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Tests and Predictions

Outline

Range of Validity

  • By our definition of a physical object, we consider that a human body may only be approximately physical.
  • Invoking various hypotheses restricts subsequent consideration to limited phenomena. For example, the assumption of conjugate symmetry presumes some kind of lateral isotropy.
  • Logical description requires the conservation of seeds. And our understanding of the meaning of a particle requires that events be very repetitious. So we only consider sensations that are stable or reproducible.
  • EthnoPhysics considers only Anaxagorean sensations. Other sensations are mostly ignored. So the description of sensation is not exhaustive.
  • So given all these limitations, we try to avoid using words like real, universal or cosmic.

Errors

The following calculated results for nuclear particles are outside of experimental uncertainty.

  • The mean life of the \rho^{\pm} mesons by 0.7%
  • The mass of the 𝙅/𝝍 (2S) meson by 0.0004%
  • The mass of the 𝞚 (1405) baryon by 0.1%
  • The mass of the 𝞢c (2455) baryon by 0.007%

The most serious of these errors is for the charged rho mesons. It is possible that quark models for the whole family of rho mesons are wrong. It is always possible to make more complicated models that work with the data. But the next least complicated arrangement is much more complicated. And the extra complexity applies to the whole family, and is out of proportion with other families.

Our method of finding quark models is just guessing-and-checking. It is not exhaustive. So perhaps we have just missed finding a good model, despite months of searching.

Another possibility is that the requirement for using only thermodynamic quarks for nuclear particles needs to be relaxed. The chemical quarks are available in principle. And eventually there must be some mixing of quark-types to explain correlations between the charge of thermodynamic quarks and the charge on chemical ions. Is that a role for the rho mesons?

The other errors are less worrisome. It may eventually be possible to mend them by readjusting parameters after fixing the rho-meson issue.

Magnetic Susceptibility

Redness is illustrated by this icon for visual sensations that are reddish or greenish.
Magnetic Susceptibility
𝜁Z \chi_{m} \rule[-6px]{0.1pt}{0.1pt}
1U2.449148
2D0.535786
3E2.093534
4G1.767340
5M-0.096763
6A0.229434
7T1.220846
8B0.360208
9S-1.953003
10C2.433428

The magnetic susceptibility is an indication of how much the perception of an Anaxagorean sensation is tinged or influenced by the redness of surrounding sensations. It is a dimensionless constant noted by  \chi_{m}. In an extension of the assumption of conjugate symmetry we presume that ordinary-quarks and anti-quarks have the same susceptibilities. Then the quark index  \zeta may be used to identify specific values for  \chi_{m}. These quantities are obtained from laboratory observations of the magnetic moments for nuclear particles.

Induced Charge

The magnetic susceptibility describes some kind of mixing between different classes of sensation. And remember that redness is ultimately defined by the sight of blood. Also recall Ernst Mach’s remark that the perception of sensation is connected to “dispositions of mind, feelings, and volitions”. So magnetic susceptibility may be viewed as a mathematical description of how the sight of blood affects other perceptions. This is especially relevant for distinguishing between safe and dangerous conditions.

The safety of a thermal sensation is described by the charge. But magnetic susceptibility is more general, so we introduce a related quantity called the induced charge which is noted by  \mathcal{Q}. Sensory imbalances are associated with risk, and they are generally written as  \Delta n. So we account for the relationship between blood and danger by defining

\mathcal{Q} \equiv e \chi_{m} \, \Delta n

The constant  e is called the elementary charge. It is measured in Coulombs and abbreviated by (C).

Magnetic Moments

Consider some particle P characterized by its period  \hat{\tau}. In a Cartesian descriptive framework, P is rotating. Then the current due to the rotation of the charge  \mathcal{Q} is given by

I = \dfrac{ \; \mathcal{Q} \; }{\hat{\tau}}

This current is measured in Coulombs per second, or Amperes, and abbreviated by (A). The magnetic moment due to the rotation of any \zeta-type quarks may be defined from the current as

\overline{\mu}^{\, \zeta} \equiv A I^{\zeta} \; \widehat{z}

where  A is P’s cross-sectional area and \widehat{z} \equiv (0, 0, 1) is P’s polar axis. 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 P is defined by a sum over quark moments

