Mathematically this is to do with the non-independence of reality (what I call singularity theory). Logic requires independent variables because it is required to keep 1 and 0 distinct. This makes logic consistent but incomplete. Reality is not incomplete and is not constrained by the distinct 1,0 assumption of logic. Time and space are not independent variables, and neither are dimensions or any other discrete logical concept. Relativity does not fix this but it helps deal with it by mathematically introducing non-independence. We effectively allow 1=0 in the limit, modellled either with statistical super-position or with relativistic functions (e.g. Lorentz transformations). Your equations are elegant models of how this non-indendence leads to the pseudo-discrete particles and events we observe.

Hi Preston Guynn

We haven't talked about this theme together with you yet, but what I understand, the solution of super conductivity can be found from the molecular distance and suitable structure. Velocity (kinetic energy) is indeed involved, but not only RMS velocity, also the molecular weight is important due to it causes the certain kinetic energy to produce certain particle free movement time.

->

Temperature = particle kinetic energy;

Particle velocity can be calculated with its mass.

Pressure = Particle free space.

->> the interaction time inter wall can be calculated through these.

According to my studies, there might be some universal time which explains superconductivity. Here's my rough paper about this topic. But I also recommend the Paper of Preston to everyone. We have landed on the same idea, but from totally different direction, Yet Preston is the one who have found the missing puzzle-piece here.

Working Paper STATES OF MATTER defined from The Speed of Light

I know two reasons, Dear Rajni Kandari

• If the external magnetic field strength H is greater than a certain Hc value, then when the metal is cooled, it is not displaced and superconductivity does not occur.
• Materials with poor electron-lattice interaction (metals with very low resistivity or conducting properties) do not create Cooper pairs and are not superconductors.

It can be seen by looking at the Tc of pure metals (the most simple systems), copper, silver, platinum, and gold do not become superconductors at very low temperatures because the interactions between the lattice and the valence electrons are simply too weak.

Best Regards.

Dear Rajni,

Your question remains open for about 100 years. However, I try to tell you a simplest answer.

The superconductivity is possible only when there are permanent electronic pairs in a metal. The key word here is ‘permanent’. Indeed, if any electronic pair breaks, then its momentum dissipates and supercurrent vanishes.

The pair permanency is possible only when the pair formation occurs at the Fermi level. Indeed, if the pairs form at an energy level (say Eλ) below the Fermi level, then new electrons can fall from upper energy levels to the level Eλ and form new pairs, giving rise to the pair recombination/breaking.

Thus the answer to your question: not all materials become superconductor, because not all materials have the pairing level Eλ closely to the Fermi level.

There is another reason I forgot to mention & discovered by Prof. Pippart in 1947, Dear Rajni Kandari

I elaborate a full answer in the last post in my thread, please check:

https://www.researchgate.net/post/Why_is_the_unitary_limit_in_the_dispersion_scattering_amplitude_in_Quantum_Mechanics_so_elusive_to_explain

But shortly is this one: R decreases in jumps to zero when performing measurements with direct current (plot 1), it varies more smoothly at frequencies of 1.2 GHz (plot 2) and 9.4 GHz (plot 3) and practically does not depend on the temperature at 2,000 GHz (4) (From Prof. A.B. Pippard. 1947). So the frequency plays a crucial role even for the BCS case.

Best Regards.

Thank you Pedro L. Contreras E. Stanislav Dolgopolov Jouni Jokela Ed Darnell Preston Guynn for the discussion and sharing the information. I come to know that there are many factors responsible for this behavior at the micron level.

Dear Rajni Kandari . Materials with poor electron-lattice interaction (metals - low resistivity means good conducting properties) do not create Cooper pairs – are not superconductors. See the link: https://www.researchgate.net/post/Why_do_bad_metals_superconduct_at_low_temperature_whereas_good_metals_eg_Cu_Ag_Au_dont

Kindly see also the following useful link: https://www.elprocus.com/what-is-superconductor-types-materials-properties/

Also check please the following useful link: https://www.google.com/amp/s/www.azom.com/amp/article.aspx%3FArticleID%3D941

The following link is also very useful: https://www.sciencedirect.com/topics/materials-science/superconducting-material

You are most welcome, Dear Rajni Kandari

Thank you Aref Wazwaz for sharing useful information.

You are most welcome dear Rajni Kandari . Wish you the best always

If you look at the US Federal Research Center's superconducting materials section Or refer to the following address

https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/superconductivity/#loginModal

You will find enough information to answer these types of questions

Although the professors' explanations were complete and comprehensive