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--- basic_tools:symmetry [2019/01/24 10:22]
jakobadmin [Why is it interesting?]
+++ basic_tools:symmetry [2019/01/24 10:23]
jakobadmin [Why is it interesting?]
@@ Line 95: / Line 95: @@
 </blockquote>
+<blockquote>In physics we use many different types of symmetries, but they have one thing in common: they are potent unifying principles because they explain how things that once appeared very different actually belong together, connected by a symmetry transformation.
-<blockquote>The symmetry requirement therefore limits the possible laws we can write down. The logic is similar to coloring a mandala. If you want the color fill to respect the symmetry of the design, you have fewer options than when you ignore the symmetry.
+<cite>Lost in Math by Sabine Hossenfelder</cite>
+</blockquote>
+<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.
+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 symmetry requirement therefore limits the possible laws we can write down. The logic is similar to coloring a mandala. If you want the color fill to respect the symmetry of the design, you have fewer options than when you ignore the symmetry.
 <cite>Lost in Math by Sabine Hossenfelder</cite>
 </blockquote>

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