Politics, Power, and Science: The Great Inversion: How Physics Mistook the Map for the Territory

Sunday, October 19, 2025

The Great Inversion: How Physics Mistook the Map for the Territory

J. Rogers
Independent Researcher, SE Ohio

Abstract

Modern physics suffers from a fundamental ontological error: we have reified our arbitrary measurement system (SI units) as "concrete reality" while dismissing the universe's natural coordinate system (Planck scale) as "abstract convenience." This paper traces the historical steps that led to this inversion, demonstrates why it represents a category error analogous to mistaking a map for the territory it represents, and shows that accepting the correct ontology requires no change to practical physics—only to our theoretical understanding. We argue that recognizing SI units as the abstraction and natural ratios as the reality resolves numerous "mysteries" in fundamental physics and redirects research toward productive questions.

1. Introduction: The Ontological Inversion

Contemporary physics operates under an implicit but profound ontological assumption: that the International System of Units (SI) represents "concrete reality" while the Planck natural unit system represents an "abstract mathematical convenience." This paper demonstrates that this assumption is precisely backwards—an inversion that has distorted theoretical physics for over a century.

The correct ontology:

Primary reality: Dimensionless ratios in natural coordinates (the Planck scale)
Human abstraction: Arbitrary measurement systems (SI, Imperial, etc.)
Emergent artifacts: "Fundamental constants" (Jacobian transformation coefficients)

The inverted ontology (current physics):

"Concrete reality": SI units and measurements
"Abstract convenience": Planck units
"Fundamental mysteries": Constants like c, ℏ, G

This inversion is not merely philosophical hairsplitting. It has led physics to treat coordinate artifacts as mysteries requiring explanation, to search for unification where unity already exists, and to build elaborate theories around the equivalent of asking "why is Greenland so large on Mercator projection maps?"

2. The Historical Steps to Reification

2.1 Step 1: The Necessary Bootstrap (Pre-1800s)

The innocent beginning: Humans needed to measure things.

Early measurement systems were based on:

Human anatomy: Feet, cubits, hands
Local materials: Barleycorns for weight
Celestial cycles: Days, lunar months, years
Practical references: A day's walk, a stone's throw

These were pragmatic, anthropocentric choices. Nobody claimed they were "fundamental to nature"—they were explicitly understood as human conventions.

The key point: This choice was necessary. You cannot measure without choosing units. The error was not in making this choice, but in what came later.

2.2 Step 2: Standardization (1700s-1800s)

As science became international, inconsistent local units became problematic. The meter was defined as one ten-millionth of the distance from the North Pole to the equator (later revised to a platinum-iridium bar, later still to wavelengths of light).

What happened psychologically:

Creating careful, internationally agreed standards made SI feel "official"
Precision and reproducibility made SI seem "objective"
Universal adoption made SI seem "natural"

The subtle shift: From "this is a useful human convention" to "this is the proper way to measure nature."

Still, no one yet claimed SI was ontologically primary—it was understood as a practical standard.

2.3 Step 3: Adding Proportionality Constants (1800s)

Newton and his contemporaries worked in proportionalities:

F ∝ m₁·m₂/r²

This explicitly acknowledged: "Here is the ratio, the pure relationship. The specific numbers depend on your unit choices."

Then came "improvement": Let's add proportionality constants to make equations "exact":

F = G·m₁·m₂/r²

What this actually did: Embedded the coordinate transformation (SI → Natural → SI) into the formula, creating a composite operation that hid its structure.

What people thought it did: "Completed" Newton's formula by discovering a fundamental property G.

The critical error: The constant G was treated as a discovery about nature rather than recognized as a consequence of unit choice.

2.4 Step 4: Measuring Constants with Increasing Precision (1800s-1900s)

Once constants were embedded in formulas, they became targets of measurement:

Cavendish measured G (1798)
Planck measured h (1900)
Michelson measured c with increasing precision

The precision trap: As measurements improved, confidence grew.

G = 6.67 × 10⁻¹¹
G = 6.674 × 10⁻¹¹
G = 6.67430 × 10⁻¹¹

Each refinement was treated as "learning more about G" rather than "measuring our coordinate system's relationship to natural units with better precision."

The reification accelerates: The more precisely we measured these values, the more "real" they seemed. The constants were now treated as properties of the universe rather than properties of our measurement system.

