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I am embarrassed.

I wish I could get the part of my life back that was spent on your manuscript and this discussion.

You have been asked to present a quantitative calculation of how the isotope effect in Tin can be fit using your model. Instead you waive your hands furiously and hope that the uneducated will think you understand what you are talking about. Here's a hint, there are probably only 3 people reading this thread anymore. 2 of them aren't fooled by this.

You haven't and can't fit the isotope effect quantitatively using your model. Hence you have no standing to complain if there are deficits with BCS. Let your model stand or fall on its own merits. The BCS complaint is a smokescreen.

Dang, where did I put my Cardinal's hat now, Gallieo?

So, as I pointed out before, there is a voltage in the normal metal contacts. [Sarcasm]You are obviously the first person to note this.[/Sarcasm]

JAG: OK, I have answered your questions. Yes, I can predict the future and tell that you disagree with my statements. Oh well, I am crushed.

JB: You are trying hard I must admit. I disagree with your statements because they violate basic physics which is nowadays available in secondary school texts.

JAG: Now, back to one (of many) problems in your theory that you never want to address.

You state that the number denisty of superconducting electrons goes down with temperature. Thus, the average distance between conduction electrons increases.

From this, you make the leap that the distance between available sites increases.

Occam's razor (and most of solid state physics) would have your first explore that the site occupancy decreases with temperature. I.e. the distance between allowed sites for electrons remains nominally the same, but the probability (ooh that bad word) of a charge carrier being on a site goes down.

So, the distance a carrier would have to tunnel in your model would remain the same. This would negate much of your conclusions.

Explain how you make the leap from reduced site occupancy to your Wigner lattice (or whatever lattice of charge carriers) expanding.

For bonus points, explain why it makes sense for charge carriers to "tunnel" from site to site--if all the sites are occupied! If the charge carriers are Fermions, it can't happen. You must have <100% site occupancy.

JB: Yes I have noted from the start that you became unstuck on this issue. Therefore I have expanded on it in my manuscript which is now available on arxive. I have definitely NOT tried NOT to address it. If you take the time to understand the formation of a Wigner crystal, you will see that it forms when the mean field approximation breaks down. Before that happens, there are no positively-charged anchor points for the electrons to form localised orbitals. Thus when the first orbital forms the posive charges forming the anchor point appears at the same time. This is the lower energy state. If it should happen that the electrons are thermally excited back to the higher energy state, the positive charges are neutralised by them. Thus your statement that : "the distance between allowed sites for electrons remains nominally the same" does not apply.

For the CuO ceramics the process is slightly different but still in principle the same: The electrons de-excite from donor levels within the crystallographic layers to form the required charge-carriers between the layers. They are then anchored by the donor charges within the crystallographic layers. When they are excited back into the donors, they cancel the charges on the donors and thus the positive anchor charges. Again your statement does NOT apply.

In the case of SC p-type diamond, the charge carriers are holes on acceptors which have a suitable energy above the valence band. As the temperature goes up more and more of the holes on the acceptors are neutralised by excited electrons and the hole density decreases. Although surrounding electrons neutralising holes on other acceptors can tunnel into existing holes, this action does not change the average hole density at a given temperature. Thus again you statement does not apply.

Bosons AND fermions can tunnel. There is no such thing as tunnelling of an electron or an electron-pair "through" a barrier. This is prevented by the Pauli principle. Only a magician can do so. Tunnelling can only occur when a charge-carrier can borrow enough energy for a long enough time to scale an energy barrier. This is controlled by Heisenberg's Uncertainty Relationship for energy and time. To tunnel and carry a current, a charge-carrier must be able to borrow enough energy to break free from its anchor point and have in addition enough speed in order to reach another charge carrier position within the allowed time interval. In this case the aanchor charges do not disappear because they stay "dynamically:" anchored by the charges on the charge-carriers. The latter ensures that the material acts at the same time as a perfect dielectric.

I hope that I have succeeded in explaining it better!

JB wrote:
"I do not believe that there is such a thing as tunnelling of an electron or an electron-pair "through" a barrier"

And an electron tunelling microscope? Another name for Swiss cheese?

You might want to try google. No need to go to the library.

Since you apparantly do not understant my statements phrased in many different ways, let's try something very simple.

I am stuck on this issue because you NEVER address it. You never state why R is temperature dependent.

You give qualitative verbage but no calculations or experimental evidence.

"This superconduction ensues when the distances between orbitals (which form a Wigner crystal) become small enough for tunneling to be possible.

I.e. the distance the charge carriers jump is the distance between orbitals in a Wigner crystal.

