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) = G_cl 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 (< 10⁻¹⁵ bit). (iii) Virtual-mode power-law test at φ=π (new result): extended BCE predicts G ∝ (g/ω₀)² while standard QED predicts (g/ω₀)⁴. The exponent η is measurable in log-log scale at >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 = G_cl + G_ent 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 η_c ≈ 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 << S_max 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.
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) = G_cl 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 (< 10⁻¹⁵ bit). (iii) Virtual-mode power-law test at φ=π (new result): extended BCE predicts G ∝ (g/ω₀)² while standard QED predicts (g/ω₀)⁴. The exponent η is measurable in log-log scale at >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 = G_cl + G_ent 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 η_c ≈ 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 << S_max 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.
We demonstrate that the standard two-level taxonomy of physical causality — propagative causality bounded by c (Special Relativity) and statistical non-locality (Bell correlations) — is formally incomplete. A photon is not merely a carrier of entropic content S(σ): it constitutes a structured causal block B(σ) encoding, via quantum Fisher information, the complete causal history acquired from emission onwards. Upon absorption, the causal information borne by this block is discharged instantaneously into the receiving system, bringing into permanent causal contact two histories that had no prior causal relation. This constitutes a genuinely new causal level (Level 3: causal conjunction) irreducible to propagation or pre-existing entanglement. We establish this irreducibility mathematically (photon absorption is a push-out in the bicategory Cbl of causal blocks, with a non-faithful forgetful functor U: Cbl → Q_CPTP), operationally (the same channel produces G(|g⟩) = 1.000 bit, G(|+⟩) = 0.601 bit, G(I/2) = 0.189 bit depending on the absorber state — a Bloch sphere hierarchy no channel property predicts), and experimentally (three falsifiable predictions in circuit-QED: φ-scan contrast 0.971 bit at 97σ; the Bloch sphere hierarchy at >40σ; double ratio R₂ = 3.81 at φ = π, derived from the full Schrieffer–Wolff integral with the causal block form factor, verified non-perturbatively). Reproducible Python scripts (experiments 01–12) are available at github.com/ARTUS10/causal-block-photon.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
We apply the (3+3) spacetime framework [1, 6] — a six-dimensional Einstein–Aether construction with three spatial and three temporal dimensions, the third time dimension compactified as a discrete two-sphere S² with N_cells = 2¹⁵² Planck-area cells — to photonic quantum computing. The framework identifies the photon as a null arc (a c-vector configuration with v_T = v_t₂ = v_t₃ = 0 and v_spatial = c) corresponding to the n = 0 Kaluza–Klein zero-mode on S². From this single identification three Level-1 structural results follow: (i) the photon's polarization Poincaré sphere is geometrically the third time dimension's S²; single-qubit gates are physical S² rotations and the Born rule is Malus's law as S² projection; (ii) photons inherit no t₃-winding decoherence channels, with cosmological coherence floor τ_cosm = 1/H₀ ≈ 14.5 Gyr [§14bis.46.4 of 6] and practical decoherence by photon loss as t₃ entrainment; (iii) the cross-Kerr nonlinearity scales as χ⁽³⁾ ∼ α² = 5.3 × 10⁻⁵ from two successive c-vector rotations each of amplitude √α. We give a self-contained derivation in §5.4 of the χ⁽³⁾ ∼ α² scaling from the Lagrangian-level photon-photon-via-radion vertex L = −(g₀/4) Φ² F_{μν} F^{μν}|_node with bare coupling g₀ = (4/9) ε_ZPE², through radion integration-out at optical frequencies, to the four-loop running g₀ → α (drawing on §16–§17 of [6]). Sections 5.5–5.9 establish the structural form of the nodal-cone TPA-suppression factor η_node: the breathing-mode contribution at the cone vanishes geometrically because the Y_{2,0}(ϑ_node) = 0 identity that defines the cone latitude also eliminates the breathing's metric perturbation there (§5.7); the higher-multipole tail is bounded at η_node|_higher ≲ 10⁻⁵ using the framework's identified spectrum from [6] (§5.8); and the same Z₃ symmetry that organises SU(3), three-generation fermion structure, and tribimaximal PMNS mixing also protects the qutrit basis at the trisection vertices (§5.9). Combining these structural results with anchored medium-specific estimates for silicon-on-insulator (K_medium ≈ 0.10–0.20), silicon nitride (0.03–0.08, lowest), and thin-film lithium niobate (0.05–0.15) (Appendix B), the framework predicts η_node ≈ K_medium ≈ 0.03–0.20 across candidate platforms — silicon nitride is identified as the optimal platform — dominated entirely by medium contributions rather than framework-vacuum dynamics, and decisively testable by the §6.7 thermal MZI experiment (2027–2030). The magic-angle latitude ϑ_node = arccos(1/√3) = 54.74° is the same magic angle as in NMR magic-angle spinning, and the underlying physics (averaging-out of Y_{2,0} dipolar interactions) is structurally identical. Six engineering proposals leverage these results: null-arc qubit encoding; the nodal-cone LOQC architecture (qubits at the magic-angle latitude where Y_{2,0} vanishes and the leading TPA channel is suppressed); (3+3) measurement protocols with t₃-entrainment-strength control; trisection qutrit photonic computing (log₂ 3 ≈ 1.585 bits per photon, with Z₃-symmetric coherence protection giving η_qutrit ≈ 0.06–0.21 comparable to qubit η_node — a 58.5% information-density gain at essentially no extra coherence cost); boson sampling reframed as null-arc network interference; and a nodal-cone photonic-crystal integrated chip. Three testable predictions are organised into a year-resolved 2026–2030+ falsifiability timeline (§6.7). All claims are explicitly tagged Level 1 (geometric, derived), Level 2 (anchored prefactor), or Level 3 (engineering speculation); the room-temperature fault-tolerance projection of §9 is an explicit Level-3 conditional argument with dependency chain made explicit. A self-contained framework digest is given in §1.7; readers unfamiliar with the (3+3) programme can read §1.7 alone to decide whether to continue.
