Physics Emmy Noether

noether brought göttingen in 1915 david hilbert , felix klein, wanted expertise in invariant theory them in understanding general relativity, geometrical theory of gravitation developed albert einstein. hilbert had observed conservation of energy seemed violated in general relativity, because gravitational energy gravitate. noether provided resolution of paradox, , fundamental tool of modern theoretical physics, noether s first theorem, proved in 1915, did not publish until 1918. not solved problem general relativity, determined conserved quantities every system of physical laws possesses continuous symmetry.

upon receiving work, einstein wrote hilbert: yesterday received miss noether interesting paper on invariants. m impressed such things can understood in such general way. old guard @ göttingen should take lessons miss noether! seems know stuff.

for illustration, if physical system behaves same, regardless of how oriented in space, physical laws govern rotationally symmetric; symmetry, noether s theorem shows angular momentum of system must conserved. physical system need not symmetric; jagged asteroid tumbling in space conserves angular momentum despite asymmetry. rather, symmetry of physical laws governing system responsible conservation law. example, if physical experiment has same outcome @ place , @ time, laws symmetric under continuous translations in space , time; noether s theorem, these symmetries account conservation laws of linear momentum , energy within system, respectively.

noether s theorem has become fundamental tool of modern theoretical physics, both because of insight gives conservation laws, , also, practical calculation tool. theorem allows researchers determine conserved quantities observed symmetries of physical system. conversely, facilitates description of physical system based on classes of hypothetical physical laws. illustration, suppose new physical phenomenon discovered. noether s theorem provides test theoretical models of phenomenon: if theory has continuous symmetry, noether s theorem guarantees theory has conserved quantity, , theory correct, conservation must observable in experiments.