Quantum reference frames and deformed symmetries

In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system undergoes an unavoidable measurement "back-action" that modifies its properties. In a quantum-gravitational setting, it has been argued that such a back-action may produce effects that are described at an effective level as a form of deformed (or doubly) special relativity. We examine this possibility using a simple constrained system that has been extensively studied in the context of quantum information. While our conclusions support the idea of a symmetry deformation, they also reveal a host of other effects that may be relevant to the context of quantum gravity, and could potentially conceal the symmetry deformation.Comment: 11 pages, revtex. Comments are welcom

ON COMPLETENESS OF HISTORICAL RELATIONAL QUERY LANGUAGES

Numerous proposals for extending the relational data model to incorporate the temporal dimension of data have appeared in the past several years. These proposals have differed considerably in the way that the temporal dimension has been incorporated both into the structure of the extended relations of these temporal models, and consequently into the extended relational algebra or calculus that they define. Because of these differences it has been difficult to compare the proposed models and to make judgments as to which of them might in some sense be equivalent or even better. In this paper we define the notions of temporally grouped and temporally ungrouped historical data models and propose two notions of historical relational completeness, analogous to Codd's notion of relational completeness, one for each type of model. We show that the temporally ungrouped models are less powerful than the grouped models, but demonstrate a technique for extending the ungrouped models with a grouping mechanism to capture the additional semantic power of temporal grouping. For the ungrouped models we define three different languages, a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show that under certain assumptions all three are equivalent in power. For the grouped models we define a many-sorted logic with variables over ordinary values, historical values, and times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped calculus extended with the proposed grouping mechanism. We believe the classification of historical data models into grouped and ungrouped provides a useful framework for the comparison of models in the literature, and furthermore the exposition of equivalent languages for each type provides reasonable standards for common, and minimal, notions of historical relational completeness.Information Systems Working Papers Serie