Megascopic Quantum Phenomena
347
approximation somehow mimics the quantum field properties where SSB can only
appear. This is probably why Sutcliffe and Woolley, see Sect. 2, have put questions
related to the transition from the isolated to the individual systems on the list of
unsolved problems in quantum theory. In fact the solution of this problem, as presented here, is the key to providing a description of the SSB archetype on the quantum
level.
As stated here the application of the classical SSB, i.e. the Mexican hat, to quantum equations, such as the J-T effect, superconductivity or the Higgs mechanism, is
a disparity. This results in a misinterpretation of related phenomena, and it reminds
of the reincarnation of the notorious medieval puzzle, namely how many angels
can dance on the apex of a needle, i.e. a comparable mismatch by combining a
material piece of a needle with the spiritual world of angels. Consequently quantum equations, grounded on the classic SSB, lead to a paradoxical situation. Hence
the scientific community appears divided in regard to the question whether SSB is
presently accounted for or not. According to Bersuker, the J-T effect is a unique
mechanism of all existing SSBs in condensed matter, while, according to Weinberg,
quantum mechanics cannot lead to any SSB. Bardeen, Cooper and Schrieffer did not
find any SSB in their theory of superconductivity, yet Weinberg wondered how they
could miss it. In standard text books, the Higgs mechanism is described as a SSB
mechanism, but gradually a strong opposition against this view has emerged, usually
quoting the Elitzur’s theorem [129], maintaining that local gauge symmetries cannot
be spontaneously broken. The tip of the iceberg is the statement by Anderson, that
ferromagnetism is not a case of SSB. His opinion was condemned by Peierls and
Kaplan, see their discussions in Ref. [130].
Finally, Unzicker in his book “The Higgs Fake: How Particle Physicists Fooled the
Nobel Committee” [131] quotes the prophetic pronouncement of Rudolf Clausius:
“Once the error is based like a foundation stone in the ground, everything is built
thereupon, nevermore it returns to light.” In the following section we will return to the
beginning of the many-body treatment in quantum physics, revealing an overlooked
secret regarding the B-O approximation. Here one may anticipate the starting point
of the whole inconsistent chain that culminates in the uncertainty of many physicists,
which phenomenon is of the SSB type and which one is not.
13 The Paradox of Bohr’s Complementarity
We begin by looking more carefully at the qualitative nature of the B-O approximation. Even if it has been successfully proven in most molecular many-body
calculations as well as its accuracy verified times and again, it is nevertheless a
very non-standard approximation. In its original derivation, via the m/M (electron
mass/nuclear mass) series expansion, it is unique in the sense that no competing series
exists, cf. the Brillouin-Wigner or the Rayleigh-Schrödinger perturbation theories.
In contrast to the latter, the B-O approximation is not only the basis of almost all
molecular quantum chemical calculations, but it provides also a fundamental concept
347
approximation somehow mimics the quantum field properties where SSB can only
appear. This is probably why Sutcliffe and Woolley, see Sect. 2, have put questions
related to the transition from the isolated to the individual systems on the list of
unsolved problems in quantum theory. In fact the solution of this problem, as presented here, is the key to providing a description of the SSB archetype on the quantum
level.
As stated here the application of the classical SSB, i.e. the Mexican hat, to quantum equations, such as the J-T effect, superconductivity or the Higgs mechanism, is
a disparity. This results in a misinterpretation of related phenomena, and it reminds
of the reincarnation of the notorious medieval puzzle, namely how many angels
can dance on the apex of a needle, i.e. a comparable mismatch by combining a
material piece of a needle with the spiritual world of angels. Consequently quantum equations, grounded on the classic SSB, lead to a paradoxical situation. Hence
the scientific community appears divided in regard to the question whether SSB is
presently accounted for or not. According to Bersuker, the J-T effect is a unique
mechanism of all existing SSBs in condensed matter, while, according to Weinberg,
quantum mechanics cannot lead to any SSB. Bardeen, Cooper and Schrieffer did not
find any SSB in their theory of superconductivity, yet Weinberg wondered how they
could miss it. In standard text books, the Higgs mechanism is described as a SSB
mechanism, but gradually a strong opposition against this view has emerged, usually
quoting the Elitzur’s theorem [129], maintaining that local gauge symmetries cannot
be spontaneously broken. The tip of the iceberg is the statement by Anderson, that
ferromagnetism is not a case of SSB. His opinion was condemned by Peierls and
Kaplan, see their discussions in Ref. [130].
Finally, Unzicker in his book “The Higgs Fake: How Particle Physicists Fooled the
Nobel Committee” [131] quotes the prophetic pronouncement of Rudolf Clausius:
“Once the error is based like a foundation stone in the ground, everything is built
thereupon, nevermore it returns to light.” In the following section we will return to the
beginning of the many-body treatment in quantum physics, revealing an overlooked
secret regarding the B-O approximation. Here one may anticipate the starting point
of the whole inconsistent chain that culminates in the uncertainty of many physicists,
which phenomenon is of the SSB type and which one is not.
13 The Paradox of Bohr’s Complementarity
We begin by looking more carefully at the qualitative nature of the B-O approximation. Even if it has been successfully proven in most molecular many-body
calculations as well as its accuracy verified times and again, it is nevertheless a
very non-standard approximation. In its original derivation, via the m/M (electron
mass/nuclear mass) series expansion, it is unique in the sense that no competing series
exists, cf. the Brillouin-Wigner or the Rayleigh-Schrödinger perturbation theories.
In contrast to the latter, the B-O approximation is not only the basis of almost all
molecular quantum chemical calculations, but it provides also a fundamental concept