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

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)).

This is OK.

My question is, can this electron be considered as 'stationary body' as Einstein considered a 'stationary body' in his paper at this link https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf .

A quote for 'stationary body' from Einstein's paper for reference, is as follows: "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. Let the energy of the body relative to the system (ξ, η, ζ) moving as above with the velocity v, be H0."

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.

Electron can emit light, as is observed in LED. In this process electron does not loose all of its mass or charge. This is as per known laws of physics.

[Rpenner said: a lot of stuff.]

Hi rpenner, you seem brilliant and very knowledgeable. But also sometimes like an arrogant thug who is sightly paranoid of new ideas threatening his nice sand castle, and is so used to thinking one way it's impossible to turn around to see the wave coming. You've missed out on the potential value this model can offer, as similar ones by others (John Blaszynski who has experimental evidence, and Chip Akins, et al, no doubt.) Hope I'm wrong. Newbie here. First impression. But I never set mind just one way.

The other thing obvious is, yes, the details need to be worked out. Especially the confinement force, nature of charge, and magnetic effects. Mistakes pointed out and corrected. Sharing logical debate instead of attacking the person, or even an entire research communications institution, a social educational media site, which fosters sharing, communication, growth, and yes brain storming (any theoretical physicist worth his brain farts knows the value there.) (Don't let the whacko ideas on these sites throw you for a double loop))

Also please don't mock self publishing as not publishing. That's stupid, and you're not. This forum is also an amatuer (which means not paid) peer review and sharing site. (Einstein began as an amatuer.) And I thought this section is supposed to encourage new ideas/models/addendums/theories?

That said, very good points you make rpenner, but I forget where because it was so annoying reading your probably valid claims. Will study...

Here are the good things, that any physicist should welcome:
Richard's model unifies an electromagnetic wave as having dual forms: light and matter. One has rest mass (confined as a standing wave.) The other travels freely (escaped.) A worthy goal it is to describe all "particles" as various forms (modes) of the same EM energy. And here Richard does it in a visual way, which is something the old standard does not do very well. It explains that mass is simply an effect of being trapped EM energy, confined in a toroidal formation, as in a black hole.

Now, you are free to attack again. It's OK.

Cheers.

Keep up the good work despite the mockery Richard.

[Rpenner said: a lot of stuff.]

Hi rpenner, you seem brilliant and very knowledgeable. But also sometimes like an arrogant thug who is sightly paranoid of new ideas threatening his nice sand castle, and is so used to thinking one way it's impossible to turn around to see the wave coming. You've missed out on the potential value this model can offer, as similar ones by others (John Blaszynski who has experimental evidence, and Chip Akins, et al, no doubt.) Hope I'm wrong. Newbie here. First impression. But I never set mind just one way.

The other thing obvious is, yes, the details need to be worked out. Especially the confinement force, nature of charge, and magnetic effects. Mistakes pointed out and corrected. Sharing logical debate instead of attacking the person, or even an entire research communications institution, a social educational media site, which fosters sharing, communication, growth, and yes brain storming (any theoretical physicist worth his brain farts knows the value there.) (Don't let the whacko ideas on these sites throw you for a double loop))

Also please don't mock self publishing as not publishing. That's stupid, and you're not. This forum is also an amatuer (which means not paid) peer review and sharing site. (Einstein began as an amatuer.) And I thought this section is supposed to encourage new ideas/models/addendums/theories?

That said, very good points you make rpenner, but I forget where because it was so annoying reading your probably valid claims. Will study...

Here are the good things, that any physicist should welcome:
Richard's model unifies an electromagnetic wave as having dual forms: light and matter. One has rest mass (confined as a standing wave.) The other travels freely (escaped.) A worthy goal it is to describe all "particles" as various forms (modes) of the same EM energy. And here Richard does it in a visual way, which is something the old standard does not do very well. It explains that mass is simply an effect of being trapped EM energy, confined in a toroidal formation, as in a black hole.

Now, you are free to attack again. It's OK.

Cheers.

Keep up the good work despite the mockery Richard.

Who is John Blaszynski and what is this evidence you refer to? I have looked him up and can only find one paper on a doubtful website called General Science Journal.

Hi rpenner, you seem brilliant and very knowledgeable. But also sometimes like an arrogant thug who is sightly paranoid of new ideas threatening his nice sand castle
My "castle" is reality, math that does a good job of describing the observable behavior of the first, and the technical jargon used to describe the second.

If words don't need to have meaning, if math doesn't have to have rigor, if reality doesn't matter to science, then I am acting like a thug.
On the other hand, maybe I'm a helpful teacher pointing out there are many, many more ways to be wrong rather than right.

