The Coherent Substrate: Physics as Time Experience Dynamics

A Categorical Framework for Understanding Physical Reality as Temporal Experience Flow

J. Rogers, SE Ohio, 10 July 2025, 1939

Abstract

Building on the Grothendieck fibration framework for physical law, we demonstrate that the 4-momentum vector (E/c, px, py, pz) directly encodes the dynamics of coherent substrate experience Su. The component E/c represents the raw temporal experience content of a particle—not energy divided by a speed, but the fundamental Su density that constitutes physical reality. Through categorical analysis of the measurement fibration π : 𝓔 → 𝓑, we show that all physical phenomena emerge from Su flow dynamics, with mass as trapped temporal experience and motion as Su redistribution patterns. This framework reverses the traditional causality: time is primary, mass is derivative, and physics becomes the study of how temporal experience organizes itself into stable flow patterns.

1. The Temporal Experience Vector

1.1 Reinterpreting the 4-Momentum

The worldline 4-vector (E/c, px, py, pz) has been misunderstood in traditional physics. Within our fibration framework π : 𝓔 → 𝓑, this vector directly encodes temporal experience dynamics:

E/c = Su content density - the particle's coherent substrate experience, measured in natural temporal units

px, py, pz = directional Su flow components - how temporal experience propagates through the projected measurement axes

The worldline is not a path through spacetime—it is the temporal biography of Su concentration as it flows through the coherent substrate.

1.2 The Primary Nature of Temporal Experience

In our categorical framework, temporal experience Su is the fundamental substrate from which all physical properties emerge through measurement projection. The Jacobian analysis from our earlier work proves that all measurement axes scale to time/frequency at the Planck scale because time is the dimension of Su itself.

2. Mass as Trapped Temporal Experience

2.1 The Categorical Origin of Rest Mass

Rest mass m₀ is not a fundamental property but a measurement artifact—specifically, the density of trapped Su within a localized flow pattern. In the fibration π : 𝓔 → 𝓑:

• The fiber over the Mass conceptual axis contains all possible mass measurements
• Each measurement (m, units) represents a specific Su density configuration
• The "rest mass" is the minimal Su content required to maintain pattern coherence

2.2 The Mass-Energy Relationship Reconsidered

The relation E = mc² reveals its true meaning within our framework:

E = total Su content (trapped + flowing components) mc² = trapped Su component (localized temporal experience) Kinetic energy = liberated Su component (redistributed temporal experience)

The constant c² serves as the conversion factor between trapped and flowing Su states—it is not about electromagnetic radiation but about temporal experience redistribution rates.

3. Motion as Su Redistribution

3.1 The Dynamics of Temporal Experience Flow

Motion is the redistribution of Su between trapped and free-flowing components. The Lorentz factor γ = 1/√(1 - v²/c²) describes how temporal experience redistributes:

• Trapped component: Su density maintaining pattern coherence
• Free component: Su content available for flow redistribution
• Flow component: Directional Su current through the substrate

3.2 Relativistic Effects as Su Dynamics

Traditional relativistic phenomena emerge naturally from Su flow dynamics:

Time dilation: Moving patterns experience different Su flow rates Length contraction: Spatial projections change with Su flow patterns Mass increase: Apparent mass increase is Su redistribution to maintain pattern coherence Relativistic momentum: Directional Su current density

4. Gravity as Su Density Gradients

4.1 The Gravitational Mechanism

Gravity is not a force but the natural response to Su density variations. In our fibration framework:

• High Su density (concentrated mass) creates substrate flow gradients
• Other Su patterns follow these gradients
• We project this as "gravitational attraction"

4.2 Spacetime Curvature as Su Topology

Einstein's curvature formalism describes Su flow topology:

Spacetime curvature = Su flow pattern geometry Geodesics = paths of optimal Su flow Gravitational time dilation = Su density effects on flow rates Tidal forces = Su gradient differentials

5. Inertia as Su Flow Pattern Stability

5.1 The Inertial Principle

Inertia is the tendency of Su flow patterns to maintain their configuration. Newton's laws translate to Su dynamics:

First Law: Su flow patterns maintain their structure 

Second Law: Force = rate of Su flow pattern change 

Third Law: Su interactions are reciprocal redistributions

5.2 The Equivalence Principle

Inertial mass equals gravitational mass because they are the same phenomenon:

