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

Discussion in 'Alternative Theories' started by Richard Gauthier, Dec 27, 2016.

1. ### Richard GauthierRegistered Member

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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? If we start with Newton's second law of motion F = dp/dt = MA where dp/dt is the time rate of change of the circling vector momentum p = Eo/c, M is the inertial mass of the circling photon-like object, and A is the centripetal acceleration c^2/R of the circling photon-like object (where R is the radius of its circle), we find with very easy math (and using the circling vector relation dp/dt = pc/R) that the inertial mass M = (dp/dt)/A = (pc/R)/(c^2/R) = p/c = (Eo/c)/c = Eo/c^2. That is, the inertial mass M of an electron (if it is composed of a circling photon-like object) is derived from the circling photon-like object's energy Eo and its circling vector momentum Eo/c to be M = Eo/c^2 or Eo = Mc^2 , which is Einstein's equation for the energy content Eo of a resting electron of inertial mass M. This result is also published at https://www.academia.edu/29799123/Inertia_Explained . This derivation of the relation of the energy content of a resting fundamental particle to its inertial mass is done without using Einstein's special theory of relativity. Note: Einstein's 1905 article in which he first derived m = E/c^2 or E = mc^2 for a resting object by using his special theory of relativity is titled "Does the inertia of a body depend on its energy-content?"

3. ### exchemistValued Senior Member

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It seems to me you need to explain what you mean by a "circling photon-like object", because on the face of it that seems like a rather implausible notion. Two questions that immediately spring to mind are:

1) circling about what axis, and by what process (objects, forces or whatever) would such circular motion be maintained?
2) how is its electric charge accounted for, if the electron is "photon-like"?

Secondly, I think you need to explain how you can have a "circling" electron with non-zero rest mass and a tangential velocity of c, which you apparently assume in your derivation. This makes it look, at least at first glance, as if your derivation relies on a further, unstated, premise that relativity is wrong. You will have an uphill struggle with that, won't you, bearing in mind the observational evidence for it?

5. ### rpennerFully WiredValued Senior Member

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You haven't explained inertia, because you only analyze a fictitious rotating system about a static origin without taking into account the dynamics* and other properties of electrons.
You mix and match Newtonian and post-Newtonian dynamics into an incoherent mess. And coherent exposition is important to students of science since a scientific theory is a communicable framework for describing precisely the observable behavior of a large class of related phenomena.

* Your model has a characteristic angular frequency: $\omega = c/R$ which for an electron in motion should (assuming special relativity) slow as relative velocity increases. For the case where tangential motion is perpendicular to electron motion, u, we have $\omega' = \omega \sqrt{1 - \frac{u^2}{c^2}}$ which tells us the helical velocity is $\sqrt{u^2 + (R \omega')^2} = c$ which, following your assumed proportionality between momentum and velocity means that the linear momentum of an electron is $\frac{u}{c} \times \frac{E_0}{c} = m u$ which is experimentally disfavored. William Bertozzi (1962).

You attempt to solve the Newtonian problem of the energy of a free particle at rest by using results from Special Relativity and Quantum Mechanics (Einstein invented the photon, also in 1905). You violate momentum conservation, which can be solved only by changing your model. Your model has angular momentum which imposes the relation $R \geq \frac{\sqrt{3} h}{4 \pi c m_e} \approx 334 \, \textrm{fm}$ which is over 300,000 times larger than the experimental upper bounds on the radius of the electron. You have not explained anything, as electron mass, $m_e$, can be measured while your expression $E_0/c^2$ merely substitutes, explaining nothing, while your R is unevidenced. Other problems arise, such as the relation between electric charge and dipole moment and that quantum mechanics forbids non-integral orbital angular momenta.

But worst of all, you are attempting to solve the wrong problem. You have mistaken the content of Special Relativity to be $E_0 = m c^2$ when it actually replaces Newtonian physics. Einstein's reasoning in his second paper on Special Relativity is based on the model explained in the first where Newtonian physics including the notions of Euclidean space and absolute time are thrown out in favor of something more compatible with observation.

