advanced_tools:internal_symmetry
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advanced_tools:internal_symmetry [2018/03/28 16:19] jakobadmin ↷ Page moved from advanced_tools:internal_symmetries to advanced_tools:symmetries:internal_symmetries |
advanced_tools:internal_symmetry [2019/01/24 10:19] (current) jakobadmin [Intuitive] |
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| - | ====== Internal Symmetries ====== | + | ====== Internal Symmetry ====== |
| - | <tabbox Why is it interesting?> | + | //see also [[basic_tools:symmetry]] and [[advanced_tools:gauge_symmetry]]// |
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| + | <tabbox Intuitive> | ||
| <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. | <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 | Both of you agree that, given the speed and direction of the toss, F = m A | ||
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| changes in the internal spin state of the ball would have to be accounted for | changes in the internal spin state of the ball would have to be accounted for | ||
| by some force being exerted on it, such as its interaction with the atmosphere | by some force being exerted on it, such as its interaction with the atmosphere | ||
| - | in the room, and we have, at least for the moment, neglected such interac- | + | in the room, and we have, at least for the moment, neglected such interactions in our calculations. It would seem proper then to regard any intrinsic |
| - | tions in our calculations. It would seem proper then to regard any intrinsic | + | |
| spinning of the ball about some axis as part of the “internal structure” of | spinning of the ball about some axis as part of the “internal structure” of | ||
| the ball, not relevant to its motion through space, but conceivably relevant | the ball, not relevant to its motion through space, but conceivably relevant | ||
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| <cite>page 22ff in Topology, Geometry and Gauge fields by Naber</cite> | <cite>page 22ff in Topology, Geometry and Gauge fields by Naber</cite> | ||
| </blockquote> | </blockquote> | ||
| - | <tabbox Layman> | ||
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| <cite>Deep Down Things by Schumm></cite></blockquote> | <cite>Deep Down Things by Schumm></cite></blockquote> | ||
| - | <tabbox Student> | + | <blockquote>„What the heck is an internal space?” you ask. Good question. The best answer I have is “useful.” It’s what we invented to quantify the observed behavior of particles, a mathematical tool that helps us make predictions. |
| + | “Yes, but is it real?” you want to know. Uh-oh. Depends on whom you ask. Some of my colleagues indeed believe that the math of our theories, like those internal spaces, is real. Personally, I prefer to merely say it describes reality, leaving open whether or not the math itself is real. How math connects to reality is a mystery that plagued philosophers long before there were scientists, and we aren’t any wiser today. But luckily we can use the math without solving the mystery. | ||
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| + | <cite>Lost in Math by Sabine Hossenfelder</cite> | ||
| + | </blockquote> | ||
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| + | <tabbox Concrete> | ||
| <note tip> | <note tip> | ||
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| </note> | </note> | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
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| - | <tabbox Examples> | + | <tabbox Why is it interesting?> |
| - | + | Internal symmetries are powerful that we use, for example, to derive the correct Lagrangians describing fundamental interactions. | |
| - | --> Example1# | + | |
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| - | + | ||
| - | <-- | + | |
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| - | --> Example2:# | + | |
| - | + | ||
| - | + | ||
| - | <-- | + | |
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| - | <tabbox FAQ> | + | |
| - | + | ||
| - | <tabbox History> | + | |
| </tabbox> | </tabbox> | ||
advanced_tools/internal_symmetry.1522246791.txt.gz · Last modified: 2018/03/28 14:19 (external edit)
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