Appendix X｜Light Bending as Lag Projection

Abstract

In this appendix, we reinterpret gravitational light bending as an inferential effect arising from lag-structured observation, rather than as a dynamical interaction or spacetime curvature acting on light itself.

Light propagates locally at a constant speed and undergoes no intrinsic force or acceleration. However, when light passes regions dominated by extremely slow-updating massive bodies, the resulting traces are sampled asynchronously across observational layers.

The apparent curvature of light trajectories emerges only at the level of inference, where observers reconstruct paths from lagged and unevenly distributed traces. No physical bending occurs at the level of propagation.

X.1 Premise: Light, Update, and Observation

We assume the following minimal premises:

  1. Light propagates locally at a constant speed.

  2. Massive bodies correspond to extremely slow update units.

  3. Observation is a retrospective reconstruction from traces, not a direct reading of states.

Under these assumptions, no intrinsic bending of light is required.

X.2 Update Asynchrony and Lag Gap

Near a massive body, the system exhibits a strong hierarchy of update granularity:

This hierarchy generates a lag gap, expressed schematically as:

\[S'''' \gg!!\gg O' \gg!!\gg S ,\]

where light updates dominate locally, while massive bodies contribute only as slow-updating environmental conditions.

This relation does not imply causal violation or superluminal signaling.
It denotes only an asymmetry in update timing and reconstruction alignment.

X.3 Where Does the “Bending” Occur?

The observed deflection:

Instead, it arises at the level of projection from updates to traces and from traces to inference.

What bends is not light itself,
but the mapping from global updates to locally accessible traces.

X.4 Three-Layer Structure: Update, Trace, Inference

The phenomenon can be decomposed into three layers:

  1. Update Layer

    • Light events propagate along locally straight paths.

    • The massive body remains largely unchanged during light passage.

  2. Trace Layer

    • Asynchronous sampling produces distorted trace density.

    • No force acts here; only uneven registration.

  3. Inference Layer

    • Observers reconstruct trajectories from incomplete and lagged traces.

    • The reconstructed path appears curved.

Light Bending as Lag Projection Update – Trace – Inference Structure Update Layer • Light propagates locally at constant speed • Massive bodies exhibit extremely slow update rates Trace Layer • Asynchronous sampling produces uneven trace density • No force or curvature acts on light itself Inference Layer • Observers reconstruct trajectories from lagged traces • The reconstructed path appears curved (gravitational lensing) Light bending emerges at the level of inference, not at the level of propagation.

Light bending as lag projection. The apparent curvature of light emerges at the inference layer from asynchronous trace sampling, rather than from forces or spacetime curvature acting on light itself.

X.5 Relation to General Relativity

In general relativity, light bending is described via:

Within the present framework, these correspond to:

Thus, this interpretation does not negate general relativity, but reframes it as a phenomenologically successful lag-effective theory.

X.6 Concluding Remark

Light does not bend.
What bends is our reconstruction of events across asynchronous updates.

Gravitational lensing is therefore not a property of light or space alone,
but a signature of lag-structured observation.

This description does not deny the empirical success of gravitational lensing models. Rather, it repositions light bending as an inferential reconstruction phenomenon, not as evidence of a force, curvature, or dynamical interaction acting on light.

SG-0｜Gravitational Lensing as a Syntactical Side Effect
SAW-AR｜Gravitational Lensing as a Syntactic Effect (Light Bending as Lag Projection)｜GR to SO lag
SAW-AR（ミニ技術ノート）｜Gravitational Lensing Revisited: What Is Bent Is Not Light, but Lag— Gravitational Lensing as a Lag-Projection Effect: An Interpretive Note

Appendix X｜遅延投影としての光の屈曲

概要

本 Appendix では、重力場近傍における光の偏向を力学的作用や時空曲率そのものではなく、更新非同期（lag）に基づく 観測再構成の投影効果として解釈する。
これは一般相対論の予測を否定するものではなく、その構文的読み替えを与えるものである。

X.1 前提：光・更新・観測

ここで重要なのは、光そのものが曲がる必要はないという点である。

X.2 更新非同期と lag gap

重力源近傍では、

という 更新階層の不整合が生じる。

これを本稿では lag gap と呼ぶ。

\[S'''' \gg!!\gg O' \gg!!\gg S\]

この関係は、因果破れや信号伝播を意味しない。
再構成写像のズレのみを意味する。

X.3 光の「曲がり」はどこで生じるか

観測される偏向は、

それは、

更新層で生成された出来事が、痕跡層を経由し、推論層に投影される際の対応関係の歪み

として現れる。

言い換えれば、

曲がっているのは光ではなく、更新→痕跡→推論の写像である。

X.4 図：Update–Trace–Inference の三層構造

遅延投影としての光の屈曲 更新 – 痕跡 –推論構造 Update Layer • 光は局所的に一定速度で伝播する • 質量の大きい物体は極めて更新レートが遅い Trace Layer • 非同期サンプリングにより痕跡密度が不均一になる • 光自体には力や曲率は作用しない Inference Layer • 観測者は遅延した痕跡から軌道を再構成する • 再構成された軌道は曲がって見える（重力レンズ効果） 光の屈折は伝播レベルではなく、推論レベルで現れる

X.5 一般相対論との関係

一般相対論が用いる：

は、本構文においては：

として理解できる。

したがって本解釈は、

一般相対論の数値予測を保持したまま、その記述構文を更新論的に再配置する

ものである。

X.6 位置づけ

光の偏向は、非同期な更新世界を、同期的に理解しようとしたときに現れる痕跡である。

光は曲がらない。
しかし、われわれの読み取りは曲がる。

時空曲率は、更新非同期を記述する有効構文である。

EgQE — Echo-Genesis Qualia Engine
camp-us.net

© 2025 K.E. Itekki
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 Feb 3, 2026 · Web Feb 8, 2026 |