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Conjugate Symmetry

Assumption of Conjugate Symmetry
\widehat{E} \left( \mathsf{O} \right)  = \widehat{E} \left( \overline{\mathsf{O}}   \right)

and

\widehat{K} \left( \mathsf{O} \right)  = \widehat{K} \left( \overline{\mathsf{O}}      \right)

Conjugate symmetry is obtained if sensations exhibit equivalent size and urgency when compared between left and right sides. If feeling a sensation on the left side always presents the same sensory magnitude as feeling it on the right, then \widehat{E}, the specific energy, of an odd conjugate seed is equal to the specific energy of an ordinary conjugate seed. And if their urgency is the same, then \widehat{K}, the vis viva, 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. 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. So using this approximation is a way of objectifying the description of sensation.

Conjugate Asymmetry

Conjugate Differences

of Internal Energy in (Β΅eV)

 \zeta \mathsf{Z} \Delta U ^{\mathsf{Z}}
1U12.2
2D-1.10
3E-0.024
4G209
5M-290
7T78.3
8B78.1
9S1.60
10C4.36
15β’Ή?
16Ⓛ39.0

all others

0

Perfect conjugate symmetry implies that a particle and its corresponding anti-particle have the same mass. This has been experimentally tested.1 W.-M. Yao et al. (Particle Data Group). J. Phys. G, 33, 1 (2006). For protons the ratio  \left| \; m^{\mathsf{p^{+}}} \! - m^{\mathsf{p^{-}}} \right| \, / \, m^{\mathsf{p}^{+}} is less than 6\mathsf{x}10^{-8} and for electrons it is less than eight parts in a billion. So the approximation is excellent for nuclear particles. But atomic spectroscopy measurements are now about a million times more exact, some are reported to a few parts in 10^{15}. And so small asymmetries may be observed in the finely-balanced mechanical system of a hydrogen atom. Variations in size between quarks and anti-quarks are described using their internal energy U. For any sort of quark \mathsf{Z}, the conjugate difference is given by

    \[ \Delta  U^{\sf{Z}}   \equiv \frac{U^{\sf{\overline{z}}}  - \, U^{\sf{z}}}{2}  \]

These energy differences are typically stated in micro electronvolts, as shown in the accompanying table. For more detail, please see the discussion of fine structure in the spectrum of hydrogen.

Audibility

In addition to questions about conjugate symmetry or asymmetry, we may also consider whether or not a sensation even has any distinct left or right-side character. So here is a binary descriptor called the audibility defined by \varepsilon \equiv  1 - 2 \left| \, \delta^{*} \right|. Recall that \delta^{*} is the oddness of a particle. So the audibility takes-on values of

\varepsilon  =  \begin{cases} -1  &{\mathsf{\text{if a sensation is somatic}}} 	\\  +1  &{\mathsf{\text{if a sensation is not somatic}}}   \end{cases}

Conjugate symmetry, or perhaps a lack of it, are whimsically suggested in baby carrier bead panel from Borneo.
Baby Carrier Panel, Kenyah people. Borneo 20th century, 34 x 25 cm. Photograph by D Dunlop.
References
1 W.-M. Yao et al. (Particle Data Group). J. Phys. G, 33, 1 (2006).