Thus the relations between energy, momentum, velocity and mass for any free particle are: $E^2 = (m c^2)^2 + (c \vec{p})^2, \quad E \vec{v} = c^2 \vec{p}$
If one assumes $m=0$ then $E = c | \vec{p} |, \quad | \vec{v} | = c$ follows. If one assumes $m > 0$ then $E = \sqrt{ (m c^2)^2 + (c \vec{p})^2 } = m c^2 \sqrt{ 1 + \left( \frac{\vec{p}}{m c} \right)^2 } =\frac{ m c^2}{\sqrt{ 1 - \left( \frac{\vec{v}}{c} \right)^2 }}$ and $\vec{p} = \frac{E}{c^2} \vec{v} = \frac{ m }{\sqrt{ 1 - \left( \frac{\vec{v}}{c} \right)^2 }} \vec{v}$.

So physics doesn't care if you write $m$ or $\frac{E_0}{c^2}$ — that's just notation, not something that explains the universe more precisely or more parsimoniously. Further, the Higgs boson discovery seems to vindicate a different dynamical model of rest mass of particles, called the Standard Model of Particle Physics. It treats the mass of protons differently than the mass of electrons in ways that show up in experiment.

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7. ### Richard GauthierRegistered Member

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Hello exchemist,
Thanks for your excellent questions. Yes, regular spin-1 photons don't circle around. My proposal for a photon-like object that could circle around to form a resting electron is a hypothesized spin-1/2 charged photon. This spin-1/2 charged photon would be a new, previously unrecognized (because it has been called an electron) variety of photon that
a) travels at light speed.
b) has the photon properties: energy E=hf, momentum p=hf/c , and wave formula c=f lambda .
c) has the charge of an electron (or a positron.)
d) has mass Eo/c^2 when curled up in a double-looping (in order to get electron spin 1/2) circular trajectory to form a resting electron,
e) has orbital spin 1/2 perpendicular the plane of its circular trajectory (having either a spin of +1/2 or spin -1/2 depending on the direction of the charged photon's circular motion in relation to the electron's velocity vector.)
f) is a fermion with spin 1/2.
g) moves along an open helical trajectory at light speed to form a relativistic electron model (moving at sub-light speed) that would continue to have spin 1/2 at highly relativistic electron velocities.
h) generates the moving electron's relativistic de Broglie wavelength h/(gamma mv) along the helical trajectory's axis.
All of these features are described in my article "Electrons are spin-1/2 charged photons generating the de Broglie wavelength" at https://www.academia.edu/15686831/E..._photons_generating_the_de_Broglie_wavelength

A centripetal force is required to move the photon-like object in a circle. In my resting electron model, the circling spin 1/2 charged photon has a calculated centripetal force on it of 0.424 Newtons, which changes the direction of the momentum of the circling charged photon but not the charged photon's energy Eo. This centripetal force is calculated for my electron model in my article "Origin of the electron's inertia and relativistic energy‐momentum equation in the spin 1/2 charged‐photon electron model" at https://www.academia.edu/25599166/O...ion_in_the_Spin_Charged_Photon_Electron_Model . The source of this large centripetal force is currently not understood.

The electron model's electric charge is accounted for by postulating the spin-1/2 electrically charged photon that can form a double-looping electron model. No one knows the origin of electric charge. In the present electron model it could be associated with the topology of the double-looping trajectory of the hypothesized spin-1/2 charged photon when it curls up to form an electron.

I accept special relativity in my model. But special relativity is not needed to derive the mass m= Eo/c^2 of a resting electron formed from a circling photon-like object of energy Eo and circling momentum Eo/c. My relativistically-moving electron model (first link above) is described in part by setting the total energy of a relativistic electron E=gamma mc^2 equal to the energy E=hf of the helically circulating photon-like object, giving (as de Broglie mathematically postulated for a relativistic electron) the equation hf=gamma mc^2 . (De Broglie used this equation to describe an electron generating waves rather than to describe a photon-like object forming an electron as I do.) This gives a relativistic frequency f of the helically circulating charged photon to be f=(gamma mc^2)/h which, using c=f lambda gives the charged-photon's wavelength lambda=h/(gamma mc) along the helical trajectory of the charged photon forming the relativistic electron. This leads easily to generate the de Broglie wavelength lambda-deBroglie = h/(gamma mv) along the longitudinal axis of the helically moving charged photon.

Last edited: Dec 27, 2016
8. ### Richard GauthierRegistered Member

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36

Hello rpenner,

I used Newton's second law to derive the inertial mass m=Eo/c^2 of a resting particle modeled by a hypothesized (fictional) circling photon-like object of energy Eo and momentum Eo/c . Inertial mass is defined using Newton's 2nd law F=dp/dt = ma so I think that this can be a good didactic approach (especially if it turns out to be physically correct) for more deeply understanding inertial mass (and not just as an unexplained proportionality constant between force and acceleration.) According to your logic, it seems that we should just start teaching about gravity using Einstein's general theory of relativity and forget Newton's law of gravity since it is superseded by the more precise and comprehensive general theory of relativity.

