Johan:To you it is complicated since the model you are believing in, is complicated. As Bernd Matthias said about the BCS model: When you have equations stretching over half a page, the model is wrong: Nature is not so complicated.
Zig: That's a deeply unscientific claim. As such, it's irrelevant here.
Not al all. This is not the only comment Bernd Matthias made about the BCS model. His most accurate criticism has been that the BCS model cannot predict anything. This is relevant here since my model can make the predictions that Bernd Matthias wanted.
Johan: My model is simple and can be visualised
Zig: Your model is utter nonsense, proped up by ignorance and misconception.
You have not raised a single physically relevant argument against my model. I am sure that Bernd Matthias would have been more open minded if he were still alive today. A pity that such a good scientist have died young and left us with incompetents in the field of superconduction.
Johan: the dependence of the critical temperature on the doping level in the ceramics;
Zig: Please, do tell. I'm especially interested to find out why there's a giant asymmetry between electron and hole doping.
If you have studied my model you would have been able to immediately see why there is this asymmetry. This asymmetry goes hand in hand with “stripe formation” within a superconductor. Although I must hasten to say that stripe formation in a material is not a sufficient condition for superconduction to be possible: It can also occur in materials that remain insulators; even super-insulators
The stripes form since in these materials, donors, within the crystallographic layers, release electrons which form stationary orbitals at an energy (delta)ESbetween the crystallographic layers, at an energy below the energy-levels of the donors within the crystallographic layers. Holes are thus left within the crystallographic layers which form a Mott-type material. The higher the density of the donors within the crystallographic layers, the more stationary electron-states can form between the layers at a temperature T. The corresponding density of holes also increases. Obviously, when the temperature decreases for a constant level of doping, one also has an increase in stationary electron-states between the layers and corresponding holes within the layers. If the stationary electron-orbitals between the crystallographic layers can reach a critical denisty at a temperature T, superconduction becomes possible at this temperature as modelled by my theory. When then increasing the donor density, it will be found that the critical temperature increases until it reaches a maximum.
The maximum is reached since the orbitals forming between the layers increasingly experience Coulomb repulsion between them as their density increases. It is easy to prove by using Schroedinger’s equation that this decreases the energy gap (delta)ES which in turn decreases the density of orbitals between then layers. Thus, at higher densities the critical temperature now starts to decrease with increasing donor-density: If the orbitals can reach a high enough density, the critical temperature can even again become zero.
It is relatively easy to write down the governing equations and to fit them to the published data. Now explain this asymmetry to me in another way? You cannot.
Johan: the presence of “stripes” in the ceramics
Zig: I'm actually surprised that you've even heard of these, though I doubt you know really know what the experimental evidence involved is.
Not al all. This is not the only comment Bernd Matthias made about the BCS model. His most accurate criticism has been that the BCS model cannot predict anything.
This is simply false. BCS can successfully predict many properties of conventional superconductors. And that's true whether or not BCS is right. To claim otherwise is deeply dishonest.
You have not raised a single physically relevant argument against my model.
How so? And why are stripes only present in the cuprates?
The stripes form since in these materials, donors, within the crystallographic layers, release electrons which form stationary orbitals at an energy (delta)ESbetween the crystallographic layers, at an energy below the energy-levels of the donors within the crystallographic layers. Holes are thus left within the crystallographic layers which form a Mott-type material. The higher the density of the donors within the crystallographic layers, the more stationary electron-states can form between the layers at a temperature T. The corresponding density of holes also increases. Obviously, when the temperature decreases for a constant level of doping, one also has an increase in stationary electron-states between the layers and corresponding holes within the layers. If the stationary electron-orbitals between the crystallographic layers can reach a critical denisty at a temperature T, superconduction becomes possible at this temperature as modelled by my theory. When then increasing the donor density, it will be found that the critical temperature increases until it reaches a maximum.
The maximum is reached since the orbitals forming between the layers increasingly experience Coulomb repulsion between them as their density increases. It is easy to prove by using Schroedinger’s equation that this decreases the energy gap (delta)ES which in turn decreases the density of orbitals between then layers. Thus, at higher densities the critical temperature now starts to decrease with increasing donor-density: If the orbitals can reach a high enough density, the critical temperature can even again become zero.
It is relatively easy to write down the governing equations and to fit them to the published data. Now explain this asymmetry to me in another way? You cannot. Just use Google and type “superconductor stripes” and you will find the experimental evidence.
