What question did this study set out to answer?

This research aims to introduce and validate a new level of physical causality, termed causal conjunction, focusing on the photon as a structured entity.

March 24, 2026Open Access

The photon as structured causal block: causal nodes and historical integration beyond the propagative model

Key Points

This research aims to introduce and validate a new level of physical causality, termed causal conjunction, focusing on the photon as a structured entity.
Develop a formal framework for causal conjunction using the photon as a structured causal block.
Perform experimental predictions utilizing circuit-QED technology.
Analyze mutual information across the Bloch sphere and extended BCE.
Experimental predictions include a giant-atom φ-scan with measurable distinctions at high significance levels.
New hierarchy established for mutual information across the Bloch sphere depending on the absorbers' initial states.
Significant contradictions in predicted behaviors between the BCE model and standard QED measurements proposed.

Abstract

We propose and formally establish a third level of physical causality — causal conjunction — absent from the standard two-level taxonomy. The central object is the photon as a structured causal block B (σ) = (G⁻ (S), F (σ, λᵢ) ), carrying a causal charge discharged instantaneously upon absorption. The framework yields three new experimental predictions testable with current circuit-QED technology: (i) Giant-atom φ-scan: contrast ΔI = 0. 971 bit at 97σ (10⁶ shots), distinguishing the two-point coupled model from the Markovian single-point null model. Observable: I (A: B) = Gcl via mutual information. (ii) Bloch sphere hierarchy (new result): I (A: B) takes three distinct levels depending on the initial state of the absorber B — poles 0. 939 bit (94σ), equator 0. 566 bit (57σ, phase-independent), mixed 0. 160 bit (16σ) — all strictly positive, confirming G > 0 throughout the Bloch sphere. Includes an analytically proven JC symmetry theorem: I (B=|g⟩) = I (B=|e⟩) exactly for all coupling angles, to machine precision (15σ, immune to prefactor uncertainties. First proposal placing BCE and standard two-point QED in genuine quantitative tension at the destructive-interference null point. Additional results include: G = Gcl + Gₑnt decomposition with operational criteria; Si₃N₄ photonic platform (~26k, no cryogenics) ; thermodynamic signature ΔW = 1. 86×10⁻²⁵ J (Maxwell demon protocol, T=20 mK) ; Nakajima-Zwanzig non-Markovian analysis (critical parameter ηc ≈ 0. 48, safety margin 21× in circuit-QED) ; solar photon empirical argument for scale-independence across 33 orders of magnitude; and Holevo bound verification (G << Sₘax in all regimes). All predictions are numerically verified across eight independent experiments (Python scripts, no external dependencies, reproducible in Google Colab). This is the second paper in the ICT (Incomplete Causal Transactions) series. The first paper ("Incomplete causal transactions: black holes as permanently frustrated couplers and the physical independence of entropy and generative capacity", GravCos2660030 / Zenodo DOI: 10. 5281/zenodo. 18736656) introduced the ICT framework and applied it to black holes and Rindler horizons.

The photon as structured causal block: causal nodes and historical integration beyond the propagative model

Key Points

Abstract

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