Axiom · Chain Position 3 of 346

[[003_A1.3_INFORMATION-PRIMACY|INFORMATION PRIMACY]]

**Statement:** Distinguishability IS information; therefore information is ontologically primitive.

Connections

Physics Layer

Quantum Information Revolution

The 20th-century revolution: physics IS information processing.

Quantum state = information carrier:

|ψ⟩ ∈ H is not a "thing" but a description of what we can predict. The Copenhagen interpretation makes this explicit: the wavefunction is epistemic (knowledge-encoding), not ontic (stuff-encoding).

Measurement = information extraction:

Observable A acting on |ψ⟩ yields eigenvalue a with probability |⟨a|ψ⟩|². This is information transfer from quantum system to observer.

Entanglement = information correlation:

|Ψ⟩ = |↑↓⟩ - |↓↑⟩ encodes correlation without transmitting any physical substance. Bell violations prove this correlation exceeds classical information limits → quantum information is primary.

Mathematical Layer

Shannon Information

Entropy as uncertainty measure:

H(X) = -\sum_{x \in \mathcal{X}} p(x) \log_2 p(x)

Properties that make it fundamental:

  • Uniquely characterized by Khinchin axioms (1957)
  • Additive for independent variables: H(X,Y) = H(X) + H(Y) if X ⊥ Y
  • Maximum for uniform distribution: H_max = log |X|
  • Operational meaning: optimal compression rate (Shannon's source coding theorem)
Evidence
Empirical Grounding
This isn't philosophy. This is measured.
  • Bekenstein Bound
  • Landauer's Principle
Defeat Conditions

To Falsify This

  1. Show a property of matter/energy that is NOT informational
  2. Define "matter" without recourse to its informational properties (mass, charge, spin, position)
  3. Explain quantum mechanics without information theory