[...]... postulates 1.11 Cosmology and first doubts about inertial frames 1.12 Inertial and gravitational mass 1.13 Einstein’s equivalence principle 1.14 Preview of general relativity 1.15 Caveats on the equivalence principle 1.16 Gravitational frequency shift and light bending Exercises 1 3 3 4 5 6 7 9 9 10 12 14 15 16 18 20 22 24 27 I Special Relativity 31 2 Foundations of special relativity; The Lorentz transformation... This page intentionally left blank 1 From absolute space and time to influenceable spacetime: an overview 1.1 Definition of relativity At their core, Einstein’s relativity theories (both the special theory of 1905 and the general theory of 1915) are the modern physical theories of space and time, which have replaced Newton’s concepts of absolute space and absolute time by spacetime We specifically call Einstein’s... of special relativity; The Lorentz transformation 2.1 On the nature of physical theories 2.2 Basic features of special relativity 2.3 Relativistic problem solving 2.4 Relativity of simultaneity, time dilation and length contraction: a preview 2.5 The relativity principle and the homogeneity and isotropy of inertial frames 2.6 The coordinate lattice; Definitions of simultaneity 2.7 Derivation of the Lorentz... Riemannian spaces 8.4 A plan for general relativity Exercises 8 165 165 169 172 177 180 9 Static and stationary spacetimes 9.1 The coordinate lattice 9.2 Synchronization of clocks 9.3 First standard form of the metric 9.4 Newtonian support for the geodesic law of motion 9.5 Symmetries and the geometric characterization of static and stationary spacetimes 9.6 Canonical metric and relativistic potentials... Introduction 1 1 From absolute space and time to influenceable spacetime: an overview 1.1 Definition of relativity 1.2 Newton’s laws and inertial frames 1.3 The Galilean transformation 1.4 Newtonian relativity 1.5 Objections to absolute space; Mach’s principle 1.6 The ether 1.7 Michelson and Morley’s search for the ether 1.8 Lorentz’s ether theory 1.9 Origins of special relativity 1.10 Further arguments... in physics, relativity meant the abolition of absolute space—a quest that had been recognized as desirable ever since Newton’s days And this is indeed what Einstein’s two theories accomplished: special relativity (SR), the theory of flat spacetime, abolished absolute space in its Maxwellian role as the ‘ether’ that carried electromagnetic fields and, in particular, light waves, while general relativity. .. reference frames S and S in uniform relative motion with velocity v Let identical units of length and time be used in both frames And let their times t and t and their Cartesian coordinates x, y, z and x , y , z be adapted to their relative motion in the following way (cf Fig 1.1): The S origin moves with velocity v along the x-axis of S, the x -axis coincides with the x-axis, while the y- and y -axes remain... ether, and when he died in 1928 he still believed in it His ether theory came to include all of Einstein’s basic findings and was, for calculational purposes, equivalent to special relativity, and less jolting to classical prejudices But it was also infinitely less elegant and, above all, sterile in suggesting new results Today it is best forgotten, except by historians 12 From absolute space and time... frame, and even enunciated and named the relativity principle’ in 1904, one year before Einstein But, unlike Einstein, he did nothing with it Einstein was the first to derive the LT from the relativity principle independently of Maxwell’s theory, as that which connects real space and real time in various inertial frames He was the first wholeheartedly to discard the ether and the old ideas of space and. .. earth (here treated as a Newtonian inertial frame), and mI and mG its inertial and gravitational mass Then f = mI a and fG = mG g, where a is the acceleration of the particle, and g is the gravitational field and thus the acceleration of the cabin The acceleration of the particle relative to the cabin is a − g (by classical ‘acceleration addition’) and so the force relative to the cabin is (a − g)mI . apology and then thoroughly used. Einstein’s special and general relativity, the theories of flat and curved spacetime and of the physics therein, and relativistic cosmology, with its geometry and. extensively with special relativity, general relativity, and cosmology. In each I have tried to report on the most important crucial experiments and observations, both historical and modern, but. an overview of all of relativity and cosmology, so that the student can appreciate from the very beginning the local character of special relativity and how it fits into the general scheme. The