The Collision Economy: How Physical Limits Create Boom-Bust Cycles and Wealth Extraction

 J. Rogers, SE Ohio

Abstract

Modern economic theory is predicated on perpetual compound growth, yet operates within the thermodynamic constraints of a finite planet. This paper argues that the boom-bust cycle is not a failure of policy or regulation, but the inevitable consequence of a theoretical framework that requires the physically impossible. We demonstrate that as growth limits are approached, the system increasingly relies on asset inflation and debt expansion to simulate growth, leading to wage stagnation and systematic wealth transfer from labor to capital. The current housing crisis, student debt burden, and wealth inequality are not aberrations but predictable outcomes of an economy repeatedly colliding with physical reality while refusing to acknowledge the collision.

1. Introduction: A Theory Requiring the Impossible

Contemporary neoclassical economic theory contains a fatal flaw: it requires perpetual compound growth for system stability. Without continuous expansion, the system experiences recession, unemployment, debt crises, and structural instability. This is not a feature that can be reformed away—it is fundamental to how the system allocates resources, prices assets, and services debt.

However, we live on a finite planet with fixed thermodynamic limits. Every economic transaction ultimately converts energy into waste heat. The Earth can only radiate heat into space at a rate determined by its surface area and temperature. At sustained growth rates of 2-3% annually in energy consumption, within several centuries we would generate more heat than the planet can dissipate, rendering Earth uninhabitable.

This creates a formal contradiction: The economic system requires something (infinite exponential growth) that physical reality makes impossible (finite energy and material throughput on a bounded planet).

A theory that requires the impossible is not a theory—it is a theology. And like all false theories, it generates predictable failures when it collides with reality. The boom-bust cycle is the sound of that collision, repeating with increasing violence as the contradictions deepen.

2. The Boom-Bust Cycle as Reality Assertion

If perpetual growth is impossible, why does the system experience periods of apparent expansion? The answer lies in understanding what "growth" actually measures and how it can be temporarily simulated.

2.1 The Anatomy of a Boom

Boom periods are characterized by:

Credit Expansion: The financial system creates new money through lending, expanding purchasing power beyond current productive capacity. This creates demand that appears to justify investment and hiring.

Resource Exploitation: New resources are discovered or become economically viable (oil fields, mineral deposits, virgin forests, new markets, new labor pools). These represent one-time stocks being converted to flows.

Technological Leverage: New technologies increase productivity or open new economic domains. However, these gains are typically one-time step-changes, not continuous exponential improvements.

Debt Accumulation: Future purchasing power is pulled into the present through loans. Growth appears to occur, but it's partially borrowed from the future.

The boom phase feels like genuine expansion because, temporarily, it is. But it's drawing down finite stocks or mortgaging future capacity.

2.2 The Inevitable Encounter with Limits

The boom cannot continue indefinitely because:

Physical Constraints Bite:

• Easy-to-extract resources are depleted, raising costs
• Market saturation occurs—everyone who can afford the product already has one
• Energy costs rise as high-EROI (Energy Return on Investment) sources are exhausted
• Environmental degradation imposes costs (pollution, climate disruption, resource depletion)

Financial Mathematics Assert Themselves:

• Debt service begins to exceed productive capacity
• Diminishing returns set in—each marginal unit of investment produces less output
• Credit expansion reaches limits (borrowers can't service more debt, lenders become risk-averse)

The "growth" was partly fictitious: It was built on one-time resource extraction, unsustainable debt accumulation, or asset price inflation rather than genuine increases in sustainable productive capacity.

2.3 The Bust: System Designed for Growth Collapses Without It

When growth falters, a system structurally dependent on expansion experiences cascading failures:

• Businesses that borrowed assuming future growth cannot service debt and default
• Workers are laid off, reducing consumption, causing more business failures (positive feedback loop)
• Asset prices collapse as speculative valuations prove unfounded
• Credit contracts as defaults mount and lenders become conservative
• Government revenues fall while safety-net expenses rise

Crucially: This is not a policy failure or a psychological panic. It is the mathematical consequence of building an economic system that requires exponential expansion in a finite environment. When expansion stops, the system breaks.

2.4 The "Recovery": Finding New Limits to Push

The system "recovers" by finding ways to temporarily restart growth:

• Discovering new resources to exploit
• Opening new markets (geographic expansion, new demographics, creating new needs)
• Technological innovation providing one-time productivity gains
• Expanding credit again (often with government backing)
• Lowering interest rates to incentivize borrowing

Each cycle requires more extreme interventions because the easy gains are exhausted:

• Interest rates hit zero and go negative
• Central banks directly purchase assets (quantitative easing)
• Government debt expands to levels previously considered catastrophic
• More marginal resources are exploited at higher energy and environmental cost

The boom-bust cycle is not a bug. It is the economy repeatedly hitting physical limits, temporarily finding ways to defer the collision, then hitting them again. Each cycle, the amplitude increases and the interventions required become more extreme.

3. The Asset Inflation Trap: Simulating Growth Through Wealth Redistribution

As genuine productivity growth slows (because we're approaching physical limits), the system increasingly relies on a different mechanism to create the appearance of expansion: asset price inflation.

3.1 The Post-2008 Paradigm Shift

The 2008 financial crisis represented a collision with limits:

• Decades of wage stagnation meant workers couldn't increase consumption from income
• The "solution" was to expand household debt (especially housing debt)
• When that debt became unpayable, the system crashed

The policy response revealed the system's true priorities:

What Happened:

• Central banks flooded the financial system with trillions in new money (quantitative easing)
• Interest rates were dropped to near-zero (or negative)
• Asset purchases directly inflated stock and bond prices

What Didn't Happen:

• Wages did not increase proportionally
• Workers did not receive the new money directly
• Debt burdens on households were not forgiven or significantly reduced

3.2 The Asymmetry: Who Captures the "Growth"

The monetary expansion created a massive wealth transfer through asset inflation:

If you owned assets in 2008:

• Your stock portfolio increased 300-400%
• Your real estate holdings doubled or tripled in value
• Your bond holdings appreciated as interest rates fell
• Your wealth multiplied with minimal additional labor

If you didn't own assets:

• Your wages stagnated or grew minimally (often below real inflation)
• The assets you might want to acquire (especially housing) became exponentially more expensive
• Your rent increased as housing became a speculative asset class
• Your effective purchasing power declined

This is not incidental—it is the mechanism by which the system simulates "growth" when real productive expansion slows. GDP increases not through more goods and services being produced per capita, but through the same assets being assigned higher monetary values.

3.3 Housing: The Clearest Example of Wealth Extraction

Housing illustrates the mechanism with brutal clarity:

Historical Norm: Housing cost approximately 2-3x median annual income. A single-income household could reasonably afford a home. Housing was primarily shelter.

Current Reality: Housing costs 5-10x median annual income in many markets. Dual-income households struggle to afford homes. Housing is primarily a financial asset.

