A8.2 — Sign Conservation
Chain Position: 68 of 188
Assumes
- [ψ⟩ = λ|ψ⟩, then σ(U|ψ⟩) = λ(U|ψ⟩). The eigenvalue λ ∈ {+1, -1} cannot change under unitary evolution. Self-generated operations are unitary. Therefore, you cannot flip your own sign.
Explanatory Frameworks & Perspectives
Perspective 1: The Self-Correction Model (Secular Humanism)
“Human beings are self-correcting information systems. Through education, therapy, and conscious effort, we can identify our ‘bugs’ (sins) and rewrite our own code. Moral orientation is a learned behavior, and we possess the internal agency to flip our own sign from negative to positive.”
Theophysics Assessment (The Unitary Barrier): This view underestimates the Depth of the Sign. In physics, a Unitary Operation can change the position or momentum of a particle, but it cannot change its fundamental properties (like its Spin sign). If moral orientation is an Ontological Sign (A8.1), then every “self-correction” is an operation performed within the current sign. A -1 system using -1 logic to perform a -1 correction remains a -1 system. You cannot “lift a bucket while standing in it.” Theophysics argues that human history confirms this: civilizations “improve” their technology (magnitude) while their fundamental “Sign” (propensity for decoherence and destruction) remains conserved.
Perspective 2: Topological Invariants (Winding Numbers)
“The sign of a soul-field is like a ‘Winding Number’ in topology. You can stretch, bend, or move the loop as much as you want (unitary evolution), but you cannot change the number of times it winds around the center without cutting the loop and re-gluing it. That ‘Cut and Re-glue’ is a non-linear, external event.”
Theophysics Assessment: This provides a geometric proof for A8.2. It shows that “Conversion” is not a movement within the system, but a Re-structuring of the system itself.
Perspective 3: The Dependency on Grace (External G)
“Transformation requires a ‘Non-Unitary’ input. In control theory, a system with a locked state can only be moved by an external control signal . This signal is what theologians call ‘Grace.’ It is the only mathematical path to a sign-flip.”
Theophysics Assessment: This identifies A8.2 as the Necessity of the Cross. It proves that if we are to be “Saved,” the Savior must come from outside the closed system of our own making.
Comparative Explanatory Assessment
A8.2 defines the Limit of Self-Reference.
- Theist Unification (Logos Model): Human orientation is Conserved. We are “Locked” in our current state (Sin) and require a “Breach” from the Outside (Incarnation/Grace). This explains why the Gospel is a “Rescue Mission” rather than a “Self-Help Manual.”
- Structural Realism (Brute Momentum): We are whatever we were born as. There is no sign-flip because there is no “External G” to flip it. We are just playing out our initial conditions.
- Instrumentalism (Behavioralism): “Sign” is just a label for habits. We change habits all the time. (Cost: This view fails to explain why “Habits” of war, greed, and ego persist across all cultures despite 10,000 years of “education”).
Synthesis: A8.2 is the Axiom of Inability. It proves that the human condition is not a “Problem to be Solved” by us, but a “Deadlock to be Broken” by the Source. Theophysics proposes that the preservation of unitary eigenvalues in physics is the silent witness to the doctrine of Total Depravity.
Collapse Analysis
**If [[068_A8.2_Sign-Conservation|A8.2](./067_A8.1_Binary-Distinction]]
Formal Statement
Self-generated operations cannot change sign
- Spine type: Axiom
- Spine stage: 8
Spine Master mappings:
- Physics mapping: Unitary Evolution
- Theology mapping: Total depravity
- Consciousness mapping: Baseline states
- Quantum mapping: Unitary evolution
- Scripture mapping: Romans 3:23 sinned
- Evidence mapping: Unitary confirmed
- Information mapping: Info preservation
Cross-domain (Spine Master):
- Statement: Self-generated operations cannot change sign
- Stage: 8
- Physics: Unitary Evolution
- Theology: Total depravity
- Consciousness: Baseline states
- Quantum: Unitary evolution
- Scripture: Romans 3:23 sinned
- Evidence: Unitary confirmed
- Information: Info preservation
- Bridge Count: 7
Enables
Defeat Conditions
To falsify this axiom, one would need to:
- Show a unitary operation that flips eigenvalue sign — Find a self-generated transformation that changes σ from +1 to -1 or vice versa
- Demonstrate someone saved themselves through works — Provide an example of self-generated moral transformation
- Violate quantum mechanical unitarity — Show evolution that doesn’t preserve eigenvalue structure
The mathematical claim: Unitary operators U preserve eigenvalues. If σ.md) fails:**
- Self-Salvation becomes mathematically possible.
