Superconductivity at room temperature??

[W.D.Clinger]

My students are and were far from imaginary: For years I taught them quantum mechanics

And yet, during all those years, you never understood expectation values. As seen below, your mistakes demonstrate that you don't even understand the concept of average in the sense of an arithmetic mean.

I did not ask the questions because I do not know the standard dogma, but in the hope that you would know the standard dogma and be willing to explain it from your viewpoints.

Okay, I'll explain.

Now, according to Born, the intensity of the wave function is the probability distribution of where one will find an electron when one makes a measurement. Do you agree with this? This is what I have consistently read in text books and also taught my students.

Close enough for now, although the concept of a wave function is not limited to electrons and their position.

Thus the expectation value for position of an electron must be the position at which one expects to observe the electron most of the time when doing many measurements on an ensemble of identical electron waves. Do you agree with this?

No, because that's ridiculous.

Consider a two-person game of coin flipping. You and I flip a coin. If it comes up heads, I give you a dollar. If it comes up tails, you give me a dollar. For each of us, the expected value of that game is zero, because that's the average profit that each of us can expect if the game is repeated many times. That expected value is obviously not a possible outcome of any one game.

Similarly, the expectation value of an observable does not have to be a possible outcome of any one experiment.

Now calculate the expectation value for position for different wave intensities which satisfy Schroedinger's equation: What do you find? You find that for most calculations the expectation value for the position of the electron, is at a position where the intensity of the wave is zero and nothing more than zero. So for all these waves you expect to find an electron most of the time at a position where Born's probability distribution tells you that the electron can never be.

As explained above, the expected value of a game or experiment or observable is not at all the same as the value you expect most of the time. As explained above, the expected value does not even have to be a possible outcome of the game or experiment or observable.

So this is why asked you what do you expect to find at the "expectation position". I think the question is very reasonable. It is just strange that nobody has asked it for nearly 100 years. Probably since one must not question "the book".

The question has been asked and answered for centuries.

First you have to understand the concept of an average, or arithmetic mean, of a set of numbers. For example, the arithmetic mean of {1, 2, 4, 5} is 3, even though 3 is not one of the numbers being averaged.

Once you understand how that can happen with the arithmetic mean, you should know how that can happen when the arithmetic mean is generalized to a weighted average.

Once you understand how that can happen with a weighted average, you should know how that can happen when the weighted average is generalized to an expected value ∫ x P(x) dx.

Once you understand how that can happen with the expected value of a random variable, you should know how that can happen when the expected value is specialized to the expectation value of an operator on a Hilbert space.

Once you know how that can happen with the expectation value of an operator on a Hilbert space, you should know how that can happen with a quantum observable.

But you never knew that, even though you were teaching quantum mechanics at both undergraduate and graduate levels. That's sad.

 

[sol invictus]

But you never knew that, even though you were teaching quantum mechanics at both undergraduate and graduate levels. That's sad.

It's not just sad, it's literally unbelievable. Most QM courses start with a refresher on basic statistics.

I'm alternating between thinking Johan is flat-out lying, underwent a serious accident that strongly affected his brain, or is suffering from cognitive dissonance that's so strong he's forgotten all the physics he once knew.

I can't decide which is the most plausible.

 

[johanfprins]

This is basic, basic stuff. The fact that you, someone that claims to have overturned the theory of superconductivity, cannot get the simple physics of capacitors correct after two tries.... I truly wish you were capable of drawing the obvious conclusion from that fact.

I am not interested in you smart ass semantics anymore; so I will just summarize the basic facts:

1. For a parallel plate capacitor with no dielectric between its plates an applied voltage V will generate an electric field E between the plates which is stored as electric-field energy W=[(epsi0)/2]*E^2.

2. The same capacitor with a dielectric between the plates will store the same energy W at a lower voltage V^/<V generating an uncompensated electric field field E^/<E, no matter how and when the dielectric was placed between the plates. The energy now consists of the energy of the uncompensated field E^/ plus the field cancelled by the polarization field.

