Nonlinear dynamics and the two-slit delayed experiment J.S. Nicolis a , G. Nicolis b, * , C. Nicolis c a Department of Electrical Engineering, University of Patras, Patras 26500, Greece b Center for Nonlinear Phenomena and Complex Systems, Universit e Libre de Bruxelles, Campus Plaine, C.P. 231, Brussels 1050, Belgium c Institut Royal M et eorologique de Belgique, Avenue Circulaire, 3, Brussels 1180, Belgium Accepted 4 August 2000 Abstract The two-slit delayed experiment is re-examined from the standpoint of nonlinear dynamics in the presence of multiple attractors and fractal basin boundaries. It is suggested that the results may be interpreted as the response of the underlying system to a temporary switch of one control parameter, rather than as a retroaction between this system and the observer. Ó 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction The evolution of a quantum system during the process of measurement has a special status in physics. As a result of the interaction of the system with the measuring apparatus, or ``the environment'' (which for many purposes can be assimilated to a macroscopic system), the plurality of the possible values of an observable of interest is abolished and the system ends up in a state in which there is a well-de®ned value of this observable. It is therefore not surprising that the quantum theory of measurement is intimately related to some of the most fundamental questions pertaining to the interpretation of quantum mechanics [1,2]. One of the most famous experiments of relevance in the above context is the two-slit delayed experiment. It has been interpreted by Wheeler [2,3] as providing evidence of a puzzling ``retroaction'' between the observer and the system under investigation ± referred to by the author as the ``observer participancy'' ± thereby apparently demolishing the view that the universe holds an independent existence. In the present paper it is proposed to view the results of the two-slit delayed experiment as the response of the underlying quantum system to a change of an external control parameter. We provide a classical example of a simple nonlinear deterministic dissipative system possessing two-point attractors ± the analogs of the eigenstates of a quantum system ± in which the dynamics generated by the underlying evolution laws leads to a behavior sharing some aspects of the exotic behavior of the two-slit delayed experiment as in- terpreted by Wheeler. Speci®cally, we show that when the process of ``categorizing'' an initial condition ± the analog of the preparation of a quantum state ± to one or the other attractor is still en route we may shift before the collapse on the expected attractor takes place a control parameter during an appropriate lapse of time and then restore it to its original value, thereby making the system switch over to the other attractor. The ontological disparity between quantum and classical systems notwithstanding [4], we provide further evidence that a nonlinear deterministic system possessing two coexisting (mutually exclusive) attractors www.elsevier.nl/locate/chaos Chaos, Solitons and Fractals 12 (2001) 407±416 * Corresponding author. 0960-0779/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 0 7 7 9 ( 0 0 ) 0 0 1 9 0 - 9