The lack of experimental results of theories concerning the ultimate space/space–time structure, leads one to think about some simple experiments that can help demonstrate the main prediction: Space–time is discrete. In this paper, an implementation of Snyder operators is applied to simple geometries, to demonstrate that the spectrum of the position operator, in standard quantum mechanics (QM), is discrete when a parameter measuring the non-commutativity of quantum operators is introduced. The geometries are specially suitable for experiments in search of the behaviour of ultracold neutrons falling in the Earth’s gravitational potential.

中文翻译：

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Snyder算符在量子力学中的实现

缺乏有关最终时空结构的理论实验结果，导致人们思考一些简单的实验，这些实验可以帮助证明主要的预测结果：时空是离散的。在本文中，将Snyder算子的实现应用于简单的几何，以证明当引入测量量子算子的非交换性的参数时，标准量子力学（QM）中位置算子的频谱是离散的。这些几何形状特别适合用于寻找落入地球重力的超冷中子的行为的实验。