论文标题
在外部概率下的杂形测量功能的方差不平等
A Variance Inequality for Meromorphic Measurement Functions under Exterior Probability
论文作者
论文摘要
已经讨论了在奇点附近测量无界系统属性的问题。已将镜片作为正式对象引入，以研究围绕奇异性的越来越精确的测量，并且已经研究了一种称为外部概率的特定镜头。已经表明，在这样的概率下，在复杂的歧管上的一阶杆周围的可测量函数的测量方差，由两个可分离的部分组成 - 一个部分随着镜头的尺度减少而减小，另一个会增加。已经讨论了该框架如何在量子尺度上为非确定性不确定性的思想提供数学支持。实际上，上述方差分解允许对这种系统的最小差异，而与测量的距离无关。如果人们认为能量/动量是复杂时空的仿药功能，则这种不平等在结构上与海森堡的不确定性关系相似。
The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses called Exterior probabilities have been investigated. It has been shown that under such probabilities, measurement variance of a measurable function around a 1st order pole on a complex manifold, consists of two separable parts - one that decreases with diminishing scale of the lenses, and the other that increases. It has been discussed how this framework can lend mathematical support to ideas of non-deterministic uncertainty prevalent at a quantum scale. In fact, the aforementioned variance decomposition allows for a minimum possible variance for such a system irrespective of how close the measurements are. This inequality is structurally similar to Heisenberg uncertainty relationship if one considers energy/momentum to be a meromorphic function of a complex spacetime.
