physical constants, from G to the Coulomb constant, are built from the exact same three 'Lego bricks'—the Planck units—arranged in different combinations. This isn't just an abstract formula; it's a literal blueprint. The recipe l_P³ / (m_P * t_P²) is the Gravitational Constant, G.

"To construct any physical constant: identify the dimensional mismatch in a physical law, then raise the fundamental Planck units to the compensating powers. That is the constant. Every time."

This powerful algorithm works for any constant in physics, transforming them from mysterious cosmic numbers into predictable, necessary consequences of our measurement choices.

4. Is Not the Fundamental Law—It's a Translation Manual

The three-worlds framework downgrades E=mc² from a fundamental law of nature to a unit conversion formula.

In the fundamental "World of Physics," where reality is a unified whole without human units, the law is simply E = m. Mass and Energy are not just equivalent; they are one and the same dimensionless thing.

So, where does the c² come from? The term c² is the Jacobian needed to translate the simple truth of E=m for use in our "World of Measurement." The conversion begins by stating that the dimensionless ratio of measured energy to Planck energy must equal the dimensionless ratio of measured mass to Planck mass (E_si / E_P = m_si / m_P). The equation we know, E=mc², is simply the algebraic rearrangement of this fundamental mapping.

"The true law is E=m. The term c² is the conversion factor—the Jacobian—required to make that simple truth legible on our distorted SI chart."

This re-frames one of the most famous equations in science. It's not a deep law discovered in nature, but rather a "user manual" for converting between our human concepts and the underlying, unified reality.

Conclusion: Is Reality Hiding in Plain Sight?

The core message of this framework is that many of the complexities and "mysterious numbers" in physics are not features of the universe itself. They are consequences of the fragmented, arbitrary language we invented to describe it. The universe is fundamentally simple; our description of it is what's complex.

As the source text powerfully concludes: "The complexity is not in the physics, but in our chosen description of it."

This leaves us with a profound question. If the constants that build our reality are just artifacts of our perspective, what other 'fundamental truths' might just be shadows cast by the measurement tools we use?