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--- advanced_tools:internal_symmetry [2018/04/15 09:37]
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+++ advanced_tools:internal_symmetry [2018/04/15 09:39]
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 ====== Internal Symmetry ======
+//see also [[basic_tools:symmetry]] and [[advanced_tools:gauge_symmetry]]//
 <tabbox Intuitive>
-<blockquote>For the case of regular [[basic_notions:spin|spin]], we had to take spin-space seriously because it was associated with a concrete, measurable, physical quantity—angular momentum. This was only mildly uncomfortable because, although spinspace has the somewhat hard-to-stomach property that you have to turn all the way around twice to get back to your original condition, it’s otherwise pretty much like regular space. Isospin space, however, is completely abstract; it bears no relation whatsoever (other than through analogy) to anything we can grasp with our faculties of perception. How could rotations in such a space possibly have anything to do with the physical world? And yet the physical manifestation of the invariance of the strong force with respect to rotations in this space, the conservation of isospin, is a solidly established fact in the world of experimental science. So, what then is isospin-space from a physical point of view? Physicists usually describe it as an internal symmetry space, but what’s that, really? It’s your old buddy again, telling you that your car’s carburetion system “works on a vacuum principle.” How’s that going to help you to understand and fix the thing? It isn’t. Regarding the physical interpretation of the notion of isospin space, again your guess is as good as mine. Perhaps its experimental manifestations are hinting at some new and deeper truth about the universe that lies just beyond the current limits of our comprehension. Perhaps not. But one thing, however, is true: The introduction of the idea of internal symmetry spaces, of which isospin space was the first example, was an essential step forward in our understanding of the universe and the nature of the laws that govern it."
-<cite>Deep Down Things by Schumm></cite></blockquote>
-<tabbox Concrete>
-<note tip>
-In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
-</note>
-<tabbox Abstract>
-<note tip>
-The motto in this section is: //the higher the level of abstraction, the better//.
-</note>
-<tabbox Why is it interesting?>
 <blockquote>You are sitting in a room with a friend and a ping-pong ball (perfectly spherical and perfectly white— the ping-pong ball, not the friend). The conversation gets around to Newtonian mechanics. You toss the ball to your friend.
 Both of you agree that, given the speed and direction of the toss, F = m A
@@ Line 77: / Line 59: @@
 <cite>page 22ff in Topology, Geometry and Gauge fields by Naber</cite>
 </blockquote>
+<blockquote>For the case of regular [[basic_notions:spin|spin]], we had to take spin-space seriously because it was associated with a concrete, measurable, physical quantity—angular momentum. This was only mildly uncomfortable because, although spinspace has the somewhat hard-to-stomach property that you have to turn all the way around twice to get back to your original condition, it’s otherwise pretty much like regular space. Isospin space, however, is completely abstract; it bears no relation whatsoever (other than through analogy) to anything we can grasp with our faculties of perception. How could rotations in such a space possibly have anything to do with the physical world? And yet the physical manifestation of the invariance of the strong force with respect to rotations in this space, the conservation of isospin, is a solidly established fact in the world of experimental science. So, what then is isospin-space from a physical point of view? Physicists usually describe it as an internal symmetry space, but what’s that, really? It’s your old buddy again, telling you that your car’s carburetion system “works on a vacuum principle.” How’s that going to help you to understand and fix the thing? It isn’t. Regarding the physical interpretation of the notion of isospin space, again your guess is as good as mine. Perhaps its experimental manifestations are hinting at some new and deeper truth about the universe that lies just beyond the current limits of our comprehension. Perhaps not. But one thing, however, is true: The introduction of the idea of internal symmetry spaces, of which isospin space was the first example, was an essential step forward in our understanding of the universe and the nature of the laws that govern it."
+<cite>Deep Down Things by Schumm></cite></blockquote>
+<tabbox Concrete>
+<note tip>
+In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
+</note>
+<tabbox Abstract>
+<note tip>
+The motto in this section is: //the higher the level of abstraction, the better//.
+</note>
+<tabbox Why is it interesting?>
+Internal symmetries are powerful that we use, for example, to derive the correct Lagrangians describing fundamental interactions.
 </tabbox>

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