predictions
RS supplies a concrete list of four predictions for how classical mechanics emerges from quantum mechanics under the J-cost framework. A physicist working on decoherence or quantum-to-classical transition would cite this list when designing mesoscopic experiments. The definition is a direct enumeration of the claims derived from the many-body J-cost scaling argument in the module.
claimThe Recognition Science predictions for classical emergence consist of the following statements: decoherence time scales as $τ_D ∼ 1/N$ for a system of $N$ particles, pointer states are minima of the J-cost function, classical mechanics arises as the coarse-grained limit of quantum mechanics for large $N$, and specific testable decoherence timescales exist for mesoscopic systems.
background
In the Recognition Science framework, the J-cost is the cost function induced by a multiplicative recognizer, defined as the derived cost of its comparator on positive ratios. The module QF-011 derives classical emergence from many-body J-cost minimization: single-particle superpositions have low J-cost, but correlated many-particle states incur J-cost scaling quadratically with particle number. Upstream, the cost of a recognition event is its J-cost, and related modules supply cost functions for observer forcing and universal forcing self-reference.
proof idea
This definition enumerates the four predictions directly from the J-cost scaling argument. It is a straightforward list definition with no computation, serving as a reference for the experimental tests listed in the sibling experiments definition.
why it matters in Recognition Science
This definition collects the testable claims of the classical emergence theorem in the Recognition Science framework, linking to the eight-tick octave and phi-ladder through J-cost minimization. It supports the paper proposition on Nature Physics submission for classical emergence from RS. No parent theorems are listed in used_by, but it grounds the quantum-to-classical transition predictions.
scope and limits
- Does not derive the J-cost scaling from first principles.
- Does not provide numerical values for decoherence times.
- Does not simulate specific experiments.
- Does not address relativistic effects or curved spacetime.
formal statement (Lean)
200def predictions : List String := [
proof body
Definition body.
201 "τ_D ~ 1/N for system size N",
202 "Pointer states minimize J-cost",
203 "Classical = coarse-grained quantum",
204 "Testable in mesoscopic experiments"
205]
206
207/-- Experimental tests:
208 1. Fullerene interference (C₆₀) - shows quantum at large N ✓
209 2. LIGO mirrors - quantum limited at 40 kg ✓
210 3. Optomechanics - cooling macroscopic objects ✓ -/