Superconductivity
Superconductivity might be very helpful in establishing electromagnetic launch systems on Luna. It is a complex topic about which various contradictory statements are offered. The value of a model is in how it can organize data to predict new useful and interesting materials and devices.
To properly understand superconductivity, one should first understand the usual cases of conductivity in such a way that superconductivity is a natural outcome of this understanding.
We begin with the proper understanding of the electron. In the double-slit experiment, results for electron diffraction can be explained by considering that the electron does not have a defined size, merely a measured cross section for any defined interaction with other particles. Cross section is usually measured in barns. The electron is diffuse enough, when not bound to an atom, molecule or crystal, to go through both slits at once, as a stream of water goes through the many holes of a sieve and comes out as a stream of water on the other side. The two slits combined merely act to deflect the electron by randomly variable amounts in turn determined by variations in initial conditions less than the Heisenberg uncertainty amount. The double slits just act like pachinko pins. A large enough number of electrons through the dual slits or pachinko balls through the set of pins will be distributed statistically according to probability. Playing pachinko could help in understanding an aspect of elementary particles.
When the electron is bound to an atom, molecule or crystal, it is always in one orbital or another. The orbitals are more restricted in space than free electrons. They are associated each with its characteristic frequency. They are most easily defined by the amount of energy lost by the electron when it becomes bound. And they have interesting characteristics in metals and other crystals that result in electrical conductivity and in certain conditions superconductivity.
Conduction orbitals are of particular interest. In sodium, silver and copper (for example) the outermost electron in each atom is loosely bound. When such an atom joins a crystal of like atoms the loosely bound outer electron becomes bound to the crystal in a conduction orbital instead of being bound to an individual atom. Electrons can move from one orbital to another only by quantum exchanges of energy and momentum. In sodium, for instance, any of the two 1s electrons, the two 2s electrons or the six 2p electrons could jump up to the conduction orbital energy level and start moving around if they first recieved the quantum of energy necessary to make the change. However photons or latice vibrations with that amount of energy are usually not available and the ten localized sodium electrons remain bound to the sodium nucleus and do not move about the crystal. If a 2p electron did absorb a quantum of energy from a photon to jump to a conduction orbital, it would leave behind a hole which would be filled by any passing conduction orbital electron. The electron droping into the 2p orbital would give off the same quantum of energy as a photon as was required to make a hole there in the first place. The process of giving off a quantum as a photon when an electron falls to a lower energy level is always available. The process of absorbing a quantum when an electron rises to a higher energy level is available only when a photon or lattice vibration of that energy is present.
Once the sodium atoms have joined a crystal, electrons no longer populate the 3s orbitals, one to a sodium atom, because the conduction orbitals are of lower energy. In order to become localized a conduction electron would need to absorb a quantum to become a 3s electron. It would then just give off that quantum again while absorbing a little momentum from the latice or another conduction electron and become a conduction electron again. There are exactly ten electrons per sodium atom in a crystal that fill localized orbitals and leaving these orbitals is a big quantum jump. There are many conduction orbitals and there is always a vacant conduction orbital a small quantum jump away from any occupied conduction orbital. So by trading small amounts of energy and momentum with the crystal latice or with other conduction electrons an electron is always able to move from one conduction orbital to another. This situation contributes to the electrical and thermal conduction of the crystal and it contributes to electrical resistance.
The situation with Yittrium, Lanthanum, and Bismuth is not so straight forward. These elements have partially filled lower energy orbitals. In ceramic crystals in which atoms become ionized the odd partially filled sets of orbitals sometimes give rise to a conduction orbital at lower energy than the ordinary conduction orbitals, but so constrained that there is no nearby empty conduction orbital that conduction electrons can jump to using the quanta of energy available in a low temperature crystal. That means electrons in this energy level must continue to conduct with the same momentum that they had when the crystal formed. They can not get enough energy to rise to a nonconduction orbital or an orbital with different momentum. The electrons can not all leave the left side of the crystal and pile up on the right side so electrostatic forces require that half of them conduct electricity to the left and half conduct electricity to the right for zero net conduction. The condition is again changed by man who forms a ring and sets more conduction electrons going one way than another. Once the pattern is set the electrons still do not have the energy to change it. They will keep on conducting electricity in a circle forever or until the temperature allows them to get enough energy to change.
In a superconductor based upon Yittrium in a ceramic crystal a conducting electron cannot change its velocity because a different velocity would be associated with a different freqency for the conduction electron orbital, and it must have a frequency to keep the nodes of the conduction orbital in the same spatial relationship with Yittrium ions. The condution orbital can accept only quantum changes in velocity and, since the Yittrium ions are spaced so far apart, the needed quantum for a change in velocity is more than the energy available in the cold crystal.
In this model normal conduction does not involve a classical fluid moving through a crystal lattice. It involves electrons in orbitals with nonzero momentum. They jump from one conduction orbital to another by quantum jumps, interacting with the lattice and other electrons only when there is another vacant orbital to jump to. There is no need to form Cooper pairs nor any need for phonon attraction between electrons. Electrons enter orbitals in spin up and spin down pairs because that is their nature. When electrons fall into a conduction orbital from which there is insufficient energy to jump out again, they cease to interact with the lattice, but continue to conduct electric current.
The reason people were led astray in analyzing the double slit electron diffraction experiment and electrical conductivity is that people repeatedly applied classical particle concepts to electrons which are quantum particles. An electron does not have a definite size. Its size depends upon the particular conditions under which it is measured. It is smaller and has a higher frequency when it has lost much energy associating with an atom nucleus. When it gets enough energy to be a completely free electron, it is blown up like a balloon. Two classical particles cannot occupy the same space. Two electrons will share as long as they have different quantum numbers and occupying the same space is the lowest energy condition for both of them. To an electron a steel plate looks like mostly empty space. It is only concerned about whether the electric fields in the steel crystal lattice will let it occupy that space with low enough energy so that it can squeeze through a slit or two neighboring slits at the same time. So, whether it goes through one slit or two, part of the electron is going through the material of the steel plate bordering the slot or slots. It is the same way with tunneling. An electron in a conductor can spread itself out a ways through a neighboring insulator. If there is a low energy conductor on the other side of a small enough barrier, it can squeeze right through. People have thought of an electron as a tiny dimensionless point that radiates charge and whizzes around in an electron orbital in an atom. Really it is a flexible compressable slippery thing that fills the whole orbital and vibrates, radiating charge from the whole orbital at once. The vibration of an electron in a localized orbital is like electric charge and magnetism fading in and out of existence in a standing wave pattern that fills an orbital. From the point of view of a nucleus, an electron in and orbital with momentum is just like a electron in a stationary orbital except that it appears at the left and disappears at the right or vice versa. In both cases the electron balances the charge in the nucleus. As long as electrons appear at the left with the same frequency that they disappear at the right there is no problem.
One might wonder why electrons in the lowest energy level, the 1s orbital, have the highest frequency and the smallest size. The high frequency of these electrons does indeed contribute to higher energy, but the proximity of the positively charged nucleus to the 1s orbital more than makes up for that. The amount of energy lost is equal to the amount that would be required to move the electron away from the nucleus that it is attracted to.
One might wonder why some have suggested that an electron should move through one slit or another in a dual slit diffraction experiment instead of both slits at once. That is a question worth considering. Keep in mind that although your finger cannot mover through steel plate, an electron is not your finger.
