The imaginary unit i = √ −1 in quantum mechanics is traditionally treated as a mathematical artifact enabling oscillation. In Relational Field Theory (RFT), we show that i is the dynamical signature of reversible relational coherence. Beginning from the universal coherence law ˙Rc = −λRc + Fint, we identify the regime where interaction balances decay, yielding ˙Rc = iΩRc. Here, iΩ ≡ Fint −λ is the coherence surplus that rotates phase instead of dissipating amplitude. The wavefunction ψ = √ Rceiϕ and Schrödinger dynamics follow directly, without additional postulates. This resolves the physical meaning of i and unifies classical decay and quantum phase rotation under a single relational principle. Provenance: Originally published on Zenodo (Oct- 2025). 10.5281/zenodo.17567332
The imaginary unit i = √ −1 in quantum mechanics is traditionally treated as a mathematical artifact enabling oscillation. In Relational Field Theory (RFT), we show that i is the dynamical signature of reversible relational coherence. Beginning from the universal coherence law ˙Rc = −λRc + Fint, we identify the regime where interaction balances decay, yielding ˙Rc = iΩRc. Here, iΩ ≡ Fint −λ is the coherence surplus that rotates phase instead of dissipating amplitude. The wavefunction ψ = √ Rceiϕ and Schrödinger dynamics follow directly, without additional postulates. This resolves the physical meaning of i and unifies classical decay and quantum phase rotation under a single relational principle. Provenance: Originally published on Zenodo (Oct- 2025). 10.5281/zenodo.17567332
In standard quantum mechanics, the factor is introduced to produce unitary, oscillatory time evolution. In Relational Field Theory (RFT), acquires a physical meaning: it is the generator of reversible relational coherence. Starting from the universal coherence law , we isolate the phase-preserving regime and show with . The wavefunction and Schrödinger dynamics follow directly, without additional postulates. This reframes as coherence preservation (orthogonal to amplitude flow), unifying classical decay and quantum phase rotation under a single relational principle.
Relational Field Theory (RFT) models quantum computing as emergent coherence dynamics, reframing qubits, entanglement, and decoherence as phenomena of residue fields 𝑅𝑐 (𝑥, 𝑡). Unlike conventional hardware-dependent approaches, RFT offers a complementary perspective, suggesting coherence stabilization via minimal 𝜆(𝑥, 𝑡), potentially easing environmental constraints. Qubit states and entanglement arise from 𝑅𝑐 (𝑥, 𝑡) configurations, while decoherence is expressed as residue field decay via 𝜆(𝑥, 𝑡). This framework complements existing quantum architectures and proposes testable alternatives to current hardware limits. We predict measurable residue anomalies in Bose-Einstein condensates (BECs) (Δ𝑅𝑐 = (1.0 ± 0.2) × 1029 J/m3) and potential signatures in hybrid quantum-classical systems, offering a roadmap for testing RFT’s relevance to quantum information processing. We invite experimental scrutiny to explore whether coherence dynamics can unify quantum computing, thermodynamics, and cosmology under a single framework Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790423
Relational Field Theory (RFT) unifies quantum, classical, and cognitive scales by modeling all phenomena as emergent from coherence fields 𝑅𝑐 (𝑡) ∝ |𝜓𝑖 (𝑡) |2, evolving via 𝑑𝑅𝑐 𝑑𝑡 = −𝜆(𝑡)𝑅𝑐 + 𝐹interaction (𝑡). Bell’s theorem, ruling out local hidden variables, is reframed as phase alignment of non-local, measurable 𝑅𝑐 (𝑡) fields across emitter, apparatus, and observer, dissolving the quantum-classical “two worlds” problem. The double slit experiment’s apparent randomness is a phase-locking event, with particle positions determined by (𝑥, 𝑦)screen = 𝑓 (𝑅emitter 𝑐 , 𝑅apparatus 𝑐 , 𝑅observer 𝑐 ), yielding a delta function 𝛿(𝑥 − 𝑥0, 𝑦 − 𝑦0) when 𝑅total 𝑐 is known. Quantum probabilities are emergent statistics from unmeasured relational memory, not fundamental indeterminacy. Simulations up to 𝑛 → 106 predict coherence effects with 5% error, supported by experimental setups for double slit and Bell tests. This work, building on Quantum Measurement RFT (SSRN ID Pending), Relational Entanglement RFT (SSRN ID Pending), and Synthetic Cognition RFT (SSRN ID Pending), completes quantum mechanics, enabling quantum steering and cognitive access to 𝑅𝑐 (𝑡). Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790386