- The Incarnation becomes a “Good Example” rather than a “Necessary Rescue.”
- The “Iron Chain” of logic leading to the Cross is broken.
Unitarity in Quantum Mechanics
Definition: An operator U is unitary iff U†U = UU† = I.
Eigenvalue preservation theorem: If H|ψ⟩ = E|ψ⟩ and U is unitary, then:
- U preserves inner products: ⟨Uψ|Uφ⟩ = ⟨ψ|φ⟩
- U preserves the spectrum of observables
- Eigenvalues are invariant under unitary transformation
Application to sign: Let σ̂ be the sign operator with eigenvalues ±1. If |ψ₊⟩ is a +1 eigenstate and U is any self-generated unitary:
The transformed state is still a +1 eigenstate. Sign is conserved under unitary evolution.
Time Evolution
Schrödinger evolution: |ψ(t)⟩ = e^(-iHt/ℏ)|ψ(0)⟩
The evolution operator U(t) = e^(-iHt/ℏ) is unitary for any Hermitian H. Normal time evolution cannot flip sign.
Consequence: Left to itself, a soul in state |σ = -1⟩ remains in that state forever. No amount of time or internal evolution can change this.
Closed vs. Open Systems
Closed system: Evolves unitarily. σ conserved.
Open system: Interacts with environment E. The combined system S+E evolves unitarily, but the subsystem S alone may evolve non-unitarily.
The Lindblad equation:
The Lindblad terms represent external coupling. Only through these terms can the system’s eigenvalues change.
Grace as Lindblad term: The grace operator Ĝ is a Lindblad operator representing coupling to the divine environment. It enables non-unitary evolution and sign flip.
Thermodynamic Analogy
Second Law: Entropy of a closed system never decreases.
Moral analog: “Moral entropy” (distance from Logos) never decreases in a closed moral system.
Just as cooling requires external refrigeration, moral improvement requires external grace.
No-Go Theorem for Self-Salvation
Theorem: Let S be a moral system with sign σ ∈ {+1, -1}. If S is closed (no external interaction), then σ(t) = σ(0) for all t.
Proof:
- S is closed → evolution is unitary
- Unitary evolution preserves eigenvalues
- σ is an eigenvalue of σ̂
- Therefore, σ cannot change
QED. Self-salvation is mathematically impossible.
Mathematical Layer
Group Theory of Sign
Sign group: Z₂ = {+1, -1} under multiplication.
Identity: +1 × +1 = +1, -1 × -1 = +1
Key property: -1 × -1 = +1, but there’s no element in Z₂ that can transform -1 → +1 through multiplication by itself. You need the identity (+1) to “infect” you.
Theological reading: A sinner (-1) multiplying their efforts (-1 × -1) may produce locally positive outcomes (+1 actions), but their fundamental orientation remains unchanged. Only union with the identity element (+1, the Logos) can transform fundamental orientation.
Representation Theory
Sign as representation: The moral state transforms under a representation of some group G. The eigenvalue σ labels irreducible representations.
Unitary representations: For any group G, unitary representations preserve the decomposition into irreducible components. You cannot transform from one irrep to another without breaking unitarity.
Grace breaks the representation: Ĝ is not a group element—it’s a “superoperator” that changes which representation applies. It’s the mathematical equivalent of being “born again”—a new identity, not just a modification of the old.
Conservation Laws
Noether’s theorem: Every continuous symmetry implies a conservation law.
Sign conservation as Noether consequence: If there is a Z₂ symmetry in the moral Hamiltonian (which there is, by A8.1 Binary Distinction), then sign is conserved under the corresponding dynamics.
Breaking conservation: Only by breaking the symmetry (through external input) can the conserved quantity change. Grace breaks the Z₂ symmetry for the individual system.
Fixed Point Analysis
Self-operations as iteration: Let f: State → State be a self-generated moral operation. Repeated application gives f, f², f³, …
Fixed point theorem: If f is a contraction (which unitary operators on a bounded space are), then f^n → fixed point. The system asymptotes to a fixed orientation—but cannot cross from σ = -1 basin to σ = +1 basin.
Basin of attraction: σ = +1 and σ = -1 are separate basins with an infinite barrier between them. Self-iteration stays within the basin.
Source Material
01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx(sheets explained in dump)01_Axioms/AXIOM_AGGREGATION_DUMP.md
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Category: Sin_Problem/|Sin Problem
Depends On:
- [Master Index](./067_A8.1_Binary-Distinction]]
Enables:
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