Relativity

I

Introduction

Relativity, theory, developed in the early 20th century, which originally attempted to account for certain anomalies in the concept of relative motion, but which in its ramifications has developed into one of the most important basic concepts in physical science (see Physics). The theory of relativity, developed primarily by German American physicist Albert Einstein, is the basis for later demonstration by physicists of the essential unity of matter and energy, of space and time, and of the forces of gravity and acceleration (see Acceleration; Energy; Gravitation).

II

Classical Physics

Physical laws generally accepted by scientists before the development of the theory of relativity, now called classical laws, were based on the principles of mechanics enunciated late in the 17th century by the English mathematician and physicist Isaac Newton. Newtonian mechanics and relativistic mechanics differ in fundamental assumptions and mathematical development, but in most cases do not differ appreciably in net results; the behavior of a billiard ball when struck by another billiard ball, for example, may be predicted by mathematical calculations based on either type of mechanics and produce approximately identical results. Inasmuch as the classical mathematics is enormously simpler than the relativistic, the former is the preferred basis for such a calculation. In cases of high speeds, however, assuming that one of the billiard balls was moving at a speed approaching that of light, the two theories would predict entirely different types of behavior, and scientists today are quite certain that the relativistic predictions would be verified and the classical predictions would be proved incorrect.

In general, the difference between two predictions on the behavior of any moving object involves a factor discovered by the Dutch physicist Hendrik Antoon Lorentz, and the Irish physicist George Francis FitzGerald late in the 19th century. This factor is generally represented by the Greek letter β (beta) and is determined by the velocity of the object in accordance with the following equation:

in which v is the velocity of the object and c is the velocity of light (see Light). The beta factor does not differ essentially from unity for any velocity that is ordinarily encountered; the highest velocity encountered in ordinary ballistics, for example, is about 1.6 km/sec (about 1 mi/sec), the highest velocity obtainable by a rocket propelled by ordinary chemicals is a few times that, and the velocity of the earth as it moves around the sun is about 29 km/sec (about 18 mi/sec); at the last-named speed, the value of beta differs from unity by only five billionths. Thus, for ordinary terrestrial phenomena, the relativistic corrections are of little importance. When velocities are very large, however, as is sometimes the case in astronomical phenomena, relativistic corrections become significant. Similarly, relativity is important in calculating very large distances or very large aggregations of matter. As the quantum theory applies to the very small, so the relativity theory applies to the very large.

Until 1887 no flaw had appeared in the rapidly developing body of classical physics. In that year, the Michelson-Morley experiment, named after the American physicist Albert Michelson and the American chemist Edward Williams Morley, was performed. It was an attempt to determine the rate of the motion of the earth through the ether, a hypothetical substance that was thought to transmit electromagnetic radiation, including light, and was assumed to permeate all space. If the sun is at absolute rest in space, then the earth must have a constant velocity of 29 km/sec (18 mi/sec), caused by its revolution about the sun; if the sun and the entire solar system are moving through space, however, the constantly changing direction of the earth's orbital velocity will cause this value of the earth's motion to be added to the velocity of the sun at certain times of the year and subtracted from it at others. The result of the experiment was entirely unexpected and inexplicable; the apparent velocity of the earth through this hypothetical ether was zero at all times of the year.

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What the Michelson-Morley experiment actually measured was the velocity of light through space in two different directions. If a ray of light is moving through space at 300,000 km/sec (186,000 mi/sec), and an observer is moving in the same direction at 29 km/sec (18 mi/sec), then the light should move past the observer at the rate of 299,971 km/sec (185,982 mi/sec); if the observer is moving in the opposite direction, the light should move past the observer at 300,029 km/sec (186,018 mi/sec). It was this difference that the Michelson-Morley experiment failed to detect. This failure could not be explained on the hypothesis that the passage of light is not affected by the motion of the earth, because such an effect had been observed in the phenomenon of the aberration of light; see Interference; Interferometer; Wave Motion.

In the 1890s FitzGerald and Lorentz advanced the hypothesis that when any object moves through space, its length in the direction of its motion is altered by the factor beta. The negative result of the Michelson-Morley experiment was explained by the assumption that the light actually traversed a shorter distance in the same time (that is, moved more slowly), but that this effect was masked because the distance was measured of necessity by some mechanical device which also underwent the same shortening, just as when an object 2 m long is measured with a 3-m tape measure which has shrunk to 2 m, the object will appear to be 3 m in length. Thus, in the Michelson-Morley experiment, the distance which light traveled in 1 sec appeared to be 300,000 km (186,000 mi) regardless of how fast the light actually traveled. The Lorentz-FitzGerald contraction was considered by scientists to be an unsatisfactory hypothesis because it could not be applied to any problem in which measurements of absolute motion could be made.

