Chapter
9

The electromagnetic field energy
of the electron

 

 

As we know, the electromagnetic field energy density is:

 

†††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††(9.1)

 

Thus the electron electromagnetic field energy is:

 

††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.2)

 

Combine equation (7.5) and (8.4), thus:

 

††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††† (9.3)

 

Thus:

 

†††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.4)

 

As we know:

 

†††††††††††† ††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.5)

 

And also:

 

††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††(9.6)

 

†††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.7)

 

Thus:

 

††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.8)

 

Thus:

 

†††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††† (9.9)

 

 

Thus:

 

††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.10)

 

As we know, the electron mass is one of the basic properties of electrons. Where does the electron mass come from? One of the most popular theories is the electromagnetic origin of electron mass.

 

From the above equation (9.10), we get the electronís electromagnetic energy; let us make an assumption here that the electronís mass origin is from the electromagnetic field energy, thus:

 

††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.11)

 

In which U is the electron electromagnetic field energy, and is the electron mass, then combine the equation (9.10) and (9.11), we can get

 

†††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††† (9.12)

 

Thus:

 

††††††††††††† ††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.13)

 

And we know that the Bohr radius is:

 

†††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.14)

 

Thus:

 

††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.15)

 

As we know, the value of fine structure constant is about:

††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.16)

 

Thus:

 

†††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††(9.17)

 

Thus:

 

††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† (9.18)

 

 

Reference

Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin
S. M. Blinder

Eur. J. Phys. 24 (May 2003) 271-275

 

General relativistic models for the electron

S. M. Blinder

Rept.Math.Phys. 47 (2001) 279-285

 

About Zitterbewegung and Electron Structure

Waldyr A. Rodrigues, Jayme Vaz, Erasmo Recami, and Giovanni Salesi

Physics Letters B 318 (1993) 623-628

 

Zitterbewegung and the Electromagnetic Field of the Electron

J.Vaz Jr e W.A.Rodrigues Jr,

Physics Letters B, 319, 203-208, (1993).

 

Spin and Electron Structure

M.Pavsic, E.Recami, W.A.Rodrigues Jr, D.G.Maccarrone, F.Raciti e G.Salesi,

Physics Letters B, 318, 481-488, (1993).

 

Mass and Spin Renormalization in Lorentz Electrodynamics

Walter Appel, Michael K.-H. Kiessling

Annals Phys. 289 (2001) 24-83

 

An Elementary Account of the Factor of 4/3 in the Electromagnetic Mass

P. Moylan

Am. J. Phys. 63, 818-820 (1995).

 

The Electromagnetic Mass of a Charged Particle

V.A. Kuligin, G.A. Kuligina, M.V. Korneva

APEIRON Vol. 3 Nr. 1 January 1996

 

 

 


What is the electron spin?
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