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Title: Quantum mechanics problems in observer's mathematics

Abstract

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.

Authors:
;  [1];  [2]
  1. Compressor Controls Corp, Des Moines, Iowa (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
22075698
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1493; Journal Issue: 1; Conference: ICNPAA 2012: 9. international conference on mathematical problems in engineering, aerospace and sciences, Vienna (Austria), 10-14 Jul 2012; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; GEOMETRY; HAMILTONIANS; INTERFERENCE; LET; MATHEMATICAL SOLUTIONS; PROBABILITY; QUANTUM MECHANICS; SCHROEDINGER EQUATION; TOPOLOGY; VARIATIONS; WAVE FUNCTIONS

Citation Formats

Khots, Boris, Khots, Dmitriy, and iMath Consulting LLC, Omaha, Nebraska. Quantum mechanics problems in observer's mathematics. United States: N. p., 2012. Web. doi:10.1063/1.4765537.
Khots, Boris, Khots, Dmitriy, & iMath Consulting LLC, Omaha, Nebraska. Quantum mechanics problems in observer's mathematics. United States. doi:10.1063/1.4765537.
Khots, Boris, Khots, Dmitriy, and iMath Consulting LLC, Omaha, Nebraska. Tue . "Quantum mechanics problems in observer's mathematics". United States. doi:10.1063/1.4765537.
@article{osti_22075698,
title = {Quantum mechanics problems in observer's mathematics},
author = {Khots, Boris and Khots, Dmitriy and iMath Consulting LLC, Omaha, Nebraska},
abstractNote = {This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.},
doi = {10.1063/1.4765537},
journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1493,
place = {United States},
year = {2012},
month = {11}
}