A new pre-quantum level physical theory underlying the quantum mechanics has been developed and its epistemological features are mainly derived from the fluctuating classical electromagnetic zeropoint field which induces random oscillations on charged particle. In complex vector space, the average random oscillations of the charged particle are treated as complex rotations so that a particle has extended structure. It is found that the quantum nature of particles arises from the superposition of internal oscillations on the center of mass motion. Using Lagrangian mechanics in complex vector space, a generalized Newton’s equation is derived and which is shown to be acceptable for both micro and macro mechanics. The generalized Newton’s equation contains additional relativistic terms at the micro level. Further, a complex Hamilton-Jacobi equation is derived and which is used to solve quantum mechanical problems in classical approach. The presence of zeropoint field also produces modifications in the central potential and the additional terms are responsible for the effects like advance of planets perihelion and deflection of light near massive objects at macro level. Further, in the case of atoms such terms lead to the estimation of Lamb shift using stochastic electrodynamics. The consideration of extended particle structure in stochastic electrodynamics allows deriving mass correction and charge correction and consequently the estimation of anomalous magnetic moment. The fundamental deeper level theory developed here, may further enhance the efforts for research connecting micro and macro aspects of matter. Keywords: Foundations of Quantum Mechanics, Geometric Algebra, Stochastic Electrodynamics, Zeropoint Energy, Gravitation. DOI : 10.7176/APTA/88-04 Publication date : June28th 2024
A new pre-quantum level physical theory underlying the quantum mechanics has been developed and its epistemological features are mainly derived from the fluctuating classical electromagnetic zeropoint field which induces random oscillations on charged particle. In complex vector space, the average random oscillations of the charged particle are treated as complex rotations so that a particle has extended structure. It is found that the quantum nature of particles arises from the superposition of internal oscillations on the center of mass motion. Using Lagrangian mechanics in complex vector space, a generalized Newton’s equation is derived and which is shown to be acceptable for both micro and macro mechanics. The generalized Newton’s equation contains additional relativistic terms at the micro level. Further, a complex Hamilton-Jacobi equation is derived and which is used to solve quantum mechanical problems in classical approach. The presence of zeropoint field also produces modifications in the central potential and the additional terms are responsible for the effects like advance of planets perihelion and deflection of light near massive objects at macro level. Further, in the case of atoms such terms lead to the estimation of Lamb shift using stochastic electrodynamics. The consideration of extended particle structure in stochastic electrodynamics allows deriving mass correction and charge correction and consequently the estimation of anomalous magnetic moment. The fundamental deeper level theory developed here, may further enhance the efforts for research connecting micro and macro aspects of matter. Keywords: Foundations of Quantum Mechanics, Geometric Algebra, Stochastic Electrodynamics, Zeropoint Energy, Gravitation. DOI : 10.7176/APTA/88-04 Publication date : June28th 2024
At the conceptual level, the quantization procedure replaces the pure particle description of classical mechanics by a particle-wave treatment satisfying the requirements of the fundamental wave–particle dualism. Technically, one can always start from a generalized wave equation and use it as a basis to discuss wave-front propagation in the form of rays following classical particle trajectories, see Sections 2.2.1 and 3.1. Consequently, any wave theory inherently contains that aspect of the wave–particle dualism. Especially, Maxwell's equations of electrodynamic theory include both wave and particle aspects of electromagnetic fields. Hence, it could be that there are no additional “quantum,” i.e., wave–particle dualistic aspects. However, as we discuss in this chapter, Maxwell's equations can be expressed in the framework of Hamilton's formulation of particle mechanics. This then suggests that in addition to the approximate ray-like behavior, electromagnetic fields do have a supplementary level of particle-like properties. Due to the fundamental axiom of wave–particle dualism, the additional particle-like aspects of electromagnetic fields must then also have a wave counterpart that can be axiomatically introduced via the canonical quantization scheme described in Section 3.2.3. Since the spatial dependency in Maxwell's equation contains wave–particle dualism already at the classical level, it is clear that the new level of quantization cannot be a simple real-space feature but has to involve some other space describing the structure of the electromagnetic fields. In fact, this quantization yields several very concrete implications such as quantization of the light energy, elementary fluctuations in the light-field amplitude and intensity, and more.
The lack of a unified geometric foundation connecting quantum mechanics and electromagnetism remains a central challenge in theoretical physics. While quantum field theory treats particles as excitations of fields and general relativity describes gravity as spacetime curvature, a direct geometric link between quantum behavior and electromagnetic phenomena is still elusive. Motivated by this gap, we propose a novel theoretical framework that extends the Schrödinger equation into a complexified spacetime manifold. In this framework, spacetime is treated as inherently complex, with the real part governing classical evolution and the imaginary part encoding quantum fluctuations. By introducing complex derivatives that obey the Cauchy-Riemann conditions, we derive a modified Schrödinger equation whose structure naturally reveals the emergence of quantum behavior from imaginary curvature. Furthermore, we reinterpret the electromagnetic field as arising from the geometric curvature of the imaginary spacetime dimension. Specifically, we show that the imaginary part of the Ricci tensor yields structures mathematically analogous to Maxwell’s equations in curved space. The standard quantum commutation relations are also preserved under this complexification, ensuring compatibility with established quantum formalism. This unified approach not only preserves core quantum and electromagnetic features but also suggests that both phenomena are manifestations of a deeper geometric substrate. By embedding quantum mechanics and electromagnetism in a shared complex geometric framework, our results open promising avenues for a broader unification that may eventually incorporate gravity. This work lays a foundation for reinterpreting field interactions, quantum dynamics, and possibly spacetime itself through the lens of complex geometry.
