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Physica Scripta

Spectroscopic Tests of Spin-Statistics Connection and Symmetrization Postulate of Quantum Mechanics

Guglielmo Maria Tino, Guglielmo Maria Tino

Published Jan 1, 2001• 5 citations
Publisher

Abstract

Recent experiments searching for violations of the spin-statistics connection and of the symmetrization postulate of quantum mechanics are reviewed. Spectroscopic tests on O 2 and CO 2 molecules are described in detail and it is shown that these should be considered as tests of the spin-statistics connection for the spin-0 oxygen nuclei. The possibility of new experiments to test the spin-statistics connection and the symmetrization postulate is discussed.

DOI
10.1238/physica.topical.095a00062

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Recent experiments searching for violations of the spin-statistics connection and of the symmetrization postulate of quantum mechanics are reviewed. Spectroscopic tests on O 2 and CO 2 molecules are described in detail and it is shown that these should be considered as tests of the spin-statistics connection for the spin-0 oxygen nuclei. The possibility of new experiments to test the spin-statistics connection and the symmetrization postulate is discussed.
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.
The search for small violations of the validity of the symmetrization postulate and of the spin-statistics connection (SSC) has been addressed in the last four decades by experimental tests performed in different physical systems of identical fermions or bosons. In parallel and consequently, theories extending the quantum mechanics to a more general level have been proposed to explain such possible violations. In this paper, we present the most stringent test to a possible violation of the SSC under permutation of the bosonic 16O^{16}\mathrm{O}16O nuclei in the 12C16O2^{12}\mathrm{C}^{16}\mathrm{O}_{2}12C16O2​ molecule. An upper limit of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ for an SSC-anomalous CO2{\mathrm{CO}}_{2}CO2​ molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden $({00}^{0}1\ensuremath{-}{00}^{0}0) R$(25) rovibrational transition of 12C16O2^{12}\mathrm{C}^{16}\mathrm{O}_{2}12C16O2​ at a $4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ wavelength. Quantum mechanics implications of this result are discussed in the frame of the qqq-mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.
We have used diode laser absorption spectroscopy of the ``A'' band of molecular oxygen near 762 nm to provide a sensitive experimental test of the symmetrization postulate of quantum mechanics. We place an upper limit of $(0.8\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ on the probability of finding two identical 16{}^{16}16O nuclei in an antisymmetric state. This is one of the first sensitive tests of the symmetrization postulate for spin-0 particles.
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.