Pregeometric modelling of the spacetime phenomenology

At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we report progress in developing a {\em Heraclitean Quantum System}. This is a particular pregeometric theory for space and time in which no classical or geometric structures are assumed, but rather the emergence of such phenomena is sought.