Electron-assisted fusion

  • "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

  • 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/


    zDixmml.png


    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 > 10-19m 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?

  • 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/


    @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?


  • 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:

    born_res.png

    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?

  • Jarek : This summary is correct. But the problem is much deeper. If we assume that the energy comes from the proton field only, then we have an asymmetry. Why should only the proton (deuteron) feel the potential mass (27.2eV) loss?


    The proton - electron system has COM very close to the proton, since electron is so much lighter. It is the system which has this P.E. mass - but realistically that approximates well the proton.


    QM is profoundly different from local models. You cannot get out of this, and it comes from experiment not theory.


    Of course the idea of locality, which we are fixated on, does not apply naturally in a quantum domain. That has profound consequences for the structure of spacetime - it is just that we have as yet not properly worked out the connections!

  • QM is profoundly different from local models. You cannot get out of this, and it comes from experiment not theory.


    Of course the idea of locality, which we are fixated on, does not apply naturally in a quantum domain. That has profound consequences for the structure of spacetime - it is just that we have as yet not properly worked out the connections!


    You are saying that if proton and electron are far apart they are "classical" corpuscular ... but when they meet they became "quantum" wave-like ... so in which moment/distance this switch happens?

    Where exactly is the classical-quantum boundary?


    Do we really need such switch? - maybe they are both at the time. Like in popular Couder's walking droplets with wave-particle duality (Veritasium video with 2.5M views, great webpage with materials and videos, a lecture by Couder, my slides also with other hydrodynamical analogues: Casimir, Aharnonov-Bohm). Among others, they claim to recreate:

    1. Interference in particle statistics of double-slit experiment (PRL 2006) - corpuscle travels one path, but its "pilot wave" travels all paths - affecting trajectory of corpuscle (measured by detectors).
    2. Unpredictable tunneling (PRL 2009) due to complicated state of the field ("memory"), depending on the history - they observe exponential drop of probability to cross a barrier with its width.
    3. Landau orbit quantization (PNAS 2010) - using rotation and Coriolis force as analog of magnetic field and Lorentz force (Michael Berry 1980). The intuition is that the clock has to find a resonance with the field to make it a standing wave (e.g. described by Schrödinger's equation).
    4. Zeeman-like level splitting (PRL 2012) - quantized orbits split proportionally to applied rotation speed (with sign).
    5. Double quantization in harmonic potential (Nature 2014) - of separately both radius (instead of standard: energy) and angular momentum. E.g. n=2 state switches between m=2 oval and m=0 lemniscate of 0 angular momentum.
    6. Recreating eigenstate form statistics of a walker's trajectories (PRE 2013).

    This way QM is just one of two perspectives/descriptions of the same system, what we already had in coupled oscillators, or their lattices: crystals, which can be described classically or through normal/Fourier modes - treated as real particles in QFT ...


    1MUFTXu.png

  • You are saying that if proton and electron are far apart they are "classical" corpuscular ... but when they meet they became "quantum" wave-like ... so in which moment/distance this switch happens?

    Where exactly is the classical-quantum boundary?


    No i'm not saying that. And agree with you that no boundary is needed. Trivially, if you use Many Worlds interpretation (or a few variants thereof) there is no waveform collapse and therefore no need to distinguish. Both classical and quantum results emerge from the same maths in different domains.


    Specifically, particles are described (in a spatial basis) as wave packets and have both particulate and wave aspects, with position and momentum uncertainty emerging naturally from this.

  • Particle like electron is more than just a wave packet - it is among others stable localized configuration (nearly singular) of electric and magnetic field:

    xAKaQQl.png


    It doesn't loose these localized properties when approaching a proton to form an atom - becoming huge probability cloud of quantum orbital - this is proper but only effective description, averaging over some hidden dynamics.

