Theory of Relativity

Einstein's Theory of Relativity

Certain theories, very few in number, have so greatly influenced scientific think­ing that they stand out above all the rest. Among them are the hypothesis of Coper­nicus concerning the motions of the plan­ets; the doctrine of universal gravitation, advanced by Sir Isaac Newton; the cell theory of Schleiden and Schwann; and Darwin's theory of organic evolution. We certainly must also include the theory of relativity, formulated by Albert Einstein and developed further by Einstein himself and several other scientists.

This theory has revolutionized our thinking. It has altered our ideas of space, time, mass, energy, motion, and gravitation. It has provided a new approach to the study of the universe. It is made up of a special theory and a general theory. Both rest on a solid mathematical foundation, and both have been confirmed by experimentation and observation.


The theory of relativity arose from the need for frame of reference-a standard that scientists could use in analyzing the laws of motion. The need for such a standard is obvious, for the moment we attempt ... to analyze motion, we must ask ourselves: "Motion with respect to what?"

Suppose that a pilot is flying a plane far above the Earth in a jet stream (a swift current of air) flowing at 300 kilometers per hour. The plane itself is flying at 300 kilometers per hour in the same direction as the jet stream. The pilot will be moving at a 300-kilometer-per-hour speed with respect to the jet stream, but at 600 kilometers per hour from the viewpoint of an observer stationed on the Earth. If the pilot flies against the jet stream, to the Earth-bound observer he will seem to be hovering motionless in the air.

To an observer on the planet Mars, a speed of 300 kilometers or 600 kilometers per hour would seem insignificant compared to the nearly 300kilomcter-per-second speed of the Earth as it revolves around the Sun. It is moving at many kilometers per second around the center of the Milky Way, the galaxy of which our solar system forms a very small part. The Milky Way itself is moving with respect to other galax­ies. Where, then, is our frame of reference?

At one time, men of science believed in a luminiferous, or light-bearing, Ether that might serve that purpose. The Ether was supposed to be a fluid, or a very elastic sol­id, occupying all the space between the atoms of which matter consisted. Light, it was thought, was transmitted in a series of waves through the Ether-waves at right angles to the direction of motion. Some scientists believed that the Ether itself re­mained motionless as the light waves passed through it. They compared the passage of light through the Ether to the movement of ocean waves in the sea. It is the ocean-wave form, or pattern, they said, that moves for­ward. The water particles themselves do not move to any marked extent. If scientists could show that the Ether had no motion of its own and that the heavenly bodies im­parted none to it as they passed through space, we would have a reliable starting point for a general analysis of motion.

In trying to prove that the Ether was stationary with respect to the Earth, one would have to consider that from our view­point the Earth is standing still. Therefore, the Ether would appear to be rushing past us "like the wind through a grove of trees," to quote the English physicist Thomas Young in the same way, the Sun seems to us to be moving around the Earth, while it is really the Earth that is revolving around the Sun.


Two U.S. scientists, Albert A. Michel­son and Edward W. Morley, tried to solve the Ether problem by making delicate mea­surements of the speed of light. Let us sup­pose, they said, that the Ether is motionless as light is transmitted through it. If the Earth were also motionless in space, light would always seem to have the same veloc­ity when measured by an observer on the Earth. But the Earth moves through space. Hence the velocity of light would appear to change according to the direction in which a light beam would be flashed - that is, in the direction of the Earth's motion, or in the opposite direction, or at right angles to it.

The two scientists analyzed the dif­ferences in the arrival times of the light beams parallel to the Earth's course and at right angles to it. No matter how many measurements they made, the light ap­peared to travel just as rapidly in the direction of the Earth's motion as against it or at right angles to it. The experimenters concluded that "if there be any relative motion between the Earth and the luminiferous Ether, it must be quite small.


The man on the motorcycle sees the ball fall straight down. An observer on the side of the road, though, sees the ball fall in an arc. This illustrates the relativity of motion: Different people see the same event in different ways.

