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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum theory as the most robust description of reproducible experiments: application to a rigid linear rotator

Hans A. De Raedt, Mikhail I. Katsnelson, Kristel F. L. Michielsen

Published Oct 1, 2013• 10 citations
Publisher

Abstract

It is shown that the Schr¨odinger equation of a rigid linear rotator can be obtained from a straightforward application of logical inference, providing another illustration that basic equations of quantum theory follow from inductive inference, applied to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.

DOI
10.1117/12.2026998

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It is shown that the Schr¨odinger equation of a rigid linear rotator can be obtained from a straightforward application of logical inference, providing another illustration that basic equations of quantum theory follow from inductive inference, applied to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.
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It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.
We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are separated as much as possible. Application to the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments are shown to support this thesis. General principles of logical inference which have been shown to lead to the Schrödinger and Pauli equation and the probabilistic descriptions of the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments, are used to demonstrate that the condition for the separation procedure to yield the quantum theoretical description is intimately related to the assumptions that the observed events are independent and that the data generated by these experiments is robust with respect to small changes of the conditions under which the experiment is carried out.
It is shown that the quantum-theoretical descriptions of idealized Stern–Gerlach and Einstein–Podolsky–Rosen–Bohm experiments result from a logical inference treatment of robust experiments, without relying on concepts of quantum theory. For concreteness, the derivation is given for the case that the Stern–Gerlach magnet deflects the beam in three different directions, which in quantum theory corresponds to a description in terms of spin-1 particles. The logical inference description of the Einstein–Podolsky–Rosen–Bohm experiment is shown to contain the quantum theoretical description as a particular case.
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.