This paper presents a Coherence Geometry interpretation of Planck’s constant as a natural action scale arising from phase closure in structured coherence fields. Planck’s constant is traditionally introduced as an empirical constant. In this paper, a natural coherence action scale $S_0$ arises from the requirement that stable $\mu$ -field structures close phase cycles in integral multiples of $2\pi$ . This quantizes action increments as $S = 2\pi n S_0$ . The standard quantum relations follow once $S_0$ is calibrated to laboratory data, yielding $S_0 = \hbar$ . The result is structural rather than numerological: the paper does not claim to derive the measured numerical value of $h$ without calibration. Instead, it argues that an action scale of the Planck type appears naturally from phase-constrained coherence geometry, with numerical value fixed by physical units and experimental comparison. Internal reference: CGI-RSR-000020.This paper presents a Coherence Geometry interpretation of Planck’s constant as a natural action scale arising from phase closure in structured coherence fields. Planck’s constant is traditionally introduced as an empirical constant. In this paper, a natural coherence action scale $S_0$ arises from the requirement that stable $\mu$-field structures close phase cycles in integral multiples of $2\pi$. This quantizes action increments as $S = 2\pi n S_0$. The standard quantum relations follow once $S_0$ is calibrated to laboratory data, yielding $S_0 = \hbar$. The result is structural rather than numerological: the paper does not claim to derive the measured numerical value of $h$ without calibration. Instead, it argues that an action scale of the Planck type appears naturally from phase-constrained coherence geometry, with numerical value fixed by physical units and experimental comparison. Internal reference: CGI-RSR-000020.

May 17, 20260 citations

Relativistic quantum mechanics and mass-quantization

Hiroshi Enatsu

Il Nuovo CimentoMar 1, 19567 citations

Relativistic Beating of Compton Clocks, Action Discretization, and the Emergence of Planck's Constant

Jonatan P. camargo

We investigate the relationship between phase interference associated with action, the relativistic dynamics of proper time, and the structural origin of action quantization. We start from the general principle of interferential compatibility of action introduced in previous works, in which the dynamic phase of a system is given by $\phi=S/\hbar$ and phase coincidences between distinct evolutions occur only when $\Delta S = 2\pi n\hbar$ . We show that when this formalism is specialized to the relativistic action of a free particle $S=-mc^{2}\tau$ , the phase evolution naturally implies an internal frequency $\omega_C = mc^{2}/\hbar$ , corresponding to the Compton clock. When two systems evolve with distinct proper times, their Compton phases diverge, producing a relativistic phase beating. We demonstrate that the interferential coherence condition $\Delta\phi = 2\pi n$ defines a discrete sequence of synchronization instants and directly implies the relation $mc^{2}\Delta\tau = nh$ , showing that discrete action increments emerge as a geometric consequence of the relativistic periodicity of the phase. We also show that the used phase coincides exactly with the rest phase of the Dirac equation solutions, establishing the connection with the relativistic dynamics of fields. The beating between Compton clocks defines an operational discretization of the action that can be interpreted as a discrete sum, whose continuous form is recovered in the limit of almost perfect synchronization between reference frames. We also discuss the relationship of this formalism with the notion of the internal clock introduced by de Broglie and with the interferential structure of relativistic matter interferometry. In this framework, Planck's constant emerges as the geometric invariant associated with the first closure of the relativistic beating between Compton clocks. Quantization can then be interpreted as a coherence condition between relativistic phases, establishing a direct bridge between quantum interference, proper time relativistic dynamics, and the variational principle of stationary action.We investigate the relationship between phase interference associated with action, the relativistic dynamics of proper time, and the structural origin of action quantization. We start from the general principle of interferential compatibility of action introduced in previous works, in which the dynamic phase of a system is given by $\phi=S/\hbar$ and phase coincidences between distinct evolutions occur only when $\Delta S = 2\pi n\hbar$. We show that when this formalism is specialized to the relativistic action of a free particle $S=-mc^{2}\tau$, the phase evolution naturally implies an internal frequency $\omega_C = mc^{2}/\hbar$, corresponding to the Compton clock. When two systems evolve with distinct proper times, their Compton phases diverge, producing a relativistic phase beating. We demonstrate that the interferential coherence condition $\Delta\phi = 2\pi n$ defines a discrete sequence of synchronization instants and directly implies the relation $mc^{2}\Delta\tau = nh$, showing that discrete action increments emerge as a geometric consequence of the relativistic periodicity of the phase. We also show that the used phase coincides exactly with the rest phase of the Dirac equation solutions, establishing the connection with the relativistic dynamics of fields. The beating between Compton clocks defines an operational discretization of the action that can be interpreted as a discrete sum, whose continuous form is recovered in the limit of almost perfect synchronization between reference frames. We also discuss the relationship of this formalism with the notion of the internal clock introduced by de Broglie and with the interferential structure of relativistic matter interferometry. In this framework, Planck's constant emerges as the geometric invariant associated with the first closure of the relativistic beating between Compton clocks. Quantization can then be interpreted as a coherence condition between relativistic phases, establishing a direct bridge between quantum interference, proper time relativistic dynamics, and the variational principle of stationary action.

