University of New Mexico UNM Digital Repository Faculty and Staff Publications Mathematics 2012 QUANTIZATION AND DISCRETIZATION AT LARGE SCALES Florentin Smarandache University of New Mexico, [email protected] Victor Christianto SatyabhaktI Advanced School of Theology - Jakarta Chapter, Indonesia, [email protected] Pavel Pintr Olomouc University Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Applied Mathematics Commons, Cosmology, Relativity, and Gravity Commons, External Galaxies Commons, Mathematics Commons, Other Astrophysics and Astronomy Commons, and the Stars, Interstellar Medium and the Galaxy Commons Recommended Citation F. Smarandache, V. Christianto, P. Pintr (eds.). QUANTIZATION AND DISCRETIZATION AT LARGE SCALES. Ohio: Zip Publishing, 2012 This Book is brought to you for free and open access by the Mathematics at UNM Digital Repository. It has been accepted for inclusion in Faculty and Staff Publications by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. QUANTIZATION AND DISCRETIZATION AT LARGE SCALES EDITED BY : FLORENTIN SMARANDACHE, V. CHRISTIANTO & P. PINTR ZIP PUBLISHING, 2012 - Columbus, Ohio, USA - ISBN.9781599732275 QUANTIZATION AND DISCRETIZATION AT LARGE SCALES Edited by: Florentin Smarandache, V. Christianto, & Pavel Pintr Including articles never before published Zip Publishing, 2012 Columbus, Ohio (ISBN-13) 9781599732275 Printed in USA i This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arbor MI 48106-1346, USA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/basic Copyright 2012 by Zip Publishing and Authors for their own articles. Zip Publishing 1313 Chesapeake Avenue Columbus, Ohio 43212 USA Tel. (614) 485-0721 E-mail: [email protected] Website: http://www.zippublishing.com Many books can be downloaded from the following Digital Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm Cover design by Sonny Agustinus (ISBN-13) 9781599732275 Printed in USA ii Preface The ongoing search of extrasolar planets is one of the most attractive fields of research in astrophysics and astronomy. Up to now, 360 extrasolar planets have been discovered near stars with similar mass as the Sun. There is also discovery related to the so-called Earth-like planets. With regards to these discoveries, one intriguing question is whether there is relationship between orbit distance of the planets and their stars. Various formulas have been suggested since 1990s, and they suggest that there may be reason to accept quantization of distances of those planets both in our solar system and also in extrasolar systems as well. This book discusses this issue (Rubcic & Rubcic), along with other interesting issues such as protoplanetary formation of solar system (Pintr, prof. Per\inova%, & dr. Luks\), precession in solar system (Pitkanen) and other topics. Another line of thought explored herein is the correspondence between cosmological phenomena and condensed matter physics, and therefore we can think that the quantization of orbit distances can be caused by superfluid helium quantization. This issue is explored by F. Smarandache and V. Christianto. Moreover, F. Smarandache also discusses possible new era of research that is pertaining to superluminal physics and instantaneous physics. Ion Patrascu and D. Rabounski discuss superluminality from their perspectives. And M. Pereira discusses his Hypergeometrical Universe model. This book is published after our previous book: Quantization in astrophyisics, Brownian motion, and Supersymmetry which was released about five years ago. Perhaps the ideas presented herein will have impact on discussions concerning quantum cosmology, which so far it cannot be observed. On the contrary, quantization at large scales can be observed. We hope that this volume will add a new chapter in our understanding of the Universe, from the viewpoint of quantization and discretization at large scales. Special thanks go to journal editors who have granted permission to reprint papers included here, including Chaos, Soliton, Fractals editor, Prespacetime Journal editor, Fizika editor, Progress in Physics editor and Apeiron editor. January 7th, 2012, January 25th 2012 FS, VC, PP www.sciprint.org iii Contents Preface iii Contents iv Planetary orbits in Solar and Extrasolar systems (A. Rubcic & J. Rubcic) Fizika A, 19 no.3, 2010 1 Areal velocities of planets and their comparison (P. Pintr, V. Per\inova%, A. Luks\) unpubl. 