Does a symmetry need to leave the whole action invariant?

In summary, symmetry in scientific terms refers to a property of an object or system that remains unchanged under a transformation or operation. It can be broken or violated, which occurs when the object or system does not maintain its original appearance or behavior. When a symmetry leaves the whole action invariant, it means that the transformation does not change the overall behavior of the system. While it is not necessary for a symmetry to leave the whole action invariant, it is an important consideration in many scientific theories. Symmetries can also be used to predict the behavior of a system by understanding how they affect the system under different conditions and transformations.
  • #1
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Typically a symmetry is taken to be something that leaves the action invariant. However, on a classical level, isn't that asking way too much? To match what we conceptually mean by symmetry, we only need something that maps solutions to solutions, so something which leaves the action invariant in the neighbourhood of extremal solutions(?) (After all who cares what a symmetry operation does to unphysical solutions?). Is it because of Noether's theorem?
 
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  • #2
Alright I solved my own problem. You need it to get Noether's theorem to work.
 

FAQ: Does a symmetry need to leave the whole action invariant?

1. What is the definition of symmetry in scientific terms?

In science, symmetry refers to a property of an object or system that remains unchanged when it undergoes a transformation or operation. This means that the object or system has the same appearance or behavior before and after the transformation.

2. Can a symmetry be broken or violated?

Yes, a symmetry can be broken or violated. This occurs when the object or system does not maintain its original appearance or behavior after undergoing a transformation. This can happen due to various factors such as external forces or interactions with other objects.

3. What does it mean for a symmetry to leave the whole action invariant?

In this context, the term "action" refers to a physical quantity that describes the behavior of a system over time. A symmetry leaving the whole action invariant means that the transformation does not change the overall behavior of the system, and the action remains the same.

4. Is it necessary for a symmetry to leave the whole action invariant?

No, it is not necessary for a symmetry to leave the whole action invariant. In some cases, the transformation may affect the overall behavior of the system but still maintain certain symmetries. However, in many scientific theories, symmetries play a crucial role in determining the behavior of a system and are therefore important considerations.

5. Can symmetries be used to predict the behavior of a system?

Yes, symmetries can be used to predict the behavior of a system. By understanding the symmetries present in a system, scientists can make predictions about how the system will behave under different conditions and transformations. This can help in developing theories and making accurate predictions about the physical world.

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