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arXiv:2210.16388

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

Ana Marı́a Cetto, Luis de la Peña

Published Oct 28, 2022• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2210.16388

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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.
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 canonical variables of the particle into quantum operators satisfying the basic commutator x^,p^=iℏ, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators a^†,a^, satisfying a^,a^†=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.
A new way of arriving at the quantum formalism is presented, based on the recognition of the reality of the random zero-point radiation field (ZPF). The quantization of both matter and radiation field is shown to emerge as a result of the permanent interaction of matter with the ZPF. Quantum mechanics (QM) is obtained both in its Schrödinger and its Heisenberg version, under certain well-defined conditions and approximations. The theory provides for an explanation of the origin of entanglement. Further, the same physical elements and hypotheses allow us to cross the doorway and go beyond QM, to the realm of (nonrelativistic) quantum electrodynamics (QED).
Quantization is derived as an emergent phenomenon, resulting from the permanent interaction between matter and radiation field. The starting point for the derivation is the existence of the (continuous) random zero-point electromagnetic radiation field (zpf) of mean energy ℏω/2 per normal mode. A thermodynamic and statistical analysis leads unequivocally (and without quantum assumptions) to the Planck distribution law for the complete field in equilibrium. The problem of the quantization of matter is then approached from the same perspective: A detailed study of the dynamics of a particle embedded in the zpf shows that when the entire system eventually reaches a situation of energy balance thanks to the combined effect of diffusion and dissipation, the particle has acquired its characteristic quantum properties. To obtain the quantum-mechanical description it has been necessary to do a partial averaging and take the radiationless approximation. Consideration of the neglected radiative terms allows to establish contact with nonrelativistic quantum electrodynamics and derive the correct formulas for the first-order radiative corrections. Quantum mechanics emerges therefore as a partial, approximate and time-asymptotic description of a phenomenon that in its original (pre-quantum) description is entirely local and causal.
Several authors have used the Heisenberg picture to show that the atomic transitions, the stability of the ground state and the position-momentum commutation relation [x,p]=ih, can only be explained by introducing radiation reaction and vacuum electromagnetic fluctuation forces. Here we consider the simple case of a nonrelativistic charged harmonic oscillator, in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrodinger picture. We consider the effects of both classical zero-point and thermal electromagnetic vacuum fields. We show that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the introduction of the zero-point electromagnetic fields in the vector potential A_x(t) used in the Schrodinger equation, generates ``double counting'', as was shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We explain, in details, how to avoid the ``double counting'' by introducing only the radiation reaction and the thermal electromagnetic fields into the Schrodinger equation.
Introduction . The purpose of this chapter is to present the quantum theory of the electromagnetic field in the absence of charges and currents. Thus the classical field discussed in the previous chapter is subjected to canonical quantization in Section 2.1, where creation and annihilation operators for plane-wave and spherical wave modes, as well as their commutation relations, are derived along with various field-field commutators related to field propagators. In the next section we introduce the concept of the photon as an elementary excitation of the electromagnetic field. The attention is focused on the ground state of the quantized electromagnetic field in the absence of sources, which is the photon vacuum. The amplitude fluctuations, or zero-point fluctuations of this vacuum, are evaluated. Excited states of the field are examined in the next sections. In particular, Section 2.3 is concerned with number states and coherent states, the latter being obtained by a Glauber transformation of the vacuum, and with their statistical properties. Squeezed states of the field are introduced in Section 2.4 by a unitary transformation leading from the normal to the squeezed vacuum, whose statistical properties are compared with those of a coherent state. Section 2.5 is devoted to a brief discussion of thermal states. The final section of this chapter is dedicated to a discussion of the nonlocalizability of the photon.
Abstract We show that the electromagnetic radiation field, conventionally introduced as a perturbation in quantum mechanics, is actually at the basis of the operator formalism. We first analyze the linear resonant response of the (continuous) variables x(t), p(t) of a harmonic oscillator to the full radiation field, i.e. the zero-point field plus an applied field playing the role of the driving force, and then extend the analysis to the response of a charged particle bound by a non-linear force, typically an atomic electron. This leads to the establishment of a one-to-one correspondence between the response functions and the respective quantum operators, and to the identification of the quantum commutator with the Poisson bracket of the response functions with respect to the normalized variables of the driving field. To complete the quantum description, a similar procedure is used to obtain the field operators as the response functions to the same normalized variables. The results allow us to draw important conclusions about the physical content of the quantum formalism, in particular about the meaning of the quantum expectation values and the coarse-grained nature of the quantum-mechanical description.