Modern physics relies on mathematical structures such as Hilbert spaces, operator algebras, quantum states, and dynamical laws. These tools have achieved extraordinary predictive success, yet they are almost always taken as fundamental ingredients of reality rather than explained. Why does nature seem to organize itself through such mathematical frameworks?
In the third paper of the Theory of Informational Selection (TSI), I explore a different possibility: that many of the mathematical structures underlying quantum theory may emerge from a more primitive informational organization. Starting from the stable informational partitions introduced in previous work, the paper investigates how increasingly sophisticated mathematical representations can arise without assuming Hilbert spaces, quantum observables, or even spacetime from the outset.
One of the most intriguing results concerns the emergence of intrinsic dynamics. The reconstruction generates a canonical modular flow, similar in spirit to the thermal time ideas developed by Alain Connes and Carlo Rovelli, but derived from a deeper informational level. In this picture, the first mathematically distinguished notion of evolution appears before geometry, spacetime, or physical clocks enter the description.
While this work does not yet address geometry or gravitation, it provides a bridge between the informational foundations of TSI and the geometric reconstruction developed in subsequent research. If successful, this program may help explain not only how physical laws operate, but why the mathematical architecture of modern physics exists in the first place.
