Electromagnetism – EthnoPhysics

Outline

Historically observed electromagnetic phenomena are complex and diverse; flashes of lightning, twirling compass needles, twitching frog-legs, and more. But on this page we just focus on some rudiments. Analysis is based on sensation, namely chromatic visual sensations – red, yellow, green and blue. These are the key experiences for understanding electromagnetic phenomena. Chromatic sensations have been objectified as leptonic seeds and leptonic quarks. Counting these quarks leads to definitions for the electric and magnetic properties of a particle.

Electric Polarity

Let a quark model of P be characterized by $\Delta n^{\mathsf{E}}$ and $\Delta n^{\mathsf{G}}$ the coefficients of its electronic quarks. These numbers are used to define another quantity $\delta_{\widehat{e}}$ called the electric polarity of P

$\delta_{\widehat{e}} \equiv \begin{cases} +1 & \mathsf{\text{if}} \; \; \Delta n^{\mathsf{G}} > \Delta n^{\mathsf{E}} \\ \; \; 0 & \mathsf{\text{if}} \; \; \Delta n^{\mathsf{G}} = \Delta n^{\mathsf{E}} \\ -1 & \mathsf{\text{if}} \; \; \Delta n^{\mathsf{G}} < \Delta n^{\mathsf{E}} \end{cases}$

If $\delta_{\widehat{e}}=+1$ we say that P is electrically positive. If $\delta_{\widehat{e}}=-1$ then we say that P is electrically negative. And if $\delta_{\widehat{e}} = 0$ then we say that P is not electrically polarized.

Recall that by the anti-commutative property of subtraction any differences in the quark-coefficients of some particle $\mathsf{P} ,$ and its conjugate-twin $\overline{\mathsf{P}} ,$ are related as $\Delta n^{\mathsf{Z}} (\mathsf{P}) = - \Delta n^{\mathsf{Z}} (\overline{\mathsf{P}}) \, .$ Then by the multiplicative property of inequality we know that if

$\Delta n^{\mathsf{G}} (\mathsf{P}) \; < \; \Delta n^{\mathsf{E}} (\mathsf{P})$

then

$\Delta n^{\mathsf{G}} (\overline{\mathsf{P}}) \; > \; \Delta n^{\mathsf{E}} (\overline{\mathsf{P}})$

This means that if $\mathsf{P}$ is positive, then $\overline{\mathsf{P}}$ is negative, and vice versa. The foregoing definition implies that particles and their conjugate-twins always have opposing electric polarities.

Sensory interpretation: Electronic seeds are objectified from yellow and blue sensations. So $\delta_{\widehat{e}}$ is a binary description of whether a complex visual sensation is net more yellowish or bluish. If P is not clearly yellowish or bluish, then $\delta_{\widehat{e}}=0$ .

When both $\delta_{\widehat{e}}$ and $\delta_{\widehat{m}}$ are zero, then P represents an achromatic visual sensation. It is not electrically or magnetically polarized, and is said to be centered around the central axis.

Magnetic Polarity

Let a quark model for some particle P be characterized by $\Delta n^{ \mathsf{M}}$ and $\Delta n^{\mathsf{A}}$ the coefficients of its muonic quarks. These quantities are used to define another number $\delta _{\widehat{m}}$ called the magnetic polarity of P as

$\delta_{\widehat{m}} \equiv \begin{cases} +1 & \mathsf{\text{if}} \; \; \Delta n^{\, \mathsf{M}} > \Delta n^{\, \mathsf{A}} \\ \; \; 0 & \mathsf{\text{if}} \; \; \Delta n^{\, \mathsf{M}} = \Delta n^{\, \mathsf{A}} \\ -1 & \mathsf{\text{if}} \; \; \Delta n^{\, \mathsf{M}} < \Delta n^{\, \mathsf{A}} \end{cases}$

If $\delta_{\widehat{m}}=+1$ we say that P is oriented to the magnetic north. If $\delta_{\widehat{m}}=-1$ then we say that P is pointed to the magnetic south. And if $\delta_{\widehat{m}} = 0$ then we say that P is not magnetically polarized.

