On the Generalized Uncertainty Principle
일반화된 불확정성 원리에 대하여
Sobre el principio de incertidumbre generalizada
Sur le principe d'incertitude généralisée
Об общем принципе неопределенности
Ming-Cheng Chen 陈明城 ¹ ², Chao-Yang Lu 陆朝阳 ¹ ², Jian-Wei Pan 潘建伟 ¹ ²
¹ Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; 中国科学技术大学 近代物理系 合肥微尺度物质科学国家研究中心
² CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; 中国科学技术大学 中国科学院 量子信息与量子科技前沿协同创新中心
ChinaXiv, 13 August 2021

Generalized Uncertainty Principle (GUP), which manifests a minimal Planck length in quantum spacetime, is central in various quantum gravity theories and has been widely used to describe the Planck-scale phenomenon. Here, we propose a thought experiment based on GUP – as a quantum version of Galileo's falling bodies experiment – to show that the experimental results cannot be consistently described in quantum mechanics.

This paradox arises from the interaction of two quantum systems in an interferometer, a photon and a mirror, with different effective Planck constants. Our thought experiment rules out the widely used GUP, and establishes a Quantum Coupling Principle that two physical systems of different effective Planck constants cannot be consistently coupled in quantum mechanics. Our results point new directions to quantum gravity.
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