发表机构
Babeş-Bolyai University（巴贝什-博尧伊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子参考系的替代定义，据此构建普朗克尺度时空模型，并展示经典时空对称性可数学保留但操作上被打破，从而以量子化参考系变换对量子时空进行分类。
AI 中文摘要
经典埃尔朗根纲领旨在完全依据其对称性来对度量空间进行分类。在物理时空中，这些对称性定义了经典参考系之间的变换，从而在参考系变换与底层几何之间建立起一一对应关系。近期，经典理想参考系的概念已被扩展到量子领域，其做法是将观察者视为受量子力学定律支配的具身物理系统。在此，我们基于这一方法，但提出对“量子参考系”这一术语的一种替代性定义，该定义与主流观点有所不同。随后，我们展示了如何利用这一定义构建一个普朗克尺度时空的简单模型，该模型与现有的量子引力现象学相联系。最后，我们展示了在新模型中，经典时空对称性如何能够“在数学上被保留但在操作上被打破”，这表明量子时空至少可以局部地依据量子化参考系之间的变换来分类。
英文摘要
The classical Erlangen Program sought to classify metric spaces entirely in terms of their symmetries. In physical spacetimes, these symmetries define transformations between classical reference frames, yielding a one-to-one correspondence between frame transformations and the underlying geometry. More recently, the classical notion of ideal frame has been extended to the quantum regime, by considering observers as embodied physical systems, subject to the laws of quantum mechanics. Here, we build on this approach, but outline an alternative definition of the term `quantum reference frame', which differs somewhat from the mainstream view. We then show how the new definition can be used to construct a simple model of Planck-scale spacetime, which makes contact with existing quantum gravity phenomenology. Finally, we show how classical spacetime symmetries can be ``mathematically preserved but operationally broken'', in the new model, suggesting that {\it quantum} spacetime may be classified, at least locally, in terms of transformations between quantised frames of reference.
Comments13 pages, no tables, 1 figure. Published version. Referee Reports, Author's Responses and Editorial Decisions are available under MDPI's Open Peer Review Policy at https://www.mdpi.com/2218-1997/12/3/84/review_report
Journal refUniverse 2026, 12(3), 84
