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Relational Mechanics Relational Principle and Implementation of Mach’S Force Gravitational with Weber’S A s s i s Relational Mechanics R Relational Mechanics ¨ A new mechanics intended to replace newtonian e mechanics and also Einstein’s theories of relativity. l a and Implementation of Mach’s Principle ¨ It implements Mach’s principle quantitatively based on t i Weber’s force for gravitation and the principle of o n with Weber’s Gravitational Force dynamical equilibrium. a l ¨ It explains Newton’s bucket experiment with the concave M figure of the water being due to a gravitational e c interaction between the water and the distant galaxies h when in relative rotation. a n i ¨ It is intended for physicists, engineers, mathematicians, c historians, philosophers of science and students. s a n d About the Author I m Andre Koch Torres Assis was born in Brazil (1962) and educated at the Uni- p l versity of Campinas – UNICAMP, BS (1983), PhD (1987). He spent the aca- e m demic year of 1988 in England with a post-doctoral position at the Culham e Laboratory (Oxfordshire, United Kingdom Atomic Energy Authority). He n spent one year in 1991-92 as a Visiting Scholar at the Center for Electro- t a magnetics Research of Northeastern University (Boston, USA). From August t i 2001 to November 2002, and from February to May 2009, he worked at the o Institute for the History of Natural Sciences, Hamburg University (Hamburg, n Germany) with research fellowships awarded by the Alexander von Hum- o f boldt Foundation of Germany. He is the author of Weber’s Electrodynamics M (1994), Relational Mechanics (1999), Inductance and Force Calculations in a Electrical Circuits (with M. A. Bueno, 2001), The Electric Force of a Current: c h Weber and the Surface Charges of Resistive Conductors Carrying Steady ’ Currents (with J. A. Hernandes, 2007), Archimedes, the Center of Gravity, s P and the First Law of Mechanics: The Law of the Lever (2008 and 2010), The r i Experimental and Historical Foundations of Electricity (2010), Ampère’s n Electrodynamics (with J. P. M. d. C. Chaib, 2011), Weber’s Planetary Model c i of the Atom (with K. H. Widerkehr and G. Wolfschmidt, 2011), Stephen p l Gray and the Discovery of Conductors and Insulators e (with S. L. B. Boss and J. J. Caluzi, 2012) and The 978-0-9920456-3-0 Illustrated Method of Archimedes: Utilizing the Law Andre Koch Torres Assis of the Lever to Calculate Areas, Volumes and Cen- ters of Gravity (with C. P. Magnaghi, 2012). He has A p been professor of physics at UNICAMP since 1989, e i working on the foundations of electromagnetism, r o gravitation, and cosmology. n Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force André Koch Torres Assis Apeiron Montreal Published by C. Roy Keys Inc. 4405, rue St-Dominique Montreal, Quebec H2W 2B2 Canada http://redshift.vif.com © André Koch Torres Assis 2014 First Published 2014 National Library of Canada Cataloguing in Publication Assis, André Koch Torres, 1962- [Mecânica relacional e implementação do princípio de Mach com a força de Weber gravitacional. English] Relational mechanics and implementation of Mach's principle with Weber's gravitational force / André Koch Torres Assis. Translation of: Mecânica relacional e implementação do princípio de Mach com a força de Weber gravitacional. Includes bibliographical references. Issued in print and electronic formats. ISBN 978-0-9920456-3-0 (pbk.).--ISBN 978-0-9920456-4-7 (pdf) 1. Mechanics. 2. Mach's principle. 3. Force and energy. 4. Gravitation. 5. Mach, Ernst, 1838-1916. 6. Weber, Wilhelm Eduard, 1804-1891. I. Title. II. Title: Mecânica relacional e implementação do princípio de Mach com a força de Weber gravitacional. English. QA808.A8713 2014 531 C2014-901225-X C2014-901226-8 Front Cover: Top left: Car at rest relative to the ground with two horizontal springs, a vessel partially filled with liquid and a pendulum supporting a test body. Top right: There are some visible effects when a car is uniformly accelerated relative to the ground (for instance, with an acceleration of a = 5 m/s2 to the right): horizontal springs are deformed, a pendulum remains inclined to the vertical and the free surface of water in a vessel remains inclined to the horizontal. What would happen with these bodies if it were possible to accelerate uniformly the set of galaxies relative to the ground, in the opposite direction, with the same magnitude (for instance, with an acceleration of a = –5 m/s2 to the left), while the car and the internal bodies remained at rest in the ground? Bottom left: Nothing would happen to the bodies according to newtonian mechanics. The springs should remain relaxed, the water horizontal and the pendulum vertical. Bottom right: According to relational mechanics, on the other hand, the same visible effects should take place in all these bodies. The deformable bodies should behave as in the top right configuration. That is, the springs should be deformed, the water should be inclined to the horizontal and the pendulum should be inclined to the vertical. The kinematic situation now is the same as that of top right configuration, with equal relative acceleration between these bodies and the set of galaxies. Therefore, the same dynamic effects should appear. Phenomena like these are discussed at length in this book. Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force a _ a _ a _ _ _ a a _ a a _ _ _ _ a a a a Newtonian Mechanics Relational Mechanics ANDRE KOCH TORRES ASSIS Institute of Physics University of Campinas — UNICAMP 13083-859 Campinas, SP, Brazil E-mail: [email protected] Homepage: <www.ifi.unicamp.br/~assis> c Andre Koch Torres Assis This book is an improved version, in English, of a work first published in 2013, Mecânica Relacional e Implementação do Princípio de Mach com a Força de Weber Gravitacional, [Ass13b]. Contents Acknowledgments i Preface iii I Classical Mechanics 1 1 Newtonian Mechanics 3 1.1 Introduction.................................... .......... 3 1.2 LawsofMotion.................................... ........ 3 1.3 UniversalGravitation . ............ 7 1.3.1 Modern Formulation of the Law of Gravitation . .............. 7 1.3.2 InertialMassandGravitationalMass . ............. 8 1.3.3 Newton’s Original Formulation of the Law of Gravitation ................ 9 1.4 TheForcesExertedbySphericalShells. ................ 10 1.4.1 Force Exerted by a Stationary Spherical Shell . ................ 10 1.4.2 Force Exerted by a Linearly Accelerated Spherical Shell ................. 13 1.4.3 Force Exerted by a Spinning Spherical Shell . ............... 14 1.4.4 Cosmological Implications from the Fact that a Spherical Shell Exerts No Force on InternalBodies..................................... ... 14 1.5 TheMeanDensityoftheEarth . ........... 15 1.6 The Measurements of Inertial Mass, Time and Space . ................. 16 1.6.1 MeasurementofInertialMass. ........... 16 1.6.2 MeasurementofTime ............................. ....... 16 1.6.3 MeasurementofSpace . .. .. .. .. .. .. .. .. .. .. .. .. ........ 18 1.7 InertialFramesofReference. .............. 20 1.8 Material Frames of Reference: The Earth, the Set of Fixed Stars, and the Universal Frame of ReferenceDefinedbytheSetofGalaxies. ............ 20 2 Other Forces of Interaction between Material Bodies 25 2.1 BuoyantForceExertedbyaFluid . ............ 25 2.2 ElasticForceExertedbyaSpring. .............. 27 2.3 FrictionalForceExertedbyaFluid . ............... 29 2.4 Electrostatic Force between Electrified Bodies . .................... 31 2.5 ForcebetweenMagneticPoles. ............. 33 2.6 Ampère’s Force betweenCurrentElements. ................ 34 2.7 Force between a Magnetic Dipole and a Current Carrying Wire................. 37 2.8 Weber’sForcebetweenElectrifiedBodies . ................ 38 2.8.1 Weber’sPlanetaryModeloftheAtom . ........... 40 3 Maxwell’s Equations and the Force Acting on an Electrified Body based upon Electro- magnetic Fields 43 3.1 Multiple Definitions of the Field Concept . ................ 43 3.2 These Different Field Definitions Contradict One Another .................... 52 3.3 Maxwell’sEquations .............................. ........... 55 3.4 Force Acting on an Electrified Body based on ElectromagneticFields.............. 56 3 4 Other Topics of Classical Mechanics 57 4.1 ConservationofLinearMomentum . ............. 57 4.2 ConservationofAngularMomentum . ............. 58 4.3 CenterofMass .................................... ........ 58 4.4 Energy.......................................... ....... 59 4.4.1 KineticEnergy ................................. ....... 59 4.4.2 PotentialEnergy ............................... ........ 59 4.4.3 Relation between Force and Potential Energy . ............... 61 4.4.4 ConservationofEnergy . ......... 62 4.5 Numerical Values of Terrestrial, Planetary and CosmologicalMagnitudes. 62 II Applications of Newtonian Mechanics 67 5 Bodies at Rest Relative to the Ground 69 5.1 BodyatRest ...................................... ....... 69 5.2 BodySuspendedbyaStringorSpring . ............. 69 5.2.1 String Inclined to the Vertical when a Horizontal Force Acts on the Suspended Body . 71 5.3 VesselatRestFilledwithaFluid. .............. 72 6 Bodies in Rectilinear Motion with Constant Velocity Relative to the Ground 75 6.1 Body Sliding Relative to the Ground while Connected to a Spring ............... 75 6.2 Body Suspended by a String or by a Spring while It Slides Relative to the Ground . 77 6.3 Vessel Sliding Relative to the Ground Partially Filled withLiquid................ 77 6.4 Galileo and Newton on the Ship Experiment . ..............
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