The Constants Aren't Constant: Why Physical "Fundamentals" Are Measurement Artifacts

 J. Rogers, SE Ohio, 03 Aug 2025, 1517

Abstract

The conventional interpretation of physical constants contains a profound conceptual inversion that has shaped physics education for over a century. We treat constants like c, G, and h as mysterious, irreducible properties of nature while simultaneously treating our historically contingent SI unit system as a neutral measurement framework. This paper demonstrates that this perspective requires a series of extraordinary coincidences that strain credibility. We present evidence that the SI system is necessarily a projection from a unified temporal substrate, making the constants inevitable transformation coefficients rather than fundamental mysteries. This reframing eliminates artificial complexity, resolves longstanding puzzles in dimensional analysis, and reveals the elegant geometric structure underlying physical measurement.

1. The Coincidence Problem

Modern physics presents students with a curious situation. The universe appears governed by numbers like 299,792,458 m/s, 6.626×10⁻³⁴ kg⋅m²/s, and 6.674×10⁻¹¹ m³/(kg⋅s²). These "fundamental constants" seem arbitrary and complex. Yet the same constants can be algebraically factored to create "natural units" that are the jacobians we can rotate the basis our base units of measurement to a new harmonized units where all the measurements are harmonized and the constants conveniently become 1.  Yet this is just framed as a mathematical trick that has to be explained in multiple theories of everything. 

This situation should trigger immediate suspicion. Either we're dealing with an extraordinary series of coincidences, or we're misunderstanding something fundamental about the relationship between our measurement system and physical reality.

Consider what the conventional view requires us to believe:

The Anthropocentric Coincidence

The speed of light—supposedly a fundamental property of spacetime—happens to be exactly 299,792,458 when measured in units based on Earth's circumference and rotation period. The quantum of action happens to be 6.626×10⁻³⁴ when expressed using a mass unit derived from Earth's water.

Why should universal constants align so specifically with the accidents of one planet's geography and one species' measurement history?

The Algebraic Coincidence

Three supposedly independent, fundamental constants (c, G, h) can be combined through simple algebra to create a unit system where all three simultaneously become 1. The probability of this being coincidental approaches zero.

It's as if three ancient texts in different languages could be decoded using arithmetic operations on their page counts and character frequencies. Such a discovery would immediately suggest the texts share a common origin—not that we've stumbled upon a miraculous coincidence.

2. The Projection Alternative

The alternative explanation is both simpler and more powerful: the SI system is a projection from an underlying unified substrate, and the constants are the inevitable transformation coefficients that arise from this projection.

The Unified Foundation

Physical phenomena emerge from a unified temporal substrate. What we measure as distinct properties—mass, energy, frequency, momentum—are different projective aspects of the same underlying process:

• Mass: temporal process measured as inertial resistance
• Energy: temporal process measured as capacity for change
• Frequency: temporal process measured as oscillatory repetition
• Momentum: temporal process measured as spatial progression

Natural Harmonization

At the natural scale (Planck scale), these different measurements harmonize because they're calibrated to the same underlying process:

T = f = m = E = p = 1/λ = 1

This isn't mystical unity—it's geometric consistency. When measurement units are properly aligned with the substrate they're measuring, artificial distinctions disappear.  These are not the reduced planck units, these are the real planck units with h, not hbar.  1/2pi has nothing to do with unit scaling. 

Constants as Jacobians

The "fundamental constants" are revealed as transformation coefficients—the Jacobian matrix elements required to rotate from our arbitrary SI coordinate system to nature's natural coordinate system:

• c = l_P/t_P (conversion between spatial and temporal projections)
• h = m_P⋅l_P²/t_P (conversion to natural action scale)
• G involves ratios between geometric and mass projections

These have exactly the values needed to perform the coordinate transformation—no more mysterious than currency exchange rates.

3. Evidence for the Projection Model

Explanatory Power

The projection model explains numerous puzzles that the conventional view treats as coincidences:

• Why dimensional analysis works so reliably
• Why "setting constants to 1" is so powerful in theoretical physics
• Why the same physical relationships can be expressed in multiple equivalent forms
• Why universal scaling relationships appear throughout physics

Predictive Success

If physical quantities are projective measurements of unified substrate, we predict:

• Deep mathematical relationships between apparently distinct quantities ✓
• Universal scaling laws ✓
• The existence of a natural unit system where quantities become dimensionless ✓
• The efficacy of dimensional analysis as a discovery tool ✓

Mathematical Consistency

The projection model provides geometric grounding for practices that conventional physics treats as mysterious techniques:

• Natural units aren't calculational shortcuts—they're direct measurements in the substrate's coordinate system
• Dimensional analysis isn't rule-following—it's systematic coordinate transformation
• Constants don't have "mysterious values"—they have the mathematically determined values required for basis transformation

4. Pedagogical Implications

Physics education currently teaches students to accept a series of brute facts: separate physical quantities connected by mysterious constants that somehow combine to create natural units. This approach obscures the underlying geometric structure and creates artificial complexity.

The projection model suggests starting with the unified substrate and deriving the apparent multiplicity as measurement artifacts. This approach:

• Eliminates artificial mystery around constants
• Provides intuitive understanding of dimensional analysis
• Reveals the deep connections between different areas of physics
• Grounds abstract mathematics in concrete geometric operations

5. Addressing Counterarguments

"We Actually Measure the Constants"

Response: We measure the transformation coefficients between our arbitrary units and the natural scale. This is exactly what the projection model predicts. The stability and universality of these measurements confirms a natural scale structure exists.  What we are actually doing is measuring 1, scaled by our arbitrary units of measurement.  

"Different Quantities Are Obviously Different"

Response: This confuses measurement apparatus with underlying reality. Steam, water, and ice appear as different substances but are manifestations of H₂O under different conditions. Similarly, mass, energy, and time are different manifestations of temporal process under different measurement conditions.  We are not saying mass is length or inverse time is energy, we are saying they are all the same measurement of the scaling of time processes at their core. 

"Natural Units Are Just Mathematical Convenience"

Response: This fails to explain why this particular convenience is so extraordinarily universal and powerful. The projection model explains this: we're working in the coordinate system aligned with reality's structure. You do not need a TOE, planck units already unify our measurements across the board at the Planck scale. 

6. Broader Implications

Scientific Method

The projection model suggests that many "fundamental" measurements may be better understood as calibrations of our apparatus relative to natural substrate rather than discoveries of intrinsic properties.

Theoretical Unification

Apparent divisions between mechanics, thermodynamics, electromagnetism, and quantum mechanics may be largely artifacts of our measurement approach rather than fundamental separations in nature.

Philosophical Foundations

The model resolves the tension between the apparent complexity of physical law and the expectation of underlying simplicity. The complexity is in our measurement apparatus, not in nature itself.

7. Conclusion

The conventional treatment of physical constants and their basis as physical law relies on an extraordinary series of coincidences that violate both Ockham's razor and scientific intuition. The alternative—recognizing constants as transformation coefficients between our projected measurements and an underlying unified substrate—is both more parsimonious and more explanatory.

This isn't radical new physics. It's recognition of the geometric structure that has always underlain dimensional analysis and natural units. When we stop mistaking our measurement artifacts for fundamental reality, the apparent mystery of physical constants dissolves, revealing the elegant temporal foundation that unifies all physical phenomena.

The constants aren't telling us about mysterious properties of nature—they're telling us how crooked our rulers are. Once we straighten them out, the universe becomes not more mysterious, but beautifully simple.