$\Delta n^{\mathsf{M}} (\mathsf{P}) \; < \; \Delta n^{\mathsf{A}} (\mathsf{P})$

then

$\Delta n^{\mathsf{M}} (\overline{\mathsf{P}}) \; > \; \Delta n^{\mathsf{A}} (\overline{\mathsf{P}})$

This means that if $\mathsf{P}$ is oriented to the north, then $\overline{\mathsf{P}}$ is directed to the south, and vice versa. The definition given above implies that particles and their conjugate-twins always have opposing magnetic polarities.

Sensory interpretation: Muonic seeds are objectified from red and green sensations. So $\delta_{\widehat{m}}$ is a binary description of whether a complicated visual sensation is net more reddish or greenish. If $\delta_{\widehat{m}}=0$ then P is not remarkably red or green.

Charge Symmetry

Let some particle P be described by a chain of events where the quarks in each orbital cycle $\mathsf{\Omega}$ can be parsed into two sets called $\mathsf{P}_{\! north}$ and $\mathsf{P}_{\! south}$ which have opposite magnetic polarities. This is expressed mathematically by writing

$\mathsf{\Omega}^{\mathsf{P}} = \left\{ \, \mathsf{P}_{\! north} \, , \; \mathsf{P}_{\! south} \right\}$

and

$\delta_{\widehat{m}} \! \left( \mathsf{P}_{\! north} \right) = - \, \delta_{\widehat{m}} \! \left( \mathsf{P}_{\! south} \right) = \pm 1$

If $\mathsf{P}_{\! north}$ and $\mathsf{P}_{\! south}$ both have the same charge $q ,$ then the outcome of any calculation using $q$ is not affected if there is any confusion about the magnetic-polarity. In quark-space, $\mathsf{P}_{\! north}$ and $\mathsf{P}_{\! south}$ are associated with opposing directions on the magnetic axis. So particles like P have a symmetric distribution of charge along the magnetic axis. Descriptions of phenomena associated with $q$ are unaltered by any swap or mix-up between north and south. This indifference is useful because it simplifies calculations and makes them less dependent on specific arrangements. So we give particles like P a special name. If

$q \! \left( \mathsf{P}_{\! north} \right) = q \! \left( \mathsf{P}_{\! south} \right)$

then we say that P has charge-symmetry on the magnetic-axis. See the quark model of atomic hydrogen for an example of this kind of symmetry.

Sensory interpretation: Magnetic-polarity describes if a complex visual experience is more reddish or greenish. So for particles with charge-symmetry on the magnetic-axis, the charge distribution does not depend on how the description distinguishes between red and green sensations. This symmetry relieves us from having to pay much attention to if a sensation is red or green. It is a way of objectifying a description.

Charge symmetry on the magnetic axis is suggested by the red and green beads of this baby carrier from Borneo. — Baby carrier panel, Bahau people. Borneo 20th century, 29 x 26 cm. Photograph by D Dunlop.

Alternatively, let P be described by a chain of events where the quarks in each orbital cycle $\mathsf{\Omega}$ can be parsed into two sets called P₊ and P_– which have opposite electric polarities. This is written as

$\mathsf{\Omega}^{\mathsf{P}} = \left\{ \mathsf{P}_{\! +} \, , \; \mathsf{P}_{\! -} \right\}$

and

$\delta_{\widehat{e}} \! \left( \mathsf{P}_{\! +} \right) = - \, \delta_{\widehat{e}} \! \left( \mathsf{P}_{\! -} \right) = \pm 1$

If P₊ and P_– both have the same charge $q,$ then the outcome of any calculation using $q$ is not affected if there is any confusion about the electric-polarity. In quark-space, P₊ and P_– are associated with opposing directions on the electric axis. So particles like P have a symmetric distribution of charge along the electric axis. Descriptions of phenomena associated with $q$ are unaltered by any swap or mix-up between positive and negative. This indifference is useful because it simplifies calculations and makes them less dependent on specific arrangements. So we give particles like P a special name. If

$q \! \left( \mathsf{P}_{\! +} \right) = q \! \left( \mathsf{P}_{\! -} \right)$

then we say that P has charge-symmetry on the electric-axis. See this quark model of an electron for an example of electric-axis charge-symmetry.

