Actually speed of charge propagation will be slightly lower than the light speed, due to interaction with ground. In coaxial cables, it is typically down to 50% of light speed due to the grounded outer conductor.

The charge spreads so fast because electrons which are already present in metal need only to be shifted by a fraction of nanometer from their previous position. Basically, the force to move electrons is created by wide cloud of virtual particles cloud surrounding the initial concentrated charge, therefore you do not need to move electrons on-by-one, instead they move in coordinated wave.

You should read Richard Feynman lectures, he was famous for explaining that process simple.

What you describe is a TEM wave, and this is different from the proces of net charging a metal. You describe a polarization of a metal wire by means of current that flows parallel to the radius of the wire.

This cannot give a wire a net charge, think of Gauss' law.

The electric field component of a TEM wave is expressed as minus the time differential of the magnetic vector potential. We do not need a net surface charge at all in order to understand a guided TEM wave, just a small charge polarization of the medium suffices to guide the TEM wave, think of a glass fiber medium.

It is interesting you mention the world of virtual particles, responsible for an instantaneous action at a distance, also known as the Coulomb force. See for instance this paper by J.H. Field.

Article Quantum electrodynamics and experiment demonstrate the nonre...

This means that Maxwell's classical theory (the way it is presented and evaluated in textbooks) is incorrect, since the Maxwellian fields and potentials are retarded with velocity 'c'. A classical field theory that describes a Coulomb much faster than 'c' is my GCED theory, however, my theory has no gauge symmetry on which the renormalisation trickery depends, essential for Feynman's Q.E.D.

You are right, the instantaneous Coulomb force partially explains the very fast 'net charging' of the surface of any metal object, but after closing a switch between a DC source and a load, the Coulomb field falls of with square distance and cannot potentialise the entire long wire at the exact same time of closing the switch.

Although this is not yet an answer to my question, could you give me an exact reference to this section of Feynman's lectures (it is online)?

Dear Koen,

You are right the transport that you are considering is not the drift electronic current which would be with a very small velocity. What you are in fact considering is the transport due to polaron polaritons on a metallic surface, which traslate as particle-waves to velocities closer to c. This issue is nowadays very well studied in nanoptics and you can enter in many papers devoted to it, but my advice is to start with the chapter 14 of Kittel, Solid State Physics (is open free in internet).

Or perhaps the extraordinary high conductivity of surface charge on any metal in whatever shape (nano, ultra flat, or the common copper wiring from our electricity system) is an unknown solid state phenomeon. The coupling of a polaron (electron or hole) with surface photons or surface phonons, it might explain the very high propagation velocity of surface charge, and it might not. A basic classical calculation of net charge that is 'injected' at one point in/on a metal object in order to 'charge' the object, shows that the conductance and propagation of net charge is located mainly at the metal surface. Kittel's book does not treat in particular the high velocity of metal surface charge propagation, and the importance of surface charge on metals for our daily existence: no DC or 50/60 Hz AC network would function without a net surface charge on all the electric wiring and the fact it can propagate with such high velocity. Exactly this surface charge is the 'voltage on the wire', for which we do not have to wait for days to build up. This isn't mentioned either in the literature on classical electrodynamics or electrical engineering. A better understanding of this phenomenon could lead to highly improved power networks.

Dear Koen,

Your question is very interesting but I think that there is not new physics behind it. The idea is that you have on the metallic surface a great density of electric charge making an electronic plasma which is not totally neutral. This makes to have a strong interaction electron-lattice, where the electrons are with very low effective mass. On the other hand the electric charge is directly related with the electromagnetic waves (velocity very close to c) forming polaritons instead of photons. Thus the whole velocity of these collective excitations provide us with motion of electric charge much higher (at least 6 orders of magnitude) than the one due to the drift electronic motion. This is a very interesting because there are many different effects as the electric screening which also has an effect to have almost ballistic electric motion because the free path for these quasiparticles is very high and therefore is scattering is much rare than in the bulk. I think that there is nowadays one important reaseach in this field from the nanooptics field.

