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Having a conversation with a friend, we where discussing about the conductivity and resistance changes of superconductors.

He insisted that available superconductors produced by universities or corporate entities that are being produced today worldwide can in practice maintain a Zero resistance state in specific laboratory conditions.

I doubted this to be the case, claiming that maintaining a conductor in a R=0 state, in practice, is nothing more than an ideal experiments are trying to achieve, the same way maintaining mass at 0ºK would. I was also claiming that experiments that would indicate that the material is in fact in a R=0 state would do this due to lack of the necessary hardware sensibility to detect the minuscule deviation from true Zero resistance and that respectable sources would make account of this documenting the experimental error.

I am unaware of experiments that show reliable methodology to indicate the viability of a true "superconducting phase". I understand that superconductivity, by definition, is a current flowing without resistance, and that this is only possible if the voltage across the junction is 0, otherwise there would necessarily be both current and voltage and therefore an effective resistance 𝑅=𝑉/𝐼. My suspicion is that the superconducting state is more akin to an 𝑅(𝐼) function, thus my doubt of extensive documentation and testing on true Zero resistance materials being produced, which leads me to my initial question:

Has a true Superconductor ever been produced AND experimentally proven to be a true superconductor?

If so, where could I find the documentation for these experimental procedures and the methodology claiming the veracity of the experimental potential of achieving this physical state in laboratory conditions? If not, to what degree of experimental error has Superconductivity been recorded?

In other words, are materials called "superconductors" popularly misnamed and/or misrepresented?

Or, is this specific matter still unknown due to the lack of the necessary sensibility of equipment, making the knowledge on the subject no more than hypotheses and speculation?

Thank you for your time.

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available superconductors... maintain a Zero resistance

According to theory, yes.

maintaining a conductor in a $R=0$ state, in practice, is nothing more than an ideal experiments are trying to achieve, the same way maintaining mass at $T=0$ would

Not a fair comparison. There's no "third law of resistances" that says you can't reach zero.

experiments that would indicate that the material is in fact in a $R=0$ state would do this due to lack of the necessary hardware sensibility to detect the minuscule deviation from true Zero resistance

Whenever physicists empirically report on something that's apparently zero, they do in fact say, "it's at most this", or "it's less than this". For example, an electron's size is less than $10^{-18}\operatorname{m}$.

Has a true Superconductor ever been produced AND experimentally proven to be a true superconductor?

What do you take as proof? Do you think we've proven all light travels at the same speed in a vacuum, or only that the speeds of individual studied rays are too near-equal to distinguish with our equipment?

When a scientific theory says something is $0$ (and $x=y$ means $x-y=0$, so claims like that are made all the time), and that something is $0$ to within experimental error, an empirical purist will say we only "know" it's however small it needs to be to be $0$ to within experimental error. But scientific insight is all about accepting certain things until they're refuted. Not that I'm chastising the "purist" approach, mind; we have to wear both hats at times.

to what degree of experimental error has Superconductivity been recorded?

I haven't managed to google the tightest known empirical bounds on an observed resistance (or resistivity) - if anyone has that, please let me know so I can edit it in - but if we consider another consequence of superconductivity, we've used a superconductor to levitate a ball for at least 26 years. When do you say you're convinced?

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Yes, in 1911 by Gilles Holst and Heike Kamerlingh Onnes in Leiden. Kamerlingh Onnes received the Nobel prize in 1913.

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