Press "Enter" to skip to content

Phase Symmetry

Consider some particle P that is defined by a chain of repetitive events. And let each repeated cycle \mathsf{\Omega} be parsed into two sets of quarks, noted by \mathsf{P}_{\mdsmwhtcircle} and \mathsf{P}_{\mdsmblkcircle}, that are out of phase with each other. This is expressed mathematically as

\mathsf{\Omega} = \left\{  \mathsf{P}_{\mdsmwhtcircle} , \,   \mathsf{P}_{\mdsmblkcircle} \rule{0pt}{9px}  \right\}

and

\delta_{\theta}   \left( \mathsf{P}_{\LARGE{\circ}} \right)  =- \, \delta_{\theta}   \left(  \mathsf{P}_{\mdsmblkcircle} \right)

The compound quarks \mathsf{P}_{\mdsmwhtcircle} and \mathsf{P}_{\mdsmblkcircle} 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 \mathsf{\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

\mathsf{P}_{\mdsmwhtcircle} =   \mathsf{P}_{\mdsmblkcircle}

then we say that P has phase symmetry. Alternatively, if \mathsf{P}_{\mdsmwhtcircle} = \overline{\mathsf{P}_{\mdsmblkcircle}} then we say that P has phase anti-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.

Solar clocks are like this radiant icon.

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.

Phase symmetry is suggested by this tightly structured Indonesian weaving.
Usap, Sasak people. Lombok, 20th century, 46 x 52 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.