1. Fundamental limit on angular measurements and rotations from quantum mechanics and general relativity
- Author
-
Xavier Calmet and Stephen D. H. Hsu
- Subjects
High Energy Physics - Theory ,Physics ,Quantum Physics ,Nuclear and High Energy Physics ,010308 nuclear & particles physics ,General relativity ,QC1-999 ,FOS: Physical sciences ,Space (mathematics) ,01 natural sciences ,High Energy Physics - Theory (hep-th) ,Quantum state ,Quantum mechanics ,Orientation (geometry) ,Qubit ,0103 physical sciences ,Gravitational collapse ,Quantum Physics (quant-ph) ,010306 general physics ,Planck units ,Rotation (mathematics) - 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?, Comment: 10 pages. Version to appear in Physics Letters B
- Published
- 2021