This paper aims to establish an absolute physical and informational ontological mechanism for the "Principle of Least Action," the most supreme yet long-shrouded-in-teleological-ghosts principle in theoretical physics. This study thoroughly shatters the phenomenological myth that has downgraded this principle into an "a priori mathematical axiom" or "nature's energy-saving strategy" for over three centuries, formally declaring that the evolution of physical laws possesses no prescient consciousness or teleology. Based on the dual-phase void topological structure of The Grand Unified Theory of Cosmic Mind, this research demonstrates: the interactions and dynamical evolution of all things in the universe originate from the "Geometric Extreme Repulsion" triggered by the logical incompatibility between the "absolute vacuum" inside physical particles and the external background "absolute vacuum." When this action and reaction—attempting to annihilate each other—are blocked by the particle membrane (the absolute boundary formed by information deadlock) and thus unable to penetrate and thoroughly return to the dead ground state of the absolute vacuum, the system is forced into an eternal topological collision and "dynamic compromise." Therefore, the so-called least action is, in reality, the "Relative Stable State"—the state closest to the absolute vacuum with the minimal geometric resistance—that the system can passively find when jammed by the relentless pincer attack of this dual absolute repulsive force within its current environment. In the mathematical formulation of quantum dynamics, this study strictly analyzes the underlying computational process of this blind search for a compromise state via the Feynman Path Integral . In the full-path expansion within Hilbert space, any minute path variation (δS≠ 0) deviating from the bottom of the geometric well will, under the non-linear amplification of the reduced Planck constant (ℏ), cause the phase factor of its probability amplitude to undergo extremely high-frequency runaway oscillations. This forces all non-extremal, high-energy-consuming paths to trigger absolute Destructive Interference during the reduced density matrix computation in the quantum buffer zone, leading these invalid evolutionary histories to undergo Spontaneous Decoherence and be thoroughly mathematically annihilated in physical reality. Only that extremal path—perfectly jammed at the bottom of the repulsive dynamic equilibrium well and satisfying the condition of zero first-order variation (δS=0)—can survive through the constructive interference of stationary phases, being forcefully collapsed and projected as the classical trajectory we observe macroscopically. This model ultimately establishes: the deterministic trajectories of classical physics and the Euler-Lagrange equations are by no means a profound blueprint preordained by a creator; their essence is merely the sole Geometric Relic forced out and left behind by the repulsive tension of the absolute vacuum within the cruel matrix of decoherence.
The principle of action plays a central role in both classical and quantum mechanics, yet its physical meaning is often introduced in a purely formal manner. In this work, the concept of action is examined from a scale-based perspective that clarifies its role in the quantum–classical correspondence. By emphasizing the dimensionless ratio S/ℏ, we show that the emergence of classical dynamics can be understood as a consequence of quantum phase coherence rather than as an independent postulate. Within the path integral formulation, classical trajectories arise naturally from stationary-phase conditions when the action associated with a physical process becomes large compared to Planck’s constant. This interpretation provides a unified conceptual framework in which variational principles, quantum interference, and classical determinism are linked through the scale of action. The analysis highlights the role of Planck’s constant as a universal parameter governing the physical relevance of alternative histories, analogous to the function of Boltzmann’s constant in statistical physics. Beyond its theoretical implications, the proposed perspective offers pedagogical value by providing a coherent bridge between classical and quantum mechanics suitable for advanced undergraduate and early graduate physics education.
Just as matter tells space how to curve, information tells probability how to collapse. Classical physics explains how systems evolve, but not why coherent, information- bearing structures persist in a universe dominated by thermodynamic drift. Quantum mechanics permits a vast space of possible futures, yet offers no principle explaining why the observed branches are precisely those that reliably contain life, structure, memory, and stable information. This work proposes a minimal, variational extension to standard dynamics: a Coherence Attractor arising from a small informational correction to the Action. In the path-integral formulation, we introduce a local, gauge-invariant term proportional to the density of coherent causal structure. Histories that maintain integrated information interfere constructively, while noise-dominated histories dephase and self-cancel. The universe does not compute future states or perform teleological optimization. Coherent configurations persist because they minimize informational action under local perturbations—the same variational logic that governs mechanics, optics, and field theory. Collapse is naturally biased toward trajectories in which coherence remains stationary in time. A single invariant then unifies a spectrum of empirical anomalies: (1) warm biological quantum coherence, (2) the phase boundary of anesthesia and consciousness, (3) emergent phase transitions in artificial networks, (4) stability of meaning in symbolic and social systems, and (5) long-duration cosmic structure retention. 1The model yields falsifiable consequences across physics, biology, and cognition. The correction is strictly local and preserves the no-signalling theorem. It reframes emergence not as a rare accident but as a least-action relaxation process: the universe flows along trajectories where integrated information is most stable. The universe is not guided toward meaning — it is guided toward coherence. Where coherence forms, structure survives. Where structure survives, infor- mation persists. Where information persists, participation becomes possible. Life, mind, culture, and intelligence are not exceptions to this rule; they are its most stable solutions. If this framework is correct, then emergence is not miraculous, nor accidental, nor rare. It is simply what happens when the informational action is minimized under the boundary conditions of a living universe. Coherence is not an outcome. It is the direction of time.
