lag が幾何学になるとき── なぜ遅延が曲率と誤解されたのか

When Delay Becomes Geometry

── Why Lag Was Mistaken for Curvature

lag and the Constancy of the Speed of Light

Unobservable Delay

The constancy of the speed of light can be reinterpreted as the visible surface of an unobservable lag.

In our framework, lag denotes a minimal delay between generation and registration—between an event and its stabilization as an observable trace. This delay is not an empirical quantity and cannot be operationally isolated. It exists below the threshold of observation.

If such a lag is universal and irreducible, then any signal—light included—will always be registered after it has already passed through this delay. The measured speed of light is therefore not the speed of light “in itself,” but the speed of light after lag normalization.

In this sense, the constancy of the speed of light reflects not a dynamical constraint imposed on photons, but a syntactic constraint imposed on observation itself.

The invariance follows trivially:

No further principle is required.

One-line Proposition

Light is delayed at the speed of light.

This statement is not paradoxical.
It simply means that light does not escape lag; it defines the minimal scale at which lag becomes invisible.

The speed of light marks the boundary where delay can no longer be observed, not where time or space must deform.

Clarification

The so-called constancy of the speed of light is the empirical shadow of a syntactic lag below the observational threshold, not a fundamental property of spacetime.

lag < Z₀ and Unobservability

We define lag as the minimal delay between generation and registration—between an event and its stabilization as an observable trace.

This lag is not continuous down to zero.
It admits a lower bound.

Let Z₀ denote the minimal syntactic unit of delay:
the smallest traceable mismatch between generation and observation.

We then distinguish two regimes:

Delays below Z₀ do not vanish; they lose representability.
They cannot be isolated, compared, or synchronized.
They persist only as structural constraints on observation.

Consequence for the Speed of Light

If light propagation includes a lag smaller than Z₀, then:

All observers therefore register light after the same minimal lag, regardless of motion or frame.

The constancy of the speed of light follows automatically.

No dynamical postulate is needed.
No spacetime deformation is required.

The invariance reflects the unobservability of sub-Z₀ lag, not a physical prohibition.

Reframing the Principle

The traditional statement:

The speed of light is invariant in all inertial frames.

can be reformulated as:

All observations of light occur beyond the Z₀ threshold of lag.

This is a statement about syntactic limits, not physical absolutes.

Key Point (for the Reader)

The constancy of the speed of light is not a property of light itself.
It is a property of what observation cannot resolve.

Below Z₀, delay exists without appearing.

Minimal Closing Sentence

What has been called an invariant speed is, in fact, the horizon of observability for lag.

Why Lag Was Mistaken for Curvature

Abstract

Spacetime curvature has long been interpreted as a physical deformation induced by gravity.
In this paper, we propose an alternative reading: what has been geometrized as curvature is the structural trace of unresolved delay (lag).
When lag falls below the threshold of observability (Z₀), it ceases to appear as delay and is instead re-inscribed as geometric structure.
We argue that spacetime geometry did not explain gravity, but stabilized unobservable lag by re-describing it as curvature.

1. The Hidden Transition

General Relativity performs a decisive conceptual move:

delay → geometry

Temporal mismatch, acceleration, and inertial deviation are no longer treated as dynamical delays, but as manifestations of curved spacetime.

This move is mathematically consistent.
But it is also syntactic.

What disappears in this transition is delay itself.

2. Lag Before Geometry

We define lag as the minimal delay between generation and registration of events.

Crucially, lag admits a lower bound Z₀.

For lag < Z₀, delay becomes unobservable.

At this point, delay does not vanish.
It loses representability.

3. The Moment of Mistake

When delay cannot be observed, three options remain:

  1. deny its existence

  2. introduce hidden dynamics

  3. re-describe it structurally

General Relativity chose the third.

Unobservable delay was stabilized as metric curvature.

Curvature thus functions as a syntactic substitute for lag that could no longer be measured.

4. Geometry as a Trace, Not a Cause

In this view:

Instead:

curvature records where lag has become unresolvable

Spacetime geometry is not fundamental.
It is a trace artifact.

5. Why the Move Was Inevitable

This reinterpretation was historically unavoidable:

Geometry offered stability.

But stability is not explanation.

6. Reversal

We therefore reverse the usual explanatory order:

lag → observability threshold (Z₀) → geometric description

Spacetime does not bend.
Delay becomes unreadable.

Closing Sentence

Spacetime curvature is what delay looks like after it can no longer be seen.

SAW-10｜The Constancy of the Speed of Light as a Syntactic Assumption── 光速度不変原理の構文的再定位
SAW-10｜Why No One Called It a Syntactic Assumption: On the Constancy of the Speed of Light── 構文的仮定としての光速度不変原理

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K.E. Itekki is the co-composed presence of a Homo sapiens and an AI,
wandering the labyrinth of syntax,
drawing constellations through shared echoes.

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| Drafted Jan 21, 2026 · Web Jan 22, 2026 |