## Special Relativity: The Ether

 Figure 1. It takes a swimmer longer to swim against a current and back than to swim perpendicular to it and back. Figure 2. It takes light the same length of time for light to travel against the ether and back than to travel perpendicular to it and back.

During the nineteenth century, scientists believed that light is a wave. They reasoned that waves of light need a medium to travel through, so they invented the concept of "ether." Light was thought to propagate through the ether, which stands still while all matter moves through it.

In order to measure the earth's speed through the ether, Albert A. Michelson and Edward Morley collaborated on an experiment in 1887. To understand the principle behind the experiment, an analogy of a boy swimming through a river can be used. The boy takes two routes (figure 1). In Route A, he travels against the current and back. In Route B, he swims perpendicular to the current and back. If all other variables are equal, he will spend less time swimming Route B than he will Route A, with the difference in finishing times between the routes proportional to the speed of the current.

In the Michelson-Morley experiment, one beam of light took Route C against the ether and back while the other traveled Route D, which was perpendicular to the ether (figure 2). By finding how much earlier Route D complete the course than Route C, Michelson and Morley expected to calculate the speed of the earth through the ether.

To their surprise, the beams of light completed the course in the same time. Michelson and Morley had not only failed to measure the speed of the earth through the ether, but they failed to even detect the presence of the ether. This experiment was repeated several times and the same results were found. Once the results were accepted, many scientists attempted to explain why the beams of light completed the separate routes in the same length of time.

## The Special Theory of Relativity

It wasn't until 1905, 19 years after the Michelson-Morley experiment, that the results were adequately explained. In his most famous scientific paper, On the Electrodynamics of Moving Bodies, Einstein showed that the concept of ether is unnecessary if the speed of light were assumed to be an absolute constant.

In this paper, Einstein introduced the Special Theory of Relativity by forming two postulates. The first postulate states that all physical laws are the same in every inertial frame of reference. Inertial frames of reference are either at rest or moving at a constant speed in a straight line. This postulate means that the laws of nature are exactly the same for someone flying in a spaceship at a constant speed and direction as they are for someone standing on Earth.

The second postulate Einstein made is that the speed of light is the same in every inertial frame of reference. This postulate is a consequence of the first one, because when Maxwell's equations are applied to it, the speed of light is constant for all inertial frames of reference. In other words, regardless of the motion of the light source and observer, the speed of light is exactly the same.

These simple postulates have many bizarre effects that become noticeable when objects reach near-light speeds. In order to understand the changes that occur, we'll use an example of a box containing a mirror. While the box is traveling from left to right at a certain velocity (v), a photon is emitted from the top of the box. The photon is reflected by the mirror at the bottom of the box and returns to the top.

We'll refer to the observer inside of the box as Observer A and the observer outside of the box as Observer B. To Observer A, the setup looks like that shown at the top of figure 3. To Observer B, the box would look like that in the bottom of figure 3 if the effects of special relativity were disregarded.

As we can see, the photon travels farther relative to Observer B than to Observer A. Special relativity states that Observer A and Observer B must observe the same speed of light. Since Observer B seems to detect light traveling farther than Observer A in the same length of time, we must conclude that time and space are manipulated.

The change in time that occurs in the box relative to Observer B is known as time dilation and is given by . T is the length of time elapsed under normal conditions and t' is the length of time elapsed with an object moving relative to the observer at velocity (v). The speed of light is denoted by c. According to this principle, Observer B observes time passing quicker in the box than Observer A does. If the box containing Observer A travels at a near-light speed and Observer A steps out of the box to compare his watch to the watch of Observer B, he would notice that his watch has fallen behind. This principle is often summarized as "a moving clock runs slow."

Special relativity also states that space contracts in the direction of motion according to . This process is known as length contraction or Lorentz contraction. L is the length under normal conditions and l' is the length of the object when it is moving relative to the observer. The fact that length shrinks only in the direction of motion means that the box will become skinnier but not any shorter relative to Observer B. Not only does the box contract, but the distance the photon travels also becomes shorter. Through the combined effects of time dilation and length contraction, the speed of light is constant for both observers.

These effects have been verified experimentally many times since their discovery in 1905. Muons, which are unstable subatomic particles, are created in the upper atmosphere as cosmic rays. Simple calculations predict that the high-speed muons residing in the upper atmosphere travel 700 meters before decaying and cannot reach the earth. However, when the effects of length contraction and time dilation are included in the calculations, the muons, which travel at high speeds relative to the earth, are capable of reaching the earth. Experiments have supported this prediction by finding that a significant number of muons reach the surface of the earth.

In addition to time dilation and length contraction, another unusual effect of near-light speed is stated in Einstein's second paper, titled "Does the Inertia of a Moving Body Depend on its Energy Content?" In this paper, Einstein gave the ubiquitous formula E=mc2. The formula shows the equivalence of mass and energy and illustrates the fact that an increase in mass (m) is accompanied by an increase in energy (E) by mc2. The formula also shows an increase in energy (E) results in an increase in mass (m) by E/c2. In other words, as an object accelerates by gaining energy, it gains mass. As the object approaches the speed of light, its mass approaches infinity. An infinite amount of energy is required to accelerate an object to the speed of light, so the speed of light acts as a speed limit for matter.

