Relativity, General
Einstein's theory of relativity consists of two major portions: The special theory of relativity and the general theory of relativity. Special relativity deals with phenomena that become noticeable when traveling near the speed of light, and with reference frames that are moving at a constant velocity (inertial reference frames). General relativity deals with reference frames that are accelerating (noninertial reference frames), and with phenomena that occur in strong gravitational fields. General relativity also uses the curvature of space to explain gravity.
History
In the seventeenth century, Isaac Newton (1642-1727) completed a grand synthesis of physics that used three laws of motion and the law of gravity to explain motions we observe both on the Earth and in the heavens. These laws worked very well, but by the end of the nineteenth century, physicists began to notice experiments that did not work quite the way they should according to Newton's understanding. These anomalies led to the development of both relativity and quantum mechanics in the early part of the twentieth century.
One such experiment was the Michelson-Morley experiment, which disproved the hypothesis that propagation of light waves requires a special medium (which had been known as ether). Einstein took the result of this experiment as the basic assumption (namely, that the speed of light is constant) that led to the special theory of relativity.
The orbit of the planet Mercury around the sun has some peculiarities that cannot by explained by Newton's classical laws of physics. As Mercury orbits the Sun, the position where Mercury is closest to the Sun is called the perihelion. The perihelion migrates a small amount each orbit. This very small but measurable effect was reported by the astronomers Urbain Leverrier (1811-1877) and Simon Newcomb (1835-1909) in 1859 and 1895, respectively. The migration rate is 43 seconds of arc per century (one second of arc is 1/3,600 of a degree), so that it takes nearly 8,400 years for this migration to add up to one degree. This precession of Mercury's perihelion can not be easily explained by Newton's laws, but it is a natural consequence of Einstein's general theory of relativity. The effect is noticeable for Mercury but not the other planets, because Mercury is closest to the Sun, where the gravitational field is strongest. General relativity differs most from Newton's law of gravity in strong gravitational fields. The rate of this migration is what general relativity predicts and provides an important experimental confirmation to general relativity.
Preliminary concepts
To understand many concepts in relativity one needs to first understand the concept of a reference frame. A reference frame is a system for locating an object's (or event's) position in both space and time. It consists of both a set of coordinate axes and a clock. An object's position and motion will vary in different reference frames. If for example you are riding in a car, you are at rest in the reference frame of the car. You are, however, moving in the reference frame of the road, which is fixed to the reference frame of the Earth. The reference frames are moving relative to each other, but there is no absolute reference frame. Either reference frame is as valid as the other. A reference frame that is moving at a constant velocity is an inertial reference frame. A noninertial reference frame is accelerating or rotating. The theory of general relativity expands on the theory of special relativity by including the case of noninertial reference frames.
Special relativity combined our concepts of space and time into the unified concept of spacetime. In essence time is a fourth dimension and must be included with the three space dimensions when we talk about the location of an object or event. General relativity allows for the possibility that spacetime is curved. Gravity is a manifestation of the geometry of curved spacetime.
General relativity
Principle of equivalence
Einstein's General Theory of Relativity, published in 1916, uses the principle of equivalence to explain the force of gravity. There are two logically equivalent statements of this principle. For the first statement, consider an enclosed room on the Earth. One feels a downward gravitational force. This force causes what we feel as weight, and causes falling objects to accelerate downward at a rate of 32 ft/s (9.8m/s). Now imagine the same enclosed room but in space far from any masses. There will be no gravitational forces, but if the room is accelerating at 9.8m/s2, then one will feel an apparent force. This apparent force will cause objects to fall at a rate of 9.8m/s2 and will cause one to feel normal Earth weight. We feel a similar phenomenon when we are pushed back into the seat of a rapidly accelerating car. This type of apparent force is an inertial force and is a result of an accelerating (noninertial) reference frame. The inertial force is in the opposite direction of the acceleration producing it. Is it possible to distinguish between the above two situations from within the room? No. According to the first statement of the Principle of Equivalence it is not possible without looking outside the room. Gravitational forces are indistinguishable from inertial forces caused by an accelerating reference frame.
