Building on a model recently proposed by F. Calogero, we postulate the existence of a universal Keplerian tremor for any stable classical system. Deriving the characteristic unit of action α for each classical interaction, we obtain in all cases α ∼ = h, the Planck action constant, suggesting that quantum corrections to classical dynamics can be simulated through a fluctuative hypothesis of purely classical origin. PACS Numbers: 03.65.Bz; 05.45.+b; 05.40.+j In a recent paper F. Calogero has put forward an intriguing conjecture on the possible gravitational origin of quantization [1]. The scheme followed by Calogero is simple but appealing. He suggests that the origin of quantization be attributed to the universal interaction of every particle with the background gravitational force due to all other particlesBuilding on a model recently proposed by F. Calogero, we postulate the existence of a universal Keplerian tremor for any stable classical system. Deriving the characteristic unit of action α for each classical interaction, we obtain in all cases α ∼ = h, the Planck action constant, suggesting that quantum corrections to classical dynamics can be simulated through a fluctuative hypothesis of purely classical origin. PACS Numbers: 03.65.Bz; 05.45.+b; 05.40.+j In a recent paper F. Calogero has put forward an intriguing conjecture on the possible gravitational origin of quantization [1]. The scheme followed by Calogero is simple but appealing. He suggests that the origin of quantization be attributed to the universal interaction of every particle with the background gravitational force due to all other particles

Jan 1, 19982 citations

Stability Principle in Non-Inertial Physics

TF Kamalov

Quantum mechanics is traditionally formulated in terms of postulates inferred from experimentalobservations. Here we propose that the statistical regularities of quantum mechanics arise as macro-scopic manifestations of stochastic fluctuations of dynamical parameters in microscopic systems gen-erated by a non-inertial physical background. Although the specific nature of this background mayvary, the universality of quantum statistics is ensured by invariant properties of stochastic dynam-ics - analogous to the role of the equivalence principle in general relativity - and by the existence ofa fundamental action scale, Planck constant h. By extending classical mechanics to include higher-order derivatives induced by non-inertial fuctuations and imposing a stability condition on admissibletrajectories, the minimal action scale h naturally emerges. In this framework quantum mechanicsappears as an effective statistical description of systems embedded in a fluctuating non-inertial envi-ronment while preserving all standard predictions of the theory.Quantum mechanics is traditionally formulated in terms of postulates inferred from experimentalobservations. Here we propose that the statistical regularities of quantum mechanics arise as macro-scopic manifestations of stochastic fluctuations of dynamical parameters in microscopic systems gen-erated by a non-inertial physical background. Although the specific nature of this background mayvary, the universality of quantum statistics is ensured by invariant properties of stochastic dynam-ics - analogous to the role of the equivalence principle in general relativity - and by the existence ofa fundamental action scale, Planck constant h. By extending classical mechanics to include higher-order derivatives induced by non-inertial fuctuations and imposing a stability condition on admissibletrajectories, the minimal action scale h naturally emerges. In this framework quantum mechanicsappears as an effective statistical description of systems embedded in a fluctuating non-inertial envi-ronment while preserving all standard predictions of the theory.

Mar 11, 20260 citations

The Action Scale and The Emergence of Classical Dynamics in Quantum Systems

Rodika Utama, Rustaman

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.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.

JURNAL ARMADA PENDIDIKANApr 30, 20260 citations

Classical dynamical origin of Feynman paths?

M. Roncadelli

Even though only the classical action explicitly appears in the Feynman path integral, quantum fluctuations show up in the fluctuating nature of Feynman paths. This prevents a classical interpretation of the latter objects. Still, it makes sense to ask whether the Feynman paths have any relation to the classical dynamical trajectories in configuration space-a possibility naturally suggested by the semiclassical approximation. Unfortunately, no such relation exists (in general). Things are quite different for the generalized Feynman paths, which actually contribute in a novel path integral giving an alternative representation of the quantum mechanical propagator. It is shown that these paths fluctuate about a classical dynamical trajectory (in configuration space) because of a certain white noise. That is to say, the generalized Feynman paths are fluctuating curves that collapse on a classical dynamical trajectory as h to 0. This result throws new light on the interplay between classical and quantum mechanics and hints at a new approach to the quantum theory.Even though only the classical action explicitly appears in the Feynman path integral, quantum fluctuations show up in the fluctuating nature of Feynman paths. This prevents a classical interpretation of the latter objects. Still, it makes sense to ask whether the Feynman paths have any relation to the classical dynamical trajectories in configuration space-a possibility naturally suggested by the semiclassical approximation. Unfortunately, no such relation exists (in general). Things are quite different for the generalized Feynman paths, which actually contribute in a novel path integral giving an alternative representation of the quantum mechanical propagator. It is shown that these paths fluctuate about a classical dynamical trajectory (in configuration space) because of a certain white noise. That is to say, the generalized Feynman paths are fluctuating curves that collapse on a classical dynamical trajectory as h to 0. This result throws new light on the interplay between classical and quantum mechanics and hints at a new approach to the quantum theory.