The Michelson-Morley experiments caused scientists to doubt the existence of the luminiferous Ether. What was even more important, they showed that the speed of light is independent of the motion of the observer. Remember that as we try to measure light, we are moving with the Earth through space. In other words, the velocity of light is a constant, which re­mains the same under all circumstances. This concept was to form the basis of Einstein's Special Theory of Relativity,


According to this theory, which was formulated by Einstein in 1905, it is impossible to measure or detect the absolute mo­tion of a body through space. However, we can accurately determine its relative mo­tion by using the speed of light as a basis. This speed comes to about 300,000 kilometers per second.

The special theory modified the ideas of classical physics with respect to space and time. According to these ideas, parti­cles move in a three-dimensional frame­work in space and at specific times. The three dimensions are length, breadth, and thickness, or height. This concept is a fa­miliar one. We know, for example, that a room has length, breadth, and height.

We can determine the position of any point in space. Suppose that we have lo­cated two points, P1 and P2. We want to trace the movement of a particle from P1 to P2, Ordinarily, we would take a time read­ing when the particle is at P1 and another when it is at P2-or rather when we would see the particle arrive at P1, and P2. Time readings of this sort would not be abso­lutely accurate, because it would take time for light to travel from a light source to the particle and to be reflected from the particle to our eyes.

The discrepancy between the apparent and actual times of arrival of a particle at a given point would not be significant ordi­narily because of the great velocity of light. Even if the particle's speed were one-tenth the speed of light, the discrepancy would be so small that it could be detected only with the most refined measurements. But at a speed of one-half that of light-150,000 kilometers per second-the discrepancy would begin to be apparent. It would be great at nine-tenths of the speed of light, and enormous at ninety-nine-hundredths of that speed.

If we were to chart accurately the progress of a particle at such great speeds, we would have to apply the special theory of relativity, which takes into account the time needed by light to traverse space. We could make the necessary calculations with accuracy. For the speed of light always re­mains the same, regardless or the particular position in which the observer may happen to be located.


According to classical physics, there are two separate factors we must consider in charting the progress of a particle in space. These factors are space (the three dimensions of length, breadth, and height) and time. According to the relativity the­ory, we cannot consider time as something apart. It represents a fourth dimension, which must be added to length, breadth, and height. We should refer not to space and time, but to space-time. As a famous German physicist, Hermann Minkowski, put it: "From now on, space by itself and time by itself are mere shadows and only a blend of the two exists in its own right."

We can represent four dimensions mathematically, but we cannot draw more than three dimensions in a diagram. Fur­ther, the fourth dimension - time - should not be thought of as a spatial dimension. In mathematics, a dimension is simply a quantity that must he specified in order to define a situation.

Most people find it hard to grasp even the idea of a fourth dimension. It would be just as hard for a dot-like man living in a world made up or two dimensions  - length and breadth - to conceive of a third one.

If our dot-man traveled from point A (see diagram) in his two-dimensional world, he would go ahead for an infinite period of time in a straight line. Suppose he were transported to a three-dimensional world­ - a sphere of enormous size. The dot-man would not be aware of any change in the surface, since the curvature, from his point of view, would be slight. But if he started from point A on the sphere and advanced in what for him would be a straight line, he would be mystified to find he returned to point A. Our dot-man could not visualize a sphere, since he would be familiar only with a two-dimensional world. However, a dot-man mathematician could explain the structure of the sphere in terms of mathematics. He could show by means of mathematical symbols and equations just what had happened to the dot-man who had returned to the place from which he had started out. But unless the dot-man traveler, were familiar with the language and methods of mathematics, the explanation would not clear up his doubts. Many humans would find it as hard to follow an explanation of the fourth dimension.

Above: a dot-man traveling from point A in a two dimensional world would go ahead for an infinite period of time in a straight line as shown.

Above: If the dot-man started from point A on a sphere and in what for him appeared to be a straight line. He would eventually return to point A


The space-time of Einstein is called a four-dimensional continuum. It is also called a space-time continuum. The point of space and the instant of time at which any event occurs represents a single point in the continuum. The interval between any two events would be represented by a finite line (one with definite limits). A succession of finite lines of this kind would make up a record of the successive positions occupied by a particle in space-time. A complete record of this sort of the total course of the particle from the first to the last moment of its existence would be called the parti­cle's world line,

To understand the principle involved, let us suppose that the two-dimensional world of the dot-man is marked out in equal squares, formed by intersecting lines (see below). The dot-man is taking a walk. He starts at point A, at the intersection of two of the lines and goes straight ahead. At the end of an hour he reaches point B, where two other lines intersect. At the end of two hours he reaches point C, and so on. If we draw a line connecting all these points, it will represent part of a world line based on

A dot-man traveling in a two dimensional world goes ahead in

a straight line from A to B; from B to C; from C to D; from D to E; from E to F. The line AF would represent part of the world line of the dot-man, the record of his movement.


