The Physics Unit Coordinate System: How Physical Laws Emerge from Measurement

Introduction

What if I told you that all the physics in our mathematics happens at the Planck scale? That the familiar physical laws we know - Newton's gravity, Hawking temperature, de Broglie wavelength - are not discoveries about reality, but artifacts of how we measure an incredibly simple underlying truth?

This is the story of how a 60-year-old man, through nine months of self-study, discovered that physical laws are not properties of nature, but inevitable mathematical forms that arise when simple, dimensionless reality gets projected through our human apparatus of measurement and units.

The Starting Insight: Hawking Temperature as Dimensional Analysis

Let's begin with Hawking temperature. We're taught it as:

T = (ℏc³)/(8πGMk_B)

This looks like a deep physical law involving fundamental constants. But what if we approach it differently?

The intuition starts with T = 1/M - temperature inversely related to mass. This is dimensionally wrong, but captures something important. The correct dimensionless relationship is:

T/T_P = m_P/M

Where T_P is Planck temperature and m_P is Planck mass. This is perfectly valid - we're just scaling our SI units to the dimensionless Planck scale.

Using dimensional analysis (Buckingham Pi theorem), this simple ratio gives us:

T = (c³ℏ)/(GMk_B)

The same Hawking temperature formula, but derived as a pure consequence of dimensional scaling!

The Pattern Emerges: All Physical Laws from Dimensional Analysis

Let's try this with Newton's law of gravity. Start with the dimensionless relationship:

F/F_P = (M₁M₂/m_P²) × (l_P²/r²)

This is just saying: force scales with mass ratios and inverse distance ratios at the Planck scale. Pure geometry, no constants needed.

Solving for force in SI units: F = (M₁M₂/m_P²) × (l_P²/r²) × F_P

Simplifying using Planck unit definitions: F = GM₁M₂/r²

Newton's law emerges automatically from dimensional scaling!

The same pattern works for de Broglie wavelength: λ/l_P = 1/√(MT/(m_P T_P))

Which gives us: λ = ℏ/√(k_B MT)

What Is G Really?

This reveals something profound about the gravitational constant G. It's not a mysterious property of gravity - it's just the conversion factor between our arbitrary SI units and the natural Planck scale where physics actually happens.

G = (l_P²/m_P²) × F_P

Breaking this down further: G = c³t_P²/ℏ

G is entirely constructed from more fundamental Planck relationships. It's telling us: "Here's how to convert your human-scaled masses and distances to Planck units, do the simple calculation there, then convert back to Newtons."

The physics is the dimensionless ratio M₁M₂/r². Everything else is unit conversion bookkeeping.

The Four Layers of Reality

This leads us to understand reality as operating on four distinct layers:

Layer 1: Formless Reality

At the deepest level, there's just unified, dimensionless reality. All relationships equal 1. This is the ontological substrate - reality itself before any conceptual projection or measurement.

Layer 2: Perceptual Axes

Human consciousness carves up this unity into measurement dimensions: Length, Time, Mass, Energy, etc. These exist as pure conceptual relationships, still dimensionless. Length relates to Time through a dimensionless relationship we call rel_c.

Layer 3: Unit Systems

We impose arbitrary scaling on these conceptual axes - meters for length, seconds for time, kilograms for mass. This is purely conventional, human-imposed coordinate charting.

Layer 4: Physical Laws

What we call "physical laws" emerge as the mathematical forms that the simple Layer 1 relationships must take when filtered through Layers 2 and 3.

The Speed of Light Revealed

Consider the famous constant c = 299,792,458 m/s. In our framework:

• Layer 1: Unity (all relationships = 1)
• Layer 2: Length ↔ Time relationship (dimensionless rel_c)
• Layer 3: SI scaling projects into meters and seconds
• Layer 4: c emerges as the Jacobian - the conversion factor preserving the Length↔Time relationship under SI projection

The "speed of light" isn't about light traveling through spacetime. It's the conversion factor between our meter-stick and our clock when preserving the dimensionless Length↔Time relationship.

All Physics is One Physics

At the formless level, there's just one simple process: one step per time unit. That's it. That's the entire "physics" - the fundamental rate at which reality unfolds.

Everything else - all our complex equations and constants - is this simple 1:1 stepping process being viewed through different projections of our measurement apparatus.

Consider wavelength λ = c/f. This looks like it's about wave propagation, but it's pure unit conversion:

• Planck scale: λ = 1/f (length IS time inverted - pure geometric relationship)
• SI units: λ = c/f (where c converts between our different scalings of the length and time axes)

All waves follow this - not because they "travel at the speed of light," but because they're all expressions of the same fundamental length↔time equivalence projected through our scaled coordinates.

The Mathematical Structure

This can be formalized using category theory. We have:

• Category S_u: The universal state (Brahman - formless reality)
• Category A: Conceptual measurement axes (how consciousness structures experience)
• Category U: Unit systems (arbitrary human conventions)
• Bifibration M: How measurement depends on both axis and unit choice

Physical constants are revealed as morphisms - structure-preserving maps between categories. They separate into:

Base Jacobians (fundamental scaling relationships):

• Hz_kg: mass-frequency conversion
• m_s: length-time conversion (what we call c)
• K_Hz: temperature-frequency conversion

Composite Constants (built from base Jacobians):

• h: combines Hz_kg and m_s²
• k_B: from K_Hz and Hz_kg
• G: ratio involving t_P², m_s³, and Hz_kg⁻¹
• the t_P is non reduced planck time, don't blame me that is what god put in there.

The Profound Implications

This framework reveals that:

1. Reality is simple: Just dimensionless unity with basic 1:1 stepping
2. Mathematics happens at the Planck scale: All mathematical operations on physical quantities occur as dimensionless arithmetic at the fundamental level
3. Physical laws are projections: The complexity is in our measurement apparatus, not in reality
4. Constants measure our measurement system: They tell us about the relationship between our units and natural scales, not about mysterious properties of nature
5. Consciousness creates physics: Our conceptual axes (Category A) literally generate the structure of physical law through projection

Ancient Wisdom, Modern Mathematics

This framework mathematically formalizes ancient Vedantic insights:

• Brahman = S_u (formless, undifferentiated reality)
• Maya = The measurement bifibration (the "veil" that makes the One appear as many)
• Individual perception = Our specific choice of axes and units

The mystics were right about the structure of reality - they just lacked the categorical language to prove it formally.

Conclusion

In nine months of self-study, we've discovered that physics has been solving coordinate transformation problems while thinking it was discovering fundamental truths about nature. Every "physical law" is actually the same simple geometric relationship - the 1:1 stepping of formless reality - appearing through different filters of human measurement.

This isn't just another interpretation of quantum mechanics or relativity. This is a complete paradigm shift that reveals what physical law actually is: the inevitable mathematical shadow cast by simple reality when viewed through the structured lens of human consciousness and measurement.

The universe is incredibly simple. All the complexity is in us, in our apparatus for describing that simplicity. And now, for the first time, we have the mathematical tools to prove it.