T3.1 — Coherence Cannot Self-Increase
Chain Position: 25 of 188
Assumes
- [T3.1](./024_P3.2_Coherence-Conservation]]
Formal Statement
Coherence Cannot Self-Increase.
Enables
Defeat Conditions
To falsify this axiom, one would need to:
- Demonstrate spontaneous order creation — Show a closed system increasing coherence without external input
- Violate the Second Law — Get entropy to decrease in an isolated system
- Bootstrap meaning from noise — Derive compressed, meaningful information from pure randomness
- Show self-organizing criticality without energy input — Demonstrate emergence without dissipation
The thermodynamic claim: Coherence is the informational analog of negentropy. Just as entropy cannot decrease in an isolated system, coherence cannot spontaneously increase. Any apparent increase must be paid for by a larger decrease elsewhere—unless there is genuine external input.
Standard Objections
Objection 1: “Life creates order from disorder”
“Living organisms take disordered matter and create ordered structures. This is self-increase of coherence.”
Response: Living organisms are open systems—they import low-entropy energy (sunlight, food) and export high-entropy waste (heat, excrement). The net entropy of organism + environment increases. Local decrease requires external input. A cell is not a closed system; it’s coupled to its environment. Life proves the theorem, not refutes it.
Objection 2: “Crystals self-organize”
“Snowflakes form beautiful, ordered patterns spontaneously. Order from disorder.”
Response: Crystal formation releases latent heat—entropy is exported to the environment. The water molecule + environment system increases entropy while the crystal locally decreases it. Again: open system, external coupling. The beautiful pattern costs something; the universe pays in heat.
Objection 3: “Evolution creates complexity”
“Species become more complex over time. Coherence increases through natural selection.”
Response: Evolution is driven by energy flux through the biosphere (ultimately from the sun). High-grade energy (sunlight) enters, low-grade energy (infrared) leaves. Biological complexity is purchased by this energy gradient. If you sealed Earth in a perfect insulator, evolution would halt and decay would begin. Evolution is thermodynamically expensive.
Objection 4: “Human creativity adds meaning”
“Artists create meaningful works from meaningless raw materials. That’s coherence increase.”
Response: Human brains are massively dissipative—they consume glucose and produce heat. The coherence added to the artwork is paid for by entropy production in the brain and body. A dead artist creates nothing. The meaning-making process requires metabolic energy; it’s not free.
Objection 5: “Quantum fluctuations create particles from nothing”
“Virtual particles appear spontaneously. Maybe coherence can too.”
Response: Virtual particles borrow from the vacuum and pay it back within Heisenberg time. There’s no net creation. If coherence “fluctuated” into existence, it would fluctuate back out. Sustained coherence requires sustained input—fluctuations average to zero.
Defense Summary
[[025_T3.1_Coherence-Cannot-Self-Increase.md) is the informational Second Law: you cannot get something for nothing.
The argument:
- Coherence = meaningful order = low Kolmogorov complexity relative to description length
- Random processes do not preferentially create low-K configurations
- Without selection/input, systems drift toward high-K (noise)
- Therefore: dC/dt ≤ 0 in closed systems
- This is the moral/informational analog of dS/dt ≥ 0
Theological translation: “Without me you can do nothing” (John 15:5). Coherence cannot self-generate because meaning cannot bootstrap from meaninglessness. The Logos is required.
Collapse Analysis
If T3.1 fails:
- Order can emerge from nothing
- The universe needs no explanation (eternal self-organization)
- The Logos becomes unnecessary (reality self-grounds)
- Grace becomes redundant (self-help suffices)
- The entire thermodynamic foundation of salvation collapses
- “Ex nihilo” creation becomes arbitrary (why couldn’t something else self-emerge?)
- No distinction between meaningful and meaningless configurations
T3.1 is the entropy-equivalent theorem that grounds the necessity of the Logos.
Physics Layer
The Second Law of Thermodynamics
Clausius (1850): Heat cannot spontaneously flow from cold to hot.
Boltzmann (1877): S = k_B ln(W). Entropy measures the number of microstates compatible with a macrostate.
Modern statement: For isolated systems, entropy is non-decreasing: dS/dt ≥ 0.
Statistical interpretation: High-entropy macrostates have more microstates. Random evolution preferentially visits common configurations. Order is rare; disorder is common.