You may say that Newton's second law F= dp/dt = ma doesn't apply in relativistic dynamics and I would agree with you. But in my opinion Newton's second law does apply for a resting object composed of a circling photon-like object. Relativistic dynamics apply when a particle or object is observed from various inertial frames, and this is treated somewhat in my relativistic electron model formed of a hypothesized helically moving spin 1/2 charged photon.

My relativistic electron model was briefly described in my reply to exchemist. The frequency of the circling charged photon INCREASES with relativistic electron's energy as f=(gamma mc^2)/h. In order to accomplish this geometrically in my electron model the radius R of the helical trajectory along which the charged photon moves is found to decrease with the electron's increasing velocity as R=Ro/(gamma^2) where Ro = hbar/2mc in my stationary electron model. This is all described in my article "Electrons are spin-1/2 charged photons generating the de Broglie wavelength" at https://www.academia.edu/15686831/E..._photons_generating_the_de_Broglie_wavelength .

In my relativistic electron model, explained in more detail at the above link, the spin 1/2 charged photon moves at speed c along its helical trajectory to form the relativistic electron. The energy of this charged photon moving along its helical trajectory is E=hf=gamma mc^2 . So the momentum P of this charged photon along its helical trajectory is P=E/c = gamma mc . The forward angle theta of this helical trajectory is in my model given by cos (theta) = v/c . So the momentum p of the relativistic electron, calculated as the longitudinal momentum of the helically moving charged photon, is p = P cos (theta) = (gamma mc) x (v/c) = gamma mv which is the momentum of a relativistic electron. The transverse component of the momentum of the helically moving charge photon in my model is Ptrans = Eo/c=mc . When this transverse component of the charged photon's total momentum is added by vector addition to the charged photon's longitudinal component of momentum p=gamma mv it gives the helically-moving charged photon's total momentum Ptotal = E/c where E is the charged photon's energy E=hf=gamma mc^2. Since m= Eo/c^2 , the electron's relativistic energy-momentum equation E^2= p^2 c^2 + m^2 c ^4 is mathematically equivalent to the equation obtained for the vector sum of the longitudinal and transverse momentum components of the helically-moving charged photon that add vectorially to give the total momentum Ptotal = E/c. Using the Pythagorean theorem this gives: Ptotal^2 = p^2 + (mc)^2 .

So my particle model is compatible with relativistic 4-dimensional energy-momentum kinematics: the invariant 4-momentum of a particle composed of a circulating photon-like object is Eo/c = mc, the energy component is E=Ptotal x c and the spatial momentum component is p = gamma mv, giving (mc)^2 c^2 = E^2 -(pc)^2 which is mathematically equivalent to (mc)^2 = (Ptotal)^2 - p^2 .

You claim that my particle model violates conservation of angular momentum. But in my electron model there is a central force 0.424 Newtons that continuously changes the momentum of the circling photon. The nature and origin of this force (if it exists) is currently unknown, but its remarkable size suggests that further investigation is needed. Is there experimental evidence for conservation of momentum WITHIN a particle like an electron that is characterized as being point-like yet having intrinsic (i.e. unexplained) spin?

Many physicists may think that since the Higgs field theory purports to explain why some particles have mass (and travel at less than light speed) while other particles don't have mass (and travel at light speed), there is nothing more to say on the topic of inertial mass. I for one am not convinced yet. The Higgs field (from what I read about it) may explain why some particles have mass while others do not. But as far as I know the Higgs field does not explain why this mass is INERTIAL mass, i.e. explains why F=ma, and why m is not just a useful number in the formula E^2 =p^2 c^2 + m^2 c^4 . I understand that physics does not answer "why?" questions. But some explanations may provide deeper understanding and insight than others. Also, I think that the Higgs field explanation does not supply the insight (supplied by my relativistic particle model) that INTERNALLY a particle with mass is traveling (via photon-like objects) at light speed, while observationally the particle is traveling at less than light speed. I think that Dirac's Nobel lecture comment has relevance here: according to his analysis, electrons travel at light speed, but due to their small amplitude and high frequency they are measured as traveling at less than light speed.

I am not at the moment trying to derive anything more than the inertial mass of fundamental particles like the electron. The proton is much more complicated. But quarks perhaps could be modeled as circulating charged gluons, while other fundamental particles like neutrinos could be modeled similarly as being composed of circulating light-speed particles. Ultimately all particles with mass might be modeled as being composed of circulating light-speed particles.

