MDPI - Publisher of Open Access Journals

18 pages, 323 KB

Open AccessReview

Entropy Considerations in Stochastic Electrodynamics

by Daniel C. Cole

Physics 2024, 6(4), 1222-1239; https://doi.org/10.3390/physics6040075 - 28 Oct 2024

Viewed by 2128

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, [...] Read more.

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh–Jeans radiation; and second, where only these radiation fields exist within a cavity. The emphasis here is on the first, more complicated, case, where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in classical statistical mechanics, involving probabilistic notions of phase-space occupation, the calculations to date for both particles and fields, or for fields alone, follow the caloric entropy method, where the notions of heat flow, adiabatic surfaces, and isothermal conditions are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have successfully gone. Full article

(This article belongs to the Section Statistical Physics and Nonlinear Phenomena)

16 pages, 1564 KB

Open AccessArticle

Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes

by Huber Nieto-Chaupis

Mathematics 2023, 11(21), 4528; https://doi.org/10.3390/math11214528 - 3 Nov 2023

Cited by 1 | Viewed by 1273

Abstract

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the [...] Read more.

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biology)

► Show Figures

Graphical abstract

12 pages, 538 KB

Open AccessReview

Vectorial EM Propagation Governed by the 3D Stochastic Maxwell Vector Wave Equation in Stratified Layers

by Bryce M. Barclay, Eric J. Kostelich and Alex Mahalov

Atmosphere 2023, 14(9), 1451; https://doi.org/10.3390/atmos14091451 - 18 Sep 2023

Cited by 2 | Viewed by 1792

Abstract

The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous media are important problems in physics and engineering, and new methods need to be developed to incorporate novel vector sensor technology. Vectorial phenomena of EM waves in stratified atmospheric layers can be [...] Read more.

The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous media are important problems in physics and engineering, and new methods need to be developed to incorporate novel vector sensor technology. Vectorial phenomena of EM waves in stratified atmospheric layers can be incorporated into governing equations by retaining the gradient of the refractive index when deriving the Maxwell Vector Wave Equation (MVWE) from Maxwell’s equations. The MVWE, as opposed to the scalar wave, Helmholtz, and paraxial equations, couples the EM field components in inhomogeneous media and thus captures important physics phenomena such as depolarization. Here, recent developments are reviewed on using sensor time series data to reconstruct electromagnetic waves that propagate through stratified media. In modern applications, often many sensors can be deployed simultaneously to observe electromagnetic waves. These networks of sensors can be used to improve the quality of the reconstructed EM wave fields and cross-validate the observed sensor time series. Lastly, the effects of noisy current densities on sensor time series are considered. Generally, as the sensor observes for longer periods of time, the variance of estimates of the wave field obtained from sensor time series data increases. As a result, longer sensor observation times do not always result in better estimates of the EM wave fields, and an optimal observation time can be obtained. Full article

(This article belongs to the Special Issue Turbulence from Earth to Planets, Stars and Galaxies—Commemorative Issue Dedicated to the Memory of Jackson Rea Herring)

► Show Figures

Figure 1

18 pages, 358 KB

Open AccessArticle

Two New Methods in Stochastic Electrodynamics for Analyzing the Simple Harmonic Oscillator and Possible Extension to Hydrogen

by Daniel C. Cole

Physics 2023, 5(1), 229-246; https://doi.org/10.3390/physics5010018 - 21 Feb 2023

Cited by 1 | Viewed by 2003

Abstract

The position probability density function is calculated for a classical electric dipole harmonic oscillator bathed in zero-point plus Planckian electromagnetic fields, as considered in the physical theory of stochastic electrodynamics (SED). The calculations are carried out via two new methods. They start from [...] Read more.

The position probability density function is calculated for a classical electric dipole harmonic oscillator bathed in zero-point plus Planckian electromagnetic fields, as considered in the physical theory of stochastic electrodynamics (SED). The calculations are carried out via two new methods. They start from a general probability density expression involving the formal integration over all probabilistic values of the Fourier coefficients describing the stochastic radiation fields. The first approach explicitly carries out all these integrations; the second approach shows that this general probability density expression satisfies a partial differential equation that is readily solved. After carrying out these two fairly long analyses and contrasting them, some examples are provided for extending this approach to quantities other than position, such as the joint probability density distribution for positions at different times, and for position and momentum. This article concludes by discussing the application of this general probability density expression to a system of great interest in SED, namely, the classical model of hydrogen. Full article

(This article belongs to the Special Issue Vacuum Fluctuations)

22 pages, 454 KB

Open AccessArticle

From Stochastic Optics to the Wigner Formalism: The Role of the Vacuum Field in Optical Quantum Communication Experiments

by Alberto Casado, Santiago Guerra and José Plácido

Atoms 2019, 7(3), 76; https://doi.org/10.3390/atoms7030076 - 7 Aug 2019

Cited by 6 | Viewed by 3489

Abstract

The Wigner formalism in the Heisenberg picture constitutes a bridge that connects Quantum Optics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelike aspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection [...] Read more.

The Wigner formalism in the Heisenberg picture constitutes a bridge that connects Quantum Optics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelike aspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection is a common denominator in both theories. In this paper, after summarising the basic rules of the Wigner approach and its application to parametric down-conversion, some new results are presented that delve into the physical meaning of the zeropoint field in optical quantum communication. Specifically, the relationship between Bell-state distinguishability and the number of sets of zeropoint modes that take part in the experiment is analysed in terms of the coupling between the phases of the different fields involved and the subtraction of the zeropoint intensity at the detectors. Additionally, the connection between the compatibility theorem in quantum cryptography and zeropoint field is stressed. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

► Show Figures

Figure 1

10 pages, 276 KB

Open AccessArticle

Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator

by Theodorus Maria Nieuwenhuizen

Atoms 2019, 7(2), 59; https://doi.org/10.3390/atoms7020059 - 10 Jun 2019

Cited by 5 | Viewed by 3216

Abstract

In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated [...] Read more.

