gravitational source Lorentz model of a field theory Maxwell's equations constrained motion Hamilton, William Rowan variational formalism energy-momentum conservation electric field electromagnetic induction equivalence principle continuum mechanics Poincaré, Henri Lorentz's auxiliary variables Hopf, Ludwig general covariance magnetic field Kaluza-Klein theory six-vector electric charge invisible mechanism Minkowski spacetime formalism Minkowski, Hermann de Sitter, Willem Zangger, Heinrich Entwurf Lagrangian Ricci-Curbastro, Gregorio differential invariants of a quadratic differential form gravitational constant Weyl, Hermann electrodynamic worldview electromagnetic theory of matter Lagrange multiplier statistical mechanics Mach, Ernst energy-momentum density Klein, Felix Born, Max Mach's bucket inertial interactions Riemann tensor astronomy rotation torsion elevator model frame of reference Ritz, Walter equipartition theorem Einstein, Albert Lanczos, Cornelius mathematical approach Copernicus process thermodynamics atomism intuitive mechanics kinetic theory of heat aether Lorentz transformations Newtonian laws inertial motion Droste, Johannes Witting, Alexander action, principle of least dielectric medium light Frank, Michael hyperbolic motion Hertz, Heinrich Lagrange, Joseph-Louis curved-surface model d'Alembert, Jean-Baptiste le Rond causality Pythagorean theorem Aristotle heaviness-causes-fall model affine connection substantivalism relationalism Mach's principle Hertz, Paul Petzoldt, Joseph Planck, Max time spacetime mass chunking, mental cognitive science Legendre transformation θ -transformation transformation Euler-Lagrange equations Hamiltonian function Lagrange equation Entwurf strategy Hamilton's equation Hamilton's principle analytical mechanics covariance quadratic form Lipschitz, Rudolf Kottler, Friedrich Bernays, Paul differential geometry context of justification context of discovery unified field theory Gauss, Carl Friedrich Coolidge, Julian Lowell Geiser, Carl Friedrich Monge, Gaspard Levi-Civita, Tullio world parameter Fokker, Adriaan D. Christoffel, Elwin Bruno Wien, Wilhelm point-coincidence argument curved-spacetime model constrained motion model Euler, Leonard Euclidean space, three-dimensional Maxwell, James Clerk elasticity theory energy density momentum density stresses hydrodynamics cosmology Lagrange formalism θ -reduced November tensor Galileo's principle Cartan, Elie trace term plane tensor point tensor Habicht, Conrad redshift in a gravitational field gravitational lens ray optics exterior derivative two-step procedure divergence Grassmann, Hermann point vector Hertz expression Euclidean metric plane vector dust, pressureless geodesic line force-free motion gravitational force Marx, Erich anti-symmetry Budde, Emil Komar, Arthur Bergmann, Peter Gabriel Minkowski spacetime epistemic paradoxes projectile motion Riemannian geometry Nordström, Gunnar Broglie, Louis de aberration, stellar vector Christoffel symbol Noether's theorem absolute differential calculus Thirring, Hans Lorentz contraction laboratory model Michelson and Morley experiment velocity addition Fresnel, Augustin Jean Young, Thomas Stokes, George Gabriel Bradley, James Fizeau experiment electric force chrono-geometry Hilbert, David Lie variation Noether, Emmy Runge, Carl symmetries and conservation laws Schrödinger, Erwin Freundlich, Erwin inertia Naumann, Otto Voigt, Woldemar Landau, Eduard de Donder, Théophile Winteler, Jost Einstein-Besso manuscript gravitation Stark, Johannes Grossmann, Marcel Riemann curvature scalar Besso, Michele Hamiltonian formulation of general relativity Entwurf field equations tensor analysis Kollros, Louis differential parameter gravitational stress-energy density energy-momentum expression of the gravitational field Bianchi identities November tensor Entwurf operator Gauss's theorem covariant divergence covariant derivative invariants of the fundamental form, algebraic and differential Riemann, Bernhard θ^ -expression θ -expression restriction θ^ -restriction Levi-Civita tensor θ -restriction heuristic principle Poisson equation classical mechanics motion-implies-force model acceleration-implies-force model Lorentz invariance coordinates equation of motion coordinate condition Entwurf theory coordinate transformation Newton's bucket Coulomb's law electrodynamics rigid body gravitational induction gravitational waves Kretschmann, Erich Lorentz gauge gauge condition electromagnetic six-vector electrodynamic potential gauge transformation Laue, Max von force force-implies-motion model electrostatic potential four-vector Kaluza, Theodor Faraday, Michael Oerstedt, Hans Christian Ampère, André-Marie mental model rotating disk Ehrenfest paradox Wright, Joseph Edmund Ricci tensor correspondence principle Newtonian limit Einstein tensor correction term gravitational field equation Ehrenfest, Paul Sommerfeld, Arnold Lorentz, Hendrik Antoon world system preclassical mechanics Newtonian mechanics special theory of relativity borderline problems Abraham, Max Nordström's theory of gravitation energy Newtonian theory of gravitation Newtonian potential slow-motion approximation Bianchi, Luigi Minkowski metric variational principle clocks