basic_tools:symmetry
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basic_tools:symmetry [2019/01/24 10:23] jakobadmin [Why is it interesting?] |
basic_tools:symmetry [2019/01/24 10:23] jakobadmin [Why is it interesting?] |
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| - | <blockquote>FOR THE physicist, a symmetry is an organizing principle that avoids unnecessary repetition. Any type of pattern, likeness, or order can be mathematically captured as an expression of symmetry. The presence of a „symmetry always reveals a redundancy and allows simplification. Hence, symmetries explain more with less. | + | <blockquote>For the physicist, a symmetry is an organizing principle that avoids unnecessary repetition. Any type of pattern, likeness, or order can be mathematically captured as an expression of symmetry. The presence of a „symmetry always reveals a redundancy and allows simplification. Hence, symmetries explain more with less. |
| For example, rather than telling you today’s sky looks blue in the west and the east and the north and the south and the southwest, and so on, I can just say it looks blue in every direction. This independence on the direction is a rotational symmetry, and it makes it sufficient to spell out how a system looks in one direction, followed by saying it’s the same in all other directions. The benefit is fewer words or, in our theories, fewer equations. | For example, rather than telling you today’s sky looks blue in the west and the east and the north and the south and the southwest, and so on, I can just say it looks blue in every direction. This independence on the direction is a rotational symmetry, and it makes it sufficient to spell out how a system looks in one direction, followed by saying it’s the same in all other directions. The benefit is fewer words or, in our theories, fewer equations. | ||
| The symmetries that physicists deal with are more abstract versions of this simple example, like rotations among multiple axes in internal mathematical spaces. But it always works the same way: find a transformation under which the laws of nature remain invariant and you’ve found a symmetry. Such a symmetry transformation may be anything for which you can write down an unambiguous procedure—a shift, a rotation, a flip, or really any other operation that you can think of. If this operation does not make a difference to the laws of nature, you have found a symmetry. | The symmetries that physicists deal with are more abstract versions of this simple example, like rotations among multiple axes in internal mathematical spaces. But it always works the same way: find a transformation under which the laws of nature remain invariant and you’ve found a symmetry. Such a symmetry transformation may be anything for which you can write down an unambiguous procedure—a shift, a rotation, a flip, or really any other operation that you can think of. If this operation does not make a difference to the laws of nature, you have found a symmetry. | ||
basic_tools/symmetry.txt · Last modified: 2019/01/24 10:23 by jakobadmin
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