What Changed:

• Not the physical houses—many are the same structures from decades ago
• Not construction costs relative to wages—those remained relatively stable
• What changed was monetary policy that deliberately inflated asset prices

The Mechanism:

1. Central banks lower interest rates and expand money supply
2. Cheap credit flows into real estate as investors seek returns
3. Housing prices inflate far beyond construction costs or rental values
4. Existing homeowners see "wealth" increase (though it's only realized if they sell and leave the market)
5. New buyers must take on crushing debt or be locked out entirely
6. Rent extraction increases as ownership becomes unattainable

The Result:

• A generation pays 40-50% of income on housing (rent or mortgage) compared to 20-25% historically
• That income goes to debt service (banks) or rent (landlords), not to consumption or productive investment
• Wealth transfers from labor (renters and new buyers) to capital (existing asset holders and financial institutions)

The "growth" in housing value is not new wealth—it's a transfer mechanism. Workers labor just as hard but receive a smaller share of the output because more is extracted through inflated asset prices they must pay to access basic needs.

3.4 The Wage Stagnation Side of the Equation

Asset inflation is only half the story. The other half is wage suppression:

Why Wages Don't Rise:

• Workers have lost bargaining power (union decline, globalization, automation threats)
• Productivity gains accrue to capital, not labor
• Full employment is deliberately avoided (central banks raise interest rates when unemployment gets "too low" to prevent "wage inflation")
• The system treats rising wages as a problem to be solved, but rising asset prices as a success

The Hidden Transfer: Wages do increase in nominal terms, but lag far behind asset inflation. This means:

• Your paycheck number goes up 2% per year
• Housing prices go up 8% per year
• You are running backwards in real terms
• The difference is captured by those who already own assets

This is sometimes called "stealth taxation" but it's more accurate to call it systemic wealth extraction via monetary policy. The people who decide how to respond to crises are the same people who benefit from asset inflation.

3.5 The Unsustainability of Asset-Inflation-Based "Growth"

This mechanism contains its own contradictions:

Consumer Demand Collapse: If workers spend 40-50% of income on housing/rent and another large portion on student debt, healthcare, and other inflated necessities, they cannot consume enough to sustain a consumption-based economy. You get secular stagnation.

Social Instability: When an entire generation is locked out of asset ownership (housing, education requiring no debt, retirement security), political instability increases. The social contract breaks.

债 Service Ceiling: There is a mathematical limit to how much debt can be serviced. When debt service exceeds the capacity to pay, defaults cascade. We approach this limit again.

Reduced Productive Investment: Money that flows into asset speculation doesn't flow into productive capacity. We get financialization—an economy that shuffles claims on wealth rather than creating new wealth.

The Next Bust: Asset bubbles always pop. When housing, stocks, or bonds crash again, those holding the debt (which is now catastrophically larger) will face another reckoning.

4. The Current Crisis: Multiple Limits Converging

We are not experiencing one crisis but a convergence of multiple limit-collisions:

4.1 Thermodynamic Limits

• Climate change imposes costs that can no longer be externalized
• Energy transition required, but with lower EROI than fossil fuels
• Increasing extreme weather events destroy capital stock

4.2 Debt Limits

• Sovereign debt at levels unprecedented in peacetime
• Household debt unsustainable relative to wages
• Corporate debt inflated by decade of cheap money
• Rising interest rates make this debt increasingly unserviceable

4.3 Social Limits

• Wealth inequality at levels associated with political instability
• Housing unaffordability creates intergenerational resentment
• Education debt locks young people out of family formation and consumption
• Trust in institutions collapsing as the extraction becomes visible

4.4 Resource Limits

• Peak cheap oil already passed
• Critical minerals for "green" transition face supply constraints
• Water, topsoil, and ecosystem services under severe stress
• Diminishing returns on resource extraction

The system's response: Try to restart growth through even more extreme monetary intervention. But the interventions themselves (negative interest rates, unlimited quantitative easing, modern monetary theory experiments) reveal that conventional tools no longer work. We're out of limits to push.

5. The False Solutions and Why They Fail

Faced with these contradictions, several "solutions" are commonly proposed. None address the fundamental problem.

5.1 "Green Growth"

The Claim: We can continue growing by switching to renewable energy and circular economies.

Why It Fails:

• Renewable energy has lower EROI than fossil fuels at their peak
• Transition itself requires massive energy and material investment
• Even 100% renewable energy doesn't escape thermodynamic limits—all economic activity generates waste heat
• "Circular" economy still requires continuous energy input to fight entropy
• Rebound effects: efficiency gains get consumed by increased usage

5.2 "Technological Innovation Will Save Us"

The Claim: New technologies will enable continued growth within physical constraints.

Why It Fails:

• Technology obeys physics too
• Historical innovation provided one-time step-changes, not continuous exponential improvement
• Low-hanging fruit already picked (electricity, antibiotics, computers)
• Many "innovations" now are incremental or purely financial (new ways to package debt)
• Technology can't repeal thermodynamics

5.3 "We'll Grow the Service/Information Economy"

The Claim: Dematerialized digital economy can grow without physical limits.

Why It Fails:

• Digital economy runs on physical servers that consume energy and generate heat
• Information processing has thermodynamic costs (Landauer's Principle)
• Service workers need food, housing, healthcare—all physical
• Historic "service economy growth" was often just financialization (shuffling money, not creating value)

5.4 "Reform Capitalism/Better Regulation"

The Claim: Keep the growth-based system but regulate it better to prevent excesses.

Why It Fails:

• Doesn't address the fundamental contradiction (infinite growth on finite planet)
• Reforms get captured or rolled back when growth pressures mount
• The system's core logic (accumulation and expansion) remains unchanged
• You can't regulate your way out of thermodynamics

6. The Actual Alternative: Steady-State Sufficiency Economics

If perpetual growth is impossible and our current approach is creating cascading crises, what's the alternative?

6.1 Defining a Sufficiency Economy

A sufficiency-based economy is characterized by:

Steady-State Material Throughput: Total energy and material consumption stabilizes within planetary boundaries. Quality of life improves through better distribution and design, not increased extraction.

Optimization for Human Wellbeing: Success measured by health, education, security, community, creative fulfillment—not GDP growth or stock prices.

Asset Stability Over Speculation: Housing as shelter, not speculative investment. Education as public good, not debt trap. Infrastructure as utility, not profit center.

Labor Share of Productivity: Productivity gains go to workers through reduced hours or increased wages, not captured entirely by capital through asset inflation.

Thermodynamic Honesty: Economic planning acknowledges physical limits. Energy budgets drive policy. Waste heat, entropy, and material flows are primary concerns.