Journal of Physics A Mathematical and GeneralSep 21, 19933 citations

Limit of classical chaos in quantum systems

Tomio Yamakoshi Petrosky, William C. Schieve

The nonlocal effect of quantum mechanics upon the classical chaos around the separatrix in a Hamiltonian system is investigated by extending the definition of the Melnikov function in the semiclassical approximation. It is shown that the quantum correction of the Melnikov function is related to the quantum fluctuation of the energy on the stable and unstable manifolds. This correction is a constant shift of the center of oscillation of the classical Melnikov function from zero. Because of this shift, the effect of quantum mechanics suppresses the classical chaos around the separatrix. Physical estimates are made of the magnitude of the quantum effect for a double-well oscillator system. As examples, we treat the case of the electron for the molecular scale and the proton for the nuclear scale, and also comment on the ammonia molecules ${\mathrm{NH}}_{3}$ , ${\mathrm{ND}}_{3}$ , and ${\mathrm{NT}}_{3}$ .The nonlocal effect of quantum mechanics upon the classical chaos around the separatrix in a Hamiltonian system is investigated by extending the definition of the Melnikov function in the semiclassical approximation. It is shown that the quantum correction of the Melnikov function is related to the quantum fluctuation of the energy on the stable and unstable manifolds. This correction is a constant shift of the center of oscillation of the classical Melnikov function from zero. Because of this shift, the effect of quantum mechanics suppresses the classical chaos around the separatrix. Physical estimates are made of the magnitude of the quantum effect for a double-well oscillator system. As examples, we treat the case of the electron for the molecular scale and the proton for the nuclear scale, and also comment on the ammonia molecules ${\mathrm{NH}}_{3}$, ${\mathrm{ND}}_{3}$, and ${\mathrm{NT}}_{3}$.

Physical Review AJun 1, 198512 citations

Introduction

Mark Sheard Child

Abstract Semiclassical mechanics is a short-wavelength link between classical and quantum mechanics, similar to that between wave and geometrical optics. Its object is to maintain contact with the structure imposed by classical mechanics, without sacrificing quantum mechanical accuracy, or, in the vivid words of Berry and Mount (1972), to ‘sew quantum mechanical flesh onto classical bones’. The overriding principles are that the classical phase space is divided into ‘accessible’ and ‘inaccessible’ regions characteristic of the type of motion, and that the boundaries of these regions impose a classical structure, which is evidenced in the quantum mechanics by interference in the bright accessible regions and exponential decay into the shadow regions. The strength of the classical skeleton is that this structure is maintained whether the observations are made in coordinate space, quantum number space, or some mixed representation. In all cases the central quantity is the classical action, whose dimensions are those of Planck’s constant; on one hand it guides the classical motion, according to the minimum action principle, and on the other it adds a phase to each classical trajectory, which gives rise both to quantum mechanical interference and, by a mathematical extension, to quantum mechanical tunnelling.Abstract Semiclassical mechanics is a short-wavelength link between classical and quantum mechanics, similar to that between wave and geometrical optics. Its object is to maintain contact with the structure imposed by classical mechanics, without sacrificing quantum mechanical accuracy, or, in the vivid words of Berry and Mount (1972), to ‘sew quantum mechanical flesh onto classical bones’. The overriding principles are that the classical phase space is divided into ‘accessible’ and ‘inaccessible’ regions characteristic of the type of motion, and that the boundaries of these regions impose a classical structure, which is evidenced in the quantum mechanics by interference in the bright accessible regions and exponential decay into the shadow regions. The strength of the classical skeleton is that this structure is maintained whether the observations are made in coordinate space, quantum number space, or some mixed representation. In all cases the central quantity is the classical action, whose dimensions are those of Planck’s constant; on one hand it guides the classical motion, according to the minimum action principle, and on the other it adds a phase to each classical trajectory, which gives rise both to quantum mechanical interference and, by a mathematical extension, to quantum mechanical tunnelling.

Jan 3, 19910 citations

{\mathrm{NH}}_{3}

{\mathrm{ND}}_{3}

, and

{\mathrm{NT}}_{3}