Is Hilbert space discrete?
High Energy Physics - Theory
2009-11-11 v1 General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Quantum Physics
Abstract
We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.
Cite
@article{arxiv.hep-th/0508039,
title = {Is Hilbert space discrete?},
author = {R. Buniy and S. Hsu and A. Zee},
journal= {arXiv preprint arXiv:hep-th/0508039},
year = {2009}
}
Comments
4 pages, revtex, 1 figure