6.2 What This Looks Like in Practice

Housing:

• Prices stabilize at 2-3x median income through public housing, land value taxation, and speculation controls
• Building codes optimize for longevity and efficiency, not maximum profit
• Housing treated as human right and utility, not investment vehicle

Labor:

• Productivity gains reduce working hours while maintaining living standards
• Strong labor rights and unions ensure workers capture share of output
• Universal basic services (healthcare, education, childcare) reduce dependence on wage labor

Finance:

• Banks as utilities, not casinos (narrow banking, public options)
• Debt primarily for productive investment, not consumption or speculation
• Interest rates reflect real productive returns, not manipulated for asset inflation

Technology:

• Design for sufficiency, longevity, and repairability (as in the Sufficiency Principle paper)
• Distributed systems over centralized extraction (local solar, community ownership)
• Open standards and interoperability over planned obsolescence

Resource Use:

• Circular material flows where thermodynamically feasible
• Energy budgets drive design decisions
• Optimization for low-throughput satisfaction of needs

6.3 The Transition Challenge

The primary obstacle is not technical but political and institutional:

Current System Benefits Incumbents: Those who already own assets benefit from inflation. Those who control capital benefit from labor's weak position. They have outsized political influence.

Debt Overhang: Trillions in debt were issued assuming future growth. Transition to steady-state would make much of this unpayable. Requires debt forgiveness or restructuring—politically difficult.

Ideological Capture: Economics profession, media, and policy elite are trained in growth-paradigm thinking. Alternatives are dismissed as "unrealistic" despite growth being thermodynamically impossible.

Coordination Problems: Requires coordinated action across nations, but competitive dynamics push toward continued extraction.

However, the alternative to planned transition is unplanned collapse. As crises deepen, the window for orderly transition narrows.

7. Conclusion: The Choice We Face

The boom-bust cycle is not a fixable flaw in an otherwise sound system. It is the inevitable consequence of an economic theory that requires perpetual compound growth on a finite planet—a mathematical and thermodynamic impossibility.

As we approach hard physical limits, the system increasingly relies on simulacra of growth: asset inflation, debt expansion, and financialization. This creates systematic wealth extraction from labor to capital, manifesting in housing unaffordability, wage stagnation, and crushing debt burdens. These are not policy failures to be corrected within the existing framework; they are the framework working as designed when real growth becomes impossible.

We face a binary choice:

1. Voluntary transition to a steady-state sufficiency economy that operates within thermodynamic limits, optimized for human wellbeing and equity rather than perpetual expansion

2. Involuntary collapse as the contradictions become unmanageable—debt defaults cascade, climate impacts accelerate, resource depletion bites, and social cohesion fractures

There is no third option. We cannot innovate or regulate our way out of physics. The boom-bust cycle will continue with increasing violence until we either redesign the system or it destroys itself.

The current housing crisis, the transfer of wealth from workers to asset holders, the mounting debt burdens, the political instability—these are all symptoms of an economy in its terminal phase, trying desperately to simulate impossible growth while the real world imposes its limits.

Physics always wins. The only question is whether we acknowledge this reality and design for it, or continue the collision until the wreckage becomes unbearable.

The mathematics are clear. The thermodynamics are non-negotiable. The choice is ours—but not for much longer.

The Sufficiency Principle: Thermodynamic Limits and the End of Growth Mythology

 J. Rogers, SE Ohio

Abstract

The prevailing paradigm in technological and economic development is one of perpetual growth and acceleration, driven by the axiom that expansion is both possible and necessary. This paper argues that this paradigm is not merely unsustainable but thermodynamically impossible. We propose a fundamental shift towards a "Sufficiency Principle," where the goal of design is not maximal performance or endless growth, but optimal fit within planetary boundaries. Drawing on thermodynamic constraints and practical examples of distributed computation, we demonstrate that human flourishing does not require unlimited expansion—it requires intelligent design for adequacy. True innovation lies not in exceeding physical limits, but in building systems that operate sustainably within them.

1. Introduction: The Thermodynamic Impossibility of Infinite Growth

For decades, the trajectory of both technology and economics has been measured by a single, dominant metric: growth. Moore's Law became more than an observation; it became a mandate. Economies must expand, energy consumption must increase, computational power must accelerate. This pursuit has yielded incredible capabilities, but it rests on a fatal flaw: it ignores the laws of physics.

Every economic transaction, every computation, every act of production ultimately converts energy into waste heat. This is not a engineering problem to be solved—it is a fundamental constraint of thermodynamics. The Earth radiates heat into space at a finite rate determined by its surface area and temperature. If human energy consumption continues to grow exponentially, we will eventually generate more heat than the planet can dissipate.

The mathematics are unforgiving: at a sustained 2.3% annual growth in energy consumption (roughly the historical average), within 400 years human energy use would equal the total solar energy hitting Earth's surface. Within 1,400 years, Earth's surface temperature would reach the boiling point of water—not from greenhouse gases, but from direct waste heat alone. Long before that, civilization would collapse.

Growth is not infinite. Growth cannot be infinite. Physics does not negotiate.

We propose an alternative framework: The Sufficiency Principle. This principle recognizes thermodynamic reality and states that the value of a technology or economic system is not intrinsic to its scale or speed, but to its fitness for human purpose within planetary boundaries. A system is "sufficient" when it enables human flourishing without requiring perpetual expansion of energy and material throughput.

2. The Myth of Decoupling: Why Efficiency Alone Cannot Save Growth

Proponents of continued growth often argue for "decoupling"—the idea that economic activity can expand indefinitely while resource consumption remains flat or even declines through improved efficiency. This argument misunderstands both thermodynamics and economic behavior.

The Rebound Effect

History shows that efficiency gains are typically consumed by increased usage (Jevons Paradox). More efficient engines led to more vehicles on the road. More efficient computation led to more complex software and higher-resolution media. The net result is often increased total energy consumption, not decreased.

The Entropy Floor

Even in a purely informational economy, there are hard thermodynamic limits. Landauer's Principle establishes a minimum energy cost for erasing information. Computation generates heat. Data centers, even maximally efficient ones, dissipate energy. A "dematerialized" digital economy still runs on physical infrastructure that obeys the laws of physics.

The Extraction Ceiling

Every efficiency improvement requires material inputs—rare earth elements for batteries, silicon for chips, copper for wiring. These materials must be extracted, refined, and manufactured, all of which consume energy and generate waste heat. There is no escape from the material basis of technology.

The uncomfortable truth: efficiency can buy us time, but it cannot enable infinite growth. At some point, we must transition from an expansion-based system to a steady-state system optimized for sufficiency.

3. Redefining Progress: From "Faster and More" to "Sufficient and Sustainable"

If perpetual growth is thermodynamically impossible, what does progress look like? The Sufficiency Principle offers a framework.

The Human Threshold

The concept of "sufficient" is not deprivation—it is optimization for actual human need. A tool is "fast enough" when its performance ceases to be the bottleneck in the user's process, allowing them to operate at their natural pace of thought and creativity.

The Creative Threshold: For a writer, a word processor is sufficient when keystrokes appear instantaneously, preserving the flow of thought. A 10x faster processor offers no meaningful benefit. For a visual artist generating concept art, an AI system is sufficient if it produces images in the time it takes to evaluate the previous result and formulate a new prompt. The bottleneck becomes the artist's creativity, not the render time.

The Contextual Threshold: "Sufficient" is deeply contextual. On a 25-watt solar-powered computer in a remote location, generating one frame of AI video every ten minutes is not slow—it is profoundly powerful. It enables a previously impossible creative act. The same speed on a university supercomputer would be considered inadequate. The metric for success is not comparison to an external benchmark, but utility within a specific set of constraints and energy budget.

