316
M. Svrˇ cek
l = mv(2λ)
(9.19)
From these results Hirsch infers: “It is natural to conclude that electrons reside in
such orbits even in the absence of an applied magnetic field, as opposed to assuming
that the 2λ orbits are somehow ‘created’ by the applied field… It should be noted
that the hypothesis that superconducting electrons reside in large orbits was made
by several researchers in the pre-BCS era [83–85].”
At this point a serious problem appears, i.e. when the classical concept of mesoscopic orbits is quantized (for details of the derivation of quantum equations see
the original paper). This forces Hirsch to declare that such a solution exceeds the
rules of quantum physics: “The Bohr atom starts from some simple assumptions and
deduces that the angular momentum of the electron in Bohr orbits is quantized in integer units of è… Similarly we point out here that from some simple assumptions it can
be deduced that electrons in superconductors reside in mesoscopic orbits with orbital
angular momentum è/2… The fact that the orbital angular momentum in these orbits
in the superconductor is found to be a half integer rather than an integer multiple of
è is very remarkable. The correct interpretation of this finding could have profound
implications. We have suggested that it indicates an intrinsic double-valuedness of
the electron wavefunction, in contradiction with conventional quantum mechanics.
Other less radical interpretations may be possible.” Hirsch closes his paper, expressing his desire to find the wavefunction, that will obey the above mentioned concept of
mesoscopic electron orbits: “What we are proposing is that the correct wavefunction
of the superconductor, when it is found, will necessarily show physical properties
consistent with the picture provided by quantized 2λ orbits with angular momentum
è/2 and the associated macroscopically inhomogeneous charge distribution. The BCS
wavefunction does not.”
No one up to now has been lucky to discover such a wavefunction, including Hirsch
himself. According to Bohr’s principle of correspondence, this wavefunction must
exist being derived ab initio from first principles, i.e. only from the knowledge of the
Schrödinger equation taking into account a certain number of nuclei and electrons.
One should note that superconductors are crystals with the same discrete translational
symmetry as other solids, yet from a mathematical point of view it is impossible to
find some type of “rotational symmetry” leading to the solution of mesoscopic circle
orbits. How is it possible to unravel such a puzzle? The answer is simple repeating
the statement that Bohr’s principle of correspondence for superconductors is broken
and quantum physics is unable to explain them.
Continuing the focus will be set on the problem of rotating superconductors,
especially on the relation between the magnetic field and the angular velocity (9.10).
The obvious question befalls: what type of mass m does appear in this equation? Is it a
bare or an effective electron mass? Hirsch argues in his paper “The London moment:
what a rotating superconductor reveals about superconductivity” [86] and quotes a
huge number of experimental work dealing with measurements of both the low-T c
as well as the high-T c superconductors. The results confirm without exception the
validity of using the bare electron mass in Eq. (9.10). Hirsch continues: “BCS theory
does not describe any change in the character of the electronic states other than the
M. Svrˇ cek
l = mv(2λ)
(9.19)
From these results Hirsch infers: “It is natural to conclude that electrons reside in
such orbits even in the absence of an applied magnetic field, as opposed to assuming
that the 2λ orbits are somehow ‘created’ by the applied field… It should be noted
that the hypothesis that superconducting electrons reside in large orbits was made
by several researchers in the pre-BCS era [83–85].”
At this point a serious problem appears, i.e. when the classical concept of mesoscopic orbits is quantized (for details of the derivation of quantum equations see
the original paper). This forces Hirsch to declare that such a solution exceeds the
rules of quantum physics: “The Bohr atom starts from some simple assumptions and
deduces that the angular momentum of the electron in Bohr orbits is quantized in integer units of è… Similarly we point out here that from some simple assumptions it can
be deduced that electrons in superconductors reside in mesoscopic orbits with orbital
angular momentum è/2… The fact that the orbital angular momentum in these orbits
in the superconductor is found to be a half integer rather than an integer multiple of
è is very remarkable. The correct interpretation of this finding could have profound
implications. We have suggested that it indicates an intrinsic double-valuedness of
the electron wavefunction, in contradiction with conventional quantum mechanics.
Other less radical interpretations may be possible.” Hirsch closes his paper, expressing his desire to find the wavefunction, that will obey the above mentioned concept of
mesoscopic electron orbits: “What we are proposing is that the correct wavefunction
of the superconductor, when it is found, will necessarily show physical properties
consistent with the picture provided by quantized 2λ orbits with angular momentum
è/2 and the associated macroscopically inhomogeneous charge distribution. The BCS
wavefunction does not.”
No one up to now has been lucky to discover such a wavefunction, including Hirsch
himself. According to Bohr’s principle of correspondence, this wavefunction must
exist being derived ab initio from first principles, i.e. only from the knowledge of the
Schrödinger equation taking into account a certain number of nuclei and electrons.
One should note that superconductors are crystals with the same discrete translational
symmetry as other solids, yet from a mathematical point of view it is impossible to
find some type of “rotational symmetry” leading to the solution of mesoscopic circle
orbits. How is it possible to unravel such a puzzle? The answer is simple repeating
the statement that Bohr’s principle of correspondence for superconductors is broken
and quantum physics is unable to explain them.
Continuing the focus will be set on the problem of rotating superconductors,
especially on the relation between the magnetic field and the angular velocity (9.10).
The obvious question befalls: what type of mass m does appear in this equation? Is it a
bare or an effective electron mass? Hirsch argues in his paper “The London moment:
what a rotating superconductor reveals about superconductivity” [86] and quotes a
huge number of experimental work dealing with measurements of both the low-T c
as well as the high-T c superconductors. The results confirm without exception the
validity of using the bare electron mass in Eq. (9.10). Hirsch continues: “BCS theory
does not describe any change in the character of the electronic states other than the