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

rpenner said:
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.
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Hello rpenner,

While quantum field theory has been extremely successful, we should remember that what I am describing is a proposal for a description at the sub-quantum level so it is not necessarily expected to immediately make different experimental predictions from those of quantum field theory. Then you might ask, what is the value of my approach? One possible answer is that in at least one area of application, quantum field theory apparently makes a very poor prediction. From Wikileaks:Cosmological Constant

"A major outstanding problem is that most quantum field theories predict a huge value for the quantum vacuum. A common assumption is that the quantum vacuum is equivalent to the cosmological constant. Although no theory exists that supports this assumption, arguments can be made in its favor.[16]

Such arguments are usually based on dimensional analysis and effective field theory. If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of
c4a13a837504c0f5c61eda73a8ed107f4374c10e
. As noted above, the measured cosmological constant is smaller than this by a factor of 10−120. This discrepancy has been called "the worst theoretical prediction in the history of physics!".[17] "

My article on the hypothetical cosmic quantum, at https://www.academia.edu/4429777/A_Transluminal_Energy_Quantum_Model_of_the_Cosmic_Quantum, is based on my transluminal energy quantum approach to modeling fundamental particles and predicts that our universe may have arisen from a single quantum dark matter boson with zero entropy. It also predicts two varieties of hypothetical dark matter WIMPs-- a boson and a fermion. Since dark matter apparently existed in our very early universe, my hypothesis could at least be plausible and worthy of a further look.
 
Richard Gauthier said:
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.
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We know that a resting electron will be having an electrical field surrounding the electron. https://en.wikipedia.org/wiki/Electric_field

In your model of 'resting electron', how will be this electrical field?
 
hansda said:
We know that a resting electron will be having an electrical field surrounding the electron. https://en.wikipedia.org/wiki/Electric_field

In your model of 'resting electron', how will be this electrical field?
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Hello hansda,

Thanks for your question. In partial response I'll give a quote from physics nobelist Frank Wilczek's article "The Enigmatic Electron" which is available at http://www3.nd.edu/~djena/ee687/nature13_wilczek_electron.pdf . He's referring the electron's magnetic field, but the same idea would apply to its electric field:
"A crude but appealing 'explanation' of the origin of the electron's magnetic field is that quantum uncertainty in position smears the electron's charge over a volume, which rotates because of the electron's spin. The electron is effectively a spinning ball of charge, and elementary electromagnetism tells us that this generates a magnetic-dipole field. The size of that ball can be estimated to roughly 2.4 x 10^-12 meters. {i.e. the Compton wavelength h/mc, as in my electron model -- Richard}. Attempts to pin down an electron's position more accurately than this require, according to the uncertainty principle, injecting the electron with so much energy that extra electrons and anti-electrons are produced, confusing the identity of the original electron."

So the electron's electric field in this "crude but appealing explanation" and in my spin-1/2 charged photon model would be the same down to a distance from the electron of roughly one Compton wavelength, at which distance measurements of the position of an actual electron (and therefore the strength and direction of its electric field) become less meaningful due to the Heisenberg uncertainty principle. In my electron model the variabilities of the position and momentum components delta X and delta Px of the circling spin-1/2 charged photon correspond to the variabilities delta X and delta Px in the electron's position and momentum components given by the Heisenberg uncertainty principle, i.e. delta X * delta Px >= hbar/2 .

Richard
 
Hello hansda,
In fact, for the basic double-looping-spin-1/2 charged-photon electron model of circular trajectory radius Ro=hbar/2mc and circling momentum p=mc, the product delta X * delta Px = Xrms * Px rms= Ro/sqrt(2) * mc/sqrt(2) = (hbar/2mc) * mc /2 = hbar/4 which is just half of the value given in the Heisenberg uncertainty relation delta X * delta Px >or= hbar/2 . Since hbar/4 is half of the minimum uncertainty relation value hbar/2 , it could be argued that the double-looped spin-1/2 charged photon model of the electron cannot be experimentally detected if the Heisenberg uncertainty relation is correct. But virtual particles like virtual photons also lie below the Heisenberg uncertainty relation: delta E * delta t < hbar/2 for virtual photons, and virtual photons are still considered to be physically 'real', i.e have physical effects like mediating Coulomb attraction between two electric charges, according to quantum field theory. The spin-1/2 charged photon model can be 'detected' indirectly because of the experimental inertial mass m=Eo/c^2 of the electron that can be derived from the spin-1/2 charged-photon model of the electron. Otherwise the origin of inertial mass is still (arguably) unexplained (despite the Higgs field).
Richard
 
Richard Gauthier said:
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
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I wonder if your theory has some predictions which are different to recent mainstream theories and if yes, can it be tested/falsified?
 
Ultron said:
I wonder if your theory has some predictions which are different to recent mainstream theories and if yes, can it be tested/falsified?
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Hello Ultron,
Yes, I wonder that also. I think my spin 1/2 charged photon approach to modeling the electron could help explain why the non-relativistic Schroedinger equation works, as is suggested in my article https://www.academia.edu/10235164/T...of_the_Electron_Fits_the_Schrödinger_Equation . The spin 1/2 charged photon model also has some resemblances to the Dirac Equation solution for a freely moving electron. But I think that further work needs to be done. I think my proposal of a transluminal energy quantum (TEQ) composing photons, electrons and other particles might open up some new ways this approach can be tested experimentally. Plus there are several cosmological predictions that developed from this approach, such as the cosmic quantum as the proposed first particle of our universe.
Richard
 
Richard Gauthier said:
What if a fundamental particle like a resting electron
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An electron may not be "at rest" any more than a photon. Even in its ground state in atomic structure, an electron can never be "at rest".

According to quantum physics, if an electron is ever at rest, its waveform collapses and it ceases to exist as an electron locally.

Or to put it another way, the Uncertainty Principle tells us that if an electron is ever "at rest" (a fixed "position"), then its momentum will be such that it will require a very, very large box to contain it.

Or to put it still another (original) way, if an electron is capable of being at rest, it must emit a photon with a wavelength that exceeds the bounds of the known universe in order to achieve that lower energy state. Got it?

I stopped reading your OP at that point. Sorry. Hope you liked the rest of the nice folks here.
 
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