III

Special Theory of Relativity

In 1905, Einstein published the first of two important papers on the theory of relativity, in which he dismissed the problem of absolute motion by denying its existence. According to Einstein, no particular object in the universe is suitable as an absolute frame of reference that is at rest with respect to space. Any object (such as the center of the solar system) is a suitable frame of reference, and the motion of any object can be referred to that frame. Thus, it is equally correct to say that a train moves past the station, or that the station moves past the train. This example is not as unreasonable as it seems at first sight, for the station is also moving, due to the motion of the earth on its axis and its revolution around the sun. All motion is relative, according to Einstein. None of Einstein's basic assumptions was revolutionary; Newton had previously stated “absolute rest cannot be determined from the position of bodies in our regions.” Einstein stated the relative rate of motion between any observer and any ray of light is always the same, 300,000 km/sec (186,000 mi/sec), and thus two observers, moving relative to one another even at a speed of 160,000 km/sec (100,000 mi/sec), each measuring the velocity of the same ray of light, would both find it to be moving at 300,000 km/sec (186,000 mi/sec), and this apparently anomalous result was proved by the Michelson-Morley experiment. According to classical physics, one of the two observers was at rest, and the other made an error in measurement because of the Lorentz-FitzGerald contraction of his apparatus; according to Einstein, both observers had an equal right to consider themselves at rest, and neither had made any error in measurement. Each observer used a system of coordinates as the frame of reference for measurements, and these coordinates could be transformed one into the other by a mathematical manipulation. The equations for this transformation, known as the Lorentz transformation equations, were adopted by Einstein, but he gave them an entirely new interpretation. The speed of light is invariant in any such transformation.

According to the relativistic transformation, not only would lengths in the line of a moving object be altered but also time and mass. A clock in motion relative to an observer would seem to be slowed down, and any material object would seem to increase in mass, both by the beta factor. The electron, which had just been discovered, provided a means of testing the last assumption. Electrons emitted from radioactive substances have speeds close to the speed of light, so that the value of beta, for example, might be as large as 0.5, and the mass of the electron doubled. The mass of a rapidly moving electron could be easily determined by measuring the curvature produced in its path by a magnetic field; the heavier the electron, the greater its inertia and the less the curvature produced by a given strength of field (see Magnetism). Experimentation dramatically confirmed Einstein's prediction; the electron increased in mass by exactly the amount he predicted. Thus, the kinetic energy of the accelerated electron had been converted into mass in accordance with the formula E=mc² (see Atom; Nuclear Energy). Einstein's theory was also verified by experiments on the velocity of light in moving water and on magnetic forces in moving substances.

The fundamental hypothesis on which Einstein's theory was based was the nonexistence of absolute rest in the universe. Einstein postulated that two observers moving relative to one another at a constant velocity would observe identically the phenomena of nature. One of these observers, however, might record two events on distant stars as having occurred simultaneously, while the other observer would find that one had occurred before the other; this disparity is not a real objection to the theory of relativity, because according to that theory simultaneity does not exist for distant events. In other words, it is not possible to specify uniquely the time when an event happens without reference to the place where it happens. Every particle or object in the universe is described by a so-called world line that describes its position in time and space. If two or more world lines intersect, an event or occurrence takes place; if the world line of a particle does not intersect any other world line, nothing has happened to it, and it is neither important nor meaningful to determine the location of the particle at any given instant. The “distance” or “interval” between any two events can be accurately described by means of a combination of space and time, but not by either of these separately. The space-time of four dimensions (three for space and one for time) in which all events in the universe occur is called the space-time continuum.

All of the above statements are consequences of special relativity, the name given to the theory developed by Einstein in 1905 as a result of his consideration of objects moving relative to one another with constant velocity.

IV

General Theory of Relativity

In 1915 Einstein developed the general theory of relativity in which he considered objects accelerated with respect to one another. He developed this theory to explain apparent conflicts between the laws of relativity and the law of gravity. To resolve these conflicts he developed an entirely new approach to the concept of gravity, based on the principle of equivalence.

The principle of equivalence holds that forces produced by gravity are in every way equivalent to forces produced by acceleration, so that it is theoretically impossible to distinguish between gravitational and accelerational forces by experiment. In the theory of special relativity, Einstein had stated that a person in a closed car rolling on an absolutely smooth railroad track could not determine by any conceivable experiment whether he was at rest or in uniform motion. In general relativity he stated that if the car were speeded up or slowed down or driven around a curve, the occupant could not tell whether the forces so produced were due to gravitation or whether they were acceleration forces brought into play by pressure on the accelerator or on the brake or by turning the car sharply to the right or left.

Acceleration is defined as the rate of change of velocity. Consider an astronaut standing in a stationary rocket. Because of gravity his or her feet are pressed against the floor of the rocket with a force equal to the person's weight, w. If the same rocket is in outer space, far from any other object and not influenced by gravity, the astronaut is again being pressed against the floor if the rocket is accelerating, and if the acceleration is 9.8 m/sec² (32 ft/sec²) (the acceleration of gravity at the surface of the earth), the force with which the astronaut is pressed against the floor is again equal to w. Without looking out of the window, the astronaut would have no way of telling whether the rocket was at rest on the earth or accelerating in outer space. The force due to acceleration is in no way distinguishable from the force due to gravity. According to Einstein's theory, Newton's law of gravitation is an unnecessary hypothesis; Einstein attributes all forces, both gravitational and those associated with acceleration, to the effects of acceleration. Thus, when the rocket is standing still on the surface of the earth, it is attracted toward the center of the earth. Einstein states that this phenomenon of attraction is attributable to an acceleration of the rocket. In three-dimensional space, the rocket is stationary and therefore is not accelerated; but in four-dimensional space-time, the rocket is in motion along its world line. According to Einstein, the world line is curved, because of the curvature of the continuum in the neighborhood of the earth.

Thus, Newton's hypothesis that every object attracts every other object in direct proportion to its mass is replaced by the relativistic hypothesis that the continuum is curved in the neighborhood of massive objects. Einstein's law of gravity states simply that the world line of every object is a geodesic in the continuum. A geodesic is the shortest distance between two points, but in curved space it is not generally a straight line. In the same way, geodesics on the surface of the earth are great circles, which are not straight lines on any ordinary map. See Geometry; Navigation.

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