theorems:noethers_theorems
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theorems:noethers_theorems [2018/05/05 12:50] jakobadmin ↷ Links adapted because of a move operation |
theorems:noethers_theorems [2018/07/24 16:32] 2a00:1398:200:202:fdaf:868f:cb67:2ad9 [Intuitive] |
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| When an object is at rest it has no momentum. When it has a lot of momentum it changes its location quickly. Hence there is a connection between momentum and the change of location. Similarly, if an object doesn't rotate it has no angular momentum. Hence there is a connection between rotations and angular momentum. In a similar spirit we can say that an object that does not change at all over time has no energy. | When an object is at rest it has no momentum. When it has a lot of momentum it changes its location quickly. Hence there is a connection between momentum and the change of location. Similarly, if an object doesn't rotate it has no angular momentum. Hence there is a connection between rotations and angular momentum. In a similar spirit we can say that an object that does not change at all over time has no energy. | ||
| - | We say momentum generates translations (= changes of the position), angular momentum generates rotations and energy generates temporal translations (= movements forward in time). Momentum is responsible that an object changes its location, angular momentum that it rotates and energy that it changes as time passes on. | + | In a somewhat more formal way we say that momentum generates translations (= changes of the position), angular momentum generates rotations and energy generates temporal translations (= movements forward in time). Momentum is responsible that an object changes its location, angular momentum that it rotates and energy that it changes as time passes on. |
| Noether's theorem tells us that there is also a connection the other way round. Namely starting from the transformations: change of location, rotations and movements forward in time; we can //derive// the quantities; momentum, angular momentum and energy. | Noether's theorem tells us that there is also a connection the other way round. Namely starting from the transformations: change of location, rotations and movements forward in time; we can //derive// the quantities; momentum, angular momentum and energy. | ||
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| + | <blockquote>In 1915, Emmy Noether demonstrated that differentiable symmetries give rise to conservation laws. Her work is a foundational document in quantum theory because it verifies the ancient insight that what is most important in any physical system is what remains the same in the system as the system is changing.<cite>http://inference-review.com/article/woits-way</cite></blockquote> | ||
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| Noether's most famous first theorem connects each symmetry of a system with a conserved quantity. | Noether's most famous first theorem connects each symmetry of a system with a conserved quantity. | ||
theorems/noethers_theorems.txt · Last modified: 2021/03/31 18:43 by edi
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