Sensory interpretation: Electric-polarity describes if a complex visual sensation is more yellowish or blueish. So for a particle with charge-symmetry on the electric-axis, the overall charge distribution does not depend on how the description distinguishes between yellow and blue sensations. This symmetry relieves us from having to pay much attention to if a sensation is yellow or blue. It is a way of objectifying a description.

The foregoing general discussion of charge can be extended to consideration of specific nuclear charges. See the following links for more detail.

The Baryonic Charge

Here is a charged particle composed from eight baryonic quarks arranged for phase symmetry. The baryonic charge is a key component of protons.

The Mesonic Charge

Here is a charged particle composed from eight baryonic quarks, but it has a baryon-number of zero. It is an essential part of all charged leptons.

$\rule{200px}{2px}$

Electromagnetic Energies

Magnetic Potential Energy

An energy associated with any magnetic effects that hold a particle together is called its magnetic potential-energy and noted by $\mathcal{U}_{m} \hspace{1px} .$ It depends on the magnetic polarity which is written as $\delta_{\widehat{m}} \! = \! \pm 1 .$ Recall that the positive constant $k_{\mathsf{F}}$ was introduced earlier. And that $k_{mm}$ marks the magnetic-component of the terrestrial metric. Then for a particle described by its magnetic radius $\rho_{m} \hspace{1px} ,$ we define the magnetic potential energy as

$\mathcal{U}_{m} \equiv \delta_{\widehat{m}} \, k_{\mathsf{F}} \sqrt{k_{mm}} \; \rho_{m}$

We can also express the magnetic-radius $\rho_{m} \hspace{1px}$ in terms of the coefficients for amperic-quarks $\Delta n ^{\mathsf{A}} ,$ and magnetic-quarks $\Delta n ^{\mathsf{M}} .$ Recall that the internal energies for these quarks are $U^{\mathsf{A}}$ and $U^{\mathsf{M}} .$ Then

$\mathcal{U}_{m} = \delta_{\widehat{m}} \sqrt{k_{mm}} \left( \Delta n^{\mathsf{A}} U^{\mathsf{A}} - \Delta n^{\mathsf{M}} U^{\mathsf{M}} \right)$

Thus the magnetic potential-energy of a particle depends only on its muonic quark content. This is often mostly due to magnetic-quarks because their lifetime is much longer, and their internal energy is much larger, than amperic-quarks. In any case, for either polarity, we can always write

$\mathcal{U}_{m}^{2} = k_{\mathsf{F}}^{2} \, k_{mm} \rho_{m}^{2}$

Electric Potential Energy

An energy associated with any electric influences that hold a particle together is called its electric potential-energy and noted by $\mathcal{U}_{e} \hspace{1px} .$ It depends on the electric polarity which is written as $\delta_{\widehat{e}} \! = \! \pm 1 .$ Recall that the positive constant $k_{\mathsf{F}}$ was introduced earlier. And that $k_{ee}$ marks the electric-component of the terrestrial metric. Then for a particle described by its electric radius $\rho_{e} \hspace{1px} ,$ we define the electric potential energy as

$\mathcal{U}_{e} \equiv \delta_{\widehat{e}} \, k_{\mathsf{F}} \sqrt{k_{ee}} \; \rho_{e}$

We can also express the electric-radius $\rho_{e} \hspace{1px}$ in terms of the coefficients for galvanic-quarks $\Delta n ^{\mathsf{G}} ,$ and electric-quarks $\Delta n ^{\mathsf{E}} .$ Recall that the internal energies for these quarks are $U^{\mathsf{G}}$ and $U^{\mathsf{E}} .$ Then

$\mathcal{U}_{e} = \delta_{\widehat{e}} \, \sqrt{k_{ee}} \left( \Delta n^{\mathsf{G}} U^{\mathsf{G}} - \Delta n^{\mathsf{E}} U^{\mathsf{E}} \right)$

Thus the electric potential-energy of a particle depends only on its electronic quark content. This is often mostly due to galvanic-quarks because their lifetime is much longer, and their internal-energy is much larger, than electric-quarks. In any case, for either polarity, we can always write

