Non-Linear Or Non-Introspective

The measurement conundrum seems to have plagued quantum mechanics for so long that impressions of an inconsistency amongst its axioms have spawned. A demonstration that such purported inconsistency is fictitious may then be in order and is presented here. An exclusion principle of sorts emerges, stating that quantum mechanics cannot be simultaneously linear and introspective (self-observing). December 1997 ♠ On leave from the Institut Rudjer Bošković, Zagreb, Croatia. Supported by the US Department of Energy grant DE-FG02-94ER-40854. 1. Axioms and Assumptions Although close to becoming a centenarian, quantum mechanics still has adolescent (although not obviously just cosmetic) problems, most notably exemplified by the conundrum known as the “quantum measurement problem”. The conundrum has been considered from very diverse points of view and phrased in many different ways, including the claim of contradiction between two of its axioms [1], hence an inherent inconsistency of quantum mechanics as a scientific theory. The purpose of this articlet is to show that this particular (apparent) contradiction stems from a slight and subtle but serious misinterpretation of the axioms — a misinterpretation which however appears to be too well hidden and all too frequent to be easily dismissed as trivial. On exposing this misinterpretation, an avenue seems to open for a possible and perhaps interesting resolution of the “quantum measurement problem”. Details of this quest are however beyond our present scope. The routine maneuver in some relevant applications is then seen to confirm the main result, stated in the title. While this will surprise no seasoned practitioner, a clear and explicit statement is to the best of knowledge of the present author nowhere to be found in print, and may therefore turn out to be welcome. —◦— Over the years, one collection of axioms 1) has become more frequently quoted than any other. For the sake of completeness, they are [2] (with slight adaptation): 1. At any given time, t, the state of a physical system is defined by specifying a statefunction (ket), |ψ〉, belonging to the state set E . 2. Every quantity A which can be measured (at least in principle) is ascribed an operator A, acting in E ; such quantities are called observables. 3. Only the eigenvalues of the operator A are possible results of a single measurement of the corresponding observable A. 4. When the observable A is measured on a system in the state |ψ〉, the probability P(an) of obtaining the non-degenerate 2) eigenvalue an of the corresponding operator A is P(an) = ∣