In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated by resonance effects only and results are derived that stem from those in the quantum ground state. For an orbit with specific position and momentum at an initial time, the average energy and the average rate of energy change are evaluated, which stem with each other. Resonance effects are highlighted along the way. An outlook on the hydrogen ground state problem is provided. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

18 pages, 3680 KB

Open AccessArticle

Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods

by Garret Moddel and Olga Dmitriyeva

Atoms 2019, 7(2), 51; https://doi.org/10.3390/atoms7020051 - 23 May 2019

Cited by 2 | Viewed by 13803

Abstract

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, [...] Read more.

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point field, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The first two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

► Show Figures

Figure 1

14 pages, 274 KB

Open AccessArticle

Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics

by Daniel C. Cole

Atoms 2019, 7(2), 50; https://doi.org/10.3390/atoms7020050 - 21 May 2019

Cited by 4 | Viewed by 3733

Abstract

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. [...] Read more.

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. The first part of this article addresses the concern by some about the related disturbing concept of “extracting energy” from this formally, enormous source of energy. The second part of this article introduces a new method for calculating probabilities of fields in SED, which can be extended to linear oscillators in SED. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

9 pages, 1034 KB

Open AccessEditor’s ChoiceArticle

Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

by Wayne Cheng-Wei Huang and Herman Batelaan

Atoms 2019, 7(2), 42; https://doi.org/10.3390/atoms7020042 - 5 Apr 2019

Cited by 12 | Viewed by 4509

Abstract

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 [...] Read more.

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 used excited harmonic oscillators to directly test this quantum feature in SED. We used 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 emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics. Full article

► Show Figures

Figure 1

12 pages, 696 KB

Open AccessArticle

The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

by G. Jordan Maclay

Atoms 2019, 7(2), 39; https://doi.org/10.3390/atoms7020039 - 31 Mar 2019

Cited by 2 | Viewed by 4409

Abstract

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, [...] Read more.

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. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, 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 fluctuations with the role of the real stochastic electromagnetic field. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

► Show Figures

Figure 1

10 pages, 218 KB

Open AccessReview

Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory

by Timothy H. Boyer

Atoms 2019, 7(1), 29; https://doi.org/10.3390/atoms7010029 - 1 Mar 2019

Cited by 25 | Viewed by 5608

Abstract

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck’s constant. Here, we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes [...] Read more.

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck’s constant. Here, we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes of the theory, and of its connections to quantum theory. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

16 pages, 627 KB

Open AccessArticle

A New Class of Retrocausal Models

by Ken Wharton

Entropy 2018, 20(6), 410; https://doi.org/10.3390/e20060410 - 26 May 2018

Cited by 21 | Viewed by 7715

Abstract

Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but not retro-signaling, respecting the conventional block universe viewpoint of classical spacetime. Several example models are [...] Read more.

Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but not retro-signaling, respecting the conventional block universe viewpoint of classical spacetime. Several example models are developed that resolve the most essential problems with using classical electromagnetic fields to explain single-photon phenomena. These models share some similarities with Stochastic Electrodynamics, but without the infinite background energy problem, and with a clear path to explaining entanglement phenomena. Intriguingly, the average intermediate field intensities share a surprising connection with quantum “weak values”, even in the single-photon limit. This new class of models is hoped to guide further research into spacetime-based accounts of weak values, entanglement, and other quantum phenomena. Full article

(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)

► Show Figures

Figure 1

15 pages, 291 KB

Open AccessArticle

On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics

by Theodorus M. Nieuwenhuizen

Entropy 2016, 18(4), 135; https://doi.org/10.3390/e18040135 - 13 Apr 2016

Cited by 11 | Viewed by 4918

Abstract

De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support [...] Read more.

De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although 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 nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

► Show Figures

Figure 1

24 pages, 1060 KB

Open AccessArticle

Cavity Quantum Electrodynamics of Continuously Monitored Bose-Condensed Atoms

by Mark D. Lee and Janne Ruostekoski

Atoms 2015, 3(3), 450-473; https://doi.org/10.3390/atoms3030450 - 23 Sep 2015

Cited by 4 | Viewed by 5447

Abstract

We study cavity quantum electrodynamics of Bose-condensed atoms that are subjected to continuous monitoring of the light leaking out of the cavity. Due to a given detection record of each stochastic realization, individual runs spontaneously break the symmetry of the spatial profile of [...] Read more.

We study cavity quantum electrodynamics of Bose-condensed atoms that are subjected to continuous monitoring of the light leaking out of the cavity. Due to a given detection record of each stochastic realization, individual runs spontaneously break the symmetry of the spatial profile of the atom cloud and this symmetry can be restored by considering ensemble averages over many realizations. We show that the cavity optomechanical excitations of the condensate can be engineered to target specific collective modes. This is achieved by exploiting the spatial structure and symmetries of the collective modes and light fields. The cavity fields can be utilized both for strong driving of the collective modes and for their measurement. In the weak excitation limit the condensate–cavity system may be employed as a sensitive phonon detector which operates by counting photons outside the cavity that have been selectively scattered by desired phonons. Full article

(This article belongs to the Special Issue Cavity Quantum Electrodynamics with Ultracold Atoms)

► Show Figures

Graphical abstract

Search Results (14)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (14)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI