Proceedings of the Introduction to Neutrosophic Physics: Unmatter & Unparticle - International Conference

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Publisher : Infinite Study
ISBN 13 : 1599731827
Total Pages : 94 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Proceedings of the Introduction to Neutrosophic Physics: Unmatter & Unparticle - International Conference by : editor Florentin Smarandache

Download or read book Proceedings of the Introduction to Neutrosophic Physics: Unmatter & Unparticle - International Conference written by editor Florentin Smarandache and published by Infinite Study. This book was released on 2011 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Universe in a glass of iced-water. Exploration in off-the-wall physic

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4./5 ( download)

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Book Synopsis Universe in a glass of iced-water. Exploration in off-the-wall physic by : Victor Christianto

Download or read book Universe in a glass of iced-water. Exploration in off-the-wall physic written by Victor Christianto and published by Infinite Study. This book was released on 2023-09-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various exploration in astrophysics has revealed many breakthroughs nowadays, not only with respect to James Webb Telescope, but also recent finding related to water and ice deposits in the Moon surface. Those new findings seem to bring us to new questions related to origin of Earth, Moon and the entire Universe.

Collected Papers. Volume XI

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 1018 pages
Book Rating : 4./5 ( download)

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Book Synopsis Collected Papers. Volume XI by : Florentin Smarandache

Download or read book Collected Papers. Volume XI written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-08-01 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.

Neutrosophic Theory and Its Applications, Vol. I

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Publisher : Infinite Study
ISBN 13 : 159973320X
Total Pages : 482 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Neutrosophic Theory and Its Applications, Vol. I by : Florentin Smarandache

Download or read book Neutrosophic Theory and Its Applications, Vol. I written by Florentin Smarandache and published by Infinite Study. This book was released on 2014-12-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang.

From Logic to Realism to Brighter Future for Humanity

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 269 pages
Book Rating : 4./5 ( download)

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Book Synopsis From Logic to Realism to Brighter Future for Humanity by : Victor Christianto

Download or read book From Logic to Realism to Brighter Future for Humanity written by Victor Christianto and published by Infinite Study. This book was released on 2022-07-01 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles explores a wide range of subject, from Godel’s incompleteness theorem, to possible technocalypse and neutrofuturology. Articles on historical debates on irrational number to electroculture, on vortex particle, or on different Neutrosophic applications are included.

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4./5 ( download)

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Book Synopsis by : Florentin Smarandache

Download or read book written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic.

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. (2nd edition)

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Publisher : Infinite Study
ISBN 13 : 1599735318
Total Pages : pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. (2nd edition) by : Florentin Smarandache

Download or read book Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. (2nd edition) written by Florentin Smarandache and published by Infinite Study. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as an extension of the classical multisets); — Neutrosophic Spherical Numbers; — Neutrosophic Overnumbers / Undernumbers / Offnumbers; — Neutrosophic Indeterminacy of Second Type; — Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations); — Neutrosophic Triplet Weak Set (and con-sequently we have renamed the previous Neutros-ophic Triplet Set (2014-2016) as Neutrosophic Triplet Strong Set in order to distinguish them); — Neutrosophic Perfect Triplet; — Neutrosophic Imperfect Triplet; — Neutrosophic triplet relation of equivalence; — Two Neutrosophic Friends; — n Neutrosophic Friends; — Neutrosophic Triplet Loop; — Neutrosophic Triplet Function; — Neutrosophic Modal Logic; — and Neutrosophic Hedge Algebras. The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding Neutros-ophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017. We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life. Keywords: neutrosophy, neutrosophic duplets, neutrosophic duplet structures, neutrosophic multisets, neutrosophic hedge algebras, neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function, neutrosophic probability in target identification,

Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity

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Publisher : Infinite Study
ISBN 13 : 1599733463
Total Pages : 130 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity by : Florentin Smarandache

Download or read book Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles, notes, reviews, blogs and abstracts on Physics. Some are published for the first time here, some were previously published in journals, and revised here. We approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists. Further, we generalize the Lorentz Contraction Factor for the case when the lengths are moving at an oblique angle with respect to the motion direction, and show that the angles of the moving relativistic objects are distorted. Then, using the Oblique-Length Contraction Factor, we show several trigonometric relations between distorted and original angles of moving object lengths in the Special Theory of Relativity. We also discuss some paradoxes which we call “neutrosophic” since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, ill-defined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table, then we introduce two neutrosophic operators (neuterization and antonymization operators), and give many classes of neutrosophic paradoxes. Other topics addressed in this book are: neutrosophic physics as a new field of research, neutrosophic numbers in physics, neutrosophic degree of paradoxicity, unparticle and unmatter, multispace and multistructure, nucleon clusters, and others.

Collected Papers. Volume X

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 1006 pages
Book Rating : 4./5 ( download)

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Book Synopsis Collected Papers. Volume X by : Florentin Smarandache

Download or read book Collected Papers. Volume X written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-06-01 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.

Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set by : Florentin Smarandache

Download or read book Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set written by Florentin Smarandache and published by Infinite Study. This book was released on 2010-08-23 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

Neutrosophic Methods in General Relativity

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Publisher : Infinite Study
ISBN 13 : 1931233918
Total Pages : 80 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Neutrosophic Methods in General Relativity by : Dmitri Rabounski

Download or read book Neutrosophic Methods in General Relativity written by Dmitri Rabounski and published by Infinite Study. This book was released on 2005-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophy is a theory developed by Florentin Smarandache in 1995 as a generalization of dialectics, which studies the origin, nature and properties of neutralities. This book applies neutrosophic method to the General Theory of Relativity, aiming to discover new effects hidden before.Studying Einstein's basic space-time, neutrosophic method displays new trajectories and particles never considered before. Such trajectories/particles are of two "mixed" kinds, which are (1) common for sub-light mass-bearing particles and massless photons (non-isotropic/isotropic trajectories) and (2) common for massless photons and super-light mass-bearing tachyons (isotropic/non-isotropic trajectories). As it is shown, such mass-bearing/light-like particles are accessible for observing, we can see them in different phenomena of nature.Solutions of Einstein's equations (evolution scenarios for the Universe) are collected in a table in this book. Each cell of the table is a cosmological model. Neutrosophic method, analyzing this cosmological table, displays new possible models of the evolution of the Universe.The foundation of Smarandache geometries is based on S-denying an axiom, i.e. in the same space an axiom is false in at least two different ways, or is false and also true. S-denying each of 4 signature conditions in Einstein's basic space-time we arrive to 4 kinds of expanded space-time for the General Theory of Relativity. The 4th expanded space-time type permits photon teleportation, well-known from the recent experiments, but which failed in the basic space-time, and also where virtual photons are permitted --- predicted by Quantum Electrodynamics instant-moving mediators between entangled regular particles.

The Ethereal Aether

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Publisher : University of Texas Press
ISBN 13 : 0292758367
Total Pages : 396 pages
Book Rating : 4.2/5 (927 download)

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Book Synopsis The Ethereal Aether by : Loyd S. Swenson

Download or read book The Ethereal Aether written by Loyd S. Swenson and published by University of Texas Press. This book was released on 2013-08-28 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ethereal Aether is a historical narrative of one of the great experiments in modern physical science. The fame of the 1887 Michelson-Morley aether-drift test on the relative motion of the earth and the luminiferous aether derives largely from the role it is popularly supposed to have played in the origins, and later in the justification, of Albert Einstein’s first theory of relativity; its importance is its own. As a case history of the intermittent performance of an experiment in physical optics from 1880 to 1930 and of the men whose work it was, this study describes chronologically the conception, experimental design, first trials, repetitions, influence on physical theory, and eventual climax of the optical experiment. Michelson, Morley, and their colleague Miller were the prime actors in this half-century drama of confrontation between experimental and theoretical physics. The issue concerned the relative motion of “Spaceship Earth” and the Universe, as measured against the background of a luminiferous medium supposedly filling all interstellar space. At stake, it seemed, were the phenomena of astronomical aberration, the wave theory of light, and the Newtonian concepts of absolute space and time. James Clerk Maxwell’s suggestion for a test of his electromagnetic theory was translated by Michelson into an experimental design in 1881, redesigned and reaffirmed as a null result with Morley in 1887, thereafter modified and partially repeated by Morley and Miller, finally completed in 1926 by Miller alone, then by Michelson’s team again in the late 1920s. Meanwhile Helmholtz, Kelvin, Rayleigh, FitzGerald, Lodge, Larmor, Lorentz, and Poincaré—most of the great names in theoretical physics at the turn of the twentieth century—had wrestled with the anomaly presented by Michelson’s experiment. As the relativity and quantum theories matured, wave-particle duality was accepted by a new generation of physicists. The aether-drift tests disproved the old and verified the new theories of light and electromagnetism. By 1930 they seemed to explain Einstein, relativity, and space-time. But in historical fact, the aether died only with its believers.

