Abstract Linear response theory is concerned with the way in which a physical system reacts to a small change in the applied forces. Here we show that quantum mechanics in the Heisenberg representation can be understood as a linear response theory. To this effect, we first address the question of the physical origin of the quantum operator formalism by considering the interaction of a bound electron with the radiation field, including the zero-point component, following the approach of stochastic electrodynamics. Once the electron has reached a stationary state, it responds linearly and resonantly to a set of modes of the driving radiation field. Such a response can lead the system to a new stationary state. Identifying a one-to-one relationship between the response variables and the corresponding operators results in the (x,p) commutator as the Poisson bracket of these variables with respect to the driving field amplitudes. To account for the order of the response variables, which is reflected in the non-commutativity of the operators, we introduce the concept of ordered covariance. The results obtained allow to establish a natural contact with linear response theory at the fundamental quantum level.

The connection between the intrinsic angular momentum (spin) of particles and quantum statistics is established by considering the response of identical particles to a common background radiation field. For this purpose, the Hamiltonian analysis previously performed in stochastic electrodynamics to derive the quantum description of a one-particle system is extended to a system of two identical bound particles subject to the same field. Depending on the relative phase of the response of the particles to a common field mode, two types of particles are distinguished by their symmetry or antisymmetry with respect to particle exchange. While any number of identical particles responding in phase can occupy the same energy state, there can only be two particles responding in antiphase. The calculation of bipartite correlations between the response functions reveals maximum entanglement as a consequence of the parallel response of the particles to the common field. The introduction of an internal rotation parameter leads to a direct link between spin and statistics and to a physical rationale for the Pauli exclusion principle.

Prior studies have shown that energy gains can result from the application of inductively generated high voltage pulses to the cathode of both Lead-Acid (Pb-A) and Lithium Iron Phosphate (LFP) batteries using specific operational parameters, including pulse repetition rate and peak pulse voltage. It has also been shown that internal enthalpy cannot be the cause of the energy gains due to a lack of correlation between measured charge capacities and those predicted from a thermodynamic analysis of the electrochemical changes occurring when measured energy releases occur, together with battery behaviour over long-term pulse delivery. The binary option of the source of energy gains being either inside or outside of the battery carries with it various implications for both the energetics of pulse induced responses of the electrochemistry and, perhaps more importantly, the inclusion of the local environment of the battery as part of an open and interactive system. With the latter having been demonstrated, the question remains as to what mechanisms, processes and energetic pathways might be involved that can result in a coefficient of performance >1 and how any that are proposed relate to currently accepted electrodynamic and field theories, classical and quantum. To this end, classical electrodynamic (CED) theory is compared with extended electrodynamic theory (EED) which is a logical and proven derivative based on decades of work by relevant parties. This work has revealed the presence of longitudinal and scalar field components that can contribute to inductive pulse charging (IPC) effects. Evidence for EED is given, along with various applications, to illustrate its potential role in signal detection, information and power transmission. Furthermore, experimental work on the extraction of energy from the quantum vacuum is considered in the context of stochastic electrodynamics (SED), which provides a bridge between classical and quantum descriptions of Nature. From these frameworks, various mechanisms are proposed that can explain the evidence obtained from IPC and with a view to adding further weight to these extended electrodynamic theories.

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.

Cosmopsychism is a novel paradigm that has the potential to respond to the hard problem of consciousness. It is based on the theoretical framework of stochastic electrodynamics. Considering both consciousness and matter as the primary reality, cosmopsychism describes the dynamic interaction of the brain with the ubiquitous field of consciousness (UFC), resulting in a number of information states. The UFC is conceived to exhibit twofold properties— extrinsic and intrinsic. The extrinsic property has the characteristics of the field of physics, whereas the intrinsic property is hard to decipher but is interpreted in terms of the characteristics of a color palate representing different shades of consciousness. Scientific analysis reveals that the concept of UFC, as theorized in cosmopsychism, resonates with the philosophical ideas of the Indian knowledge system (IKS). This article attempts to integrate the paradigm of cosmopsychism with the philosophical insights of the IKS in order to develop a holistic framework that contributes substantially to the science of consciousness

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.

In the stochastic electrodynamics, various quantum effects on particles are supposed to emerge from the interactions of the particles with the fluctuating background field. We have adopted the same supposition and further supposed that the quantum potential arises from the velocity fluctuations of particles around their local averages. Based on these suppositions we have derived the expression of the quantum potential in the framework of de Broglie–Bohm theory, which is a reformulation of Schrödinger’s. Thus we are allowed to use the wave functions and Schrödinger operators explicitly so that we have been able to derive the quantum potential in simpler and more compact manner as compared with the stochastic electrodynamics’s. A new hydrodynamical version of Schrödinger equation is also presented, which has been found in the course of our study.