You didn't explain the electron-hole asymmetry. In fact, I don't think you even know what the electron-hole asymmetry is. You talked about hole-doped cuprates. But you said nothing about electron-doped cuprates. Since the electron-hole asymmetry is about the difference in behavior between electron-doped and hole-doped cuprates (not about the difference between eletrons and holes within one material), your response obviously doesn't address the question. It's like you don't even know electron-doped cuprate superconductors exist.
The other funny thing about Johan's iron/copper analysis:
He's gone back to categorically stating that there's no net charge density anywhere, but he still wants E_iron != E_copper, i.e he wants the field to have a gradient somewhere.
Johan, do you agree that E_iron is not equal to E_copper in the original example? Right in the center, far from the interfaces?)
Can you show me what term in Maxwell's Equations you think is responsible for this difference? You seem to categorically reject charge excesses, so it's not div.E = rho. It's a static problem, so it's not curl E. I don't see any other spatial variation terms in there---do you? (Note: the answer is not "Ohm's Law".)
As a long-time lurker in this awesome train wreck of a thread, I just have to say...
...give me a *********** break.
In my area of expertise, such as it is, (law), whenever a witness tries that move while under cross-examination (i.e., compounds mistakes and lies with more mistakes and lies in an attempt to explain away the first set of mistakes and lies), I know that I have won.
But do carry on. It's all marvelously entertaining.
I cannot resist this: I have always found it very funny that people who make a living out of becoming professional liars always suspect that other people are also liars. I can assure you that if I could lie, I would have made far more money by being a lawyer.
So I can assure you that you have not won. The only person that can win against me on this thread is one who is able to argue real physics. Ben, Sol and Ziggurat are not within this league and probably never will be. This is why they hide behind anonymity. All they are doing is to use as many irrelevant arguments as they can muster as flak in order to avoid being tracked down for what they really are.
I cannot resist this: I have always found it very funny that people who make a living out of becoming professional liars always suspect that other people are also liars. I can assure you that if I could lie, I would have made far more money by being a lawyer.
Thank goodness. I'm glad not to be in a league where basic math errors and fundamental conservation law violations go unnoticed or are accepted as normal.
I cannot resist this: I have always found it very funny that people who make a living out of becoming professional liars always suspect that other people are also liars. I can assure you that if I could lie, I would have made far more money by being a lawyer.
So I can assure you that you have not won. The only person that can win against me on this thread is one who is able to argue real physics. Ben, Sol and Ziggurat are not within this league and probably never will be. This is why they hide behind anonymity. All they are doing is to use as many irrelevant arguments as they can muster as flak in order to avoid being tracked down for what they really are.
Your evident bias against the legal profession speaks no more to your personal credibility or quality than does your disdain for physics and physicists.
And, given that you also have serious problems with reading comprehension and written communication, I can assure you that you would not have made much more money - or indeed any at all - had you somehow managed to find a bar that would admit you.
Just in case it isn't clear to you (which it obviously isn't), I haven't won here - Zig, ben and Sol have. I am merely pointing it out and being entertained at the same time.
Just in case it isn't clear to you (which it obviously isn't), I haven't won here - Zig, ben and Sol have. I am merely pointing it out and being entertained at the same time.
How do you know? What is your qualifications in physics? What are the qualificatiosn in physics of Ben, Sol and Ziggurat? I can predict that they know next to nothing! You do not know any physics, but is willing to make a judgment? And it is people like you who end up as judges? No wonder innocent people are languishing in jails while rapists on parole are prowling our streets and again raping innocent young children.
I always wondered why they made a distinction between "civil" lawyers and "criminal" lawyers. I have not yet met a single lawyer in my life who did not turn out to be a criminal. And your attitude supports my disdain for the legal profession. Yes it is the oldest profession in the world, not prostitution. At least a prostititude can pass on pleasure when she rips you off: A lawyer, even when he/she wins your case, takes all the money and still sends out an additional massive account. Lawyers never consider anybody else but their own pockets! They should not be allowed to have private practises!
Do you remember how the people cheered worldwide when T. Rex ate up the lawyer in Jurrasic Park. It should make you and your ilk think; if you are capable of being objective. Which you are not, and never have been EVER! The law is not an ass, it is formulated and applied by A--holes.
How do you know? What is your qualifications in physics? What are the qualificatiosn in physics of Ben, Sol and Ziggurat? I can predict that they know next to nothing! You do not know any physics, but is willing to make a judgment? And it is people like you who end up as judges? No wonder innocent people are languishing in jails while rapists on parole are prowling our streets and again raping innocent young children.
