Special Theory of Relativity

By the middle of the nineteenth century the wave theory had become the accepted explanation for such optical phenomena as the reflection, refraction, and transmission of light. It was believed that space was filled with a universal "luminiferous ether," through which light waves propagated, in the same way that waves from a stone dropped in a pond propagated through water. In the last decades of the century, physicists devised experiments to detect the motion of the Earth as it moved through the ether in its annual revolution about the Sun. The measured velocity of light emitted from a source on the Earth should depend on the direction of the light with respect to the motion of the Earth in the ether. One of the most famous experiments to detect such variations in velocity was designed by two American physicists, Albert Michelson (1852-1931) and Edward Morley (1838-1923). Very small changes were thought to be detectible by means of an optical device known as an interferometer, which recorded the interference produced by two sets of rays moving with slightly different velocities in mutually perpendicular directions. Another method to detect the Earth's motion through the ether was based on the analysis of a phenomenon known as stellar aberration.

Despite the best efforts of experimenters, no evidence was found of the motion of the Earth through the ether. Various attempts were made to account for this failure, including the hypothesis that the length of a measuring rod contracted in the direction of motion in such a way as to exactly counteract the variations in light velocity that should otherwise be observed. Another possibility was that the Earth dragged the ether as it moved through space. In the theory of electrodynamics, there were also puzzles concerning the relative motion of bodies.

Albert Einstein, a young physicist working in a patent office in Switzerland, developed a radical revision of classical Newtonian mechanics that explained the null results of the ether experiments. Einstein's special theory of relativity of 1905 was based on incorporating the observer into the description of a physical system and recognizing that all physical events were witnessed relative to a reference frame. The special theory contains two fundamental postulates:

1. The speed of light in a vacuum is independent of the motion of its source.

2. The laws of physics are the same in all inertial reference frames.

The first postulate was true in traditional ether physics, where light, once it left the source, traveled as a disturbance in the ether at the characteristic speed of c equal to 299,792 kilometers per second. The second postulate was the revolutionary one since it implied that the velocity of light in a vacuum as measured in any inertial reference frame will have one and the same value. In particular, the velocity of light as the Earth moves through space will be found to be exactly the same in all directions, just as was found to be the case in the

Michelson-Morley experiment. The two postulates implied together that such basic concepts as space, time, and mass must be understood in relation to a given inertial reference frame. Events that are simultaneous in one reference frame will not be so as viewed in another frame moving with a nonzero velocity with respect to the first frame. Newton's belief that there were such things as absolute space and time had to be rejected altogether and a new set of equations introduced to transform space, time, and mass between reference frames. Finally, the special theory of relativity showed that however light and other electromagnetic disturbances travel through space, it is not as a result of the simple mechanical motion of a disturbance in a material ether.

General Theory of Relativity

In the years following 1905 Einstein became interested in extending the special theory of relativity to encompass gravitational phenomena, with the eventual goal of developing a comprehensive theory for all physical forces. The force of gravity acting between two bodies is proportional to the product of the masses of the bodies. The mass of a body that appears in this relation is known as the body's gravitational mass. The mass that appears in Newton's second law asserting the proportionality of force to mass times acceleration is the inertial mass and can be regarded as a measure of the body's resistance to change of motion. A series of experiments beginning with Newton had shown that the gravitational and inertial mass of a body were equal. Einstein took this fact and generalized it into something called the principle of equivalence, according to which a system of bodies in a uniform gravitational field may be regarded as equivalent to the same system in which no forces act and in which the system is subjected to a uniformly accelerated motion. The force of gravity is replaced by the acceleration of the given reference frame. The formulation of the principle of equivalence was the first step in the development of what would become known as the general theory of relativity.

Einstein was influenced by the brilliant Goettingen mathematician Hermann Minkowski (1864-1909), who had devised a geometrical interpretation of the special theory of relativity. Einstein's ultimate goal was to describe the effects of gravity in terms of the geometrical structure of space and time. To do this, he used techniques from a branch of geometry known as the absolute differential calculus, a field of research pioneered by Italian mathematicians at the end of the nineteenth century. He was introduced to the subject by his Swiss colleague Marcel Grossmann (1878-1936), who with him wrote several papers on the mathematics of gravitational theory. It was Einstein and Grossmann who gave the now standard name "tensor analysis" to the absolute differential calculus. After considerable effort Einstein finally succeeded in producing tensorial formulations of the field equations of gravitation: the action of gravity acting on a unit mass at any point in space was given in terms of equations containing energy and curvature tensors. The equations connected a physical quantity, gravitation, with a geometrical quantity, the curvature of space and time. The general theory of relativity was published in late 1915, well into World War I, in the leading physics journal of the time, the Annalen der Physik.

When Einstein published his 1915 paper, there was, of course, the already established Newtonian theory of gravitation, and the predictions of the two theories were somewhat different. Both theories held that light should bend near a massive body as a result of the gravitational attraction of the body. In particular, light coming from a star observed near the edge of the Sun will experience a small deflection as a result of the Sun's gravitation. The deflection predicted by relativity theory is about twice as large as the value given by the Newtonian theory. Observations of stars near the Sun should therefore provide a crucial test to distinguish between the two theories. Unfortunately, the only time it is possible to see stars close to the Sun is during a total eclipse.

In 1919 the English astronomer Arthur Stanley Eddington (1882—1944) led a solar eclipse expedition to test Einstein's prediction. The path of totality of the eclipse on May 29 passed from West Africa southwest to South America. Eddington and a colleague voyaged to the island of Principe off of Africa, while another team of scientists traveled to Sobral in northern Brazil. Photographic plates were exposed during the eclipse and compared to nighttime plates of the same star field taken at a different time of the year. By comparing the relative positions of the stars on the two plates, Eddington obtained an estimate of the deflection resulting from the Sun's gravitation.

At a historic joint meeting of the Royal Society and the Royal Astronomical Society in November 1919 Eddington reported that the results of the expedition confirmed Einstein's theory. Alfred North Whitehead described the mood of the meeting as follows:

The whole atmosphere of tense interest was exactly that of the Greek drama. We were the chorus commenting on the decree of destiny as disclosed in the development of a supreme incident. There was dramatic quality in the very staging—the traditional ceremonial, and in the background the picture of Newton to remind us that the greatest of scientific generalizations was now, after more than two centuries, to receive its first modification. (Bernstein 1973, 119)

Eddington's confirmation was reported widely in the press, and Einstein became a famous figure in Britain and North America.

Although Eddington's result seemed conclusive at the time, it was later subject to criticism by scientists and historians and is today seen as unreliable. It was Eddington's authority as a scientist rather than the observations themselves that led the 1919 eclipse expedition to be perceived as a decisive confirmation of the theory of general relativity. (Detailed evidence for this assertion is presented by Collins and Pinch (1993).) In fact, confirmation of the theory would not take place for over 40 years. With the development of radar technology after World War II, researchers were able to bounce radar beams off nearby planets and measure the influence of the planetary and solar gravitational fields on the radar trajectories. Pioneers in this investigation were the Lincoln Laboratory in Massachusetts, the Arecibo facility in Puerto Rico, and the Jet Propulsion Laboratory in California, which first made radar contact with the planets in the early 1960s. The predictions of general relativity could be subjected to direct experimental tests, and these have largely confirmed the theory. General relativity has provided a very successful mathematical formalism to describe the universe as a whole. In addition, a range of astronomical phenomena, from extremely dense stellar objects to the gravitational lensing of distant galaxies, have been explained using Einstein's theory of gravity.

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