ISBN-10:
1936690012
ISBN-13:
9781936690015
Pub. Date:
12/27/2010
Publisher:
Murine Publications LLC
Relativity: The Special and the General Theory

Relativity: The Special and the General Theory

by Albert Einstein, Robert W LawsonAlbert Einstein
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Overview

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes-regions of space in which space and time are distorted in such a way that nothing, not even light, can escape-as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars.

Product Details

ISBN-13: 9781936690015
Publisher: Murine Publications LLC
Publication date: 12/27/2010
Pages: 74
Sales rank: 494,560
Product dimensions: 6.00(w) x 9.00(h) x 0.31(d)

About the Author

Albert Einstein (1879–1955), one of the greatest thinkers of the twentieth century, was born in Ulm, Germany, to German-Jewish parents. He published his first great theories in Switzerland in the early 1900s while working as a patent clerk.

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Relativity

The Special & The General Theory


By Albert Einstein

PRINCETON UNIVERSITY PRESS

Copyright © 2015 Princeton University Press and The Hebrew University of Jerusalem
All rights reserved.
ISBN: 978-1-4008-6566-6



CHAPTER 1

Physical Meaning of Geometrical Propositions


In your schooldays most of you who read this book made acquaintance with the noble building of Euclid's geometry, and you remember—perhaps with more respect than love—the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. By reason of your past experience, you would certainly regard everyone with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud certainty would leave you immediately if some one were to ask you: "What, then, do you mean by the assertion that these propositions are true?" Let us proceed to give this question a little consideration.

Geometry sets out from certain conceptions such as "plane," "point," and "straight line," with which we are able to associate more or less definite ideas, and from certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as "true." Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct ("true") when it has been derived in the recognised manner from the axioms. The question of the "truth" of the individual geometrical propositions is thus reduced to one of the "truth" of the axioms. Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning. We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called "straight lines," to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept "true" does not tally with the assertions of pure geometry, because by the word "true" we are eventually in the habit of designating always the correspondence with a "real" object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry "true." Geometrical ideas correspond to more or less exact objects in nature, and these last are undoubtedly the exclusive cause of the genesis of those ideas. Geometry ought to refrain from such a course, in order to give to its structure the largest possible logical unity. The practice, for example, of seeing in a "distance" two marked positions on a practically rigid body is something which is lodged deeply in our habit of thought. We are accustomed further to regard three points as being situated on a straight line, if their apparent positions can be made to coincide for observation with one eye, under suitable choice of our place of observation.

If, in pursuance of our habit of thought, we now supplement the propositions of Euclidean geometry by the single proposition that two points on a practically rigid body always correspond to the same distance (line-interval), independently of any changes in position to which we may subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies. Geometry which has been supplemented in this way is then to be treated as a branch of physics. We can now legitimately ask as to the "truth" of geometrical propositions interpreted in this way, since we are justified in asking whether these propositions are satisfied for those real things we have associated with the geometrical ideas. In less exact terms we can express this by saying that by the "truth" of a geometrical proposition in this sense we understand its validity for a construction with ruler and compasses.

Of course the conviction of the "truth" of geometrical propositions in this sense is founded exclusively on rather incomplete experience. For the present we shall assume the "truth" of the geometrical propositions, then at a later stage (in the general theory of relativity) we shall see that this "truth" is limited, and we shall consider the extent of its limitation.

CHAPTER 2

The System of Co-ordinates


On the basis of the physical interpretation of distance which has been indicated, we are also in a position to establish the distance between two points on a rigid body by means of measurements. For this purpose we require a "distance" (rod S) which is to be used once and for all, and which we employ as a standard measure. If, now, A and B are two points on a rigid body, we can construct the line joining them according to the rules of geometry; then, starting from A, we can mark off the distance S time after time until we reach B. The number of these operations required is the numerical measure of the distance A B. This is the basis of all measurement of length.

Every description of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coincides. This applies not only to scientific description, but also to everyday life. If I analyse the place specification "Trafalgar Square, London,"· I arrive at the following result. The earth is the rigid body to which the specification of place refers; "Trafalgar Square, London," is a well-defined point, to which a name has been assigned, and with which the event coincides in space.

This primitive method of place specification deals only with places on the surface of rigid bodies, and is dependent on the existence of points on this surface which are distinguishable from each other. But we can free ourselves from both of these limitations without altering the nature of our specification of position. If, for instance, a cloud is hovering over Trafalgar Square, then we can determine its position relative to the surface of the earth by erecting a pole perpendicularly on the Square, so that it reaches the cloud. The length of the pole measured with the standard measuring-rod, combined with the specification of the position of the foot of the pole, supplies us with a complete place specification. On the basis of this illustration, we are able to see the manner in which a refinement of the conception of position has been developed.

(a) We imagine the rigid body, to which the place specification is referred, supplemented in such a manner that the object whose position we require is reached by the completed rigid body.

(b) In locating the position of the object, we make use of a number (here the length of the pole measured with the measuring-rod) instead of designated points of reference.

(c) We speak of the height of the cloud even when the pole which reaches the cloud has not been erected. By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.

