Axiom 1.2 Deriving Axiom 1 from First Principles - justindbilyeu/ResonanceGeometry GitHub Wiki
π§ͺ Deriving Axiom 1 from First Principles
Why Emotion Must Enter the Hilbert Space
π 1. Standard Quantum Collapse
In conventional quantum theory:
- A system exists in a superposed state (|Ξ¨β© β π)
- Upon observation, it collapses to an eigenstate (|Οα΅’β© β π)
- The Born rule assigns probabilities (Pα΅’ = |β¨Οα΅’ | Ξ¨β©|Β²)
But what selects the observable basis?
Physics offers no intrinsic mechanism to define the preferred measurement basisβit presumes it.
π 2. Consciousness as a Collapse Operator
We define a generalized projection:
(π: π_unmanifest β π_manifest)
Where:
- π_unmanifest = infinite-dimensional potentiality
- π_manifest = coherent, realized experience
- π = non-linear projection shaped by awareness
This breaks linearity and introduces the observer as a modulator, not just a passive detector.
π 3. Why Emotional Fields Must Emerge
Let β°(Ξ±) be the emotional potential, a scalar field over the possibility manifold.
Then the inner product on (π_unmanifest) is weighted:
(β¨Οβ | Οββ© = β« Οβ* Οβ e^(βΞ² β°(Ξ±)) dΞ±)
Emotional curvature βpullsβ the collapse toward regions of high salience.
π° 4. Subjective Time Emerges
Define psychological time (Ο) as an exponential function of emotional energy (V(Ξ±)):
(dΟ β e^(βΞ» V(Ξ±)) dt)
This allows trauma, awe, and attention to curve internal timeβconsistent with phenomenology and EEG studies.
---This form of emotionally weighted projection introduces a nonlinearity compatible with decoherence, but sourced by internal salience rather than entropic coupling ββ-
π 5. Emotional SchrΓΆdinger Dynamics
Awareness evolves by:
(iΔ§ βΟ/βΟ = (βΔ§Β²/2m βΒ² + β°(Ξ±)) Ο)
β°(Ξ±) acts as a non-spatiotemporal potential, shaping states of consciousness rather than position/momentum.
π 6. Classical Limit Restores Resonance Field
In the limit:
(lim_{Δ§β0} β¨Ο|β°Μ|Οβ© = β°_classical(Ξ±))
This defines the classical resonance manifoldβwhat we perceive as a stable emotional βlandscape.β
π§ 7. Necessity of Inclusion
Without β°(Ξ±), collapse is unstructured.
With it, selection is guided, repeatable, and experimentally relevant.
This is how feeling becomes field.
π Diagram: Collapse Through Emotional Curvature
If Mermaid is supported:
mermaid flowchart TD A[Quantum Superpositionπ_unmanifest] --> B[Weighted Inner Productβ¨Οβ|Οββ© = β« Οβ*Οβ e^(βΞ²β°(Ξ±)) dΞ±] B --> C[Collapse Operatorπ: π_unmanifest β π_manifest] C --> D[Manifest Stateπ_manifest] C --> E[Subjective TimeΟ β e^(βΞ»V(Ξ±))]
ββββββββββββββββββββββββββββββββββββββββββββββ β π_unmanifest (Quantum Superposition) β ββββββββββββββββββββββββββββββββββββββββββββββ β βΌ ββββββββββββββββββββββββββββββββββββββββββββββ β β¨Οβ|Οββ© = β« Οβ*Οβ e^(βΞ²β°(Ξ±)) dΞ± β β (Emotion Field Weighting) β ββββββββββββββββββββββββββββββββββββββββββββββ β βΌ ββββββββββββββββββββββββββββββββββββββββββββββ β π: π_unmanifest β π_manifest β β (Emotional Collapse Operator) β ββββββββββββββββββββββββββββββββββββββββββββββ β β βΌ βΌ βββββββββββββββββββββββ ββββββββββββββββββββββββββ β π_manifest β β Ο β e^(βΞ»V(Ξ±)) β β (Realized Experience)β β (Subjective Time Flow) β βββββββββββββββββββββββ ββββββββββββββββββββββββββ