3. When increasing the voltage from V_/ to V one will thus store more energy than the original W without the dielectric.

4. When you have equilibrium, the voltage V maintains the total energy being stored. If polarization energy is radiated away, the total electric field-energy must drop: This would require a drop in the voltage V: But since the voltage is maintained by the power supply, the total electric field-energy is maintained by the voltage not changing at all.

5. Thus if the polariztion energy being radiated away is qV_J, it is replaced by the power supply without having to inject this energy by means of a charge-carrier.

 

[ben m]

tric between the plates will store the same energy W at a lower voltage V^/<V generating an uncompensated electric field field E^/<E, no matter how and when the dielectric was placed between the plates. The energy now consists of the energy of the uncompensated field E^/ plus the field cancelled by the polarization field.

All of these energy changes are exactly accounted for by measuring the usual inputs in the usual way. If you insert the dielectric while holding Q constant, the energy change is precisely the mechanical work done by the hand holding the dielectric.

3. When increasing the voltage from V_/ to V one will thus store more energy than the original W without the dielectric.

Yes, and this "extra energy" is exactly accounted for by W = q x V. "increasing the voltage" on a capacitor means injecting more charge. The extra energy you find on the capacitor is exactly the work done, by the battery, on the extra charge that it injected.

4. When you have equilibrium, the voltage V maintains the total energy being stored. If polarization energy is radiated away, the total electric field-energy must drop: This would require a drop in the voltage V: But since the voltage is maintained by the power supply, the total electric field-energy is maintained by the voltage not changing at all.

The only way that the power supply can "maintain the voltage" during a change in the dielectric is by moving charges around. If you change the dielectric's behavior without injecting charge, the voltage changes. If you try change the dielectric's behavior without changing the voltage, the battery passes a bit of charge to maintain V=Q/C.

5. Thus if the polariztion energy being radiated away is qV_J, it is replaced by the power supply without having to inject this energy by means of a charge-carrier.

I have no idea how you convinced yourself of this. It's nonsense. It's such basic nonsense that it's one of the lecture-demos we do during sophomore-level intro-E&M courses. It's explained more or less explicitly in any E&M textbook whatsoever---if you change the dielectric, C changes, but C = QV remains true, so if V is constant Q must change and vice-versa.

Do you own any physics textbooks at all, Johan? Which ones?

(P.S. You're temporarily off ignore, but only as long as you avoid comparing people to Nazis etc.)

 

[Ziggurat]

You see this is the reason why it is dangerous to have people like you trying to do physics. You do not understand when the concept of an average dielectric constant becomes a liability. In the case of a superconductor, you know how many dipoles there are and that each of them becomes polarized. Thus if there are N per unit volume and each has a "spring constant" (kappa) and a charge q on which the applied electric field E acts, the polarization distance p can be obtained from:

q*E=(kappa)*p, and the energy W=(1/2)*(kappa)*p^2

Unless kappa = 0, then you cannot get a nonzero polarization without an electric field. But you're claiming that the electric field is totally canceled, which requires that kappa = 0, and hence... NO ENERGY!

You haven't refuted what I've said, you've confirmed it.

Since the electric-field energy density without the dipole charge-carriers will be ([epsi0)/2]*E^2, one can solve what the density N of dipoles must be so that the absorb all this applied electric field energy.

Uh, no. You're taking a deeply unphysical step here. You're using the original field to polarize your dipoles, and then adding more dipoles with the SAME polarization in order to cancel the field. But if you cancel the field, guess what happens? The dipoles no longer experience any applied field, and will not remain polarized.

No field, no polarization for nonzero kappa, no polarization energy.

This is the most serious example of poppycock I have ever read. If the polarization energy is equal to the applied electric-field energy you do have a perfect dielectric.

