论文标题
关于物理测量的几何形状：拓扑和代数方面
On the geometry of physical measurements: topological and algebraic aspects
论文作者
论文摘要
我们研究了测量空间概念的数学结构，该结构扩展了基于量化理论的非交换性拓扑的各个方面。这产生了物理测量的几何模型，该模型提供了现实的图片，但也可以运行，因此测量和经典信息是作为原始概念相互依存的。经典观察者的派生概念可以满足Bohr经典/量子鸿沟的数学公式。分别从C* - 代数和第二个可局部紧凑的开放式清醒拓扑类固醇获得了两种重要的测量空间。后一种经典类型的产量测量，与施温格的选择性测量概念有关。我们表明，与任何第二个可局部紧凑的Hausdorffétalegroupoid相关的降低的C* - 代数相关的测量空间在规范上配备了经典观察者，并且我们在观察者的属性和群体属性之间建立了对应关系。
We study the mathematical structure of the notion of measurement space, which extends aspects of noncommutative topology that are based on quantale theory. This yields a geometric model of physical measurements that provides a realist picture, yet also operational, such that measurements and classical information arise interdependently as primitive concepts. A derived notion of classical observer caters for a mathematical formulation of Bohr's classical/quantum divide. Two important classes of measurement spaces are obtained, respectively from C*-algebras and from second-countable locally compact open sober topological groupoids. The latter yield measurements of classical type and relate to Schwinger's notion of selective measurement. We show that the measurement space associated to the reduced C*-algebra of any second-countable locally compact Hausdorff étale groupoid is canonically equipped with a classical observer, and we establish a correspondence between properties of the observer and properties of the groupoid.