Distributed Sufficiency: A Case Study in Systemic Design

Consider the conventional model for creating and distributing video content:

1. Production: Massive render farms consuming megawatts
2. Distribution: Data centers streaming high-resolution files globally
3. Consumption: Passive displays rendering pre-determined content

Total energy cost: Enormous, centralized, and growing with demand for higher resolutions.

Now consider an alternative model built on sufficiency:

1. Production: One creator with a 25-watt computer generates compressed semantic video data over time—not raw pixels, but structural and narrative information
2. Distribution: Minimal streaming infrastructure transmitting small data payloads (the "sheet music" of the film, not the rendered performance)
3. Consumption: Local AI in the viewer's device renders the final video on-the-fly, adapted to their preferences, display capabilities, and accessibility needs

Total energy cost: A tiny fraction of the conventional model, distributed across millions of low-power devices each doing modest work.

The Personalization Dividend

In this model, the viewer's device becomes the final stage of the creative pipeline. They can choose:

• Aesthetic style (photorealistic, animated, stylized)
• Resolution appropriate to their display
• Accessibility features (high contrast, simplified compositions, audio description)
• Cultural adaptations (different rendering styles for different contexts)

The "content" becomes a flexible blueprint, not a rigid artifact. An old black-and-white film can be colorized on-the-fly at 4K resolution—or kept in its original form—based entirely on viewer preference. No centralized "remastering" needed. No gatekeeping about which films are "worth" upgrading.

The computational work happens distributed across space and time, within the thermal budget of existing consumer devices. This is sufficiency as liberation: more creative freedom, more accessibility, less total energy consumption.

4. Economic Systems in a Thermodynamic Box

If the Sufficiency Principle applies to technology design, it applies equally to economic systems. An economy predicated on perpetual GDP growth is an economy designed to violate the laws of physics.

The False Promise of "Green Growth"

Even renewable energy does not escape thermodynamic limits. Solar panels and wind turbines have manufacturing costs, material requirements, and replacement cycles. More fundamentally, the energy they capture is converted into economic activity, which generates waste heat. An economy running entirely on renewables but still growing exponentially will still eventually cook the planet through direct thermal output.

Redefining Prosperity

Sufficiency does not mean stagnation or poverty. It means:

• Optimization for human wellbeing within sustainable energy budgets
• Equitable distribution of resources rather than endless expansion for the few
• Qualitative improvement (better education, healthcare, art, community) rather than quantitative accumulation
• Stability rather than the perpetual disruption required by growth-based systems

A person creating two feature films per year on a 25-watt computer is not living in deprivation. They are living in harmony with physical reality while engaging in meaningful creative work.

The Alternative to Collapse

Economic models that require perpetual growth have only two possible endpoints:

1. Voluntary transition to steady-state sufficiency economies before hitting thermodynamic limits
2. Involuntary collapse when those limits are exceeded

There is no third option. Physics is not negotiable.

5. Implementing the Sufficiency Principle: Design for the Finite Planet

Adopting this philosophy requires fundamental changes in how we design, evaluate, and govern technological and economic systems.

Thermodynamic Accounting

Stop measuring success by GDP growth or computational speed alone. New metrics are required:

• Energy cost per unit of human wellbeing
• Material throughput per capita (with targets for reduction)
• Waste heat generation per economic activity
• Accessibility and equity of technological capability
• Stability and resilience rather than disruption and "innovation"

Design for Distributed Sufficiency

Instead of concentrating computation in massive data centers, distribute it across low-power edge devices. Instead of streaming pre-rendered content, transmit semantic information and render locally. Instead of planned obsolescence, design for longevity and repairability.

Embrace Constraint as Opportunity

The 25-watt computer is not a limitation to be overcome—it is a design constraint that forces creativity. Some of the most elegant solutions in history emerged from tight constraints. A finite energy budget is the ultimate design constraint, and working within it produces systems that are efficient, accessible, and sustainable.

Regulate for Reality

Economic policies must align with thermodynamic reality:

• Carbon pricing that reflects true thermal and ecological costs
• Subsidies for sufficiency-based design rather than maximum performance
• Antitrust enforcement against planned obsolescence
• Research funding for steady-state economic models

6. Conclusion: Technology and Economics as Harmonious Tools

The relentless pursuit of growth and speed has led us to the edge of thermodynamic impossibility. We are building systems that treat planetary boundaries as negotiable, when they are in fact absolute.

The Sufficiency Principle provides a path forward: design technology and economic systems for optimal fit within sustainable energy budgets, not for maximal expansion beyond them. The goal is not to do less, but to do what matters—human creativity, flourishing, and connection—within the finite box of a finite planet.

The image of an artist assembling a feature film on a 25-watt computer, distributed to viewers who render it locally according to their preferences, is not a picture of deprivation. It is a picture of profound intelligence: a system that enables creativity, accessibility, and cultural production while respecting the laws of physics.

The ultimate innovation is not a faster chip or a larger economy. It is a civilization that has learned to thrive within its means. Growth is not infinite. Growth cannot be infinite. The only question is whether we design for sufficiency voluntarily, or have it imposed upon us by the thermodynamics we tried to ignore.

Physics always wins. We can choose to win with it.

The Unity of Physics: Mass, Motion, and Time as One Phenomenon

A Dimensional Analysis Revealing the Hidden Structure of General Relativity

J. Rogers, SE Ohio

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Abstract

This paper demonstrates through pure dimensional analysis that the gravitational constant G and speed of light c appearing in General Relativity are not fundamental physical constants but unit conversion factors between SI units and natural dimensionless ratios. By performing algebraic substitutions using the Planck unit definitions, we prove the mathematical identity G/c² = l_P/m_P, revealing that gravitational time dilation is simply the dimensionless ratio τ = M_nat/R_nat. This identity, already embedded in existing physics equations, shows that mass, inertia, gravity, motion, and time dilation are not separate phenomena but different measurement perspectives on a single geometric reality: the structure of time itself. Using the GPS system as an empirical case study, we demonstrate that orbital motion is not independent of gravitational time dilation but is the kinetic manifestation of position within a time field. This analysis provides a physical mechanism for Mach's Principle and reveals that Newton's deliberate omission of a gravitational constant reflected a deeper understanding of coordinate-free physics than is commonly recognized.

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1. Introduction: Reading What Physics Already Says

The standard equation for weak-field gravitational time dilation is:

τ = GM/(Rc²)

where τ is the dimensionless time dilation factor, G is the gravitational constant, M is mass, R is radius, and c is the speed of light.

This paper makes no modification to this equation. Instead, we perform a rigorous dimensional analysis to reveal what it has been saying all along. We will prove that G/c² is not a fundamental coupling between mass and geometry, but rather a compound conversion factor between SI units and natural dimensionless units. This is not speculation—it is a mathematical theorem derivable from the definitions of Planck units.

The implications are profound: mass is not a substance that causes time dilation; mass IS time dilation. Gravity is not action-at-a-distance; it is local interaction between time field gradients. Motion is not primary; it is the consequence of navigating through non-uniform time geometry. These are not new theories—they are the necessary logical consequences of removing the unit-system artifacts from our existing equations.

