Coarse Graining Ambiguities

The Big, the Fast and the Complex all to arise from a genie theory that amongst (a few) other things will be able to fully describe Black Hole dynamics. Observe below the Genie theory of Physics, a yarn spun from string theory, if not from a knot from knot theory or a loop from that quantum loop theory, a twistor from...? Anyway, the kinematical theories of symmetry-group theoretical principles, the field and the concept of the canonical ensemble have their representations/realisations in the three pillars of physics (in orange) arenas which require knitting together.

Scale ambiguity is expressed in the mathematician's infinitesimal: in mechanics as the limitless desiccation of a time lapse into a dense set of instantaneous moments with stitched locations scribed as trajectory inputs for a Calculus of variations.

The Three Pillars of Physics

The three pillars of fundamental physics: Thermodynamics, Particle physics and General Relativity, at root have kinematical descriptions that hinge on the ambiguity of scale. How do their descriptive frameworks depend on the scale at which the theories are applied? Apply with precision and view their high energy microstructure or take a coarse grained view from afar. Respectively the 3 pillar descriptions hinge on the 3 Cs: the Canonical Ensemble, Coupling Constant scaling and Conformal invariance.

Canonical Ensembles as Localised Islands of Tranquility

Consider only the Ensemble. Thermodynamics, may be better termed Thermostatics, it's elements being the ensemble of system (static) states to which can be assigned Macroscopic "state" variables such as Temperature and Pressure. Such state measures are to be representative of localised aggregates (ensembles) that within ("intra") themselves are in equilibrium but between ("inter") are in flux. These ensembles are localised islands of tranquility.

That Is, the ensembles are individually homogenous enough in character as to be fairly wholly describable by such coarse-grained indicators of aggregate behaviour. In any reductionist program, these variables such as Temperature (say) are given a mechanism: the microscopic molecular kinetic energy of constituent "atoms".

Here lies the contradiction in this picture of stitched together intrinsically defined static ensembles.The static state quality assigned at a chosen coarse-grained view, implies no equilibrium exists between neighbouring islands. The island ensembles are dynamically transitioning according to the zeroth law, in mutual contact as they are at different temperatures. So take another observers less coarse-grained view of that same system of localised states deemed to be in static equilibrium and they will see rather states still in flux still dynamically moving towards localised equilibrium.

Is this merely a semantic distortion of a truer (fundamental) statistical mechanical reality or is it a convenient but artificial picture?

Is it any wonder that limitless continuity jars with discrete state ensembles and bundles of stuff and energy. The movement away from the Reductionist's preoccupation with the nouns of stuff to the verbs of process within (complex) Dynamical systems would seem a step in the right direction.

That a hologram (of merely a projected reality), the new fallout from Black Hole thermodynamics and AdS is a "thing" and not an "event" though suggests it may not be an end game.