Superconductivity at room temperature??

[ben m]

Once again, Johan, you've rejected a simple analysis, in which you cannot (despite flailing) find an actual error. You've replaced it with a hideously complex, twisted, bulging version of the system, which adds no new physics whatsoever except that it gives you room to make mistakes.

Forget it, Johan. I'm not even reading that.

You have not (despite flailing) found any mistakes in my analysis of the simple-one-dimensional case. This is because my analysis is correct and your intuition is wrong.

 

[sol invictus]

To repeat: Your so-called “divergence” in E within a conductor is caused by a cooperate effect which is, in turn, mandated by the requirement that the current I must remain the same along the circuit. It has nothing-nothing to do with an accumulation of charge anywhere: Gauss’ law does not play any role in this case.

Then you have denied the validity of Maxwell's equations, not to mention quantum electrodynamics. Gauss' law is always true: it's an absolute law of nature that is valid under all circumstances (in vacuum, in insulators, in metals, and in superconductors).

Gauss' law follows immediately from gauge invariance and the definition of electric charge. If it is ever violated by even the tiniest amount, the entire edifice of electromagnetism is incorrect and its success in explaining phenomena an incredible coincidence.

 

[ben m]

(OK, fine, I looked at Johan's whole post.)

The mistake is here:

When now following the electric-field from the right-hand contact, it is EIR until it reaches the interface B, whence it starts to “diverge” after it enters the central iron element. This “divergence” steadily decreases to become zero at x=0, whence it increases again (converges) to again become EIR at the interface A.

Sorry, Johan, you once again have failed Freshman vector calculus. In the geometry you describe, the divergence of the E field is zero. You looked at the change in field strength---it's true that the field is weaker in the bulge---and misidentified it as the divergence.

I can explain in more detail. We're looking at a 3D field with components both in the x direction and, due to the bulge, components in the radial direction (let's call it r). The correct equation for divergence is, in cylindrical coordinates,

div(E) = 1/r d/dr(r*E_r) + dE_x/dx

and this equation will show that the divergence is zero. The radial term will cancel the axial term.

You make the mistake of looking at the second term by itself,

dE_x/dx

and pretending that it's the divergence.

Your analysis of the "bulging" iron conductor is incorrect. The divergence is actually zero. The quantity that you mislabel as the "divergence" is just an x-derivative. Why would you do that? What is your problem?

(Do you disbelieve that E has radial components? I mean: draw a picture, seriously. Do you disbelieve that the divergence is zero? Try applying my analysis, and your analysis, to the current density. The vector fields are identical---they weaken in the "fat" part of the bulge. Do you believe that your analysis shows that J has a divergence? Do you know what it would mean if J had a divergence in this case? )

 

[ben m]

Let me just add: I'm amused that Johan has now misunderstood divergence in both directions. He took my 1D geometry where the E field has divergence, and made math mistakes that told him it had none. He then made up a new geometry in which the E field does not have divergence, and made a math mistake that told him it did.

 

[johanfprins]

Let me just add: I'm amused that Johan has now misunderstood divergence in both directions. He took my 1D geometry where the E field has divergence, and made math mistakes that told him it had none. He then made up a new geometry in which the E field does not have divergence, and made a math mistake that told him it did.

I am the one who is amused by your assumption that charge can accumulate within a circuit while a current I is flowng around the circuit; while you could have consulted any electronics technician who would have told you that this cannot be so: Since if it were so the rules to add resistances along an electronic circuit will then not work. Since they do work; and Kirchoff's rules for currents do work; it is your head that is not working!. Why is it so difficult for a person who can supposedly do mathematics (even though he finds a parabolic equation hideous) to also be a real physicist?

 

[johanfprins]

Then you have denied the validity of Maxwell's equations, not to mention quantum electrodynamics. Gauss' law is always true: it's an absolute law of nature that is valid under all circumstances (in vacuum, in insulators, in metals, and in superconductors).

But not at the surface of two metals with different resistances through which a current I flows.

Gauss' law follows immediately from gauge invariance and the definition of electric charge.

So what? This does not mean that it also works when you use it under conditions where it does not apply.

If it is ever violated by even the tiniest amount, the entire edifice of electromagnetism is incorrect and its success in explaining phenomena an incredible coincidence.

