# A non-relativistic derivation of Eo=mc^2 and the inertial mass of a particle

Academia.edu, researchgate.net and other online sites publish non-peer-reviewed articles. That's great! It's very difficult to get an "alternative physics" article peer reviewed and published by a standard physics journal or even on arXiv.

Technically, can a paper being posted on academia.edu; be submitted again in a standard journal for peer-review and publication?

What if a fundamental particle like a resting electron is composed of a circling photon-like object with energy Eo and vector momentum p = Eo/c where c is the speed of light?

A resting electron will only have static charge and no current or magnetic field.

Your circling photon-like object carries electrical charge. So your concept of resting electron will be having a magnetic field. Isn't this contradictory?

A resting electron will only have static charge and no current or magnetic field.

Your circling photon-like object carries electrical charge. So your concept of resting electron will be having a magnetic field. Isn't this contradictory?
Electrons do have a magnetic dipole moment.

The problem for non-relativistic mechanical models of the electron as a spinning charged object is that the magnetic moment of the electron is a bit more than twice the magnetic moment of a charged massive bit with the same angular momentum.

Explaining the factor of 2 is the math of the Poincarè group and the bit more is the math of Quantum Electrodynamics which unlike the OP's pet idea, treats electrons and photons on equal footing as excitations of fields that are only weakly coupled to each other.

A resting electron will only have static charge and no current or magnetic field.

Your circling photon-like object carries electrical charge. So your concept of resting electron will be having a magnetic field. Isn't this contradictory?

As rpenner says, electrons have an intrinsic magnetism, associated with what we call their "spin". There is a famous demonstration of this, called the Stern-Gerlach experiment: https://en.wikipedia.org/wiki/Stern–Gerlach_experiment

Yes, but we are talking about the formula p=E/c for the momentum of a photon not an electron.

Technically, can a paper being posted on academia.edu; be submitted again in a standard journal for peer-review and publication?
Good question. An academia.edu article would probably have to be tweaked slightly and then reformatted to a particular journal's publication standards. An academia.edu staff member told me about a year ago that they are planning to implement their own article peer review system in the future. That would be nice! I was invited to submit my SPIE-proceedings electron-as-spin-1/2-charged-photon article to a peer-reviewed photonics journal, but I choose to wait.
Richard

Electrons do have a magnetic dipole moment.

The problem for non-relativistic mechanical models of the electron as a spinning charged object is that the magnetic moment of the electron is a bit more than twice the magnetic moment of a charged massive bit with the same angular momentum.

Explaining the factor of 2 is the math of the Poincarè group and the bit more is the math of Quantum Electrodynamics which unlike the OP's pet idea, treats electrons and photons on equal footing as excitations of fields that are only weakly coupled to each other.

There's nothing wrong with pet ideas as long as you keep open-minded and rational about them. The atom was someone's pet idea long before it was scientifically established. The microvitum (plural microvita) was someone else's pet idea which I wrote a book about: "Microvita: Cosmic Seeds of Life", at https://www.academia.edu/28605295/Microvita_Cosmic_Seeds_of_Life . That idea led to my current ideas about electrons and inertia.

Richard

As rpenner says, electrons have an intrinsic magnetism, associated with what we call their "spin". There is a famous demonstration of this, called the Stern-Gerlach experiment: https://en.wikipedia.org/wiki/Stern–Gerlach_experiment

Thats true. A spinning electron will be having a magnetic dipole. But can a spinning electron be considered as a 'resting electron'? Rest means no relative linear or angular speed. Here the 'resting electron' is having an angular speed.

Einstein in his paper, "DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?" considered a stationary body with relative to one co-ordinate system. Here the resting body has no linear or angular speed with relative to this co-ordinate system.

https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf

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Thats true. A spinning electron will be having a magnetic dipole. But can a spinning electron be considered as a 'resting electron'? Rest means no relative linear or angular speed. Here the 'resting electron' is having and angular speed.

Einstein in his paper, "DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?" considered a stationary body with relative to one co-ordinate system. Here the resting body has no linear or angular speed with relative to this co-ordinate system.

https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf

Hello hansda,
In the spin-1/2 charged-photon model of the electron, there is a very rapid internal circulation of momentum, energy and electric charge, but the electron model as a particle is still considered to be at rest unless the particle as a whole has an external velocity.
Richard

Hello hansda,
In the spin-1/2 charged-photon model of the electron, there is a very rapid internal circulation of momentum, energy and electric charge, but the electron model as a particle is still considered to be at rest unless the particle as a whole has an external velocity.
Richard

Let us consider Einstein's paper as common. We will consider two cases. In one case we will consider the stationary body as conventional model of electron. Name this as case A. In other case we will consider the stationary body as your model of electron. Name this as case B.

In case A, will there be any magnetic field?

But, in the case B, there will be some magnetic field.

Let us consider Einstein's paper as common. We will consider two cases. In one case we will consider the stationary body as conventional model of electron. Name this as case A. In other case we will consider the stationary body as your model of electron. Name this as case B.

In case A, will there be any magnetic field?