I always wondered why they made a distinction between "civil" lawyers and "criminal" lawyers. I have not yet met a single lawyer in my life who did not turn out to be a criminal. And your attitude supports my disdain for the legal profession. Yes it is the oldest profession in the world, not prostitution. At least a prostititude can pass on pleasure when she rips you off: A lawyer, even when he/she wins your case, takes all the money and still sends out an additional massive account. Lawyers never consider anybody else but their own pockets! They should not be allowed to have private practises!
Do you remember how the people cheered worldwide when T. Rex ate up the lawyer in Jurrasic Park. It should make you and your ilk think; if you are capable of being objective. Which you are not, and never have been EVER! The law is not an ass, it is formulated and applied by A--holes.
Thanks for reminding me. But it is made impossible by people like you who believe my opponents when they make totally false statements. Will you as a lawyer allow a witness under cross-examination to get away with false statements? Or allow a witness to make irrelevant statements? You are allowing this to happen by your comments on this forum. Ziggurat is the expert when it comes to making false accusations: For exsample:
And if your (close to) zero resistance result is actually true, it suggests that you've dropped the work function to (close to) zero, not that you've discovered superconductivity.
Again, I'm amazed that you can discuss any of this without including anything about the work function.
If he would have taken the time to make sure of his facts he would have known that in my experiment the formation of a superconducting phase between the diamond surface and the anode, is determined by the electron affinity of the diamond (where the electron affinity replaces the importance of the workfunction of an undoped semiconductor when one dopes it) AND the workfunction of the anode. If you do not get these parameters correct you will not get a superconducting phase to form.
Ben is the expert on making irrelevant statemenst and distorting what I have said. When I argue that you can never accumulate enough charge to cancel an applied electric field while a current is flowing through a material where the charge-carriers have to be accelerated to obtain the current, he argues that one can get charge-accumulation during current flow. I have not said that charge cannot accumulate anywhere. I stated very clearly that charge can never accumulate enough to cancel an applied electric field within such a material while a current is flowing through it. After having challenged him many times to accurately define and explain how the electric-field can be CANCELLED by such charge accumulation, we end up discussing whether charge-accumulation is possible or not possible while a current flows; NOT whether charge accumulation can become sufficient to cancel the applied electric field. When I explain why the latter is not possible, my explanation is just ignored.
In this way Ben, Sol and Ziggurat are consistently causing this thread to stray from the actual topic of superconduction; while, unfortunately, you as a lawyer who should know better, laps it up without raising any objections. You are typical of the lawyers, who handled my cases in the past. I do not say that there cannot be decent lawyers, but that the rule is that most of you are not working for justice but to fill your pockets. When a lawyer appears who does actually work for justice, he soon finds himself to be criminalised by his peers. For example, Nelson Mandela, who had to spend 27 years in jail because he was a lawyer who believed in justice.
That lawyers, as a general rule, are dishonest, has already been pointed out 2000 yeras ago by the most knowledgeable person on law. Jesus called lawyers white-washed graves; and was crucified for talking the truth!
When I return to this thread, I will concentrate on the two main issues on which we disagree when it comes to superconduction: The following wrong arguments by Ben, Sol and Ziggurat:
!. That the charge-carriers within a superconductor can be accelerated by an applied electric-field.
2. That these free charge-carriers can cause enough accumulation of charge while they are transporting a current so that the accumulalted charge can cancel the applied electric field.
In this way Ben, Sol and Ziggurat are consistently causing this thread to stray from the actual topic of superconduction; while, unfortunately, you as a lawyer who should know better, laps it up without raising any objections.
Ben, Sol and Zig have been precisely on point throughout this thread. They are performing a service for you, if you would only recognize it.
Since the usual routes are closed to you (I cannot imagine why - you are such a pleasant, well-balanced chap), this forum appears to be your only means of seeking and receiving some form of peer review. Informal though it is, you are getting it in spades here. And us non-scientists get to acquire some new knowledge by following along as your mistakes are corrected for you.
Everyone wins. Except that you, just like every other crank that has ever appeared on this forum, are too emotionally invested in your errors to see this.
When I return to this thread, I will concentrate on the two main issues on which we disagree when it comes to superconduction: The following wrong arguments by Ben, Sol and Ziggurat:
!. That the charge-carriers within a superconductor can be accelerated by an applied electric-field.
