Passage IV

Noether's Theorem

[1]

Laws of conservation一the idea that, within a physical system, certain measurable properties such as energy or momentum can neither be created nor destroyed一are fundamental to physics. When properties are conserved,they never leave the system. Therefore, physicists can study them and predict how even complex systems will behave.

[2]

Laws of symmetry, however, are valuable for the same reason: predictability. If a physical system behaves the same way regardless of how it's orientated in space, than it’ssymmetric. If, for instance, an experiment yields the same result whether it is conducted in the United States on Tuesday or in India on Thursday, which has symmetry of space and time.(52)

[3]

The relationship between conservation and symmetry had been overlooked, though, prior to the publication of Amalie Noether's theorem in 1918. Noether, a German mathematician, found that where there is symmetry in nature, there is corresponding conservation. Noether devised a groundbreaking set of equations to apply to symmetrical systems. [A] A bicycle wheel is radially symmetrical: you can spin it on its axis and it looks the same from any direction. Applying Noether's theorem reveals that the wheel conserves angular momentum the property that keeps bicycles upright, and moving forward. [B]

[4]

Both conservation laws, and laws of symmetry predict, and explain how systems behave. Thus, knowing that conservation exists where there is symmetry creates a whole new set of information about physical systems. Including, details about the properties within them that ultimately affect how the system works. [C]

[5]

The significance of Noether's theorem has not been lost, but her name bas. Dubbed "the greatest mathematician you've never heard of," Noether,until recently, was not widely recognized for her accomplishments. [D] Her name may not be as familiar as those of Einstein and Newton, but her theorem being regularly used in modern physics.Finally, in 1928, Noether accepted a teaching position at Moscow State University.