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2. The Planck Units as Conversion Factors

2.1 The Standard Definition

Planck units are derived by setting fundamental constants equal to 1:

• h = c = G = k_B = 1

From these, we derive the Planck length, mass, and time:

• l_P = √(hG/c³) ≈ 4.051 × 10⁻³⁵ m
• m_P = √(hc/G) ≈ 5.456 × 10⁻⁸ kg
• t_P = √(hG/c⁵) ≈ 1.351 × 10⁻⁴³ s

Note: We use Planck's constant h, not the reduced constant ℏ = h/(2π). Using ℏ implicitly sets π = 1, which is a category error—treating a dimensionless mathematical constant as if it were a physical unit.

2.2 The Reinterpretation: Planck Units as Jacobians

However, we can equivalently view these as conversion factors (Jacobians) between SI units and natural dimensionless units:

• M_SI = M_natural × m_P (converts dimensionless mass to kilograms)
• R_SI  = R_natural × l_P (converts dimensionless length to meters)
• T_SI  = T_natural × t_P (converts dimensionless time to seconds)

This is not a new interpretation—it is simply making explicit what has always been true. When we measure "70 kilograms," we are implicitly stating that the object's dimensionless mass is M_natural = 70 kg / m_P ≈ 3.2 × 10⁹ in natural units.

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3. The Central Proof: G/c² is a Unit Conversion Artifact

3.1 Deriving the Identity

The Planck definitions provide us with expressions for G and c in terms of the Planck units:

From m_P = √(hc/G), we can solve for G:

• m_P² = hc/G
• G = hc/m_P²

We also know that:

• c = l_P/t_P

And from the Planck definitions:

• h = m_P × l_P²/t_P

Now we compute G/c²:

G/c² = [hc/m_P²] / [l_P/t_P]²

G/c² = [hc/m_P²] × [t_P²/l_P²]

G/c² = hc × t_P² / (m_P² × l_P²)

Substitute h = m_P × l_P²/t_P:

G/c² = [m_P × l_P²/t_P] × c × t_P² / (m_P² × l_P²)

G/c² = [m_P × l_P² × c × t_P²] / [t_P × m_P² × l_P²]

G/c² = c × t_P / m_P

Since c = l_P/t_P:

G/c² = [l_P/t_P] × t_P / m_P

G/c² = l_P / m_P

3.2 The Theorem

G/c² = l_P/m_P

This is not an approximation. It is an exact algebraic identity derived from the definitions of Planck units. The combination G/c² that appears ubiquitously in General Relativity is nothing more than the ratio of the Planck length conversion factor to the Planck mass conversion factor.

G/c² contains zero new physical information. It is a pure unit-scaling artifact.

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4. Revealing the Natural Physics: τ = M_nat/R_nat

4.1 The Substitution

Return to the standard time dilation equation:

τ = GM/(Rc²)

Rearrange to isolate G/c²:

τ = (G/c²) × (M/R)

Substitute our proven identity G/c² = l_P/m_P:

τ = (l_P/m_P) × (M_SI/R_SI)

Rearrange:

τ = (M_SI/m_P) / (R_SI/l_P)

By definition, M_SI/m_P = M_natural and R_SI/l_P = R_natural:

τ = M_natural / R_natural

4.2 The Physical Meaning

The time dilation factor—the thing we measure with atomic clocks, the thing that makes GPS work—is simply the dimensionless ratio of natural mass to natural length.

This ratio is:

• Unit-independent: Any observer using any measurement system will calculate the same τ
• Coordinate-free: It describes the geometry of spacetime, not our description of it
• Already in our equations: We just couldn't see it through the G and c² obscuring it

The physics is breathtakingly simple: gravitational time dilation is a pure geometric ratio.

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5. Mass as Time Field Geometry

5.1 The Ontological Shift

The equation τ = M_nat/R_nat forces a radical reinterpretation:

Old View:

• Mass is a substance
• Mass causes a gravitational field
• The gravitational field causes time dilation
• Mass → Field → Time Effect

New View:

• Time dilation field is fundamental (τ as a function of position)
• "Mass" is the name we give to the source term M_nat in this field
• M_nat/R_nat directly gives the local time rate
• Mass IS the time field structure

Mass does not cause time dilation. Mass IS time dilation measured at unit distance.

5.2 The Time Field

We can define a time field τ(r) = M_nat/r_nat that describes how time rate varies with position around a massive object. This is not a new field—it is simply recognizing what the metric tensor has been describing all along.

Properties of the time field:

• Stronger near massive objects (large M_nat, small r_nat)
• Weaker far from masses (small M_nat/r_nat)
• Sets the local "tick rate" of all clocks
• Objects follow geodesics through this field

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6. Gravity as Local Time Field Interaction

6.1 Newton's Law in Natural Units

The standard gravitational force equation:

F = G × m₁m₂/r²

But all G does is remove the unit scaling for si units

F/F_P = (l_P/m_P)² × m₁m₂/r²

Solve for F in si units

F = F_P × (l_P/m_P)² × m₁m₂/r²

G = F_P × (l_P/m_P)² 

In natural units (setting conversion factors aside):

F_nat = m₁_nat × m₂_nat / r_nat²

But we now understand that m_nat is actually the time field strength at unit distance. Therefore:

F_nat = (m₁_nat / r_nat) × (m₂_nat / r_nat)

F_nat = τ₁ × τ₂, separated by length r_nat

where τ₁ and τ₂ are the time field values associated with each mass.

6.2 The Physical Interpretation

Gravity is not action-at-a-distance between masses. It is the local interaction of two time field distortions separated by distance r.

• Each "mass" creates a time field distortion
• These distortions interact at their respective locations
• The "force" describes how strongly coupled they are through the geometry
• Distance r defines the geometric separation in the time field

Gravity is not mysterious action-at-a-distance. It is local time field gradient interaction.

6.3 Why Objects Fall

Objects don't fall because they are "attracted" to mass. They fall because:

1. Mass creates a gradient in the time field (∂τ/∂r ≠ 0)
2. The natural path (geodesic) through this gradient curves toward regions of slower time
3. "Falling" is following this natural path
4. "Weight" is the force required to prevent following this path

Objects move toward slower time, following the geometry of the time field.

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7. The GPS Proof: Orbital Motion as Time Field Expression

7.1 The Standard GPS Calculation

GPS satellites require time corrections for two "separate" relativistic effects:

Gravitational time dilation (GR):

Δt_grav = GM/(Rc²)

Velocity time dilation (SR):

Δt_vel = -v²/(2c²)

Engineers sum these effects and apply the total correction. The system works with extraordinary precision.

7.2 The Hidden Constraint

However, the satellite's velocity is not independent. For a stable circular orbit:

v² = GM/R

This is not optional—it is the geometric requirement for orbital motion. The velocity is completely determined by the gravitational potential at radius R.

