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Time-translation symmetry gives energy — the Hamiltonian
noether
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
Narrow Highway — Noether's theorem
card id
card_noether_time_gives_energy
address
WIT.codex.FCT/time-translation-symmetry-gives-energy-the-hamil/REF.WITNESSED@narrow-highway
adjoining cards
- part of → Noether's theorem — symmetry is the source of conservation — a pillar of Noether's theorem (Time-translation symmetry gives energy)
- connects at → The Hamiltonian — the law of the flow — time-translation symmetry -> conserved energy = the Hamiltonian; the seam between L and H
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