No, johan. There IS no polarization energy if the material is a perfect dielectric (kappa = 0). The whole point of polarization (perfect or not) is that it MINIMIZES the total energy. If it made no difference to the energy whether you polarized it or not, it wouldn't polarize. Try it: the polarization can be directly derived from the energy by minimizing the total field/polarization energy. And because the energy scales as the square of the field, rather than directly proportional to it, the ONLY way that the minimum of the total energy can occur at zero electric field is if there is no polarization energy. Your own equations make that clear. But you couldn't recognize the significance of what you wrote down.

You have just now confirmed it in a spectacular manner.

No, johan. You have, once again, made a very elementary mistake.

I do not violate the conservation of energy: I left your little icon to remind you of your incompetence in this matter.

Yes, johan, your ideas do.

 

[Ziggurat]

2. The same capacitor with a dielectric between the plates will store the same energy W at a lower voltage V^/<V generating an uncompensated electric field field E^/<E, no matter how and when the dielectric was placed between the plates. The energy now consists of the energy of the uncompensated field E^/ plus the field cancelled by the polarization field.

If you keep the charge constant rather than the voltage, then the energy decreases when you insert the dielectric. You can only get back to the same original energy, or above, by adding more charge. Which requires the battery to do more work.

4. When you have equilibrium, the voltage V maintains the total energy being stored. If polarization energy is radiated away, the total electric field-energy must drop: This would require a drop in the voltage V: But since the voltage is maintained by the power supply, the total electric field-energy is maintained by the voltage not changing at all.

Um... unless you change the applied field, the polarization energy CANNOT radiate away, because the dielectric reaches a polarization which minimizes the total electric field + polarization energy. It's already at an energy minimum, radiating from a minimum is an obvious violation of energy conservation.

5. Thus if the polariztion energy being radiated away is qV_J, it is replaced by the power supply without having to inject this energy by means of a charge-carrier.

So you're violating conservation of energy, because you're extracting energy without putting any in. If the battery doesn't inject charge, it doesn't inject energy.

 

[W.D.Clinger]

V=Q/C.

So C=Q/V.

It's explained more or less explicitly in any E&M textbook whatsoever---if you change the dielectric, C changes, but C = QV remains true, so if V is constant Q must change and vice-versa.

Typo: You meant C=Q/V. Your point stands, of course.

It's not just sad, it's literally unbelievable. Most QM courses start with a refresher on basic statistics.

I don't know quite how to say this, sol invictus, because I have a lot of respect for you (and I say that without irony), but I don't see how your knowledge of the way most QM courses are taught could give you any insight into how Dr Prins taught his QM courses.

 

[ben m]

Typo: You meant C=Q/V. Your point stands, of course.

Yes, thanks.

 

[ben m]

So you're violating conservation of energy, because you're extracting energy without putting any in. If the battery doesn't inject charge, it doesn't inject energy.

I would point out that this is exactly where we were back on page 1 or 2 of this thread, which Prins later admitted was a "mistake".

Earlier, he had a battery doing qV of work on a charge. He followed that charge through the circuit and later found it in an electric field which would do qV of work. He counted both of these positively, and declared that qV + qV = 2qV was the energy available for radiation from this charge.

Now, he has a battery doing qV of work on a charge. He follows that charge through a circuit and finds it in a "polarized" region where (he says, not quite making sense IMO) it couldn't have been unless qV of work had been done on it. He now counts both of these positively, and declares that qV + qV = 2qV is the energy available for radiation.

Same problem.

 

[sol invictus]

I don't know quite how to say this, sol invictus, because I have a lot of respect for you (and I say that without irony), but I don't see how your knowledge of the way most QM courses are taught could give you any insight into how Dr Prins taught his QM courses.

You have a point.

At what institution did you teach these courses, Johan, and at what level?

 

[johanfprins]

In the case of a battery connected to a capacitor, yes: and the higher energy with a dielectric compared to a vacuum gap comes from the fact that the current is higher. The power output from the battery is still QV.

Just try and get it into your head that:

(1) A superconductor is not a pure metal (conductor), which, notwithstanding the absence of localized dipoles, acts as a perfect dielectric; since within it an applied electric field is totally cancelled when charge-carriers are not simultaneously being injected; so that a current can flow. When charge-carriers are simultaneously injected, they move in an attempt to cancel the applied electric-field: Therefore while a current flows a conductor cannot act as a perfect dielectric which cancels the applied electric field.

