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.

If feeling a sensation on the left side always presents the same sensory magnitude as feeling it on the right, then the specific energy $\hat{E}$ of an odd conjugate seed is equal to the specific energy of an ordinary conjugate seed. And if their urgency is the same, then the vis viva $\, \hat{K}$ of an odd conjugate seed is equal to that of an ordinary conjugate seed. We often assume that all sensory experience is perfectly balanced in this way. Conjugate symmetry relieves us from having to pay very much attention to whether a sensation is experienced on the left or right side.

Assumption of Conjugate Symmetry

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

and

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

The assumption simplifies analysis because it makes ordinary-quarks and anti-quarks much the same as each other; if left and right get mixed-up, the outcome of any calculation using the specific energy or vis viva remains unchanged. Using this approximation is a way of objectifying the description of sensation. Perfect conjugate symmetry implies that a particle and its corresponding anti-particle have the same mass.

This has been experimentally tested.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.

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Conjugate Symmetry

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

Footnotes

1. W.-M. Yao et al. (Particle Data Group). J. Phys. G, 33, 1 (2006).