2. That these free charge-carriers can cause enough accumulation of charge while they are transporting a current so that the accumulalted charge can cancel the applied electric field.
Yep. Zig has been through the induction case with you. You can take my point-charge-hovering-over-a-SC-plate case if you want a straight electric field example.
Of course charge can be accelerated by an applied electric field; there is no physics problem whatsoever. This acceleration is what allows the superconductor to get to the zero-field condition that you're familiar with. The zero-field condition is not an iron-clad axiom that you need to paste on to the laws of physics---it's a consequence of those laws, it's what you expect to happen when you use normal E&M to act on charges in a zero-resistivity material.
2. That these free charge-carriers can cause enough accumulation of charge while they are transporting a current so that the accumulalted charge can cancel the applied electric field.
Of course. You wrote down the equations yourself. There's not the slightest physics difficulty here whatsover. Your attempts to prove otherwise started with (a) making a math error, (b) misapplying Gauss's Law, and (c) apparently denying the applicability of Gauss's Law altogether.
Ben, Sol and Zig have been precisely on point throughout this thread. They are performing a service for you, if you would only recognize it.
Since the usual routes are closed to you (I cannot imagine why - you are such a pleasant, well-balanced chap), this forum appears to be your only means of seeking and receiving some form of peer review. Informal though it is, you are getting it in spades here. And us non-scientists get to acquire some new knowledge by following along as your mistakes are corrected for you.
Everyone wins. Except that you, just like every other crank that has ever appeared on this forum, are too emotionally invested in your errors to see this.
Another lurker agrees with and appreciates your analysis. This thread has been both educating and entertaining. I also find it fascinating how familiar Johan's patterns of argument are - characteristic of so many posters encountering critical examination of their claims on these forums.
In Ben’s diagram the resistivity is NOT single-valued on the interfaces at all. It has a very sharp, vertical drop from the resistivity of iron to that of copper and at the other interface it is also not single valued since it has a sharp, vertical increase.
You're confused as usual. At worst, the resistivity is discontinuous at the interface. It is single valued.
Thus, you cannot use Sol’s so-called “correct formula” to derive a gradient by means of differentiation. Since both values of the resistivity is present within both interfaces, it implies that the gradient must be infinity in both cases. So according to Sol’s reasoning the divergence is infinite, which requires an infinite charge within the interface! This is obviously physics-nonsense.
If the resistivity is discontinuous, your own equation says there is a delta-function sheet of charge (as every high-school student knows, there's nothing wrong with differentiating discontinuous functions - the result is a delta distribution). While that is clearly an idealization of the true physical situation, there is nothing wrong with it. If you don't like it, all you need to do is allow the resistivity to vary smoothly but rapidly across the interface, and you'll find a smooth but thin sheet of charge instead of a delta-function. The total charge will be exactly the same.
This is all basic, basic, physics and trivial mathematics.
If the resistivity is discontinuous, your own equation says there is a delta-function sheet of charge (as every high-school student knows, there's nothing wrong with differentiating discontinuous functions - the result is a delta distribution).
Well, I knew what it was... but you're right, I exaggerated when I said "every".
What's a little more worrisome is that Johan, who claims to have a doctoral degree in physics and to have taught quantum mechanics, doesn't know what it is (and doesn't know the difference between "discontinuous" and "multi-valued").
Face facts, Johan - whatever you once knew about this topic, it's gone. All that's left is arrogance, paranoia, and a nasty stubborn streak.
I smiled when Ben posted his iron-copper-iron diagram since it was obvious what his ploy was: After I fruitlessly tried to get Ben to clearly define and state his standpoint, I decided to play along: What I expected, happened. The typical arguments one gets from clueless theoreticians: Only they will claim that you can differentiate the resistivity of a metal as if it is a physically-real continuous function of position within a metal.
If Ben, Sol and Ziggurat knew a bit of Materials Science, they would have realised that at the interfaces of two different metals with different properties one usually does get accumulation of charges, but not because there is a resistivity function that can supposedly be differentiated with position to obtain a gradient that is supposedly proportional to the charge-density. In metals the accumulation is so near to the surface that the accumulated charge within a metal at a surface can be approximated by a sheet of charge which has essentially no thickness; but NOT an infinite density of charge as the sudden change in resistivity would require when assuming that the charge-density is proportional to the gradient of the resistivity: One must be very gullible to believe the arguments of our three “experts” on this thread.
