# 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. This article is an attempt at that understanding without the mathematics usual to quantum mechanics.

## Electron properties in the dual slit experiment

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. The randomized amount of deflection for the electron can not assume arbitrary values, but has particular quantities of deflection that it can assume, such that the peaks of the electrons wavelength reinforce. The quantization of this deflection is part of what makes the theory governing electons quantum theory.

## Bound electrons are in orbitals

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. Orbitals have interesting characteristics in metals and other crystals that result in electrical conductivity and in certain conditions superconductivity. The amount of energy that the electron looses when becoming bound can only assume certain quantities because its wavelength can be only particular values and form a standing wave about an atomic nucleus, as a string can only vibrate at certain values when streatched between two points. Again quantization of lost energy leads to the name quantum theory. When the electron is bound to the crystal as a whole it is a traveling wave that moves in a particular direction with respect to the crystal lattice with its wavelength being an integral multiple of the lattice spaceing for the direction that it is moving. The energy which is dependent upon wavelength is again quantized. This results in every electron in a crystal having a definite amount of energy dependent on its orbital.

## Conduction based upon orbitals

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 received the quantum of energy necessary to make the change. That quantum is equal to the difference in energy between the conduction orbital which is a traveling wave and the atomic orbital which is a standing wave. However photons or lattice vibrations with that amount of energy are usually not available to lend their energy to ambitious electrons 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 dropping 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 translational momentum from the lattice or another conduction electron and become a conduction electron again. Energy and momentum are always ballanced. If an electron gains momentum something must loose that momentum at the same time. Electrons always seek the lowest energy condition available to them, as water runs downhill.

There are exactly ten electrons per sodium atom in a crystal that fill localized orbitals and leaving these orbitals is a big quantum jump. One electron per sodium atom is jumping around the conduction orbitals in the sodium crystal. 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 translational momentum with the crystal lattice 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.

## Low energy conduction orbitals

The situation with yttrium, 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 translational momentum that they had when the crystal formed. They cannot get enough energy to rise to a nonconduction orbital or to an orbital with different translational momentum. The electrons cannot 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 rises enough to allow them to move to another energy level.

## Superconducting orbital string linking yttrium nuclei

An isolated yttrium atom has two 1s electrons, two 2s electrons, six 2p electrons, two 3s electrons, six 3p electrons, ten 3d electrons, two 4s electrons, six 4p electrons, one 4d electron and two 5s electrons. That is a total of 39 electrons to balance the charge of the 39 protons in the nucleus making a neutral atom. There is a possibility for the yttrium in a ceramic crystal to become an ion with a plus two charge by losing the two 5s electrons. This leaves the potential ten 4d orbitals with only one electron. A single 4d electron attached to a yttrium ion in a crystal is unlikely to be the lowest energy state. So the 4d electrons of yttrium atoms are shared helping to bind the crystal together. The resulting orbitals are not pure 4d orbitals but hybrid orbitals with some 4d quality and some quality of binding neighboring yttrium nuclei. The electrons form a traveling wave bound to the whole crystal but with a special spatial relationship to the yttrium nuclei. These are the superconducting orbitals with a non zero translational momentum. A superconducting electron cannot change its velocity because a different velocity would be associated with a different frequency for the conduction electron orbital, and it must have a frequency which keeps the nodes of the conduction orbital in a particular spatial relationship with yttrium ions. The conduction orbital can accept only quantum changes in velocity and, since the yttrium ions are spaced as they are, the needed quantum for a change in velocity is more than the energy available in the cold crystal.

Whatever the charge of the yttrium ion in the ceramic crystal is and however many electrons per yttrium ion are in superconcucting orbitals, the unfilled 4d orbitals seem to have something to do with establishing the superconducting orbitals. It may be close to the description in the above paragraph. The essential feature of this theory is that the superconducting electrons are in fixed orbitals with non zero translational momentum. They can not change their conducting state without a quantum change in energy and momentum.