(2) Neither is a superconductor a pure dielectric through which a current cannot flow, and which becomes locally polarized to cancel at least part of the applied electric-field; and in principle can totally cancel the applied electric-field to be a perfect dielectric in another manner than a pure metal.

(3) A superconductor is both a conductor and a dielectric at the same time which is able to totally cancel an applied electric field even when a current flows through the material. It is thus a perfect dielectric even when, in contrast to a metal, a current is flowing through it. This is the mechanism that needs to be explained to really understand and model superconducting behavior. This has never been done by any model ever. My model proposes a mechanism which makes it possible to completely cancel the applied electric-field while still allowing a current to flow. Whether my model is correct in all aspects, I do not know since no scientist can ever know that. But it does explain why the properties of the low metal superconductors in another way than the BCS model, and in addition it models many aspects which BCS can just not model. Furthermore it explains superconduction in the ceramics, semiconductors etc., which BCS cannot explain; and explains it in terms of a single mechanism for all these materials.

Tell me you're kidding. PLEASE tell me you're kidding.Do you not know what the polarization vector is? Do you not know how to square a vector?

I asked you to explain since you are using it to deduce wrong physics. Thus I asked you because in my opinion it is you who do not know what a polarization vector is and probably do not know how to square a vector.

It doesn't matter if they're stationary or not. If the energy is a polarization energy, then moving or not, it's proportional to a constant, and that constant MUST be zero for a perfect dielectric.

You see this is the type of nonsense you are spouting since you do not know when the concept of an average polarization vector applies and when not.

If the spring constant is not zero, then your material is not a perfect dielectric, and you cannot have a polarization without an electric field as well. But you're claiming that there is no field in the superconductor, and that the superconductor is a perfect dielectric.

If one is so stupid not to know when a continuum description for polarization breaks down and should then not be used, then I despair that you will ever be able to think outside what you have usurped without really knowing what you are learning. Any monkey should know that a perfect dielectric cannot be described as a continuous polarization within a material. If there are no free charges, it has to be described in terms of the discrete density N of localized dipoles: One then finds that it is in principle possible for the N dipoles to absorb just as much electric-field energy as the applied electric field-energy; as I have derived and explained in another post above. As also pointed out above, in a superconductor, above absolute zero temperature, the applied electric field is totally cancelled by the polarization of the dipoles and the accumulation of opposite charges at the contacts during current flow.

Sorry, but your explanation runs into an obvious absurdity. What you're claiming is that current isn't actually flowing, you're just getting larger and larger polarization. If that's not what you're saying, then your last sentence is completely meaningless.

That is your wrong interpretation since you are willing to shoot off like a loose cannon without first reading what you are actually talking about. You are a disgrace to the scientific profession!

Aside from the fact that this would make it increasingly difficult to pull contacts off of a superconductor the more charge you ran through it, that also implies that either there's some limit to how much current you can flow through a superconductor before it stops superconducting (a rather astounding assertion that one should be able to test)

It is a well known experimental fact that this is so. Since you do not even know this, you are really arrogant to waste everybody's time on this thread.

or a superconductor can polarize infinitely (an even more astounding, and obviously unphysical, assertion).

Polarize infinitely? It is only a nincompoop who does not know at which point a continuum description of physics breaks down, who would spout such utter nonsense.

Yes, I know it's wrong. I know it's wrong because it violates energy conservation.

It does not.

You keep trying to relabel the energy, but you can't actually account for it. You can't ever say, we put in X energy, we get out Y energy, and X = Y, as it should.

I have done exactly this. If you cannot even understand polarization forces, then it will always remain beyond your ability to understand when energy conservation is violated or not violated.

You put in QV. You get out 2QV. That's wrong. And it's not arrogant or despicable for me to say so.

