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Breaking in the 4vectors: the fourdimensional movement ingravitation,1905–1910.InJürgenRenn, editor, The Genesis of General Relativity
, 2007
"... The law of gravitational attraction is a window on three formal approaches to laws of nature based on Lorentzinvariance: Poincaré’s fourdimensional vector space (1906), Minkowski’s matrix calculus and spacetime geometry (1908), and Sommerfeld’s 4vector algebra (1910). In virtue of a common appeal ..."
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The law of gravitational attraction is a window on three formal approaches to laws of nature based on Lorentzinvariance: Poincaré’s fourdimensional vector space (1906), Minkowski’s matrix calculus and spacetime geometry (1908), and Sommerfeld’s 4vector algebra (1910). In virtue of a common appeal to 4vectors for the characterization of gravitational attraction, these three contributions track the emergence and early development of fourdimensional physics.
Polymorphic information processing in weaving computation: An approach through cloth geometry
, 2011
"... Abstract: This report extends the scope of computation with a non standard × to the more basic case of a non standard +, where standard means associative and commutative. Two physically meaningful examples of a nonstandard + are provided by the observation of motion in Special Relativity, from eithe ..."
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Abstract: This report extends the scope of computation with a non standard × to the more basic case of a non standard +, where standard means associative and commutative. Two physically meaningful examples of a nonstandard + are provided by the observation of motion in Special Relativity, from either outside (3D) or inside (2D or more), We revisit the “gyro”theory of Ungar to present the polymorphic information processing which is created by cloth geometry, a relating computational construct framed in a normed vector space, and based on a non standard ◦+ whose commutativity and associativity are ruled (woven) by a relator.
The Relativistic CompositeVelocity Reciprocity Principle
, 2000
"... Gyrogroup theory [A.A. Ungar, Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Found. Phys. 27 (1997), pp. 881951] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vecto ..."
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Gyrogroup theory [A.A. Ungar, Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Found. Phys. 27 (1997), pp. 881951] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by exposing the Relativistic CompositeVelocity Reciprocity Principle. The breakdown of commutativity in the Einstein velocity addition # of relativistically admissible velocities seemingly gives rise to a corresponding breakdown of the relativistic compositevelocity reciprocity principle, since seemingly (i) on one hand the velocity reciprocal to the composite velocity u#v is (u#v) and (ii) on the other hand it is (v)#(u). But, (iii) (u#v) #= (v)#(u). We remove the confusion in (i), (ii) and (iii) by employing the gyrocommutative gyrogroup structure of Einstein's addition and, subsequ...
and its Applications In Honor of Stephen Smale’s 80th Birthday 123 Editors
"... the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or ..."
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the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for
On the FueterLanczos Conditions
"... ABSTRACT. We show that the Maxwell equations in vacuum and the Dirac equation without the mass term are special cases of the FueterLanczos conditions. ..."
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ABSTRACT. We show that the Maxwell equations in vacuum and the Dirac equation without the mass term are special cases of the FueterLanczos conditions.
Ritz, Einstein, and the Emission Hypothesis
"... Just as Albert Einstein’s special theory of relativity was gaining acceptance around 1908, the young Swiss physicist Walter Ritz advanced a competing though preliminary emission theory that sought to explain the phenomena of electrodynamics on the assumption that the speed of light depends on the mo ..."
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Just as Albert Einstein’s special theory of relativity was gaining acceptance around 1908, the young Swiss physicist Walter Ritz advanced a competing though preliminary emission theory that sought to explain the phenomena of electrodynamics on the assumption that the speed of light depends on the motion of its source. I survey Ritz’s unfinished work in this area and review the reasons why Einstein and other physicists rejected Ritz’s and other emission theories. Since Ritz’s emission theory attracted renewed attention in the 1960s, I discuss how the earlier observational evidence was misconstrued as telling against it more conclusively than actually was the case. Finally, I contrast the role played by evidence against Ritz’s theory with other factors that led to the early rejection of his approach.
This is page 1 Printer: Opaque this Applications of Clifford Algebras in Physics
"... ABSTRACT Clifford’s geometric algebra is a powerful language for physics that clearly describes the geometric symmetries of both physical space and spacetime. Some of the power of the algebra arises from its natural spinorial formulation of rotations and Lorentz transformations in classical physics. ..."
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ABSTRACT Clifford’s geometric algebra is a powerful language for physics that clearly describes the geometric symmetries of both physical space and spacetime. Some of the power of the algebra arises from its natural spinorial formulation of rotations and Lorentz transformations in classical physics. This formulation brings important quantumlike tools to classical physics and helps break down the classical/quantum interface. It also unites Newtonian mechanics, relativity, quantum theory, and other areas of physics in a single formalism and language. This lecture is an introduction and sampling of a few of the important applications in physics.