A note on Heisenberg's uncertainty principle and Cantorian space-time
type: Item
instance of: scholarly article
title: A note on Heisenberg's uncertainty principle and Cantorian space-time
zbMATH Open document ID: 0771.58041
DOI: 10.1016/0960-0779(92)90018-I
published in: Chaos, Solitons and Fractals
publication date: 1993-01-17T00:00:00Z
review text: Considering the Cantorian space-time as a nondifferentiable manifold with the Hausdorff dimension \(d_ c^{(\mu)}\cong 4\), which replaces the smooth classical space-time in the description of the quantum processes, the author derives the Heisenberg's uncertainty principle for a Cantorian-type free particle, called Cantorion: \[ \Delta p\cdot\Delta x=h(\eta/\lambda)^{2-{1\over\Omega}}\cdot[\Omega(1-\Omega)^{1/2}] \] where \(\eta\) is the measurement resolution, \(\lambda\) is the wavelength of the Cantorian construction and \(\Omega=2/d_ c^{(4)}\) is the intrinsic geodesic dependent probability ``felt'' by the Cantorion on its nondifferentiable Peano-like and space filling path. It can be easily observed that inserting the explicit value of \(\Omega\cong 1/2\) into the previous formula the author comes very close to exactly the same form of the uncertainty principle derived by \textit{R. P. Feynman} and \textit{A. R. Hibbs} for the two slits experiment [Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965; Zbl 0176.549)].
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 81S05
zbMATH DE Number: 96225
zbMATH Keywords: Cantorian space-time
zbMATH Keywords: Heisenberg's uncertainty principle
author: Mohamed Saladin El Naschie
reviewed by: Ciprian Dariescu
MaRDI profile type: Publication
cites work: Mathematical model for chaos and ergodic criticality in four dimensions
cites work: On the uncertainty of information in quantum space-time
cites work: Multi-dimensional Cantor sets in classical and quantum mechanics
cites work: Q3994385
cites work: Q5569065
cites work: Quantum mechanics and the possibility of a Cantorian space-time
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description: scientific article; zbMATH DE number 96225