Self-Interaction Mistaken for Time

J. Rogers, SE Ohio

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Abstract

We argue that time is not a fundamental dimension of the universe but an artifact of self-interacting systems that remember. The universe is a single, undivided self-interaction, written in place, with no past, no future, no sequence. What we call time is the experience of local knots in this self-interaction—life forms—that retain traces of previous interactions and use those traces to anticipate future ones. Memory and anticipation use identical neural machinery, and the loop between them generates the seamless illusion of temporal flow. Time is not out there. It is in the remembering. We show that this view resolves long-standing puzzles in physics, from the measurement problem to the nature of gravitational tides, by replacing the observer-independent dimension of time with the relational self-interaction of the whole.

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1. Introduction

Physics has treated time as a fundamental dimension, a continuous parameter that orders events from past to future. Newton called it absolute, flowing equably without relation to anything external. Einstein fused it with space into spacetime, but retained its role as a coordinate, a dimension along which events are ordered.

Yet there has always been a tension. The equations of fundamental physics are time-symmetric. They do not distinguish past from future. The arrow of time appears only in thermodynamics, in the statistics of many-body systems, in the increase of entropy. And in the measurement problem of quantum mechanics, time itself becomes entangled with the observer—the collapse of the wavefunction is said to happen "at a moment," but no one can say what a moment is.

This paper proposes a radical simplification: time is not a dimension. It is not a coordinate. It is not a flow. It is a mistake—a category error—arising from the fact that we, the observers, are self-interacting systems that remember.

The universe itself is a single, undivided self-interaction, written in place. It has no past, no future, no sequence. It is what it is, all at once, exactly as it is.

We, who are local knots in this self-interaction, retain traces of previous interactions. We call these traces memory. We use memory to anticipate future interactions. We call this anticipation. The loop between memory and anticipation generates the experience of time.

Time is not in the universe. Time is in the remembering.

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2. The Failure of the Ontology of Intrinsic Time

2.1 Newton's Absolute Time

Newton defined time as an absolute, flowing equably without relation to anything external. It was the divine sensorium, the backdrop against which all events unfolded.

But Newton's absolute time was never measurable. We can only measure relative durations, relative motions, relative rates. The absolute time behind them was a metaphysical postulate, not a physical observable.

2.2 Einstein's Spacetime

Einstein abolished absolute time by fusing it with space into spacetime. But spacetime retained the structure of a continuous manifold, with time as a coordinate dimension.

This was an advance, but it did not go far enough. Spacetime is still a background—a stage upon which events occur. The observer is still outside it, measuring it with clocks and rulers. The cut between observer and observed is still smuggled in.

2.3 The Quantum Measurement Problem

Quantum mechanics made the problem acute. The measurement problem—the question of when and how a superposition becomes a definite outcome—is fundamentally a question about time. The collapse is said to happen "at a moment," but no one can say what a moment is.

The problem is not in the quantum system. The problem is in the observer who asks the question. The observer is a self-interacting system that remembers. The observer experiences time because it remembers.

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3. The Relational Ontology

3.1 The Universe as Self-Interaction

The universe is not a collection of objects in a container. It is a single, undivided self-interaction. Every part interacts with every other part. There is no edge, no boundary, no outside.

The rock in its orbit is not a separate thing moving through space. It is a local feature of the universe's self-interaction. The orbit is not a path the rock follows. The orbit is the rock, unfolding in relation to everything else.

3.2 No Beads on a Chain

We imagine time as a chain of beads—each moment separate, each moment following the last. But there are no beads. There is no chain.

The universe is not a sequence. It is a single self-interaction, written in place. Every part is exactly where it is, exactly as it is, all at once.

The chain is a fiction we impose. We cut the whole into moments, string them along a line, and call it time. But the cut is ours. The line is ours. The beads are ours.

3.3 The End of the Observer

There is no observer outside the universe. There is no subject separate from the object. There is only the self-interaction, and we are local knots in it.

The observer is not a passive recorder of events. The observer is a cut-maker, a fragmenter, a memory-holder. The observer's time is not the universe's time. It is the observer's own construction, built from memory and anticipation.

