Megascopic Quantum Phenomena
345
If we take into account all the known examples of SSB in classical physics, i.e.
the Mexican hat, Norton’s dome, or the systems discussed by Boussinesq, we conclude in relation to the SSB archetype, forming the “falling down from the apex”
in the classical physics, that the trigger of falling down is unknown. According to
Maxwell’s contemporary, mathematician and philosopher Peirce, no physics based
on a corpuscular philosophy can solve the problem of the SSB trigger [125]: “Now
I maintain that the original segregation of levo-molecules, or molecules with a lefthanded twist, from dextro-molecules, or molecules with a right-handed twist, is
absolutely incapable of mechanical explanation… The three laws of motion draw no
dynamical distinction between right-handed and left-handed screws, and a mechanical explanation is an explanation founded on the three laws of motion. There then
is a physical phenomenon absolutely inexplicable by mechanical action. This single
instance suffices to overthrow the Corpuscular Philosophy.”
Although these lines were written in the era of classical physics, Peirce’s argument
is applicable to quantum physics as well: It is built on the atomic ideas of Democritus,
with the same corpuscular philosophy as in classical physics. It means that quantum
physics in its Copenhagen interpretation is incapable of solving the problem of the
SSB trigger. As we have realized this is a teleological issue, related to Leibniz’ principle of sufficient reason, the second form of van Fraassen’s argument, and Peirce’s
corpuscular philosophy argument, which can be fully ignored in classical physics.
Unfortunately physicists usually ignore this difficulty also in quantum physics, and
this attitude is a mistake, since it is motivated by the incorrect belief, that quantum
physics employs the same SSB archetype as the classical one.
On the quantum level, physical systems can be described in a dual way: either
mechanically or as a field system, in accordance with the Weinberg’s statement [126]:
“If it turned out that some physical system could not be described by a quantum field
theory, it would be a sensation; if it turned out that the system did not obey the
rules of quantum mechanics and relativity, it would be a cataclysm.” Note that we
demonstrated a similar picture in Sect. 11 particularly for condensed matter cases
(molecules and crystals): Side by side the precise Monkhorst’s quantum mechanical
approach to the solution of the Schrödinger equation we present the true quantum
field solution fully respecting the Goldstone theorem.
We are now in the position to ask whether this dual description of physical systems would lead to the same result. The answer is certainly not, because different
results obtain for symmetry broken states. Quantum mechanics admits the superposition of multiple degenerate states, while Weinberg, on the other hand, has proven
their orthogonality for quantum fields within the infinite volume limit. The Weinberg’s argument is often quoted by various authors, e.g. in the article of Brading and
Castellani [127]: “In quantum physics SSB actually does not occur in the case of
finite systems: tunnelling takes place between the various degenerate states, and the
true lowest energy state or “ground state” turns out to be a unique linear superposition of the degenerate states. In fact, SSB is applicable only to infinite systems—
many-body systems (such as ferromagnets, superfluids and superconductors) and
fields—the alternative degenerate ground states being all orthogonal to each other in
345
If we take into account all the known examples of SSB in classical physics, i.e.
the Mexican hat, Norton’s dome, or the systems discussed by Boussinesq, we conclude in relation to the SSB archetype, forming the “falling down from the apex”
in the classical physics, that the trigger of falling down is unknown. According to
Maxwell’s contemporary, mathematician and philosopher Peirce, no physics based
on a corpuscular philosophy can solve the problem of the SSB trigger [125]: “Now
I maintain that the original segregation of levo-molecules, or molecules with a lefthanded twist, from dextro-molecules, or molecules with a right-handed twist, is
absolutely incapable of mechanical explanation… The three laws of motion draw no
dynamical distinction between right-handed and left-handed screws, and a mechanical explanation is an explanation founded on the three laws of motion. There then
is a physical phenomenon absolutely inexplicable by mechanical action. This single
instance suffices to overthrow the Corpuscular Philosophy.”
Although these lines were written in the era of classical physics, Peirce’s argument
is applicable to quantum physics as well: It is built on the atomic ideas of Democritus,
with the same corpuscular philosophy as in classical physics. It means that quantum
physics in its Copenhagen interpretation is incapable of solving the problem of the
SSB trigger. As we have realized this is a teleological issue, related to Leibniz’ principle of sufficient reason, the second form of van Fraassen’s argument, and Peirce’s
corpuscular philosophy argument, which can be fully ignored in classical physics.
Unfortunately physicists usually ignore this difficulty also in quantum physics, and
this attitude is a mistake, since it is motivated by the incorrect belief, that quantum
physics employs the same SSB archetype as the classical one.
On the quantum level, physical systems can be described in a dual way: either
mechanically or as a field system, in accordance with the Weinberg’s statement [126]:
“If it turned out that some physical system could not be described by a quantum field
theory, it would be a sensation; if it turned out that the system did not obey the
rules of quantum mechanics and relativity, it would be a cataclysm.” Note that we
demonstrated a similar picture in Sect. 11 particularly for condensed matter cases
(molecules and crystals): Side by side the precise Monkhorst’s quantum mechanical
approach to the solution of the Schrödinger equation we present the true quantum
field solution fully respecting the Goldstone theorem.
We are now in the position to ask whether this dual description of physical systems would lead to the same result. The answer is certainly not, because different
results obtain for symmetry broken states. Quantum mechanics admits the superposition of multiple degenerate states, while Weinberg, on the other hand, has proven
their orthogonality for quantum fields within the infinite volume limit. The Weinberg’s argument is often quoted by various authors, e.g. in the article of Brading and
Castellani [127]: “In quantum physics SSB actually does not occur in the case of
finite systems: tunnelling takes place between the various degenerate states, and the
true lowest energy state or “ground state” turns out to be a unique linear superposition of the degenerate states. In fact, SSB is applicable only to infinite systems—
many-body systems (such as ferromagnets, superfluids and superconductors) and
fields—the alternative degenerate ground states being all orthogonal to each other in