Sergio_Prats

I used incorrectly the word "punctual", I would say "point particle" . When I say "particle" I refer to protons or electrons whose wave functions can be extended over the space. I agree with that, but we are still using formulae based on Maxwell equations in modern physics. For example, the QED Lagrangian contains a term that is -(1/4) FuvFuv, this term is the classical field energy. If the fact that electrons and protons does not exert electric field over themselves entails a correction in the field energy, then this QED term should be reviewed. The EM field (induced or radiated) propagates not instantly but with the speed of light. In a electrostatic scenario this fact can be ignored but it cannot be in the general electrodynamic scenario, however, this does not not affect my approach. We only need to remove the field create by the own charge distribution at d/t seconds when d is the distance of each point respect the point we are evaluating. Of course it makes the calculations harder but it is essentially the same.

In fact we are saying the same thing: that a charge distribution that belongs to the same particle does not exert force on itself, but as far as I know, if we follow strictly the Maxwell equations we cannot "trick" the Lorentz Force to ignore the contribution to the field caused by the own charge distribution: the field is the field no matter what particle has created it. However, it turns out that this is not a trick and Quantum Mechanics behaves this way: a particle's generated potential does not affect itself. So some adjustments must be done in the classical electromagnetism to take this fact into account. I have seen several theories about the electromagnetic mass and the electro self-energy but as far as I have seen, they are not completely satisfactory, you can find a description of some of them here: http://www.feynmanlectures.caltech.edu/II_28.html But if we assume that a particle does not interact with itself, why just to remove the effect of that particle over itself? As far as I know, the only thing that needs to change is the energy stored in the EM field. Basically, since a particle "alone in the universe" does not need any energy to bring together its charge, we have to remove from the field energy expression, the energy that each of these particles would have alone. I have a candidate formula that has been successful in comparing the electron’s potential energy with the field energy for the Hydrogen atom radial levels (n=1, l=0, m=0) and (n=2, l=0, m=0). When I say "particle", I do not mean zero dimensions. I would say "punctual particle" for that. I understand a particle such as an electron can have a wave function and therefore can be distributed through space. Since electros are fermions, they should not be mixed in the same space, so everyone of them would requiere a particular space even if they were puntual particles. An additional charge would feel the overall EM field but, in fact that charge would also add another field that would add another field which would not be able to detect itself, so we are only able to detect the field created by the system but not the field created by the probe.

The Coulomb law is the force caused between two static charged particles, it also represents the field that one particle creates at some point. I consider "classical" all the non quantum electrodynamics, so any electrodynamic system based on Maxwell equations is classical, I also find very useful the formulae of the generated by a punctual particle with speed v and acceleration a as they tell the field that this particle extert at any point. The fact is that under classical EM, if we have, for example, a uniformly charged sphere with radius R, any point at distance r from the radius will suffer a force ρ(r)*Q/r3 r where Q is the charge inside that r radius. That will make the sphere quite unstable unless you remove that force by ignoring the self generated field. This is exactly what is not derived from "pure" Maxwell equations. I agree, the small object also attracts the big one, but I don't see the relation with my concern, in gravity its very hard to know if a particle attracts itself because gravity constant is so small. Which theory is it?

In classical electromagnetism we have two space vector fields E and H for the electric and magnetic field and a four vector made with spatial charge density and current [ρ, J] with determines EM field together with external sources and whose dynamic is affected by those E and H fields according to the Lorentz force. Classical electromagnetism assumes that each point of the charge density interacts with fields E and H and moves independently on how the rest of the charge moves (except, of course because the dynamics of the rest of the charge will affect the future EM field). However, in nature there are not infinitesimal charges that move freely, but discrete particles such as electrons and protons. In quantum mechanics at first order a particle EM field does not interact on itself. An example of this is the Hydrogen's electron Hamiltonian, the potential we see is the one created by the proton and there is no contribution from the electron itself. At higher levels, we may find interactions due to the vacuum but they are much weaker, for example, the Lamb Shift in the Hydrogen atom (4*10^-6 eV) is much smaller that the difference between radial levels 1 and 2 (10.2 ev), so I consider a good approach to say that in general, the EM field generated by discrete a particle does not affect itself. So, can we assume that a particle only interacts with the field created by other particles? In that case (still in the classic non-quantic theory), we would have N charged particles that require N Hilbert spaces to define the charge and current distribution for each of them. Each particle “sees” a different EM field because it has to exclude its own contribution to the EM field, so we would have N spaces with EM fields plus an overall field. As far as I can see, we can have this way a theory with discrete particles that respects Maxwell equations, however, the field energy density should be reviewed because in absence of other charges, there is no work done to “bring together” the density of charge needed to build a particle since the own field does not affect particle. Explained from another point of view, we can have a charged sphere which generates an electric field, which should have energy, but we don’t have spent any energy to bring together its charge. Let the formula for the EM field density of energy be: u = (ε/2)E2 + (μ/2)H2 Therefore, some correction must be done to remove the term of the energy needed to build isolated particles and once this is done, I consider this approach would be consistent.