Completely Discretized, Finite Quantum Mechanics

Foundations of Physics 53 (6):1-13 (2023)
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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, Schrödinger 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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Sean M. Carroll
Johns Hopkins University

Citations of this work

Finitism in geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.

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References found in this work

Elementary Quantum Metaphysics.David Albert - 1996 - In James T. Cushing, Arthur Fine & Sheldon Goldstein (eds.), Bohmian mechanics and quantum theory: an appraisal. Springer. pp. 277-284.
Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal.Sean M. Carroll & Ashmeet Singh - 2019 - In Anthony Aguirre, Brendan Foster & Zeeya Merali (eds.), What is Fundamental? Cham: Springer Verlag. pp. 95-104.

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