Completely Discretized, Finite Quantum Mechanics

• URL: http://arxiv.org/abs/2307.11927v2
• Date: Wed, 1 Nov 2023 20:00:04 GMT
• Title: Completely Discretized, Finite Quantum Mechanics
• Authors: Sean M. Carroll
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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