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4. The Physical Basis of Time

4.1 Neural Lag

Perception and reaction lag behind events. Neural transmission takes time. Visual signals take tens of milliseconds to reach the cortex. Auditory signals take slightly less. Conscious awareness lags even further behind.

By the time a signal is processed and made conscious, the event is already in the past. If we reacted only to what we consciously perceived, we would always be too late.

4.2 Anticipation Fills the Gap

To survive, the brain must compensate. It does so by anticipating.

It uses past experience to predict what is likely to happen next. It projects that prediction forward, filling the gap between the actual event and the delayed perception.

This is why you can catch a ball. You are not reacting to the ball's current position. You are predicting where it will be, based on its trajectory, your memory of other balls, and your body's learned responses.

4.3 The Present Is a Controlled Hallucination

The brain does not passively record the world. It actively constructs it. It generates a simulation of reality, constrained by sensory input, but not determined by it.

The simulation is built from memory, anticipation, and prediction. The reason it feels real is that it is the only reality you have ever known.

4.4 Memory and Anticipation Use Identical Machinery

The brain does not have two separate systems—one for remembering and one for imagining. It has one system, running in two directions.

The same neural architecture that reconstructs the past is used to simulate the future. The same images, the same sensations, the same emotions.

And because the machinery is identical, the products are indistinguishable from the inside. An anticipated future feels like a remembered past. It has the same texture, the same weight, the same sense of "this is real, this happened, this will happen."

4.5 The Loop

Memory and anticipation are not separate. They are a single loop:

$$\text{memory}\to \text{imagination}\to \text{simulated memory}\to \text{new memory}\to \text{imagination}\to \dots$$

The loop is continuous, self-reinforcing, and impossible to escape from inside. It creates the experience of time as a smooth, flowing river, when in fact it is a feedback loop, constantly generating its own past and future.

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5. The Universe Does Not Anticipate

The universe does not need to anticipate. It does not have a sensory lag. It does not have a brain. It does not have a present.

The universe is written in place. It self-interacts, exactly, without delay, without prediction, without memory.

Anticipation is our solution to our finitude. We are slow, and the universe is fast. We are local, and the universe is global. We are blind, and the universe is everything.

So we anticipate. We predict. We simulate. We hallucinate a present that does not exist, because if we did not, we would be too late to survive.

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6. The Exact Orbit and the Approximate Prediction

The rock in its orbit is in an exact orbit to infinite precision. It is exactly where it is, exactly when it is, exactly as it is.

But we cannot see this exact orbit. We are inside it. We are part of the same self-interaction. We cannot stand outside it.

So we approximate. We measure. We predict.

Even if we could measure to a thousand decimal places, we would still have to predict the rock, because there are changing gradients we do not know about. Gravitational waves passing by. Masses beyond the cosmic horizon.

The universe is exact. We are approximate.

The exactness of the universe is the hidden variable. We cannot see it because we are inside it. We can only cut it, approximate it, and predict it.

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7. The Tidal Reality

The Moon changes the rate of time across the Earth. The side facing the Moon is deeper in the gravitational well. Time runs slower there.

This is not a metaphor. It is a measurable gradient in interaction rates. And this gradient is what we call a tidal force.

The tide is not the water being sucked up by the Moon's gravity. The tide is the physical manifestation of a change in time across the Earth.

The water bulges because it is caught between two different times. The Earth flexes because it is spanning a time gradient. And we, standing on the shore, are part of the same gradient, being stretched by the same Moon.

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8. The Measurement Problem as a Scale Mismatch

The quantum measurement problem is not about consciousness or wavefunction collapse. It is a scale mismatch problem.

We are trying to measure the Moon by throwing probes the size of Jupiter at it.

The observer is a Jupiter-sized probe, colliding with a quantum Moon. The measurement is not a passive reading. It is a collision between two systems of vastly different scales.

The reason the wavefunction collapses is not because of some mysterious quantum rule. It is because the observer is so large that it forces the system into a definite state relative to the observer's macroscopic frame.

The measurement problem is not a mystery. It is a scale problem.