    They can perform real acrobatics on magnetic dipoles of these electron, like Larmor precession or even spin echo: https://en.wikipedia.org/wiki/…on_paramagnetic_resonance

    GWM_HahnEchoDecay.gif


    Coupled wave created by internal clock of electron (de Broglie's, zitterbewegung, experimental confirmation: https://link.springer.com/article/10.1007/s10701-008-9225-1 ) has to become standing wave to minimize energy of atom - described by Schrodinger, giving quantization condition. It is nicely seen in Couder's walking droplet quantization, nice videos.


    If lenr is possible, there is needed a non-thermal way to overcome the huge Coulomb barrier between nuclei - the only mechanism I could imagine is (localized) localized electron staying between nucleus and proton due to attraction - screening their repulsion.

  • Not sure this is the correct thread, but I have a basic QM question about virtual particles. From Wikipedia, "Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. " From Gordon Kane, director of the Michigan Center for Theoretical Physics at the University of Michigan at Ann Arborhttp://www.scientificamerican.…re-virtual-particles-rea/

    the quote from "Quantum mechanics allows, and indeed requires, temporary violations of conservation of energy". I fail to see how this is a well understood theory if two different experts say the opposite thing. I understand how with the uncertainty principle that position and momentum can not be known together at infinite precision, but yes or no, do these particles obey conservation of energy? That should be an easy qustion to answer without handwaving. Thanks if you can clear it up. The reason it came up in my mind was Rossi's probably ridiculous claim that his ecat power was from virtual particles annihilating or something to that effect. And I was wondering how these virtual particles could possibly violate COE.

  • I am not aware of any evidence for violation of energy or momentum conservation - they are at heart of Lagrangian mechanics we successfully use from QFT to GRT.


    Regarding virtual particles - they are used in Feynman diagrams in perturbative approximation of QFT - assuming QFT is fundamental, perturbative QFT/Feynman diagrams is still an effective picture - practical approximation ... leading to countless number of divergences, usually removed by hand.

    But it is extremely universal practical tool defining objects as point particles through their interactions - it is very general algebra on particle-like objects ... like algebra properly concluding that "apple + apple = two apples" without any insights what apple is ... which can also handle non-point objects like fields by approximating them with a series of virtual particles.


    The basic example is Coulomb interaction e.g. proton - electron, which in pertubative (approximation of) QFT is handled with a series of point-like photons, instead of continuous EM field.

    It brought dangerous common misconception that EM field is always quantized, while it is just a continuous field, which optical photons are quantized due to discrete atomic energy levels ... but e.g. linear antenna produces cylindrically symmetric EM radiation - which energy density drops like 1/r to 0 - cannot be quantized to individual discrete photons localizing finite portions of energy.


    We have lots of quasi-paricles especially in solid state physics - starting with phonons: classically just Fourier/normal modes of the lattices, but perturbatve QFT treats them as real particles ... point-like.
    There is also virtual pair creation - while we imagine pair creation as a zero-one process, it is in fact continuous - field can perform a tiny step toward pair creation, represented as real (virtual) pair creation in perturbative QFT. Continuity of this process is nicely seen using topological charge as charge:

  • Electron Structure, Ultra-Dense Hydrogen and Low Energy Nuclear Reactions


    Abstract:

    In this paper, a simple Zitterbewegung electron model, proposed in a previous work, is presented from a different perspective that does not require advanced mathematical concepts. A geometric-electromagnetic interpretation of mass, relativistic mass, De Broglie wavelength, Proca, Klein-Gordon and Aharonov-Bohm equations in agreement with the model is proposed. Starting from the key concept of mass-frequency equivalence a non-relativistic interpretation of the 3.7 keV deep hydrogen level found by J. Naudts is presented. According to this perspective, ultra-dense hydrogen can be conceived as a coherent chain of bosonic electrons with protons or deuterons at center of their Zitterbewegung orbits. The paper ends with some examples of the possible role of ultra-dense hydrogen in some aneutronic low energy nuclear reactions.