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" The Principles of Electromagnetic Theory and of Relativity. "
Tonnelat, M.
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BL
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774542
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b594537
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| Main Entry
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Tonnelat, M.
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| Title & Author
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The Principles of Electromagnetic Theory and of Relativity.\ Tonnelat, M.
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| Publication Statement
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Springer Verlag, 2013
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| ISBN
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9401035504
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: 9789401035507
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| Contents
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Preface.- One/Electromagnetic Theory.- I/Electrostatics.- 1. The experimental laws. Coulomb's law.- 2. The general laws of electrostatics.- 3. The first law. Gauss' theorem.- 4. Applications. The electric field on the surface of a conductor. Electrostatic pressure.- 5. The second law. Definition of the potential.- 6. The solutions of Laplace's and Poisson's equations.- 7. Poisson's equation and boundary conditions.- 8. Applications.- 9. Dielectrics.- 10. Dielectrics and dipoles.- 11. Polarization and displacement.- II/Magnetostatics.- 1. Permanent states. The experimental law of Biot and Savart.- 2. The general laws of magnetism.- 3. Magnetic dipoles.- 4. Magnetic media.- 5. The magnetic moment of a layer. Magnetic permeability and susceptibility.- III/Electromagnetism.- A. Electromagnetic Induction. Displacement Current.- 1. Faraday's experimental law.- 2. Conduction current. Displacement current.- B. Maxwell's Equations.- 3. Systems of units.- 4. Basic relations.- 5. The potential.- 6. Equations of propagation. Retarded potentials.- C. Electromagnetic Energy. Energy Flux.- 7. Electric and magnetic energy densities.- 8. Poynting vector and Poynting's theorem.- D. Electromagnetic Waves.- 9. Equations for the propagation of fields.- 10. Plane waves.- 11. Wave-trains.- 12. Spherical waves.- E. Electromagnetic Equations Valid for Non-Magnetic Bodies in Slow Motion.- 13. Application of Maxwell's theory to moving media.- 14. Motion of a conductor or an insulator in an electric field.- 15. Displacement of a conductor or an insulator in a magnetic field.- 16. Hertz' and Lorentz' hypotheses.- IV/Sources of the Electromagnetic Field. Lorentz' Theory.- 1. "Microscopic" fields and potentials connected with an electron.- 2. "Structure" of the Lorentz electron.- 3. Potentials and fields created by a distribution of electrons.- 4. Equations for the mean values and Maxwell's macroscopic theory.- 5. Interpretation of the fields and the inductions of Maxwell's theory. Electromagnetic equations for the case of matter at rest.- 6. Lorentz' theory and electrodynamics of moving bodies.- Two/Special Relativity.- V/The Principle of Relativity.- A. The Principle of Relativity before Einstein.- 1. The principle of relativity in classical mechanics.- 2. The principle of relativity in electrodynamics.- 3. Experimental possibilities of detecting absolute motion by optical means.- 4. First-order effects. The hypothesis of a partial dragging of light by transparent bodies.- 5. Lorentz's theory of electrons and first-order effects. The hypothesis of a motionless ether.- 6. Second-order effects.- 7. The Fitzgerald-Lorentz hypothesis.- B. The Principle of Special Relativity.- 8. Einstein's basic postulate.- 9. Critique of the concept of simultaneity.- 10. The Lorentz transformation.- 11. Consequences of the transformation formulas.- 12. Proper time.- 13. Geometrical representation of the Lorentz formulas.- 14. Other expressions of the special Lorentz transformation.- 15. The general Lorentz transformation. C. Moller's method.- 16. Change of inertial system for a moving object. The clock paradox.- VI/Four-Dimensional Formalism of Special Relativity.- 1. The pseudo-Euclidean universe of Special Relativity.- 2. Notational conventions.- 3. Reduced forms of the ds2 in Special Relativity.- 4. Space-like four-vectors. Time-like four-vectors. Isotropie four-vectors.- 5. The invariance of the ds2 under the displacement group in four-dimensional Euclidean space.- 6. The general Lorentz transformation and the special transformation.- 7. Expression of the coefficients in the general Lorentz transformation.- 8. Application to the special Lorentz transformation.- 9. Examples.- 10. The addition of velocities and the general Lorentz transformation.- 11. Application. Case where one of the systems is a proper system.- VII/Relativistic Kinematics.- A. Relativistic Law of Addition of Velocities.- 1. The velocity four-vector.- 2. The modification of velocities in a Lorentz transformation.- 3. The Lorentz transformation and the general formula for the addition of velocities.- 4. Length and direction of the velocity vector.- 5. The limiting velocity.- 6. Asymmetry of the parts played by the "relative" velocity and the "coordinate displacement velocity".- 7. The special case of the addition of parallel velocities.- B. Wave Propagation and Relativistic Kinematics.- 8. Propagation of a plane wave in refractive media moving uniformly with respect to each other.- 9. Huygens' principle and Special Relativity 198 10. Phase velocity and propagation velocity.- VIII/Relativistic Dynamics.- A. Relativistic Dynamics of a Point-Mass.- 1. Momentum, energy and proper mass of a particle.- 2. Minkowski force. The basic law of relativistic dynamics.- 3. Equivalence of mass and energy.- 4. Modification of velocities and basic quantities (momentum, energy, force) of dynamics in a Lorentz transformation.- 5. Systems of free particles.- 6. Systems of bound particles.- B. The Relativistic Dynamics of Continuous Media.