Spontaneous Symmetry Breaking -Conceptual Question

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SUMMARY

The discussion centers on the relationship between unstable equilibria and spontaneous symmetry breaking, specifically using the example of a pencil balanced on its eraser. The pencil represents a system with U(1) symmetry that is spontaneously broken when disturbed, leading to a new state at an angle. This scenario illustrates how spontaneous symmetry breaking occurs in systems transitioning from a symmetric to an asymmetric state. The conversation confirms that unstable equilibria can exist without symmetry, further clarifying the concepts involved.

PREREQUISITES
  • Understanding of spontaneous symmetry breaking in physics
  • Familiarity with U(1) symmetry concepts
  • Knowledge of unstable equilibria in dynamical systems
  • Basic grasp of equilibrium states and their properties
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  • Research the mathematical framework of U(1) symmetry in quantum mechanics
  • Explore examples of spontaneous symmetry breaking in particle physics
  • Study the implications of unstable equilibria in chaotic systems
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Physicists, students of theoretical physics, and anyone interested in the principles of symmetry and stability in physical systems.

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what is the relationship between unstable equilibria and spontaneous symmetry breaking?

Would this qualify as an example of spontaneous symmetry breaking?
Take a (perfectly round and unlabeled) pencil standing upright on its eraser so there is a U(1) symmetry on its original position which is spontaneously broken when the system is disturbed and the pencil falls over to point at some angle on a circle around its original position?
 
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That is an example of spontaneous symmetry breaking, right.

An unstable equilibrium could be somewhere without symmetry.
 
Ok, thanks.
 

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