Conjugate Symmetry

Bead Panel from a baby carrier, Bahau people, Borneo 20th century, 34 x 25 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop. |

Assumption of Conjugate Symmetry |

$\; \; \; \; \hat{E} \left( \sf{O} \right) = \hat{E} \left( \sf{\overline{O}} \right)$ |

and |

$\; \; \; \; \hat{K} \left( \sf{O} \right) = \hat{K} \left( \sf{\overline{O}} \right)$ |

^{1}For protons $\left| \; m^{\sf{p^{+}}} \! - m^{\sf{p^{-}}} \right| \, / \, m^{\sf{p}^{+}}$ is $< 6\sf{x}10^{-8}$ and for electrons the ratio is less than eight parts in a billion. So the approximation is excellent for nuclear particles. But atomic spectroscopy measurements are now being made to a few parts in $10^{15}$, that is, to more than a million times higher precision. And so small asymmetries may be observed in the finely-balanced mechanical system of a hydrogen atom. Variations between quarks and anti-quarks are described using $\, U$, their internal energy. For any sort of quark $\sf{Z}$, the

**conjugate difference**is

$\begin{align} \Delta \hspace{-2px} U^{\sf{Z}} \equiv \frac{U^{\sf{\overline{z}}} - \, U^{\sf{z}}}{2} \end{align}$

These differences are typically stated in *micro* electron-Volts, as shown in the accompanying table. For more detail, see the discussion of forces and fields.

Related WikiMechanics articles.

Summary |

adjective | Definition | |

Conjugate Difference | $\begin{align} \Delta \hspace{-2px} U^{\sf{Z}} \equiv \frac{U^{\sf{\overline{z}}} - \, U^{\sf{z}}}{2} \end{align}$ | 4-8 |