Abstract

Quantum mechanics is a linear theory. This is a strange fact. Why should nature be so convenient? Perhaps linearity is simply a consequence of small perturbations against a relatively uniform background. This can be formalized within the mathematical notions of weak solution and linearization. The true picture is unlikely to be so and some more appropriate framework may be required to deal with theories where this uniformity is lost, such as for example quantum gravity. A geometric model of quantum interaction provides a useful illustration. In this case the equations are quadratic, but both their weak form and linearization leads to a striking analogue of the Schrödinger equation.