What if the room in space is not accelerating? There will be no gravitational forces, so objects in the room will not fall, and the occupants will be weightless. The same room is now magically transported back to Earth, but by a slight error it ends up 100 feet above the ground rather than on the surface. The Earth's gravity will accelerate the room downward at 9.8m/s2. Just as when the room is accelerating in space, this acceleration will produce an inertial force that is indistinguishable from the gravitational force. But in this case the inertial force is upward, and the gravitational force is downward. Because there is no way to distinguish between inertial and gravitational forces, and they are in the opposite direction, they cancel out exactly. Hence the occupants of the room are weightless. In general, objects that are in free fall will be weightless. This prediction allows us to experimentally test the Principle of Equivalence. Simply let an object fall freely and see if it is weightless. Astronauts in the space shuttle are weightless, not because there is no gravity, but because they are in free fall. You can show yourself that freely falling objects will be weightless. Put a small hole in the bottom of an empty plastic milk jug and fill the jug with water. Drop the jug. While it is falling, no water will leak out the bottom, because as a consequence of the principle of equivalence, freely falling objects will be weightless.
The second statement of the principle of equivalence involves the concept of mass. Mass appears in two distinct ways in Newton's Laws. In Newton's second law, the amount of force required to accelerate an object increases as its mass increases. It takes more force to accelerate a refrigerator than the can of soda that is in the refrigerator. The mass in Newton's second law is the inertial mass. In Newton's law of gravity, the gravitational force between two objects increases as the mass of the objects increases. That is why you will weigh more on a massive planet, such as Jupiter, than on the Earth. The mass in the law of gravity is the gravitational mass. Newton did not seriously consider the possibility that these two masses might be different. Einstein did. Are the inertial mass and the gravitational mass identically the same thing? Yes. According to the second statement of the principle of equivalence, the inertial mass and the gravitational mass are equal.
These two statements of the principle of equivalence are logically equivalent. That means that it is possible to use either statement to prove the other. This principle is the basic assumption behind the general theory of relativity.
Geometrical nature of gravity
From this principle, Einstein was able to derive his general theory of relativity, which explains the force of gravity as a result of the geometry of spacetime. To see how Einstein did this, consider the example above of the enclosed room being accelerated in space far from any masses. The person in the room throws a ball perpendicular to the direction of acceleration. Because the ball is not being pushed by whatever is accelerating the room, it follows a curved path as seen by the person in the room. You would see the same curved path if you threw a ball sideways in a moving car, but be careful not to hit the driver. Now replace the ball by a light beam shining sideways in the enclosed room. The person in the room sees the light beam follow a curved path, just as the ball does and for the same reason. Be careful, though--the deflection of the light beam is very much smaller than the ball, because the light is moving so fast it gets to the wall of the room before the room can move very far.
Now consider the same enclosed room at rest on the surface of the Earth. The ball thrown sideways will follow a downward curved path because of the Earth's gravitational field. What will the light beam do? The principle of equivalence states that it is not possible to distinguish between gravitational forces and inertial forces. Hence, any experiment will have the same result in the room at rest on the Earth as in the room accelerated in space. The light beam will therefore be deflected downward in the room on the Earth just as it would in the accelerated room in space. So, in the room on Earth, gravity deflects the light beam.
Light is deflected by a gravitational force! How? Light has no mass. According to Newton's law of gravity only objects having mass are affected by a gravitational force. What if spacetime is curved? Then we would see light and other objects follow an apparently curved path. Einstein therefore concluded that the presence of a mass curves spacetime and that gravity is a manifestation of this curvature.
Prior to Einstein, people thought of spacetime as being flat and having a Euclidean geometry. This geometry is the geometry that applies to flat surfaces and that is studied in most high school geometry classes. In general relativity however, spacetime is not always Euclidean. The presence of a mass curves or warps spacetime near the mass. The warping is similar to the curvature in a sheet of rubber that is stretched out with a weight in the center. The curvature of spacetime is harder to visualize, because it is four-dimensional spacetime rather than a two-dimensional surface. This curvature of spacetime produces the effects we see as gravity. When we travel long distances on the surface of the Earth, we must follow a curved path because the Earth is not flat. Similarly an object traveling in curved spacetime near a mass follows what we see as a curved path. For example, the Earth orbits the Sun because the spacetime near the Sun is curved. The Earth travels in a nearly circular path around the Sun as a small marble would in a circular path around a curved funnel. An object falling near the surface of the Earth is then like the marble rolling straight down the funnel.