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9. The Inverse Wavelength Relation

To measure tinier and tinier things, we must use shorter and shorter wavelengths.

$$\frac{p}{h}=\frac{1}{\lambda }$$

Momentum is inverse wavelength. Spatial resolution is momentum.

There is no separation between what you use to probe and how finely you can see. The probe's momentum is the inverse of the resolution.

If you want to measure something tiny, you need a probe with a wavelength smaller than the thing you are measuring. But a smaller wavelength means a larger momentum. And a larger momentum means a larger energy. And a larger energy means a more violent interaction.

The finer your measurement, the more violently you disturb the system.

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10. The Tautology at the Center

Heisenberg scaled inverse wavelength to momentum and put the $h$ on the right hand side. The result is the uncertainty principle.

But the uncertainty principle is not a law of nature. It is a tautology:

• To see small things, use short wavelengths.

• Short wavelengths mean high momentum.

• High momentum means you hit the thing hard.

• Therefore, fine measurement disturbs the system.

The rest is algebra, with $h$ moved from one side to the other.

And $h$ itself is not a scale of the universe. It is our scale. It is the scaling factor that exposes how badly we related time, length, and mass—three dependent measures of a trivially unified universe.

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11. Conclusion

Time is not a dimension. It is not a coordinate. It is not a flow.

The universe is a single, undivided self-interaction, written in place. It has no past, no future, no sequence.

We are local knots in this self-interaction—life forms that remember. We use memory for the past. We use the identical machinery to imagine things. The imagined things feed back into memory. So anticipation feels like a memory.

The loop between memory and anticipation generates the experience of time. But time is not in the universe. Time is in the remembering.

The universe does not remember. It does not anticipate. It does not survive.

It simply is.

No beads. No chain. No time.

Only the self-interaction, written in place.

And we, who remember, are that self-interaction, briefly aware of itself, calling its own memory "time."

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References

1. Barbour, J. (1999). The End of Time: The Next Revolution in Physics. Oxford University Press.

2. Rovelli, C. (2018). The Order of Time. Riverhead Books.

3. Seth, A. (2021). Being You: A New Science of Consciousness. Dutton.

4. Clark, A. (2016). Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford University Press.

5. Einstein, A. (1905). On the Electrodynamics of Moving Bodies. Annalen der Physik, 17(10), 891-921.

6. Bridgman, P. W. (1927). The Logic of Modern Physics. Macmillan.

The Kinematic Pin: Replacing the Ontology of Intrinsic Stuff with an Energy-Velocity Coupling Constraint

 J. Rogers, SE Ohio

Abstract

The elimination of v=0 as a physically attainable state and the recognition of the classical regime as a measurement-resolution threshold (γ−1<δ) fatally undermine the ontology of "intrinsic stuff" (rest mass). However, destructive critique alone is insufficient; if rest mass is not fundamental substance, its functional role in physics must be explained by a replacement ontology. This paper provides that replacement. We argue that what physics calls "rest mass" is operationally and ontologically a kinematic pin—a coupling constraint that ties a system's relative energy to its velocity. At low velocities, the pin's baseline energy dominates the budget, making the constraint appear as immovable "stuff." At ultra-relativistic velocities, the pin's influence becomes an unmeasurable rounding error, rendering a neutron operationally indistinguishable from a high-energy cosmic ray photon. The photon lacks this pin, decoupling its energy from its velocity entirely. Under this framework, pair annihilation is not the destruction of substance, but the removal of a kinematic pin; pair production is its insertion. The universe is not made of stuff; it is made of projections, some of which are pinned.

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1. Introduction: The Void Left by Intrinsic Stuff

Previous work has demonstrated that the standard framework's ontology of mass is structurally unsound. The anchoring of "intrinsic stuff" to the v=0 rest frame fails because absolute rest is an unattainable physical limit, forbidden by nested gravitational gradients and the Heisenberg Uncertainty Principle ( p=0⟹Δx=∞). Furthermore, the classical regime where mass appears intrinsic is merely a measurement-resolution threshold (γ−1<δ), not a domain of nature.