The only people who violated the applicability of Gauss' law have been Ben, you and Ziggurat on this thread! I did not see that your misuse of this law caused "the entire eidifice of electromagnetism to be incorrect". You are overestimating your powers

 

[sol invictus]

Gauss' law is always true: it's an absolute law of nature that is valid under all circumstances (in vacuum, in insulators, in metals, and in superconductors).

But not at the surface of two metals with different resistances through which a current I flows.

Very well.

So you deny the validity of essentially all the cornerstones of physics: conservation of energy, Maxwell's equations, quantum mechanics, etc. And you wonder why you have trouble getting your ideas accepted, Johan? Really?

 

[ben m]

Johan, I am right on both divergences. In the original setup---the one with no bulge---the field has no components other than Ex. Ez=0 and Ey=0. Do you think otherwise? In this case it is TRUE that the x-derivative is the same as the divergence. are you going to write down the divergence equation and tell me I'm wrong?

If you don't believe me, go look up something the flat-plate capacitor and look at how Gauss's Law is applied there.

 

[dasmiller]

Gauss' law is always true: it's an absolute law of nature that is valid under all circumstances (in vacuum, in insulators, in metals, and in superconductors).

But not at the surface of two metals with different resistances through which a current I flows.

So, does Gauss's law apply only for homogeneous materials, or does it apply only when there's no current?

 

[johanfprins]

So you deny the validity of essentially all the cornerstones of physics: conservation of energy, Maxwell's equations, quantum mechanics, etc. And you wonder why you have trouble getting your ideas accepted, Johan? Really?

Where have I done this? In the beghinning of this thread I violated the conservation of energy when a current flows through a Josephson junction since I did not totally rid myself of Josephsons nonsensical model. I corrected this. Where have I since then denied the validity of Maxwell's equations, Schroedinger's equation etc.?

I do concur that I do not agree with the Copenhagen interpretation, but there are many other physicists who also do not, and did not: Like Bohm, Einstein, Schroedinger, de Broglie etc. Do you claim that they "denied"the "cornerstones" of physics? Please grow up!!

 

[johanfprins]

Johan, I am right on both divergences. In the original setup---the one with no bulge---the field has no components other than Ex. Ez=0 and Ey=0. Do you think otherwise? In this case it is TRUE that the x-derivative is the same as the divergence.

Not while a current is flowing, since as I have proved that while a current I is flowing, it must be the same along the whole circuit and there can then not be an accuimulation of charge at any interface between two different elements within the circuit. The reason why the electric-field changes is precisely because the current I must be the same at every point along the circuit. Thus when the current enters an element with lower resistivity, the current I can only be maintained when the speed of the charge-carriers become less: An this mandates that the electrical field must immediately become less.

are you going to write down the divergence equation and tell me I'm wrong?

You would have been correct if there were not a current flowing. But there is a current flowing so that charge-accumulation cannot occur. It is quite ironic once you realise that a superconductor has a maximum current it can pass, and that this current is reached at precisely the point when charge has to accumulate at the injection contact. The superconductor then closes down totally and forms a normal conductor to prevent such an accumulation.

If you don't believe me, go look up something the flat-plate capacitor and look at how Gauss's Law is applied there.

Very good: I am planning to post some thought-experiments on the flat-plate capacitor. I am formulating these posts now. But want to make sure that I do not make another dyslexic mistake. You know dotage can be dangerous! If you remain patient I will start posting them soon.

 

[johanfprins]

So, does Gauss's law apply only for homogeneous materials, or does it apply only when there's no current?

It applies in all cases where you have an accumulation of charge. In a metal, charge can only accumulate at interfaces when an electric-field is applied without injecting charge-carriers at the same time: i.e when there is no current flowing through the metal. Within semiconductors one can create charge-accumulation at the surfaces while a current is flowing by doping the semiconductor.

 

[ben m]

Not while a current is flowing, since as I have proved that while a current I is flowing, it must be the same along the whole circuit and there can then not be an accuimulation of charge at any interface between two different elements within the circuit.

Nope. You noticed that the divergence of the current was zero under DC fields. This means that dQ/dt is zero---the charge accumulations, if any, cannot be changing. It does not mean the charge accumulations are zero.

(Which is funny, because, again, you apparently convinced yourself that in a wire-with-a-bulge the divergence of the current was nonzero.)