Thank you Daniel. Indeed, Polariton in a Jellium model of the metal surface, that takes into account electron-electron coupling might explain it. A polariton explains the high velocity charge transport.

I have not yet found papers that say anything about Jellium and metal surface conductivity. The Jellium model clarifies metal 'surface workfunction' and metal 'surface 'adsorption'.

I believe the high efficiency of Tesla's high frequency (100KHz) 'single wire' electric energy tranmission system, could have something to do with high density of net surface charge and the apparant high conductivity of net surface charge. If drift velocity current had nothing to do with this method of energy transmission, then it could not have shown a skin effect either (the usual reasoning not to apply high frequencies for electric energy transmission).

The TEM wave coupled with plasma waves (polaritons) at the metal surface explains things like the colour of metal surfaces; the TEM wave is in that case perpendicular to the metal surface. Zenneck waves are TEM wave modes that propagate parallel to the surface, however, I think it is a long stretch of imagination to couple an electron plasma wave with a Zenneck wave (the Zolariton???).

When the net charge density (rho) at a metal surface is such that d(rho)/dt is a very high factor, then we automatically have a high div(J) factor as well, and no one ever considers a classical 'scalar' magnetic field B = -div(A), sourced by a non divergence free current distribution, because of the incorrect/falsified 'Lorentz premise' (i.e. the Coulomb field and electric potential travel with speed 'c' in vacuum), combined with the Lorentz gauge. The scalar magnetic field naturally gives rise to the LEM wave mode (Longitudinal ElectroMagnetic).

A LEM wave coupled with a plasmon might be a better option to explain the high propagation velocity of net charging a metal surface, since the LEM wave also has max velocity 'c', and I might call its quantum a 'lemon'. The coupling of a lemon with a plasmon is very natural, and this becomes a plemon. A lemon is not the same as a phonon, btw; a phonon is not a pure field quantum, it is a more like a 'sound wave' quantum. Phonon propagation is too slow with respect to charge propagation on a metal surface.

Dear Daniel, I was looking into definitions of 'effective mass' of electrons and holes, a difficult concept to grasp, however, in modern solid state physics analysis this concept is very useful. The effective mass of electrons and holes at a metal surface with (high) net surface charge must be way different from charge neutral metal. Also ionic impurities in semiconductors (dopant) have an effect on the effective mass of the charge carriers in the conductance band. This subject is 'low hanging fruit' for improved economy, since there is copper wire surface with net charge almost everywhere in the world. It is truly amazing that I can find almost no information on the internet that answers my question. The hypothesis is that the effective mass of electrons/holes is diminished greatly in a charged metal surface, due to electron-electron and hole-hole interaction, which implicates much higher velocities of charge carriers and which explains the light(ning) fast transport of 'electrostatic' electricity in the surfaces of conductors. In the following reference, there is NO information "On the effective mass of charge carriers in the charged surface of conductors" (good title for a paper, btw).

https://www.sciencedirect.com/topics/chemistry/effective-mass

I return to this question with a new hypothesis. The effective mass of the excess charges (electrons/holes) at the surface of an electricially charged conductor is not different from the charge in the conduction energy band. What is different though are the shortest distances between the particles that constitute the excess charge at the conductor surface which is still many lattice distances wide, even for the highest possible excess charge densities (before voltage breakdown occurs). This means that Pauli's exclusion principle does not hold for the excess charge relative to the excess charge. Since the excess charge is pushed to the outer layer (surface) of the conductor, Pauli's exclusion principle does not hold either for the excess charge with respect to the other particles in the conduction band that are not 'excess charge'. Secondly, during a 'nonequilibrium' electrostatic excess charge flow, the surface charge carriers do not pass each other because of the Coulomb forces; the surface charge carriers only push each other along the conductor surface. Thirdly, the mean free path for accelerated excess charge carriers is much longer than the mean free path for accelerated bulk charge carriers, because there is no (or little) lattice phonon interaction with the excess charge carriers at the surface. The Ohmic friction for the excess surface charge is therefore many orders of magnitude smaller, in case of nonequilibrium electrostatics, in comparison with the Ohmic friction for the bulk charge. It is for these reasons that the excess surface charge can have velocities close to the speed of light and have no 'Fermi velocity limit', resulting in conductor line voltages that propagate with close the speed of light. The nonequilibrium dynamics of excess surface charge on conductors is the most important and underrated physical phenomenon of Electric Engineering. And yet this physical phenomenon is not described well (basically ignored) in standard physics textbooks (such as classical electromagnetism or solid state physics) and in the EE educational literature.

