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arXiv:quant-ph/9907028 · Fortschritte der Physik

Testing the Symmetrization Postulate of Quantum Mechanics and the Spin-Statistics Connection

Guglielmo Maria Tino

Published May 1, 2000• 11 citations
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Abstract

Recent experimental tests of the symmetrization postulate of quantum mechanics are discussed. It is shown that in a strict sense these experiments cannot test the validity of the symmetrization postulate, but in most cases do test the spin-statistics connection. An experiment is proposed that would allow to search for possible violations of the symmetrization postulate.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<537::aid-prop537>3.0.co;2-c

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Recent experimental tests of the symmetrization postulate of quantum mechanics are discussed. It is shown that in a strict sense these experiments cannot test the validity of the symmetrization postulate, but in most cases do test the spin-statistics connection. An experiment is proposed that would allow to search for possible violations of the symmetrization postulate.
We propose an experiment to look for possible small violations of the symmetrization postulate of quantum mechanics, in systems composed of three identical particles. Such violations could be detected by investigating the population of particular rotovibrational states of symmetrical molecules containing three identical nuclei. We discuss the symmetry properties of such states, and the implications of the symmetrization postulate and the spin statistics connection. A high-sensitivity spectroscopic investigation of simple molecules such as SO3,{\mathrm{SO}}_{3},SO3​, BH3,{\mathrm{BH}}_{3},BH3​, and NH3{\mathrm{NH}}_{3}NH3​ could lead, to our knowledge, to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.
A review is given of experiments that have been used to infer an upper bound on the degree (β2) to which the symmetrization postulate might be violated in nature. A proposed grouping of the experiments into seven different categories is put forth, based on different conceptual difficulties associated with interpreting them. Some comments are made about the strengths and weaknesses of representative experiments from several of the categories. It is suggested that there may be a considerable body of existing experimental data that could be analyzed to infer additional limits on SP-violation; as an example of this I consider the suppression of molecular recombination in spin-polarized atomic hydrogen by strong magnetic fields. While this article is limited to experiments involving fermions, an extensive bibliography on both theory and experiments related to the spin-statistics connection in general is referred to.
We investigated the spectrum of the 16O2{}^{16}{\mathrm{O}}_{2}16O2​ molecule by high-sensitivity laser spectroscopy and searched for transitions involving states which are antisymmetric under the exchange of the nuclei. These states are forbidden by the symmetrization postulate of quantum mechanics. This is the first reported experiment to test the symmetrization postulate for integer-spin particles to high precision. Our data set an upper limit of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ to a possible violation of this postulate.
An accurate test of the symmetrization postulate of quantum mechanics has been performed on the spin-0 16O{}^{16}\mathrm{O}16O nuclei, by looking for transitions in the CO2{\mathrm{CO}}_{2}CO2​ spectra involving states which are antisymmetric in the exchange of the nuclei. Using high-sensitivity laser spectroscopy, a bound of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ has been set to a possible violation of such postulate, with an improvement of more than 2 orders of magnitude with respect to the previous limit.