Why do clocks tick?

Drawing on recent developments in the matrix model approach to string theory and the causal set program for quantum gravity we address the question of the origin of time as one aspect of the phase transition from a topological quantum field theory to a quantum theory of gravity. We construct a model with two phases which can be interpreted as containing clocks which either do not tick or tick exactly once. This demonstrates that while a theory based on causal sets may appear to have inherent notions of time and causality, the existence of a phase transition means, that as Saint Augustine wrote in hisConfessions, the time, if such we may call it, when there was no time was not time at all.Received an Honorable Mention in the 1992 Gravity Research Foundation Essay Contest—Ed.     

An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method

An efficient and robust integration scheme tailored to the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method is presented. An error estimation allows the automatical adjustment of the step size and hence controls the integration error. The integration scheme decouples the MCTDH equations of motion into several disjoined subsystems, of which one determines the time evolution of the MCTDH-coefficients. While the conventional MCTDH equations are non-linear, the working equation for the MCTDH-coefficients becomes linear in the present integration scheme. To investigate the integrator’s performance it is applied to the photodissociation process of methyl iodide. The results of the novel integration scheme are in perfect agreement to those obtained by solving the MCTDH working equations conventionally. The computation time, however, is reduced by a factor of about ten when the new integration scheme is used to propagate large systems.     

Structures and magnetic properties of tetranuclear nickel(II) complexes with unusual mu3-1,1,3 azido bridges

Pyrazolate-based dinucleating ligands with thioether-containing chelate arms have been used for the synthesis of a family of novel tetranuclear nickel(II) complexes [L2Ni4(N3)3(O2CR)](ClO4)2 that incorporate three azido bridges and one carboxylate (R = Me, Ph). Molecular structures have been elucidated by X-ray crystallography in four cases, revealing Ni4 cores with a unique topology in which two of the azido ligands adopt an unusual mu3-1,1,3 bridging mode. The compounds were further characterized by mass spectrometry, IR spectroscopy, and variable-temperature magnetic susceptibility measurements. Magnetic data analyses indicate a combination of significant intramolecular ferromagnetic and antiferromagnetic exchange interactions that give rise to an overall S(T) = 0 ground state. The sign and the magnitude of the individual couplings have been rationalized in the framework of the common magnetostructural correlations for end-to-end and end-on azido linkages, suggesting that these correlations also remain valid for the respective fragments of multiply bridging mu3-1,1,3 azido ligands.     

Cu4O12-Baugruppen aus planaren CuO4-Polygonen im Barium-Vanadyl-Oxocuprat(II)-phosphat Ba(VO)Cu4(PO4)4

Cu₄O₁₂ Groups Built of Square Planar CuO₄ Polygones in the Barium Vanadyl Oxocuprate(II) Phosphate Ba(VO)Cu₄(PO₄)₄ Single crystals of Ba(VO)Cu₄(PO₄)₄ have been prepared by solid state reactions just below the melting points of the reaction mixtures of BaP₂O₆, Cu₃(PO₄)₂, CuO, V₂O₅ and V₂O₃ in evacuated closed quartz glas tubes. The compound crystallizes with tetragonal symmetry, Space group D? P42₁2, a = 9.560(2), c = 7.160(2) Å, Z = 2. Special and new features of the crystal structure are to each other isolated Cu₄O₁₂ and (VO)(PO₄)₄ groups. The crystal chemistry of the Cu₄O₁₂ groups is discussed with respect to other compounds containing out of plane connected square planar MO₄ polygones.     

Mitteilungen aus dem Institut für Radiumforschung

Zusammenfassung Es wurde mit Hilfe des schon früher beschriebenen Quarzapparates Thoriumbromid aus reinem Thoroxyd dargestellt, das nach zwei verschiedenen Methoden gereinigt war und auf Grund spektroskopischer Untersuchung als absolut rein und frei von seltenen Erden angesehen werden mu\te.Das geschmolzene Thorbromid wurde nach zwei Methoden analysiert und dabei die beiden VerhÄltnisse ThBr₄4 Ag und ThBr₄4 AgBr bestimmt.Zwei unabhÄngige Serien von 12, respektive 15 Analysen gaben die folgenden Resultate:Serie I. 54·45867g Thorbromid verbrauchten 42·58666g Silber und gaben 74·13448g Silberbromid, entsprechend einem Atomgewicht des Thoriums Th=232·15±0·016.Serie II. 74·30630g Thorbromid verbrauchten 58·11096g Silber und gaben 101·15848g Silberbromid, woraus sich das Atomgewicht Th=232·12±0·014 berechnet.Als Mittel dieser beiden Werte ergibt sich Th=232·135.Da aber die Analysenserie aus den oben besprochenen, uns triftig erscheinenden Gründen als die zuverlÄssigere angesehen werden mu\, glauben wir, da\ der aus ihr resultierende WertTh=232·12 als das derzeit wahrscheinlichste Atomgewicht des Thoriums anzusehen ist, wenn Ag=107·880 angenommen wird. Aus dem in 27 Bestimmungen gefundenen VerhÄltnis von angewandtem Silber zu gefundenem Silberbromid, AgAgBr= 0·574453, ergibt sich dann das Atomgewicht des Broms zu Br=79·916 in vollster übereinstimmung mit der von Baxter seinerzeit gefundenen Zahl.     

Synthese und Kristallstruktur von Hydronium-tris-ethylendiamin-cobalt(rhodium)-μ-trichloro-nonachlorotrirhenat(II)-chlorid,H3O[MEn3][Re3Cl12]Cl (M=Co,Rh)

Synthesis and Crystal Structure of Hydronium-tris-ethylenediamine-cobalt(rhodium)-μ-trichloro-nonachlorotrirhenate(III)-chloride, H₃O[MEn₃][Re₃Cl₁₂]Cl (M=Co, Rh) The chlorides H₃O[MEn₃][Re₃Cl₁₂]CI (M = Co, 1 ; Rh, 2 ) crystallize from hydrochloric acid solutions of ReCl₃ and MEn₃ · 3H₂O as deep red hexagonal columns. They are isotypic and crystallize with the hexagonal system (P6 , Z = 1; 1: a = 1010.87(3); c = 794.30(4) pm, R = 0.023, R_w = 0.016; 2: a = 1018.58(3); c = 794.74(4) pm, R = 0.026, R_w = 0.018). The anions [Re₃Cl₁₂]^3? are connected via H₃O₊ cation (C.N. 3). The large channels that run in the [001] direction contain, alternatively, the cations [MEn₃]³⁺ and the lonesome Cl^?-anions     

Molecular mechanics of organic halides. III. Fluorinated olefins

A molecular mechanical force field for fluorinated ethylenes and propylenes is described. The field computes geometries, dipole moments, and energy differences between isomers and rotamers. Component analysis indicates that “classical” strains alone (skeletal, nonbonded, electrostatic) cannot account for energy relationships. The discussion is supplemented by a semiempirical quantum chemical comparison of cis- and trans-FCH?CHF and of gauche- and anti-FCH₂CH₂F.