Koen van Vlaenderen The problem is that in current theory, we have no idea what "charge" is. Maxwell's equations essentially describe a phenomenological model that is based upon the assumption that some kind of fundamental quantity called “charge” exists, to which a unit of measurement in Coulombs [C] has been assigned.

I've just uploaded my revision of Maxwell's equations for your consideration and comments:

https://www.researchgate.net/publication/341931087

What we found is that "charge" is actually a longitudinal compression/decompression of a "charged" particle, which results in the emission of a longitudinal superluminal "Tesla" wave, which is what the Coulomb force actually is.

What we also found is that "current density" actually represents the vorticity of the medium, while the medium actually supports both rotational (magnetic) movements as well as translational (dielectric) movements, the latter of which enables superluminous signal transmission as demonstrated by Tesla.

Quite interestingly, I performed an experiment just a couple of days ago, which is essentially what you write: "Suppose we connect a long copper wire at one end with a battery's positive terminal or negative terminal, the wire receives a plus or minus surface charge that spreads with almost the speed of light to the other end of the wire."

I've repeated Wheatstone's 1834 experiment, whereby I switched a charged capacitor using a mercury wetted relay onto two relatively long copper wires and measured the propagation of the signals, whereby I measured a nice edge arriving after about 95 ns, which is caused by a longitudinal Tesla wave, while the EM edge arrives after about 180 ns. Still have to analyse further and work things out, but you can take a look at the results so far here:

http://www.tuks.nl/wiki/index.php/Main/ObservingSuperluminalSignalPropagationAlongASingleWireTransmissionLine

So, what explains your question is that the movements of electrons is caused by the currents and waves propagating trough the medium and that the medium simply moves much faster than the electrons.

Dear Arend, your answer is perhaps an answer to another question, but not to this question.

Koen van Vlaenderen May be I misunderstood, but I understood the question was how to explain a faster velocity of surface charge as can be caused by moving electrons, which is related to the question of what "charge" is and what a "field" is.

The aether simply moves much faster than particles, which are made out of aether, so there is not really a distribution of "charge", but you get two surface waves that propagate along your conductor. One of them is what's known as the "near" field, which Elmore has shown to be guideable along a completely unshielded conductor:

Article Introduction to the Propagating Wave on a Single Conductor

The other one is Tesla's superluminal longitudinal mode, which propagates quite a lot faster than light. I've measured it to propagate at about 1.8 times the speed of light with my particular setup.

So, these are the transient phenomena that one can measure with an oscilloscope, preferably with a capacatively coupled active probe, that do not involve movements of "charge", but they eventually cause charge carriers to move.

In other words: it's a matter of cause and effect and the measurement of a voltage caused by a transient wave in no way implies the actual movement of "surface charge" as you seem to assume. There is no propagation of charge, it's the aether that moves, or better: vibrates.

Dear Arend, I know the difference, and it is a common mistake to view a line voltage as just ‘field’ without considering the important role of the net surface charge on a conductor with non zero electric potential. Just review the chapter ‘electrostatics’ of any book on electromagnetism. Even J.D. Jackson dedicated a paper on the important role of surface charge in electric circuits. I want to know the physics that further explains the very fast flow of surface charge (in comparison with the very slow bulk current), that is all.