Mar 10, 20260 citations

Quantum relativistic action at a distance

Donald Salisbury, Michael Pollot

Foundations of PhysicsDec 1, 19893 citations

Bridge Between Quantum and Classical Bremsstrahlung

Mert Yücemöz

This article uses a formula for Action, the path that minimizes energy, which can be written in the Lagrangian form as $ \int (T-V) dt$, which has a solution of a whole number multiple of the quantum of action ”nh”. Hence, $ \int (T-V) dt = nh$ where n is a whole number multiple, and h is Planck’s constant. The article uses $n h = \int mv ds $ and substitutes the position vector that incorporates the bremsstrahlung asymmetry quantity, R, inside. The article rearranges the formula to find the relationship between bremsstrahlung asymmetry, R, as a function of the whole-number multiple of the quantum of action ”n”, R(n). This is thought to be possible due to angular momentum, which has the same units as action, using a similar procedure to Bohr used when he decided to discretize the angular momentum. Finally, following similar tuning procedure as Planck did to get Planck’s constant, h value, this report tunes the parameter, whole multiple of quantum of action ”n” until it gets the correct scale of the graph which is from Figure 1c to Figure 1d matching and describing the classical prediction of Bremsstrahlung asymmetry in Figure 1a. This allowed predicting the whole number multiple of quantum of action ”n” which follows the Bohr correspondence principle, that when the quantum number ”n” becomes very large, the quantized behaviour predicted by quantum mechanics should start to look like the smooth, continuous behaviour described by classical physics.This article uses a formula for Action, the path that minimizes energy, which can be written in the Lagrangian form as $ \int (T-V) dt$, which has a solution of a whole number multiple of the quantum of action ”nh”. Hence, $ \int (T-V) dt = nh$ where n is a whole number multiple, and h is Planck’s constant. The article uses $n h = \int mv ds $ and substitutes the position vector that incorporates the bremsstrahlung asymmetry quantity, R, inside. The article rearranges the formula to find the relationship between bremsstrahlung asymmetry, R, as a function of the whole-number multiple of the quantum of action ”n”, R(n). This is thought to be possible due to angular momentum, which has the same units as action, using a similar procedure to Bohr used when he decided to discretize the angular momentum. Finally, following similar tuning procedure as Planck did to get Planck’s constant, h value, this report tunes the parameter, whole multiple of quantum of action ”n” until it gets the correct scale of the graph which is from Figure 1c to Figure 1d matching and describing the classical prediction of Bremsstrahlung asymmetry in Figure 1a. This allowed predicting the whole number multiple of quantum of action ”n” which follows the Bohr correspondence principle, that when the quantum number ”n” becomes very large, the quantized behaviour predicted by quantum mechanics should start to look like the smooth, continuous behaviour described by classical physics.

Jul 24, 20250 citations

Second Quantization for Non-relativistic Identical Particles

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

UNITEXT for physicsJan 1, 20260 citations

S_0

arises from the requirement that stable

\mu

-field structures close phase cycles in integral multiples of

2\pi

. This quantizes action increments as

S = 2\pi n S_0

. The standard quantum relations follow once

S_0

is calibrated to laboratory data, yielding

S_0 = \hbar

. The result is structural rather than numerological: the paper does not claim to derive the measured numerical value of

h

without calibration. Instead, it argues that an action scale of the Planck type appears naturally from phase-constrained coherence geometry, with numerical value fixed by physical units and experimental comparison. Internal reference: CGI-RSR-000020.

\phi=S/\hbar

and phase coincidences between distinct evolutions occur only when

\Delta S = 2\pi n\hbar

. We show that when this formalism is specialized to the relativistic action of a free particle

S=-mc^{2}\tau

, the phase evolution naturally implies an internal frequency

\omega_C = mc^{2}/\hbar

, corresponding to the Compton clock. When two systems evolve with distinct proper times, their Compton phases diverge, producing a relativistic phase beating. We demonstrate that the interferential coherence condition

\Delta\phi = 2\pi n

defines a discrete sequence of synchronization instants and directly implies the relation

mc^{2}\Delta\tau = nh

, showing that discrete action increments emerge as a geometric consequence of the relativistic periodicity of the phase. We also show that the used phase coincides exactly with the rest phase of the Dirac equation solutions, establishing the connection with the relativistic dynamics of fields. The beating between Compton clocks defines an operational discretization of the action that can be interpreted as a discrete sum, whose continuous form is recovered in the limit of almost perfect synchronization between reference frames. We also discuss the relationship of this formalism with the notion of the internal clock introduced by de Broglie and with the interferential structure of relativistic matter interferometry. In this framework, Planck's constant emerges as the geometric invariant associated with the first closure of the relativistic beating between Compton clocks. Quantization can then be interpreted as a coherence condition between relativistic phases, establishing a direct bridge between quantum interference, proper time relativistic dynamics, and the variational principle of stationary action.