Time as Self-Interaction: How the Apparent Arrow Arises from a Single Dimensionless Substrate

J. Rogers, SE Ohio

Abstract

We present a framework in which time is not a fundamental dimension but an emergent label humans place on the sequential updating of a single dimensionless substrate X. The universe has no units — it does not measure itself. X is a dimensionless ratio, and every physical quantity we measure is a projection of X onto a human-chosen axis. The Lorentz factor γ is itself dimensionless, and a boost does not separately affect time, mass, length, and momentum as distinct phenomena — it changes X, and γ is that change. The six Planck-scaled projections of X:

E/Eₙ = f·tₙ = m/mₙ = T/Tₙ = lₙ/λ = p/pₙ = X

are not six different physical laws. They are one thing — X — read on six different human axes. Any pair of these six yields a known physical relationship, producing 15 such relationships from a single identity. This holds in every unit system imaginable, because X is dimensionless and the universe has no preferred unit chart. Past states are not stored in a separate temporal dimension; they exist only as patterns in the current configuration of X.

1. Introduction

Standard physics treats time as a fourth dimension with a fixed metric signature and postulates an independent arrow of time. This leads to persistent conceptual difficulties: the problem of the past, the asymmetry between time and space dimensions, and the apparent paradoxes of retrocausality in quantum experiments.

We propose an alternative grounded in a single observation: the universe does not measure itself. Units — seconds, kilograms, meters — are human inventions. Any quantity that carries dimensions is already a projection, a reading of the universe through a human-chosen instrument. The universe itself operates on something prior to measurement.

We call that prior thing X: a dimensionless, unitless ratio that completely describes the state of reality at any instant. X does not evolve in time. The transition X → X' is what we call time. There is no external clock. There is no dimension being traversed. There is only X updating.

2. X Is Dimensionless — Not Because We Choose Clever Units, But Because the Universe Has None

A key error in discussions of natural units is the implication that setting c = ħ = 1 makes things simpler by choice. This misses the point. Natural units are still units — still a human coordinate system. The universe does not operate in natural units any more than it operates in SI.

X is dimensionless not as a result of any unit choice. It is dimensionless because dimensions are human annotations applied to projections of X. The universe just does X. We then read X through six different instruments and assign six different dimensional labels to what we find.

The Planck units are significant not because they are 'natural' but because they are the specific Jacobian at which the human unit chart admits that all six projections yield the same number. They are conversion factors between human axes, not fundamental features of the universe. The constants h, c, and G — used unreduced, never ħ — are the three such Jacobians between the three independent ways humans chose to measure reality.

3. The Six Projections of X

Every physical quantity we measure is X read on a different axis. The six Planck-scaled projections are:

E/Eₙ = f·tₙ = m/mₙ = T/Tₙ = lₙ/λ = p/pₙ = X

where subscript P denotes Planck units constructed from h, c, and G (unreduced). Each ratio is dimensionless. Each ratio is identical. This is not a collection of proportionalities — it is a single identity written six times in six different human languages.

From six projections taken two at a time, C(6,2) = 15 pairs arise. Each pair is a known physical relationship:

E/Eₙ = f·tₙ → Planck relation E = hf

E/Eₙ = m/mₙ → mass-energy equivalence E = mc²

m/mₙ = p/pₙ → momentum-mass relation p = mv (relativistic form)

f·tₙ = lₙ/λ → de Broglie relation λ = h/p

And so on for all 15 pairs. These are not 15 different laws discovered independently. They are 15 different ways of writing X = X, each pair using two of the six human axes. Physics discovered them separately because it was looking at pairs of projections and calling each pair a law, never seeing that all six projections are the same single dimensionless quantity.

4. The Boost Changes X — γ Is That Change

The Lorentz factor γ is dimensionless. X is dimensionless. This is not coincidental.

When a boost occurs, X changes. γ is the ratio of the new X to the old X as measured on any chosen axis. Because X appears identically on all six axes simultaneously, γ applies to all six axes simultaneously.

This is why a boost appears to change mass, time rate, length, momentum, and energy all at once. Physics treats these as separate relativistic effects linked by the Lorentz transformations, implying they are different phenomena that happen to correlate. They are not. There is one phenomenon — X changing — and γ is that change. The six axis-readings change together because they were always readings of the same single thing.

