Completely Discretized, Finite Quantum Mechanics
Quantum Physics
2023-11-03 v2
Abstract
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.
Cite
@article{arxiv.2307.11927,
title = {Completely Discretized, Finite Quantum Mechanics},
author = {Sean M. Carroll},
journal= {arXiv preprint arXiv:2307.11927},
year = {2023}
}