Fundamental Limit on Angular Measurements and Rotations from Quantum Mechanics and General Relativity

• URL: http://arxiv.org/abs/2108.11990v2
• Date: Wed, 3 Nov 2021 12:25:55 GMT
• Title: Fundamental Limit on Angular Measurements and Rotations from Quantum Mechanics and General Relativity
• Authors: Xavier Calmet, Stephen D.H. Hsu
• Abstract summary: We show that the precision of an angular measurement or rotation is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse) 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?
• Score: 0.21320960069210473
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $r^{-1}$ in Planck units, where $r$ is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states $S_1$ and $S_2$ 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?

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