The Intelligent Principle of the Universe is a beginningless and endless entity considered a fundamental property of the universe. It is in the energetic intimacy of the Psychosoma, its unquestionable “morphogenetic field” that the cells are aggregated to finally model your future physical body. On the other hand, the mind, seat of Consciousness is, therefore, the non-material brain of Consciousness where all the informational content of the human being is stored, since forever. Undoubtedly, the mind is the psychophysical basis of all mind/brain/body phenomena, that is, the mind allows experiences to be created in an interactive and participatory way. The mind, then, is a subtle form of field, an information-processing agent involving the brain’s physical system. The mental domain, as well as the material, is complementary aspects of the same reality. In fact, the existence of a “body image” has been demonstrated, certainly a “biological organizer” agent, a three-dimensional image of the physical body different from the perceived body that forms the energetic anatomical structures. He is portrayed here as Psychosoma. In fact, we propose an integrative framework of Consciousness, mind and matter based on information, seen as one of the most fundamental entities in nature to describe reality. It is an integrative theoretical framework and a neurobiological model based on an informational field involving various theories such as Shannon’s information theory, quantum holographic theory, communication theory, complexity theory, quantum field theory and other information theories. In addition, we introduce concepts of stochastic electrodynamics, a theory derived from quantum field theory more suitable to explain the mechanisms by which living beings relate to nature in order to create a healthy life and a more lasting and sustainable interrelationship. This approach was described as follows: 1) Basic notions about information theories and stochastic electrodynamics; 2) Conscience: intelligent organizing principle of life; 3) Mind: non-material brain; 4) Psychosoma: organizing model of biological life; 5) Consciousness and information; 6) Action of consciousness on matter; 7) Consciousness and physical body; 8) Consciousness and neuronal connection.

I expose nonrelativistic quantum electrodynamics in the Weyl–Wigner representation. Hence, I prove that an approximation to first order in Planck constant has a 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.

Abstract In this paper, the expression of the electrostatic interaction force between two charged particles is derived in the framework of Stochastic Electrodynamics. The fundamental assumption is that the electrically charged particle can be modeled as a two-dimensional oscillator that scatters the classical zero point field background radiation. The correct expression of the electrostatic force is obtained if the natural pulsation of the oscillator is equal to the Zitterbewegung angular velocity.

Within the framework of stochastic electrodynamics we derive the noise spectrum of a laser beam reflected from a suspended mirror. The electromagnetic field follows Maxwell's equations and is described by a deterministic part that accounts for the laser field and a stochastic part that accounts for thermal and zero-point background fluctuations.Likewise, the mirror motion satisfies Newton's equation of motion and is composed of deterministic and stochastic parts, similar to a Langevin equation. We consider a photodetector that records the power of the field reflected from the mirror interfering with a frequency-shifted reference beam (heterodyne interferometry). We theoretically show that the power spectral density of the photodetector signal is composed of four parts: (i) a deterministic term with beat notes, (ii) shot noise, (iii) the actual heterodyne signal of the mirror motion and (iv) a cross term resulting from the correlation between measurement noise (shot noise) and backaction noise (radiation pressure shot noise). The latter gives rise to the Raman sideband asymmetry observed with ultracold atoms, cavity optomechanics and with levitated nanoparticles. Our classical theory fully reproduces experimental observations and agrees with the results obtained by a quantum theoretical treatment.

We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field (zpf), with the purpose of revealing the mechanism that takes it from the initially classical description to the final quantum-mechanical one. The combined effect of the zpf and the radiation reaction force results, after a characteristic time lapse, in the loss of the initial conditions and the concomitant irreversible transition of the dynamics to a stationary regime controlled by the field. In this regime, the canonical variables x, p become expressed in terms of the dipolar response functions to a set of field modes. A proper ordering of the response coefficients leads to the matrix representation of quantum mechanics, as was proposed in the early days of the theory, and to the basic commutator \(\left[ {\hat{x}},{\hat{p}}\right] =i\hbar \). Further, the connection with the corresponding Fokker–Planck equation valid in the Markov approximation, allows one to obtain the (nonrelativistic) radiative corrections of qed. These results reaffirm the essentially electrodynamic and stochastic nature of the quantum phenomenon, as proposed by stochastic electrodynamics.

