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touqra
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How does symmetry breaking occur?
What does it mean to be an "equivalent" solution. Does it just mean that both S and T are members of some solution set with no preference of selecting one over the other?vanesch said:... when you take a symmetry operation g in G, then g S = T and T is an "equivalent" solution.
I'm a little confused by the term "solution." What are we solving?vanesch said:Now, it can be that for some reason, we have to choose ONE SINGLE solution. Imagine it is a solution from S0. In that case, we have to choose a specific point O, and the solution we take is {O,O}.
How is that? If we translate the origin, the distance between the points is still zero, isn't it?vanesch said:Everything we will do with this particular solution HAS BROKEN THE TRANSLATION SYMMETRY of the problem.
turin said:1) I'm a little confused by the term "solution." What are we solving?
2) How is that? If we translate the origin, the distance between the points is still zero, isn't it?
3) Can you give a more physical example? I am lost in the abstraction.
turin said:So is there always this effective reduction in (non-trivial) degrees of freedom in the problem when symmetry breaking is induced?
Symmetry breaking is a phenomenon in physics where a system that is initially symmetrical, or has the same properties in all directions, undergoes a change and becomes asymmetrical. This can occur in various systems, including particles, crystals, and even in the early universe.
Symmetry breaking can occur through a variety of mechanisms, such as through the introduction of external forces or through spontaneous symmetry breaking, where the system undergoes a change without any external influence. It can also occur through phase transitions, where the system changes from one phase to another.
Symmetry breaking plays a crucial role in understanding the behavior and properties of various physical systems. It helps explain how certain systems can have different states or phases, and how these states can change under different conditions. It also has implications in fields such as particle physics, cosmology, and condensed matter physics.
Yes, symmetry breaking can be observed in many everyday phenomena. For example, the formation of snowflakes or crystals is a result of symmetry breaking, as the molecules arrange themselves in a specific pattern, breaking the initial symmetry. It can also be seen in magnets, where the alignment of magnetic fields breaks the symmetry of the material.
Symmetry breaking is studied through various theoretical and experimental approaches in physics. Theoretical models, such as the Higgs mechanism, help explain how symmetry breaking occurs in particle systems. Experimental methods, such as scattering experiments and phase transitions, allow scientists to observe and study symmetry breaking in physical systems.