342
M. Svrˇ cek
of superconductivity and all other teleological phenomena be revealed and seriously
discussed.
This evokes the question: Does there exist a general formulation of the relationship between broken symmetries and the respective physical phenomena, valid both
in classical and quantum physics? Pierre Curie proposed already in 1894 a formulation [116], fully based on causality, predating an analysis, which according to Bohr’s
principle of correspondence would apply to an extension from classical to quantum
physics. The English translation of Curie’s formulation with further extensive analysis can be found in the book of Brading and Castellani [117]. We quote here only the
essential part: “Curie was led to reflect on the question of the relationship between
physical properties and symmetry properties of a physical system by his studies
on the thermal, electric and magnetic properties of crystals, these properties being
directly related to the structure, and hence the symmetry, of the crystals studied…
His conclusions, systematically presented in his 1894 work “Sur la symétrie dans les
phénomènes physiques”, can be synthesized as follows:
(a) A phenomenon can exist in a medium possessing its characteristic symmetry or
that of one of its subgroups. What is needed for its occurrence (i.e. for something
rather than nothing to happen) is not the presence, but rather the absence, of
certain symmetries: “Asymmetry is what creates a phenomenon”.
(b) The symmetry elements of the causes must be found in their effects, but the
converse is not true; that is, the effects can be more symmetric than the causes.
Conclusion (a) clearly indicates that Curie recognized the important function
played by the concept of symmetry breaking in physics (he was indeed one of the
first to recognize it). Conclusion (b) is what is usually called “Curie’s principle” in
the literature, although one should notice that (a) and (b) are not independent of each
other.”
One might observe that Curie uses solely the pair of concepts: symmetry—asymmetry, and does not explicitly speak about SSB. Therefore Curie’s formulation reveals
only half of the truth about SSB, i.e. it deals only with causal phenomena arising
from the multiplicity of asymmetric solutions of physical equations. It says nothing
about the teleological phenomenon descending from the transitions between these
asymmetric states. As an example the causal effect, related to ferromagnetism, is
well explained in quantum physics. On the other hand, the associated teleological
Einstein-de Haas effect has no quantum physical explanation, even if it was well
described in the framework of classical physics in 1915 [118], before the concept
of the electron spin was known, leaving only Ampère’s hypothesis that magnetism
is caused by microscopic circular motions of electric charges as a sufficient background. Superconductivity is an another example: Quantum physics can only solve
the causal condensation of a conductor to the superconducting phase with multiple
asymmetric ground states, but the explanation of the teleological transition between
these ground states lies beyond the limits of quantum physics.
The SSB is primarily associated with two phenomena, i.e. one causal and one
teleological. Curie’s formulation deals with the first one. The phenomena in question
correspond to the following symmetry argument that was formulated by van Fraassen
M. Svrˇ cek
of superconductivity and all other teleological phenomena be revealed and seriously
discussed.
This evokes the question: Does there exist a general formulation of the relationship between broken symmetries and the respective physical phenomena, valid both
in classical and quantum physics? Pierre Curie proposed already in 1894 a formulation [116], fully based on causality, predating an analysis, which according to Bohr’s
principle of correspondence would apply to an extension from classical to quantum
physics. The English translation of Curie’s formulation with further extensive analysis can be found in the book of Brading and Castellani [117]. We quote here only the
essential part: “Curie was led to reflect on the question of the relationship between
physical properties and symmetry properties of a physical system by his studies
on the thermal, electric and magnetic properties of crystals, these properties being
directly related to the structure, and hence the symmetry, of the crystals studied…
His conclusions, systematically presented in his 1894 work “Sur la symétrie dans les
phénomènes physiques”, can be synthesized as follows:
(a) A phenomenon can exist in a medium possessing its characteristic symmetry or
that of one of its subgroups. What is needed for its occurrence (i.e. for something
rather than nothing to happen) is not the presence, but rather the absence, of
certain symmetries: “Asymmetry is what creates a phenomenon”.
(b) The symmetry elements of the causes must be found in their effects, but the
converse is not true; that is, the effects can be more symmetric than the causes.
Conclusion (a) clearly indicates that Curie recognized the important function
played by the concept of symmetry breaking in physics (he was indeed one of the
first to recognize it). Conclusion (b) is what is usually called “Curie’s principle” in
the literature, although one should notice that (a) and (b) are not independent of each
other.”
One might observe that Curie uses solely the pair of concepts: symmetry—asymmetry, and does not explicitly speak about SSB. Therefore Curie’s formulation reveals
only half of the truth about SSB, i.e. it deals only with causal phenomena arising
from the multiplicity of asymmetric solutions of physical equations. It says nothing
about the teleological phenomenon descending from the transitions between these
asymmetric states. As an example the causal effect, related to ferromagnetism, is
well explained in quantum physics. On the other hand, the associated teleological
Einstein-de Haas effect has no quantum physical explanation, even if it was well
described in the framework of classical physics in 1915 [118], before the concept
of the electron spin was known, leaving only Ampère’s hypothesis that magnetism
is caused by microscopic circular motions of electric charges as a sufficient background. Superconductivity is an another example: Quantum physics can only solve
the causal condensation of a conductor to the superconducting phase with multiple
asymmetric ground states, but the explanation of the teleological transition between
these ground states lies beyond the limits of quantum physics.
The SSB is primarily associated with two phenomena, i.e. one causal and one
teleological. Curie’s formulation deals with the first one. The phenomena in question
correspond to the following symmetry argument that was formulated by van Fraassen