Ana María Cetto

Stochastic theory for classical and quantum mechanical systems

We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newtons second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrödinger equation, which is derived here with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section.

Excellence or quality? Impact of the current competition regime on science and scientific publishing in Latin America and its implications for development

The current competition regime that characterizes international science is often presented as a quest for excellence. It diversely affects research in Latin America and research in the Organization for Economic Co-operation and Development (OECD) countries. This article asks how this competition regime may orient the direction of research in Latin America, and to whose advantage. It is argued that, by relating excellence to quality differently, a research policy that seeks to improve the level of science in Latin America while preserving the possibility of solving problems relevant to the region can be designed. Competition, it is also argued, certainly has its place in science, but not as a general management tool, especially if the goal is to improve overall quality of science in Latin America. Scientific competition is largely managed through journals and their reputation. Therefore, designing a science policy for Latin America (and for any ‘peripheral’ region of the world) requires paying special attention to the mechanisms underpinning the production, circulation and consumption of scientific journals. So-called ‘international’ or ‘core’ journals are of particular interest as local, national, or even regional journals must struggle to find their place in this peculiar publishing eco-system.

THE QUANTUM HARMONIC OSCILLATOR REVISITED: A NEW LOOK FROM STOCHASTIC ELECTRODYNAMICS

We apply the theory of stochastic electrodynamics to the study of the (nonrelativistic) harmonic oscillator by using the Fokker–Planck method. It is demonstrated that the equilibrium distribution in phase space is exactly equal to that given by quantum statistical mechanics, i.e., the corresponding Wigner distribution, and that analysis of this distribution by means of a decomposition in terms of canonical densities leads automatically to the usual description of quantum mechanics in terms of excited states. All fundamental equations of quantum mechanics are recovered as aprproximations to zero order in the radiation terms; the first‐order terms lead to the radiative corrections predicted by quantum electrodynamics, namely, the decay of states and the Lamb shift of the energy levels. The necessary differences between both treatments of the oscillator and their implications are briefly discussed.

Does quantum mechanics accept a stochastic support

Arguments are given in favor of a stochastic theory of quantum mechanics, clearly distinguishable from Brownian motion theory. A brief exposition of the phenomenological theory of stochastic quantum mechanics is presented, followed by a list of its main results and perspectives. A possible answer to the question about the origin of stochasticity is given in stochastic electrodynamics by assigning a real character to the vacuum radiation field. This theory is shown to reproduce important quantum mechanical results, some of which are presented explicitly to illustrate its potentialities. Finally the main problems and some perspectives of research within stochastic electrodynamics are discussed.

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigners pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.

Quantization as an emergent phenomenon due to matter-zeropoint field interaction

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 ?/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.

Quantum Theory and Linear Stochastic Electrodynamics

We discuss the main results of Linear Stochastic Electrodynamics, starting from a reformulation of its basic assumptions. This theory shares with Stochastic Electrodynamics the core assumption that quantization comes about from the permanent interaction between matter and the vacuum radiation field, but it departs from it when it comes to considering the effect that this interaction has on the statistical properties of the nearby field. In the transition to the quantum regime, correlations between field modes of well-defined characteristic frequencies arise, which coincide with the transition frequencies of quantum mechanics and are therefore directly related with the energy quantization. The Heisenberg equations of motion of (non-relativistic) quantum electrodynamics are thus obtained. After a detailed consideration of the significance of the approximations made, we present a discussion on some of the most delicate or controversial features of quantum mechanics from the perspective provided by the present theory.

Quantum phenomena and the zeropoint radiation field. II

A previous paper was devoted to the discussion of a new version of stochastic electrodynamics (SED) and to the study of the conditions under which quantum mechanics can be derived from it, in the radiationless approximation. In this paper further effects on matter due to the zeropoint field are studied, such as atomic stability, radiative transitions, the Lamb shift, etc., and are shown to be correctly described by the proposed version of SED. Also, a detailed energy-balance condition and a fluctuation-dissipation relation are established; it is shown in particular that equilibrium is attained only with a field spectrum ∼Ω3.The proposed approach is shown to suggest an understanding of quantum mechanics as a kind of limitcycle theory. Finally, a brief discussion is included about the nonchaotic behavior of the (bounded) SED system in the quantum regime, as measured by Lyapunov exponents.

A Bell inequality involving position, momentum and energy

Abstract A Bell inequality involving only variables with a classical analog is derived, and it is shown to be violated by quantum mechanics.

Emergence of quantization: the spin of the electron

In previous papers, the quantum behavior of matter has been shown to emerge as a result of its permanent interaction with the random zero-point radiation field. Fundamental results, such as the Schrodinger and the Heisenberg formalism, have been derived within this framework. Further, the theory has been shown to provide the basic QED formulas for the radiative corrections, as well as an explanation for entanglement in bipartite systems. This paper addresses the problem of spin from the same perspective. The zero-point field is shown to produce a helicoidal motion of the electron, through the torque exerted by the electric field modes of a given circular polarization, which results in an intrinsic angular momentum, of value /2. Associated with it, a magnetic moment with a (g-factor of 2 is obtained. This allows us to identify the spin of the electron as a further emergent property, generated by the action of the random zero-point field.