A classical basis for one‐dimensional Schrödinger quantum theory is constructed from simple vacuum polarization harmonic oscillators within standard stochastic theory. The model is constructed on a two‐dimensional phase configuration surface with phase velocity vectors that have a speed of light zitterbewegung behaviour character. The system supplies a natural Hermitian scalar product describing probability density which is derived from angular momentum considerations. The generality of the model which is extensive is discussed.
A classical basis for one-dimensional SchrSdinger quantum theory is constructed from simple vacuum polarization harmonic oscillators within standard stochastic theory. The model is constructed on a two-dimensional phase configuration surface with phase velocity vectors that have a speed of light zitterbewegung behaviour character. The system supplies a natural Hermitian scalar product describing probability density which is derived from angular momentum considerations. The generality of the model which is extensive is discussed.
In this chapter, which covers part of the course given at ELAF, a straight-forward procedure is presented that leads from the basic postulates of stochastic electrodynamics to the usual formalism of quantum theory. The theory thus developed is called linear stochastic electrodynamics, to underline that one of its basic features is the (asymptotic) linear response of atomic systems to the background field. The chapter starts with a brief discussion of some open questions in quantum theory and of the possibility to find an answer to them by resorting to the zeropoint radiation field as the source of the quantum behavior of matter. The basic properties of this field are discussed, and a brief enumeration is made of some of the positive results and vital shortcomings of standard stochastic electrodynamics. After identifying the source of these shortcomings in the assumption that the background field is not altered by its interaction with matter, linear stochastic electrodynamics is developed and shown to lead, under certain approximations, to a consistent picture of both matter and field quantization. In the concluding part, it is shown that also the electron spin can be considered to be generated by the interaction of the particle with the zeropoint field; in particular, the two-valuedness of the spin projection is associated with the existence of just two independent states of polarization of the field.
As part of a probabilistic reconstruction of quantum theory (QT), we show that spin is not a purely quantum mechanical phenomenon, as has long been assumed. Rather, this phenomenon occurs before the transition to QT takes place, namely in the area of the quasi-classical (here better quasi-quantum) theory. This borderland between classical physics and QT can be reached within the framework of our reconstruction by the replacement
p→M(q,t), where
p is the momentum variable of the particle and
M(q,t) is the momentum field in configuration space. The occurrence of spin, and its special value
1/2 , is a consequence of the fact that
M(q,t) must have exactly three independent components
Mk(q,t) for a single particle because of the three-dimensionality of space. In the Schrödinger equation for a "particle with spin zero", the momentum field is usually represented as a gradient of a single function
S. This implies dependencies between the components
Mk(q,t) for which no explanation exists. In reality,
M(q,t) needs to be represented by three functions, two of which are rotational degrees of freedom. The latter are responsible for the existence of spin. All massive structureless particles in nature must therefore be spin-one-half particles, simply because they have to be described by
4 real fields, one of which has the physical meaning of a probability density, while the other three are required to represent the momentum field in three-dimensional space. We derive the Pauli-Schrödinger equation, the correct value
g=2 of the gyromagnetic ratio, the classical limit of the Pauli-Schrödinger equation, and clarify some other open questions in the borderland between classical physics and QT.
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of objectively existing vacuum fluctuations whose action on massive particles is calibrated by Planck's constant and effects an additional irregular motion. We describe a one-particle system by introducing two equally large sub-ensembles for each of which one obtains an equation of motion that has the form of a Navier-Stokes- or ''anti''-Navier-Stokes-type equation, respectively. By averaging over the total ensemble one obtains a new equation of motion which can be converted into the time-dependent Schroedinger equation. The concept allows the inclusion of electromagnetic fields and can be extended to interacting N-particle systems. We analyze the problem of how an experimental setup can consistently be decomposed into the quantum system under study and the residual quantum system ''apparatus''. The irregular extra motion of the particle under study allows a decomposition of the associated ensemble into two sub-ensembles the members of which perform, respectively, a right-handed or left-handed irregular circular motion about a given axis which becomes physically relevant in the presence of a magnetic field. We demonstrate that this orientation-decomposed ''Zitterbewegung'' behaves - in accordance with Schroedinger's original idea - as a spin-type angular momentum which appears in addition to a possible orbital angular moment of the particle. We derive the non-relativistic time-dependent Pauli equation and propose a theory of the Stern-Gerlach experiment. The Dirac equation can be derived similarly.
The dissipation and decoherence (for example, the effects of noise in quantum computations), interaction with thermostat or in general with physical vacuum, measurement and many other complicated problems of open quantum systems are a consequence of interaction of quantum system with the environment. These problems are described mathematically in terms of complex probabilistic process (CPP). Particularly, treating the environment as a Markovian process we derive an Langevin-Schroedinger type stochastic differential equation (SDE) for describing the quantum system interacting with environment. For the 1D randomly quantum harmonic oscillator (QHO) model L-Sh SDE is a solution in the form of orthogonal CPP. On the basis of orthogonal CPP the stochastic density matrix (SDM) method is developed and in its framework relaxation processes in the uncountable dimension closed system of "QHO+environment" is investigated. With the help of SDM method the thermodynamical potentials, like nonequilibrium entropy and the energy of ground state are exactly constructed. The dispersion for different operators are calculated. In particular, the expression for uncertain relations depending on parameter of interaction with environment is obtained. The Weyl transformation for stochastic operators is specified. Ground state Winger function is developed in detail.