Showing papers on "Introduction to the mathematics of general relativity published in 2013"
TL;DR: A review of the teleparallel equivalent of general relativity is presented in this paper, where the equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations.
Abstract: A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincare group.
468 citations
TL;DR: In this paper, the explicit equations of motion for nonspinning compact objects to 2.5 post-Newtonian order, or O(v/c{)}^{5}$ beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity were calculated.
Abstract: We calculate the explicit equations of motion for nonspinning compact objects to 2.5 post-Newtonian order, or $O(v/c{)}^{5}$ beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity. We use the formalism of the direct integration of the relaxed Einstein equations (DIRE), adapted to scalar-tensor theory, coupled with an approach pioneered by Eardley for incorporating the internal gravity of compact, self-gravitating bodies. For the conservative part of the motion, we obtain the two-body Lagrangian and conserved energy and momentum through second post-Newtonian order. We find the 1.5 post-Newtonian and 2.5 post-Newtonian contributions to gravitational radiation reaction, the former corresponding to the effects of dipole gravitational radiation, and verify that the resulting energy loss agrees with earlier calculations of the energy flux. For binary black holes we show that the motion through 2.5 post-Newtonian order is observationally identical to that predicted by general relativity. For mixed black-hole neutron-star binary systems, the motion is identical to that in general relativity through the first post-Newtonian order but deviates from general relativity beginning at 1.5 post-Newtonian order, in part through the onset of dipole gravitational radiation. But through 2.5 post-Newtonian order, those deviations in the motion of a mixed system are governed by a single parameter, dependent only upon the coupling constant ${\ensuremath{\omega}}_{0}$ and the structure of the neutron star, and are formally the same for a general class of scalar-tensor theories as they are for pure Brans-Dicke theory.
135 citations
TL;DR: Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity as mentioned in this paper, which in some regimes can be rewritten as nonlinear Poincar\'e algebras with momentum-dependent deformations of commutators between boosts and time translations.
Abstract: Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be rewritten as nonlinear Poincar\'e algebras with momentum-dependent deformations of commutators between boosts and time translations. In contrast to deformed special relativity, the deformations are derived for generators with an unambiguous physical role, following from the relationship between canonical constraints of gravity with stress-energy components. The original deformation does not appear in momentum space and does not give rise to nonlocality issues or problems with macroscopic objects. Contact with deformed special relativity may help to test loop quantum gravity or restrict its quantization ambiguities.
66 citations
TL;DR: In this article, the authors present a general relativistic variable Eddington tensor radiation transport equation, which is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry.
Abstract: We present conservative $3+1$ general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.
63 citations
TL;DR: Einstein regarded as one of the triumphs of his 1915 theory of gravity -the general theory of relativity -that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of general relativity supposedly violated it as mentioned in this paper.
Abstract: Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920.
34 citations
Book•
01 Jan 2013
TL;DR: The Lorentz transformation as discussed by the authors has been used for the conservation of energy-momentum and the principle of equivalence in the relation between different dimensions of spacetime. But it has not yet been applied to general relations.
Abstract: PART I: THE RELATIVISTIC WORLD 1. Basic ideas 2. The Lorentz transformation 3. Moving light sources 4. Dynamics 5. The conservation of energy-momentum 6. Further kinematics 7. Relativity and electromagnetism 8. Electromagnetic radiation PART II: AN INTRODUCTION TO GENERAL RELATIVITY 9. The Principle of Equivalence 10. Warped spacetime 11. Physics from the metric PART III: FURTHER SPECIAL RELATIVITY 12. Tensors and index notation 13. Rediscovering electromagnetism 14. Lagrangian mechanics 15. Angular momentum 16. Energy density 17. What is spacetime?
30 citations
TL;DR: In this paper, a summary of recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity is presented.
Abstract: The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide. The paper is therefore divided into three parts corresponding to the different formal methods used. 1) CARTAN VERSUS VESSIOT: The quadratic terms appearing in the " Riemann tensor " according to the " Vessiot structure equations " must not be identified with the quadratic terms appearing in the well known " Cartan structure equations " for Lie groups and a similar comment can be done for the " Weyl tensor ". In particular, " curvature+torsion" (Cartan) must not be considered as a generalization of "curvature alone" (Vessiot). Roughly, Cartan and followers have not been able to " quotient down to the base manifold ", a result only obtained by Spencer in 1970 through the "nonlinear Spencer sequence" but in a way quite different from the one followed by Vessiot in 1903 for the same purpose and still ignored. 2) JANET VERSUS SPENCER: The " Ricci tensor " only depends on the nonlinear transformations (called " elations " by Cartan in 1922) that describe the "difference " existing between the Weyl group (10 parameters of the Poincare subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined by a canonical splitting, that is to say without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly, the Spencer sequence for the conformal Killing system and its formal adjoint fully describe the Cosserat/Maxwell/Weyl theory but General Relativity is not coherent at all with this result. 3) ALGEBRAIC ANALYSIS: Contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be " parametrized ", that is the generic solution cannot be expressed by means of the derivatives of a certain number of arbitrary potential-like functions, solving therefore negatively a 1000 $ challenge proposed by J. Wheeler in 1970. Accordingly, the mathematical foundations of mathematical physics must be revisited within this formal framework, though striking it may look like for certain apparently well established theories such as electromagnetism and general relativity. We insist on the fact that the arguments presented are of a purely mathematical nature and are thus unavoidable.
