The road not taken after 1905: a mechanistic route to unifying quantum theory and gravity

This bird's-eye view explains, for a physicist who is not a specialist, the motivation and structure of the$E_8\times\omega E_8$ octonionic unification programme built on generalised trace dynamics in the forthcoming book. The guiding idea is a thought experiment: suppose that after special relativity in 1905 one had refused to give upNewton's mechanistic world-view, and instead made two minimal changes - letting dynamical variables bematrices, and letting a spacetime point be an algebraic object richer than four real numbers. Wedescribe what follows, how matter and geometry are proposed to interact, and which parts of thepicture are established, which are conjectural, and which are simply not yet known.