Another preprint on greatly enhanced pair-production by tailored electric fields --

Assisted Vacuum Decay by Time Dependent Electric Fields

https://arxiv.org/abs/1801.09943

"In a recent paper published in JCMNS 2017, Celani et al. argued that Maxwell equations rewritten in Clifford algebra are sufficient to describe electron and also ultra-dense deuterium reaction process as proposed by Homlid et al. Apparently, Celani et al. believedthat their Maxwell-Clifford equations are quite excellent candidate to surpass both ClassicalElectromagnetic and Zitterbewegung QM. However, in a series of papers, Bo Lehnert proposed anovel and revised version of Quantum Electrodynamics (RQED) based on Proca equations. It ishoped that this paper may stimulate further investigations and experiments in particular for finding physics of LENR and UDD reaction from classical electromagnetics"

Lehnert's Revised Quantum Electrodynamics as Alternative to Celani's et al's Maxwell-Clifford equations: Towards a New Approach to LENR and Ultra-dense Deuterium Fusion

Alot like Blood, Polynuclear slow shell decay.

The size of the electron is an interesting topic.

Here is an informed summary of the experimental evidence: http://www.pbs.org/wgbh/nova/b…14/10/smaller-than-small/

All we can say is that no evidence of finite size has yet been seen, and that bounds size to 10^-19 m or so.

Another way of looking at it is this. As normally seen, at atomic scale, electrons are delocalised and have a large size. To squish them down to something smaller you need higher momentum because delataP.deltaX is bounded so for small deltaX you need large deltaP. Large momentum implies large energy and hence the best controlled evidence for squished electrons comes from the LHC at the moment (there is also less controlled evidence from GCRs (galactic cosmic rays) which can be higher energy than LHC but naturally are difficult to observe precisely!).

Once you have enough energy in a collision to allow the "inherent" electron size to be seen then - if it has an inherent size - this shows up as behaviour different from the point particle ideal.

Thus far both quarks and electrons have no known size, and (equivalently) no known internal structure. That is because as soon as you can observe that a particle has some finite size you can ask what is its internal structure - and test structures to see whether they give the correct size and other behaviours.

One motivation for going to bigger collider energies, as with the LHC, is that at higher energies such internal structure might be revealed. Alas for the LHC (which has so far been profoundly uninteresting for theoretical physics) no such structure has yet been disovered. There is the chance that more will be uncovered about the properties of the Higgs boson however.

Quote from Jarek

we are interested in size of resting electron

I assume you mean electron size at the lowest possible speed?

If we model the electron as a two dimensional flux of magnetic field lines, then is difficult to see a border/size. (Magnet fields expand to infinity) As soon as you add energy (motion) to an electron it slightly expands into a third mass-like dimension. According Mills calc this boarder (Schwarzschild radius) starts at 10e-57 meters. Now you see the problem: A mass function/interaction gives you a point mass, but a magnetic/electric interaction size depends on the type(force) of measurement.

In my opinion the only interesting point in the electron case is the de Broglie/Compton radius. All other sizes are of virtual nature and problem/measurement dependent.

On the right we can see cross-section for electron-positron collision.

Naively we would like to interpret cross-section as area of particle - the question is: cross-section for which energy should we use?

As there is Lorentz-contraction affecting the collision, and we are interested in size of resting electron, we should extrapolate the line without resonances (sigma ~ 1/E^2) to gamma=1 resting electron ... this way we get r ~ 2fm for electron.

Can you defend Dehmelt's fitting parabola to two points?

Or maybe you know some other experimental evidence for e.g. these 10^-19m radius?

It is the other way round. There is no evidence for internal structure at radius > 10^-19m or so. That figure comes from the momentum bounds of well-observed collisions. Which does not prove radius is 10^-19 m at all, merely that if electrons are not point particles they are smaller than that bound.

It is also obvious that no experiments at lower momenta than this can ever hope to establish electron size, since quantum effects delocalise the electron, hence anhiliation data except at very high momenta could not do this.

To validate these figures, we have in fact a limit of lower than this from the LHC if you assume that all of the collision energy (13TeV max) could be electron momentum. In reality that will not be true so 10^-19 m (10X larger than the 10^-20 m limit from QM) looks a reasonable ball pack figure: or at least something around this. . All figures SI except for final energy in eV.

You can be sure that if any evidence of electron size existed from collider statistics it would be big news, hence the limit is safe. (perhaps some uncertainty in how much of the available collision energy could become electron energy as is needed to probe small sizes).

Ballpark figures:

Perhaps this is a naive question, but could the slow electron size be estimated/extrapolated by double-slit experiments, changing the slit size, slit displacement, and electron speeds, and comparing the interference patterns? Probably this has been done?

Could stable pseudo-slits be made by (a series of) calibrated interference of alternating high frequency magnetic fields?

(A magnetic field grate)

Quote from Jarek

By resting I have meant just not Lorentz contracted (gamma=1, v=0), what affects the size we are interested in.

@ THHuxleynew,

Regarding requirements for electron size, the energy of electric field E ~ 1/r^2 is infinity if integrating from r=0.

In pair creation field of electron-positron is created from 2 x 511keV EM radiation - energy of electric field cannot exceed 511keV - for this purpose we would need to integrate from r~1.4fm instead of 0.

So energy conservation requires to deform electric field on femtometer scale - no 3 smaller fermions as Dehmelt writes, no electric dipole, just deformation of E~1/r^2 electric field not to exceed 511keV energy.

Regarding collision evidence, I have put plot for GeV-scale electron-positron collision cross-section in my previous post.

Interpreting it, we need to have in mind that there is enormous Lorentz contraction there, e.g. gamma ~ 1000 for 1GeV.

We are not interested in size of 1000-fold contracted electron, but of a resting electron (gamma=1).

Extrapolating line (no resonances) in that plot to gamma=1 resting electron, you get ~100mb cross-section, corresponding to r ~ 2fm.

See discussion exactly about it: https://www.scienceforums.net/…ies-for-size-of-electron/

@Paradigmnoia

In double-slit experiment we have material built of ~10^-10m size atoms - huge comparing to e.g. ~10^-15m scale deformation of electric field required not to exceed 511keVs.
Maybe behavior of positronium would allow for some boundaries for size of electron?

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Jarek - there is no physical basis that I know for that extrapolation.

The de Broglie wavelength scales as 1/E^2 - and this is what we would expect to be relevant from QM considerations as well as dimensional analysis.

https://physics.weber.edu/schroeder/feynman/feynman3.pdf

Further, as in the above link, calculations for electron as point particle correctly predict cross section (both energy and angular dependence) at these energies.

Quote from Jarek

In pair creation field of electron-positron is created from 2 x 511keV EM radiation - energy of electric field cannot exceed 511keV

My understanding is that pair creation always has a finite cross section. Electrons are sometimes used as nuclear probes and can have far, far above 511 keV kinetic energy. (E.g., in the GeV range.) I'm probably misunderstanding what you have in mind with the 511 keV limit you're suggesting.

Jarek : Two days ago I made an interesting find: If you look at the CODATA deuterium ion mass (= deuteron) and add one electron mass

then we notice an excess of 13.643eV compared to the measurement of the bound Deuterium.

This implies, either the orbiting electron looses mass, or the rest field goes into the mass difference.

In the later case this would imply that an electron approaching the nucleus would lead to a mass reduction of the nucleus. May be Jarek knows whether this only happens for regular orbits?