مشخصات کتاب

Relativity. The special and the general theory

دسته بندی: نظریه نسبیت و گرانش
ویرایش: The Masterpiece Science Ed 
نویسندگان: Albert Einstein,  Roger Penrose,  Robert Geroch,  David C. Cassidy  
سری:  
ISBN (شابک) : 0131862618, 9780131862616 
ناشر: Pi Press 
سال نشر: 2005 
تعداد صفحات: 290 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 1 مگابایت 

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بخش 17. فضا-زمان

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From the Commentary by Robert Geroch (The corresponding section of Einstein’s text can be found below the comment. Please note that in the book, the Commentary is placed after the complete text of Relativity.)

Section 17. Space-Time

Minkowski’s viewpoint represents a "geometrization" of relativity. These ideas have, over the years, come to the forefront: They reflect the perspective of the majority of physicists working in relativity today. Let us expand on this viewpoint. The fundamental notion is that of an event, which we think of as a physical occurrence having negligibly small extension in both space and time. That is, an event is "small and quick," such as the explosion of a firecracker or the snapping of your fingers. Now consider the collection of all possible events in the universe—all events that have ever happened, all that are happening now, and all that will ever happen; here and elsewhere. This collection is called space-time. It is the arena in which physics takes place in relativity. The idea is to recast all statements about goings-on in the physical world into geometrical structures within this space-time. In a similar vein, you might begin the study of plane geometry by introducing the notion of a point (analogous to an event) and assembling all possible points into the plane (analogous to space-time). This plane is the arena for plane geometry, and each statement that is part of plane geometry is to be cast as geometrical structure within this plane. This space-time is a once-and-for-all picture of the entire physical world. Nothing "happens" there; things just "are." A physical particle, for example, is described in the language of space-time by giving the locus of all events that occur "right at the particle." The result is a certain curve, or path, in space-time called the world-line of the particle. Don’t think of the particle as "traversing" its world-line in the same sense that a train traverses its tracks. Rather, the world-line represents, once and for all, the entire life history of the particle, from its birth to its death. The collision of two particles, for example, would be represented geometrically by the intersection of their world-lines. The point of intersection—a point common to both curves; an event that is "right at" both particles—represents the event of their collision. In a similar way, more complicated physical goings-on—an experiment in particle physics, for example, or a football game—are incorporated into the fabric of space-time. One example of "physical goings-on" is the reference frame that Einstein uses in his discussion of special relativity. How is this incorporated into space-time? The individuals within a particular reference frame assign four numbers, labeled x, y, z, t, to each event in space-time. The first three give the spatial location of the event according to these observers, the last the time of the event. These numbers completely and uniquely characterize the event. In geometrical terms, a frame of reference gives rise to a coordinate system on space-time. In a similar vein, in plane geometry a coordinate system assigns two numbers, x and y, to each point of the plane. These numbers completely and uniquely characterize that point. The statement "the plane is two-dimensional" means nothing more and nothing less than that precisely two numbers are required to locate each point in the plane. Similarly, "space-time is four-dimensional" means nothing more and nothing less than that precisely four numbers are required to locate each event in space-time. That is all there is to it! You now understand "four-dimensional space-time" as well as any physicist. Note that the introduction of four-dimensional space-time does not say that space and time are "equivalent" or "indistinguishable." Clearly, space and time are subjectively different entities. But a rather subtle mixing of them occurs in special relativity, making it convenient to introduce this single entity, space-time. In plane geometry, we may change coordinates, i.e., relabel the points. It is the same plane described in a different way (in that a given point is now represented by different numbers), just as the land represented by a map stays the same whether you use latitude/longitude or GPS coordinates. We can now determine formulae expressing the new coordinate-values for each point of the plane in terms of the old coordinate-values. Similarly, we may change coordinates in space-time, i.e., change the reference frame therein. And, again, we can determine formulae relating the new coordinate-values for each space-time event to the old coordinate-values for that event. This, from Minkowski’s geometrical viewpoint, is the substance of the Lorentz-transformation formulae in Section 11. A significant advantage of Minkowski’s viewpoint is that it is particularly well-adapted also to the general theory of relativity. We shall return to this geometrical viewpoint in our discussion of Section 27.

