Phase Symmetry
//Usap//, Sasak people. Lombok, 20th century, 46 x 52 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.
Usap, Sasak people. Lombok, 20th century, 46 x 52 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.

Consider a particle P described by a chronologically ordered chain of events where each orbital cycle $\sf{\Omega}$ can be expressed as a pair of events

$\sf{\Omega} = \left\{ \sf{P}_{\LARGE{\circ}} , \sf{P}_{\LARGE{\bullet}} \vphantom{Q^{2}} \right\}$

that are out of phase with each other so that

$\delta _{\theta} \left( \sf{P}_{\LARGE{\circ}} \right) =- \, \delta _{\theta} \left( \sf{P}_{\LARGE{\bullet}} \right) = \pm \rm{1}$

Then $\sf{P}_{\LARGE{\circ}}$ and $\sf{P}_{\LARGE{\bullet}}$ are called phase components of P. If these two sets are composed from the same selection of quarks, then a description of the whole cycle $\sf{\Omega}$ is unaffected if there is any confusion or mix-up about the sign of the phase. This robust indifference to the phase is useful, so we give particles like this a special name. Definition: if

$\sf{P}_{\LARGE{\circ}} = \sf{P}_{\LARGE{\bullet}}$

then we say that P has phase symmetry. The most important examples of particles with phase symmetry are protons and electrons in their ground-states. So it is possible to make descriptions of protons and electrons that ignore the phase. Alternatively, if $\sf{P}_{\LARGE{\circ}} = \overline{\sf{P} _{\LARGE{\bullet}}}$ then we say that P has phase anti-symmetry.

sun.png
Sensory interpretation: When the phase indicates whether an event is diurnal or nocturnal, then indifference to phase means that a description does not depend on whether it is day or night. So physicists in different time-zones can easily work together when considering particles like protons and electrons.
Right.png Next step: other clocks.
Summary
Adjective Definition
Phase Symmetry $\sf{P}_{\LARGE{\circ}} = \sf{P}_{\LARGE{\bullet}}$ 6-22
Adjective Definition
Phase Anti-Symmetry $\sf{P}_{\LARGE{\circ}} = \overline{\sf{P} _{\LARGE{\bullet}}}$ 6-23
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