2.5 Step 5: Planck's Discovery Goes Unrecognized (1899)

Max Planck derived natural units by combining c, G, and h:

t_P = √(hG/c⁵)
l_P = c·t_P = √(hG/c³)
m_P = h/(c²·t_P) = √(hc/G)

What Planck showed: There exists a unique coordinate system where all dimensional constants equal 1.

What physics should have recognized:

These are the natural coordinates of the universe
Our constants are Jacobians relating our arbitrary units to these natural units
SI is the abstraction, Planck scale is the reality

What actually happened:

"Interesting mathematical curiosity"
"Impractical because scales are so extreme"
"Maybe relevant for quantum gravity someday"

Why the insight was missed: By 1899, the inversion was already complete. SI felt concrete (we use it daily), Planck felt abstract (can't build a meter stick at 10⁻³⁵ m).

2.6 Step 6: The 2019 SI Redefinition—and Continued Blindness

In 2019, the SI system was redefined by fixing the values of constants by committee vote:

c = 299,792,458 m/s (exact, by definition)
h = 6.62607015×10⁻³⁴ J·s (exact, by definition)
e = 1.602176634×10⁻¹⁹ C (exact, by definition)

What this explicitly acknowledged: We define our units via these constants. They are not measured properties; they are definitional standards.

What this proves: Constants are human choices embedded in our measurement system.

What physics did: Continued teaching and researching as if constants were fundamental mysteries, often using ℏ (h/2π) in formulas—a notational convenience that further obscures the actual unit scaling structure.

The ultimate irony: We officially acknowledged constants define our units, then immediately went back to theorizing about "why these values" and "could they vary."

You cannot have it both ways. If constants define units, they cannot also be unexplained properties of nature.

3. Why the Inversion Happened: Psychological and Sociological Factors

3.1 Anthropocentric Bias

SI units feel real because:

We use them every day
They're human-scale
Our instruments measure in them
Our intuitions are calibrated to them

Planck units feel abstract because:

We never directly measure them
They're far from human experience
They require calculation to access
We have no intuitive grasp of 10⁻³⁵ meters

The error: Confusing accessibility with ontological priority.

The fact that we can't directly perceive Planck scales doesn't make them less fundamental—any more than our inability to perceive atoms made them "less real" than the objects we can see.

3.2 Temporal Priority Confusion

Order of human discovery:

Choose arbitrary units (SI)
Measure things in those units
Discover constants (as Jacobians)
Calculate natural units from constants

This felt like: SI → Constants → Planck (derivation chain)

Actual logical structure: Natural ratios → (Human choice of SI) → Constants emerge as necessary Jacobians → Solving reveals the pre-existing natural scale

The confusion: We mistook the order of discovery for the order of ontological dependence.

3.3 Practical Success Bias

SI works perfectly for:

Engineering
Everyday measurement
Experimental design
Communication of results

This practical success created the illusion: "If SI works so well, it must be fundamental."

The error: A map can work perfectly for navigation while still being a map. Mercator projection works beautifully for ship navigation—that doesn't make it "more real" than a globe.

3.4 Sunk Cost and Institutional Inertia

By the time Planck units were discovered:

Entire educational system built on SI
All textbooks in SI
All scientific literature in SI
All instruments calibrated to SI
Careers built on refining SI measurements

To acknowledge the inversion would mean:

Admitting 200 years focused on coordinate artifacts
Rewriting theoretical foundations
Rethinking "fundamental" research programs
Acknowledging that precision in measuring G is just precision in measuring Jacobians

The psychological barrier: Easier to maintain the inversion than to admit the error.

3.5 The "Setting c=1" Handwave

Physicists regularly "work in natural units" by "setting c=1, h=1."

What they claim: "This is a convenient mathematical trick."

What it actually is: Rotating from SI coordinates to natural coordinates via the Jacobian transformation.

Why the handwave persisted:

If they formalized what "setting c=1" means, they'd have to acknowledge constants are Jacobians
If constants are Jacobians, SI is arbitrary
If SI is arbitrary, what have we been doing for 200 years?

Solution: Keep it informal. Call it "convenience." Never write down the formal transformation. The cognitive dissonance remains buried.

Note: Many physicists use ℏ=h/2π instead of h, mixing a notational convenience (useful for rotational symmetries) with the actual fundamental constant. This further obscures the unit scaling structure. The measurement standard is h; the factor of 2π is geometric notation, not unit scaling.