$\mathcal{U}_{e}^{2} = k_{\mathsf{F}}^{2} \, k_{ee} \rho_{e}^{2}$

Coulomb Energy

Another sort of energy that accounts for the combined presence of both electronic and muonic quarks is called the Coulomb potential-energy in honour of Charles-Augustin de Coulomb . Having both these types of quarks in a particle adds an extra electromagnetic term given by

$\mathcal{U}_{em} \equiv \delta_{\widehat{e}} \, \delta_{\widehat{m}} \, k_{\mathsf{F}} \sqrt{\, 2k_{em} \, \rho_{e} \rho_{m} \; }$

Recall that $k_{em}$ notes the electromagnetic-component of the terrestrial metric. Particle radii can be eliminated from this expression to put $\mathcal{U}_{em}$ in terms of quark coefficients as

$\mathcal{U}_{em} = \delta_{\widehat{e}} \, \delta_{\widehat{m}} \, \sqrt{\, 2k_{em} \left( \Delta n^{\mathsf{G}} U^{\mathsf{G}} - \Delta n^{\mathsf{E}} U^{\mathsf{E}} \right) \left( \Delta n^{\mathsf{A}} U^{\mathsf{A}} - \Delta n^{\mathsf{M}} U^{\mathsf{M}} \right) }$

Thus $\mathcal{U}_{em}$ depends only on the leptonic quarks contained in a particle. And it may be greater or less than zero. But for any sign we always have

$\mathcal{U}_{em}^{2} = 2k_{\mathsf{F}}^{2} \, k_{em} \, \rho_{e} \rho_{m}$

This electromagnetic term is combined with the electric and magnetic potential-energies discussed above, to define the Coulomb potential energy as

$\mathcal{U}_{\! Coul} \equiv \delta_{\widehat{e}} \, \delta_{\widehat{m}} \, \sqrt{ \, \mathcal{U}_{e}^{2} + \mathcal{U}_{em}^{2} + \mathcal{U}_{m}^{2} \; }$

Then for any combination of quarks we can always write

$\mathcal{U}_{\! Coul}^{2} = \mathcal{U}_{e}^{2} + \mathcal{U}_{em}^{2} + \mathcal{U}_{m}^{2}$

$\rule{200px}{2px}$

The foregoing discussion of electromagnetic potential-energy can be extended. After some consideration of photons and waves, it is developed into ideas about electromagnetic fields. Here is a link for more detail.

Electromagnetic Fields

A summary of various leptonic quanta used to specify electric and magnetic fields. Electromagnetic monopoles, dipoles and quadrupoles are defined.

Bahau bead panel number 12. — Baby carrier panel, Bahau people. Borneo 20th century, 27 x 24 cm. Photograph by D Dunlop.

Weak Potential Energy

The energy stored by any little twists in a particle is called its weak potential-energy, and noted by $\mathcal{U}_{\! weak} \hspace{1px} .$ This energy describes the joint presence of both rotating quarks and leptonic quarks. Having both of these types of quarks in a particle introduces two extra terms. The electroweak contribution to the potential-energy is

$\mathcal{U}_{ew} \equiv \delta_{\widehat{e}} \, k_{\mathsf{F}} \sqrt{2k_{ez} \, \rho_{e} \rho_{z} \, }$

and a magnetoweak term is given by

$\mathcal{U}_{mw} \equiv \delta_{\widehat{m}} \, k_{\mathsf{F}} \sqrt{2k_{mz} \, \rho_{m} \rho_{z} \, }$

The constants $k_{ez}$ and $k_{mz}$ are components of the terrestrial metric. Also remember that particle radii can be stated in terms of quark-coefficients and internal-energies as shown above. Then $\mathcal{U}_{ew}$ and $\mathcal{U}_{mw}$ can be expressed as

$\mathcal{U}_{ew} = \delta_{\widehat{e}} \sqrt{2k_{ez} \, \mathcal{B} \! \left( \Delta n^{\mathsf{G}} U^{\mathsf{G}} - \Delta n^{\mathsf{E}} U^{\mathsf{E}} \right) \, }$

and

$\mathcal{U}_{mw} = \delta_{\widehat{m}} \sqrt{2k_{mz} \, \mathcal{B} \! \left( \Delta n^{\mathsf{A}} U^{\mathsf{A}} - \Delta n^{\mathsf{M}} U^{\mathsf{M}} \right) \, }$