Newton’s force law [Formula: see text] is derived from the Schrödinger equation for isolated macroscopic bodies, composite states of e.g. [Formula: see text] atoms and molecules, at finite body temperatures. We first review three aspects of quantum mechanics (QM) in this context: (i) Heisenberg’s uncertainty relations for their center of mass (CM), (ii) the diffusion of the CM wave packet, and (iii) a finite body temperature which implies a metastable (mixed-) state of the body: photon emissions and self-decoherence. They explain the origin of the classical trajectory for a macroscopic body. The ratio between the range [Formula: see text] over which the quantum fluctuations of its CM are effective, and the body’s (linear) size [Formula: see text], [Formula: see text] or [Formula: see text], tells whether the body’s CM behaves classically or quantum mechanically, respectively. In the first case, Newton’s force law for its CM follows from the Ehrenfest theorem. We illustrate this for weak gravitational forces, a harmonic-oscillator potential, and for constant external electromagnetic fields slowly varying in space. The derivation of the canonical Hamilton equations for many-body systems is also discussed. Effects due to the body’s finite size such as the gravitational tidal forces appear in perturbation theory. Our work is consistent with the well-known idea that the emergence of classical physics in QM is due to the environment-induced decoherence, but complements and completes it, by clarifying the conditions under which Newton’s equations follow from QM, and by deriving them explicitly.
Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations. Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.
I propose that quantum mechanics is a stochastic theory and quantum phenomena derive from the existence of real vacuum stochastic fields filling space. I revisit stochastic electrodynamics (SED), a theory that studies classical systems of electrically charged particles immersed in an electromagnetic (zeropoint) radiation field with spectral density proportional to the cube of the frequency, Planck's constant appearing as the parameter fixing the scale. Asides from briefly reviewing known results, I make a detailed comparison between SED and quantum mechanics. Both theories make the same predictions when the stochastic equations of motion are of first order in Planck constant, but not in general. I propose that SED provides a clue for a realistic interpretation of quantum theory.
In a previous paper, we showed that the Hamilton equations of motion of a quantum particle are obtained as group velocities of the wave packet describing this particle only if the time dependent phase of a particle wave is proportional to the Lagrangian, not to the Hamiltonian as in a solution of the conventional Schrodinger equation. When a Lagrangian of relativistic form is considered, the wave packet of a quantum particle takes a physical form, with a finite spectrum of a cut off velocity (c). Based on a relativistic quantum principle, asserting the invariance of the time dependent phase for an arbitrary change of coordinates, we obtained the relativistic kinematics and dynamics, the electromagnetic field equations, the spin and the electromagnetic and gravitational interactions. When the Lagrangian is considered as a function of the Hamiltonian, we obtain a Schrodinger type equation with an additional term depending on the velocity and the momentum operator. Based on this equation, we investigate the dynamics of a relativistic quantum particle. In this framework, such a particle is described as a continuous distribution of conservative matter, according to the general theory of relativity. In an electromagnetic field, any time dependent phase variation is modified with a term proportional to a vector potential conjugated to the spatial coordinates and a scalar potential conjugated to time. However, this classical description tells us nothing about the structure of the physical world. Only Quantum Mechanics tells us something about the structure of this world. Namely, that this world is composed of species of identical quantum particles. On one hand, experimentally, it has been found that these particles are of a wavy nature. On the other hand, one could find that the simplest way to define a quantum particle is by a wave packet, with momenta conjugated to coordinates and energy conjugated to time Consider a quantum particle as a wave packet, and find that the group velocities in the coordinate and momentum spaces are in agreement with the Hamilton equations only when the Lagrangian is considered in the time dependent phases, instead of the Hamiltonian in the conventional forms of these waves as solutions of the Schrodinger equation. We define a relativistic quantum principle, and derive a wave equation for a relativistic quantum particle, the relativistic kinematics and dynamics of the particle waves, the Maxwell equations and the Lorentz force of a field interacting with the particle waves, the relativistic transform of such a field, and the spin as a characteristic of the particle waves. We consider a quantum particle as a distribution of conservative matter propagating according to the General Theory of Relativity. We obtain the dynamics of this matter in a gravitational field, the propagation in plane waves perpendicular to geodesic tracks, and equations of conservation. We describe the matter dynamics as a positively defined density and show that, according to the general theory of relativity, such a distribution can be conceive only as of a fragment of matter with a finite mass equal to a mass , as a characteristic of the matter dynamics, – the matter quantization. The group velocities of the Fourier conjugate representations in the coordinate and momentum spaces describe the dynamics of a quantum particle in agreement with the Hamiltonian equations. Under the action of an external (non-gravitational) field, the acceleration of the quantum matter has two components: 1) A component perpendicular to the velocity, given by the relativistic mechanical component of the time dependent phase, and 2) A component given by the additional field terms of this phase. A free quantum particle is described by a non-dispersing wave function , contrary to the solution of the Schrodinger equation. A coherent electromagnetic field, in resonance with a system of active quantum particles in a Fabry-Perot cavity, has a wave vector approximately proportional to the metric elements, as the resonance frequency is approximately constant – a gravitational wave can be detected by the transmission characteristics of an active Fabry-Perot cavity. In a constant gravitational field, a quantum particle undertakes a velocity and an acceleration, which, at the boundary of a black hole are null – absorption and evaporation processes at the boundary of a black hole arise only by gravitational perturbations. Generally, a quantum particle is described by a time-space volume, called graviton, with a spin 2, and a distribution of a specific matter in this volume, with a half-integer spin for Fermions and an integer spin for Bosons. A graviton Lagrangian is obtained as a curvature integral on a graviton volume, and a Hamiltonian tensor is obtained for the gravitational coordinates and velocities. In a gravitational field, the time space coordinates are deformed. In such a field, any plane wave remains perpendicular geodesic, while an additional acceleration is possible in the wave plane.