A critique of the disturbance theory of indeterminacy in quantum mechanics

David Glick

Yu-Xiang Zhang, Zu-En Su, Xuanmin Zhu +2 more

The indeterminacy of quantum mechanics was originally presented by Heisenberg through the tradeoff between the measuring error of the observable A and the consequential disturbance to the value of another observable B. This tradeoff now has become a popular interpretation of the uncertainty principle. However, the historic idea has never been exactly formulated previously and is recently called into question. A theory built upon operational and state-relevant definitions of error and disturbance is called for to rigorously reexamine the relationship. Here by putting forward such natural definitions, we demonstrate both theoretically and experimentally that there is no tradeoff if the outcome of measuring B is more uncertain than that of A. Otherwise, the tradeoff will be switched on and well characterized by the Jensen-Shannon divergence. Our results reveal the hidden effect of the uncertain nature possessed by the measured state, and conclude that the state-relevant relation between error and disturbance is not almosteverywhere a tradeoff as people usually believe.

Willem M. de Muynck

xi 4.5.24.5.3The double-slit experiment The microscope 4.6 Meaning of the 'complementarity' concept 4.6.1 4.6.24.6.34.6.44.6.5 4.6.6 4.6.7 Two meanings of 'to determine' Heisenberg's disturbance theory of measurement Complementarity according to Bohr Particle-wave duality Parallel and circular complementarity Complementarity and the projection postulate Complementarity and consciousness 4.7 Critique of the complementarity principle Einstein Margenau Ballentine Recent developments Complementarity and empiricist interpretation The Einstein-Podolsky-Rosen problem 6 Individual-particle and ensemble interpretations of quantum mechanics 275 6.

William G. Pollard

A suggestion of Bohr's to the effect that numerous situations exist among the life sciences and the social sciences which exhibit characteristics of complementarity strikingly parallel to those of quantum physics is developed further in this paper. The supposition is advanced that there may exist for biological systems inherent relations of indeterminacy between sets of observable properties of such systems analogous to the Heisenberg indeterminacy relations between canonically conjugate pairs of observables in quantum mechanics. The existence of such indeterminacies would be manifested, as it is in physical systems, in disturbances, uncontrollable in principle, produced when such systems interact with instruments and apparatus used to gain information about them. The fact that radical disturbances, whether incidental or inherent, accompany the process of observation in the life sciences is, of course, quite obvious. If a well-defined portion of such disturbances should turn out to be inherent, indeterminacy and probability would be introduced into biological phenomena as basic elements. Further progress in scientific explanation and synthesis of knowledge in these fields would then require a redefinition of the state of a biological system analogous to the necessity for using quantum ψ-functions for specifying the state of a physical system with the attendant possibility of wholly new insights, such as those in physics which ultimately depend on the symmetry properties of ψ-functions. This new, and presently unknown, scheme for specifying the state of biological systems would then presumably result in the typically complementary aspects of phenomena in these fields to which Bohr has called attention. A number of familiar examples of apparently complementary phenomena among the biological and social sciences are described, and the possibility that they may arise from inherent indeterminacies basic to the systems which exhibit these phenomena is considered. It is concluded that these considerations lead to the expectation that an approach along such lines in future investigations in the life sciences holds considerable promise, and that the physics teacher is in a unique position to assist in stimulating such an approach and in pointing out by analogy the means at each stage which are likely to prove best suited for carrying it through.

Brigitte Falkenburg, Friedel Weinert