A Comment on the Question of Degeneracies in Quantum Mechanics

Abstract

The problem of degeneracies, descending from the Born-Oppenheimer (B-O) approximation serves as a “comeback backdoor” of the principle of complementarity, but on a much more subtle level. Quantum mechanics incorporates both mechanical and field theory features, which results in the well-known particle-wave aspects of complementarity. The degeneracy problem, however, prompts a new type of “property-object” complementary phenomena. This leads to serious consequences: Field theoretical methods, unlike mechanical ones, are incapable of separating the internal and the external degrees of freedom with respect to the centre of gravity, but on the other hand adapt relativistically in a natural manner very similar to the space-time formulas of Maxwell’s equations. The solutions of the quantum field equations, relativistic in the mentioned specific sense, yield singularities at symmetric points that correspond to the well-known B-O degeneracies giving the latter in actual fact a metaphysical attribute. However, Nature has in this case a more sophisticated method or modus operandi to avoid degenerations and to instigate symmetry violations.