Axiom · Chain Position 45 of 346

SUPERPOSITION

**Statement:** Pre-observation, systems exist in superposition of all possible states.

Connections

Assumes

  • None

Enables

  • None
Mathematical Layer

Hilbert Space Formulation

State space: Complex Hilbert space H.

Pure states: Rays in H (equivalence classes of unit vectors).

Superposition principle: If |ψ₁⟩ and |ψ₂⟩ are states, so is α|ψ₁⟩ + β|ψ₂⟩.

This is an axiom of quantum mechanics—not derived, but postulated and confirmed by experiment.

Defeat Conditions

To Falsify This

  1. **Provide a hidden variable theory that works** — Show pre-existing definite values that reproduce quantum predictions (violates Bell)
  2. **Explain interference without superposition** — Account for double-slit patterns without wave overlap
  3. **Demonstrate measurement-independent properties** — Show quantum systems have definite values before observation
  4. **Violate quantum tomography** — Find a state not representable as superposition of basis states