Self-Organization and Emergence

Heinz von Foerster 100

Organizing Institutions:

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

Herbert Schwabl, Johannes Mesa Pascasio, Siegfried Fussy, Gerhard Grössing

A classical framework to explain quantization

Austrian Institute for Nonlinear Studies

Akademiehof, Friedrichstr. 10, 1010 Vienna, Austria

We start with two classical models. Firstly, a classical, damped oscillator is assumed to be coupled to its environment's energy bath, which we choose to be that of the zero-point energy (ZPE). The stationary solution yields a distinct invariant, which can be identified as some angular momentum which we denote as h.

Secondly, we propose a three-dimensional Brownian motion of a particle, also assumed to be driven by its thermal environment. The work-energy of the particle is related to the temperature T_0 of the surrounding energy bath via a constant k.

We combine the two model systems in a way that the classical oscillator on the one hand exchanges energy with the thermal zero-point energy and, on the other hand, pumps this energy back and forth w.r.t. the Brownian particle. Under the condition that the total work-energy balance remains zero over one oscillatory cycle, the combination of the two mechanisms leads finally to the energy spectrum of the harmonic oscillator. The formula E = hbar.omega does not refer to a classical "object" oscillating with frequency omega, but rather to a process of a "fleeting constancy", i.e., a constant absorbing and emitting of heat quantities such that in sum the "total particle energy" emerges as hbar.omega.

Our model allows us to outline some features of the nature of the embedding vacuum's ZPE and its coupling to the system of interest. The thermal ZPE environment is oscillating itself and couples specifically to each immersed particle according to the particle mass m. As an outlook, diffusion processes in the ZPE medium can be used to model the behavior of quantum systems.

Herbert Schwabl was born in Vienna in 1961; Technical University (Physics) in Vienna; graduation as Ph.D. 1994. Scientific work in the fields of environmental sciences and self organization. Founding member of the Austrian Institute for Nonlinear Studies, Vienna, since 1990. Currently chairman of Padma AG in Schwerzenbach, Switzerland.