Hallo, I agree with paddoboy approach.
If we have to advance in any field, first comes the IDEA, a rational idea, than the proofs.
So I appreciate also the insight of Richard Gautier that the electron is derived from a photon, until now we did not have any theory apart the wave-particle solution. Its seems to be logical from the point of view of Weinberg "the first 3 minute of the universe". That if after 10 seconds the universe was ONLY LIGHT (it may not be true, because a suitable percentage of the aerial particles wich give life to light, must have remain):

In physical cosmology, the photon epoch was the period in the evolution of the early universe in which photons dominated the energy of the universe. The photon epoch started after most leptons and anti-leptons were annihilated at the end of the lepton epoch, about 10 seconds after the Big Bang.[1] Atomic nuclei were created in the process ofnucleosynthesis which occurred during the first few minutes of the photon epoch. For the remainder of the photon epoch the universe contained a hot dense plasma of nuclei, electrons and photons. 379,000 years after the Big Bang the temperature of the universe fell to the point where nuclei could combine with electrons to create neutral atoms. As a result, photons no longer interacted frequently with matter, the universe became transparent and the cosmic microwave background radiation was created and then structure formation took place. (https://en.wikipedia.org/wiki/Photon_epoch)

it means the electrons etc., are produced from photons, being that the raw material, coupled with strong centripetal forces...

So I feel Richard Gautier approach being in line also with cosmological relevances.

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?

Hello hansda,
In my spin 1/2 charged-photon electron model it is the point-like circulating photon that carries the electric charge -e. So the repelling force between two electrons would be the repelling force between the two circulating charged point-like photons. In QED, virtual photons exchanged between two electrically charged particles produce the attracting or repelling force between the two charged particles. The same should apply for the electric forces between the circulating charged photons. The AVERAGE repelling forces between two sufficiently separated electron models would be along the line from the center of the circle of the first electron model to the center of the circle of the second electron model. This average force result could change if the electron models are sufficiently close to each other. By the way, my electron models are not in flat two-dimensional circles. The circle is only the trajectory of the circulating photon, which would be expected to have some additional cyclic motion extending into the third-dimension of the electron model.

This is OK.
My question is, can this electron be considered as 'stationary body' as Einstein considered a 'stationary body' in his paper at this link https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf .
Yes. The consistency of the model of the electron as a quantum point particle with intrinsic angular momentum with the theory of special relativity was demonstrated in Wigner's 1939 paper.

Yes. The consistency of the model of the electron as a quantum point particle with intrinsic angular momentum with the theory of special relativity was demonstrated in Wigner's 1939 paper.

In that case, what is energy E of electron at rest?

Is it E=mc^2 or E^2= (pc)^2 + (mc^2)^2 ; where m is mass of electron, c is speed of light and p is angular momentum of electron.

In my spin 1/2 charged-photon electron model it is the point-like circulating photon that carries the electric charge -e.

This is the 2D version of your electron model.

So the repelling force between two electrons would be the repelling force between the two circulating charged point-like photons. In QED, virtual photons exchanged between two electrically charged particles produce the attracting or repelling force between the two charged particles. The same should apply for the electric forces between the circulating charged photons. The AVERAGE repelling forces between two sufficiently separated electron models would be along the line from the center of the circle of the first electron model to the center of the circle of the second electron model. This average force result could change if the electron models are sufficiently close to each other.

Here you considered only the 2D version of your model.

By the way, my electron models are not in flat two-dimensional circles. The circle is only the trajectory of the circulating photon, which would be expected to have some additional cyclic motion extending into the third-dimension of the electron model.

What is the 3D version of your electron model?

In that case, what is energy E of electron at rest?

Is it E=mc^2 or E^2= (pc)^2 + (mc^2)^2 ; where m is mass of electron, c is speed of light and p is angular momentum of electron.

For a free electron it's $$E^2= (pc)^2 + (mc^2)^2$$ where for a free electron at rest we have $$p=0$$ as the linear momentum of the electron. Angular and linear momentum have different units so you can't plug one in for the place of the other.

For a free electron it's $$E^2= (pc)^2 + (mc^2)^2$$ where for a free electron at rest we have $$p=0$$ as the linear momentum of the electron. Angular and linear momentum have different units so you can't plug one in for the place of the other.
OK. Thanks.

... The circle is only the trajectory of the circulating photon, which would be expected to have some additional cyclic motion extending into the third-dimension of the electron model.

If the circulating photon, is having some additional cyclic motion extending into the third-dimension; then it has a choice for two axes. Which one it will choose? In this process the resultant trajectory of the circulating photon may not be a circle also. Can you clarify this?