## No Cooper pairs

In this model normal conduction does not involve a classical fluid moving through a crystal lattice. It involves electrons in orbitals with nonzero translational 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.

## Poor use of classical particle concepts

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. In this model it is considered to be a flexible compressible slippery thing that fills the whole orbital and vibrates, radiating charge from the whole orbital at once. The calculation of an orbital's shape is not the mere probability of an electron being in a particular location within the orbital, it is the mass and charge of the electron diffused through the entire space at once. The intensity of the mass and charge of an electron varies with location within the orbital. 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 an orbital with nonzero translational momentum is just like an electron in an orbital with zero translational momentum 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.

## Energy and frequency

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 energy lost by being close to the positively charged nucleus 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.

## False path assumptions

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 move through steel plate, an electron is not your finger.

## Example of a dual slit experiment

A fine example of the dual slit experiment is given by Hitachi. The company provides details of the experiment: The electrons follow paths on both sides of a filament thinner than one thousandth of a millimeter in diameter. The electrons are accelerated to 50,000 volts.

Electrons can form an interference pattern only when they go by both sides of the filament at once. Electrons are emitted only one at a time. Electrons form an interference pattern. The obvious conclusion is that Each electron goes on both sides of the filament at once. It acts as a swollen diffuse particle that can slip around both sides of the filament and through the spaces between the nuclei of the atoms making up the filament at the same time. It thus interferes with itself making a diffraction pattern on the detector like pachinko balls make a probability based distribution in the game.

## Experimental confirmation

How can one decide which explanation best models reality? Does each electron become large enough to go through both slits of a dual slit apparatus at once and then shrink back to atomic dimensions when its outer skin is punctured like a balloon by the detector; or does each electron split into two phantoms to go through both slots and interfere with each other then split into more phantoms directed to each probable detection location with the final detection of one phantom according to its probability destroying all the other phantoms?

The superposition of phantom electrons comes from a theory that considers only the geometry of the two slit diffraction device, not the material out of which the barrier with two slits in it is made. The giant free electron theory has the electron moving in part through the material in which the two slots are constructed. So to differentiate between theories multiple copies of a dual slit apparatus should be made with exactly the same dimensions but different materials. If the material of the apparatus in no way affects the intensity, shape or distribution seen in the diffraction pattern, the giant free electron theory seems less likely. If the material of the barrier does affect the intensity, shape, or distribution, then the two state superposition theory has failed to consider a relevant factor and the results will be consistent with the giant free electron theory. Variations in intensity, shape, or distribution might still be explained within the two state superposition theory, but the need for such explanations would make the two state superposition theory seem less likely.

Materials out of which a two slit diffraction barrier might conceivably be constructed include sugar, salt, silver, silicon, gold, iron, nylon, beryllium, lithium, bismuth, tungsten, copper, polyethylene, polyurethane, and graphite in various crystallographic orientations to the slits and electron beam directions.

The first results of such experimentation may be posted in the discussion section of this article.

## Probability

In both the giant free electron theory and the two state superposition theory of electron defraction there is a superposition of sign waves that represent the probability of an electron being detected at any particular position beyond the dual slits. In the two state superposition theory there is a phantom electron for every probable location. All but one of the phantoms disappears when that one is detected. In the giant free electron theory there is always only one electron. It is big enough and flexible enough to go through both slits at once and diffuse enough that a portion of it can go through the barrier between the two slits. That one electron has a chance of going to any detector in the experiment with the probability as indicated by the superposition of sign waves representing that probability.

In the electron orbitals the functions which represent the shapes of the orbitals (where this can be calculated) in some theories can be considered the probability of an electron being in one or another spot in the orbital. In other theories including the giant free electron theory the functions representing the shapes of the orbitals represent the intensity of the electron at various spots while it is diffused throughout the orbital.

## Non monolithic theory

The giant free electron theory is merely a collection of ideas. Some may be helpful, some may not. Inspiring thought and experiment is a goal of the theory.