I.e. R must be related to the lattice parameter of a Wigner Crystal.

therefore, for your model to work, the lattice parameter of a Wigner crystal must have a temperature dependence that matches that you assume for R.

Please, since I am ignorant of anything beyond grade-school math and science, educate me.

What is the equation (including temperature) for the lattice parameter of a Wigner crystal. Derive it or show a reference.

Compare this to the temperature dependence of R in your paper.

If they are not the same, you are in trouble.

There is no evidence that I can find--theoretically or experimentally--for a Wigner crystal in common superconductors such as Nb, Sn, Ta, etc.. I don't expect you to be able to find the temperature dependence.

My understanding (and, take this from someone who doesn't know anything beyond grade-school math and science) is that the problem isn't "tunneling" but "through".

He would argue that the mechanism isn't due to the wave function having a finite value on the opposite side of the barrier. Most of us would figure based on Freshman or Sophomore physics (which I hope to take someday) gives a finite probablity that the particle will move "through" the barrier and appear on the other side. Something having to do with the square of the wave function.

Instead, he proposes that the mechanism is that the particle approaches the barrier and gains the energy to overcome the barrier temprarily via the uncertainty principle. This propels the particle "over" the barrier.

It is a model that treats the particle as only a particle.

He doesn't give a quantitative explanation of this idea.

If, in the end, they give the same quantitative answer, they are likely in reality the same physics.

For what it is worth, they are the same physics, in my mind.

Whether you think of a particle with a delta-E, or a particle/wave with a little delta-X or a wave-packet with a probability of being on the other side, the physics is the same.

I seem to recall that you can derive the Heisenberg uncertainty relationships assuming a gaussian wave-packet for a particle. So, if you claim that it is the uncertainty principle, you are using the same physics.

[please see the post below where I point out the error in the above]

If anyone wishes to dissect this further then the very least then can do is:

Define "BARRIER"

Actually, on further thought, the physics is not necessarily the same for the methods I mentioned.

take an electron with energy E at a barrier with a height of 1eV. In JB's formalism, the electron temporarily is promoted to an energy above the barrier--i.e. it gains >1eV--through the uncertainty principle. It easily travels across the barrier since it has enough energy.

I.e. the electron enters the second electrode with an energy of E'>E+1eV

Now, consider these two cases

1) the material at the other side of the barrier has states available at this energy, E'. The electron can pass into the electrode.

2) the second electrode has no states available at E'. I.e. the density of states (DOS) is zero at E'. The electron is scattered or reflected back to the first electrode.

I.e there is a clear method to distinguish the two descriptions of tunneling (through vs. over the barrier).

If JB's description of tunneling were correct, tunneling spectroscopy wouldn't work.

For those who tend to misinterpret what I say, I am disagreeing with JB and claiming that much experimental data shows him to be wrong.

You are funny I must say; but it is clear that you do not know your solid state physics. To calculation to do the isotope effect on the energy levels in tin, you need to know the elastic constants of tin (which I am sure are available) and then you have to derive spring constants etc. It is quite a lengthy calculation; but it works and has been done many times in, for example. diamond. There are experts that can do this better than I can; unless I spend a lot of time strudying up the required mathematics. I know in principle how this can be done; but have more important issues on my plate right now. In this case D A Morgan's suggestion of having a co-author, who do such calculations on a daily basis, would apply.

My model does stand on the merit that it calculates aspects that BCS theory just cannot do. As I have said BCS cannot explain how a current can flow so that the charge carriers have a velocity without having kinetic energy. If they have kinetic energy, this energy has to be dissipated and this is the source of resistance as any schoolboy should know.

Of course there is a contact resistance between different materials; however, you are still missing the point completely. I will thus try and explain it on a simpler level. Resistance within a normal conductor is caused by scattering of the charge carriers. The charge carriers are accelerated for an average distance (say L) and then scatter; they are then again accelerated and scatterred etc. When they reach the contact they are also scattered in the contact; so as to lose the last bit of kinetic energy they have generated on their way from one contact to the other. In other words, resistance manifest because all the kinetic energy generated during the transit of the charge carriers are dissipated.

Now assume that one makes the length of the material less than L: The charge carriers will then on average not scatter within the material. Does this mean that the material is now a superconductor? Obviously not!! The kinetic energy that was generated during their journey from one contact to the other is still dissipated completely (now mostly within the contact) and resistive energy is still "wasted". Now it should be obvious that if non-scattering charge carriers require kinetic energy to move from one contact to another, all this energy will be dissipated within the contact; BUT THIS MEANS THAT ALL THE KINETIC ENERGY GENERATED DURING TRANSIT IS STILL DISSIPATED (JUST AS IN THE CASE OF A NORMAL CONDUCTOR). SO YOU DO NOT HAVE A RESISTANCE FREE FLOW OF CHARGE CARRIERS: I.E. YOU DO NOT HAVE SUPERCONDUCTION!!

