Special Relativity

Type of physical science: Relativity

Field of study: Special relativity

The special theory of relativity was introduced by Albert Einstein as an alternative to classical physics. The new theory rejected unworkable concepts, such as absolute motion and absolute time, and introduced such new ideas as relative length, mass, and time.

Overview

In 1905, Albert Einstein published several significant papers which solved some long-debated problems in physics, one of which, "On the Electrodynamics of Moving Bodies," became known as the special theory of relativity. In this paper, Einstein introduced such concepts as relativistic mass, length, and time, casting off the ideas of absolute motion and absolute time.

The special theory of relativity was one of several theories which would turn away from classical concepts and revolutionize physics in the early 1900's.

The science of classical mechanics was based mainly on the theories of Galileo and Newton. Galileo had devised a system whereby motion in one frame of reference could be described mathematically by an observer in another frame of reference. This system became known as the Galilean transformation equation. The basis of the mechanics of Galileo was the principle of relativity. According to this principle, if an experiment is performed in a laboratory at rest, and the same experiment is performed in a laboratory moving at a constant velocity, then the results of the two experiments will be identical.

According to the classical viewpoint, velocities of various bodies may be added together in order to determine an overall velocity. For example, suppose that a passenger is riding in a train which is traveling at a rate of 45 kilometers per hour. The passenger then throws a ball toward the front of the car. The ball is thrown with a velocity of 45 kilometers per hour.

According to the passenger, the ball has a velocity of 45 kilometers per hour. If the event was observed by someone standing by the tracks, then that observer would calculate the velocity of the ball to be 90 kilometers per hour; the observer would simply add the velocity of the ball to the velocity of the car. This method would accurately explain what has been observed.

Following Galileo, Newton published his laws of motion and the universal law of gravitation in the 1687 volume, Philosophiae Naturalis Principia Mathematica. Using Newton's laws, it was possible to define an inertial frame of reference. In an inertial frame of reference, Newton's laws of motion are valid. It follows that such a frame of reference must be either at rest or in a state of uniform motion along a straight line. A good example might be an airplane. As long as there is no air turbulence and the aircraft is neither accelerating nor decelerating, one may walk down the aisles and eat or drink without difficulty. On a rapidly rotating merry-go-round, however, such would not be the case. This type of reference frame, which is rotating, is an example of a noninertial frame of reference. The passenger and observer from the first example are both in inertial frames of reference. Because the addition of velocities is valid in these inertial frames of reference, it may be said that the laws of Newton are invariant under the Galilean transformation equation.

In the 1860's, James Clerk Maxwell examined the research that had been done in the area of electricity and magnetism. He was able to combine the work of Michael Faraday, Andre-Marie Ampere, and Charles-Augustin de Coulomb into a set of four equations. These equations specify, among other things, how electric and magnetic fields vary in space and time.

Maxwell also predicted the existence of electromagnetic waves. An electromagnetic wave consists of two perpendicular, oscillating force fields--one electric, the other magnetic. Maxwell calculated the speed of these electromagnetic waves through space and found the value to be 300,000 kilometers per second. This figure matched nearly identically the known speed of light.

Maxwell later theorized that light is a form of electromagnetic radiation. Returning to the train and the observer at rest with respect to the train, suppose that the passenger, instead of throwing a ball, fires a beam of light toward the front of the moving car.

The passenger will observe the beam to be traveling at c, the speed of light. What about the observer at rest? According to classical physics, the observer will calculate the beam to be traveling at c plus 45 kilometers per hour, the velocity of the car. In other words, the velocity of light is added to the velocity of the car. It was eventually found that this conclusion is not possible.

In 1887, Albert Abraham Michelson and Edward Williams Morley attempted to detect the effects of the so-called ether wind. According to this theory, as the earth moves through the ether (a hypothetic substance), it will encounter light waves being carried by the ether. An observer on the surface of the earth would measure the speed of light as c plus the velocity of the earth through the ether. Light approaching from the direction opposite the motion of the earth would have a velocity of c minus the velocity of the earth. It was widely believed that Michelson and Morley would discover this variation in the velocity of light. After attempting the experiment several times, however, they were unable to find any difference in the velocity of light. No matter how their apparatus was adjusted, the speed of light was always the same. By failing to detect the effects of the ether, Michelson and Morley proved that the speed of light is always a constant, regardless of the motion of the observer. The experiment showed that electromagnetism is not Galilean invariant.

In 1905, Einstein proposed that the laws of physics must be mathematically invariant in all inertial frames of reference. Essentially, this is a restatement of the Galilean principle of relativity, but with a broader scope. Einstein's proposal included all physical phenomena, mechanical and electromagnetic. Another way of stating the new principle is as follows: There is no experiment that can be conducted which can establish a condition of rest or absolute uniform motion.

A second postulate of the special theory of relativity states that the speed of light is always the same, regardless of the motion of the observer or the source. This statement explains why Michelson and Morley failed to detect any variation in the speed of light. Therefore, the speed of light is a fundamental universal constant and, in fact, is the only universal constant. The classical concepts of mass, length, and time were no longer valid in the new world of relativity.