25 citations
TL;DR: In this paper, a review of the initial value problem for Einstein's gravitational field theory in general relativity is presented, where the authors discuss the arguments which show that the problem is well-posed, in the sense that for any given set of initial data satisfying the Einstein constraint equations, there is a (maximal) spacetime solution of the full set of Einstein equations, compatible with the given sets of data.
Abstract: This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students who have taken a first course in general relativity, the article first discusses how to reformulate the spacetime fields and spacetime covariant field equations of Einstein's theory in terms of fields and field equations compatible with a 3+1 foliation of spacetime with spacelike hypersurfaces. It proceeds to discuss the arguments which show that the initial value problem for Einstein's theory is well-posed, in the sense that for any given set of initial data satisfying the Einstein constraint equations, there is a (maximal) spacetime solution of the full set of Einstein equations, compatible with the given set of data. The article then describes how to generate initial data sets which satisfy the Einstein constraints, using the conformal (and conformal thin sandwich) method, and using gluing techniques. The article concludes with comments regarding stability and long term behavior of solutions of Einstein's equations generated via the initial value problem.
23 citations
TL;DR: In this article, the authors reformulate the general theory of relativity in the language of Riemann-Cartan geometry, and they show that the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field.
Abstract: We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.
22 citations
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TL;DR: The Einstein tensor is derived from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system and naturally contains essential information of the energy-momentum tensor of a classical scalar field.
Abstract: We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system. We find that the tensor naturally contains essential information of the energy-momentum tensor of a classical scalar field, when the entropy data or the spectrum data of the system are embedded into the classical field as the field strength. Thus, we can regard the Einstein equation as the equation of coarse-grained states for the original microscopic system behind the classical field theory. We make some remarks on quantization of gravity and various quantum-classical correspondences.
12 citations
TL;DR: In this paper, the authors proposed generalized Bondi-Sachs equations for Cauchy-characteristic matching (CCM) to solve the problem of the inner caustics in the inner near zone.
Abstract: The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.
TL;DR: In this paper, the authors focus on the numerical solution of elliptic partial differential equations, which arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes.
Abstract: Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here, we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise.
TL;DR: In this article, the modified equations for Newton's law of gravitation, modified Newtonian dynamics and Einstein's general relativity were derived, considering the effects of generalized uncertainty principle in the black hole entropy-area relation.
Abstract: With Verlinde's recent proposal which says that gravity can be identified with an entropic force and considering the effects of generalized uncertainty principle in the black hole entropy-area relation we derive the modified equations for Newton's law of gravitation, modified Newtonian dynamics and Einstein's general relativity. The corrections to the Newtonian potential is compared with the corrections that come from Randall-Sundrum II model and an effective field theoretical model of quantum general relativity. The effect of the generalized uncertainty principle introduces a $\sqrt{\text{Area}}$ type correction term in the entropy area relation whose consequences in different scenarios are discussed.
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TL;DR: For a spacelike 2-surface in spacetime, the authors proposed a new definition of quasi-local angular momentum and center of mass as an element in the dual space of the Lie algebra of the Lorentz group.
Abstract: For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined quasi-local energy-momentum, this completes the definition of conserved quantities in general relativity at the quasi-local level. We justify this definition by showing the consistency with the theory of special relativity and expectations on an axially symmetric spacetime. The limits at spatial infinity provide new definitions for total conserved quantities of an isolated system, which do not depend on any asymptotically flat coordinate system or asymptotic Killing field. The new proposal is free of ambiguities found in existing definitions and presents the first definition that precisely describes the dynamics of the Einstein equation.
01 Jan 2013
TL;DR: The solution of the field equations, which describes the field outside of a spherically symmetric mass distribution, was found by Karl Schwarzschild only two months after Einstein published his field equations.
