{"id": "card_noether_time_gives_energy", "kind": "reference", "title": "Time-translation symmetry gives energy — the Hamiltonian", "body": "The laws do not change in time; Noether turns that one symmetry into conservation of energy - and energy is exactly the Hamiltonian. So the Lagrangian's symmetry produces the Hamiltonian's conserved quantity: Noether is the seam between the two floors.", "source": {"label": "Narrow Highway — Noether's theorem", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "noether", "bands": ["noether", "pillar", "time_gives_energy", "one map"], "subject": "Time-translation symmetry gives energy — the Hamiltonian", "connections": [{"to_card_id": "card_floor_noethers_theorem", "relationship": "part_of", "evidence": "a pillar of Noether's theorem (Time-translation symmetry gives energy)"}, {"to_card_id": "card_floor_the_hamiltonian", "relationship": "connects_at", "evidence": "time-translation symmetry -> conserved energy = the Hamiltonian; the seam between L and H"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.noether", "facets": {"subject": ["one map", "pillar", "time_gives_energy"]}, "presentation": {"glyph": "•", "kind_label": "noether", "by": "Narrow Highway — Noether's theorem", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_noethers_theorem", "title": "Noether's theorem — symmetry is the source of conservation", "relationship": "part of", "why": "a pillar of Noether's theorem (Time-translation symmetry gives energy)", "href": "/card/card_floor_noethers_theorem", "resolved": true}, {"id": "card_floor_the_hamiltonian", "title": "The Hamiltonian — the law of the flow", "relationship": "connects at", "why": "time-translation symmetry -> conserved energy = the Hamiltonian; the seam between L and H", "href": "/card/card_floor_the_hamiltonian", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_noether_time_gives_energy", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_noether_time_gives_energy"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}