TFNR - The Principle of Least Action
The Principle of Least Action (or Stationary Action) represents the specification of the Principle of Conservation at the most elementary level of Physical Reality.
The Principle of Conservation
This Principle states that the mutations described by the Principle of Variation, which always tend to propagate as described by the Principle of Propagation, the incessant variations of the dynamic conditions of Entities, the Events, always tend to conserve.
Events interact with other Events, creating dynamic structures that, mainly through cyclic Processes, acquire causal permanence.
Any variation of a Field produced by a Force (Event) tends to conserve in the Field temporarily (and so propagating spatially), conserving the Action of those Forces, the Events, in the Fields, conserving Causes, Causality, through Action.
The conservation of causes, of Forces, is represented by the permanence in Time of the effects of the Action produced by those Causes/Forces.
The general Principle of Conservation is the foundation of all derived principles of conservation operating at the various Levels of Reality.
It is the primary and fundamental expression of Variationality, in the mode we call Temporality.
At the level of the Elementary Field operates the Principle of Least Action; at the level of Physical Reality the principle of conservation of Energy, momentum, etc.; while at the level of Physical Structures of Information and the quanta operates the principle of conservation of Information.
On a biological level this principle applies to the conservation of genetic information in DNA, while on a cognitive level it manifests in the conservation of experiences, the storage of memories, the various phenomena related to the formation of culture, etc.
The principle of Least Action
The Principle of Least Action describes the formation of rotational reactions (Rotation), arising from the interactions between translational actions, tending to preserve inhomogeneities or anisotropies in the pre-temporal distributions of sub-elementary pre-spatial fluctuations.
This principle is the root and foundation of all the laws of conservation, principles that state that "a certain physical property or quantity does not change in the course of time within an isolated physical system" (conservation of mass-energy, linear momentum, angular momentum, electric charge, color charge, weak isospin, CPT symmetry, etc.).
In common physics this principle has various names such as "stationary-action principle" or "principle of least action". It is a variational principle that can be applied, for example, to the action of a mechanical system, producing the equations of motion. It also has different formulations: the Lagrangian and Hamiltonian ones (after the formulations of Maupertuis, Leibniz, and Euler), or that of General Relativity/Einstein-Hilbert action. Moreover, this principle appears in the formulation of Maxwell's equations, in Quantum Mechanics (through the stationary action method), in Quantum Electrodynamics, and in particle physics.
In summary, in this model, the principle of Least Action manifests wherever a Source produces Action, wherever a Force expresses Action upon a Field, and wherever the variations, inhomogeneities, and symmetry‑breakings manifested by the Field tend to be conserved.
The principle manifests wherever produced effects propagate in Time and persist. These effects (potentials) will continue to exist and may in turn become causes for new effects.
The Principle tells us that the Action manifested by a Field (variation, deformation) is always minimized.
This conservation manifests in the Mode / Component that I here call Rotation.
Stated in the terms of the Dynamics of Elementary Action, the elementary pre‑spatial fluctuations and their pre‑temporal distributions at the level of each event‑point produce a conservation within those same event-points, tending toward the preservation of dynamic inhomogeneity.
Links to the tables of contents of TFNR Paper