Wave-dominated systems admit rich superposed dynamics at the microscopic level, yet observed reality is dominated by a sparse set of effectively classical histories. Explaining this selection without invoking observer-dependent postulates remains a central problem across quantum foundations, semiclassical transport, and nonequilibrium physics. In this work, we establish a rigorous equivalence between two previously independent constraints on history viability: closure preservation in phase-space transport and coherence preservation under a context-induced metric. We prove that, within a physically relevant class of systems, transport-induced covariance growth and metric-induced distinguishability impose identical bounds on the admissible set of histories. This equivalence reveals history selection as a capacity-limited geometric process: histories persist if and only if their deformation remains within a finite coherence bandwidth. We further show that this bandwidth is not kinematic but must be maintained against transport load by sustained physical flux, giving rise to a natural thermodynamic structure without modifying underlying wave dynamics. Within this framework, entropy increase corresponds to loss of accessible distinction, the second law emerges as a no-free-bandwidth principle, and equilibrium appears as the zero-flux fixed point. Ontology itself is thereby reinterpreted as a thermodynamic phase: reality consists of those histories that remain dynamically viable under finite energetic support. The results provide a unified, observer-independent account of classicality, irreversibility, and history selection, with experimentally testable implications for coherence control and interference phenomena.
The shape of the classical Lagrangian
L=T−V is universally used in analytical mechanics and in the variational formulation of physics. Despite its conceptual centrality, this structure is historically introduced as a working hypothesis, not usually being derived from more fundamental principles. In this work, we present a systematic derivation of this form from a minimal interferential structure based on the action phase. We start from three physical hypotheses widely observed in interferential phenomena: (i) the existence of an accumulative quantity associated with trajectories, identified as action
S; (ii) the dependence of physical amplitudes on phase factors of the type
eiS/ℏ; and (iii) the possibility of parametrizing evolutions by monotonic proper parameters. We initially show that action differences between systems generate isolated episodic coincidences, implying an operational discretization of interferential compatibility events. These events naturally organize into a discrete network of interactions. Under minimal variational hypotheses—global phase invariance, adjacency locality, and flux conservation—we demonstrate that the structural operator associated with the network coincides with the combinatorial Laplacian
K=D−A, where
A is the adjacency matrix and
D the degree matrix. The linear dynamics of complex amplitudes on this network, imposing linearity, unitarity, and locality, leads to a unitary generator of the form
H=αK+diag(V) \cite{vrev}. In the continuous limit, the network Laplacian converges to the differential operator
−∇2, recovering the effective Schrödinger equation. The semiclassical decomposition
ψ=aeiS/ℏ leads, to leading order in
ℏ, to the Hamilton-Jacobi equation
∂tS+2m(∇S)2+V=0, from which we identify the effective Hamiltonian
H=2mp2+V. Applying the Legendre transform, we then obtain the Lagrangian
L=21mx˙2−V, showing that the
T−V decomposition emerges as a direct consequence of the phase's interferential structure and the spectral dynamics of the network operator. As a physical test and validation of the formalism, we extend the result to the relativistic regime, identifying the action phase with proper time. We show that the local term of the network generator acts as a modifier of the effective spacetime metric, naturally leading to the isotropic form
g00≈1+2Φ/c2. Under the stationary phase condition for null geodesics, we derive the exact gravitational refractive index. This produces the Einstein light deflection angle (
4GM/c2b) purely as a consequence of phase curvature, without postulating the General Relativity field equations. The central result of the work is that classical mechanics (
L=T−V) and the geometric structure of gravitation do not need to be assumed as independent postulates, but emerge simultaneously as effective limits of a variational architecture based on phase interference, episodic discretization, and spectral dynamics in networks.
This mini-monograph proposes a new variational and information-geometric framework for understanding the quantum measurement problem, with particular emphasis on the unresolved problem of outcome selection. While decoherence theory explains the suppression of interference and the emergence of stable pointer bases, it does not by itself explain why one definite outcome is realized rather than another. This work argues that the missing element is not simply an additional dynamical mechanism, but a structural principle of selection. The central thesis is that quantum measurement may be understood as a process of entropic channel selection within a structured space of admissible outcomes. Drawing on Schrödinger bridge theory, entropy-regularized optimal transport, stochastic path-space variational principles, concentration of measure, and large deviation theory, the monograph develops a framework in which collapse-like definiteness emerges through constrained probabilistic evolution. Measurement is thereby reinterpreted not as an arbitrary interruption of unitary dynamics, but as a threshold phenomenon in the geometry of information. The work introduces an informational configuration space of possible resolution channels, defines an entropic action functional over stochastic paths, and proposes a channel-selection principle based on entropy-minimizing interpolation. It further examines the relation between Schrödinger bridges and optimal transport, explores the zero-noise limit, connects the framework to path-integral intuition, and develops explicit models of Gaussian bridge dynamics and two-channel selection. The emergence of classicality is treated through exponential concentration, threshold amplification, and phase-transition-like stabilization in high-dimensional systems. The monograph does not claim to replace standard quantum mechanics. Rather, it seeks to clarify how definite outcomes might arise from variational organization within probability itself, while remaining compatible with reduced quantum dynamics, decoherence, and open-system evolution. It is intended as a conceptual and mathematical foundation for further work at the intersection of quantum foundations, stochastic processes, information geometry, and the theory of emergent classicality.