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9. ### rpennerFully WiredValued Senior Member

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Why must it be a "variety of photon" when it is not very photon-like. A photon is described by its (1) rest mass, (2) intrinsic spin, (3) coupling to electric charge, (4) lack of coupling to other quantum numbers like chromodynamic charge. Likewise all other quantum particles are defined by their rest mass, spin, and couplings.

Well since it is in a stationary state, we are talking about a angular dependence of the wave function such that we have a standing wave. Wouldn't that mean p = h/λ = h/(2 π R) ? And thus angular momentum L = R × p = h/(2 π) = ℏ, not ½ℏ as you claim in e.

Double-looping is not a function of waves in space-time. You have a complex an uncommunicated metaphysical model which you cobble on part by part to try and justify the extraordinary claim that electrons are made of something else but that this something else works according laws which appear alien to any physicist's experience of the behavior of the universe. Double-looping requires that λ = 4 π R (and thus $R = \frac{h}{4 \pi m_e c} \approx 193 \, \textrm{fm} >> 0.001 \, \textrm{fm}$) but also that the complex value of the wave function be double-valued with opposite signs everywhere. Functions cannot be double-valued anywhere. The principle of superposition says that the amplitude of such as wave is uniformly zero. Thus existing physics says your mechanism is fictional. Therefore you have to rewrite all the rules of relativity and quantum mechanics in a way that conforms with experiment just to justify as theoretically sound the unevidenced metaphysical proposition that the electron is a massless whirligig.

These assumptions are incompatible with electrons behaving like spin-1/2 particles or you bear the burden of rewriting the composition of angular momenta.

Not evidence of sanity. It's a social media site, not a peer-reviewed journal.

F = ω p = (c/R) (h/λ) = ch/(4 π R^2) = 4 π m² c³ / h ≈ 424 mN. Instead of modeling this as a pair of particles connected by a string of force 386 fm long, you model this as a single mass on a string 193 fm long connected to nothing at the center, thus adding an ad hoc suspension of local conservation of momentum, despite observation of good agreement with conservation laws down to at least scales of 0.001 fm.

Especially since you insist on calling your whirligig a "variety of photon" since photons notoriously don't self-interact strongly, while the nuclear forces have negligible influence over a distance of 193 fm.

10. ### exchemistValued Senior Member

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Excuse me if I take this slowly, starting with my original question.

You say you accept Special Relativity, and yet you postulate an entity with rest mass, moving at c. How can that be possible?

11. ### Richard GauthierRegistered Member

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That's the main point of my original posting -- the derivation of the rest mass/inertial mass m=Eo/c^2 of a resting particle hypothetically composed of a circling photon-like object of energy Eo. IF a photon-like object of energy Eo and vector momentum p=Eo/c CAN move in a circle, it follows from Newton's second law F = dp/dt = ma applied to this circling photon-like object that m = Eo/c^2 is the inertial mass of the circling photon-like object composing the particle, and therefore m=Eo/c^2 is the rest mass (or invariant mass) of the particle. This result (given the hypothesis of a circularly moving photon-like object) should not be surprising since any photon of energy E is in general relativity considered to have inertial mass = gravitational mass = E/c^2 . So if a photon-like object can move in a circle it will still have inertial mass E/c^2 through general relativity . If a photon-like object's energy E equals Eo, the rest energy of a resting particle proposed to be composed of this photon-like object, then this resting particle will have an inertial mass (or rest mass or invariant mass) equal to the photon-like object's inertial mass =Eo/c^2 . This is not in contradiction with current Special Relativity which doesn't recognize (and therefore doesn't have a formula for) photon-like objects moving in a circle and therefore having a rest mass. All photons currently known move linearly (generally speaking) and have zero mass (zero rest mass). The relativistic energy-momentum equation E^2 = p^2 c^2 + m^2 c^4 applies to particles with mass like electrons and to linearly moving photons and gives m=0 for such linearly moving photons since E=pc for linearly moving photons and therefore m=0 for such photons according to the equation. Circularly moving photon-like objects would also have E=pc but would have mass m=E/c^2 because they move in a circle.

So to answer your question, How can that be possible? It can be possible if a photon-like entity having energy E and momentum E/c moves in a circle. Clearly the next question should be: Can a photon-like object move in a circle?