7.3 The Unification

Substitute the orbital constraint into the velocity term:

Δt_vel = -(GM/R)/(2c²)

Now sum the two "separate" effects:

Δt_total = GM/(Rc²) - GM/(2Rc²)
Δt_total = GM/(2Rc²)

The two effects collapse into a single unified potential.

7.4 In Natural Units

Convert to natural units using G/c² = l_P/m_P:

Δt_total = (1/2) × (l_P/m_P) × (M/R)
Δt_total = (1/2) × (M_nat/R_nat)

The GPS satellite is directly measuring the dimensionless geometric ratio M_nat/R_nat at its orbital radius. The factor of 1/2 emerges from the orbital constraint—it is the geometric expression of circular motion within the time field.

7.5 The Profound Implication

The satellite's velocity is not causing "special relativistic time dilation" that adds to "general relativistic time dilation."

The velocity is the kinetic manifestation of being at that position in the gravitational time field.

The two "effects" were never separate. They are two partial views of a single geometric reality: the unified time field value at radius R.

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8. Motion as Navigation Through Time Geometry

8.1 Redefining Motion

If time field geometry is fundamental, then motion must be reinterpreted:

Old View:

• Objects have position and velocity
• Forces change velocity
• Time dilation is a side effect of motion

New View:

• Time field geometry exists (primary)
• Objects follow geodesics through this geometry
• Motion is the spatial manifestation of navigating time field contours
• Velocity is not independent—it reflects position in the field

8.2 Free Fall as Natural Motion

When you are in free fall:

• You follow a geodesic through the time field
• No forces act on you
• You experience weightlessness
• This is the natural state

8.3 Standing Still as Forced Acceleration

When you stand on Earth's surface:

• The ground prevents you from following your geodesic
• Electromagnetic forces continuously accelerate you upward
• You experience weight (proper acceleration ≈ 9.8 m/s²)
• This is a forced, non-natural state

You are not "at rest." You are being continuously accelerated away from your natural geodesic by the ground beneath your feet.

8.4 Weight is Not Gravity

The sensation of weight is not the sensation of gravity pulling you down. It is the sensation of the ground pushing you up, preventing you from following the time field gradient.

Weight is gravity being denied, not gravity being felt.

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9. Inertia and Mach's Principle

9.1 The Historical Problem

Mach's Principle (1883) states: "The inertia of a body is determined by the distribution of all other masses in the universe."

This remained a philosophical intuition without a physical mechanism for over 140 years.

9.2 The Mechanism: Cosmically-Defined Time

If all motion is orbital (nested hierarchy from planets to galaxies), then our local time rate is determined by:

τ_local = Σ (M_nat,i / R_nat,i)

where the sum is over all masses in the observable universe.  And probably from places we cannot currently observe depending on how old the universe really is.

Our local "dt"—the thing we use to define acceleration and inertia—is a relational property set by the cosmic mass distribution.

9.3 Inertia Emerges

Inertia is defined as:

F = m × a
a = dv/dt

Therefore m = F/(dv/dt).

But if dt itself is set by Σ(M_i/R_i) from all cosmic masses, then:

The inertial mass we measure is a direct consequence of the total mass distribution of the universe.

9.4 The Thought Experiment

Universe A (ours):

• Filled with galaxies
• Σ(M/R) is large
• Local dt is set by this cosmic sum
• Inertia exists with measured values

Universe B (empty):

• No other masses exist
• Σ(M/R) ≈ 0
• Local dt is undefined by cosmic structure
• Inertia as we know it would not exist

Mach's Principle is not a separate postulate. It is a necessary consequence of time being a relational, globally-coupled property.

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10. The Unity of Five Concepts

We can now see that five apparently distinct phenomena are one:

10.1 Mass

What it is: The source term M_nat in the time field equation τ = M_nat/R_nat

Physical meaning: The magnitude of time field distortion at unit distance

10.2 Time Dilation

What it is: The local value of the time field τ(r) = M_nat/r_nat

Physical meaning: The actual, measurable rate of clock ticking at position r

10.3 Gravity

What it is: The gradient of the time field ∇τ = -M_nat/r_nat²

Physical meaning: The geometric curvature that defines geodesic paths

10.4 Inertia

What it is: Resistance to displacement through the cosmically-defined time field

Physical meaning: m = F/(dv/dt) where dt is set by Σ(M_i/R_i)

10.5 Motion

What it is: Navigation through time field geometry

Physical meaning: Spatial manifestation of position within non-uniform time structure

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11. Newton's Wisdom Recovered

11.1 The Deliberate Omission

Isaac Newton wrote:

F ∝ m₁m₂/r²

He did not write F = k × m₁m₂/r² with a specific constant k (our G) because:

1. As Master of the Royal Mint, he understood that conversion constants are conventional, not fundamental
2. He knew that any specific numerical k would be unit-dependent
3. His ratio method canceled the constant in every calculation
4. He was working at a higher level of abstraction than his successors

11.2 The Lost Principle

Newton's proportional reasoning was architecturally rigorous:

• Work only with dimensionless ratios
• Cancel unknown constants systematically
• Keep physics independent of measurement conventions

His moon-apple calculation:

a_apple/a_moon = (r_moon/R_earth)²

This is coordinate-free physics. The ratio is the same for any observer using any units. Both k (our G) and M_earth cancel perfectly.

11.3 The Modern Error

When Cavendish measured G in 1798, physics celebrated it as "completing" Newton's theory. But:

• Newton's theory was already complete (proportionally)
• Cavendish calibrated it for a specific unit system (SI)
• We mistook the calibration for the physics
• We embedded unit-system artifacts into "fundamental constants"

Newton didn't omit G from ignorance. He omitted it from deeper understanding.

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12. Why This Was Hidden

12.1 The Pedagogical Trap

Physics education presents:

F = G × m₁m₂/r²

with G ≈ 6.674 × 10⁻¹¹ m³/(kg·s²)

Students learn:

• G is a "fundamental constant of nature"
• It has the value it does for "deep reasons"
• Finding that value was a triumph of experimental physics

They don't learn:

• G's value is entirely determined by our choice of kilogram, meter, and second
• Change the unit system → change G
• The physics is in the dimensionless ratio, not in G

12.2 The Conceptual Barrier

We teach that:

• Mass is fundamental (measured in kg)
• Length is fundamental (measured in m)
• Time is fundamental (measured in s)
• G connects them

This obscures that:

• M_nat, R_nat, T_nat are dimensionless (the actual physics that are invariant under all measurement)
• m_P, l_P, t_P are conversion factors (unit system artifacts)
• G is built from these conversions

We've been teaching unit conversions as if they were physics.

12.3 The Mathematical Camouflage

The equation τ = GM/(Rc²) looks like it contains fundamental constants G and c. But:

τ = (l_P/m_P) × (M_SI/R_SI)

reveals that G and c are merely the machinery for converting SI measurements to natural dimensionless ratios.

The constants were hiding the physics, not revealing it.