 

[ben m]

Where have I since then denied the validity of Maxwell's equations

For starters, you said that Gauss's Law does not apply to fields in conductors. This explicitly contradicts Maxwell's Equations. For the 10th time I point out that drawing Gaussian surfaces inside metals is a routine and uncontroversial feature of Freshman E&M problem sets around the world.

 

[sol invictus]

Where have I since then denied the validity of Maxwell's equations, Schroedinger's equation etc.?

What is wrong with you, Johan? You just denied the validity of Gauss' law (which is one of Maxwell's equations - did you not know that?) in the very post I responded to.

Here it is again:

Gauss' law is always true.

not at the surface of two metals with different resistances through which a current I flows.

 

[W.D.Clinger]

I do concur that I do not agree with the Copenhagen interpretation, but there are many other physicists who also do not, and did not: Like Bohm, Einstein, Schroedinger, de Broglie etc. Do you claim that they "denied"the "cornerstones" of physics? Please grow up!!

None of those luminaries rejected the Born rule.

Dr Prins rejects the Born rule.

It has become increasingly apparent that Dr Prins identifies the Born rule with the Copenhagen interpretation, and does not realize that all viable interpretations of quantum mechanics accept the Born rule.

Dr Prins also rejects superposition of quantum states, the very definition of expectation values, the relativity of simultaneity, the very definition of acceleration, and many consequences of Maxwell's equations (as both ben m and sol invictus pointed out above).

That is by no means a complete list of the well-established science that Dr Prins rejects out of hand.

 

[johanfprins]

Nope. You noticed that the divergence of the current was zero under DC fields. This means that dQ/dt is zero---the charge accumulations, if any, cannot be changing. It does not mean the charge accumulations are zero.

(Which is funny, because, again, you apparently convinced yourself that in a wire-with-a-bulge the divergence of the current was nonzero.)

You are funny! You just claimed that an electric-field can change with position while such a change is not a "divergence". Now you claim that the change in electric-field through the interface between iron and copper must be a "divergence". Why must (d/dx)E in this case be a "divergence" and not just a change with position which does not require an accumulation of charge. If you were a bit more practical, which you clearly are not, and never will be, you will know that electronic-devices which are non-ohmic are generated exactly when charge accumulates at interfaces. While the elements are "ohmic", as in your example, there cannot be an accumulation of charge at the interfaces, and therefore the change in electric-field across the interface cannot be a "divergence" ever.

I wish theoretical physisists will just realise that they just do not understand real physics! The taxpayer will save billions of dollars as soon as we get rid of these "airy-fairy" persons. Oh Higgs!!

 

[johanfprins]

For starters, you said that Gauss's Law does not apply to fields in conductors. This explicitly contradicts Maxwell's Equations. For the 10th time I point out that drawing Gaussian surfaces inside metals is a routine and uncontroversial feature of Freshman E&M problem sets around the world.

I did not say that: "Gauss' law does not apply to fields in conductors". For the 100th time, I am saying that when you apply it, you should know what you are doing! You must not do it in a stupid manner as you, Sol and Ziggurat are doing it. Just get it through your heads that when you have an ohmic circuit, there cannot be charge accumulation at interfaces between elements; since such charge-accumulation must make the circuit non-ohmic

 

[johanfprins]

What is wrong with you, Johan? You just denied the validity of Gauss' law (which is one of Maxwell's equations - did you not know that?)

I have not denied the validity of Gauss' law when there is an accumulation of charge. I just claim that it does not apply when there is not an accumulation of charge.

 

[ben m]

You would have been correct if there were not a current flowing. But there is a current flowing so that charge-accumulation cannot occur.

I give up.

You seem to think that the new E&M law you made up a month ago, "there is no charge accumulation in the presence of current", is so unassailable that, when you learn that it contradicts Gauss's Law, you decide to discard Gauss's Law.

Why'd we waste our time, Johan? Why did you fight so hard to show that the divergence was zero, or ill-defined, or nonsense? You could have said from the beginning: "I see, you are trying to show that the E field divergence implies a charge. That assumes Gauss's Law is true, but it does not.."

But you didn't say that. You yourself thought that Gauss's Law would prove you right---as long as you could find errors in my divergence statements. When that dark alley petered out, you abandoned it and searched for a new one. That's where you go beyond "challenging the status quo by doing new thought experiments". That's where you go into "I am a crackpot, whose theory is correct, so I have license to contradict anyone who objects."

That also pretty much exhausts my interest in your theory. Thanks for making your stance so clear.