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14. ### rpennerFully WiredValued Senior Member

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How would I categorize it?
A poorly-motivated and unevidenced claim of systemic violation of the quantum field theory of particles (including parts that separately violate special relativity and quantum physics and the locality inherit in a point-particle theory), momentum conservation, angular momentum conservation, observational bounds on the structure of electrons, and (since you insist R varies with longitudinal velocity to keep helical velocity = c) the principle of relativity which is postulated because (so I believe based on reading your posts) the author believes explaining the rest mass of the electron is a problem that needs to be solved and that specifying an conceptual model (with little generalization to other fermions or gauge bosons) where the mass is an input parameter rather than a derived value is a fundamental explanation, both principles I disagree with.​

How would I name it, since I object to the term "a variety of photon"?
Since the model differs from other composite models of the electron in that there is but a single hypothetical component, I would call it a U-quasiparticle, where the "U" stands for both (1) "ur-electron" since you claim it is somehow more fundamental than the electron when QED treats electrons and photons as distinct but without a hierarchy (indeed, in Electroweak theory, the photon is a superposition of force carriers which are distinct before symmetry breaking) and (2) "unbalanced rotor" as you claim the momentum follows a helical path through space-time and quasiparticle because both (1) rather than being bound than existing theories of momentum, quantum physics and special relativity, you wish to cherry pick some algebraic relations derived from those theories without actually working with the content of those theories and (2) you provide no communicable method to make the leap from your hypothetical helical propagation of momentum to precise predictions of new observations of phenomena that depend on the existence of your quasiparticles or R > 0.001 fm.​

https://en.wiktionary.org/wiki/ur-#Prefix
https://en.wikipedia.org/wiki/Electroweak_interaction

An older, distinct idea actually based on quantum field theory of fermions:
https://en.wikipedia.org/wiki/Zitterbewegung
https://en.wikipedia.org/wiki/Foldy...ty_operator_in_the_Dirac-Pauli_representation
(But see the next section)

Last edited: Dec 28, 2016

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16. ### rpennerFully WiredValued Senior Member

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I explained in the next paragraph why λ = 4 π R was incompatible with your assumption that your invention was compatible with quantum mechanics.
Double-looping is not a function of waves in space-time. You have a complex an uncommunicated metaphysical model which you cobble on part by part to try and justify the extraordinary claim that electrons are made of something else but that this something else works according laws which appear alien to any physicist's experience of the behavior of the universe. Double-looping requires that λ = 4 π R ... but also that the complex value of the wave function be double-valued with opposite signs everywhere. Functions cannot be double-valued anywhere. The principle of superposition says that the amplitude of such as wave is uniformly zero. Thus existing physics says your mechanism is fictional. Therefore you have to rewrite all the rules of relativity and quantum mechanics in a way that conforms with experiment just to justify as theoretically sound the unevidenced metaphysical proposition that the electron is a massless whirligig.​
To which you wrote:
In opinion, he's something of an outlier. Yes, his spacetime algebra has seen good application but not all of his interpretations of that algebra stand as uncontroversial. ( See http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/PathsTunnellingAndDiffraction.pdf between eqns 2.12 and 2.13)

Basically Hestenes gets at the geometric content of Dirac's model of the electron at the heart of QED and runs from there. But his approach is motivated by beauty rather than truth and doesn't extend to bosons. QED without photons is boring.

Further, you haven't based your model on his spacetime algebra, but instead a mechanical model incompatible with his spacetime algebra.

Sure they do. $\textrm{phase}(\theta) \propto e^{i \theta / 2} \Rightarrow \textrm{phase}(\theta) + \textrm{phase}(\theta + 2 \pi) = \textrm{phase}(\theta) \times \left( 1 + e^{i \pi} \right) = 0$ Because geometrically, $\theta$ and $\theta + 2 \pi$ describe the same angle.

I disagree because you are not consistent with those rules; take for example your dependence between R and the velocity of the electron which means measuring R in any way tells you absolute velocity.

Such a wavelength is determined because electrons with such-and-such a wavelength interfere even with themselves. So you have the math of phase cancellation working in the two slit experiment and then not working in the assumption of the double-loop.