Consider the following problem. Two bicyclists, X and Y, are standing on each side of a road and are tossing a ball back and forth between them. An observer, O, standing nearby measures the velocity of the ball accurately. The two bicyclists then ride down the road, continuing to toss the ball between them. If they measure the velocity of the ball, they will find (ignoring the effects of air resistance) that the velocity is identical to the situation when they were at rest. The observer standing by the road will disagree, seeing the ball move forward as well as back and forth between the bicyclists. To the observer, the path of the ball appears to be slightly longer (the hypotenuse of the triangle). The observer will then conclude that the true velocity of the ball is the vector sum of the ball's velocity with respect to both the bicyclists and the ground. The bicyclists and the observer then determine different velocities for one toss of the ball, which must be the case because the path lengths are different but both the observer and the bicyclists see the ball arrive at X at the same time.

Suppose that the ball is replaced by a beam of light. The question becomes: Will the bicyclists and the observer continue to measure different velocities? The answer, according to special relativity and the Michelson-Morley experiment results, is no. The two measured velocities must be the same.

A point of confusion arises: How can a beam of light travel two different distances (X-Y and X-X') with the same velocity and arrive at the same time? The only alternative that can explain this phenomenon is time; the recorded times must be different. The clocks of the bicyclists and of the observer must keep different times when one is in motion relative to the other. A mathematical analysis of the problem indicates that the clock in motion runs slightly slower than the clock at rest, at least from the observer's point of view. The effects of this phenomenon, known as time dilation, become more pronounced with greater velocities. As the speed of light is approached, clocks continue to slow. Theoretically, at the speed of light, time would stop.

When the postulates of special relativity are applied in the transformation of length and mass to other inertial frames, some rather strange effects are noted. Einstein incorporated the Lorentz-FitzGerald contraction hypothesis into his theory and showed that space is affected by relative motion. For example, an observer at rest will observe an accelerating spaceship to contract along its axis of motion. The closer the spaceship gets to the speed of light, the shorter it appears to the observer. If the ship could achieve c, then its length would shrink to zero.

The theory also indicates that the faster an object travels, the more difficult it becomes to accelerate the object. As the object approaches the speed of light, its relativistic mass approaches infinity and its acceleration approaches zero. This relationship seems to indicate that the speed of light is the limiting velocity in the universe.

A further consequence of the special theory of relativity is the equivalence of mass and energy. In his analysis, Einstein equated inertial mass with the energy possessed by a moving body and concluded that energy must have mass. His equation of this equivalence, E = mc2 is, without a doubt, the best-known relationship in physics.

Applications

The mass-energy relationship that is predicted by the special theory of relativity is confirmed each time a nuclear reaction takes place. Two such reactions are known: fusion and fission. Fusion is the process that powers the sun and the other stars. The simplest form of a fusion reaction, the proton-proton cycle, involves the joining together of hydrogen nuclei to form helium, which is the energy-producing process that goes on within the sun. In more massive stars, other fusion cycles form heavier elements. In each reaction, some mass is destroyed and changed directly into energy. This energy is carried away from stellar cores in the form of gamma rays and chargeless, massless particles called neutrinos.

The second nuclear reaction, fission, is the breaking down of the nuclei of heavy elements such as uranium. An example of a fission reaction is the formation of the elements barium and krypton from an isotope of uranium. During this process, some matter is destroyed and converted into energy. Fission is the process that powers commercial nuclear plants and atomic bombs. In both fusion and fission reactions, the amount of matter that is converted into energy is predicted by Einstein's equation, E = mc².

There are other instances in which matter is changed into energy, but the amount of mass and energy is too infinitesimal for ordinary calculations. For example, an old-fashioned wristwatch which has been wound has slightly more mass than when it has run down. In the process of ticking, some of the mass of the watch is being changed into energy.

In research reactors, scientists have observed that energy sometimes changes into mass.

Virtual pairs of elementary particles often spontaneously appear in the high-energy environment of the reactor and then quickly vanish. The evidence for their existence is only a thin spiraling line on a photograph.

Time dilation is another aspect of special theory which has been confirmed. Relativistic time is often explained by the use of a story called the "twin paradox." According to the story, one twin becomes an astronaut. When they reach the age of thirty-five, the astronaut goes on a long journey in space, traveling at the speed of light. He is gone for thirty-five years. When he returns to Earth, he finds that his twin brother is seventy years old while he is still thirty-five years old. According to the special theory, moving clocks run slower than those at rest and, at c, time stops.

In the early 1960's, two American physicists, David H. Frisch and James H. Smith, conducted an experiment which would prove Einstein's time-dilation concept. For their clocks, they chose a radioactive particle called a muon. Muons are created in the upper atmosphere by cosmic rays. They are short-lived, however, changing quickly into other nonradioactive particles.