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13. Experimental Verification

13.1 This is Not a New Theory

Critically, this paper proposes no new physics. It is a dimensional analysis of existing theory. Therefore:

• All existing experimental confirmations of GR remain valid
• GPS continues to work precisely as calculated
• No new experiments are needed to "test" this framework

13.2 What Changes

What changes is interpretation:

Before: "GPS satellites experience GR time dilation + SR time dilation"

After: "GPS satellites measure their position in Earth's unified time field"

The numbers are identical. The understanding is transformed.

13.3 A Testable Prediction

If inertia is set by Σ(M_i/R_i) over the cosmos, and the universe is expanding, then:

• R_i to distant galaxies increases over time
• Σ(M_i/R_i) slowly decreases
• Local inertial mass ratios might shift subtly

Prediction: Ultra-precise measurements over decades might detect:

• Drift in fundamental mass ratios
• Changes in fine structure constant
• Anomalies in atomic clock comparisons

This is at the edge of current measurement capability but in principle detectable.

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14. Philosophical Implications

14.1 The Nature of Constants

"Fundamental constants" fall into two categories:

Type 1: Pure numbers (dimensionless)

• Fine structure constant α ≈ 1/137
• Proton/electron mass ratio ≈ 1836
• These are coordinate-free physics

Type 2: Unit-dependent values

• G = 6.674 × 10⁻¹¹ m³/(kg·s²)
• c = 299,792,458 m/s
• These are conversion factors

We've been treating Type 2 as if they were Type 1, asking "why does G have this value?" when the answer is "because we defined the kilogram, meter, and second this way."

14.2 The Structure of Physical Law

Physical laws should be:

• Coordinate-free (same for all observers)
• Dimensionless (pure geometric ratios)
• Unit-independent (not tied to human conventions)

Newton understood this. General Relativity embodies it (in the tensor formulation). But our pedagogical presentation obscures it.

This paper is a call to teach the dimensionless physics first, and the unit conversions second.

14.3 The Unity of Reality

The deepest implication is ontological:

Mass, time, space, motion, and inertia are not separate substances or properties. They are different linguistic descriptions of a single geometric reality.

Just as:

• Temperature and kinetic energy are one thing (viewed macroscopically vs microscopically)
• Electricity and magnetism are one thing (viewed in different reference frames)

So too:

• Mass and time dilation are one thing (viewed as source term vs field value)
• Gravity and geodesic curvature are one thing (viewed as force vs geometry)
• Inertia and cosmic time coupling are one thing (viewed locally vs globally)

Physics is unified not because we found connections between separate phenomena, but because we recognized they were never separate.

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15. Conclusion

This paper has proven through dimensional analysis that:

1. G/c² = l_P/m_P (exact algebraic identity)
2. τ = M_nat/R_nat (gravitational time dilation is a pure dimensionless ratio)
3. Mass is time field geometry (not substance causing time dilation)
4. Gravity is local time field interaction (not action-at-a-distance)
5. Motion is navigation through time geometry (not independent phenomenon)
6. Inertia emerges from cosmic time coupling (Mach's Principle mechanism)

None of this required new physics. It required only:

• Recognizing Planck units as conversion factors
• Performing algebraic substitution
• Reading what the equations already say

GPS satellites orbiting overhead prove this framework every nanosecond: their orbital motion is not independent of their gravitational time dilation—it is the kinetic expression of their position within Earth's time field.

Newton's deliberate omission of a gravitational constant reflected his understanding that constants are conventional, not fundamental. His proportional reasoning kept the physics coordinate-free. We lost this wisdom when we reified G as fundamental.

The physics is not in G, c, or any unit-dependent constant. The physics is in the invariant, dimensionless ratios of the universe—ratios that are true no matter how they are measured.

Mass does not cause time change. Mass IS time change.

Gravity is not a force. Gravity is the geometry we navigate.

Motion is not primary. Motion is the manifestation of existing in non-uniform time.

These are not speculations. They are the necessary logical consequences of removing unit-system artifacts from equations that have been validated for over a century.

We have been doing coordinate-free physics all along. We just couldn't see it through the coordinates.

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References

1. Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica

2. Einstein, A. (1915). "Die Feldgleichungen der Gravitation." Sitzungsberichte der Preussischen Akademie der Wissenschaften

3. Cavendish, H. (1798). "Experiments to Determine the Density of the Earth." Philosophical Transactions of the Royal Society

4. Mach, E. (1883). Die Mechanik in ihrer Entwicklung

5. Rogers, J. (2025). "The Constant of Proportionality: Newton's Deliberate Omission of G and the Lost Principle of Invariance"

6. Rogers, J. (2025). "From GPS to Mach's Principle: On the Unity of Motion, Time, and Inertia"

7. Ashby, N. (2003). "Relativity in the Global Positioning System." Living Reviews in Relativity, 6(1)

8. Planck, M. (1899). "Über irreversible Strahlungsvorgänge." Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften

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Appendix A: Mathematical Summary

Planck Definitions (using h, not ℏ):

• l_P = √(hG/c³)
• m_P = √(hc/G)
• t_P = √(hG/c⁵)

Unit Conversions:

• M_SI = M_nat × m_P
• R_SI = R_nat × l_P
• T_SI = T_nat × t_P

The Central Identity:

G/c² = l_P/m_P

Time Dilation (Standard Form):

τ = GM/(Rc²)

Time Dilation (Natural Form):

τ = M_nat/R_nat

Gravity (Standard Form):

F = Gm₁m₂/r²

Gravity (Natural Form):

F_nat = τ₁ × τ₂ / r_nat²

GPS Unified Potential:

Δt_total = (1/2) × GM/(Rc²) = (1/2) × M_nat/R_nat

Mach's Principle:

τ_local = Σᵢ (M_nat,i / R_nat,i)
m_inertial ∝ 1/τ_local ∝ Σᵢ (M_nat,i / R_nat,i)

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Appendix B: For the Skeptical Reader

Objection 1: "This is just playing with units. You haven't changed the physics."

Response: Exactly. That's the point. The physics already says this. We've been obscuring it with unit-dependent notation.

Objection 2: "But G and c are measured experimentally. They're real."

Response: Their numerical values are measured. But those values depend entirely on our definitions of kg, m, and s. Change the unit system, and G and c change. The dimensionless ratio M_nat/R_nat does not change.

Objection 3: "This doesn't make testable predictions."

Response: It makes one: if inertia is set cosmically via Σ(M/R), then cosmic expansion should cause subtle shifts in inertial mass ratios over cosmological time. This is testable with sufficient precision.

Objection 4: "Einstein already knew spacetime was curved. This isn't new."

Response: Einstein knew geometry was physics. But we still teach that "mass causes curvature" as if they were separate. This framework shows they are not separate—mass IS the curvature (specifically, of time).

Objection 5: "Why hasn't anyone pointed this out before?"

Response: They have. Physicists working in natural units understand this. But it's been treated as a "mathematical convenience" rather than revealing the actual structure of physical law. And it's not taught this way to students, who learn to think of G and c as fundamental.

The GPS system proves this interpretation daily. Every satellite measures τ = M_nat/R_nat. We just call it "GM/(Rc²)" because we insist on working in SI units.

