Completely discretized, finite quantum mechanics. (English) Zbl 1541.81002
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. 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.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 31C20 | Discrete potential theory |
| 03D05 | Automata and formal grammars in connection with logical questions |
| 51F25 | Orthogonal and unitary groups in metric geometry |
Keywords:
quantum mechanics; Hilbert space; discrete theories; mathematical realism; finitism; automataReferences:
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