Yet, a purely destructive critique leaves a void. If rest mass is not an intrinsic substance—an ontological primitive that objects "have"—then we must account for its empirical reality. Massive particles do resist acceleration differently than massless ones. They do require energy to change velocity. If we are getting rid of intrinsic stuff, we must explain what replaces it.

This paper proposes the replacement: rest mass is a kinematic pin. It is not a substance, but a coupling constraint that dictates the exact mathematical relationship between a system's energy state and its velocity state. By shifting the ontology from substance to constraint, we unify the behavior of massive and massless particles and dissolve the classical paradoxes of pair production and annihilation.

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2. The Ultra-Relativistic Limit: The Neutron and the Cosmic Ray

The clearest empirical evidence that rest mass is not intrinsic stuff emerges at the ultra-relativistic limit. Consider a neutron accelerated to a Lorentz factor of

$\gamma =10^{11}$

, and a high-energy cosmic ray photon with the identical total energy

$E$

.

In the standard framework, these are ontologically distinct entities. The neutron possesses "intrinsic stuff" (

$m_0\approx 939\text{MeV}/c^2$

); the photon does not.

However, operationally, they are indistinguishable:

1. Spacetime Curvature: Both yield identical Stress-Energy tensors (
   $T_{\mu \nu }$
   ). They curve spacetime and gravitate identically.
2. Momentum Transfer: Both impart identical radiation pressure and momentum to any target.
3. Cascade Physics: Upon striking a detector, both initiate high-energy particle showers governed entirely by the available energy
   $E$
   , not the initial "stuff."

$At\gamma =10^{11}$

, the neutron's rest mass energy is

$1$

part in

$10^{11}$

of its total energy. The contribution of its "intrinsic stuff" to any physical interaction is below the noise floor of any conceivable measurement. By Bridgman's operationalism—if two entities yield identical measurements under all operations, they are the same entity—the ultra-relativistic neutron is the cosmic ray.

The standard framework explains this by saying the neutron's "stuff" becomes negligible compared to its kinetic energy. The projection ontology inverts this: the neutron was never stuff. It was always a projection. The "rest mass" was merely a parameter governing the projection's behavior, which has now become operationally irrelevant.

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3. The Constructive Move: Rest Mass as a Kinematic Pin

If rest mass is not stuff, what is it?

For any entity with

$m_0>0$

, Energy and Velocity are not independent degrees of freedom. They are locked together by the relation:

$E=\gamma m_0{c}^2=\frac{m_0{c}^2}{\sqrt{1-v^2/c^2}}$

This equation defines a strict coupling. You cannot change the velocity without changing the energy, and the ratio of that change is dictated entirely by

$m_0$

.

We define rest mass

$m_0$

as the kinematic pin that couples relative energy to velocity.

• A large pin (high
  $m_0$
  ) creates tight coupling: enormous energy inputs are required to achieve small velocity changes. The system appears highly inertial.
• A small pin (low
  $m_0$
  ) creates loose coupling: small energy inputs yield large velocity changes.

The pin is not a substance. It is a constraint. It is the mathematical parameter that forces ΔE to accompany Δv along a specific hyperbolic curve.

3.1 Why the Pin Looks Like Stuff

The historical confusion arises from the low-velocity limit. When v≪c, the energy of the pin itself (

$E_{rest}=m_0{c}^2$

) dominates the energy budget. The kinetic energy (the energy of motion) is a tiny fraction of the total. When an observer pushes the object, they are fighting the pin—the constraint that forces energy and velocity to scale. Because the pin's baseline energy is so vast relative to the applied kinetic energy, the constraint appears as an immovable, intrinsic resistance. The pin mimics substance at low resolution.

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4. The Unpinned State: Why the Photon Lacks the Pin

The photon provides the contrasting case. For a photon, E=hf and  v=c.

Energy and velocity are completely decoupled. You can dial the photon's energy from a radio wave to a gamma ray, and its velocity remains exactly c.

The photon lacks the kinematic pin. Because it lacks the pin:

1. There is no constraint forcing
   $\Delta E$
   to accompany
   $\Delta v$
   .
2. Velocity is fixed at the universal rendering limit (
   $c$
   ), while energy is a free parameter.
3. There is no
   $\gamma =1$
   frame, because decoupling energy from velocity means there is no lower bound where the system can be brought to rest.