// Edit: anyway -> any way

Last edited: Dec 28, 2016
17. ### Richard GauthierRegistered Member

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Hi rpenner,

I showed at https://www.academia.edu/25599166/O...ion_in_the_Spin_Charged_Photon_Electron_Model that the relativistic energy-momentum equation for an electron E^2 = p^2 c^2 + m^2 c^4 translates mathematically in my electron model to P^2 = p^2 + (mc)^2 where P=E/c is the total momentum of the helically circulating photon carrying the electron's total energy, p is the longitudinal component of the charged photon's total momentum momentum (which is equal to the relativistic momentum p= gamma mv of the electron being modeled by the helically moving charged photon), and mc (the relativistically invariant momentum of the electron model) is the transverse component of the total momentum P. This Pythagorean relationship of the charged photon's total momentum P and momentum components p and mc implies that the momentum mc (which along with the radius hbar/2mc generates the spin of a resting electron) is always perpendicular to the velocity v and momentum p of the electron so that the derived angular momentum of a nearly resting electron will be either hbar/2 or -hbar/2 i.e. spin up and spin down in relation to the velocity of the electron.

As the velocity of the electron increases, the transverse helical radius R of the helical trajectory decreases as R= Ro/gamma^2 = (hbar/2mc)/gamma^2 as I said before. (Your comment that detecting this decreasing value of R of a moving electron with the electron's increasing velocity would shows the absolute velocity of the electron doesn't makes sense to me since these are all relative velocities.) The helically moving charged photon itself has spin 1/2 (which doesn't contribute significantly to the electron model's longitudinal spin component at very slow electron speeds when the charged photon's trajectory is nearly circular and the electron model's spin is due to mc x Ro = hbar/2). As the electron model's velocity increases, the longitudinal component of the spin 1/2 of the helically circulating charged photon comes to dominate the decreasing contribution to the longitudinal spin component due to mc times the decreasing double-looped helical radius Ro/gamma^2 . So the electron model will also have spin 1/2 even at highly relativistic velocities since the longitudinal component of the helically-moving spin-1/2 photon's spin approaches 1/2 hbar as the angular direction theta of the charged photon's velocity approaches 0 degrees (due to cos(theta) = v/c approaching 1 at highly relativistic velocities.) An actual electron has experimentally measured spin 1/2 (or -1/2) at all velocities. This match of the electron model's calculated spin 1/2 to an actual electron's spin 1/2 at both slow velocities and highly relativistic velocities is the best spin match to an actual electron that I have at the moment. Ideally a good spin-1/2 charged-photon electron model will have spin 1/2 at intermediate velocities as well.

Academia.edu is not a peer-reviewed site, but is a way to publish alternative physics articles which gives them registered publication dates and as well as access to interested readers for their possible comments. I recommend it to other readers, as well as researchgate.net which I also use.

18. ### rpennerFully WiredValued Senior Member

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My point, which you didn't pick up on, is that if the orbital spin is 1/2 and the ur-electron itself has intrinsic spin 1/2 then the angular momentum of the system is either 1 (spins aligned) or 0 (spins anti-aligned) with no other cases.

You also seem to not pick up on that you claim R and the mean velocity of the electron are perpendicular but that Lorentz length contraction doesn't affect lengths parallel to motion. So if R is dependent on the mean velocity of the electron and largest when that velocity is zero. So if we beam electrons with all different velocities but all parallel to a chosen axis, one of them must have the largest R. And if the observer changes his state of motion parallel to R, that same electron will still have the largest R thus showing that its a function of absolute, not relative velocity (or that you have otherwise re-written the law of Special Relativity). Repeating along other axes quickly establishes what absolute rest is in your model.

“In mathematics we do not appeal to authority, but rather you are responsible for what you believe.”
-Richard Hamming, American Math Monthly @ vol 105 no 7​

“A scientific theory is a communicable framework for describing precisely the observable behavior of a large class of related phenomena.”
-Me, often.​

tl;dr

If $\lambda_0 = \frac{h}{m_e c}$ and $R_0 = \frac{\lambda_0}{4 \pi}$ and $v_{\parallel}$ is the mean absolute velocity of the electron, and $\gamma \equiv \left( 1 - \frac{v_{\parallel}^2}{c^2} \right)^{-1/2} \geq 1$ and $R(v_{\parallel}) = R_0 \left( 1 - \frac{v_{\parallel}^2}{c^2} \right) = R_0 \gamma^{-2}$ and the helical motion is at constant speed c, then it follows that the velocity component perpendicular to $v_{\parallel}$ is $v_{\perp}(v_{\parallel}) = \sqrt{c^2 - v_{\parallel}^2} = c \sqrt{1 - \frac{v_{\parallel}^2}{c^2}} = c \gamma^{-1}$.

