The electron moves in such a way that the spin axis coincides with the direction of motion. It is in error to assume that the electron spins only to the left with respect to the direction of transfer. Since it doesn't seem to care whether it is backing up or moving forward with respect to the vortex motion, it may spin left or right as it moves. If there are many electrons in the flow, the possibility of spin pairing appears.

If a change in direction is imposed on the electron in the flow, the spin must re-orient itself with respect to the new direction. The change in direction cannot occur without an energy loss from the electron in the form of photon emission. Further, any change in direction must cause interference with other electrons in the flow so that they also change direction and experience a radiation energy loss. This energy loss can be replaced only at the expense of a voltage source to maintain the flow. Since the photon energy must be thermal in nature, there appears a heating effect which in electrical theory would be attributed to a resistance in the flow.

The law of entropy associates a condition of disorder with photon activity in a system. In this case we must attribute the original disturbance in the electron to a general background of photon activity which is independent of the flow. The condition of room temperature as applied to earth is determined by a background of photon activity beyond description. A free electron in such an environment is kicked around seven ways from Sunday by photon interaction. The average velocity at room temperature is calculated to be about 10⁷ centimeters per second.

According to the analysis presented, we can expect a reduction in electrical resistance to be associated with a reduction in temperature on the absolute scale. If this trend continues without change, it is implied that no superconductivity exists at any temperature above absolute zero.

Things don't always act in the manner to be expected. In 1911, the Dutch physicist, Kamerlingh Onnes, demonstrated superconductivity in mercury at about 4 degrees Kelvin. Further investigation in the years following revealed the fact that a reduction in resistance with temperature followed the expected trend until the region below ten degrees absolute was reached. Many materials tested then showed a narrow region of transition with temperature below which they were truly superconducting. It was not until 1960 that Johm Bardeen and his associates at the University of Illinois introduced the concept that superconductivity depended on the pairing of electrons in the flow with opposite spins. This work led to a Nobel prize in 1972.

There immediately appeared a problem. The configuration of the electron as a toroid was not known. To the writers for the popular magazines in science, the electron was a spinning sphere that carried a negative charge. Further, it could move only with a left hand spin as described with respect to its direction of advance. In the event of pairing with opposite spins, one-half the total number of electrons in the flow had to move in the reverse direction. How they could remain paired, and how the current could be carried in one direction only, threw the entire field into confusion.

The reality of the situation presently existing is that all theories are suspect. The investigators continue their search for the magical material which will conduct electricity at room temperature with no voltage applied and no resistance in the flow. How it is possible to transfer electrical energy at zero voltage is not made clear. We are reminded of the search for the philosopher's stone.

In speaking of the conduction process, the term "electron gas" is used. In the present development we use the term "electron fluid" as being more appropriate. The term fluid implies a continuity which may be at odds with the model of a system of electrons as discrete points. It must be remembered that each electron has a physical space which extends beyond the surface boundary of the particle. Also the electron in motion generates an associated matter wave with a wavelength that can be calculated and a frequency associated with the energy of motion. We wish to apply the concepts of quantum theory with the requirement that the velocity of the matter wave is the velocity of the electron which generates it. Calculation of the matter wave amplitude indicates a value of 1.67 X 10^-7 centimeters at a temperature of 300 degrees Kelvin. Since this is about ten atomic diameters, we observe that continuity in the electron fluid is assured in the general case.

We appeal to the standard procedure of dimensional analysis as applied to a fluid in motion. The equation for the coefficient of viscosity describes a pressure drop with distance in a flow in terms of the coefficient of viscosity and the transverse change in velocity with distance. The change in velocity is from zero to the final velocity V in the distance of one wave amplitude. Since pressure by definition is force per unit area, multiplying numerator and denominator by unit length yields energy loss per unit volume imposed by the existence of a viscosity in the flow.

If we equate the energy loss per unit volume to the kinetic energy per unit volume in the flow, we find a most surprising result. The coefficient of viscosity existing in the flow is equal to the total spin per unit volume. This is given as the product of the number of electrons per unit volume in the flow multiplied by the magnitude of spin of a single electron.

The fact that viscosity depends on spin is not as strange as it may seem. The helium atom has two electrons contributing to its orbital angular momentum. Then we can say that spin applies to the helium atom. At room temperature, helium is a gas, but as the temperature is lowered, it can finally enter a liquid phase termed helium II. In this state of existence, it exhibits zero viscosity. This occurs only in case adjacent atoms of helium in the liquid are paired with opposite spins. The condition exists only as long as the spin pairing can be maintained.

The equation as applied to electrons in the flow requires a single velocity for the group and all spins adding. If there exists a certain amount of pairing in the flow, this fact requires a reduction in the number of electrons contributing to the viscosity. In this case, we introduce a pairing coefficient as a multiplier of the electron density. This coefficient can vary from zero to unity with unity describing the unpaired state. The value of zero requires the absence of viscosity in the flow. This condition requires the pairing of spins of adjacent electrons to provide a zero net viscosity at all points. If this condition can be imposed and maintained, no frictional losses can occur in the flow.

