Rosinger, Elemer Elad (2011) Heisenberg Uncertainty in Reduced Power Algebras. Prespacetime Journal, 2 (2). pp. 157-169. ISSN 2153-8301 (Unpublished)

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## Abstract

The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re formulated within far wider frameworks of {\it scalars}, namely, within one or the other of the infinitely many {\it reduced power algebras} which can replace the usual real numbers $\mathbb{R}$, or complex numbers $\mathbb{C}$. A major advantage of such a re-formulation is, among others, the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics". The use of reduced power algebras also opens up a foundational question about the role, and in fact, about the very meaning and existence, of fundamental constants in Physics, such as Planck's constant $h$. A role, meaning, and existence which may, or on the contrary, may not be so objective as to be independent of the scalars used, be they the usual real numbers $\mathbb{R}$, complex numbers $\mathbb{C}$, or scalars given by any of the infinitely many reduced power algebras, algebras which can so easily be constructed and used.

Item Type: Article Q Science > Q Science (General)A General Works > AS Academies and learned societies (General)Scientific Institution > University of Latvia > DI Institute of Literature, Folklore and Arts > A General Works > AS Academies and learned societies (General)A General Works > AS Academies and learned societies (General)Q Science > QC Physics > QC00 Physics (General)Q Science > Q0 Interdisciplinary sciencesQ Science > QA Mathematics (General)Q Science > QC Physics > QC01 Quantum mechanics [1] Gillespie, D T : A Quantum Mechanics Primer, An Elementary Inroduction to the Formal Theory of Nonrelativistic Quantum Mechanics. Open University Set Book, International Textbook Company Ltd., 1973, ISBN 0 7002 22901 [2] Rosinger, E E : What scalars should we use ? arXiv:math/0505336 [3] Rosinger, E E : Solving Problems in Scalar Algebras of Reduced Powers. arXiv:math/0508471 [4] Rosinger, E E : From Reference Frame Relativity to Relativity of Mathematical Models : Relativity Formulas in a Variety of non-Archimedean Setups. arXiv:physics/0701117 [5] Rosinger, E E : Cosmic Contact : To Be, or Not To Be Archimedean ? arXiv:physics/0702206 [6] Rosinger, E E : String Theory: a mere prelude to non-Archimedean Space-Time Structures? arXiv:physics/0703154 [7] Rosinger, E E : Mathematics and "The Trouble with Physics", How Deep We Have to Go ? arXiv:0707.1163 [8] Rosinger, E E : How Far Should the Principle of Relativity Go ? arXiv:0710.0226 [9] Rosinger, E E : Archimedean Type Conditions in Categories. arXiv:0803.081 171 Emeritus Professor Elemer Elad Rosinger 06 Jan 2011 15:43 30 Aug 2011 11:10

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