SUPERCONDUCTIVITY: 1. INTRODUCTION The chief characteristic of superconductiv ity is the
complete absence of the electrical resistance. As the temperature is decreased,
the change from the normal to the superconducting state takes place abruptly
at a critical temperature T The tunneling and flux quantization experiments firmly
established the presence of electron pairs. However, the The explanation of the phenomenon of superconductivity from the point of view of the Reciprocal System, however, has not yet been attempted. Larson himself refers to the phenomenon with nothing more than a passing remark [1]. As the present author sees, progress toward this end would not have been possible in the R.eciprocal System, as it needed the discovery of a new development, which emerged only recently. This is the new light thrown by the study of the “photon controversy,” leading to the discovery of birotation [2]. It has been shown there that the two equal, and opposite rotational components of a birotation manifest as a linear Simple Harmonic Motion (SHM). The knowledge of this now opens the way toward understanding the phenomenon of superconductivity. 2. The Origin of the Phenomenon It has been well-recognized that superconductivity,
from the abruptness of its occurrence at the temperature T 2.1 The Perfect Conductor Larson points out: “... the electron is essentially
nothing more than a rotating unit of space.” [4] He identifies the
movement of the electrons (rotating units of space) through matter (a
time structure) as the electric current. We might note that there is no
electric charge associated with these electrons. One of the causes, according
to Larson, of the resistance to the flow of current is the spatial component
of the thermal motion of the atoms. “If the atoms of the matter through
which the current passes are effectively at rest..., uniform motion of
the electrons (space) through matter has the same general properties as
motion of matter through space. It follows Newton’s first law of
motion . and can continue indefinitely... This situation exists in the
phenomenon known as We would like to point out that the actual situation is somewhat different. Firstly, as we will see later, superconductivity is not solely a phenomenon of zero resistance which we shall call the perfect conduction (that is, infinite conductivity), which is what Larson seems to imply by ‘superconductivity’ in the para cited above. The second fact is concerning the resistance caused by the impurity atoms due to their space displacement. Since the current moves, according to the Reciprocal System, through all the atoms of the conductor (including the impurity atoms), and not through the interstices between the atoms, there is a large contribution by the impurity atoms to the resistance.[5] Mere reduction of the thermal motion, therefore, cannot serve to eliminate the cause of resistance to the current. 2.2 The Electron Pair as a Birotation In the “uncharged state the electrons cannot move
with reference to extension space, because they are inherently rotating
units of space, and the relation of space to space is not motion. ...In
the context of the stationary spatial system the uncharged electron, like
the photon, is carried outward by the progression of the natural reference
system.”[6] But as the temperature is decreased below the critical
value T Remembering that the electron is a unit of rotational
space, when two of them with antiparallel rotations approach each other
to an effeetive distance of less than one compound unit of space, the
two opposite rotations form into a birotation. As explained in detail
elsewhere [2] a birotation manifests as an SHM. We might call this process
the “pair condensation,” following the conventional nomenclature.
The formation into the birotation (that is, SHM) has two distinct effects
which need to be noted: 2.3 The Zero Electrical Resistivity The rotational space, that is the electron, may be regarded
as a circular disk area. We see that the effect of the dimensional-reduction
is to turn the disk area into a straight line element (of zero area).
What causes the electrical resistance in normal conduction is the finiteness
of the projected area of the electron in the direction of current flow.