\displaystyle \overline{\mu}^{\, \mathsf{P}} \equiv \sum_{\zeta=1}^{10} \overline{\mu}^{\, \zeta}

All quark moments are aligned with the polar axis, so by these definitions

\displaystyle \mu^{\, \mathsf{P}} = \sum_{\zeta=1}^{10} \mu^{\, \zeta} = A \sum_{\zeta=1}^{10} I^{\zeta} = \pi R^{2} \sum_{\zeta=1}^{10} I^{\zeta}

where  R is the orbital radius of P. This radius is given by

R \equiv \dfrac{hc}{2\pi} \dfrac{ \sqrt{\textsl{\textsf{J}} \; }}{E} = \dfrac{ h \sqrt{\textsl{\textsf{J}} \; }}{2\pi \, mc}

where  \textsl{\textsf{J}} is P’s total angular momentum quantum number, and  E is P’s mechanical energy. We assume that P is at rest or in slow motion so that the energy can be expressed as E= m c^{2} where  m is P’s rest mass. We may also write the cross-sectional area in terms of these quantities as

A \equiv \pi R^{2} = \dfrac{h^{2} \textsl{\textsf{J}} }{4\pi \, m^{2}c^{2}}

The foregoing equations may all be combined to state the magnetic moment of P as

\displaystyle \mu^{\mathsf{P}} = \dfrac{h^{2} \textsl{\textsf{J}} }{4\pi \, m^{2} c^{2}} \sum_{\zeta=1}^{10} I^{\zeta}

We can also use Planck’s postulate to express the current as

I^{\zeta} = \dfrac{ \; \mathcal{Q}^{\zeta} \; }{\hat{\tau}} = \dfrac{\mathcal{Q}^{\zeta} E}{h} = \dfrac{\mathcal{Q}^{\zeta} mc^{2}}{h}

Then the magnetic moment of P may be written as

\displaystyle \mu^{\mathsf{P}} = \dfrac{h \textsl{\textsf{J}} }{4\pi \, m} \sum_{\zeta=1}^{10} \mathcal{Q}^{\zeta}

Recall that the induced charge  \mathcal{Q} is related to the magnetic susceptibility  \chi_{m} by

\mathcal{Q} \equiv e \chi_{m} \, \Delta n

where  n notes P’s quark coefficients and  e is a constant. Then finally we can express the magnetic moment in terms of these quark coefficients as

\displaystyle \mu^{\mathsf{P}} = \dfrac{eh}{4\pi} \dfrac{ \textsl{\textsf{J}} }{m} \sum_{\zeta=1}^{10} \chi_{m}^{\zeta} \Delta n^{\zeta}

Experimental Comparison

The forgoing expression summarizes all thirteen known nuclear magnetic moments to within experimental error.1J. Beringer et al. (Particle Data Group), The Review of Particle Physics, Phys. Rev. D86, 010001, 2012., 2J. DiSciacca et al. (ATRAP Collaboration), One-Particle Measurement of the Antiproton Magnetic Moment Phys. Rev. Lett. 110, 130801, 2013., 3G. Lopez Castro, A. Mariano, Determination of the Delta++ Magnetic Dipole Moment arXiv:nucl-th/0006031, 2001. The representation uses ten adjustable parameters, i.e. the magnetic susceptibilities of the ten different types of thermodynamic quarks.

Using 10 parameters to represent 13 observations is an underwhelming feat of data compression. But the quark coefficients of other nuclear particles are already known from mass and lifetime experiments. So this regular pattern might be used to make predictions for particles that have not yet had their magnetic moments measured.

The magnetic moments of baryons are shown in this graph comparing calculations with experiment.
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.
References
1J. Beringer et al. (Particle Data Group), The Review of Particle Physics, Phys. Rev. D86, 010001, 2012.
2J. DiSciacca et al. (ATRAP Collaboration), One-Particle Measurement of the Antiproton Magnetic Moment Phys. Rev. Lett. 110, 130801, 2013.
3G. Lopez Castro, A. Mariano, Determination of the Delta++ Magnetic Dipole Moment arXiv:nucl-th/0006031, 2001.