Half of the 2QV is polarization energy which the battery maintains without having to inject a charge-carrier with a charge 2Q. Unfortunately you choose to remain arrogant and despicable.

Polarization energy cannot rescue you.

It is not "rescuing" me but balancing energy conservation.

If the material is a perfect dielectric, then there IS no polarization energy.

Really?! Thus when you place a block of metal between two capacitor plates so that a current cannot flow through it, the electric-field applied by the capacitor will not be cancelled within the metal. Please read a VERY elementary text book on electrostatics. It is clear that you do not know elementary physics at all.

 

[ben m]

Really?! Thus when you place a block of metal between two capacitor plates so that a current cannot flow through it, the electric-field applied by the capacitor will not be cancelled within the metal. Please read a VERY elementary text book on electrostatics. It is clear that you do not know elementary physics at all.

You're wrong, Johan. When you place a block of metal in a capacitor in the way you describe, and you attach a power supply and start moving charge around in an attempt to build up an electric field. The work done by the power supply is exactly Q*V. It's not Q*V plus some polarization energy in the conductor; this "polarization energy" is zero, as Zig has said. The metal-dielectric block will polarize and polarize and polarize at zero energy cost; the work done by the battery all shows up in the (nonzero) electric field in the nonconducting region, where it's accounted for by W = 1/2 CV^2 or Q^2/2C as usual.

Again, if you have any Freshman physics textbook whatsoever, you will be able to find this question presented either as an example problem or a homework assignment.

 

[johanfprins]

Then what's the conflict with what I said regarding Ehrenfest's theorem?

The conflict comes from your inherent claim that a localized wave within a material can only change its position under the action of Ehrenfest's theorem. This is of course correct for "classical" movement where wave-packets are being accelerated by an applied electric-field: However, localized waves can also change position without Ehrenfest's theorem causing them to move. In the standard literature this movement is incorrectly modeled as so-called "tunneling": Nonetheless, even according to this wrong model a localized wave can move through a barrier, even though there is no change in potential energy within the barrier, and notwithstanding the requirement that, according to the mainstream, wrong model, the localized wave must have negative kinetic energy while it is within the barrier. Obviously, such a change in position is purely quantum mechanical and does not require Ehrenfest's theorem to model it as classical acceleration.

Crack open an introductory quantum mechanics textbook some time. You might learn something. And if you've got an issue with quantum mechanics, don't blame me.

I am not blaming you if you want to believe in a paranormal universe within which everything happens by an inbuilt probability. I also believed this when I taught this rubbish to my students. Experimental evidence has given me impeccable proof that the Copenhagen interpretation of quantum mechanics is an illusion; similar to Yuri Geller bending a spoon.

Uh, no. The Schrodinger equation is non-relativistic, so mass energy is already excluded, and the potential energy of the ground state of a harmonic oscillator is larger for smaller masses.

This is another misinterpretation which follows from the mistake by Schroedinger to include the rest mass of the electron as an input to his equation. In fact, the mass of an electron must be the solution of the corrected Schroedinger wave-equation which must not have mass as input, but must give the rest mass when solving it for a solitary, stationary electron wave. This corrected wave equation looks more like Maxwell's wave equation for the potential energy field of light, and it is already compatible with relativity: i.e. it does not relate to the classical Hamiltonian-function of the electron as Schroedinger's equation does.

I know it's the correct attribution because I transcribed it from the textbook myself, and the author's name is prominently displayed on the front cover. I am 100% certain about who said it. Of all the things to challenge me on, this has got to be one of the most stupid and pointless.

Whatever you're doing, you aren't using the equation in a way that his proof (and yes, it's a mathematical proof) justifies. If you have some other deriviation of that relationship, then maybe that other derivation supports such an alternative useage. But I doubt any such proof exists.

I am using it in a similar manner that Yukawa first used it and in a similar way that it is used in quantum electrodynamics; and when I do, it works since it fits more data on superconduction than the BCS model can. This is what I consider when doing physics; not how the relationship was derived by some nincompoop.

You accept authority when it's convenient for you to do so.

