Collision experiments imply that an electron must be smaller than 10-18 m. The equation for the energy in an electric field external to radius r produced by charge e is: Eext = αħc/2r. (where α is the fine structure constant). Therefore, a sphere with radius r = 10-18 m and charge e would have energy of about 1.2 x 10-10 J in its electric field. An electron’s annihilation energy is about 8 x 10-14 J. Therefore, assuming the electric field equation applies down to 10-18 m, the energy in an electron’s electric field would be about 1400 times more energy than an electron’s annihilation energy. The explanation usually given is that vacuum polarization becomes dominate for the large electric field generated by charge e with small radius. This sounds good if the electron was the only charge e particle. However, a proton has positive charge e and radius of about 9 x 10-16 m. Using the previous equation, the implied energy in a proton’s electric field external to the proton radius is about 10-13 J. This is about 1.6 times more energy than an electron’s annihilation energy but about 0.1% of the proton’s annihilation energy. Therefore, the vacuum polarization does not seem to affect the proton’s electric field. The magnitude of the proton’s charge exactly matches the magnitude of the electron’s charge. If vacuum polarization is assumed to be a factor in determining the macroscopic charge, the effect of vacuum polarization must be exactly calibrated to match these two charges.
I propose this problem is caused by the point particle model of an electron. There is a proposed physical model of an electron which incorporates a single universal field which generates all the other fields of the standard model. An electron is an “excitation” of this universal field. Details of this electron model are given in the referenced paper below. There are two ways of determining the radius of this model. Since a Planck length distortion of spacetime is undetectable, this electron model has undetectable radius. However, this Planck length distortion is a rotating wave (spherical vortex) distributed over a volume with mathematical radius equal to an electron’s reduced Compton wavelength ≈ 3.86 x 10-13 m. Using this larger radius, the electron’s electric field energy external to this larger radius is about α/2 ≈ 0.4% times an electron’s annihilation energy.
What do you think? Other explanations incorporate extra dimensions or merely considering it a mystery beyond human understanding.
Dear @John, I suggest that you read a paper, in my profile, called "fundamental electromagnetics". It is clear logic with simple mathematics, it gives a different view on the electron. I hope it might clarify your understanding of the electron and the EM in general.
Stellan,
I looked at your reference up to about page 16. I did not find anything that could answer the question. Can you state a specific percentage or give a page number which contains the answer?
John
Dear John,
The energy (mass) of an electron is completely in its EM potential. At some distance from the center, the energy follows exactly the classical potential energy. But, some "classical radii" away the characteristics of the electron change, reducing the part of the energy contained in each radial interval. Ending at zero at the electron center.
In a dynamic reaction the electron deforms and gain energy (mass). It's therefore difficult to obtain a correct dependence for a single electron. You have a figure showing the most important parameters behaviour relative to the electron radius.
In figure 3.2; page 22 you have the the E-field(o), the mass and the charge, relative to the electron radius. This a single undisturbed electron.
John,
I agree that the point model of the electron makes no sense.
You say:
"The tremendously large impedance of spacetime (c3/G) permits small amplitude waves in spacetime to be the universal building block. "
This is a fundamental, easy to calculate fact which is ignored (for 'quantum reasons') by virtually all physicists.
The amount of information and energy that can be carried at high frequencies in GW is enormous, enough to power all of quantum mechanics and electromagnetism, etc.
As an example at a LIGO detectable amplitude of h=10^(-24) and a ~Compton frequency, one gets 3.00e+29 watts/m2. This fact provides a huge, unexplored parameter space for physicists to play in. Why don't we?