The Metrological Origin of Gravity: A Reinterpretation of G/c² as the Jacobian of a Unified Time Field

J. Rogers, SE Ohio

Abstract:
The term G/c², ubiquitous in General Relativity, is traditionally interpreted as the fundamental coupling constant linking mass to the geometry of spacetime. This paper presents a formal proof that this interpretation is a category error. We demonstrate through direct algebraic substitution that G/c² is not a physical constant but a composite metrological artifact—a Jacobian—whose sole function is to translate physical law from its native, dimensionless form into the arbitrary human-invented SI unit system. The mathematical identity G/c² = l_P/m_P is derived, revealing that the accepted equations for gravitational time dilation reduce to the simple, scale-free ratio: change in time is proportional to natural mass over natural length. This re-frames gravity not as a force or a curvature of space, but as the local interaction between these time fields. Using the GPS satellite as a prime example, we show that orbital motion is a direct manifestation of this time field, unifying the apparently separate kinematic and gravitational effects. We conclude that mass, inertia, motion, and gravity are not distinct phenomena but are different observational facets of a single, unified reality: the experience of time.

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1. Introduction: The Illusion of a Coupling Constant

In the architecture of General Relativity, the term G/c² serves as the cornerstone, the universal constant that dictates the "strength" of gravity by coupling mass-energy to the curvature of spacetime. Its appearance in formulas for gravitational lensing, time dilation, and the Schwarzschild radius has cemented its status as a fundamental feature of the universe.

This paper challenges that dogma. We will demonstrate that the perceived physical significance of G/c² is an illusion created by our insistence on using an arbitrary, human-centric measurement system (the SI units of meters, kilograms, and seconds). By treating the physical constants G and c not as fundamental properties but as the necessary conversion factors they are, we will show that the term G/c² contains no physical information. Instead, it is a purely mathematical artifact—a Jacobian matrix component—that vanishes when physical law is expressed in its proper, dimensionless form.

2. The Mathematical Identity: Deconstructing G/c²

The foundation of our argument is not a new theory, but a rigorous simplification of existing definitions. The Planck "units" are not fundamental scales, but the conversion factors relating our SI system to the universe's natural, relational structure. The constants G and c are defined by these conversion factors:

• Gravitational Constant (G): G = l_P³ / (m_P · t_P²)

• Speed of Light Squared (c²): c² = (l_P / t_P)² = l_P² / t_P²

Here, l_P, m_P, and t_P represent the Jacobian conversion factors for length, mass, and time, respectively. Now, we perform the division of these two terms:

G / c² = [ l_P³ / (m_P · t_P²) ] / [ l_P² / t_P² ]

The t_P² terms in the denominators cancel immediately, leaving:

G / c² = ( l_P³ / m_P ) / l_P²

Simplifying the expression for l_P yields the final, stunning identity:

G / c² = l_P / m_P

This is not a physical law; it is a mathematical theorem of our measurement system. It proves that the entire G/c² term is nothing more than the ratio of the length-conversion-factor to the mass-conversion-factor. Its role is purely linguistic, not physical.

3. The Physical Law Revealed: Time Dilation as a Natural Ratio

With this identity in hand, we can now translate the standard weak-field equation for gravitational time dilation and reveal the true physical law it has been obscuring. The standard formula for the dimensionless time dilation factor (τ_factor) is:

τ_factor = G · M_si / (R_si · c²)

Where M_si and R_si are the mass and radius in SI units. We now replace the G/c² term with our proven identity:

τ_factor = (l_P / m_P) · (M_si / R_si)

We can rearrange this into a more insightful form by grouping the terms into dimensionless ratios. The dimensionless "natural mass" (M_nat) is the SI mass divided by its conversion factor (M_nat = M_si / m_P), and likewise for length (R_nat = R_si / l_P). This gives:

τ_factor = (M_si / m_P) / (R_si / l_P)

Substituting the natural, dimensionless quantities, we arrive at the true physical law:

τ_factor = M_nat / R_nat

The change in time is simply the ratio of natural mass to natural length. The entire complexity of G and c was scar tissue from the translation. This reveals the profound truth: mass does not cause time dilation; mass is the measure of a source of time dilation. The term M/R is a time field.

4. Gravity as the Interaction of Local Time Fields

This re-frames our entire understanding of gravity. It is not a mysterious "action at a distance." It is a purely local phenomenon. Every object is the source of a time field defined by its M_nat / R_nat. The interaction we call "gravity" is the relationship between these fields.

Newton's Law, F ∝ m₁m₂ / r², can be seen as the SI-unit expression for the interaction between two time-field sources (m₁/r and m₂/r). The "force" is the result of two objects navigating the combined gradient of their time fields. The interaction is local at every point in space, mediated by the structure of time itself.

5. The GPS Satellite: Motion as a State of Time

The GPS satellite provides the definitive example of this unified reality. It experiences two "time dilation" effects that, in the standard model, are treated as separate:

1. Gravitational Time Dilation (GR): Its clock runs faster because it is in a weaker gravitational potential (a shallower time field).

2. Kinematic Time Dilation (SR): Its clock runs slower because of its high orbital velocity.

However, the satellite's orbital velocity is not an independent variable. It is determined by the potential: v² = GM/r. When this constraint is respected, the two effects are revealed to be two sides of the same coin. An object in a stable orbit is not just moving through a time field; its motion is a manifestation of it. The satellite is following a path—a geodesic—of constant temporal potential. Its velocity is precisely what is required to balance the change in the time field's depth, maintaining a consistent "time experience." Motion is not separate from gravity; it is how an object remains in equilibrium with the local structure of time.

6. The Grand Unification: Mass, Inertia, and Gravity as Experiences of Time

This framework dissolves the boundaries between physics' most fundamental concepts, revealing them as different perspectives on the single phenomenon of time:

• Time Dilation: The fundamental reality. The local rate of time is a field, described by M_nat / R_nat.

• Mass: The name we give to the source, or magnitude, of a localized time field.

• Gravity: The gradient of the time field, which dictates the natural paths of objects.

• Motion (Geodesic): The natural state of following a path of constant temporal potential through the landscape of the time field.

• Inertia: The resistance to being displaced from one's natural geodesic. To accelerate an object is to force its time-field distortion to move, which requires energy. Inertia is the measure of this resistance, and E=mc² is the energy cost of creating or moving a time distortion of magnitude m.

These are not five separate ideas. They are one idea, viewed from five different angles.

7. Conclusion: Beyond the Dogma of Measurement

The reification of G/c² as a fundamental constant is a historical error born from mistaking the map for the territory. A simple, formal algebraic substitution proves that this term is a metrological artifact, a Jacobian required to translate the simple, dimensionless reality of time change ~ mass / length into our arbitrary SI unit system.

This insight reveals that mass is a measure of time dilation, gravity is the interaction of time fields, and inertia is the resistance to being moved through the landscape of time. This is not a new theory that requires new evidence. It is the mathematical truth already embedded within our current equations, waiting to be seen once the dogma of measurement is set aside. The future of fundamental physics lies not in finding new constants, but in rediscovering the simple, proportional, and unified reality they have been obscuring all along.