But, in the case B, there will be some magnetic field.

Hello hansda,
You need to be more specific about which "Einstein's paper" you are talking about: 1905 E=mc^2 paper ? EPR paper? and please pose the questions more precisely. Thanks!
Richard

Hello hansda,
You need to be more specific about which "Einstein's paper" you are talking about: 1905 E=mc^2 paper ? EPR paper? and please pose the questions more precisely. Thanks!
Richard

Follow this paper https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf .

A quote from the above paper says
Einstein said:
Let there be a stationary body in the system (x, y, z), and let its energy— referred to the system (x, y, z) be E0.

With reference to the above quote,

case A considers the stationary body as conventional model of electron.

case B considers the stationary body as your model of electron.

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Thats true. A spinning electron will be having a magnetic dipole. But can a spinning electron be considered as a 'resting electron'? Rest means no relative linear or angular speed. Here the 'resting electron' is having an angular speed.

Einstein in his paper, "DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?" considered a stationary body with relative to one co-ordinate system. Here the resting body has no linear or angular speed with relative to this co-ordinate system.

https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf

Yes but the experimental evidence is that the "spin" of the electron - and that of other fundamental particles - is intrinsic. In other words you cannot stop them "spinning". Therefore, if you consider the "spin" of the electron to be a form of classical motion, then you cannot have an electron "at rest", as you put it.

I put "spin" and "spinning" in inverted commas as, while we can for some purposes think of these entities as little balls spinning, that is evidently not quite what they are, at least according to quantum mechanics.

Therefore, if you consider the "spin" of the electron to be a form of classical motion, then you cannot have an electron "at rest", as you put it.

That exactly is my point. A spinning electron can not be considered as a 'resting electron'.

Thats true. A spinning electron will be having a magnetic dipole. But can a spinning electron be considered as a 'resting electron'? Rest means no relative linear or angular speed. Here the 'resting electron' is having an angular speed.
You are mixing definitions. In the math of special relativity, the Poincaré group was realized by Wigner in 1939 to permit representation of particles in quantum theories with intrinsic angular momentum. Thus nothing need be "spinning" for such point-like particles to represent actual, conserved, angular momentum, $$\vec{S}$$.
Wigner, E P. On the unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40:149-204, (1939).
The same Poincaré group is why the magnetic dipole momentum is close to 2 times the classically expected value ($$\vec{\mu} \approx -2.00231930436 \frac{|e|}{2 m_e} \vec{S}$$) while the details of how the electron quantum field and the electromagnetic quantum field couple are responsible (in currently accepted physical theory) for why the ratio is not exactly 2 but closer to $$2 + \frac{\alpha}{\pi}$$ with $$\alpha$$ being the famous fine structure constant of quantum electrodynamics.

An electron is defined (in QED and the standard model of particle physics) as an excitation of the quantum field that is characterized by spin-1/2, rest mass ~ 0.5 MeV and couples to the electromagnetic and weak boson fields as a lepton of charge -1. So it will always have an intrinsic angular momentum measured as +1/2 or -1/2 along any axis you might choose (in units of h/(2 π)).

That exactly is my point. A spinning electron can not be considered as a 'resting electron'.
Is your point, then, that "resting electrons" do not exist?

If an electron is composed of a spin 1/2 charged photon circulating at c, clearly it is only this charged photon's average position which can be "at rest" since the charged photon itself is circulating at c. In a relativistically moving electron, the charged photon would be moving in a helical trajectory at c, with its longitudinal velocity component being the velocity v of the moving electron. That's one reason why I'm suggesting that what we call an "electron" is actually one type of circulating spin-1/2 charged photon.
Richard

Follow this paper https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf .

A quote from the above paper says

With reference to the above quote,

case A considers the stationary body as conventional model of electron.

case B considers the stationary body as your model of electron.

hansda,
In Einstein's E=mc^2 article that you link to, the resting body sends out 2 plane waves of light in opposite directions. Whether the body that you propose is a conventional (Standard Model) electron or a spin-1/2 charged photon model of electron, it cannot send out even two single photons in opposite directions, because the electron would then end up having a mass less than 1 electron mass and would no longer be an electron (or any other charged particle). The electron could not even send out two photons in opposite directions with each photon having half of the rest energy of the electron. Then nothing at all would be left of the electron, but conservation of electric charge would be violated since the two emitted photons have no net charge but the original electron had electric charge -e. So your question about magnetic fields doesn't arise in this situation since the situation you propose can't occur even for a standard model electron, following known physical laws.

If an electron is composed of a spin 1/2 charged photon circulating at c, clearly it is only this charged photon's average position which can be "at rest" since the charged photon itself is circulating at c. In a relativistically moving electron, the charged photon would be moving in a helical trajectory at c, with its longitudinal velocity component being the velocity v of the moving electron. That's one reason why I'm suggesting that what we call an "electron" is actually one type of circulating spin-1/2 charged photon.
Richard

I have another question.

We know that two electrons will repel each other. Direction of this repelling force will be in a straightline joining the two electrons. In your model of electron, what will be the direction of this repelling force?