The vanishing of this pro jected area on pair formation eliminates the
cause for the resistance and turns the material into a perfect conductor
(zero resistivity). It should be emphasized that a dimension-reduction
from a three-dimensional spatial extension (say, a spherical volume) to
a two-dimensional spatial extension (a circular disk) could not have accomplished
such an elimination of projected area. This is only possible when the
reduction is from a two-dimensional spatial extension to the one-dimension. 3. The Meissner Effect This an interaction between superconductivity and magnetic
field and serves to distinguish a superconductor from the so-called “perfect
conductor.” If we could place a perfect conductor in an external
magnetic field, no lines of magnetic flux would penetrate the sample since
the induced surface currents would counteract the effect of the extern,al
field. Now imagine a normal conductor. placed in the magnetic field and
the temperature lowered, such that at T But the situation is quite different in the case of the
superconductor. As can be seen from the bottom row of Fig.l, a metal placed
in an external magnetic field and cooled through the superconducting transition
temperature T Now the crucial point that should be noted is that a
constant magnetic flux threading a conductor that is stationary relative
to it does not induce an electric current. What induces a current is a
The perfect Conductor The Superconductor
But in the case of the superconductor, the Exactly for identical reasons, we find that in the present
too, there is no need to resort to the purely hypothetical exchange interaction
explanation. The reason why a steady magnetic field threading the superconductor
induces a current in it follows from the 4. The Non-locality of the Pairing It has been found that “the size of the electron pairs is on the order of 10-4cm and the motion of electrons at different points of the metal shows correlations over distances of this order.”[8] Richard Feynman points out: “I don't wish you to imagine that the pairs are really held together very closely like a point particle. As a matter of fact, one of the great difficulties of understanding this phenomenon originally was that that is not the way things are. The electrons which form the pair are really spread over a considerable distance; and the mean distance between pairs is relatively smaller than the size of a single pair. Several pairs are occupying the same space at the same time.”[9] By any standard of conventional thinking this is rather a strange state of affairs. From the point of view of the 5. Superconductivity and Magnetic Ordering As both magnetic ordering and superconductivity are the result of the respective motions entering the time region, it would be of interest to examine whether and how they affect each other. In the ferromagnetic arrangement of the directions of all the atomic dipoles are mutually parallel. Sueh a state of ordering precludes the electron pair formation required in superconductivity since the spins of the electrons are disposed to orient parallel to each other. As such, we can predict that superconductivity and ferromagnetism cannot coexist. On the other hand, in the antiferromagnetic ordering,
adjacent magnetic dipoles are oriented antiparallel to each other. Since
the rotational space that is the electron will have greater chance of
assuming the directions of these dipoles, adjacent electrons with opposite
spin directions would be readily available for pairing. Consequently,
we can conclude that the antiferromagnetic ordering can co-exist with
or even promote the electron pairing that underlies superconductivity.
If this is so, it might lead to the development of high T 6. Thermodynamical Aspects The observable relationships among the superconducting and the normal states follow directly from the quadratic nature of the relationship between the corresponding quantities of the time region and the outside region [10]. 6.1 Specific Heat Relations Quoting Larson: “:.. the relation between temperature
and energy depends on the charaoteristics of the transmission process.
We have seen earlier that the phenomenon of birotation of the electron pair is identical to that of the birotation of photons (except for the absence of the rotational base in the latter). Consequently, the time region energy associated with the electron pairs is proportional to the fourth power of the temperature. Therefore, considering unit volume of the material, the expression for the thermal energy in the superconducting state can be written as
where Kg is a constant and suffix s denotes the supercondueting state. Differentiating this equation one gets the expression for the specific heat in the superconducting state,
This cubic relationship is confirmed experimerr tally.
where K
We know that the entropy of both the states, Sn and Ss, must be equal both at Tc and at 0 kelvin (by the third law of thermodynamics). Using dS = dE/T, we have from Eqs. (1) and (3),
At T = T
Using Eqs. (2), (4) and (7), we can now find that at the transition the excess specific heat is given by
The above result is experimentally corroborated. 6.2 External Magnetic Field Below the critical temperature T
where H 7. Conclusion The foregoing explanation of supercon ductivity adds one more item that
demonstrates the coherence and generality of the - The formation of electron pairs,
- the non-locality of the pairing,
- the zero electrical resistance,
- the expulsion of magnetic field,
- the abrupt change in the specific heat at the transition,
- the manner of variation of the critical field with temperature, all of these are shown to follow logically from the theory.
References 1. Dewey B. Larson, |