Abstract
We propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system. We call this approach hyper-dilation and cover it under the label of measurement-oriented physics (MOP) as compared with state-oriented physics (SOP). The essential difference between the two concerns the concepts of state to which they refer. MOP deals with two different concepts of state; non measured states with infinite precision and measured states with finite precision. The measurement process is expressed as a dynamically changing interface between them. SOP deals with one single concept of state and does not comprise a corresponding distinction. We show fundamental differences between MOP and SOP with respect to the noise characteristics of complex systems around critical states. MOP can give rise to exact and universal 1/f noise, while SOP shows 1/fα noise with α ≠ 1 in general. In MOP a self-similar return map can be degenerate with a Cantor set, rendering a solution for a basic measurement paradox. The significance of this degeneracy as a model for emergent properties is discussed.
Original language | English |
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Pages (from-to) | 27-54 |
Number of pages | 28 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 101 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 1997 Jan 1 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics