arXiv subjects

Ana María Cetto

Publications and source records attributed to Ana María Cetto.

14 recordsLinked to original sources

arXiv2025

Signature of matter-field coupling in quantum-mechanical statistics

The connection between the intrinsic angular momentum (spin) of particles and the 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. 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.

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arXiv2025

Origin of the quantum operator formalism and its connection with linear response theory

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.

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arXiv2022

The electromagnetic vacuum field as an essential ingredient of the quantum-mechanical ontology

Abstract This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the particle canonical variables into quantum operators satisfying the basic commutator \left[\hat{x},\hat{p}\right]=i\hbar, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators \hat{a}^{\dagger},\hat{a}, satisfying \left[\hat{a},\hat{a}^{\dagger}\right]=1. This allows for an explanation of quantum features such as quantum fluctuations, stationary states and transitions, and establishes a natural contact with (nonrelativistic) quantum electrodynamics.

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arXiv2022

Completing the quantum ontology with the electromagnetic zero-point field

This text begins with a series of critical considerations on the initial interpretation of quantum phenomena observed in atomic systems. The bewildering explanations advanced during the construction of quantum mechanics are shown to have distanced the new theory from the rest of scientific knowledge, by introducing indeterminism, acausality, nonlocality, and even subjectivism as part of its interpretative framework. The conclusion drawn from this unsatisfactory interpretative landscape is that quantum mechanics lacks a key ontological ingredient. Arguments are given in favour of the random zero-point radiation field (ZPF) as the element needed to complete the quantum ontology. The (wave-mediated) quantum stochastic process is shown to be essentially different from Brownian motion, and more amenable to an analogy with the hydrodynamic case. The new perspective provided by the introduction of the ZPF is used to explain some salient features of quantum systems, such as the stationary atomic states and the transitions between them, and the apparent nonlocality expressed in the entangled states. Notably, the permanent presence of the field drastically affects the dynamics of the (otherwise classical) particle, which eventually falls under the control of the field. This qualitative change is reflected in the transition from the initial classical description in space-time, to the final quantum one in the Hilbert space. The clarification of the mechanism of quantization leads us to consider the possibility that a similar phenomenon occurs in other physical systems of corpuscles subjected to an oscillating background, of which the walking-droplet system is a paradigmatic example.

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arXiv2022

Electron spin correlations: a geometric representation

An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin correlation are then derived on the basis of a probability distribution function and its associated geometric representation, both for a pair of projections of a single-particle spin and for the bipartite system in singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical image of the electron spin, as discussed at the end of the paper.

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arXiv2022

Geometric model for the electron spin correlation

The quantum formula for the spin correlation of the bipartite singlet spin state, $C_{Q}(\boldsymbol{a},\boldsymbol{b})$, is derived on the basis of a probability distribution $ρ(ϕ)$ that is generic, i. e., independent of $(\boldsymbol{a},\boldsymbol{b})$. In line with a previous result obtained within the framework of the quantum formalism, the probability space is partitioned according to the sign of the product $A=αβ$ of the individual spin projections $α$ and $β$ onto $\boldsymbol{a}$ and $\boldsymbol{b}$. A specific partitioning and a corresponding set of realizations {$ ϕ$} are associated with every measurement setting $(\boldsymbol{a},\boldsymbol{b})$; this precludes the transfer of $α$ or $β$ from $C_{Q}(\boldsymbol{a},\boldsymbol{b})$ to $C_{Q}(\boldsymbol{a},\boldsymbol{b'})$, for $\boldsymbol{b'}\neq\boldsymbol{b}.$ A geometric model that reproduces the spin correlation serves to validate our approach, giving a concrete meaning to the quantum result in terms of a (local random variable) probability distribution.

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arXiv2022

Role of the electromagnetic vacuum in the transition from classical to quantum mechanics

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 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.

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arXiv2021

Solution of quantum eigenvalue problems by means of algebraic consistency conditions

We present a simple algebraic procedure that can be applied to solve a range of quantum eigenvalue problems without the need to know the solution of the Schrödinger equation. The procedure, presented with a pedagogical purpose, is based on algebraic consistency conditions that must be satisfied by the eigenvalues of a couple of operators proper of the problem. These operators can be either bilinear forms of the raising and lowering operators appropriate to the problem, or else auxiliary operators constructed by resorting to the factorization of the Hamiltonian. Different examples of important quantum-mechanical textbook problems are worked out to exhibit the clarity and simplicity of the algebraic procedure for determining the spectrum of eigenvalues without knowing the eigenfunctions. For this reason the material presented may be particularly useful for undergraduate students or young physicists.

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arXiv2020

On the physical origin of the quantum operator formalism

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 field modes. A proper Hamiltonian analysis of this response allows us to unequivocally trace the origin of the basic quantum commutator, 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.

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arXiv2020

How fast is a quantum jump?

A proposal is put forward for an estimate of the duration of a transition between atomic states. The proposal rests on the consideration that a resonance of the atomic electron with modes of the zero-point radiation field of Compton's frequency is at the core of the phenomenon. The theoretical result, given essentially by the expression (αω_{C})^{-1}, where αis the fine structure constant and ω_{C} the Compton angular frequency for the electron, lies well within the range of the recently experimentally estimated values of the order of attoseconds (10^{-18} s).

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arXiv2020

Connecting two stochastic theories that lead to quantum mechanics

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.

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arXiv2019

On the spin projection operator and the probabilistic meaning of the bipartite correlation function

Spin is a fundamental and distinctive property of the electron, having far-reaching consequences in wide areas of physics. Yet, further to its association with an angular momentum, the physics underpinning its formal treatment remains obscure. In this work we propose to advance in disclosing the meaning behind the formalism, by first recalling some basic facts about the one-particle spin operator. Consistently informed by and in line with the quantum formalism, we then proceed to analyse in detail the spin projection operator correlation function $C_Q(\boldsymbol{a}, \boldsymbol{b}) = \langle(\hatσ\cdot\boldsymbol{a})(\hatσ\cdot\boldsymbol{b})\rangle$ for the bipartite singlet state, and show it to be amenable to an unequivocal probabilistic reading. In particular, the calculation of $C_Q(\boldsymbol{a}, \boldsymbol{b})$ entails a partitioning of the probability space, which is dependent on the directions $(\boldsymbol{a}, \boldsymbol{b})$. The derivation of the CHSH- or other Bell-type inequalities, on the other hand, does not consider such partitioning. This observation puts into question the applicability of Bell-type inequalities to the bipartite singlet spin state.

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arXiv2018

Proposed physical explanation for the electron spin and related antisymmetry

We offer a possible physical explanation for the origin of the electron spin and the related antisymmetry of the wave function for a two-electron system, in the framework of nonrelativistic quantum mechanics as provided by linear stochastic electrodynamics. A consideration of the separate coupling of the electron to circularly polarized modes of the random electromagnetic vacuum field, allows to disclose the spin angular momentum and the associated magnetic moment with a $g$-factor 2, and to establish the connection with the usual operator formalism. The spin operator turns out to be the generator of internal rotations, in the corresponding coordinate representation. In a bipartite system, the distinction between exchange of particle coordinates (which include the internal rotation angle) and exchange of states becomes crucial. Following the analysis of the respective symmetry properties, the electrons are shown to couple in antiphase to the same vacuum field modes. This finding, encoded in the antisymmetry of the wave function, provides a physical rationale for the Pauli principle. The extension of our results to a multipartite system is briefly discussed.

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arXiv2013

Atomic radiative corrections without QED: role of the zero-point field

We derive the atomic radiative corrections predicted by QED using an alternative approach that offers the advantage of physical clarity and transparency. The element that gives rise to these corrections is the fluctuating zero-point radiation field (ZPF) of average energy (hbar ω)/2 per mode, which - in contrast with QED - is taken here as a primordial real entity in permanent interaction with matter and responsible for its quantization. After briefly recalling how quantum mechanics itself emerges as a result of the balance between the ZPF and radiation reaction, the most important higher-order effects of the radiative terms on the atom are studied. The nonrelativistic QED formulas for the lifetimes and the Lamb shift, as well as the corrections to the latter due to external factors that modify the vacuum field, are thus obtained in a self-consistent approach and without the need to resort to second quantization to the present order of approximation.

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