The work of John Bardeen and his group assumed that the pairing was instigated by lattice forces that were effective only at the low temperature of the transition region. The point to be made is that if the condition of pairing can be instigated and maintained, the temperature of operation is immaterial.

By means of electrical theory, we can write the equation for the energy loss per unit volume per unit time in the flow. This is equal to the resistivity multiplied by the square of the current density. In this case we can associate the viscosity in the medium with the electrical resistivity and thus with the pairing coefficient. The procedure is elementary, but fairly involved. If the pairing coefficient is neglected, we find that the electrical resistivity is proportional to the absolute temperature and inversely proportional to the conduction electron density. This confirms the expected trend that electrical resistance is reduced to approach superconductivity only at absolute zero. Then we conclude that any condition of superconductivity which appears at any temperature higher than that of absolute zero depends exclusively on the pairing process.

The atomic density is given by Avogadro's number divided by gram atomic weight and multiplied by the mass density. For the element copper, we assume that one electron per atom is furnished to the conduction process. Use of the value thus found, with a temperature of 20 degrees on the Centigrade scale, predicts a resistivity for copper given by 1.62 X 10^-6 ohm centimeters. This is in exact agreement with the listed value. We conclude that no pairing of electrons exists in copper at room temperature.

As applied to the resistivity equation, introduction of the pairing coefficient affects the numerator only. A coefficient of unity describes the unpaired state and a coefficient of zero describes superconductivity. We must assume that any value between may apply. The factors determining the value of the pairing coefficient must be investigated.

It is certain that thermal agitation at room temperature interferes with the pairing process. If we assume a thermal velocity of 10⁷ centimeters per second for the electron at room temperature, we speculate that this magnitude of velocity must exist in the flow before any significant amount of pairing can be expected.

There is a difficulty which becomes apparent. In a metal such as copper, the conduction electron density is so high that the velocity of the electron in the process of carrying a current is quite low. It is estimated to be not more than 0.1 centimeters per second. This fact is indiicated by the term "drift velocity" used to describe the action. The velocity of thermal agitation in comparison to the drift velocity in the flow indicates the necessity of increasing the flow velocity by eight orders of magnitude before any appreciable pairing can be introduced and maintained. We are not surprised that a copper conductor exhibited no pairing.

The analysis shows quite clearly why superconductivity as presently known is a low temperature phenomenon. The reduction in the thermal activity with temperature is a step in the right direction, but there are other aspects of the problem which must be considered as well.

Superconductors in general are classed as "soft" or "hard." The soft superconductors are generally pure metals. They are characterized by the fact that no current can exist in the interior. The current is carried in a sheath of very limited thickness on the surface of the conductor. Then it appears that the velocity of electrons in the flow is greatly increased over that which appears in the ordinary conduction process. By measurement, the thickness of the sheath is about 10^-5 centimeters. Calculation indicates that the velocity of the electron in the conducting sheath is of the order of 10⁵ centimeters per second. The new value represents an increase of six orders of magnitude with respect to the ordinary conduction velocity. There are two facts to emphasize. The superconducting electron is a paired electron, and the superconducting electron is a fast electron. Then we conclude that an increase in the flow velocity of the electron aids in the process of instigating and maintaining the pairing in the flow.

If transverse motions can be limited by the physical dimension of the conductor, this fact would have a bearing on the analysis. In the case of the superconducting sheath, we have found a sheath thickness of 10^-5 centimeters. Calculation of the matter wave amplitude at the stated velocity is found to be equal to the thickness of the conducting sheath. It appears that transverse motions in the radial direction of a cylindrical conductor are prevented by the limited thickness of the conducting sheath.

The point of significance for the hard superconductors is that they are transition metals in the form of alloys. The constituents of the alloys generally have four or five electrons in the outer shell. It is no longer true that each atom furnishes an electron to the conduction process. As an example, a representative value for bismuth is one conductor electron per million atoms. In this case we can expect an increase in flow velocity for the electron in bismuth to be significant in the pairing process.

In the case of the superconducting alloys, the current is no longer carried on a surface sheath. Instead, we find the current to be confined to a limited number of filaments in the interior of the structure. Since this automatically requires a further increase in the flow velocity over that applying to the surface sheath, we can expect the superconducting alloys to operate at temperatures in excess of those applying to the soft superconductors. This is actually the case, but the temperature of operation is still far below the desired goal of room temperature superconductivity.