Neutrosophy

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Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Neutrosophy by : Florentin Smarandache

Download or read book Neutrosophy written by Florentin Smarandache and published by . This book was released on 1998 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Review of Seven Applications of Neutrosophic Logic: In Cultural Psychology, Economics Theorizing, Conflict Resolution, Philosophy of Science, etc.

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

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Book Synopsis A Review of Seven Applications of Neutrosophic Logic: In Cultural Psychology, Economics Theorizing, Conflict Resolution, Philosophy of Science, etc. by : Victor Christianto

Download or read book A Review of Seven Applications of Neutrosophic Logic: In Cultural Psychology, Economics Theorizing, Conflict Resolution, Philosophy of Science, etc. written by Victor Christianto and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this short communication, we review seven applications of NFL that we have explored in a number of papers: (1) Background: the purpose of this study is to review how neutrosophic logic can be found useful in a number of diverse areas of interest; (2) Methods: we use logical analysis based on NL; (3) Results: some fields of study may be found elevated after analyzed by NL theory; and (4) Conclusions: we can expect NL theory to be applied in many areas of research too, in applied mathematics, economics, and physics. Hopefully the readers will find a continuing line of thoughts in our research from the last few years.

Michelson-morley Experiments: An Enigma For Physics And The History Of Science

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Publisher : World Scientific
ISBN 13 : 981327820X
Total Pages : 194 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Michelson-morley Experiments: An Enigma For Physics And The History Of Science by : Maurizio Consoli

Download or read book Michelson-morley Experiments: An Enigma For Physics And The History Of Science written by Maurizio Consoli and published by World Scientific. This book was released on 2018-12-16 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book should be an interesting read for advanced students within the field and for experts working in it.'Contemporary PhysicsIn 1887, Michelson and Morley tried to observe in laboratory the 'ether drift' by measuring a small difference in the velocity of two perpendicular light beams. The result of their measurements, however, was much smaller than the classical prediction and interpreted as a 'null result'. This was crucial to stimulate the first pioneering formulations of relativity and, as such, it represents a fundamental step in the history of science. Since then, many repetitions of that original experiment have been performed with better and better sensitivity and the standard conclusion has been always the same: no genuine ether drift has ever been detected. However, in the authors' new scheme, the small irregular residuals observed in laboratory show surprising correlations with the direct observations of the Cosmic Microwave Background (CMB) with satellites in space. This opens the possibility of finally linking the CMB to a fundamental reference frame for relativity, with substantial implications for the interpretation of non-locality in the quantum theory. The importance of the issue would require new dedicated experimental tests and significant improvements in the data analysis. Otherwise, without such more stringent checks, these crucial experiments will remain forever as an enigma for physics and the history of science. The book illustrates the many facets of this research together with historical accounts on some leading scientists involved in these measurements.

Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science

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Publisher : Infinite Study
ISBN 13 : 1599730138
Total Pages : 140 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science by : Florentin Smarandache

Download or read book Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!

Neutrosophy, Paradoxism and Communication

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Publisher : Infinite Study
ISBN 13 : 606114346X
Total Pages : 200 pages
Book Rating : 4.0/5 (611 download)

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Book Synopsis Neutrosophy, Paradoxism and Communication by : Ştefan Vladutescu

Download or read book Neutrosophy, Paradoxism and Communication written by Ştefan Vladutescu and published by Infinite Study. This book was released on 2014-10-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are people for whom are too few things they do not know how to do, to approach them, to understand them. There are people who is enough to look at them because they understood the significance in your eyes, are people for whom you have not finished the uttered sentence and they are given the solution, there are ...people!