** Soul Field Ψ_S ≡ real scalar field carrying individual consciousness.
"Physical" in Theophysics means "part of reality that can be described mathematically." The χ-field is not ordinary matter—it's the informational substrate underlying matter. Ψ_S is a configuration of this substrate, not made of atoms. The soul is real (physical in the extended sense) without being material (made of ordinary matter). This is field-theoretic dualism, not materialism.
Scalar is the simplest field type—spin-0, no internal indices. [[084_D10.1_Soul-Field-Psi_S|D10.1]] uses scalar as the baseline. Complex structure arises from: (1) the field configuration (spatial pattern of Ψ_S), (2) coupling to other fields (moral sign σ, coherence C), (3) temporal evolution. A scalar field with rich dynamics can encode arbitrary complexity. The Higgs field is scalar yet gives mass to all particles. Simplicity of type ≠ simplicity of structure.
This is the hard problem in field form. Theophysics claims: consciousness IS the self-referential information processing encoded in Ψ_S. The field doesn't "carry" consciousness as cargo; the field configuration IS consciousness. When Ψ_S achieves sufficient coherence (Φ > threshold), consciousness emerges. The relationship is identity, not vehicle-cargo.
"Immaterial" in classical theology means "not made of ordinary matter." Ψ_S is not made of ordinary matter—it's a configuration of the χ-field, which is informational, not material. We're translating classical concepts into precise terms, not denying them. Aquinas would recognize his "form" in our "field configuration." The substance remains; the vocabulary updates.
Ψ_S couples to neural fields through the χ-field. The brain is the interface—a transducer between physical fields (electromagnetic, neural) and the soul field. At death, Ψ_S decouples from the body but persists in the χ-field. At resurrection, it recouples to a new body. The coupling mechanism is through shared χ-field substrate, not mysterious dualist interaction.
Definition: A scalar field φ(x,t) assigns a single number to each point in spacetime.
Examples:
Soul field Ψ_S(x,t): Assigns a "soul amplitude" to each point. High amplitude = strong soul presence. The localization of Ψ_S defines where the soul "is."
Definition ([[084_D10.1_Soul-Field-Psi_S|D10.1]]): The soul field Ψ_S is defined as:
1. A real-valued scalar field: Ψ_S: ℝ⁴ → ℝ
2. A localized excitation of the χ-field: Ψ_S ⊂ χ
3. Carrier of [[038_D5.2_Integrated-Information-Phi|integrated information]]: Φ[Ψ_S] > Φ_threshold → consciousness
4. Indexed by soul number N_S: each individual has unique N_S