4. The Category Error: Map vs. Territory

4.1 The Cartographic Analogy

Consider a student of geography who says:

"Greenland is enormous—nearly the size of Africa. The Mercator projection shows this clearly. Why is Greenland so much larger than other landmasses? What special properties of Greenland's terrain cause this?"

We would immediately correct them:

"No, Greenland is not enormous. It's the map projection that distorts sizes near the poles. Greenland appears large on Mercator maps because of how spherical surfaces are projected onto flat planes. The 'largeness' is a property of the map, not the territory."

The student's error: Treating a projection artifact as a property of the territory.

4.2 The Physics Analogy

Modern physics asks:

"The gravitational constant G = 6.67430×10⁻¹¹ m³/(kg·s²). This is a fundamental property of the universe. Why does nature choose this specific value? What deep principle explains it?"

The correction should be:

"No, G is not a property of the universe. It's a coordinate transformation coefficient. G has this value because of how we chose to define meters, kilograms, and seconds. The 'value' is a property of the measurement system, not the universe."

Physics' error: Treating a coordinate artifact as a property of nature.

4.3 The Structural Identity

Cartography	Physics
Territory (globe)	Reality (natural ratios)
Map projection (Mercator)	Coordinate system (SI)
Projection distortions (Greenland size)	Constants (G, c, h values)
"Why is Greenland huge?"	"Why does G have this value?"
Answer: It's not—it's projection artifact	Answer: It doesn't—it's coordinate artifact

In both cases: The error is reifying the representation and mistaking projection artifacts for properties of what's being represented.

4.4 Maps Are Useful—And Still Maps

Do we stop using Mercator projection? No. It's excellent for navigation.

Do we claim it represents reality? No. We know it's a distorted projection.

Do we research "why Greenland is so large?" No. We recognize this is the wrong question.

Analogously for physics:

Do we stop using SI units? No. They're excellent for engineering.

Do we claim they represent fundamental reality? No. They're an arbitrary measurement convention.

Do we research "why G has this value?" No. We recognize this is the wrong question.

5. The Correct Ontology: Natural Coordinates as Primary

5.1 What Actually Exists

The universe contains: Dimensionless ratios—pure proportions between physical quantities that hold regardless of measurement system.

Examples:

Energy ~ Mass ~ Frequency ~ 1/Length (all scale together 1:1)
Time dilation potential: Δt/t ~ m/r (dimensionless ratio)
Escape velocity: v/c ~ √(2m/r) (dimensionless ratio)
Fine structure constant: α ≈ 1/137 (dimensionless)

These are coordinate-free. They're the same in every unit system. This is reality.

5.2 The Natural Coordinate System

The Planck scale is not "a choice"—it's the unique coordinate system where all dimensional constants equal 1.

Proof of uniqueness: Given measured values of c, h, G in any unit system, solving the equations:

c = l_P/t_P
h = m_P·l_P²/t_P
G = l_P³/(m_P·t_P²)

produces exactly one solution for (l_P, t_P, m_P):

t_P = √(hG/c⁵)
l_P = c·t_P = √(hG/c³)
m_P = h/(c²·t_P) = √(hc/G)

This is not arbitrary. It's not conventional. It's mathematical necessity.

The Planck scale is the coordinate system aligned with reality's native structure.

5.3 Arbitrary Human Coordinates

SI, Imperial, or any other system: Arbitrary choices made for human convenience.

Meter: Based on Earth's circumference
Second: Based on Earth's rotation
Kilogram: Based on water's density

These scales have no relationship to fundamental physics. They're as arbitrary as choosing base-10 for counting or putting north at the top of maps.

5.4 Constants as Coordinate Transformations

When we measure in arbitrary units (SI) instead of natural units (Planck), we need conversion factors.

That's what "constants" are: Jacobian components of the coordinate transformation between SI and natural coordinates.

Example: G = 6.674×10⁻¹¹ is telling you: "Your mass, length, and time units are this far off from the natural scales."

Change your units → G changes
But the physics (m₁m₂/r² in natural units) is invariant

6. Evidence That We Got It Wrong

6.1 The Coherence Requirement

If constants were fundamental properties, they could be independent. Different domains of physics might reveal different "natural" scales.

