Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.     

Triply bridged thiobenzoato carbonyl manganates(I) and rhenates(I). The crystal and molecular structure of caesium tris(μ-thiobenzoatos(S))bis(tricarbonyl rhenate)

By reaction of potassium or caesium monothiobenzoate (mtb) with manganese or rhenium pentacarbonyl bromide the binuclear triply S-monothiobenzoato bridged complexes [(CO)₃M(μ-mtb)₃M(CO)₃]^- have been obtained as salts. The title compound crystallizes in the orthorhombic space group P2₁2₁2₁ with a 15.239(6), b 15.234(6), c 15.209(6) » and Z = 4. The Re atoms are octahedrally coordinated. The two octahedra share a common face. The rhenium atoms are not equivalent with respect to their bonds to the thiobenzoato ligands, leading to two sets of ReS bond lengths, 2.545(4) and 2.504(5) ».     

Carbon-13, 1H spin-spin coupling. V—π-benzenechromium tricarbonyl and the π-tropyliumchromium tricarbonyl cation

The ¹³C, ¹H spin-spin coupling constants have been determined for π-benzenechromium tricarbonyl (3) and the π-tropyliumchromium tricarbonyl cation using the ¹³C{²H}double resonance technique described in a previous paper. In addition, conventional analysis of the ¹H-coupled ¹³C NMR spectrum of 3 was carried out and the ¹H NMR spectrum of 3 partially oriented in the nematic phase was analysed. Both treatments also allowed the determination of the ¹H, ¹H coupling constants for this compound. The ⁿJ(CH) results are discussed on the basis of structural data and the theoretical results available. The complexation effects for ¹J(CH) are found to correlate with the C? H overlap population and hybridization changes, and those for ³J(CH) with the CC bond lengths and π-bond orders. The dependence of ²J(CH) on CC bond length as well as on the CCH bond angle is indicated. The liquid crystal results are compared with those of related studies.