Frisch and Smith intended to measure the number of muons at a high altitude and determine how many of them would survive long enough to reach the surface of the earth. They set up their detector on the summit of Mt. Washington in New Hampshire at an altitude of 1,800 meters.

Muons of a certain frequency were detected at the rate of 563 per hour. According to the theory of radioactive decay, only twenty-seven of these muons would reach the earth's surface before decaying. Because the velocity of these particles was known to be about 99 percent of the speed of light, relativistic effects were considered. Einstein's theory predicted that four hundred muons would be detected at the surface. The detector was moved to sea level and readings were taken.

The number of muons counted per hour was 408, or almost exactly what the special theory of relativity had predicted.

Context

From the time of Newton until the turn of the twentieth century, the nature of light was a topic of considerable debate. The two schools of thought were the followers of Newton, who subscribed to the corpuscular or particle theory, and those of Robert Hooke and Christiaan Huygens, who advocated the wave theory. Over the years, several experiments were carried out that seemed to support the wave theory.

By the early 1800's, the wave theory was virtually universally accepted by the scientific community. Scientists then needed a conducting medium, which would occupy all the universe, to carry these light waves. They decided to call this substance the "ether." In addition to having some rather unique properties, the ether was believed to be in a state of absolute rest. A substance in such a state could be used as an absolute frame of reference, a point from which all motion could be measured.

It was believed that the speed of light could vary depending on the motion of the observer. Light encountered by the earth in its journey through the ether would be found to have a velocity of c plus the velocity of the earth. Light coming from the other direction, catching up with the earth, would be found to have a speed of c minus the velocity of the earth through the ether. In their experiment, Michelson and Morley failed to detect a difference in the speed of light coming from any direction.

The failure of the 1887 experiment of Michelson and Morley to detect the ether sent a shock wave through the physics community. The ether was so vital to classical physics that several theories were developed which suggested ways to save it in spite of Michelson and Morley's results. Probably the most bizarre of these theories was developed independently by Hendrik Antoon Lorentz and George Francis FitzGerald. This so-called contraction hypothesis proposed that an object shrinks along its axis of motion. They were convinced that the motion of the earth through the ether had caused a contraction in the apparatus used by Michelson and Morley, thus preventing them from detecting any difference in the speed of light.

In 1895, physicist Jules-Henri Poincare rejected the contraction hypothesis and other ad hoc solutions to the ether problem. He went on to suggest that a new science of mechanics be created, one in which no velocity could exceed that of light. This very concept would be the basis for Einstein's special theory of relativity.

Principal terms

ELECTROMAGNETIC WAVES: forms of radiant energy (such as light) which are transmitted through space in the form of two waves, one electric and one magnetic, that have the same velocity, are in phase with each other, and are perpendicular to each other

ETHER: a hypothetical substance which was believed to fill the entire universe and serve as a medium for the conduction of waves

FRAME OF REFERENCE: a point of reference from which motion is measured

INERTIAL FRAME OF REFERENCE: a frame of reference which moves at a constant velocity and for which Sir Isaac Newton's laws of motion are valid

INVARIANT: the same regardless of the position or motion of the observer

Bibliography

Barnett, Lincoln. THE UNIVERSE AND DR. EINSTEIN. New York: William Sloane Associates, 1948. This very readable volume covers the special and general theories of relativity and the history of their development. Well suited for the layperson.

Gardner, Martin. THE RELATIVITY EXPLOSION. New York: Random House, 1976. This volume is the updated version of the popular 1962 volume, RELATIVITY FOR THE MILLION. This well-written, well-illustrated volume covers special and general relativity theories. The new chapters cover topics such as pulsars, quasars, black holes, and cosmology. Highly recommended for the layperson.

Hoffmann, Banesh. RELATIVITY AND ITS ROOTS. New York: W. H. Freeman, 1983. This volume considers both the special and general theories of relativity, as well as the historical background leading to their development. This volume is somewhat technical, and the reader should have some understanding of basic physics.

Inglis, Stuart J. PHYSICS: AN EBB AND FLOW OF IDEAS. New York: John Wiley & Sons, 1970. This volume traces the development of physics from the ancient Greeks through relativity and quantum theories. Although this book has been used as a college text for nonscience majors, it is accessible to the general reader.

Kim, S. A. PHYSICS: THE FABRIC OF REALITY. New York: Macmillan, 1975. This volume covers topics related to relativity and quantum physics. The reader should have some understanding of basic physics.

Williams, L. Pearce. RELATIVITY THEORY: ITS ORIGINS AND IMPACT ON MODERN THOUGHT. New York: John Wiley & Sons, 1968. This volume is a collection of original papers on topics relating to relativity theory. Papers by Albert Einstein, Ernst Mach, Albert Abraham Michelson, Hendrik Lorentz, and Jules-Henri Poincare are included. Some of the writings are quite technical; others are more historical.

Zee, Anthony. FEARFUL SYMMETRY. New York: Macmillan, 1986. A fairly technical volume concerning topics in modern physics. Contains a very informative section on special and general relativity. The reader should have some physics background.