Lorentz Invarience and Spontaneous Symmetry Breaking

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Main Question or Discussion Point

Spontaneous symmetry breaking


I’m not sure if I understand spontaneous symmetry breaking.


In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider (I.e. deformations in the hat due to manufacturing imperfections, temperature in the hat’s material differences causing or caused by the same, an imperceptible breeze from the room’s ventilation, time divots in the marble)?


Could someone please explain to me why I’m horribly wrong here?


How does this relate to Lorentz invariance in the context of particle invariance?

The idea of a particle altering a magnetic field doesn’t really alter the traditional understanding of Lorentz invariance does it (observational invariance)? Therefore, is this idea of particle invariance generally accepted or even useful? How is it useful?


I understand there seem to be properties relating to CERN experiements worth the Higgs boson that may prove and explain spontaneous symmetry breaking?
 

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In other words, can someone explain to me how exactly Spontaneous Symmetry Breaking (as related to Lorentz Invariance and even possibly the Standard Model Extension) has validity?
 

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