This paper introduces the Causal Quaternionic Field Theory (CQFT), a theoretical framework that redefines the foundational axioms of quantum mechanics and general relativity by rejecting the fungibility of numerical values. We propose that physical space possesses a non-Markovian topological memory encoded within the imaginary axes (i,j,k) of a quaternionic metric tensor. By introducing the Causal Tensor Product (⊠) governed by a strict chronological index (τ), we resolve the tensor product problem that historically hindered quaternionic quantum mechanics (e.g., S. Adler). In this framework, causal asymmetry is strictly preserved, logically prohibiting retrocausality at the algebraic level. Furthermore, we reinterpret quantum entanglement not as non-local statistical collapse, but as a deterministic topological tunnel shared within the hidden axes of the field. The paper outlines the mathematical framework, proposes the architecture for Photonic Causal Tensor Chips (PCTC), and presents a falsifiable experimental setup—the Causal Hysteresis Test of Entangled Photons—to empirically distinguish our model from the standard Copenhagen interpretation.
This paper introduces the Causal Quaternionic Field Theory (CQFT), a theoretical framework that redefines the foundational axioms of quantum mechanics and general relativity by rejecting the fungibility of numerical values. We propose that physical space possesses a non-Markovian topological memory encoded within the imaginary axes (i,j,k) of a quaternionic metric tensor. By introducing the Causal Tensor Product (⊠) governed by a strict chronological index (τ), we resolve the tensor product problem that historically hindered quaternionic quantum mechanics (e.g., S. Adler). In this framework, causal asymmetry is strictly preserved, logically prohibiting retrocausality at the algebraic level. Furthermore, we reinterpret quantum entanglement not as non-local statistical collapse, but as a deterministic topological tunnel shared within the hidden axes of the field. The paper outlines the mathematical framework, proposes the architecture for Photonic Causal Tensor Chips (PCTC), and presents a falsifiable experimental setup—the Causal Hysteresis Test of Entangled Photons—to empirically distinguish our model from the standard Copenhagen interpretation.
Linear optical computing has emerged as a promising paradigm to bypass the thermodynamic constraints of von Neumann architectures and the Landauer dissipation limit (Emin = kBT ln2). However, existing integrated photonic accelerators remain fundamentally Markovian: they are restricted to commutative matrix-vector multiplications that systematically erase computational history during state aggregation. Here, we present the hardware architecture and operational principles of the Photonic Causal Tensor Processor (PCTP). Grounded in Causal Quaternionic Field Theory (CQFT), the PCTP natively executes the non-commutative Causal Tensor Product (⊠) governed by a rigorous chronological index (τ). We demonstrate how the four algebraic components of the quaternion (qa, qi, qj, qk) are directly mapped onto physical, orthogonal degrees of freedom of coherent optical wavepackets: real amplitude and longitudinal carrier phase, polarization states on the Poincaré sphere, and transverse orbital angular momentum (OAM) modes. We provide the physical layout of non-reciprocal causal logic gates utilizing low-loss Silicon Nitride (Si3N4) waveguides, magneto-optic Bismuth Iron Garnet (BIG) Faraday isolators, and synthetic diamond nitrogen-vacancy (NV) phase latches. The proposed processor executes deterministic causal tensor algebra at the speed of light with near-zero thermodynamic entropy generation, establishing an empirical hardware framework for post-quantum computing.
This work presents a minimal reinterpretation of quantum entanglement based solely on the causal structure inherent in relativistic spacetime. No new physical entities, parameters, or modifications to existing theories are introduced.The discussion remains entirely within the established frameworks of general relativity and quantum mechanics, with particular emphasis on Lorentz invariance and relativistic causality. The central idea is that the causal structure of spacetime is unique and invariant, while spatial separation corresponds to different references (foliations) to this structure rather than its duplication.Within this viewpoint, quantum entanglement is understood as a local readout of correlations already encoded in a shared causal structure, without invoking nonlocal influences or superluminal information transfer. This document is intended as a conceptual clarification and archival record rather than a proposal of a new theory.It is provided to preserve a logically consistent interpretation that may be of interest for future foundational discussions.