- 7. The non-relativistic equations of a fluid in a system of orthogonal coordinates.- 8. The relativistic equations of a continuous medium.- 9. The material energy-momentum tensor.- 10. The case of a perfect fluid.- C. Use of Curvilinear Coordinates.- 11. Trajectory of a material point expressed in any arbitrarily chosen system of coordinates.- 12. The basic law of the dynamics of a point.- 13. Motion of a homogeneous fluid. The matter tensor.- 14. Equations of conservation and equations of motion.- 15. A special case: the equations of conservation and of motion for a perfect fluid.- IX/Relativistic Electromagnetism.- A. The Covariant Form of Maxwell's Theory.- 1. The electromagnetic field, a tensor of second rank.- 2. The electromagnetic potential.- 3. Maxwell's equations and the general Lorentz transformation.- 4. The Lorentz electron theory. The energy momentum tensor.- 5. Lorentz equations and Maxwell's equations.- 6. The energy-momentum tensors.- 7. Use of arbitrary curvilinear coordinates.- B. Extensions of Maxwell's Theory.- 8. The deduction of Maxwell's equations from a variational principle.- 9. Mie's Theory 267 10. The theory of M. Born and L. Infeld.- X/The Experimental Verifications of Special Relativity.- A. The Retardation of Moving Clocks.- 1. The theory of the Doppler effect and the slowing-down of clocks.- 2. Ives and Stillwell's experiments (1941).- 3. The mean lifetime of mesons.- B. The Variation of Mass with Velocity.- 4. The motion of a charged particle in an electromagnetic field.- 5. The deviation of charged particles subjected to the action of parallel electric and magnetic fields perpendicular to the initial velocity of the particles.- 6. The elastic collision of two particles.- 7. The Compton effect.- C. The Equivalence of Mass and Energy.- 8. Mass defect and nuclear energy.- 9. The balance of energy and momentum in nuclear reactions.- Three/General Relativity.- XI/General Relativity.- A. The Newtonian Law of Gravitation.- 1. The Newtonian law of gravitation and observational data.- 2. The gravitational potential and its properties. The equivalence of gravitational mass and inertial mass.- 3. Poisson's law.- 4. Newton's law and the principle of Special Relativity.- B. The Principle of Equivalence and the Introduction of a Non-Euclidean Universe.- 5. Accelerated reference systems and "fictitious" inertial forces. The limits of the principle of Special Relativity.- 6. The local equivalence of gravitational and inertial forces.- 7. Introduction of a non-Euclidean universe.- 8. Study of a special case: the problem of the rotating disc.- C. Einstein's Law of Gravitation.- 9. The law of gravitation outside matter.- 10. The law of gravitation inside matter or in the presence of an electromagnetic field.- 11.
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The trajectories of a particle subjected to a gravitational field are the geodesics of a Riemannian space.- XII/The Development of General Relativity and Some of Its Consequences.- A. The Equations in Various Approximations.- 1. The gravitational potential in the Newtonian approximation.- 2. The equations of the gravitational field in a system of De Donder and quasi-Galilean coordinates.- 3. Application to a continuous material medium treated as a perfect gas.- 4. Equations of the exterior case.- 5. Equations of the field and motion of the sources.- B. Study of a Rigorous but Special Solution of the Field Equations: Schwarzschild's Solution.- 6. The gravitational field created in the neighbourhood of a static mass possesssing spherical symmetry.- 7. The field created in the neighbourhood of a spherically symmetric charged particle.- 8. The trajectory of a neutral particle in the neighbourhood of a static mass having spherical symmetry.- 9. The experimental verifications of Schwarzschild's solution.- XIII/Unified Theories of Electromagnetism and Gravitation Characteristics of a Pure Field Theory Unified theories and Non-Dualistic Theories.- A. Unified Theories.- 1. Unified theories until the advent of General Relativity.- 2. General Relativity and the construction of unified theories.- 3. Interpretation of the electromagnetic and gravitational fields proposed by unified theories.- 4. Classical unified theories and the possibilities of further predictions.- 5. Unified theories and quantum theories.- B. Non-Dualistic Theories.- 6. The field and its sources.- 7. Non-linearity and the characteristics of a pure field theory.- C. Unified and Non-Dualistic Theories.- Four/Mathematical Supplement.- XIV/Tensor Calculus In An Euclidean Vector Space.- A. Rectilinear Axes.- 1. Covariance and contravariance.- 2. The norm of a vector. The scalar product of two vectors.- 3. Transformation of rectilinear axes.- 4. Invariants, four-vectors and tensors.- 5. Symmetry and antisymmetry.- 6. Transformation of the metric tensor. A special case : Utilization of orthogonal frames of reference.- 7. The rotations of axes in a four-dimensional Euclidean space.- B. Use of Arbitrary Curvilinear Coordinates.- 8. Passage from one system of curvilinear coordinates to another in an Euclidean vector space.- 9. Differential relations between the components of the metric tensor.- 10. Covariant differentiation.- 11. Tensor densities.- XV/Tensor Calculus in a Non-Euclidean Metric Manifold. Application to a Riemannian Space.- 1. Metric space and tangent Euclidean space.- 2. Affine connection.- 3. Representation of the first order.- 4. Representation of the second order.- 5. Vectors and tensors associated with a metric manifold.- 6. Covariant derivation.- 7. The parallel transport of a vector.- 8. The conditions of integrability and the structure of space.- 9. The curvature of Riemannian space. The Riemann-Christoffel tensor.- 10. Properties of the Riemann-Christoffel tensor.- 11. The geodesics of Riemannian space as analogues of the straight lines of Euclidean space.
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QC670.T666 2013
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| Added Entry
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Tonnelat, M.
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