Fundamental Limit on Angular Measurements and Rotations from Quantum Mechanics and General Relativity
arXiv:2108.11990 · doi:10.1016/j.physletb.2021.136763
Abstract
We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The limiting precision is in Planck units, where is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states and cannot be experimentally distinguished from each other if they differ by a sufficiently small rotation. Experiments cannot exclude the possibility that the space of quantum state vectors (i.e., Hilbert space) is fundamentally discrete, rather than continuous. We discuss the implications for finitism: does physics require infinity or a continuum?
arXiv comment10 pages. Version to appear in Physics Letters B
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