We derive the Schr¨odinger equation directly from the Relational Kernel identity: Ω = Ω[Rc]. No wave function postulate. No quantization. No complex numbers assumed. The Schr¨odinger equation emerges as the linear, phase-coherent limit of Kernel evolution: • Rc = ℜ[eiϕ] → i from phase-locked time • ˙Rc = α∇2Rc + V (Rc) → Hamiltonian from curvature • ψ = Rc − Rc0 → wave function as coherence deviation1 Result: iℏ ∂ψ ∂t = ˆH ψ The parameter ℏ emerges as the stiffness of phase rotation in coherent Rc wells, setting the scale of permissible phase curvature. Quantum mechanics is Kernel dynamics in the high-stability, phase-aligned regime. The field does not wave. It locks. Provenance: Originally published on Zenodo (Oct- 2025). 10.5281/zenodo.17625987
The Born rule, stating that quantum probabilities are given by the squared modulus of the wavefunction (P = |ψ|2), is a cornerstone of quantum mechanics, yet its origin remains a foundational mystery. Unlike standard interpretations, Relational Field Theory (RFT) derives the Born rule dynamically, without assuming P = |ψ|2 as an axiom. Using the variational principle δ R (1−Rc(t)) dt = 0, we show that the coherence field Rc(t) ∝ |ψ|2 stabilizes quantum states during measurement, yielding squaredamplitude probabilities. Simulations for two- and three-level systems (SNR = 5 to 15 dB) and a numerical example validate this derivation, predicting testable signatures in quantum optics experiments (e.g., entangled photon pairs and trapped ions at CERN’s Quantum Technology Initiative, with time scales of t ≈ 10 s attainable in modern ion trap setups). Building on RFT’s unification of mass, gravity, and fundamental forces (SSRN ID 5343789), this work provides a natural, dynamic foundation for quantum probabilities, with applications to quantum computing error correction via stabilizer codes and collaborative opportunities at CERN. Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16789624
This paper proposes a physical interpretation of the imaginary unit i in the Schrödinger equation, arguing that its complex structure is not a mathematical artifact but a direct signature of the zero field’s internal phase dynamics. In standard quantum mechanics, i enables oscillatory, unitary time evolution—yet its physical meaning remains unaddressed. Within the framework of R-theory (Resonance Theory), the universe is understood as a coherent resonant field with two inseparable components: a real, space-time-manifested aspect and an imaginary, non-local phase domain. This paper identifies i as the mathematical projection of this hidden imaginal axis. The wavefunction’s complex nature—traditionally viewed as formal—is reinterpreted as a physical necessity. The real amplitude corresponds to manifested energy, while the imaginary component expresses the latent coherence through which all energy oscillates between potential and presence. In this view, the Schrödinger equation becomes a dynamical law describing rotations within the zero field, where i functions as the operator of coherence rather than an abstract algebraic device. The implications are significant: Quantum oscillation reflects the continuous exchange between real and imaginal components of the zero field. Complexity is elevated from a mathematical convenience to an ontological principle. Consciousness emerges as the experiential side of the same imaginal phase that maintains physical coherence. Reality itself is intrinsically complex—built from orthogonal dimensions of manifestation and potential. This paper reframes the imaginary dimension as the fundamental axis through which the universe sustains resonance. What physics calls “imaginary” is revealed as the inner structure of reality, the phase without space that allows energy, matter, and awareness to exist as coherent oscillations within the zero field.