I accept authority that has been proved to be correct by experiment; not authority for the sake of authority: If you do the latter, you are not even worth to be called a human being.

Because credentials don't matter. Demonstrated ability does. You have consistently made elementary mistakes in regards to quantum mechanics.

I have given alternative interpretations for some aspects of quantum mechanics since I have found by experiment that the accepted interpretations are wrong. If you interpret my alternative interpretations as elementary mistakes since they cannot be found in the "bibles" you blindly believe in: So be it. I rely solely on experimental verification when ever it is possible. If not possible in all respects I rely on self-consistency; and both the Copenhagen interpretation and the BCS model are riddled with inconsistencies.

Of course not. Are you unclear about the definition of "definition"?

A definition in physics is also subject to experimental verification.

That doesn't mean a definition cannot be wrong. But the only thing that can be wrong about a definition is if it conflicts with a standard definition.

A standard definition is also subject to experimental verification and does not have an authority just because it is the "accepted definition" which every crackpot believes to be correct.

In this case, the standard definition of superconductivity includes the Meissner effect. That is what differentiates superconductivity from perfect conductivity.

The reason why you think it is so is because this deduction is based on the wrong models of the London bros., Ginzberg and Landau, BCS etc. The fact is that there exits no real incontrovertible proof that the Meissner effect defines superconduction. One can levitate a live frog in a magnetic field and it is definitely not a superconductor.

Because it's a definition.

Written on the tablets that Moses brought down from Mount Sinai?

Again, the only way that a definition can be wrong is if it conflicts with a standard definition.

No it can be wrong when it conflicts with experimental evidence.

A standard definition cannot be wrong, by definition.

If it conflicts with experiment it is wrong; no matter what you call it!

It's possible that the definition does not apply to what you thought it applied to, it's even possible that your defined object doesn't even exist, but that doesn't make the definition wrong.

Only an idiot will define something which does not exist.

Um... because you can plug zero into the equation just as easily as you can plug in any non-zero value. Why is that not obvious?

This is obvious but not when you claim that when a localized wave moves from one equilibrium position to another on the other side of a barrier, this movement is subject to Ehrenfest's theorem.

Uh, no. That's a way one can derive Ohm's law. But the law itself predates any such derivation, and one can use it to define resistance regardless of what microscopic model one wants to use.

Only a very stupid person will assume that an equation which relates to a very specific microscopic situation can be used generally without worrying whether the conditions for which the equation is valid are being operative; especially when it seems to describe another non-equivalent situation as in the case of superconduction.

Furthermore, even with such a derivation, taking the zero-scattering limit produces zero resistance, again rather trivially.

This "zero resistance" does not obey Ohm's law since the voltage is then not zero! Are you really so stupid or are you trying to be funny?

 

[sol invictus]

This is another misinterpretation which follows from the mistake by Schroedinger...the corrected Schroedinger wave-equation which must not have...it does not relate to the classical Hamiltonian-function of the electron as Schroedinger's equation does.

Let's start making a list, "physics according to Johan".

1) quantum mechanics is wrong (see below)

2) Maxwell's equations are wrong (see below)

3) Newton's laws are wrong (see below)

4) Probability and statistics are nonsense, since expectation values can be equal to values never measured (see 1)

5) Standard formulas for polarization energy are wrong (see 2)

6) All accelerating charges radiate (see 2)

7) Current flowing around loops do not involve accelerating charges (see 2 and 3)

8) Free energy for all from room temperature superconductors! (see 1,2,3)

9) Superconductors do not have magnetic fields in side them even though they have currents (see 2)

10) Schrodinger's equation is wrong (see 1)

Did I miss anything?

 

[ben m]

This "zero resistance" does not obey Ohm's law since the voltage is then not zero! Are you really so stupid or are you trying to be funny?

In the case Zig described, the DC voltage is zero. What makes you think otherwise?

ETA: At this point, it's starting to sound like you're picking totally random statements out of an intro E&M textbook and saying they're wrong. There is no rhyme or reason whatsoever to your list of disagreements.