The charge-sheets are caused by physics, not pie-in-the sky mathematics. For example, when joining two metals with different work functions, a dipole, consisting of a positive charge-sheet and a negative charge-sheet, forms across the surface to align the Fermi levels of the two metals: This happens even if the two metals might have the same resistivities: This sheet-dipole cancels the voltage difference between the two metals which existed before they were joined.
When sending a current through such an interface, the dipole adjusts and the electric-fields on both sides of the layer also adjust. This adjustment cannot be calculated by differentiating the resistivity as if it is a real a continuous and single-valued function of position; as have been argued by our three “experts” on this thread. Only a clueless theoretical physicist (of which we have far too many at present on our planet) will argue in this manner. This is why it has become imperative that all physics departments at all universities should be placed under the jurisdiction of the engineering faculties.
I hope that Ben, Sol and Ziggurat know enough about Ohm’s law that they will at least agree that when you have a conductor with an electrical resistance R, and apply a voltage V across its ends, and wait a while for equilibrium to manifest, a current I will flow through the conductor which can be written as:
I=V/R--------------------------------------(1)
This is Ohm’s law which one can one look up in any elementary book on physics (try it Ben, Sol and Ziggurat). Provided that the physics inherent in the situation allows it, one can also write this equation in an intrinsic format as:
Where E(x) is the electric-field at a point x within the conductor, (rho) is a “resistivity of the material” at point x, and J(x) is the current density at the point x. Note that for this equation to apply, the conditions must be such that you can approximate (rho) to have the same value at any two points (i.e. as if it is a continuous constant field), and J(x) as being, just like E(x), a continuous field that can change with position within the metal: If the latter approximations cannot be made, then Eq. 2 is meaningless; but Eq. 1, can still be used to calculate an overall resistance for the whole conductor; even when this resistance” cannot relate to a continuous resistivity-field (rho) within the conductor.
What remains valid, however, is that E(x) is a continuous field, even when the current density and resistivity cannot be approximated to be continuous fields: So that the voltage V across the conductor can be written as:
V=(the integral over the length L of the conductor)E(x)dx---------------(3)
If the material has a constant cross-sectional area A through which the current I flows, E(x) will have the same constant value E at every point position x, so that one can write for Eq. 3 that:
V=EL------------------------------------(4)
Thus E is the same at every position within the material and, if Eq. 2 can be used, the current-density J as well as the resistivity (rho) will be the same at all the positions along the length of the device: i.e. one can write that:
J=E/(rho)-----------------------------------(5)
I wish I could have generated a diagram on, for example, PowerPoint and pasted it here. Since I do not know whether this is possible or how to do this, if it is possible, I decided to modify Ben’s diagram so that it illustrates the real physics that is involved when a current flows through the iron-copper-iron sandwich. For simplicity, it is assumed that the cross-sectional area through which the current is flowing is everywhere the same.
I decided to ignore the small difference in the work-functions of the copper and iron. It is thus assumed here that when there is no current flowing, the charge-accumulation at the interfaces can be taken as zero.
To illustrate what happens when a current actually flows; charge-sheets have been placed at the interfaces as they will appear within the copper when a current is flowing through the iron-copper-iron device. The source-charges at the endpoints of the iron blocks are also shown.
There is not an extra accumulation of charge within the copper as Ben, Sol and Ziggurat argued in their normal clueless fashion. The electric-field lines entering the copper have the same density as the electric field-lines leaving the copper. Thus, according to Gauss’ law there is no net divergence of the field lines. Furthermore, the change in resistivity is abrupt at the interface so that the accumulation of charge cannot be derived by applying the differential gradient operator to the resistivity; even when trying to fudge the result by invoking the Dirac delta-function.
So what is the real physics-reason why a positive charge-sheet forms at the left hand interface within the copper while a negative charge-sheet forms at the right-hand interface within the copper? Charge-accumulation is solely required since, when a current flows through a sandwich consisting of three conductors each of which adheres to Ohm’s law, the current must be the same along the whole length of the device: Thus, assuming that Eq. 5 applies, one can use the current density J and the resistivities (rho)C for copper and (rho)I for the iron, to calculate different values for the electric-fields EI within the iron and EC within the copper, so that:
Since the current being injected into the copper is determined by the resistivity (rho)I and field EI within the iron, this requires that the electric-field within the copper must become less than within the iron. This can only be achieved by an opposite polarisation field Ep within the copper. This field is generated by the accumulation of the two oppositely-charged charge-sheets within the copper at its interfaces. One must thus have for the polarisation-field that:
I can now hear Ben, Sol and Ziggurat exclaiming that this is essentially the same as what they have been arguing even though they did it by the clueless assumption that they can take the gradient of the resistivity to reach the “same” conclusion: They will probably excitedly point out that when setting (rho)C equal to zero in Eq. 8, the polarisation-field is equal to the field within the iron and it “must” thus totally cancel the electric-field within the copper.