This paper introduces a mathematically unified, fully local, and realistic framework for quantum entanglement by deriving non-local correlations directly from the global invariants of a smooth, inherently non-commutative operator field manifold. Moving away from background-dependent spacetime stress tensors, we establish a strict ontological hierarchy where the universe is governed by a global operator invariant constraint, formulated as an eigenvalue equation (A^+B^)∣Ψ⟩=I∣Ψ⟩. We resolve previous fragmentation in topological interpretations by explicitly constructing the operators A^ and B^ as localized spatial integrals of a quantized winding density operator Ω^top(x) and establishing their formal evaluation action on the state space. In a zero-baseline vacuum (I=0), the states of localized field excitations are shown to be structural mirror images. Crucially, by modeling measurement as a geometric projection (the ``Shadow'' view), we provide the explicit algebraic derivation connecting the holistic state vector to the characteristic quantum cosine correlation −cos(θ1−θ2). This framework naturally violates Bell's inequalities up to the Tsirelson bound (22) while strictly preserving local causality, offering a mathematically cohesive alternative to the Copenhagen probability collapse.
Quantum entanglement is widely regarded as the most puzzling feature of quantum theory, apparently violating local realism through nonlocal correlations between spacelike-separated particles. Although violations of Bell inequalities are experimentally confirmed, their standard theoretical explanation relies on wavefunction collapse or nonlocal hidden variables. In this work, we present an alternative explanation based on Trembling Spacetime Relativity Theory (TSRT). In this framework, intrinsic metric fluctuations generate proper-time-synchronized geodesic ensembles whose deterministic trajectories give rise to statistical correlations across spacetime. Measurement outcomes are reinterpreted as geometric responses to these fluctuating backgrounds, without invoking quantum collapse or nonlocal influence. We show that the Clauser–Horne–Shimony–Holt (CHSH) inequality can be violated deterministically within a locally causal geometric structure. These violations emerge as macroscopic imprints of shared spacetime curvature, not quantum superposition. The resulting correlation function reproduces quantum predictions at short ranges but decays with separation—yielding testable deviations in long-baseline and gravitationally modulated experiments. TSRT thus offers a realist, Lorentz-invariant, and falsifiable account of entanglement grounded in the causal structure of spacetime.
Quantum nonseparability is central to most philosophical puzzles related to quantum mechanics. Yet, it is not an exclusive property of quantum mechanics, as it is also found in theoretical generalizations thereof. Investigating the implications of quantum nonseparability in a broader context could shed a new light on the conceptual problems in quantum physics. This work focuses on an operational theory called the process matrix formalism that generalizes quantum mechanics by relaxing the assumption of a well-defined causal structure. That broader theoretical context allows for the existence of quantum processes that are causally nonseparable, i.e. for which there is no definite global causal order among its interacting elements. Therefore, this notion of causal nonseparability somehow extends the notion of entanglement to the geometry of spacetime.
I am pleased to submit our extended theoretical draft, "Photon Rotor Theory: Phase-Ordering Dynamics, Precursor Localization, and the Resolution of Quantum Non-Locality," for publication as a regular research article. The foundational conflict between the continuous propagation of electromagnetic fields and the discrete nature of detection events remains one of the most resilient conceptual challenges in modern electrodynamics. Standard quantum mechanics bypasses this through wave-particle complementarity, which inevitably introduces non-locality (as seen in EPR correlations) or retrocausality (as illustrated by Wheeler's delayed-choice experiments). Our manuscript addresses this bottleneck by introducing a novel phase-topological interpretation of electromagnetic localization. Rather than treating the photon as an independent point-like particle, we model it as a transient phase-ordering event (a propagating rotor knot) embedded within a continuous Maxwellian field. We would like to draw the reviewers' attention to three critical, high-impact features of this framework: Circumvention of Bell's Theorem: Unlike traditional local hidden variable models that fail due to Bell's inequalities, our theory shifts the physical ontology from discrete particles to a continuous, topologically connected field. Because the synchronization dynamics are strictly governed by a contextual non-linear source term ( ), the model preserves local realism and Lorentz invariance without violating the mathematical axioms established by Bell (see Section 5). Resolution of Wheeler's Paradox: The framework demonstrates that the "delayed choice" is an illusion generated by the sub-femtosecond evolutionary dynamic of the phase field , avoiding any need for retrocausal or superluminal signaling ( ) (see Section 4). Strict Experimental Testability: The central mathematical consequence of our model is the phase shift between energy-density extrema ( ) and phase-transition maxima ( ). This predicts a distinct, causal phase precursor ( ) on a femtosecond scale ( ). We propose a concrete, testable experimental setup — a modified Lebedev radiation-pressure experiment with synchronized ultrafast phase and pressure channels — to verify these claims (see Section 7). Crucially, this theory does not attempt to replace Maxwellian electrodynamics or QED. Instead, it acts as an effective phase-localization framework that leaves standard field equations structurally intact while providing a clean, causal geometric mechanism for the collapse process.