From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measures to make ourselves independent of the existence of marked positions (possessing names) on the rigid body of reference. In the physics of measurement this is attained by the application of the Cartesian system of co-ordinates.

This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body. Referred to a system of co-ordinates, the scene of any event will be determined (for the main part) by the specification of the lengths of the three perpendiculars or co-ordinates (x, y, z) which can be dropped from the scene of the event to those three plane surfaces. The lengths of these three perpendiculars can be determined by a series of manipulations with rigid measuring-rods performed according to the rules and methods laid down by Euclidean geometry.

In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available; furthermore, the magnitudes of the co-ordinates are not actually determined by constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations.

We thus obtain the following result: Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for "distances," the "distance" being represented physically by means of the convention of two marks on a rigid body.

CHAPTER 3

Space and Time in Classical Mechanics


The purpose of mechanics is to describe how bodies change their position in space with "time." I should load my conscience with grave sins against the sacred spirit of lucidity were I to formulate the aims of mechanics in this way, without serious reflection and detailed explanations. Let us proceed to disclose these sins.

It is not clear what is to be understood here by "position" and "space." I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve. I now ask: Do the "positions" traversed by the stone lie "in reality" on a straight line or on a parabola? Moreover, what is meant here by motion "in space"? From the considerations of the previous section the answer is self-evident. In the first place we entirely shun the vague word "space," of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by "motion relative to a practically rigid body of reference." The positions relative to the body of reference (railway carriage or embankment) have already been defined in detail in the preceding section. If instead of "body of reference" we insert "system of co-ordinates," which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground (embankment) it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (lit. "path-curve"), but only a trajectory relative to a particular body of reference.

In order to have a complete description of the motion, we must specify how the body alters its position with time; i.e. for every point on the trajectory it must be stated at what time the body is situated there. These data must be supplemented by such a definition of time that, in virtue of this definition, these time-values can be regarded essentially as magnitudes (results of measurements) capable of observation. If we take our stand on the ground of classical mechanics, we can satisfy this requirement for our illustration in the following manner. We imagine two clocks of identical construction; the man at the railway-carriage window is holding one of them, and the man on the footpath the other. Each of the observers determines the position on his own reference-body occupied by the stone at each tick of the clock he is holding in his hand. In this connection we have not taken account of the inaccuracy involved by the finiteness of the velocity of propagation of light. With this and with a second difficulty prevailing here we shall have to deal in detail later.

CHAPTER 4

The Galileian System of Co-ordinates


A is well known, the fundamental law of the mechanics of Galilei-Newton, which is known as the law of inertia, can be stated thus: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. This law not only says something about the motion of the bodies, but it also indicates the reference-bodies or systems of co-ordinates, permissible in mechanics, which can be used in mechanical description. The visible fixed stars are bodies for which the law of inertia certainly holds to a high degree of approximation. Now if we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this system, every fixed star describes a circle of immense radius in the course of an astronomical day, a result which is opposed to the statement of the law of inertia. So that if we adhere to this law we must refer these motions only to systems of coordinates relative to which the fixed stars do not move in a circle. A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a "Galileian system of co-ordinates." The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galileian system of co-ordinates.

CHAPTER 5

The Principle of Relativity (in the Restricted Sense)


In order to attain the greatest possible clearness, let us return to our example of the railway carriage supposed to be travelling uniformly. We call its motion a uniform translation ("uniform" because it is of constant velocity and direction, "translation" because although the carriage changes its position relative to the embankment yet it does not rotate in so doing). Let us imagine a raven flying through the air in such a manner that its motion, as observed from the embankment, is uniform and in a straight line. If we were to observe the flying raven from the moving railway carriage, we should find that the motion of the raven would be one of different velocity and direction, but that it would still be uniform and in a straight line. Expressed in an abstract manner we may say: If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative to a second co-ordinate system K', provided that the latter is executing a uniform translatory motion with respect to K. In accordance with the discussion contained in the preceding section, it follows that:

If K is a Galileian co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to K' the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K.


(Continues...)

Excerpted from Relativity by Albert Einstein. Copyright © 2015 Princeton University Press and The Hebrew University of Jerusalem. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents

Relativity
Introduction by Nigel Calder
Suggestions for Further Reading
Preface by Albert Einstein

Part I: The Special Theory of Relativity

1. Physical Meaning of Geometrical Propositions
2. The System of Co-ordinates
3. Space and Time in Classical Mechanics
4. The Galileian System of Co-ordinates
5. The Principle of Relativity (in the Restricted Sense)
6. The Theorem of the Addition of Velocities Employed in Classical Mechanics
7. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity
8. On the Idea of Time in Physics
9. The Relativity of Simultaneity
10. On the Relativity of the Conception of Distance
11. The Lorentz Transformation
12. The Behaviour of Measuring-Rods and Clocks in Motion
13. Theorem of the Addition of the Velocities. The Experiment of Fizeau
14. The Heuristic Value of the Theory of Relativity
15. General Results of the Theory
16. Experience and the Special Theory of Relativity
17. Minkowski's Four-Dimensional Space