Thus the most important property of a superconductor is that its charge carriers must be ablE to manifest a velocity without requiring kinetic energy. BCS cannoT model this. In fact BCS accepts that the charge carriers can increase their kinetic energies: This iS why it cannot model superconduction at all. The fact that it seems to give reasonable results for the low temperature metals is interesting; but, most probably, fortuitous.

There are two ways to explain tunnelling: 1. is to assume the electron can move through a barrier (Copenhagen magic"; 2. to assume that Heisneberg's Uncertainty relationship for energy and time allows an electron orbital to temporary borrow the required energy to scale the energy barrier. The two give the same result when applied to tunnelling and thus also to the tunnelling microscope. You should be able to pick this up in any elementary textbook on QM. I do not believe Copenhagen magic and therefore favour the second interpretation.

What you state here is nonsense. The formation of a Wigner crystal constitutes a metal-insulator transition; as anybody with Solid State knowledge should know that such a transition is temperature dependent; i.e. a phase transition occurs requiring an activation energy. This means that not all the electrons suddenly de-activates to form Wigner-type orbitals. Some will be in the higher mean-free states and others will be in the lower energy states. This is treated very clearly in my manuscript. It should also be clear that at higher temperatures the density of Wigner orbitals will be less than at lower temperature; i.e. the distances between them will be larger at higher temperatures. By using these assumptions I can generate excellent fits to available experimental data.

You are now playing a game, by challenging me to do in effect ab initio calculations on Wigner crystals before you will accept that my model might have merit. If this is the norm that is required Solid State Physics would never have developed. It seems you even though you lectured me on the validity of models, you are not following what you are preaching. We have BCS and I point out that I have a mechanism that seems to model all superconductors discovered to date. This in itself should make the model interesting so that it has to be published. This gives other researchers in the field the opportunity to either disprove me or find additional results in support. To expect from me that i should first do all possible calculations before the model is published is patently unfair.

Nobody has looked for it have they? Everybody accepted Cooper pairs. It is amazing how you can sometimes only look for what you expect. So this is not a good argument you have raised. It falls in the same league as the arguments that were used against poor Ludwig Boltzmann: "atoms do not exist because we have not seen them and probably never will".

JB wrote:
"Thus the most important property of a superconductor is that its charge carriers must be ablE to manifest a velocity without requiring kinetic energy."

Precisely why do you think that your assumptions can ONLY point to this single solution? I see nothing that supports the leap from premise to conclusion.

JB wrote:
"I do not believe Copenhagen magic"

I don't either. But you specifically stated "I do not believe that there is such a thing as tunnelling of an electron or an electron-pair"

It seems your answer contradicts your statement. Can you reconcile them?

I understand what you are trying to explain; and if the current Copenhagen dogma is correct I will be willing to agree with you; however, I believe and am sure that I will be vindicated in the future that the wave intensity does NOT represent a probability distribution in the sense that Born postulated. It is for this reason that the "tunneling tail" cannot depict a probabilty that the "particle" can magically appear on the other side of the barrier; however, let us rather stick to superconduction.

Your last sentence is incorrect, and this also causes the rest of your reasoning to be incorrect. The electron only borrows the energy while it tunnels. The amount of energy it borrows determines the time it can spend during tunnelling (subject to Heisenberg's Uncertainty Relationship for energy and time). When it reaches the other side of the barrier, its "time is up" to have this extra energy, and it thus has the same energy that it has had before tunnelling. As I admitted above this is equivalent to "tunnelling through"; but tunnelling through requires one to accept the Copenhagen interpretation to be correct. After believing in it for years I have now lost faith in it.

Thanks for asking a scientific question.

I have oulined my reasoning on this aspect to JAG above by comparing resistance in a normal conductor to to resistance in a conductor with no scattering.

What I say is that I do not believe that the entity moves through the barrier when it tunnels but rather scales the barrier by borrowing energy for the time interval that it moves across the barrier. I suppose that whatever the actual mechanism is, we are stuck with the term "tunnelling" when referring to it.

It isn't a matter of faith, it is a matter of science.

Either there is a difference in what the two methodologies predict, or they are equally valid. Present an experiment which determines the difference between the two interpretations or admit you have been wating my time.