Experimental verification
Bending of light
The first experimental confirmation of general relativity occurred in 1919, shortly after the theory was published. Because light has no mass, Newton's law of gravity predicts that a strong gravitational field will not bend light rays. However as discussed above, general relativity predicts that a strong gravitational field will bend light rays. The curved spacetime will cause even massless light to travel in a curved path. The most convenient mass large enough to have a noticeable effect is the Sun. The apparent position of a star almost directly behind the Sun should be shifted a very small amount as the light rays are bent by the Sun. But, we normally can not see these stars. It is daytime. We must wait until a total solar eclipse to be able to see the stars that are almost directly behind the Sun. Shortly after Einstein published his general theory Arthur Eddington (1882-1944) mounted an expedition to observe the total eclipse of May 29, 1919. Einstein was right. The apparent positions of the stars shifted a small amount. Subsequent eclipse expeditions have further confirmed Einstein's prediction.
More recently, we see this effect with gravitational lenses. If a very distant quasar is almost directly behind a not-as-distant galaxy, the mass of the galaxy can bend the light coming from the more distant quasar. When this occurs we see a double image of the quasar with one image on each side of the nearer galaxy. A number of these gravitational lenses have been observed.
Binary pulsar
The 1993 Nobel Prize in physics was awarded to Joseph Taylor and Russell Hulse for their 1974 discovery of a binary pulsar. A pulsar, or rapidly rotating neutron star, is the final corpse for some stars that occurs when it collapses to about the size of a small city. A binary pulsar is simply two pulsars orbiting each other. Because pulsars are so collapsed they have strong enough gravitational fields that general relativity must apply. Binary pulsars can therefore provide an excellent experimental test of general relativity. About 40 binary pulsars have been discovered since Hulse and Taylor's original discovery.
Mercury's orbit shows a migration in its perihelion as it orbits the Sun. The binary pulsar displays a similar effect as the pulsars orbit each other. The effect is much greater as expected from general relativity because the pulsars have a much stronger gravitational field.
General relativity also predicts that gravity waves should exist in a way that is analogous to electromagnetic waves. Light, radio waves, x rays, infrared light, and ultraviolet light are all examples of electromagnetic waves that are oscillations in electric and magnetic fields. These oscillations can be caused by an oscillating electron. As the electron oscillates, the electron's electric field oscillates causing electromagnetic waves. Similarly as the pulsars oscillate by orbiting each other, general relativity predicts that they should cause the gravitational field to oscillate and produce gravity waves. Gravity waves have so far not been detected directly, even though several groups have been trying for over 20 years. But the binary pulsar is slowing down at a rate that suggests it is losing energy by emitting gravity waves. So, it could be said that the gravity waves predicted by general relativity have been detected indirectly.
Consequences of General Relativity
Karl Schwarzschild first used general relativity to predict the existence of black holes, which are stars that are so highly collapsed that not even light can escape. Because the gravitational field around a black hole is so strong, we must use general relativity to understand the properties of black holes. Most of what we know about black holes comes from theoretical studies based on general relativity. Ordinarily we think of black holes as having been formed from the collapse of a massive star, but Stephen Hawking has combined general relativity with quantum mechanics to predict the existence of primordial quantum black holes. These primordial black holes were formed by the extreme turbulence of the big bang during the formation of the universe. Hawking predicts that over sufficiently long times these quantum black holes can evaporate.
General relativity also has important implications for cosmology, the study of the origin of the universe. The equations of general relativity predict that the universe is expanding. Einstein noticed this result of his theory, but did not believe it. He therefore added a "cosmological constant " to his equations. This cosmological constant was basically a fudge factor that Einstein was able adjust so that his equations predicted that the universe was not expanding. Later Edwin Hubble (1889-1953), after whom the Hubble Space Telescope was named, discovered that the universe is expanding. Einstein visited Hubble, examined Hubble's data, and admitted that Hubble was right. Einstein later called his cosmological constant the biggest blunder of his life. Modern cosmology uses general relativity as the theoretical foundation to understand the expansion of the universe and the properties of the universe during its early history.
Albert Einstein's general theory of relativity fundamentally changed the way we understand gravity and the universe in general. So far, it has passed all experimental tests. This, however, does not mean that Newton's law of gravity is wrong. Newton's law is an approximation of general relativity. In the approximation of small gravitational fields, general relativity reduces to Newton's law of gravity. If at some time in the future someone does an experiment that does not agree with the theory of relativity, we will have to modify the theory just as relativity modified Newton's classical physics.
This is the complete article, containing 2,784 words
(approx. 9 pages at 300 words per page).