But it is exactly at this point where one separates the competent physicist from the nitwit-retards that are at present in charge of physics-dogma on our planet. As will now be shown, you cannot set (rho)C equal to zero in Eq. 8 to obtain a zero electric-field within a conductor with free charge-carriers which can be accelerated. To prove this we will assume that we are able to tune down the resistivity (rho)C of the copper towards becoming zero, and see what real physics demands when this happens.
To do this, one must go back to basics: Let us see where the resistivity (rho)C comes from for a material, like copper, which have free charge-carriers that can be accelerated. Using Drude’s approximation, as the London Bros. also did (which they did in a stupid manner since they assumed that one can choose the relaxation time (see below) to be infinitely large in order to obtain zero resistivity within a metal), one finds that the resistivity is given in terms of a relaxation time (tau)C in copper, as:
Where NC is the density of charge-carriers in the copper, q is the charge per charge-carrier, and m is the mass of each charge-carrier. The current density JC can, in turn, be written as:
Where vDC is the drift speed of the charge-carriers within the copper. From Eqs. 6, 9 and 10, one can obtain the drift speed vDC in terms of (tau)C and the electric field EC, as:
What does (tau)C physically mean? It is a parameter that hides many sins, since it is incorporated into an equation, which is not commensurate with the rules of calculus, in order to make the equation commensurate to the rules of calculus. It is in reality a fudge factor, which can be very useful when the person who invokes it is not a fool. There are obvious limitations when using this factor. The most important one is that for a given physical size of the conductor, the relaxation time must be smaller than a critical number. If it is not, one does not achieve the objective to allow calculus to be used: The incorporation of the relaxation time is then a fruitless exercise. This simple fact has for 80 years not penetrated the skull of a single physicist, amongst the hundreds of thousands of physicists, who devoted their research to superconduction.
Nonetheless, when the relaxation time is small enough so that calculus can be used to derive a physics-answer, this parameter must relate to the average time interval (tau)SC between two consecutive scatterings of a charge-carrier. One can then argue that on average a charge-carrier is accelerated by the electric-field E for a time-interval (tau)SC, before it scatters: Thus, assuming that a charge-carrier loses all its kinetic energy when it scatters, one can calculate the average maximum speed vM that it reaches before being scattered by using Newton’s second law F=ma; which, since the acceleration a is now equal to (q*EC)/m can be written as:
One expects that vDC must be approximately equal to (1/2)vM; and thus that (tau)SC is approximately (1/2)tauC. Nonetheless it is clear from the identical mathematical expressions in Eqs. 11 and 13, that when (tau)C increases (tau)SC increases proportionally. One can thus estimate the average mean free distance that a charge carrier moves between two consecutive scatterings as:
Eq. 9 requires that (tau)C must increase in order for the resistivity to decrease, while Eq. 14, requires that the distance sDC must increase in concert as the square of 2*(tau)C.
Now assume that the length of the copper is LC, and we allow its resistivity to decrease towards zero. Before the resistivity reaches zero, one will reach a point at which sDC becomes equal to LC and exceeds it. This means that there is then no scattering within the material anymore: Which must mean that the charge-carriers are now moving through the copper without experiencing any resistance to their motion within the material. Does this mean that (rho)C is now zero? In essence yes; BUT the total resistance across the copper is not zero; since one can measure a voltage V across the copper, and a constant current I through the iron-copper-iron sandwich. How is it possible that you can have resistance without any resistivity?
It should be obvious, except of course to an “expert” on superconduction, that sDC is now pinned to stay equal to LC: This means that (tau)DC, the time between consecutive scatterings is also pinned, and that (tau)C is now meaningless. This pinning stays valid even when one stupidly, like the London Bros., assumes that (tau)C can become infinitely large. This is utter stupidity since Eq. 9 does not apply anymore.
