Johanfprins, some of your ideas are very attractive.
I have read only this thread and some links that appears in it, so I have not an elaborate opinion, but I want to made a little contribution in a point in which appears you place a lot of importance. I understand you, it is an important point: the zero or not zero resistance included as definition of superconductivity.
I am not making science neither engineering, my interest is only an intellectual one, and I would try to explain as better as possible, because I am not a native English speaker.
First a brief summary about Ohm´s law.
It is very clear that Ohm's Law is only referred to a material. It has not sense to use it for the "vacuum": the empty space is not a material (there are some comments about this).
Both intensity and electrical potential (and so difference) are previously defined, but resistance is not previously defined. So resistance is clearly defined within the Ohm's Law:
- Resistance is the division between electrical potential difference applied to the material and the electrical intensity.
- Resistance is a real number because operands of the division are real numbers.
- Conceptually, It appears that the resistance is the magnitude that quantify the opposition a material offers to the flow of current.
- Conductivity and resistivity are related with the resistance (previously and macroscopically defined )
- Resistivity can conceptually be seen in a similar way as the resistance.
- Both conductivity and resistivity, also, are real numbers.
After that, the Microscopic Ohm Law can be theoretically related with the macroscopic Ohm's Law and with other concepts of electromagnetism and even quantum physics. Again it is supposed a "material", not empty space (see by example
http://hyperphysics.phy-astr.gsu.edu/hb ... hmmic.html).
I want to stop at the point in which we have the direct proportional relationship between current density and "applied electric field" which is supposed uniform in the material (constant current). At that point:
Resistivity, conductivity and resistance are real numbers. Remember, the real numbers are included in the complex numbers so there is no problem with the Complex Ohm's Law. I think it is not worth to enter on the complex ohm law.
Ending the brief not all materials are "ohmic materials" and also we must be very carefully with the difference between "electromotive force" and "electrical potential difference".
First thing I want to remark is that those three (resistance, resistivity and conductivity) magnitudes are defined and very clearly defined, I think. I disagree with those statement that they are not clearly defined. Well, you may think they should be redefined, or must be changed their definitions, or better to define another different magnitudes for a best interpretation of this phenomenon. But they are clearly defined, I believe it.
After said that I want to remark again that they are real numbers. Why I do remark it? Because as real numbers...
- what may occur if they are zero?
- could them be zero?
- in which conditions they could be zero?
There is not problem with the macroscopic Ohm's Law. If the electrical potential difference, applied to the material, is zero and the intensity is finite, the material must have zero resistance.
With the microscopic form of Ohm's Law, the case is more subtle. At first glance, if resistivity is zero then there is a division by zero.
But you have remarked that there is not electric field everywhere within your material. The microscopy Ohm's Law is valid in every section in the material. So, in such case you have a zero (=conservative electric field) divided by zero (=resistivity) or, if you prefer, an infinite (=conductivity) multiplied by zero (=conservative electric field), which is a much more different problem. As I see it, the problem is not the zero resistance; it is this indetermination and why it occurs. But again, the only possible explanation, within the Microscopic Ohm's Law, is: if the current density is finite and the (conservative) electric field is zero, the resistivity must be zero, so again the resistance must be zero.
From your measures, you must conclude your material has zero as value of resistance. So, I don't understand your radical opposition to use of zero resistance in the definition of superconductor. Couldn't you conciliate the zero resistance with your theory? It would be the best way to go, I think.
By example, you said: "So it is not zero resistivity that cancels the electric field but the cancellation of the electric field which we use to define zero resistivity".
I agree with you that "it is not resistivity that cancels the electric field", it is obvious. But about your asseveration "but [is] the cancellation of the electric field which we use to define zero resistivity": I am not only disagree with it, but also I think you don't need it.
The “cancellation of the electric field” doesn’t define the "zero resistivity": it is previously defined. You are not defining the "zero resistivity". The zero is valid value of the resistivity; furthermore (as I said) it must be zero with those values of voltage and current you got. What you have made is to measure current across your material and to measure voltage between two points, then you inferred that the (conservative) electrical field is zero and then calculated the resistivity and the value result you got was zero. You calculated the value of resistivity, and you got zero which is within the valid range of values of the microscopic and the macroscopic versions of the Ohm´s Law. As I said previously I think the problem is the indetermination and why it occurs, but the result is clearly a finite current (or a finite current density). The indetermination has been physically resolved into a finite current, so actually the only problem is why it occurs.
Again, if you got a zero voltage between every two points of your material and got a finite current, I don't understand your radical opposition to use the zero resistance in a definition of superconductor. Why?
Only another question, I think is only about redaction. You said "when I measure zero voltage over two points there is no net electric field between the two points".
I understand, I think, what you want to say but I disagree with how you said. The expression "no net electric field between the two points" has a lot of problems. I apologise if I have understood it in a wrong way or if I am no able to express with clarity what I want to mean: as you well know, the electric field is defined in every point, it is not defined "between two points", much less "net electric field between two points". I suppose what you want to mean is that everywhere within your material (in every point), the (net, or total) electric field is zero. If it is so, I agree with you that, if we assume that along your material the electric field is uniform, you only need to measure the voltage between two points of your material.