and rods simultaneity Poisson, Henri action at a distance gravitational field Newtonian spacetime gravitational potential centrifugal force Coriolis force hole argument relativity principle classical physics epistemology, historical optics mechanics continuity condition energy-momentum tensor Beltrami invariants core operator weak-field approximation cosmological constant Mercury, perihelion motion of line element curvature Lagrangian d'Alembertian operator coordinate restriction acceleration electromagnetic field charge-current density default assumption Laplace operator θ -metric metric vacuum heuristic strategy perihelion paper vector analysis of the action of energy relativity of special relativity and unimodular of the weak-field metric weak field of a system with inertial forces geometry Kyoto lecture ellipsoid forNovember theory spacetime formalism analogy with Maxwell's equations trace of the laws and principles stationary approximate solution to uniform charity principle Einstein-Grossmann theory of gravitation for weak static fields in rotating coordinates theoretical Beltrami, Eugenio manifold of spacetime calculus metric theory of gravitation of moving bodies dynamical equivalence to energy gravitational and inertial curvilinear bucket model integration of mental models heuristics clock relation to vanishing divergence of stress-energy tensor aether as generalized relativity principle and heat radiation isothermal in Newtonian physics non-linear model non-autonomous of a tensor integration absolute inertial system law of heat radiation due to gravity line point density energy-momentum conservation and validity of comoving inertial foundational problems of generalized Schwarzschild, Karl Frauenfeld lecture Besso memo role in the constitution of matter Maxwellian character of of a single mass point kinematics of absolute space correspondence principle and acting on material point at rest aether model of binary gravitational definition of extension of admissible analogy to electrodynamics Coriolis field Oppolzer, Theodor Egon von electromagnetic behavior of special relativistic of Newtonian gravitational theory Gaussian theory of matter of the sun Mari¶, Mileva equation θ -equation Maxwell's harmonic conservation formulation of the equation of motion for a static field structural identity in Entwurf theory and general relativity justified for the free Maxwell field cosmic Wolfskehl lecture tensor as curvature of spacetime connection with energy-momentum conservation conservation principle and motion geodesic mathematical strategy linearized of the metric tensor image of physical meaning generalized operator components deflection in a gravitational field Lagrange formalism and infinitesimal in the theory of gravitation Hertz four-acceleration fateful prejudice for weak fields as the divergence of gravitational energy-momentum density opportunist streak in his modus operandi deflection of light in from energy-momentum conservation Lorentz's electrodynamics equality of active and passive gravitational integrability condition in accelerated frames of reference Vienna lecture inertial force non-Euclidean Newton, Sir Isaac of a field equation double strategy transferred from gravitational field to matter for the electromagnetic field for rotation inertial points, individuation of transformation of acting as its own source for general relativity of a system with gravitational force emission theory of rotating analysis resources of accelerated motion of ponderomotive magnetic for a static gravitational field physical strategy kinetic compatibility with gravito-inertial structure active hydrogen atom linear of a particle determinant of gravitation and practical velocity of light static in an epistemological formulation in special relativity wave theory of of ray optics non-locality of of matter account of rotation Lorentz field theory keyword molecular gravitational mass of restriction of Herbert Spencer lecture four-dimensional revision of the concept of bending of light in Minkowski spacetime accelerated frame of reference relation between definitions critique of mechanics velocity of constitution of inertia and of classical physics Euclidean matter connection with covariance rotating frame of reference trace centrifugal linear orthogonal general linear uniformly rotating law of lecture notes on mechanics Mie, Gustav spatial architecture of Coriolis deflection for mechanics and coincidence homogeneous of space and time measurements algebraic ether of the metric covariant dynamics Cartesian perihelion problem shared in classical physics electromagnetic theory intuitive Entwurf paper spacetime manifold gravitating of closed systems relativized second law dynamics of stress-energy tensor Lorentz's weak key to the “solution” gravitational tensor of a rotating bucket general covariance and in unimodular coordinates for Entwurf theory rigidity condition motion along a surface for pressureless dust relative existence of symmetric knowledge hypothesis of corpuscular quanta interaction with light adapted rotational theory of surfaces analogy to general relativity aether-drag hypothesis uniqueness problem for solutions of field equations autonomous