Abstract: The solution of the field equations, which describes the field outside of a spherically symmetric mass distribution, was found by Karl Schwarzschild only two months after Einstein published his field equations Schwarzschild performed this work under rather unusual conditions In the spring and summer of 1915 he was assigned to the eastern front There he came down with an infectious disease and in the fall of 1915 he returned seriously ill to Germany He died only a few months later, on May 11, 1916 In this short time, he wrote two significant papers, in spite of his illness One of these dealt with the Stark effect in the Bohr-Sommerfeld theory, and the other solved the Einstein field equations for a static, spherically symmetric field From this solution he derived the precession of the perihelion of Mercury and the bending of light rays at the surface of the sun Einstein had calculated these effects previously, by solving the field equations in the post-Newtonian approximation
TL;DR: In this article, the authors discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem and in the context of the recently launched LAser RElativity Satellite (LARES).
Abstract: According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem, and in the context of the recently launched LAser RElativity Satellite (LARES). Being possibly the highest mean density orbiting body in the Solar system, this satellite provides the best realization of a test particle ever reached experimentally and provides a unique possibility for testing the predictions of General Relativity.
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TL;DR: In this article, the authors introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds having the corresponding smoothness properties.
Abstract: We introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds having the corresponding smoothness properties.
TL;DR: In this paper, the authors investigated spacetimes in which the energy-momentum tensor obeys a linear constraint and derived an exact solution for a wide variety of compact objects, among them black holes and wormholes.
Abstract: The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane world scenarios. In this paper we investigate spacetimes in which the energy-momentum tensor obeys a linear constraint. Extensions of the usual vacuum and electrovacuum solutions of general relativity are derived and an exact solution is presented. The classes of geometries obtained include a wide variety of compact objects, among them black holes and wormholes. The general metric derived in this work generalizes several solutions already published in the literature. Perturbations around the exact solution are also considered.
TL;DR: In this paper, a theory of (N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR), where the fundamental gravitational field variables are the (N + 1)-dimensional vector fields, defined globally on a manifold M, and the gravitational field is attributed to the torsion.
Abstract: A theory of (N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR). The fundamental gravitational field variables are the (N+1)-dimensional vector fields, defined globally on a manifold M, and the gravitational field is attributed to the torsion. The form of Lagrangian density is quadratic in torsion tensor. We then give an exact five-dimensional spherically symmetric solution (Schwarzschild (4+1)-dimensions). Finally, we calculate energy and spatial momentum using gravitational energy—momentum tensor and superpotential 2-form.
Book•
09 Jul 2013
TL;DR: In this paper, the equivalence principle in action was used to solve the Einstein Equation of Gravity and General Relativity in action. But it was not shown to be applicable to our case.
Abstract: 1 Light, Matter, and Energy.- 2 Light, Time, Mass, and Length.- 3 Light, Electricity, and Magnetism.- 4 Acceleration and Inertia.- 5 Inertia and Gravity..- 6 Equivalence Principle in Action.- 7 How Mass Creates Gravity.- 8 Solving the Einstein Equation of Gravity.- 9 General Relativity in Action.- 10 Epilogue.- 11 Appendix.
01 Jan 2013
TL;DR: In this article, Bejancu et al. obtained the 4D-Einstein equations in a general (5D) Kaluza-Klein space with electromagnetic potentials.
Abstract: Based on the new point of view on space–time–matter theory developed in our paper (Bejancu, Gen Rel Grav, 2013), we obtain the \(4D\) Einstein equations in a general \(5D\) Kaluza–Klein space with electromagnetic potentials. In particular, we recover the \(4D\) Einstein equations obtained by Wesson and Ponce de Leon (J Math Phys 33:3883, 1992) in case the electromagnetic potentials vanish identically on \(\bar{M}\). The Riemannian horizontal connection and the \(4D\) tensor calculus on \(\bar{M}\), are the main tools in the study.
02 Oct 2013
TL;DR: Thesis as discussed by the authors, Ph.D, Physics, Engineering Physics and Astronomy, Queen's University, 2013-09-30 14:02:55.865, 2013
Abstract: Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-30 14:02:55.865
TL;DR: In this article, it was shown that for n ≥ 3 dimensions, the vanishing holds for the pseudo-tensor when extended to n spatial dimensions, and the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified.
Abstract: It was noted earlier that the general relativity field equations for
static systems with spherical symmetry can be put into a linear form when the
source energy density equals radial stress. These linear equations lead to a
delta function energymomentum tensor for a point mass source for the
Schwarzschild field that has vanishing self-stress, and whose integral
therefore transforms properly under a Lorentz transformation, as though the
particle is in the flat space-time of special relativity (SR). These findings
were later extended to n spatial
dimensions. Consistent with this SR-like result for the source tensor,
Nordstrom and independently, Schrodinger, found for three spatial dimensions
that the Einstein gravitational energy-momentum pseudo-tensor vanished in
proper quasi-rectangular coordinates. The present work shows that this
vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is
further justified; 2) the Tolman expression for the mass of a static, isolated system is
generalized to take into account the dimensionality of space for n ≥ 3.
