[...]... Galileo’s law of inertia To Aristotle a constant force was required to maintain the constant velocity of a body To Galileo a constant force provided a constant acceleration for a body Galileo was dealing with motion absent all external influences in his treatment of impetus and inertia, closer to the world of Plato’s ideal forms than to Aristotle’s everyday world But Galileo’s ideas needed the refinement and... the natural circular motion of heavenly bodies that was other than the center of the universe In Plato’s formalistic approach this was readily accepted In Aristotle’s realistic approach a natural circular motion cannot take place otherwise than round the immovable centre of the universe in this case the earth The resulting conflict between Aristotelian physics and the astronomy that was to bear... his major works into their historical context, with an emphasis on the pathbreaking works of 1905 and 1916 It also develops the detail of his papers, taking the reader through the mathematics to help the reader discover the simplicity and insightfulness of his ideas and to grasp what was so “revolutionary” about his work As with any revolution, the story told after the fact is not always an accurate... rotating on its axis, but rejected them as not fitting into his total worldview To Plato, whose guiding principle is to save the phenomena,” a stationary earth with circular motion in the heavens or a rotating earth with the heavens stationary would be equally acceptable if they each predicted the motions of the stars with equal accuracy and precision To Aristotle, the central location of the earth... composition, fall with the same acceleration in a given gravitational field? From considerations such as these came the realization that the effects of gravity and those of an accelerating reference frame are equivalent and, eventually, that gravity is expressible Introduction xix as a property of space itself, but of a four-dimensional space that has curvature and is non-Euclidean This chapter concludes with a. .. theory he had no such physical phenomena to guide him This book looks not only to detail the major works of Albert Einstein, it also attempts to set Einstein’s work into a historical and philosophical context Perhaps a disclaimer, a “truth in advertising” is appropriate My training is as a physicist and as a teacher of physics, not as a philosopher or historian of science I am interested in broadening... Newton’s third law of motion: To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.55 Newton’s laws of motion were valid in absolute space But if valid in absolute space, it was determined they also were valid in any reference frame moving in uniform translational motion relative to absolute... results on calculus in 1736 in On the Method of Series and Flucxions (nine years after his death).52 Newton’s major contribution to mechanics was to pull together what had been separate and fragmentary knowledge, and to assemble it into a systematic and consistent mathematical system.53 Newton incorporated the impetus of Galileo and the Paris Terminists He broke with the concept that one body a ected the... clarity: astronomy is the science that so combines circular and uniform motions as to yield a resultant motion like that of the stars When its geometric constructions have assigned each planet a path which 1.2 Historical Background 3 conforms to its visible path, astronomy has attained its goal, because its hypotheses have then saved the appearances.”8 Eudoxus (c 408 BC–c 355 BC), a student of Plato and... Relativity 5.2.3 The Space-Time Continuum Requirement of General Covariance for the Equations Expressing General Laws of Nature 5.2.4 The Relation of the Four Coordinates to Measurement in Space and Time Part B: “Mathematical Aids to the Formulation of Generally Covariant Equations” 5.2.5 5.2.6 5.2.7 5.2.8 5.2.9 Contravariant and Covariant Four-Vectors Tensors of the Second and Higher Ranks Multiplication