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Understanding Relativity

Understanding Relativity: A Simplified Approach to Einstein's Theories

Copyright Date: 1996
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    Understanding Relativity
    Book Description:

    Nonspecialists with no prior knowledge of physics and only reasonable proficiency with algebra can now understand Einstein's special theory of relativity. Effectively diagrammed and with an emphasis on logical structure, Leo Sartori's rigorous but simple presentation will guide interested readers through concepts of relative time and relative space. Sartori covers general relativity and cosmology, but focuses on Einstein's theory. He tracks its history and implications. He explores illuminating paradoxes, including the famous twin paradox, the "pole-in-the-barn" paradox, and the Loedel diagram, which is an accessible, graphic approach to relativity. Students of the history and philosophy of science will welcome this concise introduction to the central concept of modern physics.

    eISBN: 978-0-520-91624-1
    Subjects: General Science

Table of Contents

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  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Preface
    (pp. xi-xii)
  4. Acknowledgments
    (pp. xiii-xiv)
  5. 1 Galilean Relativity
    (pp. 1-25)

    A child walks along the floor of a moving train. Passengers on the train measure the child’s speed and find it to be 1 meter per second. When ground-based observers measure the speed of the same child, they obtain a different value; observers on an airplane flying overhead obtain still another. Each set of observers obtains a different value when measuring the same physical quantity. Finding the relation between those values is a typical problem in relativity.

    There is nothing at all startling about these observations; relativity was not invented by Albert Einstein. Einstein’s work did, however, drastically change the...

  6. 2 The Michelson-Morley Experiment
    (pp. 26-47)

    The Michelson-Morley experiment occupies a special niche in the pantheon of relativity. Contrary to many accounts, the experiment did strongly influence Einstein’s discovery of special relativity.¹ It nonetheless provides strong experimental underpinning for the theory and was instrumental in promoting its widespread acceptance. Albert A. Michel son’s experiment was rooted in late-nineteenth-century ideas concerning the nature of light. I begin therefore with a brief exposition of those ideas.

    That the speed of light is very great had been known for a long time. Galileo had tried to measure it but did not succeed. The first determination of the speed of...

  7. 3 The Postulates of Relativity and Their Implications
    (pp. 48-96)

    In 1905 Albert Einstein, a twenty-six-year-old technical expert third class at the Swiss patent office in Bern, published three monumental papers in theAnnalen der Physik.One of those papers set forth the theory now known as special relativity.¹ The theory is based on two postulates, which I paraphrase as follows:

    Postulate 1 (Principle of Relativity): The laws of nature are the same in all inertial frames.

    Postulate 2 (Constancy of the Velocity of Light): The speed of light in empty space is an absolute constant of nature and is independent of the motion of the emitting body.

    All of...

  8. 4 The Lorentz Transformation
    (pp. 97-138)

    The fundamental problem of relativity is the transformation of coordinates: ifx, y, z,andtdenote the coordinates of an event measured in some frameS,what are the coordinatesx’, y’, z’,andt’of the same event measured in another frame,S’, that moves at velocityVrelative toS?

    As we have already noted, the classical solution to the problem, the Galilean transformation (eq. [1.1]), is inconsistent with Einstein’s postulates and must be rejected. Our task here is to derive its replacement, the Lorentz transformation.

    The new transformation law must satisfy several requirements:

    (i) The transformation...

  9. 5 Space-Time Diagrams
    (pp. 139-165)

    This chapter introduces the space-time diagram, a geometric representation of relativity that illustrates and clarifies several important features of the theory. Consider first a problem in which events are confined to one spatial dimension. In a given frame of reference, an event is specified by two coordinates,xandt.We can therefore represent each event by a point in a two-dimensional diagram, in which distance is plotted along the vertical axis and time along the horizontal. It is convenient to usectrather thantas the “time” variable; both scales then have the dimension of length. Such a...

  10. 6 Paradoxes of Relativity
    (pp. 166-201)

    A paradox is an apparent inconsistency or contradiction in a theory or in any logical system. If the paradox cannot be satisfactorily resolved, the theory in question fails and must be abandoned or at least modified.

    In this chapter we analyze several paradoxes based on special relativity which have attracted attention over the years. All of them involve length contraction or time dilation. One, the twin paradox, has generated a great deal of controversy. Careful study of the paradoxes and of their resolution helps clarify many subtleties in the theory. The space-time diagram, introduced in chapter 5, proves useful in...

  11. 7 Relativistic Mechanics
    (pp. 202-242)

    We conclude our study of special relativity by examining its implications for energy, momentum, and mass. It is in this area that most of the applications of the theory are found. Several fundamental ideas of classical mechanics must be modified.

    The famous relation between mass and energy, which for many people epitomizes relativity, appeared first in a short paper published by Einstein in September 1905,¹ just three months after his first paper on relativity. Einstein’s argument was based on the transformation properties of electromagnetic radiation. In the first paper, he had shown that if an electromagnetic plane wave of energy...

  12. 8 General Relativity
    (pp. 243-292)

    In special relativity, as in Newtonian mechanics, inertial frames enjoy a preferential status. The principle of relativity applies only to them. The laws of nature are the same in all inertial frames and no experiment can distinguish between one and another. An inertial frame is one in which Newton’s law of inertia holds: a body subject to no net external force remains at rest or moves in a straight line with uniform velocity.

    All inertial frames move uniformly relative to one another. IfKis an inertial frame andK’is accelerated relative toK,thenK’is noninertial. The...

  13. 9 Cosmology
    (pp. 293-356)

    Cosmology is concerned with the nature and the history of the universe. Although men and women have pondered these questions for millennia, early cosmologies were little more than myths. Scientific cosmology began with the Greeks some 2,500 years ago but was for a long time largely speculative. Only in the present century have observational data become available that bear directly on the questions posed by cosmology. The evidence points strongly toward the world picture currently in favor—the “big bang” and expanding universe. Einstein’s conception of curved spacetime, described in chapter 8, provides the framework for all modern cosmological models....

  14. Index
    (pp. 357-368)
  15. Back Matter
    (pp. 369-369)