The standard framing says: motion causes time dilation, and also causes length contraction, and also causes relativistic mass increase. Each 'also' is a mistake. There is no cause and effect chain between a boost and its consequences. The boost is the change in X, and γ is that change, and everything else is humans reading X on their chosen axes.

Asking why time dilates when you boost is like asking why a circle looks like an ellipse when you tilt it. You changed your projection angle. The circle did not do anything. X did not do anything to time separately from what it did to mass separately from what it did to length. It changed once. γ is that one change.

5. Inertia Is Not a Mystery

An object in motion stays at its current X. This is not a law requiring explanation. There is nothing pushing the object and nothing to stop it from changing unless another interaction occurs. Inertia is the substrate maintaining its current state until X → X' is forced by an interaction.

Newton's first law looked like a law requiring a mechanism. In this framework it is a tautology: X stays X until something makes it X'. The 'something' is another interaction — a collision, a field, a measurement — that forces an update. Between interactions there is no time passing in any meaningful sense. There is just X, unchanged.

6. No Past, Only Patterns

The substrate X does not retain a separate past state. When an interaction occurs, X' completely replaces X. The only record of any previous state is in patterns carried forward in the current configuration — the arrangement of atoms in a memory device, photons not yet absorbed, quantum correlations not yet collapsed.

The past is not a place. It is a pattern in the present. When that pattern is erased or overwritten, the past appears to change — but no time travel occurred. There was no past state to travel to. The trace simply did not survive the update.

This resolves the quantum eraser without invoking retrocausality. The experimenter's choice to measure or erase which-path information participates in a single self-consistent update of X. There is no earlier photon path being retroactively affected. There is only the final correlation pattern — the final X — which is self-consistent with all interactions that participated in producing it.

7. The Arrow of Time

The arrow of time is the direction of accumulating X → X' updates. It points the way it does because interactions are irreversible in practice: the final X retains less information about previous states than would be required to reconstruct them. This is not a fundamental asymmetry built into the geometry of a time dimension. It is a consequence of pattern loss during updates.

A broken egg does not reconstruct itself because the pattern required to reverse the update was not carried forward in X. The arrow exists because information is lossy, not because time has a preferred direction geometrically.

8. Relation to the 2019 SI Redefinition

The 2019 SI redefinition fixed c, h, and k₂ as exact values. This was officially described as redefining units, not changing physics. In our framework, this is precisely correct: c, h, and G are unit-chart Jacobians — conversion factors between the axes onto which humans project X. Fixing them as exact is an admission that they are not physical discoveries about the universe. They are bookkeeping choices about how to align human measurement axes.

The speed of light c is not a speed the universe obeys. It is the ratio between the human time-axis and the human space-axis. When both axes are projections of the same X, their ratio is fixed — not by physics, but by the geometry of projection.

9. Falsifiability

The framework makes a clear falsifiability criterion. A genuine logical contradiction between a stored trace and a later outcome — a dead cat that was previously alive with no causal chain, a photon arriving before it was emitted — would disprove it. No such experiment exists. Every apparent retrocausal result is consistent with a single self-consistent X update in which the 'earlier' trace was simply never stored in a way that survived.

Additionally: if any physical quantity required separate dimensional status — if any measurement could not be expressed as a dimensionless ratio to its Planck-scale counterpart — the framework would be incomplete. Every quantity so far reduces to X on one of the six axes.

10. Conclusion

The universe has no units because it does not measure itself. Every physical quantity is X — a dimensionless ratio — projected onto a human-chosen axis. The six Planck-scaled projections are identical. Their 15 pairwise combinations are the known laws of physics, each one a different human reading of the single identity X = X.

A boost changes X. γ is that change. Mass dilation, time dilation, length contraction, momentum change — these are not separate effects that happen together. They are one change in X read on multiple axes simultaneously.

Time is not a dimension. It is the accumulation of X → X' updates. The arrow of time is the direction of pattern loss during those updates. Inertia is X staying X between interactions. Retrocausality is an illusion caused by misreading pattern overwriting as backward causation.

The framework does not add new physics. It removes the unnecessary scaffolding — dimensions, separate constants, causal chains between correlated projections — and reveals that what remains is X, dimensionless, unitless, and singular.