Thus the angular velocity is $\omega(v_{\parallel}) = \frac{v_{\perp}(v_{\parallel})}{R(v_{\parallel})} = \frac{c}{R_0} \left( 1 - \frac{v_{\parallel}^2}{c^2} \right)^{-1/2} = \gamma \omega_0 = \gamma \frac{c}{R_0} = \gamma \frac{4 \pi c}{\lambda_0} = \frac{4 \pi \gamma m_e c^2}{h}$. In other words, the higher the velocity, the higher the angular speed, but in a way incompatible with the deBroglie relation $E = \frac{h}{2 \pi} \omega$ which would give $\color{red} { E(v_{\parallel}) = 2 \gamma m_e c^2 }$.

Now if $p_{\perp}(v_{\parallel}) R(v_{\parallel}) = \frac{h}{4 \pi}$ (conservation of angular momentum) then $p_{\perp}(v_{\parallel}) = m_e c \left( 1 - \frac{v_{\parallel}^2}{c^2} \right)^{-1} = \gamma^2 m_e c$ and if $c \sqrt{p_{\perp}^2 + p_{\parallel}^2} = E = \gamma m_e c^2$ then it follows that $\color{red} {p_{\parallel}(v_{\parallel}) = \sqrt{ 1 - \gamma^2 } \gamma m_e c = i \gamma^2 m_e v_{\parallel} }$, which is another problem.

The physical theories of special relativity and quantum mechanics are mathematical, thus rigid and unforgiving about misuse. Your postulates are incompatible with this mathematical framework.

Revisit. If $R = R_0 \gamma^{\alpha}$ then $p_{\perp} = m_e c \gamma^{-\alpha}$, $p_{\parallel} = \sqrt{ \gamma^2 - \gamma^{-2\alpha} } m_e c$ the last equation of which requires $\alpha = 0$ to be compatible with special relativity.

Last edited: Dec 29, 2016
19. ### hansdaValued Senior Member

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Can you still get your paper published in a peer-reviewed journal?

20. ### rpennerFully WiredValued Senior Member

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Reading his CV, he has been shopping versions of this model around the presentation circuit since 2003, and according to one source has been exploring helices as particle models since 1993 but still has no articles published in journals.

However, since he presented something, he is included in
• American Physical Society, APS April Meeting, April 22-26, 2006
• 2009 APS April Meeting Volume 54, Number 4
• The Physics of Reality: Space, Time, Matter, Cosmos : Proceedings of the 8th Symposium Honoring Mathematical Physicist Jean-Pierre Vigier, Covent Garden, London, UK, 15 -18 August 2012
• APS April Meeting 2015
• Unified Field Mechanics: Natural Science Beyond the Veil of SpacetimeProceedings of the IX Symposium Honoring Noted French Mathematical Physicist Jean-Pierre Vigier, 2016
Vanity-/self- published in
So the problem isn't that his ideas aren't out there to find, but that his peers for the most part don't think his work is both correct and interesting enough to refer to.

Cited in
• The Spacetime Origin Of the Universe With Visible Dark Matter & Energy Vladimir Ginzburg 2015, pp. 43-46.
• Hu, Huping and Wu, Maoxin (2008) “Concerning Spin as Mind-pixel: How Mind Interacts with the Brain through Electric Spin Effects. ” (likewise https://arxiv.org/abs/quant-ph/0208068 )
• “Quantum Complex Matter Space” International Journal of Theoretical and Mathematical Physics 2014; 4(4): 159-163
• Akande, R.O. & Oyewande, E.O. Int Nano Lett (2016) 6: 243 (very weird cite)
and I think at least double that number of self-cites, but it's hard to count his papers as many have similar titles.

Listed in
• The Worldwide List of Dissidents Scientists: Critics and alternative theories
There seems to be some cross-pollination with Farsight (some very familiar looking pictures, similarly skilled at responding to fact-based criticism). Because he is not letting the behavior of phenomena be the judge of what ideas he accepts as worthy of repeating, he is not advancing the frontiers of science. His motivations seem murky in that his claim that he is only trying to "explain" electron mass when he introduces it as a free parameter in his model doesn't hold water. His fixation on electrons as somehow less "fundamental" than photons seems based on nothing, while his ignoring the other particles and interactions of the standard model of particle physics seems oddly parochial in that humans almost never encounter single-electron phenomena so it behooves one to learn the details of modern physical theory of the electron and its relations to other particles before attempting to expand the frontiers of physics.

danshawen and hansda like this.
21. ### hansdaValued Senior Member

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2,424
You consider 'a resting electron is composed of a circling photon-like object'. If the electron spins, what will be the resultant speed of this photon-like object?

danshawen likes this.
22. ### danshawenValued Senior Member

Messages:
3,950
Evidently this poster is responsible also for this:

http://www.superluminalquantum.org

"The electron’s TEQ quantum moves superluminally 57% of the time and subluminally 43% of the time in a closed helical trajectory."

