The Concept of Light

Of all the senses, vision supplies us with more information, both in quantity and in detail, than all the others combined. What we see depends fundamentally on the properties of light as well as the physical and psychological processes of interpretation. It is no wonder that the nature of light has always been a subject of great speculation and interest. In spite of this wide interest and many attempts at explanation, just what light is remained in dispute until the first decade of the twentieth century.

At the time of Newton, debate about light centered on the question of whether light consists of a stream of particles, or "corpuscles," or whether it is some sort of wave phenomenon. Newton favored the corpuscular idea, and because of his prestige, many others were inclined to accept this view. In 1803 Thomas Young presented the result of an experiment in which light from two sources displayed interference patterns similar to those one would expect from two overlapping waves. At about this same time, the speed of light passing through water was measured, and found to be slower than the speed of light in air. Since Newton's corpuscular theory held that light should move faster in water, this was a second piece of evidence contradicting that theory. As a result, the wave theory became the dominant concept of light, to be given a rigorous mathematical foundation in the 1860s by the extraordinary work of Maxwell.

One would think, then, that by 1900 the wave nature of light would have been reasonably well understood and widely accepted. However, the interaction of light with matter, both in how light is emitted and in how it is absorbed, remained puzzling. The spectrum of light emitted by heated solids (blackbody radiation) and by simple atoms such as those of hydrogen, could not be explained adequately by a wave theory of light. A phenomenon known as the photoelectric effect, in which electrons are ejected from metal surfaces illuminated by light, was successfully explained in 1905 by Einstein, using the idea that light interacts with the electrons as if it consists of a stream of particles. Through the development of quantum theory during the twentieth century, we have come to an uneasy truce with the idea that under certain circumstances, light behaves as a wave, while under different circumstances, it behaves as a stream of mass less particles called photons.

The correspondence between wavelengths and colors shown here is only approximate. Colors such as bluegreen and orange occupy the intermediate regions.

Light waves are electromagnetic and thus consist of an oscillating electric field perpendicular to and in phase with an oscillating magnetic field. The wavelengths of visible light lie in the range of 400 to 700 nm. Wavelength range corresponds to a frequency range of 4.3 x 1014 to 7.5 x 1014 Hz. The electric field for a wave propagating in the x direction is shown in Fig. Notice that the oscillating E field is perpendicular to the x-axis. Hence, light waves are transverse waves, since the wave oscillation is perpendicular to the direction of propagation. As such, they have many properties in common with other transverse waves such as waves on a string or waves on a water surface. One of the most direct pieces of evidence that light is a transverse wave is that light can be polarized. Only transverse waves have this property.

FIGURE

The electric field of an electromagnetic wave vibrates perpendicular to the direction of propagation. Hence the wave is transverse.

THE SPEED OF LIGHT

In the SI, the speed of light in vacuum is defined to be exactly c = 299,792,458 m/s, which we usually round off to 3.0 x 108 m/s. This definition was chosen so as to agree with the measured speed of light in terms of the meter. Prior to the adoption of this standard, many attempts were made to measure c. One of the first to try was Galileo; he was unsuccessful, concluding only that light transmission "if not instantaneous, was extremely rapid." The first quantitative result came in 1675 when the Danish astronomer Roemer used the relative motion of earth and one of Jupiter's moons to conclude that light traveled at about 2.1 x 108 m/s. Most of Roemer's error can be attributed to an incorrect value for the radius of earth's orbit. In 1849 the French physicist Fizeau measured the time it took light to make a roundtrip from one mountain to another 8.6 km away. Fizeau's results gave a value of c = 3.1 x 10⁸ m/s.

A simplified drawing of Michelson's method for measuring the speed of light. If the mirrored cube is rotating at just the proper speed, the beam will be reflected into the eye of the observer. In practice, the distance D is much larger than shown.

The first highly precise measurements were carried out by the American A. A. Michelson in the 1920s. Michelson measured the time of flight of a light beam over the roundtrip distance of 70 km between Mt. San Antonio (now Mt. Baldy) and Mt. Wilson in California. A beam of light from the source is reflected from one side of a cube that has mirrored surfaces on four sides. The beam is then reflected from mirror M back to the cube, where it is reflected again as shown. If the cube is at just the right position, the beam will enter an observer's eye in the position indicated.

Suppose, however, that the cube is rotating about an axis through its center, perpendicular to the page. When the cube is in the position indicated by the heavy lines, the beam is reflected to the mirror. By the time the beam returns to the cube from the mirror, however, the cube will have rotated, perhaps to the position represented by the lighter lines, and so the beam will not be reflected into the observer's eye. If the beam is to be reflected to the eye, the cube must rotate through 0.25 rev during the time the beam takes to travel to the mirror M and back, for only then will the cube again be in a position given by the heavy lines and reflect the beam to the eye.

The measurement technique is to vary the speed of rotation of the cube until the reflected beam enters the eye. At that speed of rotation, we know that the time taken for onefourth of a cube rotation is equal to the time the light takes to travel a distance 2D. It is necessary to know only the speed of rotation of the cube and D in order to compute the speed of the light. Michelson's experiments resulted in a value of 2.99796 x 10⁸ m/s.

The experiments that established the present value of c were carried out in the early 1970s, using wavelength and frequency measurements on light emitted by lasers. These remain among the most precise measurements made of any physical constant.

Light travels fastest through vacuum. Its speed in other materials is always less than c. Moreover, its speed in materials other than vacuum depends on the wavelength of the light as well as on the material.

THE SPEED OF LIGHT AS A LIMTING SPEED

Using Einstein's two postulates, we can prove by logic alone that “No material object can be accelerated to speeds in excess of the speed of light in vacuum.”

The validity of this statement is easily demonstrated in the following simple way. We prove it by the technique called reductio ad absurdum, in which we disprove a proposition (in this case, that an object can travel faster than c) by showing that it leads to a known false result (in this case, that an observer will measure a value different from c for the speed of light).

Suppose we have two non-accelerating stations in space. They act as inertial reference frames. Observers at A and B have instructed the spaceship operator to follow a straightline path between A and B, traveling at the spaceship's top constant speed. Just as it passes A, it is to send a light pulse from the front of the ship toward B. Of course, A and B, working in partnership, can determine the speed of the spaceship by timing its flight from A to B. Let us make the false assumption that they find the speed to be 2c.

The spaceship sent out a pulse of light as it passed A, and since the laws of nature must apply to all three inertial observers (A, B, and the person in the ship), the light pulse must behave in a normal way for each of them. Remember, the observer in the ship cannot tell whether or not the ship is moving, except in a relative sense. Therefore, the observer in the ship must see the light pulse precede the ship at the speed c and reach B before the ship does. Therefore A and B, working together, would see the light pulse moving faster than the ship. But they measure the ship as moving with speed 2c, and so they find that the speed of the light pulse is greater than 2c. But this is an impossible result, since it contradicts the known fact that all observers will always obtain c for the speed of light. We therefore conclude that our original assumption was false; the spaceship could not have been moving between A and B with a speed of 2c.

This experiment will always lead to this contradiction as long as we insist that the speed of the ship exceed c. We therefore conclude that the spaceship cannot exceed the measured speed of light c. Indeed, we can enlarge this line of reasoning to include all material objects and signals that carry energy. As a result we can state:
“Nothing that carries energy can be accelerated to the speed of light c.”

As we proceed, we will see that this result of Einstein's theory also has repeatedly been tested carefully and has been found correct in every test.