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 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 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.
The Principle of Least (or Stationary) Action in the terms of the Dynamics of Elementary Action
Within the Dynamics of Elementary Action, the Principle of Least Action does not appear as an abstract mathematical rule imposed from above, but as the natural consequence of how Reality organizes its own unfolding at the most elementary level.
Elementary Action is any inhomogeneity in the dynamism of a local event‑point (or a region of event-points of the Field) that both varies (according to the Principle of Variation) and propagates (according to the Principle of Propagation). Yet this propagation does not occur arbitrarily: it is shaped by the global constraints expressed by the Principle of Conservation.
The Principle of Least Action is precisely the mechanism through which these constraints are respected.
Propagation does not "choose" a trajectory; rather, the dynamism of the Field itself selects, among all the relationally possible paths, those that maintain global invariants while minimizing the internal tension generated by variation and counter‑variation.
In this sense:
- Variation opens a spectrum of possible evolutions,
- Propagation distributes these variations through relational interactions,
- Conservation restricts the admissible transformations.
Least Action identifies the actual trajectory as the one that satisfies these constraints with the minimal dynamical expenditure.
This is, of course, not the result of any mechanism of evaluation, calculation, or deliberate application. The statement that "Nature knows how to proceed, how to function" might suggest that there is some "thing" directing the traffic, so to speak—something that chooses trajectories by evaluating them globally before they are followed. Nothing of the sort.
Trajectories define themselves and come into being point by point, event-point by event-point, Elementary Event by Elementary Event, pre-spatial fluctuation after pre-spatial fluctuation. At each event‑point, the "natural" composition—according to the familiar rule of vector composition of forces, as in classical mechanics, yet influenced by the incessant chaotic, indeterminate, and uncertain fluctuations of the Field resonating around the Planck scale—of the Actions manifesting in the Field at the most elementary level, through their continuous interaction, produces the ongoing "optimization" of the Elementary Action as it is manifested, propagated, and conserved.
We can observe, or imagine, this formative dynamism from an even more fundamental, sub‑elementary perspective: in those pre‑spatial and pre‑temporal aspects that support Elementary Action, the most elementary form of Existence. As already emphasized, these are conceptual, pre‑physical viewpoints that help us describe and understand how the dynamism of the Elementary Field develops and gives rise to Elementary Action and to all the formative Processes that lead to more complex forms of Existence.
For example, we may imagine the interaction between a Translational component present in the Field (a potential motion, an acceleration, such as that associated with metric/gravitational phenomena produced by massive structures) and the Translational component expressed by an InfoStructure propagating through the Field (an expressed, inertial motion associated with the kinetic behavior of that Structure).
In the region of the Field where this translational kinetic interaction occurs—an interaction that will produce the acceleration of the Structure (a change in speed or in the direction of motion)—the Elementary Action associated with the kinetic potential of the Field and the Elementary Action associated with the expressed kinetic state of the Structure will combine, at each event‑point, according to the simple rule embodied in the parallelogram law so central to classical mechanics, although in a less deterministic form that incorporates the stochastic component of sub‑elementary chaotic/indeterminate/uncertain fluctuations.
The degree of uncertainty introduced by these chaotic fluctuations will make the trajectory slightly indeterminate, causing it to fluctuate around the "ideal" trajectory that would be followed if Reality were completely deterministic. From this, we understand how, in this model, Reality at the most elementary—indeed, sub‑elementary—level is intrinsically creative as well as evolutionary. Chaos and order interact incessantly within the continuum, producing the ongoing reorganization of natural Processes—reorganization that we observe as the formation of new Information/Energy alongside the conservation and transformation of Information / Energy already present.
Translated into the terms of classical mechanics, it becomes evident that the Principle of Stationary Action, or Least Action, is grounded in the interaction of three quantities: potential energy, kinetic energy, and time—the very same quantities that reappear at the elementary level in this model, and even in the pre‑physical, sub‑elementary perspective of the dynamism of each event‑point:
- the pointwise manifestation of the structural component associated with the potential of the Field (potential energy),
- the pointwise manifestation of the structural component associated with the InfoStructure propagating within the Field (kinetic energy),
- the pre‑temporal dimension (the event‑point’s own pre‑Time) with its physical projection as the proper Time of the micro‑region of the Field that, at every instant, supports the Existence and the Essence / Form of the InfoStructure,
- to these components we must add the stochastic contribution associated with the spontaneous chaotic dynamism of the Field resonating around the Planck scale.
The condition of stationarity of the temporal integral of the Lagrangian (kinetic energy minus potential energy) thus emerges. A condition that—within their respective domains and with their respective specifications—applies both to apples falling from trees and to the sub‑elementary dynamics that, event‑point by event‑point, support Existence and, through their correlation patterns, the Essence / Form of the entire infinite Universe.
In summary
- Principle of Least (or Stationary) Action as a specification of the Principle of Conservation
- Here the focus is: conservation provides the global constraint, and least action is the "optimal" way in which evolution unfolds under those constraints.
- General Principle of Conservation: in every formative Process there exist global quantities (energy, information, structure) that are conserved, imposing constraints on the possible transformations.
- Principle of Least / Stationary Action (specification): among all trajectories compatible with conservation constraints, formation realizes those for which the Action is stationary (often minimal) with respect to the allowed variations.
- In this framework: formation is not merely "whatever happens", but a structural selection of trajectories compatible with conservation — a kind of ontological economy of Action.
Links to the tables of contents of TFNR Paper
"We do not see the trajectory as it builds itself continuously in time and space. We only observe that the actual trajectory follows the principle of least action, and based on this principle, we can predict it deterministically or probabilistically (in a quantum context, for example). However, this happens because we lack the ability to observe what occurs at the elementary level, let alone the sub-elementary level. As stated, there is no optimization of the entire trajectory, nor a choice between different trajectories—in fact, different trajectories do not even exist.
The trajectory forms within the pre-spatial and pre-temporal continuum through the dynamic contribution of each event-point of the Elementary Field, which supports the InfoStructure (an electron, a photon/e.m. wave) or the Form (an apple) that we observe moving in Spacetime. Spacetime itself, the Metric, is incessantly formed thanks to the elementary dynamism of the Field. The entire Universe is incessantly formed in this way: all the trajectories of all atoms, of all particles, of turbulence and dark structures, of large cosmic structures, as well as the smallest objects. Everything exists and transforms based on the elementary dynamism of the Field, which is in turn supported by sub-elementary dynamism."
