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.

Consider a particle P described by an 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: 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. 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.

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.

 Adjective Definition Phase Symmetry $\sf{P}_{\LARGE{\circ}} = \sf{P}_{\LARGE{\bullet}}$ 6-24
 Adjective Definition Phase Anti-Symmetry $\sf{P}_{\LARGE{\circ}} = \overline{\sf{P} _{\LARGE{\bullet}}}$ 6-23