It is thus totally senseless to assume, as the London Bros. have done nearly 80 years ago, that to have no resistance to the motion of charge-carriers which can be accelerated into, through, and out of a material, one must set (tau)C equal to infinity. To repeat, it was, and still is, an incredibly stupid assumption. What is even more incredible, is that that tens of thousands of “respectable” physicists followed like nincompoops in the footsteps of the London Bros., and are still doing so while calling themselves “experts” on superconduction. For the record, let’s name some of these “experts”: Ginzberg, Landau, Abrikosov, Bardeen, Cooper, Schrieffer, Josephson, Pippard, etc. etc. etc. What is even more frightening is that we still have large concentrations of similar “experts” at the University of Cambridge and along the West Coast of the USA.
In addition, it is compelling to argue that long before sDC reaches the value of LC, the assumption that a material has a resistivity (rho)C which can be modelled as a continuous constant of position at every point within the material, must totally break down. One expects that this approximation can only be valid when sDC<<<<LC. Even if one wants to still moronically argue that, owing to the high density of charge carriers NC within the copper, Eq. 9 stays valid right up to the point where sDC reaches LC, one cannot deny the fact that beyond this critical condition the charge-carriers must experience no resistivity within the material to their accelerated movement through the material, even while the current through the whole device does not change with time.
Now the relevant question: Can the applied electric-field within the copper become cancelled by the accumulation of charges at the surface of the copper after sDC has reached the value LC so that the resistivity to current-flow through the copper becomes zero? Not at all! Why not? Since Eq. 8 is now not valid anymore. Any charge-carrier at the injection contact is immediately accelerated all the way to the ejection contact. They can thus not accumulate at this contact anymore. Since they are accelerated, the current within the copper is now not the same along the length of the copper, since the injected charge carriers are accelerated from having an injected speed vI at the injection contact to reach a speed vCtarget just before entering the target contact. The current at the injection contact is thus:
JCinjection=q*NC*vI--------(15)
And at the ejection contact it is:
JCtarget=q*NC*vCtarget-----(16)
Clearly one now has that JCtarget>JCinjection.
Thus, the current that arrives at the target contact is much larger than the current that flows through the iron block into the low-resistance copper. The reason why it is larger is that these impinging charge-carriers have a higher speed than they require within the iron after they have entered. It is precisely for this reason why you still measure a resistance; since on entering the iron (on the right) the electrons MUST dissipate this extra kinetic energy by scattering. Thus, when these conditions apply, charge-carriers cannot accumulate at the surfaces of the copper at all anymore: They are “vacuumed” away by acceleration from the injection contact in order to end up with an increase in kinetic-energy within the target contact. There is thus no way in which charge-carriers can accumulate at the interfaces to cancel an applied electric-field within such a material.
This is always the case for any material which has free charge-carriers that can be accelerated: Kinetic energy is always generated by acceleration; and even though this kinetic-energy does not, when sDC> LC, dissipate within the material itself through which they are accelerated, the kinetic energy does dissipate within the target contact. Thus, the compelling conclusion is that as long as the kinetic-energy, required for the motion of the charge-carriers through a material, dissipate anywhere within our universe, such a material cannot be a superconductor EVER!!!
Thus one can never reach the situation where one can claim that in a conductor, which has free charge-carriers that can be accelerated, one can have a zero electric field while a current is flowing through it. Such a conductor cannot accumulate any charge at its interfaces to cancel an applied electric-field (not even a part of it) within it; as is incorrectly suggested by Eq. 8 when setting (rho)C equal to zero. A material which have free charge-carriers that can be accelerated, can thus never be a superconductor while a current is flowing through it. Although a situation can be reached for which charge-carriers that can be accelerated experience no resistivity, while transporting a current between an injection and an ejection contact, this absence of such a resistivity, does not mean that there is an absence of resistance, so that such a material can never cancel the presence of an electric-field within itself while a current is flowing through it.
The fact that Ohm’s relationship works for a superconductor when setting (rho)C equal to zero, requires another explanation: One has to find out how superconducting charge-carriers can flow with a constant drift speed through a material without being accelerated and scattered all the time (in order to have such an average drift speed); how the electric-field is cancelled while this is occurring; how the charge-carriers acquire kinetic energy to move when there is no electric-field present to accelerate them; and why this kinetic energy does not dissipate anywhere within the material; and also not within the target contact, and also not anywhere else within our universe. No model on superconduction has EVER explained these fundamental questions, except my model.
<SNIP>
<SNIP>'ed, breach of rule 0, rule 11, rule 12. Please keep it civil, on topic, and address the argument vs attack the arguer.