فهرست مطالب

RELATIVITY The Special and General Theory......Page 4
Commentary and Historical Essay © 2005 by Pearson Education, Inc.......Page 5
CONTENTS......Page 6
INTRODUCTION......Page 10
NOTE ON THE TEXT......Page 28
PREFACE†......Page 32
1. PHYSICAL MEANING OF GEOMETRICAL PROPOSITIONS......Page 34
2. THE SYSTEM OF CO-ORDINATES......Page 38
3. SPACE AND TIME IN CLASSICAL MECHANICS......Page 42
4. THE GALILEIAN SYSTEM OF CO-ORDINATES......Page 45
5. THE PRINCIPLE OF RELATIVITY (IN THE RESTRICTED SENSE)†......Page 47
6. THE THEOREM OF THE ADDITION OF VELOCITIES EMPLOYED IN CLASSICAL MECHANICS......Page 52
7. THE APPARENT INCOMPATIBILITY OF THE LAW OF PROPAGATION OF LIGHT WITH THE PRINCIPLE OF RELATIVITY†......Page 54
8. ON THE IDEA OF TIME IN PHYSICS......Page 58
9. THE RELATIVITY OF SIMULTANEITY......Page 63
10. ON THE RELATIVITY OF THE CONCEPTION OF DISTANCE†......Page 67
11. THE LORENTZ TRANSFORMATION......Page 69
12. THE BEHAVIOUR OF MEASURING-RODS AND CLOCKS IN MOTION†......Page 76
13. THEOREM OF THE ADDITION OF VELOCITIES. THE EXPERIMENT OF FIZEAU......Page 80
14. THE HEURISTIC VALUE OF THE THEORY OF RELATIVITY......Page 85
15. GENERAL RESULTS OF THE THEORY†......Page 87
16. EXPERIENCE AND THE SPECIAL THEORY OF RELATIVITY......Page 94
17. MINKOWSKI’S FOUR-DIMENSIONAL SPACE†......Page 101
18. SPECIAL AND GENERAL PRINCIPLE OF RELATIVITY......Page 106
19. THE GRAVITATIONAL FIELD†......Page 111
20. THE EQUALITY OF INERTIAL AND GRAVITATIONAL MASS AS AN ARGUMENT FOR THE GENERAL POSTULATE OF RELATIVITY......Page 115
21. IN WHAT RESPECTS ARE THE FOUNDATIONS OF CLASSICAL MECHANICS AND OF THE SPECIAL THEORY OF RELATIVITY UNSATISFACTORY?......Page 121
22. A FEW INFERENCES FROM THE GENERAL PRINCIPLE OF RELATIVITY......Page 124
23. BEHAVIOUR OF CLOCKS AND MEASURING-RODS ON A ROTATING BODY OF REFERENCE†......Page 130
24. EUCLIDEAN AND NON-EUCLIDEAN CONTINUUM......Page 135
25. GAUSSIAN CO-ORDINATES......Page 140
26. THE SPACE-TIME CONTINUUM OF THE SPECIAL THEORY OF RELATIVITY CONSIDERED AS A EUCLIDEAN CONTINUUM......Page 145
27. THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM†......Page 148
28. EXACT FORMULATION OF THE GENERAL PRINCIPLE OF RELATIVITY†......Page 152
THE SOLUTION OF THE PROBLEM OF GRAVITATION ON THE BASIS OF THE GENERAL PRINCIPLE OF RELATIVITY......Page 156
30. COSMOLOGICAL DIFFICULTIES OF NEWTON’S THEORY......Page 162
31. THE POSSIBILITY OF A “FINITE” AND YET “UNBOUNDED” UNIVERSE......Page 165
32. THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY†......Page 172
1. SIMPLE DERIVATION OF THE LORENTZ TRANSFORMATION......Page 176
2. MINKOWSKI’S FOURDIMENSIONAL SPACE (“WORLD”)......Page 184
3. THE EXPERIMENTAL CONFIRMATION OF THE GENERAL THEORY OF RELATIVITY......Page 187
COMMENTARY......Page 200
THE CULTURAL LEGACY OF RELATIVITY THEORY......Page 254
SELECTED BIBLIOGRAPHY......Page 276
INDEX......Page 280

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