Purpose As any attempts at explaining quantum theory in terms of simple, local “cause‐and‐effect” models have remained unsatisfactory, approaches from the perspectives of systems theory seem called for, which is rich in a variety of more complex understandings of causality. Design/methodology/approach This paper presents one option for such approaches, which the author has introduced previously as “quantum cybernetics”: considering waves (but not “wave functions”!) and “particles” as mutually dependent system components, and thus defining “organizationally closed systems” characterized by a fundamental circular causality. Using such an approach, a new look can be achieved on both classical and quantum physics. Findings It was found that quantum theory's most fundamental equation, the Schrödinger equation, can actually be derived from classical physics, once the latter is considered anew, i.e. under said approach involving both particles and (Huygens) waves. In fact, the only difference to existing views is that Huygens waves are here considered to be real, physically effective waves in some hypothesized sub‐quantum medium, rather than mere formal tools. Originality/value What is particularly new in the present paper is that quantum systems can be described by what Heinz von Foerster has called “nontrivial machines”, whereas the corresponding classical counterparts turn out to behave as “trivial machines”. This should provide enough stimulus for discussing system theoretical issues also in the context of the foundations of quantum theory.
Despite all negative accounts in many popular and superficial discussions of quantum theory causal and realistic interpretations of the quantum me chanical formalism can be demonstrated to work perfectly well They accept nonlocality as a well established fact and mostly consider a quantum system as analyzable into a local particlelike nonlinearity of a generally nonlocal wavelike mode of some subquantum structure of the vacuum Dirac ether In this view a particle can be considered as being guided along one specific route by the generally nonlocal configurations of superimposed waves which spread along all possible paths of an experimental setup Moreover in the approach of quantum cybernetics an additional focus is on the fact that the energy and momentum of a particle also determine the wave behavior Thus waves and particles are mutually and self consistently defined and quantum cybernetics puts particular emphasis on the circular relationship mediated byplane waves between a quantum system and its macroscopically defined boundary conditions To show how firmly rooted this picture is in the orthodoxquantum theory an example is discussed here on the basis of the standard formalism that makes a systemic approach called for
Sec. I. This paper inverts certain quantum mechanical ideas by constructing a "probability of presence" from first principles. If
xi=fi(s,a1,a2) represents a 2-parameter family of curves in 3-dimensional space, the density of the functions
fi with respect to the parameters
a1a2 is defined by means of an expression for the normal cross section of a sheaf of curves. This density plays the role of a probability. Its derivative along a curve of the family is independent of the parameters
a1a2. This circumstance permits a special density to be constructed, called the "characteristic" or "smoothest" density, which is independent of the parameters and which can be found by solving a linear second-order partial differential equation. The extension to
n-dimensional space and ($n\ensuremath{-}1$) parameters is given. Sec. II. The concept of orbital density is the dynamical equivalent of the density of Sec. I. Dividing the orbital density by the velocity of the representative point gives the quantity we call kinematical probability
P, which satisfies the fundamental equation (2.8), and which has the same force as any other probability of presence. Equation (2.8) is used to derive from the Hamilton-Jacobi equation a "wave" equation for $\ensuremath{\surd}P$ for a system of
n planets moving around a sun under the condition that the space average of the mutual interactions of the planets is a minimum. This provides a new approach to planetary dynamics and yields an equation that is very much like Schroedinger's equation for the stationary states of
n particles, and has the same basic interpretation. Sec. III. A non-conservative system of
n particles is assumed to be in a state such that the action function can be written $W=\ensuremath{-}Et+R({x}_{i},t)$ in which
R still contains the time explicitly. Starting with the Hamilton-Jacobi equation, using Eq. (2.8), and imposing the condition that the space average of $\frac{\ensuremath{\partial}R}{\ensuremath{\partial}t}$ is a minimum, an equation [viz., (3.10)] is derived which differs from Schroedinger's equation for stationary states only in certain respects that cannot be regarded as fundamental. Despite this basic equivalence of Schroedinger's equation and our equation (3.10), conflicts in interpretation and formalism arise which are briefly discussed. Sec. IV. Complex
U' s are introduced into Eq. (3.10) in a simple way which fails to bridge the gap between our formalism and that of quantum mechanics. The kinematical probability defined by Eq. (3.10) is shown to have the "smoothest" property. To account physically for the stationary states an electromagnetic wave system is proposed which has the property that a particle moving in it may be in "phase-mechanical" resonance with it. Macroscopic examples of this kind of resonance are given. This concept represents an inversion of physical ideas of quantum mechanics corresponding to the mathematical inversion with which we began.
Underpinning the axiomatic formulation of quantum theory presented in this undergraduate textbook is a review of early experiments, a comparison of classical and quantal terminology, a Schroedinger-equation treatment of the one-dimensional quantum box, and a survey of relevant mathematics. Among the many concepts comprehensively discussed are: operators; state vectors and wave functions; experimental observables; classical/quantal connections; and symmetry properties. The theory is applied to a wide variety of systems including the non-relativistic H-atom, external electromagnetic fields, and spin1/2. Collisions are described using wave packets. Various time-dependent and time-independent approximations are discussed; applications include electromagnetic transition rates and corrections to the H-atom energies. The final chapter deals with identical-particle symmetries and their application to the He atom, the Periodic Table and diatomic molecules. There are also brief treatments of advanced subjects such as gauge invariance and hidden variables.
Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrodinger, the father of the wave function. Nonetheless, Schrodinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of [3]]: "That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message." Rather, it was that