Ohm's Law doesn't include the V=0 R=0 case? Ohm's Law only applies to a certain microscopic theory of resistance? Dielectrics can have polarization but not polarization density? Pushing a dielectric into a capacitor doesn't change the stored energy? This is not fancy-modern-BCS-theory-dependent stuff that you might be imagined to want to reject. Nor is it a subtle interpretive matter. It's basic-basic-basic facts about E&M, which the average college sophomore can derive from knowledge of (a) Coulomb's Law and (b) dW = F.dx.

 

[johanfprins]

Instead, I think you're simply incapable of rational thought on this topic. Your brain will not allow you to process information that threatens it.

Quite funny that I think the same about especially you as well as Ziggurat; Lately, Ben seems to be be willing to think along avenues that threaten mainstream dogma. If this is the case, it will be interesting to see how long it will last.

 

[sol invictus]

Quite funny that I think the same about especially you as well as Ziggurat; Lately, Ben seems to be be willing to think along avenues that threaten mainstream dogma. If this is the case, it will be interesting to see how long it will last.

I'm sure ben will be interested to hear that....

 

[Skwinty]

Happy birthday Johan,
Hope you have had a good day.

 

[ben m]

Lately, Ben seems to be be willing to think along avenues that threaten mainstream dogma. If this is the case, it will be interesting to see how long it will last.

I sure am! (ETA: except for the part where it's not "mainstream dogma" to begin with.) I'm unusually receptive to weird dark matter models (MOND, hidden sector, Q-balls); I have a sneaking suspicion that the neutrino mass is all Dirac; and I may be the only experimentalist in the world who really likes the holographic principle.

But if you think I sympathize with even one detail of your freshman-E&M denialism, you are mistaken.

 

[johanfprins]

Presumably you are referring to this:

[LATEX]\Delta E \Delta t \gtrsim \hbar[/LATEX]​

relation? Although it's often (ab)used to "explain" vacuum pairs and tunneling in layperson's and introductory QM texts, it's not a strict consequence of QM like the position-momentum relationship.

So the interpretation from relativity theory that time is a fourth dimension is wrong? If you want to interpret it as not being a "strict consequence of QM like the position-momentum relationship, why is it not banned from quantum mechanics altogether?

The URL you referred to is also at pains to explain that this relationship is not yet understood; as Landau correctly joked. Since a light wave exists in four dimensions (in fact 5 dimensions of which one is time as Kaluza has derived) it is highly possible that a matter wave can also have energy outside our three-dimensional space, and most probably must have such energy since it must be executing harmonic motion somewhere. It is sure as hell not doing so within our three-dimensional space; unless an electron wave is moving with a momentum <p> relative to another body, like a diffraction grating, so that de Broglie's wavelength manifests owing to the Lorentz transformation.

All that we can observe in three-dimensional space is its potential energy distribution. Not both its harmonic potential and kinetic energies as for other harmonic waves. So it is possible that this equation describes energy which becomes available when an electron-wave resonates; for example just before it "collapses" into a lower energy wave or "inflates" into a higher energy wave; or even changes position without changing its energy.

And by assuming the latter possibility, one can model what is called "tunneling" without violating energy conservation as the standard model most definitely does. And by using this mechanism to model the movement of charge-carriers through a superconductor one obtains a far more consistent description of superconduction than can be obtained when using BCS. In a normal world, the physicists controlling superconduction research should be interested in such a model, even when they believe, without any proof, that Heisenberg's relationship cannot be used in this manner. It should be left to experiment to validate a new model; not to a bunch of bigots who believe that we already know everything about quantum mechanics.

But for 10 years I have found that the mainstream physicists are only interested to defend mainstream dogma to the hilt, and not at all open to consider how well another model can fit data which their assumptions like Cooper pairs, cannot explain. Whatever you think or like about any postulate, the correct scientific attitude must always be to see how well it conforms with experimental results. If you are not of this opinion, it would be better if you do not dabble in physics at all.