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Keywords = København quantum theory

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17 pages, 340 KiB  
Opinion
Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics
by Koen Thas
Physics 2023, 5(4), 1109-1125; https://doi.org/10.3390/physics5040072 - 8 Dec 2023
Viewed by 2389
Abstract
In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum [...] Read more.
In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum theory, and propose a new approach to this problem (based on the Lefschetz principle). Rather than a theorem–proof paper, this paper describes two new research programs on the foundational level, and focuses on basic open questions that arise in these programs. Full article
(This article belongs to the Section Classical Physics)
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13 pages, 330 KiB  
Article
Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion
by Koen Thas
Symmetry 2019, 11(2), 174; https://doi.org/10.3390/sym11020174 - 2 Feb 2019
Viewed by 2041
Abstract
In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in [...] Read more.
In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F 1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces). Full article
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