International Encyclopedia of Systems and Cybernetics

The destruction of symmetry in space-time.

J. COLLINS and I. STEWART write: "The simplest oscillator network that demonstrates symmetry-breaking consists of just two coupled, identical oscillators. Because they are identical, the system behaves in the same way if the oscillators are interchanged – that is the symmetry. While the symmetry remains unbroken, the two oscillators are in phase: they are synchronized. But when the symmetry breaks, group theory reveals that only one other pattern of behavior is possible: antisynchrony, in which the oscillators are half a cycle out of phase with each other. Not all symmetry need to be lost when symmetries break, however. The antisynchronous motion has its own symmetry: the oscillation pattern is unchanged if the two oscillators are interchanged and their respective phases shifted by half a cycle" (1994, p.38-9).

Symmetry-breaking is one of the very basic features of nature, possibly since the big-bang itself and is deeply connected with thermodynamics.

Classical thermodynamics already introduced time dissymmetry during the 19th century. even if this was not clearly perceived at the time (f. ex. in BOLTZMANN vain efforts to reconcile reversibility with thermodynamics). However, the full impact of thermodynamics became clear after PRIGOGINE's work on systems undergoing giant fluctuations and dissipative structuration. He definitively showed that, in the factual world, true reversibility is impossible, as a result of time symmetry breaking.

As giant fluctuations and dissipative structuration result of increasing energy inputs, it is "… an external field which imposes the way the symmetry must be broken". And "Thus the ability to break symmetries corresponds to an adaptive capacity… It is also an advantage to be able to break symmetries all the time, that is to maintain oneself just in the vicinity of the phase transitions, or in a self organized critical state" (E. BONABEAU, 1993, p. 830-1).

E. JANTSCH states: "Passing from… the thermodynamic to the dissipative structures level, implies breaking the spatial symmetry between subject and object, observer and observed. This general breaking of spatial isotropy leads to a non-equilibrium world in which "order through fluctuation" can become an evolutionary principle" (1975, p.95). In synthesis, symmetry breaking leads to dissymmetry, which in turn leads to complementary organization.