Nonstandard physics/Monopoles

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Monopoles - physical particles with gradient fields, that potentially could be associated with elementary particles (such as electric monopole or magnetic monopole).

General

Monopoles could be formed from the following fundamental physical charges and masses.

Electric charge quantum, first proposed by G.Stoney (1881):

$q_{EQ} = e = 1.60217653\cdot 10^{-19}$C.

Magnetic charge quantum, first proposed by Paul Dirac (1931):

$\phi_{MQ} = h/e = 4.135667427\cdot 10^{-15}$J/A,

where $h$ is the Planck constant. Gravitational mass (or electric-like) quantum is the electron mass:

$m_{GQ} = m_N = 9.1093826\cdot 10^{-31}$kg.

Gravitational magnetic-like quantum, or velocity circulation quantum, presented in the superfluid and inversion layers of MOSFETs, first discovered by Yakymakha (1994):

$\phi_{GQ} = h/m_N = 7.273895101\cdot 10^{-4} m^2/s.$

Forming electron mass

Let us consider an interaction between two physical values: electric static charge ($e$) and gravitational dynamic mass ($h/m_N$):

$F_{EG}(e,h/m_n) = \frac{1}{4\pi \sqrt{\epsilon_E\mu_G}}\cdot \frac{e(h/m_N)}{r^2}, \$

where $\epsilon_E = 8.8541878170\cdot 10^{-12}$F/m is the electric constant, and $\mu_G = \frac{4\pi G}{c^2} = 9.331848\cdot 10^{-27} \$m/kg is the gravitational magnetic-like constant. The work done by this interaction could be equated to the s.c. electron rest energy:

$A_N = F_{EG}\cdot r_{xN} = \frac{1}{4\pi \sqrt{\epsilon_E\mu_G}}\cdot \frac{e(h/m_N)}{r_{xN}} = m_Nc^2, \$

where $c = 2.99792458\cdot 10^8$m/s is the velocity of light. The interaction radius could be derived from above equation in the form:

$r_{xN} = \frac{\hbar }{2m_Nc}\cdot \sqrt{\frac{\alpha_N}{\alpha_S}} = \frac{\hbar }{2m_Sc} = 0.5l_S, \$

where

$\alpha_S = \frac{e^2}{2hc\epsilon_E} = 7.297352568\cdot 10^{-3}$

is the Stoney scale gradient force constant;

$\beta_N = \frac{(h/m_N)^2}{2hc\mu_G} = 1.4271161\cdot 10^{44}$

is the Natural scale rotor force constant;

$l_S = \frac{\hbar}{m_Sc} = 1.892009\cdot 10^{-34}$m is the Stoney length, and

$\frac{m_S}{m_N} = \sqrt{\frac{\alpha_S}{\alpha_N}} \$

is considered. Note that, $\alpha_N = \frac{1}{4\beta_N}.$

Forming magnetic monopole mass

Let us consider an interaction between two physical values: magnetic static charge ($h/e$) and gravitational static mass ($m_N$):

$F_{MG}(m_n,h/e) = \frac{1}{4\pi \sqrt{\epsilon_G\mu_E}}\cdot \frac{m_N(h/e)}{r^2}, \$

where $\epsilon_G = \frac{1}{4\pi G} = 1.1923148\cdot 10^{09} kg s^2/m^3$ is the gravitational electric-like constant, and $\mu_E = 1.2566370614\cdot 10^{-06} N/A^2$ is the magnetic constant. The work done by this interaction could be equated to the s.c. planckion rest energy:

$A_M = F_{MG}\cdot r_{xM} = \frac{1}{4\pi \sqrt{\epsilon_G\mu_E}}\cdot \frac{m_N(h/e)}{r_{xM}} = m_Pc^2, \$

where $m_P = \sqrt{\frac{c\hbar}{G}} = 2.17645\cdot 10^{-08}$ is the Planck mass. The interaction radius could be derived from above equation in the form:

$r_{xM} = \frac{\hbar }{2m_Pc}\cdot \sqrt{\frac{1}{\alpha_S}} = \frac{\hbar }{2m_Sc} = 0.5l_S. \$

Electric monopole properties

We considered above only one mixed force, which formed the ‘’rest mass’’ of electric monopole. Now we can consider the next three forces. The most weak force is due to the gravitational interaction of the rest masses:

$F_G(m_N,m_N) = \alpha_N \frac{\hbar c}{r^2}. \$

As usual, this force is neglected. The Coulomb force is more stronger:

$F_C(e,e) = \alpha_S \frac{\hbar c}{r^2} \$.

This force take part in the atomic and other more complex particles formation. But the most power force is connected with magnetic-like (or dynamic) mass interaction:

$F_G(h/m_N,h/m_N) = \frac{1}{4\alpha_N}\frac{\hbar c}{r^2} \$.

This force could be responsible for the spin interactions.

Classical radius of the electric monopole:

$r_{Ec} = \alpha_S l_N, \$

where $l_N = \frac{\hbar}{m_Nc}$ is the Natural scale length.

Magnetic monopole properties

We considered above only one mixed force, which formed the ‘’rest mass’’ of magnetic monopole. Now we can consider the next three forces. The most weak force is due to the gravitational interaction of the $m_N$ masses:

$F_G(m_N,m_N) = \alpha_N \frac{\hbar c}{r^2} \$.

As usual, this force is neglected. The gravitational force of the Planck mass interaction is more stronger:

$F_G(m_P,m_P) = \alpha_P \frac{\hbar c}{r^2}, \$

where $\alpha_P = 1$ is the force constant of the Planck scale. This force could be associated with the s.c. “strong interactions”.

The most powerful force considers the magnetic charge (or dynamic charge) interaction:

$F_M(h/e,h/e) = \frac{1}{4\alpha_S}\frac{\hbar c}{r^2} \$.

This force forms the main property of the magnetic monopole. Strange to say, but it is seems that magnetic monopoles have no any spin, since there are no any force responsible for such interaction. Thus, magnetic monopoles could not form any complex particles, “magnetic atoms”, for example.

Classical radius of the magnetic monopole:

$r_{Mc} = \frac{1}{4\alpha_S} l_P = \sqrt{\beta_S}\frac{l_S}{2} = 5.53708\cdot 10^{-34} \$m.

Note that it about 2.5 times greater then the Stoney scale length.

Summary

Thus, in the both cases interactions between "static" and "dynamic" masses and charges lead to the half value of the Stoney length:

$r_{xN} = r_{xM} = \frac{l_S}{2},$

where $l_S = \frac{l_P}{\sqrt{\alpha_S}}$ is the Stoney length. So, the electron rest mass $m_N$ could be considered as some "energy gap" for the electric monopole, and the planckion rest mass $m_P$ - for magnetic monopole.

See also

• Magnetic monopole
• Planck scale
• Stoney scale
• Natural scale

References

• Stoney G. On The Physical Units of Nature, Phil.Mag. 11, 381–391, 1881
• Latest (2006) values of the constants [1]
• Paul Dirac, "Quantised Singularities in the Electromagnetic Field". Proc. Roy. Soc. (London) A 133, 60 (1931). Free web link
• Putterman S.J. (1974). Superfluid hydrodynamics. North-Holland, Amsterdam.
• Yakymakha O.L., Kalnibolotskij Y.M. (1994). "Very-low-frequency resonance of MOSFET amplifier parameters". Solid- State Electronics 37(10),1739-1751 Pdf