In spite of the low conduction electron density in bismuth, the measured resistivity is not more than two orders of magnitude greater than that of copper. This can be true only in the event that a certain amount of pairing exists in the flow at room temperature. If we calculate the conduction electron density and apply the resistivity equation, we can use the measured resistivity to calculate the value of the pairing coefficient. The calculated value of the pairing coefficient for bismuth at 20 degrees Centigrade is found to be 2.5 X 10^-5. The conclusion is that bismuth is not far removed from superconductivity at room temperature. We wonder what can be done to augment the effect.

It appears that the criterion for the testing of materials as possible superconductors is low conduction electron density coupled with low resistivity. Bismuth was chosen for further study on the basis of the fact that the pN product was a minimum as given from available data.

The analysis serves to emphasize the fact that pairing occurs spontaneously in the flow. If the paired condition can be maintained, superconductivity at any temperature can be achieved. In order to accomplish the desired aim, all transverse electron motions must be eliminated. We are forced to consider the possibility of manufacturing filaments of bismuth so small in cross section that transverse motion of electrons cannot occur.

The fact that an electric current in bismuth will transfer heat has been known for at least a hundred years. In the present instance, the efficiency of the device is limited by the development of heat by the current. The fact that heat is transferred indicates that at least some of the electrons in the flow have thermal velocities. If higher velocities can be attained, and resistance heating does not apply, the possibility of a heat transfer device which will match the resonance frequencies of the atomic shells appears. This may well be termed a resonance absorber. The application to the release and control of nuclear energy on the basis of the disruption process is indicated.

We have the perfect analogy to the electromagnetic wave guide in the microwave region and the optical fiber in the case of visible light. In the same manner, we can think of the bismuth filament as an electron wave guide. The question to be resolved is: How can filaments of the proper size be manufactured and maintained.

It is to be stressed that nothing in research is set in solid concrete. Bismuth is not necessarily the best or the only material to be used. Carbon shows promise either in the free state or in the form of compounds. A recent Russian news release claims superconductivity at room temperature in filaments of oxidized polypropylene of 100 angstrom width.

There is a growing body of evidence in favor of the present analysis. Recent work at the University of Alabama at Huntsville confirms the findings of Ronald C. Bourgoin (my former student) presently of Rocky Mount, N.C. Current densities were calculated to be of the order of 10¹⁰ amperes per square centimeter.

Since the standard tests for superconductivity cannot be applied to such thin filaments but the current density measurements cannot be denied, the phenomenon has been given the name hyperconductivity. The Russians claim that they have succeeded in detecting a Meisner effect. This action requires a filament closed upon itself. The basic fact which appears is that the flow in the filament must be one-dimensional. A great deal of experimental work remains to be done

At no place in the analysis of superconductivity has the effect of the lattice structure of the metallic conductor been mentioned. The fact that the analysis in the case of copper gave the correct value of the measured resistance should be sufficient to indicate that the presence of the lattice can be neglected. Electron-electron interactions coupled with photon-electron interactions then appear to be the only source of energy loss in the flow. Considering the fact that the lattice atoms are so massive in relation to the electron, plus the fact of binding between atoms to create a solid structure, it appears that the impedance mismatch is so extreme between electron and lattice that no energy loss to the lattice occurs. Since impedance matching in the mechanical sense must be considered, we conclude that energy transfer between masses is at a maximum only when the two masses are equal.

If we apply the given philosophy to the release of mesons in the upper atmosphere of earth, we conclude that the energy of the meson cannot be accounted for by cosmic ray activity from outer space. The conclusion must be that the decay of protons and neutrons released mesons in the process of nuclear disruption. The energy is inherent in the structure in the first place and manifest when the particle disrupts. Since quantum state 7 applies to the neutron ring and there are 1860 electrons and positrons involved, we can expect seven more or less equal units to be released. The rest mass of the meson is then equal to 266 electron masses to the nearest integer. If the existing mass defect is considered, this represents the mass of the -meson.

Another case in which impedance matching appears necessary is involved in the effort to reach absolute zero. In the cooling process by the evaporation of liquid helium under reduced pressure, it is to be observed that only molecular motions are involved. It is certain that any frequency removed from the system should be in the molecular range. According to the third law of thermodynamics, a no-win system applies. The process is that of transferring lower and lower frequencies as the zero frequency is approached. The final question is, "How do you transfer a zero frequency?" The goal of reducing the molecule to a condition of rest has no bearing on the nuclear disruption process. The molecular frequencies involved are so far off resonance from those applying to the electron shells that no effect can apply.

An extremely important application of the resonance absorber is that of the disposal of nuclear wastes. The phenomenon of K-capture occurs in a heavy nucleus in order to establish a condition of stability. The other side of the coin is that of induced K-capture. This must result in a nuclear instability to trigger a spontaneous decay to result in a lower mass number for the nucleus. with a few of these steps induced in the natural decay sequence, the final effect would be that of a stable atom. The inference is that the decay times of radioactive wastes could be shortened to the point at which they pose no hazard.