On the Generalized Uncertainty Principle

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.