In quantum mechanics, light cannot be described in terms of waves and particles at the same time. However, the question about light "as it really is" implies a description that is independent from the constraints of measurement. It is rather preferable to incorporate both aspects in a causal ontological theory, especially if it simplifies explanation and improves predictions. Hence, the photon can be described as an extended longitudinal association of discrete indivisible constituents, which are held together by the effect of their own waves on each other. The same waves can then be used to interpret the force of interactions between different pulses of light, or between light and matter. The concept of wavemediated interaction between sub-photonic entities is entirely consistent with the observations of quantum mechanics. The key is to assume that elementary sources of waves never collide, and that they have constant parameters. Novel experimental implications follow from this approach. For example, the speed of propagation of changes within magnetic or electrostatic fields may not be equal to the speed of light. Also, interference fringes should be detectable beyond the volume of overlap of two non-entangled beams, but only in special experimental settings.
The Bloch sphere provides a powerful abstract representation of a qubit state but does not by itself specify a microscopic physical ontology. In this work we formulate an effective geometric qubit model within the Helix–Light–Vortex (HLV) framework. The computational basis states are interpreted as two stable helical resonance modes of an effective discrete space-bit degree of freedom, while superposition corresponds to coherent evolution in the associated two-dimensional Hilbert subspace. Starting from the HLV kinetic modulation ansatz, we construct a two-level effective Hamiltonian Heff(t) = ω0 2 σz +gϕsin(Ωϕt)σx +gχfχ(t)σx, where the oscillatory terms represent phase- and memory-channel modulations inherited from the time-dependent kinetic prefactor A(t). The construction is not presented as a derivation of quantum mechanics from first principles, but as a controlled effective model whose deformation parameters vanish continuously in the standard quantum limit. The model predicts falsifiable signatures in qubit platforms: weak harmonic sidebands in spectroscopy, bounded deviations from exponential Ramsey dephasing, and correlated modifications of entanglement decay in multi-qubit states. We state explicit recovery limits, clarify non-claims regarding measurement and the Born rule, and identify null results that would falsify the proposed geometric interpretation.
We develop a structural ontology of quantum light in which the photon is not a particle, not a wave, and not an excitation of a field, but the boundary-projection of an underlying β-structure. The β-field encodes the structural capacity of existence: intrinsic configurations with 0 < β < 1 support coherent organization and allow a system to maintain internal tension, whereas the limit β → 1 eliminates all internal structure and produces a projection event. In this framework, the wavefunction ψ is not an element of physical reality but a linear statistical shadow of β-modes; measurement accesses only the projection frequencies |ψ|² because projection occurs solely at β = 1, where intrinsic structure no longer exists. A “photon” therefore corresponds not to a single β-configuration but to an equivalence class of β-modes that collapse to the same β = 1 boundary signature. The apparent indivisibility, lack of rest frame, invariant propagation speed, discrete polarization, interference capability, and entanglement of photonic phenomena emerge from this multi-existence ensemble rather than from particle attributes. Wave-like behavior arises entirely from the β-phase geometry in the intrinsic domain, while particle-like detections correspond to boundary collapses of β-ensembles. Interference, delayed-choice behavior, polarization transformations, and entanglement correlations follow naturally from the global coherence of β-structure prior to projection. The framework preserves all operational predictions of quantum mechanics while supplying an ontological layer clarifying why ψ is unobservable and why photonic behavior appears paradoxical under particle or wave descriptions. The model predicts boundary-sensitive and geometry-dependent deviations—nanometer-scale fringe shifts, polarization-mode distortions, structured entanglement modulation, and stable residual phases in balanced interferometers—that originate from the nonlinear structural response of β near projection. These effects are experimentally testable with current photonic technology. The β-projection ontology thus provides a unified, falsifiable, and structurally grounded account of quantum light, explaining photonic phenomena as manifestations of β-mode ensembles interacting with the nonlinear boundary at β = 1 rather than as properties of a classical or quantized particle.