But they can't be independent. They must satisfy strict coherence relations:

If you calculate Planck mass from relativity (using c), from quantum mechanics (using h), and from gravity (using G), you must get the same answer.

This coherence is not guaranteed for arbitrary fundamental properties. It's required for components of a coordinate transformation.

The coherence proves: Constants are Jacobians, not independent properties.

6.2 The 2019 Redefinition

We voted on the exact values of c, h, e, k_B.

You cannot vote on properties of nature.

You can vote on how to define your measurement standards.

This is an explicit confession that constants define our units—they're not properties we discovered.

6.3 The "Setting Constants to 1" Practice

Physicists routinely "set c=1, ℏ=1" and everything works fine.

If constants were fundamental, this would be changing physics.

Since they're Jacobians, this is just choosing aligned coordinates (natural units).

The practice proves the framework: We already work in natural coordinates; we just don't formally acknowledge it.

6.4 GPS Operates in Natural Coordinates

GPS time dilation formula:

Δt/t = (G/c²)·(m/r)

This is the calculation in natural units:

Δt/t = m_natural/r_natural

The (G/c²) = (l_P/m_P) factor is just the Jacobian converting SI inputs to natural calculation and back.

GPS engineers use natural coordinates every day without realizing it.

7. Accepting the Correct Ontology: What Changes and What Doesn't

7.1 What Does NOT Change

Practical physics: Every formula still works exactly the same.

F = G·m₁·m₂/r² still gives correct answers
E = mc² still works
All engineering calculations unchanged

SI units: Still used for practical measurements.

Still measure in meters, kilograms, seconds
Still calibrate instruments to SI
Still communicate in SI

Mathematical predictions: Every prediction remains identical.

Experimental results: Every experiment gives the same results.

7.2 What DOES Change

Theoretical understanding:

Constants are coordinate transformations, not mysteries
SI is human convention, not fundamental reality
Natural ratios are the physics, not the SI formulas

Research priorities:

STOP: Asking "why these constant values?"
STOP: "Fine-tuning problems" for dimensional constants
STOP: Treating constants as fundamental
START: Asking "why these dimensionless ratios?"
START: Understanding structure of natural coordinate relationships
START: Recognizing unity that already exists

Education:

STOP: "Constants are mysterious"
STOP: "Setting c=1 is a trick"
STOP: Teaching naive substantivalism
START: "Constants are Jacobians"
START: "Natural coordinates are where constants=1"
START: Teaching structural realism

Philosophy of physics:

Accept that structure (ratios) is real
Accept that measurement systems are abstract
Accept that constants are emergent from unit choice

7.3 The Map-Territory Resolution

Keep using the map (SI):

For navigation (engineering)
For communication (standard reference)
For practical work (convenient scales)

But know it's a map:

Don't treat projection artifacts as territory features
Don't research "why the map has this distortion"
Don't build theories around map coordinate values

Study the territory (natural ratios):

What is the actual structure?
Why do these dimensionless ratios exist?
What determines the geometry of natural relationships?

8. Resolving Pseudo-Problems

8.1 The "Fine-Tuning Problem"

The claim: "Constants appear fine-tuned. Why these specific values?"

The resolution: You're asking "why is Greenland so large on this map?"

Constants' "values" are determined entirely by which arbitrary units you chose. Change units → values change.

There is no fine-tuning problem for dimensional constants. The question is meaningless.

Legitimate questions: Why dimensionless ratios (α, mass ratios) have their values. These are coordinate-independent.

8.2 The "Varying Constants Problem"

The claim: "Could constants vary over time or space?"

The confusion: Mixing two separate questions:

Could dimensionless ratios vary? (Meaningful—they're coordinate-free)
Could dimensional constants vary? (Meaningless—they're coordinate-dependent)

Resolution:

Dimensionless constants (α) might vary—this is real physics
Dimensional constants (c, G, h) cannot "vary"—they define your units

Asking if c varies is like asking if "the number of meters per meter" varies. It's definitionally 1.

8.3 The "Why These Values?" Problem

The question: "Why does G = 6.674×10⁻¹¹?"

The answer: Because you chose meters, kilograms, and seconds based on Earth and water.

The deeper question: "Why does the gravitational coupling have the strength it does relative to other natural scales?"

This is a question about dimensionless ratios—a real question.

8.4 The "Unification Problem"

The claim: "We must unify four separate forces."