Matter will have an effect on the net­work of the space-time continuum. Matter distorts, the network. Without matter, the continuum would be Euclidean, and go on forever in straight lines in any direction. We can show this warping in three dimensions by imagining a network of rubber bands, criss-crossing like a fly screen. Without matter nearby, the rubber bands would be flat in two dimensions.

Now if we drop a billiard ball into this net, the net will be distorted, and more distorted near the ball. In the same way, matter can be thought of as distorting a four-dimensional continuum. A small ball, free to roll, might fall toward a central, large billiard ball, or might circle it, depending on its speed and direction. This would be similar to a meteor coming in from outer space; or, in the case of the small ball circling the larger, to the Earth revolving around the Sun.


The special theory of relativity is indis­pensable in the study of objects traveling at very great speeds, approaching that of light. Interesting things happen to such objects. For one thing, they contract in the direction of their motion. This is called the Fitzger­ald-Lorentz contraction, from the names of the two physicists who advanced the idea in the 1890s. It was proposed independently by the Irish physicist G. F. Fitzgerald and the Dutch physicist Hendrik Antoon Lorentz. At the same time that the object con­tracts, its mass increases and its time slows down.

If a rocket travels at a speed of 30,000 kilometers per hour, there will be no appreciable change in its shape. The reason is that its speed is negligible, compared to the velocity of light. Suppose now that the rocket whizzes past an observer on the Earth at a speed that begins to approach that of light. If the observer would be capable of making out details, he would note that the rocket would have contracted greatly in the direction of its motion. If there were a watch inside the rocket, its time would run slow compared with that of a watch held by the observer on the Earth.

As the speed of the rocket came nearer to that of light, its length in the direction of its motion would approach zero. It would turn into a flat disk. As its speed increased, its mass would approach infinity and its time would slow down more and more. Since it would require an infinite force to accelerate an infinite mass, we conclude that no physical object will ever move with quite the speed of light. It could approach that speed closely, however, if enough force were available.

Can we prove that when objects ap­proach the speed of light, they contract in the direction of their motion? Can we prove also that their mass increases and that their time slows down? The answer to all three questions is "Yes."

The contraction of objects in the direc­tion of their motion has been demonstrated by the study of cosmic radiation. When primary cosmic ray particles collide with nitrogen and oxygen nuclei at high levels in the atmosphere, they give rise, among other things, to particles called mu mesons. These particles are extremely penetrating, making their way through the layers of atmosphere to sea level. They can be readi­ly counted with radiation counters and can be positively identified in cloud chambers. They have a half life of two microsec­onds-that is, two millionths of a second. In two millionths of a second, half of the mu mesons should have decayed into ordinary electrons. But in a millionth of a second a particle traveling at even the speed of light could move only 300 meters or so. How could any mu mesons reach us, since they are formed mostly at the 20,000 kilometer altitude level? They should all have de­cayed by the time they reached sea level.

One reason is that the "clock" that is, the half life of the mu mesons has slowed down by a very large amount. In 200 microseconds of our elapsed time, the "clock" of the mu mesons will have moved ahead only two microseconds.

The slowdown of clocks at speeds ap­proaching that of light is the basis of the famous "clock paradox." A 20-year-old astronaut takes off in a space ship, destina­tion Arcturus, 36 light-years from Earth. He travels at a speed close to the speed of light. His twin brother stays home. When the astronaut returns to Earth, 72 years la­ter, he will have aged one day. His twin brother, however, will have aged 72 years.


The German physicist A. H. Bucherer, around 1910, first demonstrated experi­mentally the increase of mass with velocity. He made mass measurements of beta parti­cles .electrons emitted from naturally ra­dioactive substances. He found that the mass increased with velocity, just as the special theory had predicted.

The time variations at velocities approaching light was demonstrated by the U.S. Physicist H.E. Ives about 1925. He showed that hydrogen atoms, emitting an accurately known frequency of radia­tion, changed their frequency if they were accelerated to speeds approaching that of light, by exactly the amount Einstein pre­dicted.

