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. (shrink)

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be (...) adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a ‘delay’ torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics. (shrink)

Some postulates are introduced to go from the classical Hamilton-Jacobi theory to the quantum one. We develop two approaches in order to calculate propagators, establishing the connection between them and showing the equivalence of this picture with more known ones such as the Schrödinger's and the Feynman's formalisms. Applications of the above-mentioned approaches to both the standard case of the harmonic oscillator and to the harmonic oscillator with time-dependent parameters are made.