An attempt to reverse-engineer the wave function of the internal state of the electron from its properties leads to proposals of answers about forces stabilizing the electron and an electromagnetic input to its annihilation energy.
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The wave function of the internal state of the electron
Compare g and H from eq. (11): g = (ƛ/T^2)(2π)^2, H = j(ƛ/T^2)(2π)^2 with small angle approximation of the pendulum period T=2π√(ƛ/g) derived from equation of a harmonic oscillator.
... I may want to add that I see mass and charge vectors (as well as their derivatives: gravitational field and electric field) as three dimensional , and circulation and magnetic flux vectors (as well as their derivatives: 2D mass current and 2D charge current aka magnetic field) as two dimensional. Since all the four "charges" (as well as their derivatives: "fields") are mutually orthogonal, I guess it leads us to require a 10D + time = 11D model. This recalls the M-theory, but I still cannot grasp how the 11D model translates into our 4D experience: the compactified, small-scale dimensions approach is not the one I'm a fan of.
We experience 3D gravitation and 3D electric field which seem to be technically orthogonal to each other in our 3D space. We also experience magnetic field which is technically orthogonal to the electric field (hence the need for complex numbers to describe both in one equation), ... But the fields are not compactified. They pervade all of the 3D space, is the 3D space actually a complex 10D space with such relations between its 3D/2D/3D/2D components that we perceive it as 3D? just speculating freely here ...
So is 3D space a product of 10D of different fields? Where time as the 11th D fits here?
Note, that the unit-of-measure transformation constant j may be probably better physically explained when written as
j = (r_se/2πƛ_C)(c/G)(e_0/m_e),
so as a product of three relations: 1. electron event horizon/electron Compton wavelength, 2. speed of light/Newtonian gravitational constant, 3. elementary charge/electron rest mass.
Also note, that
Coulomb constant k_e = (α/2π)(hc/e^2)
and Newtonian gravitational constant G = (π/2π)(hc/m_e^2) (r_se/2πƛ_C)
giving another possible approach to unit-of-measure alignment
G/k_e = (π/α)(e^2/m_e^2) (r_se/2πƛ_C)
Both notations (of j and of G/k_e) include the factor r_se/2πƛ_C (electron event horizon/electron Compton wavelength) that expresses the relative strength of gravitation vs electrostatic force.
For electron, Einstein equations break at r_se (event horizon) and Maxwell equations break at ƛ_C√α (Schwinger limit).
Compare g and H from eq. (11): g = (ƛ/T^2)(2π)^2, H = j(ƛ/T^2)(2π)^2 with small angle approximation of the pendulum period T=2π√(ƛ/g) derived from equation of a harmonic oscillator.
ReplyDelete... I may want to add that I see mass and charge vectors (as well as their derivatives: gravitational field and electric field) as three dimensional , and circulation and magnetic flux vectors (as well as their derivatives: 2D mass current and 2D charge current aka magnetic field) as two dimensional. Since all the four "charges" (as well as their derivatives: "fields") are mutually orthogonal, I guess it leads us to require a 10D + time = 11D model. This recalls the M-theory, but I still cannot grasp how the 11D model translates into our 4D experience: the compactified, small-scale dimensions approach is not the one I'm a fan of.
ReplyDeleteWe experience 3D gravitation and 3D electric field which seem to be technically orthogonal to each other in our 3D space. We also experience magnetic field which is technically orthogonal to the electric field (hence the need for complex numbers to describe both in one equation), ... But the fields are not compactified. They pervade all of the 3D space, is the 3D space actually a complex 10D space with such relations between its 3D/2D/3D/2D components that we perceive it as 3D? just speculating freely here ...
So is 3D space a product of 10D of different fields? Where time as the 11th D fits here?
Note, that the unit-of-measure transformation constant j may be probably better physically explained when written as
ReplyDeletej = (r_se/2πƛ_C)(c/G)(e_0/m_e),
so as a product of three relations:
1. electron event horizon/electron Compton wavelength,
2. speed of light/Newtonian gravitational constant,
3. elementary charge/electron rest mass.
Also note, that
Coulomb constant
k_e = (α/2π)(hc/e^2)
and
Newtonian gravitational constant
G = (π/2π)(hc/m_e^2) (r_se/2πƛ_C)
giving another possible approach to unit-of-measure alignment
G/k_e = (π/α)(e^2/m_e^2) (r_se/2πƛ_C)
Both notations (of j and of G/k_e) include the factor r_se/2πƛ_C (electron event horizon/electron Compton wavelength) that expresses the relative strength of gravitation vs electrostatic force.
For electron, Einstein equations break at r_se (event horizon) and Maxwell equations break at ƛ_C√α (Schwinger limit).