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Thomas Rigby
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I read about Noether's theorem that says how for every symmetry there is a conserved quantity. Seems kind of obvious. Does anyone understand it well enough that they can explain precisely why that notion is profound?
Well, what's "profound" is something of a matter of taste, but...Thomas Rigby said:I read about Noether's theorem that says how for every symmetry there is a conserved quantity. Seems kind of obvious. Does anyone understand it well enough that they can explain precisely why that notion is profound?
And yet, if you phrase Noether's Thm in that too-simplistic way, the statement is false.Thomas Rigby said:I read about Noether's theorem that says how for every symmetry there is a conserved quantity. Seems kind of obvious.
One can deduce various features of a (class of) systems by examining its symmetries, more easily than exhaustively solving its equations of motion. E.g., solving for Kepler orbits leads to a transcendental equation which cannot be solved analytically. But a study of the various symmetries of that problem (energy conservation, momentum conservation, the LRL vectors, and the K3 dilation symmetry) allow many useful features of the orbits to be deduced. E.g., what's the relation between orbital radius and tangential velocity, and so on.Thomas Rigby said:Does anyone understand it well enough that they can explain precisely why that notion is profound?
She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics.Nugatory said:Well, what's "profound" is something of a matter of taste, but...
Please, prove it.Thomas Rigby said:Seems kind of obvious.
Noether's theorem is a fundamental theorem in physics that relates symmetries in a physical system to conservation laws. It was developed by mathematician Emmy Noether in the early 20th century.
Noether's theorem is important because it provides a deep understanding of the fundamental laws of physics, such as conservation of energy, momentum, and angular momentum. It also allows for the prediction of new physical laws based on symmetries.
Symmetries in physics can include spatial symmetries, such as rotational or translational symmetries, as well as symmetries in time or in the laws of physics themselves. For example, the laws of physics are the same for all observers regardless of their location or orientation in space.
Noether's theorem shows that the laws of motion, such as Newton's laws, are a consequence of the underlying symmetries in a physical system. This means that the laws of motion are not arbitrary, but rather they arise from fundamental principles of symmetry.
Yes, Noether's theorem has been applied to other fields such as economics, biology, and engineering. It can also be used in mathematics to prove theorems about geometric and algebraic structures.