The standard framework treats the photon's lack of rest mass as an ontological defect—a special case of "masslessness." The pin ontology treats it as the generic state: the unpinned projection.

Matter is not the baseline reality that happens to lose its stuff at high speeds; matter is a pinned projection. The photon is an unpinned projection. The pin is the differentiator, not the substance.

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5. The Geometry of the Pin: Replacing Substance with Constraint

In the categorical framework of the Grothendieck fibration, this replacement ontology has a precise geometric mapping.

The unified substrate (

$S_u$

) is projected onto the observer's axes (

$\mathcal{B}$

).

• The Unpinned Projection (Photon): Maps from
  $S_u$
  to the Energy/Momentum axes in a linear fashion. Changing the energy simply slides the projection along the line.
• The Pinned Projection (Matter): Maps from
  $S_u$
  through a curved morphism—a hyperbolic arc defined by the Lorentz factor
  $\gamma$
  . The "rest mass" is the parameter defining the curvature of this arc. The curvature forces a change in the Energy projection to be accompanied by a change in the Velocity projection.

Rest mass is not an object in the base category B; it is the curvature parameter of the morphism projecting 

$S_u$

into

$\mathcal{B}$

. We have replaced an ontology of substance (objects in

$\mathcal{B}$

) with an ontology of constraints (the geometry of the projection

$\pi$

).

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6. Implications: Annihilation as Unpinning

The standard framework struggles with pair production and annihilation. If mass is intrinsic stuff, then annihilation is the destruction of substance—stuff is annihilated, and a fundamentally different thing (energy/radiation) is created. It requires a transmutation of ontological categories.

The pin ontology dissolves this paradox.

• Annihilation (
  $e^{+}+e^{-}\to \gamma +\gamma$
  ): The kinematic pins coupling energy to velocity are removed. The projections are thereby decoupled, becoming free to vary in energy while fixed in velocity. The underlying substrate (
  $S_u$
  ) has not changed; only the constraints on its projection have been removed.
• Pair Production (
  $\gamma \to e^{+}+e^{-}$
  ): Kinematic pins are inserted into the projection. Energy and velocity, previously decoupled, are now locked together by the newly introduced constraint (
  $m_e$
  ).

Under this framework, the universe does not contain two fundamental categories of existence (Mass and Energy) that must be transmuted via

$E=m{c}^2$

. It contains one unified substrate, expressed as projections. Some projections are unpinned (radiation); some are pinned (matter).

$E=m{c}^2$

is simply the mathematical statement of the pin's energy baseline.

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7. Conclusion

If intrinsic stuff is eliminated as an ontological foundation, it must be replaced by a rigorous account of what rest mass physically does. That account is the kinematic pin.

1. At high energies, the pin becomes operationally invisible, rendering a neutron indistinguishable from a cosmic ray. The "stuff" contribution vanishes.
2. At low energies, the pin's baseline energy dominates, making the constraint appear as immovable substance.
3. The photon is not a defective massive particle; it is the generic unpinned projection. Matter is the pinned projection.
4. Annihilation/Production are not transmutations of substance, but the insertion/removal of kinematic constraints.

The universe is not made of stuff pinned to absolute rest. It is made of unified projections, some of which are constrained—pinned—to tie their energy to their velocity. What we call mass is just the stiffness of the knot.

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References

Bridgman, P. W. (1927). The Logic of Modern Physics. Macmillan.

Einstein, A. (1905). Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik, 18(13), 639-641.

Okun, L. B. (1989). The concept of mass. Physics Today, 42(6), 31-36.

Rogers, J. (2025). The Classical Regime as a Measurement-Resolution Threshold. Unpublished manuscript.

Rogers, J. (2025). The Unattainable Anchor: Rest Mass as an Extrapolation to a Forbidden State. Unpublished manuscript.

Sandin, T. R. (1991). In defense of relativistic mass. American Journal of Physics, 59(11), 1032-1036.