The resolution: Forces are already unified in natural coordinates. Different "forces" are different projections of the unified structure.

The appearance of separation comes from using SI coordinates that artificially separate what's naturally unified.

9. The Path Forward

9.1 Immediate Steps

1. Acknowledge the inversion:

SI is the abstraction
Planck scale is the natural coordinate system
Constants are Jacobians

2. Update education:

Teach proper ontology from the start
Show students the Jacobian structure
Explain "setting c=1" formally

3. Redirect research:

Stop funding "constant value" research
Focus on dimensionless ratios
Study natural coordinate structure

9.2 Medium-Term Changes

4. Formalize natural coordinate physics:

Develop textbooks in natural coordinates
Make Jacobian transformations explicit
Provide tools (like the Physics API) for both approaches

5. Separate coordinate-free from coordinate-dependent:

Distinguish real physics (ratios) from artifacts (constants)
Recognize what's universal vs. what's conventional

6. Apply structural realism consistently:

Structure (ratios) is real
Substances (measured quantities) are projections
Constants encode projection geometry

9.3 Long-Term Impact

7. Unified theoretical framework:

Physics is already unified (Planck Equivalence Web)
Different domains are different projections
Stop searching for unity—understand the unity that exists

8. Focus on genuine mysteries:

Why these dimensionless ratios?
What determines natural coordinate structure?
What is the geometry of the underlying reality?

9. Philosophical clarity:

End naive substantivalism
Accept structural realism
Distinguish map from territory

10. Objections and Responses

10.1 "But SI is practical and Planck is impractical"

Response: Correct—and irrelevant to ontology.

Mercator projection is practical for navigation. That doesn't make it ontologically primary. Use SI for practice, acknowledge Planck for understanding.

10.2 "We derived Planck from SI, so SI is primary"

Response: Order of discovery ≠ order of ontological dependence.

We discovered America by sailing from Europe. That doesn't make Europe "primary" to America's existence.

10.3 "Constants are measured, not chosen"

Response: Since 2019, they're officially chosen (fixed by definition).

And even before: measuring G in SI units is measuring "how far is SI from natural units?" Not discovering a property of gravity.

Additional note: The choice to use ℏ in many quantum formulas instead of h is purely notational convenience for handling rotational symmetries. It has nothing to do with unit scaling. This choice further confused the distinction between actual measurement standards (h) and mathematical convenience (h/2π).

10.4 "This is just philosophy, not physics"

Response: It has concrete consequences:

Redirects research away from pseudo-problems
Clarifies what requires explanation vs. what doesn't
Reveals unity already present in physics
Makes implicit structure explicit

Philosophy matters when it affects what questions we ask.

10.5 "Natural units are inaccessible"

Response: GPS uses them every day. Every physics calculation operates in them.

They're "inaccessible" for direct measurement, but so are many real things (atoms were once "inaccessible"). Ontology isn't determined by what we can directly perceive.

11. Conclusion: Moving Forward with Clarity

The reification of SI units and dismissal of natural coordinates as "abstract" represents one of the most consequential category errors in the history of physics. We have spent over a century treating the map as if it were the territory, building elaborate theories to explain the properties of our coordinate system while mistaking them for properties of nature.

The correction is simple in principle:

Recognize SI as useful abstraction (the map)
Recognize natural ratios as reality (the territory)
Recognize constants as coordinate transformations (projection coefficients)

The correction is difficult in practice:

Requires admitting long-standing confusion
Demands redirecting research programs
Necessitates educational reform
Challenges deeply held intuitions

But the correction is necessary:

Resolves pseudo-problems (fine-tuning, constant values)
Reveals genuine unity (already present)
Clarifies what physics should study (dimensionless structure)
Ends confusion about what's fundamental

And the correction is compatible with practice:

Keep using SI for engineering
Keep existing formulas
Keep practical measurements
Just understand what they mean

We can accept that SI is the abstraction and keep moving forward—just as cartographers accept Mercator is a projection while continuing to use it for navigation. The map is useful. But it's not the territory.

Physics will advance when we stop theorizing about the shape of our maps and start studying the structure of reality they represent.

The natural ratios are real. The constants are Jacobians. SI is conventional. Moving forward requires accepting this and refocusing our efforts accordingly.

The territory was always there. We just mistook our map for it. Time to correct the error and study reality directly.