Special Relativity

Description

This Element presents the philosophy of special relativity: from the foundations of the theory in Newtonian mechanics, through its birth out of the ashes of 19th Century ether theory, through the various conceptual paradoxes which the theory presents, and finally arriving at some of its connections with Einstein's later theory of general relativity. It illustrates concepts such as inertial frames, force-free motion, and dynamical versus geometrical understandings of physics, the standard hierarchy of classical spacetimes, the concept of a symmetry of a physical theory, Poincaré invariant, Einstein's 1905 derivation of the Lorentz transformations, spacetime structure from Aristotle to Minkowski, general covariance, dynamical and geometrical approaches to spacetime, the conventionality of simultaneity, Frame-dependent effects, and the twin paradox. Cover Title page Copyright page Special Relativity Contents 1 Newton's Laws 1.1 Newton’s Laws 1.2 Inertial Frames 1.3 Force-Free Bodies 1.4 Summary of the Views 1.5 Newton’s Third Law 1.6 Summary 2 Symmetries and Invariance 2.1 The Relativity Principle 2.2 Active versus Passive Transformations 2.3 Galilean Transformations 2.4 Newton on Galilean Invariance 2.5 Poincaré Transformations 3 The Michelson–Morley Experiment 3.1 The Michelson–Morley Experiment 3.2 Lorentz’s Programme 4 Einstein's 1905 Derivation 4.1 Principle and Constructive Theories 4.2 Einstein’s 1905 Article 4.2.1 Einstein’s Operational Understanding of Coordinates 4.2.2 The Definition of Simultaneity 4.2.3 Einstein’s Two Postulates 4.2.4 Homogeneity, Isotropy, and Reciprocity 4.2.5 Linearity of the Transformations 4.2.6 Lorentz Transformations up to ϕ(v) 4.2.7 Final Steps 4.3 Einstein versus the Trailblazers 4.4 Einstein’s Later Misgivings 4.5 The Ignatowski Transformations 5 Spacetime Structure 5.1 Two Conceptions of Geometry 5.2 Spacetime Structure in Newtonian Physics 5.2.1 Aristotelian Spacetime 5.2.2 Newtonian Spacetime 5.2.3 Neo-Newtonian/Galilean Spacetime 5.2.4 Maxwellian/Newton–Huygens Spacetime 5.2.5 Leibnizian Spacetime 5.2.6 Machian Spacetime 5.2.7 Summary 5.3 Spacetime Structure in Special Relativity 5.4 Further Reflections on Spacetime 6 General Covariance 6.1 Physical Laws 6.2 General Covariance 6.3 The Riemannian Conception of Geometry 6.4 What Is Special Relativity? 7 Dynamical and Geometrical Approaches 7.1 Bell’s Lorentzian Pedagogy 7.2 Constructive and Principle Theories, Reprised 7.3 Arrows of Explanation 7.4 Geometrical Sub-views 7.5 Norton’s Challenge 8 The Conventionality of Simultaneity 8.1 The Relativity of Simultaneity 8.2 The Conventionality of Simultaneity 8.3 Arguments against Conventionality 8.3.1 Slow Clock Transport 8.3.2 Malament’s 1977 Theorem 9 Frame-Dependent Effects 9.1 Time Dilation 9.2 Length Contraction 9.3 Bell’s Rockets 9.4 Assessing Frame-Dependent Effects 9.5 Fragmentalism 10 The Twin Paradox 10.1 The Clock Hypothesis 10.2 The Twin Paradox 10.2.1 Inertial Frames 10.2.2 Geometrical and Dynamical Explanations 10.3 Frame-Relative Accounts 10.4 General Relativity References Acknowledgements