Magnetic Moments
Notice: this page is actively under construction
Notice: this page is actively under construction

Consider a particle $\sf{P}$ of mass $m$ that is at rest or in slow motion so that its mechanical energy is just $E= m c^{2}$. Let $\sf{P}$ be characterized by its quark coefficients $n$. These coefficients determine the spin $\sigma$, orbital radius $R$ and also $\sf{P}$'s cross-sectional area $\, A$. If $\sf{P}$ is rotating then the current $\, I \,$ due to the motion of any induced charge $\, \mathcal{Q}$ is

$I = \mathcal{Q} \, / \, \hat{\tau}$

where $\hat{\tau}$ is period of $\sf{P}$. The current is measured in Coulombs per second, or Amperes, and abbreviated by (A). Definition: the magnetic moment due to the rotation of the $\zeta$-type quarks in $\sf{P}$ is

$\begin{align} \overline{\mu} ^{\, \zeta} \equiv A I^{\zeta} \, \hat{z} \end{align}$

where $\hat{z} \equiv (0, 0, 1)$ notes the polar axis of $\sf{P}$. The norm of a moment is written without an overline as $\mu \equiv \left\| \, \overline{\mu} \, \right\|$. By this definition the magnetic moment is given by the product of a current and an area, so the measurement units used for $\mu$ are abbreviated as (A∙m2). The magnetic moment of the whole particle $\sf{P}$ is given by a sum over quark moments

$\begin{align} \overline{\mu} ^{\, \sf{P}} \equiv \sum_{\zeta =1}^{10} \overline{\mu} ^{\, \zeta} \end{align}$

$\begin{align} \mu ^{\sf{P}} = \frac{ h \sigma \, k_{q} }{4 \pi \, m} \sum_{\zeta =1}^{10} \chi_{m} ^{\zeta} \Delta n^{\zeta} \end{align}$


The forgoing expression summarizes all thirteen known nuclear magnetic moments to within experimental error.1,2,3 The representation uses ten adjustable parameters, i.e. the magnetic susceptibilities of the ten different types of thermodynamic quark. For more detail about comparisons with measurement click here.
A comparison of calculated and observed magnetic moments for baryons. The electron and muon are far off the scale of this graph, but the moments of both particles are within experimental error as well.
A comparison of calculated and observed magnetic moments for baryons. The electron and muon are far off the scale of this graph, but the moments of both particles are within experimental error as well.

As discussed earlier, the spin, mass and magnetic susceptibilities of ordinary-quarks and anti-quarks are the same as each other. Also, the net number of quarks $\Delta n$ in particle $\sf{P}$ and its anti-particle $\overline{\sf{P}}$ are related as $\rm{\Delta} \it{n} ^{\zeta} \left( \sf{P} \right) = - \rm{\Delta} \it{n}^{\zeta} \left( \sf{\overline{P}} \right)$. So the theorem above implies that the magnetic moments of particles and anti-particles are related as

$\overline{\mu} \left( \sf{P} \right) = - \overline{\mu} \left( \sf{\overline{P}} \right)$

Bangladeshi.GIF
Sensory Interpretation: The magnetic moment quantifies the response of a particle to the redness of surrounding sensations because of its dependence on the magnetic susceptibility. And remember that redness is defined by the sight of human blood. So one possible sensory interpretation of the magnetic moment is that it describes how the emotion of fear affects particle motion when sensations are objectified. Recall that reference sensations are benchmarks from which all perceptions are judged and recognized. These reference sensations are mathematically represented by constants. Accordingly, we associate a magnetic constant with the sight of human blood.

$\mu_{\sf{o}} \equiv 4 \pi \times 10^{-7}$ (N∙A-2)

Summary
Reference Sensations Constant (Units)
knut.jpeg Touching ice $T^{\sf{b}} \equiv 0$ (℃)
steam.jpg Touching steam $T^{\sf{c}} \equiv 100$ (℃)
achromatic.jpg Seeing the Sun $U^{\sf{d}} \equiv 0$ (MeV)
Bangladeshi.GIF Seeing blood $\mu_{\sf{o}} \equiv 4 \pi \times 10^{-7}$ (N∙A-2)
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