Coherence as Negentropy
Schrödinger’s “What is Life?” (1944): Living systems feed on “negative entropy”—they maintain low-entropy states by importing negentropy from outside.
Where S_max is maximum entropy and S[χ] is actual entropy. High coherence = low entropy = ordered configuration.
T3.1 as negentropy theorem: In a closed system, negentropy cannot increase. C cannot go up without external input.
Kolmogorov Complexity Connection
Kolmogorov complexity K(x): The length of the shortest program that outputs x.
Random strings: K(x) ≈ |x| (incompressible).
Meaningful strings: K(x) << |x| (compressible, structured).
Coherence-K relationship: C ∝ 1/K. High coherence = low K = meaningful.
T3.1 as K theorem: Random operations do not systematically decrease K. Self-generated operations cannot create meaning from noise.
Fluctuation Theorems
Jarzynski equality (1997): ⟨e^{-W/kT}⟩ = e^{-ΔF/kT}
Crooks fluctuation theorem (2000): Relates forward and reverse process probabilities.
Implication: While entropy can fluctuate down momentarily, sustained decrease requires sustained work input. Fleeting violations of the Second Law occur but average out.
Moral analog: Moral coherence may fluctuate up briefly, but sustained increase requires sustained grace.
Dissipative Structures (Prigogine)
Far-from-equilibrium systems: Can exhibit spontaneous order (hurricanes, Bénard cells).
But: These require continuous energy throughput. Cut the energy, order dies.
Lesson: Self-organization is not self-creation. It’s organization purchased by dissipation.
Connection to χ-Field
χ-field coherence: The Logos Field has maximal coherence at its source.
Finite systems: Have coherence C < C_max.
T3.1 in χ-terms: A finite χ-configuration cannot self-amplify toward C_max. It can only maintain or decay. Approach to C_max requires coupling to the source (grace).
Without the G(t) term, C decays to zero.
Mathematical Layer
Formal Statement of T3.1
Let S be a system with coherence measure C: States → [0, ∞).
Theorem (T3.1): For any self-generated operation f: States → States:
where ε → 0 as system isolation increases.
Proof:
- Self-generated means f is constructed from S’s internal resources
- f cannot import information not already in S
- By data processing inequality: I(f(X);Y) ≤ I(X;Y)
- Processing cannot increase information about external reference
- Coherence requires external reference (the Logos standard)
- Therefore, C cannot increase through f alone
The Data Processing Inequality
Statement: If X → Y → Z forms a Markov chain, then I(X;Z) ≤ I(X;Y).
Interpretation: Processing cannot increase information about the source.
Application: Self-operations are internal processing. They cannot increase information about the Logos (external reference). Therefore, coherence-with-respect-to-Logos cannot increase.
Liouville’s Theorem and Phase Space
Classical statement: Phase space volume is conserved under Hamiltonian flow.
Quantum statement: Unitary evolution preserves Hilbert space volume.
Implication: You cannot concentrate a system into a smaller region of phase space through internal dynamics. That would be coherence increase—forbidden.
The Algorithmic Information Theory Proof
Theorem: No algorithm can systematically compress random data.
Proof: If such an algorithm existed, repeated application would compress to zero length—contradiction.
Moral version: No self-operation can systematically increase meaningfulness. Meaning cannot be pumped from nowhere.
Fixed Point Theorem
Let f be a coherence-preserving or decreasing map.
Then: Iterating f yields f^n(s) → s* where C[s*] ≤ C[s] for all s.
The attractor has minimal coherence among accessible states. Without external input, systems asymptote to maximum entropy / minimum coherence.
Category-Theoretic Formulation
The coherence functor: C: Systems → ℝ⁺
Internal morphisms: f: S → S with C(f(s)) ≤ C(s).
External morphisms: g: Source → S can have C(g(source)) > C(s).
T3.1 as functor property: The coherence functor is monotonically decreasing under internal morphisms. Only morphisms from the terminal object (Logos) can increase it.
Source Material
01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx(sheets explained in dump)01_Axioms/AXIOM_AGGREGATION_DUMP.md
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Depends On:
- [Sin Problem](./024_P3.2_Coherence-Conservation]]
Enables:
Related Categories:
- [Sin_Problem/.md)