In an attempt to provide a novel approach to foundations of quantum mechanics, we have built a scheme of superdeterministic theories, where reality is governed by a classical nonlinear field equation. We show that under certain mathematical conditions that we have identified and that we substantiate in terms of algebra and invariance, the postulates of quantum mechanics can be deduced from them. Specifically, we show that these conditions essentially express properties of the structure of the invariance group of the nonlinear field equation, and we argue that there is no a priori reason why they cannot be satisfied. If these conditions were satisfied, quantum mechanics would acquire the status of a mathematical method for predicting what is predictable in an essentially chaotic world, a paradigm that would have many concrete consequences in physics.
PACS Numbers : 03.65.Ud