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A theoretically symmetrical system is one where outcomes are equally likely. The Standard Model presumes a symmetrical system, but the hard facts of existence shatter that pristine symmetry. This incongruity between physical model and actuality is patched with math; a clear indicator that the map is decidedly not the territory.
Spontaneous Symmetry Breaking
Spontaneous symmetry breaking (SSB) is ubiquitous in Nature. The examples include magnets, superfluids, phonons, Bose-Einstein condensates, and neutron stars. ~ Japanese physicists Haruki Watanabe & Hitoshi Murayama
Spontaneous symmetry breaking (SSB) is a simple concept: nothing more than stating that actualization breaks an idealized (mathematical) symmetry. SSB is a way of explaining how a perfectly symmetrical physical model can appear broken in view of physical manifestation, yet, paradoxically, the model still be presumed valid.
SSB smashes mathematical symmetry on the stones of sampling. If a symmetrical system is acted upon, a specific outcome arises out of the wave of possibilities. The symmetry breaks. That does not necessarily discredit the underlying symmetry, which by manifestation appears broken, but is simply a hidden symmetry.
A ball sitting on top of a conic hill is in a symmetric state: it could roll down any which way. When the ball actually moves by some force, the symmetry is broken – SSB in action.
A mathematical ideal is balanced until it actuates. By manifesting, perfection becomes imperfect. Phenomena arise from defects.
Particle physics pilfered the concept of SSB from solid-state physics: a discipline that particle physicist Murray Gell-Mann called “squalid-state physics” (an ironic deprecation: for a Standard-Model man to deride the crutch upon which SM depends). Solid-state physics is the study of the intense atomic interactions in solids.
Modeling solids evinced equations that characterized their lowest energy state. The model results were rotationally symmetric, but the solids were not; hence spontaneous symmetry breaking.
SSB is emblematic of the handedness that occurs throughout Nature. Chirality is essential in the basic molecular interactions of life. That asymmetry is also fundamental to physics is unsurprising.
The strong nuclear force, electromagnetism, and gravity all respect symmetry. The weak force, responsible for nuclear decays and neutrino interactions, does not.
The charged W± boson, which mediates weak interactions, is responsible for the broken parity symmetry. By their cross-influences, the troika of W±, Z0, and Higgs0 bosons provide the theoretical patchwork by which the Standard Model is reputedly redeemed despite SSB.
Via the Higgs mechanism hypothesis, W & Z bosons acquire non-vanishing mass through SSB. SSB is invoked to explain the massive mass discrepancy between theory and observed actuality of these bosons.
Supposedly weightless until caught in the act, W & Z manifest with an immense presence. SSB is also the basis upon which the Higgs particle is predicated in the Standard Model.
A sidekick in the Standard Model – Nambu-Goldstone bosons (NGBs) – facilitate coherent collective behavior in a material. NGBs mystically appear whenever symmetry is spontaneously broken.
The nominal case in SSB is that the number of Nambu-Goldstone bosons equals the number of broken symmetries. But in exotic materials, such as neutron stars, Bose-Einstein condensates, and superfluids, the number of NGBs is less than the number of broken symmetries. A deficit of Nambu-Goldstone bosons makes matter go crazy, as it does in these outlandish coherent constructs.
SSB is not ubiquitous in Nature but is instead commonplace in symbolic representations of Nature. Spontaneous symmetry breaking is a necessary artifice for physical models that provide an inadequate approximation of intricacy in Nature that is beyond human mathematical skill to capture.
