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
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"
Alot like Blood, Polynuclear slow shell decay.
It is crucial to understand size of electron here - while "everybody knows that electron is point-like", I have spent a few days to find experimental evidence to bound its size ... and literally nothing.
There is usually referenced Dehmelt's paper extrapolating from g-factor by fitting parabola to two points (seriously!): composed of 3 fermions (proton and triton), concluding for electron as composed of 3 fermions.
Cross-section for electron-positron collisions can be naively interpreted as area of particle. The question is: cross-section for which energy should we use? As we are interested in size of resting electron, to rescale Lorentz contraction we should extrapolate to gamma=1, but it suggests huge ~2fm radius.
Some discussions with images and formulas:
https://www.scienceforums.net/…ies-for-size-of-electron/
https://physics.stackexchange.…ries-for-size-of-electron
https://www.reddit.com/r/AskPh…ies_for_size_of_electron/
Is there a single experiment really bounding the size of electron????
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.
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.
Please elaborate - I couldn't find any details in this link? ... Or previously looking through literature for a few days ... or trying to discuss it in a few forums.
Sure, Wikipedia points Dehmelts 1988 paper with e.g. 10^-22 m ( http://iopscience.iop.org/arti…031-8949/1988/T22/016/pdf ) - figure on the left below.
As we can see, he took two particles composed of 3 fermions (proton and triton) and fitted parabola to these two points (!) - to get r = 0 for g=0 for electron built of three smaller fermions ... what allowed him to conclude these tiny sizes ... but it's "proof" by assuming the thesis.
Additionally, while g-factor is said to 1 classically, it is for assuming equal density of mass and charge - without this assumption we can get any g by changing mass/charge distribution - see formula in one of these links with longer explanations, e.g. https://www.scienceforums.net/…ies-for-size-of-electron/
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?
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^{-19}m 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?
I assume you mean electron size at the lowest possible speed?
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/
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?
Could stable pseudo-slits be made by (a series of) calibrated interference of alternating high frequency magnetic fields?
(A magnetic field grate)
Could stable pseudo-slits be made by (a series of) calibrated interference of alternating high frequency magnetic fields?
(A magnetic field grate)
Sounds like optical lattice ( https://en.wikipedia.org/wiki/Optical_lattice ) - made by laser beams ... but I don't think you could test electron size this way - they are light and repulse each other.
Display MoreBy 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/
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?
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.
Exactly, as this Feynman's lecture says: "the dependence on E is uniquely determined by dimensional analysis", getting sigma ~ 1/E^2.
This is the line I was referring to.
We are interested in size of non-Lorentz-contracted electron, so we need to extrapolate this sigma ~ 1/E^2 line to energy of non-Lorentz-contracted electron, getting sigma ~ 100mb, or ~2fm size.
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.
511keV is just rest mass of electron - required e.g. to build it from photons (EM waves) during pair creation.
Hence, energy conservation doesn't allow energy of electric field of electron to exceed 511 keVs.
However, naive E ~ 1/r^2 assumption for point charge has infinite energy if integrating from r=0.
We would get 511keV from energy of E ~ 1/r^2 electric field if integrating from r~1.4fm.
Hence, energy conservation alone requires some femtometer scale modification of E ~ 1/r^2 electric field around electron.
Is there experimental evidence forbidding deformation/regularization in this scale? (doesn't need e.g. 3 smaller fermions or electric dipole)
The main problem with discussing dynamics of electrons below the probability clouds is the general belief that violation of Bell inequalities forbids us using such local and realistic models.
While the original Bell inequality might leave some hope for violation, here is one which seems completely impossible to violate - for three binary variables A,B,C:
Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1
It has obvious intuitive proof: drawing three coins, at least two of them need to give the same value.
Alternatively, choosing any probability distribution pABC among these 2^3=8 possibilities, we have:
Pr(A=B) = p000 + p001 + p110 + p111 ...
Pr(A=B) + Pr(A=C) + Pr(B=C) = 1 + 2 p000 + 2 p111
... however, it is violated in QM, see e.g. page 9 here: http://www.theory.caltech.edu/…ill/ph229/notes/chap4.pdf
If we want to understand why our physics violates Bell inequalities, the above one seems the best to work on as the simplest and having absolutely obvious proof.
QM uses Born rules for this violation:
1) Intuitively: probability of union of disjoint events is sum of their probabilities: pAB? = pAB0 + pAB1, leading to above inequality.
2) Born rule: probability of union of disjoint events is proportional to square of sum of their amplitudes: pAB? ~ (psiAB0 + psiAB1)^2
Such Born rule allows to violate this inequality to 3/5 < 1 by using psi000=psi111=0, psi001=psi010=psi011=psi100=psi101=psi110 > 0.
I have just refreshed https://arxiv.org/pdf/0910.2724 adding section III about violation of this inequality using ensemble of trajectories: that proper statistical physics shouldn't see particles as just points, but rather as their trajectories to consider e.g. Boltzmann ensemble - it is in Feynman's Euclidean path integrals or its thermodynamical analogue: MERW (Maximal Entropy Random Walk: https://en.wikipedia.org/wiki/Maximal_entropy_random_walk ).
For example looking at [0,1] infinite potential well, standard random walk predicts rho=1 uniform probability density, while QM and uniform ensemble of trajectories predict different rho~sin^2 with localization, and the square like in Born rules has clear interpretation:
Considering ensembles (uniform, Boltzmann) of paths also allows to violate Bell in similar as QM way (through Born rules) - this is realistic model, and in fact required if we e.g. think of general relativity: where we need to consider entire spcatime, particles are their paths.
It is not local in "evolving 3D" picture, but it is local in 4D spacetime/Einstein's block universe view - where particles are their trajectories, ensembles of such objects we should consider.
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.
measured mass | 1'876'123'941.563 |
measured mass CODATA deuteron + e | 1'876'123'955.206 |
delta particle CODATA mass | 13.643 |
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?
Wyttenbach , 13.6eV is Rydberg constant - energy difference comes from Coulomb potential.
Potential energy is negative: deuteron + electron -> deuterium + 13.6eV