Part II: The General Theory of Relativity

18. Special and General Principle of Relativity
19. The Gravitational Field
20. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity
21. In What Respects Are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory?
22. A Few Inferences from the Genral Principle of Relativity
23. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference
24. Euclidean and Non-Euclidean Continuum
25. Gaussian Co-ordinates
26. The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum
27. The Space-Time Continuum of the General Theory of Relativity Is Not a Euclidean Continuum
28. Exact Formulation of the General Principle of Relativity
29. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity

Part III: Considerations on the Universe as a Whole

30. Cosmological Difficulties of Newton's Theory
31. The Possibility of a "Finite" and Yet "Unbounded" Universe
32. The Structure of Space According to the General Theory of Relativity

Appendices

1. Simple Derivation of the Lorentz Transformation
2. Minkowski's Four-Dimensional Space ("World")
3. The Experimental Confirmation of the General Theory of Relativity
(a) Motion of the Perihelion of Mercury
(b) Deflection of Light by a Gravitational Field
(c) Displacement of Spectral Lines towards the Red

Index

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Relativity 3.6 out of 5 based on 0 ratings. 91 reviews.
Guest More than 1 year ago
Six years of college physics courses never made relativity intuitively understandable for me. Academic texts concentrate on mathematical descriptions, manipulations and proofs to present theories. Einstein, in simple text, leads us through his very logical and understandable thought process, which led him to the relativity theories. I could manipulate the mathematics of relativity and come up with answers but never really had an intuitive feel for what really is going on till I read this book. I only wish I had read this first before plowing through graduate physics courses. The only other book I have ever read that was more enlightening was the Bible.
Baildog More than 1 year ago
While this is obviously an excellent book that everyone should have to read at some point in their life, this version suffers---as others have warned---from a glitch that fails to print the majority of the equations. DO NOT BUY THIS VERSION, find a complete version somewhere else.
Anonymous More than 1 year ago
Would have probably been a good read, but the equations are all missing. Everywhere you expect to see an equation, is a tag that says: eq. 'n': file eq'n'.gif
Anonymous 12 months ago
I'm still here;)
Anonymous More than 1 year ago
I know its 2019 but anyone?
Anonymous More than 1 year ago
HOW DO YOU JOIN A CLAN, AND PLEASE WRITE MORE OF THOSE SRORIES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! . . . . .
Anonymous More than 1 year ago
Heeeyyyy!!! So ill fu<_>ck u...but was also wandering if u wanted to be my rp boyfriend at war and peace?
LynnB on LibraryThing More than 1 year ago
This book is subtitled "A clear exlanation that anyone can understand". Unfortunately, I found that to be untrue, although I must admit I have no science training at all. For me, though, this book made a nice companion piece to the biography on Einstein I'm reading, and the Einstein for Dummies book (which does provide a clear explanation that anyone can understand). It was nice to read Dr. Einstein's own words.
jmccamant on LibraryThing More than 1 year ago
I abandoned this to re-read Hawking after an uninspiring start. I think relativity is most interesting with a little more time and cosmology under out collective belt.
Snakeshands on LibraryThing More than 1 year ago
Not what they'd call "popular" today, but it's written at exactly the level that if I squint and focus my brain real hard, I can follow the arguments despite not having done a real math or physics (intro astro or Fractals for Nonmajors don't count) class since high school.A few of the suspicions and conclusions are a wee bit corrected since the time (quantum happened, Unified Field Theory didn't so far), but this book is really good at giving you a deeper look at the _why_ of relativity, the parts that always get glossed over or oversimplified ("oh yeah, space is curved") for people who can't do the math on their own. His sentences on this stuff aren't luminously obvious, but he never pulls his punches either.
figre on LibraryThing More than 1 year ago
Let¿s face it. If you think you want to read this, then you may as well go ahead and dive in. The surprise¿it is relatively easy to read. (Last time for that word, honest) I have slogged through a number of books trying to get a grasp of the concepts within Einstein¿s theories. Every time I feel like I make some headway, but it feels like some of it is always out of my grasp. With the promise that Einstein himself was the best to explain it, I dove in. The good news is that he does try to take it down to our level. The bad news is he uses some math in doing so. Accordingly, at the end of it all, I have made more headway, but I still can¿t get my head around gravity being just a bend in space. (Or maybe, that isn¿t what it is, and that shows the ignorance I¿ve still got to overcome.) Bottom line, you really can¿t beat the primary source. Maybe if I read it one more time¿.
mrfalljackets on LibraryThing More than 1 year ago
Diminished my presumption of my own supreme intelligence. Completely inaccessible somewhere around chapter 9 but then again I probably wasn't his intended audience. I have zero scientific training. Loved how he used phrases such as "the observer will immediately notice..." or "the reader will obviously infer from the following...". I found very little either immediate or obvious.
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I'm around
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The book really helped me with my project. It gave me so many details.
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Understand anything.
Anonymous More than 1 year ago
Text conversion fail. Spend enough time translating to lose the author... not good for this kind of book.
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