John A. Macken I tend to think of the electron energy not in terms of particle energy or field energy but in terms of the energy of a looped wave in the medium of space. This is the Spacetime Wave theory.

The total energy of the electron is then calculated from E=hf where f is the frequency. You can see how this works in the case of the hydrogen bond:

Preprint The Hydrogen Bond (June 2022)

The video presentation link describing the underlying theory:

https://youtu.be/zEu-_0ACl3I

Richard

John A. Macken

As per my understanding, about 35 percent of electron's total mass-energy is located in its electrostatic field.

As per the modern concept, a field is a fundamental physical quantity that could independently exist at each and every point of the space occupied by the field. But Maxwell had supposed that the deformation of luminiferous aether, along with associated stresses and strains, represented various fields of physics including the electromagnetic field.

Intrinsic Electric Field

Consider one electron located at an isolated point P in space - far removed from all other charges. This isolated electron will produce an (intrinsic) electric field around point P that spreads everywhere in surrounding space. This intrinsic electric field or the electrostatic field of an electron is an integral part of the electron charge and does not depend upon the presence or absence of any other charge in its vicinity - not even any test charge. In Maxwell's terminology of 'deformations of aether' we might call it 'strain field' or 'strain wave field' around the electron and consider it as an integral part of the electron structure - whatever it be.

Coulomb Field

However, for practical applications we quantify this electric field of the electron by measuring its interaction with a positive test charge positioned at a certain point Q at distance r from point P. The force on second charge or test charge is caused by the mutual interaction between the electric fields of the two charges and is governed by Coulomb's Law of electrostatics. The intrinsic electric field of an electron when quantified with a test charge, using Coulomb's law, may now be termed as Coulomb electric field of the electron. This Coulomb field of the electron will map the force acting on test charge located at Q as well as map the interaction energy released due to the mutual interaction of the superposed intrinsic electric fields of the electron at P and test charge located at Q.

Ambiguity

Mapping of thethe notion of Electric Field of the electron. Ambiguity is in the lack of distinction between the Intrinsic electric fields of isolated electron and isolated test charge and the Coulomb electric field of their interaction forces and energies. Moreover, this mapping of interaction forces and energies cannot represent a physical field since the forces and energies mapped at different field locations Q1, Q2, Q3 etc. do not physically exist when the test charge is physically located at Q. Unfortunately, in Modern Physics the Coulomb electric field is de-facto treated as the Intrinsic electric field of the electron.

Gurcharn Singh Sandhu

Thank you for your long reply. I appreciate that you actually attempted to develop a wave-based structural model of an electron. I believe the wave approach is correct, but I disagree with the numerical values you propose. The hardest part of making a wave-based model is having the wave-based model achieve an electron's de Broglie wave properties. The link below is my work on this subject. The computer simulations in this article show that to achieve an electron's de Broglie wave properties, it is necessary for the frequency of standing waves to equal an electron's Compton frequency (1.24x1020 Hz). You used 8x1024 Hz, a factor of about 64,000 too high.

Also, the energy external to radius r from charge e is: Eext = αħc/2r. Inserting your value r = 1.61x10-15 into this gives Eext = 7.16x10-14 J. This is about 87% of an electron's energy. This is too high.

The model and numbers in my model give not only an electron's energy and de Broglie wave properties (wavelength, phase velocity and group velocity) but also give an electron's gravity and electrostatic force. I am currently writing a new paper that goes much further.

Preprint A quantum vacuum model unites an electron's gravitational an...

John A. Macken

Dear John,

You wrote: "This question is ultimately about an electron’s structure. It is a common belief that an electron is a point particle."

Actually, we "mathematically represent" an electron as a point particle for trajectory calculations purposes, just like we "mathematically represent" the Earth and Moon as localized point-like when calculating their trajectories.

We know full well however that the Earth and Moon are not such dimensionless points in reality.

Don't you think that the same would apply to electrons?

You wrote: "An electron’s energy has been measured to an accuracy of about 10-23 J."

Seems to me that the exact rest mass of the electron was established as 9.10938188E-31 kg, and the wavelength of the energy making up this rest mass is the electron Compton wavelength, established as λc=2.426310215E-12 m. From both methods, the exact energy in joules corresponding to the electron rest mass then comes out as 8.18710414E-14 joules.

Don't you think that these values are exactly representative?

Your question as to what percentage of an electron's energy is in its electric field is totally pertinent.

I don't know if you are aware of this information, but Paul Marmet succeeded in 2003 in deriving from the Biot-Savart equation the evidence that the magnetic field of the electron rest mass corresponds to exactly half of the energy of its rest mass (his Equation 24), which de facto leaves the other half (50%) as corresponding to its electric field.

His 2003 article is here:

http://www.newtonphysics.on.ca/magnetic/index.html

The first wave of derivations from this Equation 24 from Marmet was published in 2007 in the same Kazan State University Engineering Journal, defining the E and B fields equations of the electron rest mass energy, for use in the Lorentz force equation:

Article Field Equations for Localized Photons and Relativistic Field...

Hope this helps you research.

Best Regards, André

André Michaud

Thank you for the long answer. I have not seen any survey on the subject, but I estimate that over half of physicists would answer that an electron is a point particle, if pressed. It is not a question that most physicists want to answer because there are difficulties with any answer. Everybody understands the concept of mathematically treating an object as a point, but an electron is different because there is no clear evidence for any other size. Most physicists believe a black hole has a singularity (point mass) at its center. The reason they believe an electron has "intrinsic" angular momentum, not physical rotation, is because a point particle cannot achieve ħ/2 (Z axis) angular momentum.

The model I suggest is a wave rotating at an electron's Compton frequency (7.76x1020 rad/s). It has a mathematical radius equal to an electron’s Compton radius (3.86x10-13 m) but there is no sharp edge. In fact, the electric field is a standing wave that decreases in amplitude with 1/r and therefore extends indefinitely. The equation for the energy in an electron's charge e electric field, external to radius r is (Eext = αħc/2r). Therefore, the electron's electric field energy in my model represents about α/2 = 3.65x10-3 of the electron's total energy.

Dear John A. Macken

Did you have a look at Marmet's 2003 derivation and at the subsequent derivations published in 2007 for the E and B fields of the electron rest mass?

They were meant as direct answer to your question.

Best Regards, André