2011 15 Distribution of distances in solar system (P. Pintr, V. Per\inova%, A. Luks\) Chaos , Soliton, Fractals 2007 27 New cosmological model of universe and possible quantization of the Hubble parameter (P.Pintr) unpublished paper, Dec. 2011 39 Do we really understand the solar system? (M. Pitkanen) Nov. 27th 2011 50 Inflation and TGD (M. Pitkanen) Dec. 10th 2011 70 QCD and TGD (M. Pitkanen) Dec. 19th 2011 78 Quantum arithmetics and the relationship between real and p-adic physics (M. Pitkanen) Dec. 12th 2011 94 A blind pilot: who is super-luminal observer? (D. Rabounski) Progress in Physics Vol.2, 2008 126 Scientist deduced the existence of particles with faster-than-light speeds recently discovered by CERN. (I. Patrascu) Progress in Physics Vol.4, 2011 127 Superluminal physics and Instantaneous physics as new trends in research (F. Smarandache) 129 The Hypergeometrical Universe: Cosmology and Standard Model. (M.A. Pereira). Jan. 2012 134 On astrometric data and time-varying sun earth distance in light of Carmeli metric (V. Christianto) Prespacetime Journal Vol.1 no.9, 2010 161 What gravity is. Some recent considerations. (V. Christianto & F. Smarandache) Progress in Physics Vol. 3, July 2008 168 Schrodinger equation and the quantization of celestial systems (F. Smarandache & V. Christianto) Progress in Physics vol.2, April 2006 173 A Cantorian superluid vortex and the quantization of planetary motion (V. Christianto) Apeiron Vol.11 no.1, January 2004 178 iv QUANTIZATION AND DISCRETIZATION AT LARGE SCALES 1 Printed ISSN 1330–0008 Online ISSN 1333–9125 CD ISSN1333–8390 CODEN FIZAE4 PLANETARY ORBITS IN SOLAR AND EXTRASOLAR SYSTEMS ANTUN RUBCIˇ C´ and JASNA RUBCIˇ C´ Department of Physics, Faculty of Science, University of Zagreb, Bijeniˇckac. 32, 10000 Zagreb, Croatia E-mail address: [email protected] Received 20 May 2010; Revised manuscript received 18 December 2010 Accepted 5 January 2011 Online 20 February 2011 The analysis of orbital parameters of planets and main planetary satellites of the solar system, published by the present authors, suggests that the Sun’s system could be a “prototype” for the distribution of orbits in extrasolar planetary sys- tems. Owing to the recent endeavours in detecting exoplanets, it became possible and suitable to check this assumption. Particularly useful in this work are the mul- tiple extrasolar system with at least four planets. Unfortunately, there are only four stars satisfying this requirement. At the present time eleven stars with three planets have also been observed, which may also be taken into account in reaching reasonable assertions. Quantization of orbits in the solar system by orbital number, the integer n, and quantization of the product nvn (vn is the orbital velocity) by the spacing number, integer k, is also found in extrasolar planets. It is expected that new discoveries will support the present findings. PACS numbers: 95.10.Ce, 95.10.Fh, 95.30.-t UDC 523.2, 531.35 Keywords: quantization of orbits, solar planets, satellites of planets, extrasolar planetary systems 1. Introduction In our previous articles [1a, b, c, d], the square law for orbits has been deduced by the analysis of orbital parameters of Sun’s planets and main satellites of Jupiter, Saturn and Uranus. The Sun’s planets are classified in two subsystems: terrestrial and Jovian. Therefore, there are five subsystems in the solar system, for which the orbital distributions follow the square law in the form 2 rn = r1n . (1) The values of n are consecutive integer numbers in a definite range and r1 is the radius of the orbit with n = 1, dependent on the subsystem. The existing orbits, as an example, for terrestrial planets are distributed from n = 3 for Mercury and ending with n = 8 for Ceres. Similar results are obtained for other systems, as will FIZIKA A (Zagreb) 19 (2010) 3, 133–144 133 QUANTIZATION AND DISCRETIZATION AT LARGE SCALES 2 rubciˇ c´ and rubciˇ c:´ planetary orbits in solar and extrasolar systems be shown later in relevant graphs and tables. In the terrestrial system of planets, the Earth’s moon, by hypothesis, had its primordial orbit n = 7 between Mars (n = 6) and Ceres (n = 8). Thus, the Moon is considered to be a planet, which was captured by the Earth [1e]. This hypothesis is supported by the analysis of masses, volumes and periods of all terrestrial planets. Why the Moon at orbit n = 7 migrated through the orbit of Mars to become a satellite of the Earth at n = 5 is not clear, as well as the problem of its chemical constitution. If the Moon was born at orbit n = 7, then it would be expected to contain a significant amount of water, like both Mars and Ceres. However, the absence of volatile elements and water in Moon’s materials brought by astronauts suggests another origin: a giant impact of a body as large as Mars with the Earth. But it is hard to accept that such a cataclysmic process could have resulted in the Earth’s satellite with parameters compatible with that of the present Moon and with those of all terrestrial planets. Therefore, the problem of the origin of the Moon remains open. Here we treat the Moon as a small planet of the terrestrial group of planets. Physical basis for the square law (1) is a quantization of the specific angular momentum of planets. Details are presented in Ref. [1]. Equation (1) in extended form [1c,d] is given by 1 n2 rn = 2 GM 2 .