Equations · equation
Noether's Theorem
Classical Field Theory · 1918
- Equation
- ∂L/∂(∂_μφ)·δφ = J^μ, ∂_μJ^μ = 0
- Field
- Classical Field Theory
- Named After
- Emmy Noether
- Year
- 1918
Symbols
L the Lagrangian density · φ the field · δφ a symmetry: a change that leaves L alone · J^μ the resulting current, whose flow ∂_μJ^μ vanishes — the conserved charge
Significance
Every continuous symmetry produces a conserved quantity — physics' deepest theorem. Time looks the same tomorrow, so energy is conserved; space is the same over there, so momentum is; turn around and angular momentum is; rotate a quantum phase and electric charge is. Proved by a woman Göttingen wouldn't pay; Einstein called her a creative mathematical genius.
Referenced by
equation
theory
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