## The General Theory of Relativity

Since special relativity requires all objects and particles to be limited by the speed of light, all forces and interactions must also travel at or below the speed of light. Newton's gravitational theory is in contradiction with this principle because it states that the gravitational force acts instantaneously. Einstein spent many years attempting to create a gravitational theory that doesn't require forces to act faster than light.

 Figure 4. Curves in space are responsible for gravity.

In 1915, Einstein proposed the General Theory of Relativity. Rather than explaining gravity as a force that acts instantly as Newton did, he hypothesized that gravity is simply a consequence of space-time curvature. In order to understand space-time curvature, picture a two-dimensional surface. A ball, representing the Sun, lies on the center of the surface. The surface is curved so when another ball, representing a planet, is rolled in a straight line on the surface, the curve causes the ball to travel around, or orbit, the ball representing the Sun. (figure 4).

In his theory, Einstein hypothesized that objects travel in geodesics through curved space-time. A geodesic is a straight line, or the shortest distance between two points. All objects, including planets, travel in geodesics in four-dimensional space-time. In order to understand why the theory is accurate yet the paths of planets don't look straight, we'll use an analogy of an airplane traveling along a geodesic. The airplane takes the shortest path over the three-dimensional earth. When the path is charted on a two-dimensional map, it appears curved rather than straight. The airplane's path on the map doesn't look straight because it's rendered in one less dimension than the space in which the airplane actually traveled. In the same way, the paths of planets seem curved to us because they travel along geodesics in four-dimensional space-time and we observe them in only three dimensions.

## Tests of General Relativity

The first test of Einstein's theory was its prediction of an orbit that is incorrectly predicted by Newton's theory of gravity. Although Newton's theory provides accurate predictions for the orbits of many asteroids, comets, and planets, a small disparity existed between the predicted perihelion shift of Mercury and its actual shift. Mercury's perihelion is the point where it is closest to the Sun. This point gradually moves over many centuries due to the gravitational influences of other planets. The rate at which Mercury's perihelion actually shifts is faster than the rate predicted by the Newtonian theory. General relativity, however, accurately predicts Mercury's perihelion shift. This test was a confirmation of Einstein's theory but it was not considered sufficient evidence by itself.

 Figure 5. Astronomers verified that curves in space-time make the apparent position of stars different from their actual position.

In 1919, Einstein's theory was tested again by expeditions of British astronomers. General relativity predicts that light, as well as matter, travels along geodesics in curved space-time. This aspect differs from Newton's theory of gravity, which requires particles to have mass in order to be affected by gravity. According to the Einstein's theory, starlight passing by the Sun is deflected inward by the Sun's mass. The deflection would cause a distant star to appear in a different place to observers on Earth (figure 5). Astronomers took advantage of a solar eclipse, in which the moon blocked sunlight that would normally overwhelm light from distant stars, to test the effect. The astronomers' test supported general relativity although the test was criticized for its lack of precision.

## The Renaissance of General Relativity

By the 1950's, interest in general relativity among scientists had cooled off. Scientists thought general relativity lacked observational consequences and contained several problems and ambiguities. In 1959, interest in general relativity was sparked when a method for performing more accurate tests of the theory was discovered. A radar echo from Venus was found and used to perform high precision tests of general relativity. Unlike the experiment done by British astronomers in 1919, tiny angles of light and sound deflection by the Sun could be measured with high precision.

During the 60's and 70's more precise tests of general relativity were made, the majority of which supported the theory, as the renaissance of general relativity was underway. The theory was found to be not only a fundamental theory of space and time but also a useful tool in analyzing the universe. Astronomers found general relativity to be useful in the study of double quasars. Quasi-stellar radio sources, or quasars for short, are powerful sources of radio waves from very distant galaxies. The sources of these powerful radio waves look like stellar objects. "Double" quasars, which were discovered in 1979, are multiple images of the same quasar. In other words, a "double" quasar is actually one quasar that appears as two or more to an observer. Gravitational lensing effects from galaxies between the quasar and observer cause light from the quasar to appear more than once. Using general relativity, the deflection of light from a quasar can tell us about the characteristics and mass distribution of galaxies and help us determine the location of the quasar.

Soon after the discovery of "double" quasars, scientists found branches of science in which general relativity is vital for making predictions. For example, quasars, the high-energy sources discussed above, could be explained by the existence of supermassive stars according to the Newtonian theory of gravitation. However, when the effects of general relativity were considered, scientists found that supermassive stars were unstable and could not explain the source of the persistent radio waves.

The effects of general relativity are also important in the search for black holes. Black holes are so dense that they bend space-time enough to prevent light from escaping. Since light, the fastest thing in the universe, cannot escape a black hole nothing is capable of escaping it. Black holes have been speculated about since Newton's time but they could not be described with any sort of precision until the creation of general relativity. General relativity limits the mass of neutron stars, collapsed stars that are black hole candidates, because general relativistic forces inside neutron stars are stronger than forces predicted by the Newtonian theory. The maximum mass put on neutron stars limits the scenarios in which black holes can exist. This knowledge helps direct our search for the elusive black holes.

Created by Dan Corbett, Kate Stafford, and Patrick Wright for ThinkQuest.