{"id": "card_lag_path_integral", "kind": "reference", "title": "The path integral — all paths, e^(iS/ℏ), the classical one by interference", "body": "Feynman: a quantum system takes ALL paths, each weighted by e^(iS/hbar); they interfere, and where the action is stationary the phases reinforce (the classical path), elsewhere they cancel; as hbar -> 0 only the least-action path survives. The many paths are real; the one emerges by interference. Sealed on stick_the_principle_of_least_action.", "source": {"label": "Narrow Highway — the Lagrangian", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "lagrangian", "bands": ["lagrangian", "pillar", "path_integral", "one map"], "subject": "The path integral — all paths, e^(iS/ℏ), the classical one by interference", "connections": [{"to_card_id": "card_floor_the_lagrangian", "relationship": "part_of", "evidence": "a pillar of the Lagrangian (The path integral)"}, {"to_card_id": "card_floor_the_capstone", "relationship": "connects_at", "evidence": "the many paths are real; the classical one emerges by interference"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.lagrangian", "facets": {"subject": ["one map", "path_integral", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "lagrangian", "by": "Narrow Highway — the Lagrangian", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_the_lagrangian", "title": "The Lagrangian — the Hamiltonian's dual, the path chosen", "relationship": "part of", "why": "a pillar of the Lagrangian (The path integral)", "href": "/card/card_floor_the_lagrangian", "resolved": true}, {"id": "card_floor_the_capstone", "title": "The capstone — one source, many potentials, one end", "relationship": "connects at", "why": "the many paths are real; the classical one emerges by interference", "href": "/card/card_floor_the_capstone", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_lag_path_integral", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_lag_path_integral"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}