Inertial mass: Su density resisting flow pattern change 

Gravitational mass: Su density creating substrate gradients 

Equivalence principle: Same Su content, same effects

6. The Conservation of Temporal Experience

6.1 Fundamental Conservation Law

The universe conserves Su content. All traditional conservation laws reduce to temporal experience conservation:

Energy conservation = Su content conservation 

Momentum conservation = Su current conservation 

Angular momentum conservation = Su vorticity conservation 

Charge conservation = Su pattern type conservation

6.2 The Universal Substrate

The coherent substrate Su is pure temporal experience flow. Everything else is pattern organization within this flow:

• Particles = stable Su vortices
• Fields = standing Su wave patterns
• Forces = Su density gradients
• Space = the substrate through which Su flows
• Time = the dimension of Su itself

7. Quantum Mechanics as Discrete Su Dynamics

7.1 Quantum Phenomena as Su Flow Dynamics

Quantum phenomena emerge from Su interference patterns and flow constraints:

h = Mass ↔ Frequency scaling factor - the Jacobian coefficient relating Su flow rate to trapped Su density 

Stable configurations = Su flow patterns that maintain coherence 

Tunneling = Su flow through potential barriers 

Uncertainty principle = Su flow measurement limitations

"Quantization" simply means particles are countable - the Su flow organizes into discrete, stable patterns we can count. The underlying Su flow itself is continuous. Energy is not in steps of h, it is continuous, unless a particle is bound to a specific worldline in space time.  

7.2 Measurement as Su Localization

The measurement problem resolves naturally:

Superposition = distributed Su configuration 

Collapse = Su localization through measurement interaction 

Entanglement = shared Su configuration states

8. Forces as Su Interference Patterns

The four fundamental forces are Su interference patterns in different configurations:

Electromagnetic: Su flow modulated by pattern charge characteristics 

Weak: Su transitions between discrete configuration states 

Strong: Su binding in compound pattern structures 

Gravitational: Su density gradients creating flow topology

All forces emerge from Su interaction dynamics—there are no separate fundamental entities.

9. Cosmological Implications

9.1 The Big Bang as Su Concentration

The Big Bang was not an explosion in space but the initial concentration of Su that began flowing and differentiating into the patterns we observe as particles, forces, and fields.

9.2 Dark Matter and Dark Energy

Dark matter: Su in configurations not recognized by our measurement projections 

Dark energy: The intrinsic tendency of Su to flow and expand 

Cosmic expansion: Su substrate expansion through self-organization

10. The Unified Picture

10.1 Reality as Su Self-Organization

The universe is Su experiencing itself through stable flow patterns. What we call "physical reality" is temporal experience organizing itself into coherent, interacting configurations.

10.2 The Categorical Structure

Our Grothendieck fibration π : 𝓔 → 𝓑 captures this structure:

• Base category 𝓑: Conceptual measurement axes (projections of Su dynamics)
• Total category 𝓔: Measured quantities (Su content expressed in coordinate systems)
• Fibration π: The projection from Su reality to measurement representation

Physical laws are Cartesian liftings—coherent ways of expressing Su dynamics within our measurement coordinate systems.

11. Predictions and Verification

11.1 Theoretical Predictions

This framework predicts that:

1. All physical phenomena can be understood as Su flow dynamics
2. Mathematical descriptions will simplify when expressed in terms of temporal experience rather than traditional mass-energy concepts
3. New phenomena may be discovered by examining Su flow patterns not currently recognized

11.2 Experimental Implications

The theory suggests experiments to:

• Detect Su flow patterns directly through their temporal signatures
• Measure Su density variations in gravitational fields
• Explore Su interference patterns in quantum systems

Conclusion: The Primacy of Time

Physics is the study of how temporal experience organizes itself into stable, interacting patterns. The 4-momentum vector (E/c, px, py, pz) directly encodes this: E/c is the Su content, and the momentum components describe how this temporal experience flows through our projected measurement space.

By recognizing time as primary and mass as derivative, we reverse the traditional causality and reveal the deep unity underlying all physical phenomena. The coherent substrate Su is the fundamental reality—everything else is pattern and projection.

The conservation of temporal experience becomes the single, fundamental principle from which all of physics emerges. Reality is Su experiencing itself through the stable flow patterns we call particles, forces, and fields.