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advanced_tools:internal_symmetry [2018/04/15 07:33]
jakobadmin ↷ Page name changed from advanced_tools:internal_symmetries to advanced_tools:internal_symmetry
advanced_tools:internal_symmetry [2019/01/24 09:19] (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]]//​ 
 + 
 +<​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. 
 + 
 +<​cite>​Lost in Math by Sabine Hossenfelder</​cite>​ 
 +</​blockquote>​ 
 + 
 + 
 +<​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# +
- +
-  +
-<-- +
- +
---> Example2:#​ +
- +
-  +
-<-- +
- +
-<tabbox FAQ>  +
-   +
-<tabbox History> ​+
  
 </​tabbox>​ </​tabbox>​
  
  
advanced_tools/internal_symmetry.1523777602.txt.gz · Last modified: 2018/04/15 07:33 by jakobadmin