Replying to this modbox in thread will be off topic Posted By: Locknar
Only they will claim that you can differentiate the resistivity of a metal as if it is a physically-real continuous function of position within a metal.
No we didn't. First you were unable to differentiate a vector function correctly (wrong). Then you claimed that mathematically you can't differentiate a step function, and claimed that this invalidates the whole approach (wrong again). You seemed unwilling to apply Gauss's Law to this situation in the standard intro-E&M way (wrong yet again).
The difference between the perfect-step-function and the smooth-resistivity change is utterly irrelevant to the general E&M behavior. Either case shows a charge layer of the same sheet density; the width of the transition zone sets the volume density but has no effect outside of the transition zone itself.
The charge-sheets are caused by physics, not pie-in-the sky mathematics. For example, when joining two metals with different work functions, a dipole, consisting of a positive charge-sheet and a negative charge-sheet, forms across the surface to align the Fermi levels of the two metals: This happens even if the two metals might have the same resistivities: This sheet-dipole cancels the voltage difference between the two metals which existed before they were joined.
Yes, this is the work function. Please notice that it is not responsible for the E field difference between the iron and copper---that difference is proportional to j, the work function behavior is not.
Nicely done Johan! You have drawn a picture of a positively charged sheet on one side and a negatively charged sheet on the other side. You've drawn an accumulation of free charge, in a conductor, that cancels an electric field. That's exactly what we said would happen and that you objected to violently.
There is not an extra accumulation of charge within the copper as Ben, Sol and Ziggurat argued in their normal clueless fashion. The electric-field lines entering the copper have the same density as the electric field-lines leaving the copper. Thus, according to Gauss’ law there is no net divergence of the field lines. Furthermore, the change in resistivity is abrupt at the interface so that the accumulation of charge cannot be derived by applying the differential gradient operator to the resistivity; even when trying to fudge the result by invoking the Dirac delta-function.
First, the "field lines" you have drawn represent different field magnitudes (in the same direction). You've seen the divergence equation already. Do you know what divergence means? For a vector { Ex , Ey, Ez } the divergence is dEx/dx + dEy/dy + dEz/dz. The "parallel field lines" in the picture above sets Ey=0 and Ez=0. The remaining term is dEx/dx, which Ohm's Law (which you evaluated correctly) tells us is NOT zero.
Secondly, the usual statement "the flux of field lines is conserved"---the usual justification for statements like "the number of field lines is the same, so the fields are the same"---is only true in a source-free region, which this is not.
Third: how can you draw a picture showing excess charges and then deny that they are excess charges?
I can now hear Ben, Sol and Ziggurat exclaiming that this is essentially the same as what they have been arguing even though they did it by the clueless assumption that they can take the gradient of the resistivity to reach the “same” conclusion: They will probably excitedly point out that when setting (rho)C equal to zero in Eq. 8, the polarisation-field is equal to the field within the iron and it “must” thus totally cancel the electric-field within the copper.
But it is exactly at this point where one separates the competent physicist from the nitwit-retards that are at present in charge of physics-dogma on our planet. As will now be shown, you cannot set (rho)C equal to zero in Eq. 8 to obtain a zero electric-field within a conductor with free charge-carriers which can be accelerated. To prove this we will assume that we are able to tune down the resistivity (rho)C of the copper towards becoming zero, and see what real physics demands when this happens.
Any charge-carrier at the injection contact is immediately accelerated all the way to the ejection contact. They can thus not accumulate at this contact anymore. Since they are accelerated, the current within the copper is now not the same along the length of the copper, since the injected charge carriers are accelerated from having an injected speed vI at the injection contact to reach a speed vCtarget just before entering the target contact. The current at the injection contact is thus:
Good, good, good. Did you notice that you've just inserted current divergence? If the current is different at different ends of the copper, then charge is being depleted at one end and accumulating at the other. (Conservation of charge: d rho/dt = div J). This depletion of charge is where the charge sheets come from, Johan. You've now identified the out-of-equilibrium behavior that leads to the equilibrium behavior that you objected to above.
The end of your post has been reported to the mods.
Yes, this is the work function. Please notice that it is not responsible for the E field difference between the iron and copper---that difference is proportional to j, the work function behavior is not.
One additional note here: the work function difference will create a charge separation at the boundary (positive charges on one side, negative charges on the other). It DOES NOT lead to any net charge at the boundary. The field produced is thus confined to the boundary region.
The charge which accumulates at the boundary because of the current, however, WILL be a net charge, as it must be to change the field throughout the copper.
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