Electron can emit light, as is observed in LED. In this process electron does not loose all of its mass or charge. This is as per known laws of physics.

Hello Hansda,
When an atom emits light (a photon) as when an electron drops from a higher energy level to a lower energy level in the atom, it is not the electron that is emitting the light. The electron is merely moving to a lower potential energy level in the atom, and this difference in the electron's potential energy between the higher and lower energy levels is emitted as a photon. The electron retains its full rest energy (and mass). But a resting electron in isolation cannot emit a photon (or 2 photons in opposite directions) because the resting electron would lose some of its own rest energy (and mass) and so would no longer be an electron. P.S. how does one become a "Valued Senior Member"?

P.S. how does one become a "Valued Senior Member"?
1) Comply with forum rules.
2) Post posts.

This is the 2D version of your electron model.

Here you considered only the 2D version of your model.

What is the 3D version of your electron model?

Hello hansda,
I've just published my 3-D internally transluminal model of a spin-1/2 charged photon at https://www.academia.edu/30899196/T..._a_Spin-_Charged_Photon_Composing_an_Electron . This spin-1/2 charged photon model (unlike my internally superluminal spin-1 uncharged photon model) makes two helical turns per photon wavelength instead of one turn per wavelength. The radius of the spin-1/2 charged photon model is lambda/4pi (compared to lambda/2pi for the spin-1 photon model.) The spin-1/2 charged photon's helical axis makes a double loop of total length one Compton wavelength to form a 3-D model of a resting electron. The transluminal energy quantum in the resting electron model moves transluminally on the surface of a mathematical horn torus (donut with no hole). If you have a 3-D graphics program you can generate this 3-D electron model -- it's very interesting!

For a free electron it's $$E^2= (pc)^2 + (mc^2)^2$$ where for a free electron at rest we have $$p=0$$ as the linear momentum of the electron. Angular and linear momentum have different units so you can't plug one in for the place of the other.

Hello hansda,
So to answer your question, a resting electron has momentum p=0. So the energy of the resting electron comes out to equal mc^2 . That resting energy of an electron is often called Eo to distinguish it from the energy E of a relativistically moving object where E=gamma mc^2.

// Edit: anyway -> any way
Hello hansda,
I've just published my 3-D internally transluminal model of a spin-1/2 charged photon at https://www.academia.edu/30899196/T..._a_Spin-_Charged_Photon_Composing_an_Electron . This spin-1/2 charged photon model (unlike my internally superluminal spin-1 uncharged photon model) makes two helical turns per photon wavelength instead of one turn per wavelength. The radius of the spin-1/2 charged photon model is lambda/4pi (compared to lambda/2pi for the spin-1 photon model.) The spin-1/2 charged photon's helical axis makes a double loop of total length one Compton wavelength to form a 3-D model of a resting electron. The transluminal energy quantum in the resting electron model moves transluminally on the surface of a mathematical horn torus (donut with no hole). If you have a 3-D graphics program you can generate this 3-D electron model -- it's very interesting!

Hello rpenner,
Have you seen the implication of the spin-1/2 charged photon making two helical turns per longitudinal photon wavelength as described above, for the double-looping model of the electron? During the first circular loop of the helical axis, the spin-1/2 photon makes the first complete helical turn and has gone thorough a 360-degree phase shift. During the second circular loop of the helical axis, the spin-1/2 photon makes the second complete helical turn and has gone through a second 360-degree phase shift and so is in phase with the first helical loop. So there is no phase cancellation in the double-looping electron model with the spin-1/2 charged photon, which would occur with charged photon making a double loop of total length one wavelength (so that each loop would be 1/2 wavelength), assuming the two loops were co-linear.
Richard

Hello rpenner,
I chalked it up just as another way your system is not mathematically self-consistent.

You have your ur-electron claimed to be "like a photon" so one would think you were using the model of quantum field theory but then
1) it doesn't obey conservation of momentum
2) it doesn't obey the deBroglie relationship
3) it doesn't seem to be a quantum particle at all
4) its motion isn't independent of choice of standard of rest.

So, given that it's motivated by no compelling divergence of observation from theory, it seems you are willing to throw the baby out with the bathwater in favor of filling the tub with tapioca. You are trying to understand the 1928 Dirac single-particle model for electrons in terms of a conceptual mechanical model and ignoring the (c. 1934) quantum field theory many-particle physics which doesn't have the same problems. It is the latter approach which is used in (c. 1950) quantum electrodynamics which has had the successful descriptions of electron interactions at all scales down to fractions of a femtometer.