The Pebbles of Newton: gravitation and quantum theory as emergent phenomena

We are all the children of Newton. He gave us modern physics, while himself standing on the shoulders of Copernicus, Galileo and Kepler. Newton gave us calculus, inertia, forces, law of motion, law of gravitation, absolute space, absolute time.

It could be said that since his time, we have been incrementing Newton. The law of motion is derived from the principle of least action. Other forces have been discovered since, and the laws of motion have been generalised. However, I tend to disagree that relativity and quantum theory overthrew Newton; better to say there has been incremental generalisation.

Because if the attached action principle is to be believed, we are back to Newton, maybe a pebble little prettier, but very Newtonian still. There is absolute time, the Connes time. There is kinetic energy, and the same equation of motion as his; the second law. Gravity, electromagnetism, strong force and weak force have all been bundled together, as also relativity and quantum theory. His three dimensional space has become octonionic space, real numbers have been replaced by matrices made of Grassmann numbers. Maybe the picture will simplify further, and become a geometric algebra. But everything we have found since Newton is still very Newtonian, when captured in this attached action principle. Locality and causality are only emergent - in a refined Newtonian sense, we have action at a distance!!

PS: Adler's Trace Dynamics, from which the action principle below is inspired, already has a Newtonian feel to it, because it is a Lagrangian dynamics. However, it has a conserved charge, the Adler-Millard charge = Sum_i [q_i, p_i] which Newton's classical dynamics does not have, making this a pre-quantum theory. Newtonian in its Lagrangian dynamics, but more quantum than quantum theory! This action represents an elementary particle which carries all its fields around with itself, in a very particulate sense. When there is no commutative background physical space anymore, it may not be meaningful anymore to talk of fields. But a matrix-valued particle should be just fine.