RELATIVITY THE SPECIAL AND THE GENERAL THEORY ALBERT EINSTEIN "Relativity", Albert Einstein page i EB, v.1.2, July-2008 RELATIVITY THE SPECIAL AND GENERAL THEORIES ALBERT EINSTEIN authorised translation by Robert W. Lawson original version 1916, translated 1920 appendices 3 and 4 added 1920 appendix 5 added to English translation 1954 transcribed and converted to Windows HelpFile format 1995 converted to PDF format 2008 transcription and conversion by Eric Baird typesetting and additional material © E. Baird 2008 www.relativitybook.com file version 1.2 / July 2008 COPYRIGHTS Original copyright This work itself ("Relativity: the Special and the General Theories", by Albert Einstein) has been published in the UK since the 1950's with its original copyright notice removed, and has also been published in the US for some time without a copyright notice. It is supplied in good faith on the basis that (at the time of writing) it appears to be non-copyright in these two countries. 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"Relativity", Albert Einstein page ii EB, v.1.2, July-2008 Albert Einstein "Relativity", Albert Einstein page iii EB, v.1.2, July-2008 Preface and Notes Preface THE present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a "stepmotherly" fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for trees. May the book bring some one a few happy hours of suggestive thought! December, 1916 A. EINSTEIN Note to the Fifteenth Edition IN this edition I have added, as a fifth appendix, a presentation of my views on the problem of space in general and on the gradual modifications of our ideas on space resulting from the influence of the relativistic view-point. I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept "empty space" loses its meaning. June 9th, 1952 A. EINSTEIN "Relativity", Albert Einstein page iv EB, v.1.2, July-2008 Analytical Contents Contents and Summary: Portrait ____________________________________________________ iii Preface, & Note to the Fifteenth Edition ___________________________ iv Contents and Summary:_______________________________________ v PART I: SPECIAL RELATIVITY 1 1: Physical Meaning of Geometrical Propositions ___________________ 3 Geometrical concepts and the nature of geometrical “truth” 2: The System of Co-Ordinates_________________________________ 5 Coordinate systems. Methods for attaching “labels” to events and places according to their measured distances and direction from a known reference-system. 3: Space and Time in Classical Mechanics________________________ 7 Space and time. A dropped stone moves in a straight line (in space) according to someone standing above it: to someone passing by, the accelerating stone's progress with time can appear to mark out a curve. 4: The Galileian System of Co-Ordinates _________________________ 8 The laws of Newton and Galileo are only totally consistent for comparing paths that appear as straight lines for all observers: therefore these laws are only totally consistent for simple motion in straight lines at constant velocity. 5: The Principle of Relativity (in the restricted sense) ________________ 9 Defining “Galilean” reference systems as those that only involve objects or points that move past or through each other in a simple way, at fixed speed in straight lines. 6: The Theorem of the Addition of Velocities employed in Classical Mechanics _____________________________________________ 11 A “Galilean” system implies that if a set of three objects lying in a straight line separate from their neighbours at v1 and v2, the total separation of the end objects is “v1+v2” 7: The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity __________________________________ 12 The idea that the speed of light is globally fixed doesn't seem compatible with the idea that physics acts in the same way for all inertial observers. How can the same lightbeam appear to be progressing at the same speed for different observers with different states of motion? "Relativity", Albert Einstein page v EB, v.1.2, July-2008 Analytical Contents 8: On the Idea of Time in Physics ______________________________ 14 We cannot define what it means to say that two distant events are simultaneous without defining how we believe that light travels through space. If two flashes arrive together the same point, then all observers at that location will see the flashes at the same time. But if they have different states of motion, and each believe that lightspeed is fixed within their own reference frame, then they might interpret the same result as meaning that flash A “really” happened earlier than flash B, or vice versa, once signal transmission timelags are taken into account. If observers make different assumption about how light propagates, then their concept of the simultaneity of distant events will be different. 9: The Relativity of Simultaneity _______________________________ 16 If we use reference-systems that assign dates and locations to distant events based on when we see their signals, and on the idea that light travels at fixed speed in our own frame, then whether or not two events are declared to be simultaneous will depends on which coordinate system we are using. 10: On the Relativity of the Conception of Distance ________________ 18 If different observers can disagree as to the original timings of distant events, they can also disagree as to the supposed distances between two events. If an observer holds a torch and emits two flashes of light, they might argue that both flashes originated at the same position (spatial separation of events = zero). But a different observer who sees the flashlight to be moving can argue that both flashes originated at different positions (spatial separation of events > zero). So for two agreed events, differently-moving observers applying equivalent (but different) coordinate-system arguments can disagree as to the “real” distance between the two events. Distances defined in this way can have different values depending on the observer's state of motion. 11: The Lorentz Transformation _______________________________ 19 If we use our flat coordinate system arguments to project nominal distances and times onto an experiment, we can argue that the speed of a lightbeam has exactly the same value in metres per second, regardless of which inertial frame we choose as a reference, provided that our definitions of “distance” and “time” vary between the different coordinate systems in a particular way. If a light-signal is created at one event and is absorbed at another, two observers may disagree as to how far the light “really” travelled, and how long it “really” took to arrive, but the light's nominal speed in (disputed) metres per (disputed) second can give the same final value for both observers. The special rescaling for lengths and times that can produce this end-result is known as the Lorentz Transformation. 12: The Behaviour of Measuring-Rods and Clocks in Motion _________ 22 Assuming that the speed of light is globally constant for all simple inertial observers, we then get the result that, using this Lorentz Transform, the values that we assign to particular distances and times need to be different in different coordinate systems by the Lorentz factor, 1:SQRT[1-vv/cc], where v tells us how fast the two coordinate systems are moving relative to one another. If I carry a metre-rule and a wristwatch, and use these to measure out local distances and times, then someone moving past me who applies the Lorentz transform to my measurements will argue that, the distances that I measure appear in their coordinate system to be shorter, and the times that I measure appear in their coordinate system to be longer. Applying the Lorentz transforms to the nominal distances and times that appear in different coordinate-system projections of the same experiment, we find that “moving” rods appear to contract, and “moving” clocks appear to run slow ..