Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Cole and Zou in 2003 and Nieuwenhuizen and Liska in 2015 found that the SED field prevented the electron orbit from collapsing into the proton but eventually the atom became ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian which is used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum flucuations with the role of the real stochastic electromagnetic field.
I expose nonrelativistic quantum electrodynamics in the Weyl-Wigner representation. Hence I prove that an approximation to first order in Planck constant has formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.
The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we use excited harmonic oscillators to directly test this quantum feature in SED. We use two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerg…
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 predic…
The wave-particle duality is one of the most mysterious phenomena of the quantum theory, in this paper first it's studied the rise of the wave properties of matter from the theory of stochastic electrodynamics (SED), in which de Broglie's idea of a guiding wave that follows the particle and determine its trajectory is taken back. In the frame of the theory (SED) this wave is of electromagnetic character and is a traveling wave that propagates within the zero point field (ZPF) which according the SED is a classic electromagnetic field that permeates all universe. The wave rise from the interact…
The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to yield agreement with the probability density distribution of Schroedinger's wave equation for the ground state of hydrogen. These results, obtained without any fitting parameters, again raise the possibility that the main tenets of stochastic electrodynamics (SED) are correct, thereby potentially providing a more fundamental basis of quantum mechanics. The present methods should help propel yet deeper investigations into SE…
Intracavity and external third order correlations in the damped nondegenerate parametric oscillator are calculated for quantum mechanics and stochastic electrodynamics (SED), a semiclassical theory. The two theories yield greatly different results, with the correlations of quantum mechanics being cubic in the system's nonlinear coupling constant and those of SED being linear in the same constant. In particular, differences between the two theories are present in at least a mesoscopic regime. They also exist when realistic damping is included. Such differences illustrate distinctions between qu…
In a recent paper [arXiv:1502.06856] the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approx…
de la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Peña-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuc…
During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (SED) with a view to establishing it as the foundation for quantum mechanics. The theory had several important successes, but failed when applied to the study of particles subject to nonlinear forces. An analysis of the failure showed that its reasons are not to be ascribed to the principles of SED, but to the methods used to construct the theory, particularly the use of a Fokker-Planck approximation and perturbation theory. A new, non perturbative approach has been develop…
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar ω$ in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham -- Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency compone…
The many experimental puzzles of solid hydrogen, that seem to defy the generally accepted view of condensed matter, are shown to be a rather straightforward consequence of a new approach to condensed matter physics, that takes into account the coherent electrodynamic processes, predicted by Quantum ElectroDynamics (QED) that have been so far overlooked. As a consequence, a revision of the present view, based on electrostatic forces only, is called for.
The idea about a quantum nature of Planck's blackbody radiation law is deeply rooted in minds of most physicists. Einstein's work, in which the coefficients of spontaneous and induced emission were introduced, has always been regarded as a proof that quantum energy discreteness of an atom plays a crucial role in the derivation of this law. In our paper we avoid this standpoint. It may be shown that the de Broglie wave assigned to every material particle is a result of interaction of the particle with zero-point vibrations of electromagnetic ground field. The energetic spectrum of a harmonic os…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field, an "electron wave", which is held in a limited region of space by the electrostatic field of the proton. It is shown that quantum mechanics must be considered to be not a theory of particles but a classical field theory in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in interpreting the results of the theory. In …
We numerically solve the functional differential equations (FDE's) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard-Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODE's). The ODE formulation is mathematically suspect since FDE's and ODE's are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for…
The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed). Important commonalities and complementarities between the two theories are identified, notwithstanding their dissimilar origins and approaches. Further, the dynamical equation of sqm is completed with the radiation terms that are an integral element in sed. The central problem of the transition to the quantum dynamics is addressed, pointing to the key role of diffu…
Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE) with reduced mass as the substitution of original electron mass is stressed. The theoretical basis of RDE lies on two symmetries, the invariance under the space-time inversion and that under the pure space inversion. Based on RDE and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bo…
We investigate the possibility of detecting the Podolsky generalized electrodynamics constant $a$. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of $a$. In order to set up bounds for $a$ we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom req…
The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born-Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born-Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well below the original value proposed by Born. This work exten…
In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into $π$, $η$ mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.
On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $α(Zα)^5$ to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.
The energy interval $ (3S-1S) $ in muonic hydrogen is calculated on the basis of quasipotential approach in quantum electrodynamics. We take into account different corrections of orders $α^3÷α^6 $, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections including the above. Nuclear structure effects are expressed in terms of the charge radius of the proton in the case of one-photon interaction and the proton electromagnetic form factors in the case of two-photon exchange interaction. The value of the energy…
A theory determining the electric and magnetic properties of vortex states in Bose-Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system which we derive correct to the first order in the atomic centre of mass velocity. For the first time using centre of mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov-Casher and the Roentgen interaction terms. The constitu…
The Lamb Shift (LS) of Hydrogenlike atom is evaluated by a simple method of quantum electrodynamics in noncovariant form, based on the relativistic stationary Schrödinger equation. An induced term proportional to $\overrightarrow{p}^4$ in the effective Hamiltonian is emphasized. Perturbative calculation of second order leads to the LS of $ 1S_{1/2}$ state and that of $2S_{1/2}-2P_{1/2}$ states in H atom with the high accuracy within 0.1%
We investigate the interaction of metastable 2S hydrogen atoms with a perfectly conducting wall, including parity-breaking S-P mixing terms (with full account of retardation). The neighboring 2P_1/2 and 2P_3/2 levels are found to have a profound effect on the transition from the short-range, nonrelativistic regime, to the retarded form of the Casimir-Polder interaction. The corresponding P state admixtures to the metastable 2S state are calculated. We find the long-range asymptotics of the retarded Casimir-Polder potentials and mixing amplitudes, for general excited states, including a fully q…
A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, …
The Schrödinger spectrum of a hydrogen atom, modelled as a two-body system consisting of a point electron and a point proton, interacting with a modification of Coulomb's law proposed, in the 1940s, by Bopp, Landé--Thomas, and Podolsky (BLTP). The BLTP theory hypothesizes the existence of an electromagnetic length scale of nature --- the Bopp length $\varkappa ^{-1}$ ---, to the effect that the electrostatic pair interaction deviates significantly from Coulomb's law only for distances much shorter than $\varkappa^{-1}$. Rigorous lower and upper bounds are constructed for the Schrödinger energy…
The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but al…
We review the Lee-Friedrichs model as a model of atomic resonances in the hydrogen atom, using the dipole-moment matrix-element functions which have been exactly computed by Nussenzveig. The Hamiltonian $H$ of the model is positive and has absolutely continuous spectrum. Although the return probability amplitude $R_Ψ(t)=(Ψ,{t\exp(-iHt)Ψ)$ of the initial state $Ψ$, taken as the so-called Weisskopf-Wigner (W.W.) state, cannot be computed exactly, we show that it equals the sum of an exponentially decaying term and a universal correction $O(β^{2}\frac{1}{t})$ for large positive times $t$ and smal…
The motion of a multi-electronic atom in an external electro-magnetic field is reconsidered. We prove that according to classical mechanics and electrodynamics, the assumption that the interaction with the magnetic field is described by means of a potential energy is no valid, and the trajectory of the center of mass can be deflected by a magnetic field, even if the internal angular momentum is zero. The characteristic equation of the corresponding hamiltonian is not separable in three degrees of freedom for the hydrogen atom.