Several stochastic situations in stochastic electrodynamics (SED) are analytically calculated from first principles. These situations include probability density functions, as well as correlation functions at multiple points of time and space, for the zero-point (ZP) electromagnetic fields, as well as for ZP plus Planckian (ZPP) electromagnetic fields. More lengthy analytical calculations are indicated, using similar methods, for the simple harmonic electric dipole oscillator bathed in ZP as well as ZPP electromagnetic fields. The method presented here makes an interesting contrast to Feynman’s path integral approach in quantum electrodynamics (QED). The present SED approach directly entails probabilities, while the QED approach involves summing weighted paths for the wave function.

The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection between the two theories, to exhibit the role of stochasticity and diffusion in the process leading from the originally classical+zpf regime to the quantum regime. Quantumlike phenomena present in other instances in which a mechanical system is subject to an appropriate oscillating background that introduces stochasticity, may point to a more general appearance of quantization under such circumstances.

We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously—using the tools of stochastic electrodynamics—to be central in allowing a particle subject to a conservative binding force to reach a stationary state of motion. Here we focus on the stationary states, and consider the role of the vacuum as a driving force. We observe that the particle responds resonantly to certain modes of the field. A proper Hamiltonian analysis of this response allows us to unequivocally trace the origin of the basic quantum commutator, \(\left[ x,p\right] =i\hbar \), by establishing a one-to-one correspondence between the response coefficients of x and p and the respective matrix elements. The (random) driving field variables disappear thus from the description, but their Hamiltonian properties become embodied in the operator formalism. The Heisenberg equations establish the dynamical relationship between the response functions.

The hydrogen ground state problem is a touchstone for the theory of Stochastic Electrodynamics. Recently, we have shown numerically and theoretically that the H-atom self-ionizes after a characteristic time. In another approach we reconsidered the harmonic oscillator and renormalized the stochastic force in order to suppress high-frequency tails so that all frequency integrals are dominated by the physical resonances. In the present work we consider the regularization of the noise in the hydrogen ground state problem. Several renormalization schemes are considered. Some are well behaved, while in other ones, the high frequency renormalization induces pathologies at low frequencies. In no situation we find a way to escape from the previously signaled self-ionization.

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 diffusion in the emergence of quantization.

The main goal of this article consists in addressing two fundamental issues of consciousness research and cognitive science, namely, the question of why declarative memory functions are inextricably linked with phenomenal awareness and the question of the physical basis of memory traces. The presented approach proposes that high-level cognitive processes involving consciousness employ a universal mechanism by means of which they access and modulate an omnipresent background field that is identified with the zero-point field (ZPF) specified by stochastic electrodynamics (SED), a branch of physics that deals with the universal principles underlying quantum systems. In addition to its known physical properties and memory capacities, the ZPF is hypothesized to be an immanently sentient medium. It is propounded that linking up to a particular field mode of the ZPF activates a particular phenomenal nuance, implying that the phase-locked coupling of a set of field modes, i.e., the formation of a so-called ZPF information state, constitutes an appropriate mechanism for the amalgamation of elementary shades of consciousness into a complex state of consciousness. Since quantum systems rest exactly on this mechanism, conscious memory processes in the brain are expected to differ from unconscious processes by the presence of the typical features of many-body quantum systems, particularly long-range coherence and attractor formation, which is supported by a huge body of empirical evidence. On this basis, the conceptual framework set out in this article paves the way for a new understanding of the brain as a write–read head interacting with the ZPF, leading to self-consistent interpretations of the neural correlates of memory formation and memory retrieval and explaining why these memory processes are closely intertwined with phenomenal awareness. In particular, the neural correlates suggest that the brain produces consciously perceived memory traces by writing sequences of information states into the ZPF and retrieves consciously experienced memory traces by reading sequences of information states from the ZPF. Using these theoretical foundations, altered states of consciousness and memory disorders can be traced back to impairments of the ZPF write–read mechanism. The mechanism should reveal itself through characteristic photon emissions, resulting in testable predictions.

We observe a density-dependent collective suppression of optical pumping between the hyperfine ground states in an array of submicrometer-sized clouds of cold rubidium atoms. The suppressed Raman transition rate can be explained by strong resonant dipole-dipole interactions that are enhanced by increasing atom density. The observations are consistent with stochastic electrodynamics simulations that incorporate the effects of the nonlinear population transfer via internal atomic levels embedded in a coupled-dipole model.

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.