Other experiments have verified the variations of mass, length, and time with speed, as predicted by the special theory of relativity. Physicists now consider that these variations have been demonstrated beyond the shadow of a doubt.

The law of addition of velocities; each car travels at 60 kilometers (40 MPH); they approach each other at 130 kilometers (80 MPH) because 60 + 60 = 130 or 40 + 40 = 80 (MPH.) However the addition of velocities of two spacecrafts approaching the speed of light can not exceed the speed of light, so that 270,000 kilometers per second (168,000 miles) plus 270,000 kilometers  = 297,000 kilometers (184,000 miles) per second. 


Velocities comparable to that of light might seem to be purely theoretical, but that is not the case. The speeds of particles in the beams of large accelerating ma­chines, such as cyclotrons, synchrotrons, and betatrons, are up in this range. In working with such particles, scientists use the calculations of the special theory of relativity. In fact they often refer to accel­erated particles traveling at speeds that are close to the speed of light as relativistic par­ticles.

A proton or other particle in a synchro­tron reaches a speed substantially equal to that of light. As one continues to accelerate it, it does not move faster but it becomes heavier. Scientists have suggested that such big particle accelerators should be called ponderators (from the Latin pondus, mean­ing weight), or weight-bestowers, since they increase the mass of the particles they accelerate.

In the 1940s, engineers had to use rel­ativistic formulas to calculate correctly the trajectories of electrons in the beams of fast cathode-ray oscilloscopes. In this age of space flight, scientists are devoting more and more attention to the curious phenom­ena that take place at speeds approaching that of light.


The application of the principles of special relativity to the measurements of speeds produces some peculiar results. Suppose, for example, that two rockets are approaching each other at very high speeds, almost equal to that of light. Let us say that, with relation to the Earth, each is traveling at nine-tenths the velocity of light. What is the relative speed of these two rockets with respect to each other?

One might imagine that we would use the same type of calculation in this instance as we would in considering the case of two automobiles speeding toward each other. If each of these cars is traveling at 65 kilome­ters per hour, they are approaching each other at the rate of 65 plus 65, or 130, kilo­meters per hour. On this basis, since each of our rockets is traveling at nine-tenths the speed of light-that is, approximately, 270,000 kilometers per second their speed with relation to each other would be two times 270,000, or 540,000, kilometers per second. Actually, the combined speed of the two rockets would come to less than the speed of light, that is, less than 300,000 kilometers per second.

For one thing, the speed of light is the ultimate speed, which no combination of speeds can possibly surpass. Also, we must remember that at speeds approaching that of light, time is slowed up. Speed is a quan­tity measured in units of length per unit time. The time of our two speeding rockets would slow up sufficiently so that their combined speeds would amount to some ninety-nine hundredths the speed of light-approxi­mately 297,000 kilometers per second.

The special theory of relativity concerns itself with the transformations of energy. Nineteenth-century physicists knew that there are different forms of en­ergy: kinetic energy (energy of motion), electrical energy, chemical energy, thermal (heat) energy, potential energy, and so on. They also realized that one form of energy can be transformed into another. In the twentieth century scientists came to realize that energy can be transformed into mass, and mass into energy. Mass and energy are regarded as equivalent.

In his special theory, Einstein worked out the equation for this transformation. This was the famous mass-energy-transfor­mation equation: E=MC 2 in which E rep­resents the energy in ergs, M the mass in grams, and C the velocity of light in centi­meters per second. Modern nuclear physics has proved beyond the shadow of a doubt the correctness of this equation. It has played an all-important part in the devel­opment of nuclear energy, as well as the advent of space exploration.

The sum total of energy, or its equiva­lent in mass, always remains the same in the
universe or in any closed system. A nu­cleus that is about to undergo radioactive decay has, locked up in itself, energy that is in the form of mass. This turns up later in the form of the kinetic energy that is re­leased as the particle disintegrates. If we weigh the particle before and after decay, weigh the products of decay, and measure the kinetic energies of the alpha particles and gamma rays (if any have been emitted), we can show that nothing of the original particle has been lost.

