First off, claiming it's quantum mechanical doesn't help. Quantum mechanics still has acceleration defined as <a> = d2<x>/dt2, and that's still nonzero here.
Yes when Ehrenfest's conditions apply so that you have a force defined by a gradient in you applied voltage: I state that one does not have such a gradient within a superconductor. Neither have
you given any experimental proof that there is such a gradient!
Although I agree that one cannot measure "zero voltage"; all the experimental results are self-consistent with there being not such a gradient within a superconductor. And the definitions of superconduction within text books are all commensurate with their not being such a gradient. And we know that if there is such a gradient, and the charge-carriers do not scatter, as in the case of a vacuum diode, you do
not have superconduction. In addition, in the latter case the accelerating charge-carriers emit EM since they are accelerating. Thus all the evidence are compelling that the charge-carriers within a superconductor must move without acceleration. But
you know better since "classical" Newtonian mechanics
must,
according to you, apply.
And second, by Ehrenfest's theorem, <a> = <-dV/dx>/m. So if you've got a potential barrier, you've got a gradient to your potential (a field, if you like), you've got the quantum mechanical analogue to a force, and you've got a quantum mechanical acceleration.
Do you accept that what is called "tunneling" , no matter how it actually occurs, does happen? Please answer: YES or NO. Do you now maintain that this is caused by Ehrenfest's theorem which accelerates the charge-carrier first
against the gradient of the potential barrier, and then
with the gradient on the other side of the barrier? Please answer YES or NO. If your answer is NO, where does acceleration come into the equation when "tunneling" occurs?
I already told you: hexagonal lattices have the highest packing fraction.
I have not seen this and apologise if I have missed it.
Vortices repel, so they minimize their energy by adopting a high packing fraction.
I agree that this could be the only reason and should not have slipped up on this.
The idea that it's due to hexagonally arranged orbitals is nonsense,
No it is not just nonsense since the stationary orbitals are formed by harmonic standing waves trapped by induced positive charges. This is also the reason why in most metals (note not all metals) one has a isotope effect. The orbitals and their induced charges can relocate under the action of Coulomb forces between them, and you then find that the orbitals trapping a flux quantum form a hexagonal ring. Nonetheless, even through the latter is a fact, I concede that close-packing could be a sufficient reason for causing the hexagonal arrangement.
Well, no. It's not possible quantum mechanically, you have only declared it to be so.
So you dispute that an electron can change position by what is called "tunneling" in the literature?
And you have even done so without addressing what acceleration even is quantum mechanically.
And you state unequivocally that "tunneling" can only happen when Ehrenfest's law applies? Well be my guest and think what you want, but time will prove that you are wrong. I just hope that when this happens, and you are still alive, you will have the decency to come clean and not disappear behind a screen of anonymity.
I have told you what it is. You have not demonstrated or even suggested that the quantity I defined is nonzero.
Why should I? When Ehrenfest's law applies there is obviously acceleration, but it does not apply to the charge-carriers within a superconductor since these charge-carriers do not radiate any EM. That they must radiate when they are accelerated is proved by Josephson tunneling through an insulator with a voltage across it. When these
same charge-carriers are now accelerated (while moving through the junction) they
do emit EM. This is incontrovertible proof that they are not accelerating when they move through the superconductor itself.
First, there's nothing wrong with producing kinetic energy in a superconductor with an applied voltage, and second, if the resultant acceleration is perpendicular to the direction of motion (as in the case of a persistent circular current), then no, kinetic energy is NOT generated.
Yes you are correct, but the charge-carriers will emit radiation as they do when they accelerate through a Josephson junction with a voltage across it!
Of course it's not superconduction, there's no Meissner effect.
Let's leave for the time being the Meissner effect aside since it is not understood by the main stream crackpots at all. Let us just for the time being concentrate on you false claim that charge-carriers do accelerate when they transport a current through a superconductor.
And second, you're wrong, there is scattering. Electrons in a vacuum diode can still scatter off each other.
That is not correct: They only repel each other laterally: That is not scattering and dissipating kinetic energy.
No. That is not what happens with a superconducting magnet. The required voltage is not the result of charge injection, but is the result of the inductance of the superconductor.And by the way, every conductor has inductance. It's impossible to not have inductance, because the electron's non-zero mass creates inductance.
I have not disputed the fact anywhere that a superconductor has an induced magnetic field around it: What I do dispute is the stupid idea that this same magnetic field bootstraps an applied voltage within the superconductor: This is utter nonsense! If this could be the case, one would be able to lift oneself into the air by pulling on your bootstraps.
But there IS an applied voltage when you're changing the current in a superconducting magnet, or in fact ANY superconductor.
I have been talking all along about equilibrium conditions. Obviously when you change the EMF around the circuit containing a superconducting element, there will be a transient voltage within the superconductor which will fade away to zero as soon as equilibrium with a higher (or lower) current has been established.
You're trying to draw some artificial boundary between the physics of AC and DC conditions, when no such sharp distinction exists.
It does in a superconductor since an applied DC voltage is cancelled by polarization of the localized charge-carriers. When the voltage changes, this polarization changes, and when you apply an alternating voltage, the dipoles will vibrate and generate EM-radiation when they vibrate in phase with the voltage. You see; there is a hell-of-a-difference.
Furthermore, if you want to talk about DC only, then you are rather automatically NOT talking about the general case, but only a very specific case, so you cannot make absolute declarations of any sort based only on what happens for DC.
I have not made "absolute" declarations: It was clear from the start that we are talking about movement of charge-carriers during the flow of a DC current. It has been people like you who wanted to bring in other boundary conditions all the time. You cannot really be so stupid that you do not realize this? Can you really be?
It's never been described before because it's simply not true. The idea that charges can start moving without accelerating makes no sense, and quantum mechanics cannot and will not rescue this nonsensical idea.
If you became stuck in the 17th century, it will not make sense to you. But during the 20th century new momentous discoveries have been made, which, although wrongly interpreted as paranormal behavior, do make movement of electrons without acceleration possible.
WE have lightning again. So goodbye for now
