Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions

We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum comp...

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Vydáno v:	Mathematics (Basel) Ročník 11; číslo 1; s. 68
Hlavní autor:	Gerck, Ed
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 01.01.2023
Témata:	19th century algebraic Algorithms Analysis Calculus communication Functions, Discontinuous Mathematical research Mathematics nature physical numbers Physics Prejudice Prime numbers Quantum computing Quantum mechanics Relativity tri-state United States
ISSN:	2227-7390, 2227-7390
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Abstract	We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum computation. DDF have been thought to exist not in the classical sense, but using distributions. However, DDF using distributions still is defined in terms of mathematical real-numbers (MRN), and do not address the Problem of Closure, here investigated. These facts lead to contradictions using MRN, solved by this work, providing a new unbounded class of physical solutions using physical numbers in quantum mechanics (QM), that were always there (just hidden), allowing DDF without distributions, or MRN. It is worthwhile to see this only in mathematics, to avoid the prejudices found in physics, as this reforms both general relativity and QM. This confirms the opinions of Nicolas Gisin that MRN are non-computable with probability 1, and Niels Bohr that physics is not reality, it is a fitting story about reality. Mathematics can get closer to reality, surprisingly. We just have to base mathematics on nature, not on how it defines nature.
AbstractList	We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum computation. DDF have been thought to exist not in the classical sense, but using distributions. However, DDF using distributions still is defined in terms of mathematical real-numbers (MRN), and do not address the Problem of Closure, here investigated. These facts lead to contradictions using MRN, solved by this work, providing a new unbounded class of physical solutions using physical numbers in quantum mechanics (QM), that were always there (just hidden), allowing DDF without distributions, or MRN. It is worthwhile to see this only in mathematics, to avoid the prejudices found in physics, as this reforms both general relativity and QM. This confirms the opinions of Nicolas Gisin that MRN are non-computable with probability 1, and Niels Bohr that physics is not reality, it is a fitting story about reality. Mathematics can get closer to reality, surprisingly. We just have to base mathematics on nature, not on how it defines nature.
Audience	Academic
Author	Gerck, Ed
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Cites_doi	10.33693/2313-223X-2021-8-3-29-35 10.1007/s12559-020-09782-w 10.1002/j.1538-7305.1948.tb00917.x 10.1086/425941 10.1515/9780691220383 10.3390/app10186451 10.1016/j.neunet.2019.05.002 10.1016/j.cnsns.2017.09.005 10.1016/0771-050X(80)90020-0 10.33693/2313-223X-2021-8-3-13-18 10.1103/PhysRevA.26.662 10.1063/1.3059856 10.1007/978-1-4615-4687-0 10.1007/978-3-642-99554-5 10.1007/BF01206656 10.1103/RevModPhys.47.773
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SubjectTerms	19th century algebraic Algorithms Analysis Calculus communication Functions, Discontinuous Mathematical research Mathematics nature physical numbers Physics Prejudice Prime numbers Quantum computing Quantum mechanics Relativity tri-state
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Title	Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions
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