Generally only a part of a given particle is converted into kinetic or electromagnetic energy. However, there are several exam­ples of a complete transformation of mass into energy. When, for example, a negative electron collides with a positive electron, otherwise known as a positron, the entire mass of both electrons is instantly converted into gamma rays in a violent explosion. This process is called "annihilation."

The special theory of relativity is valid because it correctly describes the important physical properties of any system. It has not caused the older theories of Galileo, Newton, and others to become obsolete. The differences between the calculations of classical physics and those of the special theory, when applied to bodies traveling at speeds far less than that of light, are insig­nificant, and we can ignore them. But when we deal with speeds approaching that of light, we find that the calculations of classical physics will not serve. We must apply the special theory of relativity if we are to avoid serious error.


The clock paradox. One twin goes on a space trip at relativistic speeds. The other twin stays home. The traveling twin returns 40 years later, to find his brother has aged-although he has not.

This theory, advanced by Einstein in 1915, deals with fields of force. The theory may also be regarded as a geometrical rep­resentation of gravitation. To show how fields of force operate, let us imagine that an observer is shut up in a box. He cannot see out of the box and therefore can make no observations of the exterior world. However, he is amply provided with instruments with which he can measure various forces.

We shall suppose, first, that the box is resting upon the surface of the Earth. By using a pendulum, the observer inside the box would discover that he is inside a gravitational force field. He would notice that all objects in the box-as well as the observer himself are attracted to a point, in this case the center of the Earth.

Next, suppose that the box, with observer still in it, is transported to some distant point, far from any mass exerting gravitational force. If the box were stationary, or if it were moving at a constant speed there would be no measurable forces in the interior. The observer himself and any objects in the box would float aimlessly, since they would have no weight.

We must now imagine that some out side agency applies a force to the box and causes it to have a uniform acceleration in a given direction. All the objects in the box would then be acted on by this force, and they would acquire weight. They would act in exactly the same way as the objects that undergo the effects of gravity. The man in the box would not be able to tell whether it was stationary and affected by a gravitational field or whether it was being accelerated uniformly in free space.

Suppose we connected the box by a cable to some central point and caused it to revolve about this point. The centrifugal effect (the force acting away from the cen­ter) would then produce the same effect as that of gravitation or of uniform accelera­tion in one direction.

Anything falling directly toward the black hole, such as a light beam or an ob­ject, would he accelerated to very high speeds and could not escape. Yet the black hole would still have a gravity field sur­rounding it and a planet or a second star could circle it in the same way that Earth circles the Sun

Astronomers now believe that black holes exist in the universe. The theory of relativity does not say that black holes exist, merely that they could.


"Cosmology" is a word that means a study of the structure and geometry of the universe. Today, many different cosmolo­gies are known. Observational astronomers try by various measurements to find which one most closely fits the actual universe. It is not known conclusively today which comes nearest. In fact, it is not known which type of geometry gives the "best fit."

The geometry may be "closed," as we illustrated above with spherical (or elliptic) curvatures. It may be "open," like hyper­bolic ("saddle-shape") geometry, and ex­tend to infinity. Both solutions are con­sistent with general relativity. Whether the universe is open or closed depends on the average density of matter. This is not well enough known today to permit a definite statement to be made.

In his early papers, Einstein proposed a theory of the universe based upon his general theory of relativity. He pointed out that if space were entirely empty, it would extend to infinity in all directions. In such space, light would travel in a straight line. However, we know that space is not empty. It contains matter, very tenuous in most areas, highly concentrated in others. In regions where matter is concentrated, the world lines for the path of light would de­scribe curves rather than straight lines. The average density of matter in space is so low that the net effects of the presence of matter would be small. However, in view of the immense extent of the universe, Einstein thought it likely that if a beam of light could be kept moving for thousands upon thou­sands of millions of years, the curved course it would follow would cause it to return at last to its starting point.

Leading theoretical physicists like Stephen Hawking of Britain are attempting to explain how all the fundamental forces of nature acted during that first millisecond of creation. Such a "Grand Unification The­ory" would go one step further than Ein­stein's theories. For although Einstein produced a model of how the universe grew out of the Big Bang, he was unable to ex­plain how subatomic forces came into being. Indeed, many modern physicists ap­proach cosmology from the standpoint of what happened before the Big Bang.









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