Exactly: this will be the case when an electron-wave is accelerated by an electric-field, but not when there is no gradient in the potential energy.
It you're looking at a potential barrier, then obviously there is.
I am glad that you mentioned Ehrenfest's theorem because it is the most direct proof that the Copenhagen-interpretation based on probability waves is wrong.
That's irrelevant to our discussion. What's relevant is whether or not there's an acceleration when an electron moves in a circle. And there is. Quantum mechanics is not any different than classical mechanics in this respect.
Yes this is true for "classical motion" of an electron wave under which the boundary conditions apply that makes Ehrenfest's theorem valid.
Ehrenfest's theorem doesn't depend on boundary conditions. It ALWAYS applies.
But it is not true otherwise since an electron-orbital can also "tunnel" from one position to the next, under conditions when Ehernfest's theorem does not apply. This means that it then changes position without being accelerated.
For an atomic electron orbital in an energy eigenstate, <x> is constant, so both its first and second time derivatives are obviously zero. Ehrenfest's theorem DOES apply, and it TELLS you that there's no acceleration for an atomic orbital eigenstate. It doesn't change position at all.
But that's not the case for the scenario we're talking about.
The fact that you use the term "uncertainty" means that you do not understand it at all since it has nothing to do with uncertainty.
It absolutely does. This is standard textbook quantum mechanics.
It is not an "uncertainty" relationship but the effect of this relationship by Heisenberg is observable: It is responsible for the widths of atomic emission lines which means that a standing electron-wave, around a nucleus can increase or decrease its energy by (delta)E as long as it does not exceed a time interval (delta)t.
As long as
what doesn't exceed a time interval dt? I don't think you even know.
In the case of "tunneling" it thus allows a localized (standing) orbital to increase its energy by (delta)E for a time-limit (delta)t, so that it can end up at a another position with the same energy.
Absolutely wrong.
During this process Ehrenfest's theorem does not apply
Also wrong.
and therefore there is no acceleration involved.
And... wrong again.
As I have just explained it is a quantum-mechanical change in position during which Ehrenfest's theorem does not apply
Ehrenfest's theorem
always applies. You keep inventing exceptions to standard physics and attributing it to quantum mechanics, when quantum mechanics makes no such claims.
It should be clear that if you can follow the logic above, that it is you who are wrong!
There is no logic. There is only an unsupported assertion that quantum mechanics somehow allows you to violate laws which in fact are part of that very same quantum mechanics.
I have no argument with that.
You
did.
In fact, since I have discovered superconduction at room temperature 10 years ago I have been consistently confronted by the main stream crackpots asking me to prove experimentally that the voltage is zero. I consistently had to point it out to them that it is not possible; and has never been done for any superconductor. The only proof you can ever have that it is actually zero is that it is self-consistent with being zero.
That's not really good enough. The problem is that nobody believes that your limits on your voltage measurements are small enough to show that anything even unusual is happening.
Because at the end of the day, the voltage isn't what you want to show gets close to zero, the resistivity is. THAT is what Onnes was actually concerned about, not voltage. The best way to do that is not actually through current-voltage measurements, but by inducing eddy currents and measuring their decay (or lack thereof). That gets you much lower limits on the maximum resistivity. So if you can't do that, if you're stuck trying to read off the voltage from a fluke multimeter, well, that won't convince anyone that you don't just have a low
but normal resistance. You're making an extraordinary claim. You should not be surprised if people expect extraordinary evidence. Yes, you can't (and don't have to) prove that the voltage is identically zero, but you DO need to prove that its upper bound is so low that the resistance is not ordinary.
The reason why it has to be exactly zero in a superconductor is that otherwise the charge-carriers will be accelerated
No. That is not a problem. You keep claiming it is, but your reasoning is circular.
and even if they do not scatter within the superconductor, kinetic energy will be generated that will be dissipated within the target contact.
Kinetic energy is only generated if the acceleration is along the direction of motion. And so what if it gets dissipated within the "target contact"?
I have never said that this would be the case. We have all along talked about an equilibrium current flowing.
No. You have made general claims, and when I prove that your general claims are false by showing how it fails in a time-varying situation, you claim that we're not talking about such scenarios. When I point out that the SAME failures occur in static scenarios, you declare this to be impossible because your general claim is true, even though your general claim is not.
Just the opposite: Ehrenfest's theorem does not apply within a superconductor since their is not a gradient in potential energy.
First off, Ehrenfest's theorem always applies. Secondly, if a potential gradient is zero, that doesn't mean Ehrenfest's theorem doesn't apply, that just means you stick in a zero for that term. And third, nothing prevents a potential energy gradient from existing within a superconductor, you have simply declared this to be so.
It does apply within a Josephson junction with a voltage across it and only then the superconducting charge-carriers are accelerated
The junction itself, even with zero field, has a potential energy gradient. If it didn't, there wouldn't BE a barrier. So even in the absence of any external voltage, electrons passing through the junction will still be accelerated.
And they then emit EM radiation just as I have claimed all along that they must when they are being accelerated.
And you've also claimed that they radiate more energy than you put into the system. A point you still haven't addressed.