Modern Physics for Scientists and Engineers (2nd Edition)

Book Preface

Most physical measurements are made relative to a chosen reference system. If we measure the time of an event as seconds, this must mean that t is 5 seconds relative to a chosen origin of time, If we state that the position of a projectile is given by a vector we must mean that the position vector has components relative to a system of coordinates with a definite orientation and a definite origin, If we wish to know the kinetic energy K of a car speeding along a road, it makes a big difference whether we measure K relative to a reference frame fixed on the road or to one fixed on the car. (In the latter case of course.) A little reflection should convince you that almost every measurement requires the specification of a reference system relative to which the measurement is to be made.We refer to this fact as the relativity of measurements.

The theory of relativity is the study of the consequences of this relativity of measurements. It is perhaps surprising that this could be an important subject of study. Nevertheless, Einstein showed, starting with his first paper on relativity in 1905, that a careful analysis of how measurements depend on coordinate systems revolutionizes our whole understanding of space and time, and requires a radical revision of classical, Newtonian mechanics.

In this chapter we discuss briefly some features of relativity as it applies in the classical theories of Newtonian mechanics and electromagnetism, and then we describe the Michelson–Morley experiment, which (with the support of numerous other, less direct experiments) shows that something is wrong with the classical ideas of space and time.We then state the two postulates of Einstein’s relativity and show how they lead to a new picture of space and time in which both lengths and time intervals have different values when measured in any two reference frames that are moving relative to one another. In Chapter 2 we show how the revised notions of space and time require a revision of classical mechanics.We will find that the resulting relativistic mechanics is usually indistinguishable from Newtonian mechanics when applied to bodies moving with normal terrestrial speeds, but is entirely different when applied to bodies with speeds that are a substantial fraction of the speed of light, c. In particular, we will find that no body can be accelerated to a speed greater than c, and that mass is a form of energy, in accordance with the famous relation

Einstein’s theory of relativity is really two theories. The first, called the special theory of relativity, is “special” in that its primary focus is restricted to unaccelerated frames of reference and excludes gravity.This is the theory that we will be studying in Chapters 1 and 2 and applying to our later discussions of radiation, nuclear, and particle physics.

The second of Einstein’s theories is the general theory of relativity, which is “general” in that it includes accelerated frames of reference and gravity. Einstein found that the study of accelerated reference frames led naturally to a theory of gravitation, and general relativity turns out to be the relativistic theory of gravity. In practice, general relativity is needed only in areas where its predictions differ significantly from those of Newtonian gravitational theory. These include the study of the intense gravity near black holes, of the largescale universe, and of the effect the earth’s gravity has on extremely accurate time measurements (one part in or so). General relativity is an important part of modern physics; nevertheless, it is an advanced topic and, unlike special relativity, is not required for the other topics we treat in this book. Therefore, we have given only a brief description of general relativity in an optional section at the end of Chapter 2.