Would you mind explaining where these probability densities for the velocity of the luminal or superluminal energy of the came from, other than subtraction from a certainty of 1 for the complementary one? Is the same photon both luminal/superluminal? Why can't the energy be superluminal 100% of the TIME? Photons don't have charge, so what is the reason a superluminal photon does?

TEQ evidently means "Transluminal Energy Quantum".

I like some aspects of this idea, specifically that the quantum spin of the structure is superluminal. But the structure is too simple to work, and I don't get how something that is superluminal to begin with can slow down to luminal or subliminal, or how the whole electron may also have relative motion with respect to other electrons in this model. Composite spins are evidently needed, and we don't yet have the means of probing this domain, particularly in the case of electrons. No mention of relativity's time dilation at all. How does that work with superluminal energy, exactly? More dilation, less dilation, what? What is entanglement, exactly, and how fast is that?

I seem to remember getting lambasted here for an idea similar to your M = Eo/c^2 idea, and rightly so. Good luck with that one.

23. ### Richard GauthierRegistered Member

Messages:
36
Hello rpenner,

The first mistake you make is incorrectly assuming that the orbital rotational angular frequency omega w in my double looping resting electron is given by hbar w = mc^2 . The double-looping orbital rotational angular frequency w in the resting electron model is the zitterbewegung (from the Dirac equation) electron angular frequency w-zitt =2mc^2/hbar. This w-zitt (due to the double looping of the charged photon in the electron model for each photon wavelength) is twice the angular frequency Wo corresponding to the actual resting energy of the electron where hbar Wo=mc^2 . The angular frequency Wo corresponds to the photon's actual frequency of fo = Wo/2pi given by hfo=mc^2, or fo=mc^2/h , which is half the zitterbewegung frequency f-zitt=2mc^2/h. When you use the actual photon frequency fo of the circling photon in the resting electron and f=gamma fo for the frequency of the helically moving photon in the moving electron, the energy E=hf of the helically circulating photon that corresponds to an electron moving with velocity v comes out E = hf = gamma mc^2 and not E=2gamma mc^2 as you incorrectly calculated. So the energy of the helically circulating photon IS compatible with the de Broglie energy relation E=hf=gamma mc^2. In fact, I started with this de Broglie energy relation E=hf=gamma mc^2 to determine the frequency f of the helically circulating photon in the moving electron model. The photon's looping frequency (as in the resting electron model) continues to be twice the photon's actual frequency f as the photon frequency increases with photon energy with higher electron speed. But note that the wavelength lambda of the helically circulating photon decreases as lambda = Lambda-compton/gamma =(h/mc)/gamma as the frequency f of the circulating photon increases as f=gamma fo (since lambda f = c , the speed of the helically circulating photon .) This decreasing photon wavelength lambda with increasing photon frequency f combine to force the radius R of the helical trajectory of the helically moving photon to decrease as R=Ro/gamma^2

Then, when you assume conservation of angular momentum for the orbital angular momentum in my model, you are forgetting about the increasing contribution to the total longitudinal spin of the moving electron model from the helically circulating spin 1/2 charged photon as the speed of the electron model increases. The orbital angular momentum contribution R x p-trans to the electron model's total longitudinal spin component decreases with increasing electron speed (since R decreases with increasing electron speed as Ro/gamma^2 while the circling transverse momentum component p-trans=mc remains constant with increasing electron speed.) But the longitudinal spin component from the helically circulating spin 1/2 charged photon (this longitudinal spin component is zero for electron speed v => 0) increases with increasing electron speed since the photon's forward helical angle theta decreases as cos(theta)= v/c as the electron model's speed increases. So the electron model COULD maintain a total longitudinal spin component of 1/2 hbar at increasing electron speeds when the orbital and spin components are added together. Currently my model doesn't show a calculated longitudinal spin 1/2 at all electron velocities, but it has spin 1/2 hbar (from its double-looping orbital spin) at very low velocities and also spin 1/2 hbar (from the spin 1/2 of the charged photon) at highly relativistic velocities, which I think is not so bad for now.