TL;DR: In this article, the B(3) field tensor is shown to be a sub-structure of the Lie group of general relativity and the basic structure of O(3)-electrodynamics.
Abstract: By considering the irreducible representations of the Einstein group (the Lie group of general relativity), Sachs [1] has shown that the electromagnetic field tensor can be developed in terms of a metric qμ, which is a set of four quaternion-valued components of four-vector. Using this method, it is shown that the electromagnetic field vanishes [1] in flat spacetime, and that electromagnetism in general is a non-Abelian field theory. In this paper the non-Abelian component of the field tensor is developed to show the presence of the B(3) field of the O(3) electrodynamics, and the basic structure of O(3) electrodynamics is shown to be a sub-structure of general relativity as developed by Sachs. The extensive empirical evidence for both theories is summarized.
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TL;DR: The first three sections of this article contain a broad brush summary of the profound changes in the notion of time in fundamental physics that were brought about by three revolutions: the foundations of mechanics distilled by Newton in his Principia, the discovery of special relativity by Einstein and its reformulation by Minkowski, and, finally, the fusion of geometry and gravity in Einstein's general relativity.
Abstract: The first three sections of this article contain a broad brush summary of the profound changes in the notion of time in fundamental physics that were brought about by three revolutions: the foundations of mechanics distilled by Newton in his Principia, the discovery of special relativity by Einstein and its reformulation by Minkowski, and, finally, the fusion of geometry and gravity in Einstein's general relativity. The fourth section discusses two aspects of yet another deep revision that waits in the wings as we attempt to unify general relativity with quantum physics.
TL;DR: In this paper, by adding a constant to the Einstein-Hilbert action, the authors derived field equations for a non-vacuum space and derived a general solution for these field equa- tions, considering a de Sitter like initial geometric constraint.
Abstract: In this article, by adding a constant to Einstein-Hilbert action, we derive field equations for a non-vacuum space. Also we derive a general solution for these field equa- tions, considering a de Sitter like initial geometric constraint. It is shown that how this addi- tional constant can affect usual gravitational field equations, which are derived from general relativity.
TL;DR: The Neo-classical Theory of Relativity as mentioned in this paper uses concepts of Classical Mechanics and Classical Electromagnetism to describe the relativity of inertial motion better than it is described in the special theory of relativity conceived by Albert Einstein in 1905.
Abstract: The Neo-classical Theory of Relativity uses concepts of Classical Mechanics and Classical Electromagnetism to describe the relativity of inertial motion better than it is described in the Special Theory of Relativity conceived by Albert Einstein in 1905.
01 Oct 2013
TL;DR: The main credit for the work on relativity which resolved these problems is usually attributed to Albert Einstein, and the first half of this article will focus primarily on the particular line of thinking which led him to the discovery of what is now called special relativity theory as discussed by the authors.
Abstract: In 1900 the field theory of electromagnetism, which owes it origins primarily to the work of James Clerk Maxwell, had been under rapid development for two decades. In the 1880s a number of British physicists, beginning with Oliver Heaviside, had developed Maxwell’s work into a successful body of theory which was able to explain a number of important features of electrodynamics. During the 1890s this new theory encountered some difficulties which, as Jed Buchwald (1985) has shown, were connected with the earlier theory’s inattention to the physical nature of the sources of the field, the moving charges themselves. This directed attention towards problem of microphysics and the nature of the electron and towards a theory of electromagnetism which focused on the reality of charged particles as agents of the field. This was accompanied by a geographical shift away from Britain, whose leading figures came to play a less important role in the development of the theory, to the continent, in particular to Holland and the German speaking areas of Europe. The new continental theory had important successes, which inspired a hope that was expressed in the term electromagnetic world-view, that all physical phenomena would be expressible in terms of the electromagnetic field. In spite of major achievements by Hertz, Lorentz and others, the new theory still found itself troubled by a number of issues, several of which are now seen to have had a common origin in the subject of relativity theory, and how the new electromagnetic theory was to be reconciled with it. The chief credit for the work on relativity which resolved these problems is usually accorded to Albert Einstein, and the first half of this article will focus primarily on the particular line of thinking which led him to the discovery of what is now called special relativity theory. The contributions of others, particularly Lorentz and Henri Poincare, will not be neglected, but the adoption of a schema based on the structure of Einstein’s theory, while justified by his enormous influence on subsequent research, will inevitably force their contributions into a framework which was not