Concepts Of Modern Physics

CONCEPTS OF MODERN PHYSICS

In 1905 a young physicist of twenty-six named Albert Einstein showed how measurements of time and space are affected by motion between an observer and what is being observed. To say that Einstein’s theory of relativity revolutionized science is no exaggeration. Relativity connects space and time, matter and energy, electricity and magnetism-links that are crucial to our understanding of the physical universe. From relativity have come a host of remarkable predictions, all of which have been confirmed by experiment. For all their profundity, many of the conclusions of relativity can be reached with only the simplest of mathematics.

SPECIAL RELATIVITY

All motion is relative; the speed of light in free space is the same for all observers.

When such quantities as length, time interval, and mass are considered in elementary physics, no special point is made about how they are measured. Since a standard unit exits for each quantity, who makes a certain determination would not seem to matter-everybody ought to get the same result. For instance, there is no question of principle involved in finding the length of an airplane when we are on board. All we have to do is put one end of a tape measure at the airplane’s nose and look at the number on the tape at the airplane’s tail.

But what if the airplane is in flight and we are on the ground? It is not hard to determine the length of a distant object with a tape measure to establish a baseline, a surveyor’s transit to measure angles, and knowledge of trigonometry. When we measure the moving airplane from the ground, though, we find it to be shorter than it is to somebody in the airplane itself. To understand how this unexpected difference arises, we must analyze the process of measurement when motion is involved.

Frames of Reference

The first step is to clarify what we mean by motion. When we say that something is moving, what we mean is that its position relative to something else is changing. A passenger moves relative to an airplane; the airplane moves relative to the earth; the earth moves relative to the sun; the sun moves relative to the galaxy of stars (the Milky Way) of which it is a member; and so on. In each case a frame of reference is part of the description of motion. To say that something is moving always implies a specific frame of reference.

An inertial frame of reference is one in which Newton’s first law of motion holds. In such a frame, an object at rest remains at rest and an object in motion continues to move at constant velocity (constant speed and direction) if no force acts on it. Any frame of reference that moves at constant velocity to an inertial frame is itself an inertial frame.

All inertial frames are equally valid. Suppose we see something changing its position with respect to us at constant velocity. It is moving or are we the laboratory moving? Suppose we are in a closed laboratory in which Newton’s first law holds. Is the laboratory moving or is it at rest? These questions are meaningless because all constant-velocity motion is relative. There is no universal frame of reference that can be used everywhere, no such thing as “absolute motion.”

The theory of relativity deals with the consequences of the lack of a universal frame of reference. Special relativity, which is what Einstein published in 1905, treats problems that involve inertial frames of reference. General relativity, published by Einstein a decade later, describes the relationship between geometry and the geometrical structure of space and time. The special theory has had an enormous impact on much of physics, and we shall concentrate on it here.

Postulates of Special Relativity

Two postulates underlie special relativity. The first, the principle of relativity, states:

The laws of physics are the same in all inertial frames of reference.

This postulate follows from the absence of a universal frame of reference. If the laws of physics were different for different observer in relative motion, the observers could find from these differences which of them were “stationary” in space and which were “moving.” But such a distinction does not exist, and the principle of relativity expresses this fact.

The second postulate is based on the results of many experiments:

The speed of light in free space has the same value in all inertial frames of reference.

This speed is 2.998 x 108 m/s to four significant figures.

To appreciate how remarkable these postulates are, let us look at a hypothetical experiment basically no different from actual ones that have been carried out in a number of ways. Suppose I turn on a searchlight just as you fly past in a spacecraft at a speed of 2 x 108 m/s (Fig 1.1). We both measure the speed of the light waves from the searchlight using identical instruments. From the ground I find their speed to be 3 x 108 m/s as usual. “Common sense” tells me that you ought to find a speed of (3-2) x 108 m/s, or only 1 x 108 m/s, for the same light waves. But you also find their speed to be 3 x 108 m/s, even though to me you seem to be moving parallel to the waves at 2 x 108 m/s.

Albert A. Michelson (1852-1931) was born in Germany but came to the United States at the age of two with his parents, who settled in Nevada. He attended the U.S. Naval Academy at Annapolis where, after two years of sea duty, he became a science instructor.

To improve his knowledge of optics, in which he wanted to specialize, Michelson went to Europe and studied in Berlin and Paris. Then he left the Navy to work first at the Case School of Applied Science in Ohio, then at Clark University in Massachusetts, and finally at the University of Chicago, where he headed the physics department from 1892 to 1929.Michelson’s specialty was high precision measurement, and for many decades his successive figures for the speed of light were the best available. He redefined the meter in terms of wavelengths of a particular spectral line and devised an interferometer that could determine the diameter of a star (stars appear as points of light in even the most powerful telescopes):

Michelson’s most significant achievement, carried out in 1887 in collaboration with Edward Morley, was an experiment to measure the motion of the earth trough “ether,” a hypothetical medium pervading the universe in which light waves were supposed to occur. The notion of the ether was hangover from the days before light waves were recognized as electromagnetic, but nobody at the time seemed willing to discard the idea that light propagates relative to some sort of universal frame of reference.

To look for the earth’s motion trough the ether, Michelson and Morley used a pair of light

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