Einstein Completes His Theory of General Relativity Summary

  • Last updated on November 10, 2022

Einstein proposed that physical laws appear the same in any reference frame, even one accelerated under the influence of gravitational fields.

Summary of Event

When Albert Einstein was young, a two-hundred-year-old principle of relativity already existed. This principle stated that there is no standard of absolute motion or rest; the velocities of all objects are defined only in relation to other objects. This is a statement of Galilean relativity, Galilean relativity named for the Italian physicist, mathematician, and astronomer Galileo (1564-1642). General relativity Relativity;general Physics;general relativity [kw]Einstein Completes His Theory of General Relativity (Nov. 25, 1915) [kw]General Relativity, Einstein Completes His Theory of (Nov. 25, 1915) [kw]Relativity, Einstein Completes His Theory of General (Nov. 25, 1915) General relativity Relativity;general Physics;general relativity [g]Germany;Nov. 25, 1915: Einstein Completes His Theory of General Relativity[03870] [c]Science and technology;Nov. 25, 1915: Einstein Completes His Theory of General Relativity[03870] [c]Physics;Nov. 25, 1915: Einstein Completes His Theory of General Relativity[03870] Einstein, Albert Grossman, Marcel Newton, Sir Isaac Maxwell, James Clerk Mach, Ernst

On the other hand, changes in velocity, or accelerations, do not depend on the observer’s velocity. Suppose there is a train moving at 100 kilometers per hour and two observers: one in a car traveling alongside the train at 60 kilometers per hour and one standing on a station platform. If the observer on the platform observes the train accelerate by 20 kilometers per hour to 120 kilometers per hour, the observer in the car will also see that the train has accelerated by 20 kilometers per hour, to 60 kilometers per hour. Thus velocities have only a relative meaning, whereas accelerations have an absolute one.

From these two facts, Sir Isaac Newton deduced, in 1687, that the physical laws of nature must be based on the acceleration of objects, not their velocities. The physical laws of nature (or, in mathematical terms, the equations of motion) thus appear the same to all observers each moving at any arbitrary velocity, as long as their velocities do not change with time. Such special observers are said to be in inertial frames of reference.

In 1865, however, the Scottish physicist James Clerk Maxwell presented his theory of electricity and magnetism, which required that the speed of light be the same number for an observer moving at any constant velocity. Here, a velocity (the speed of light) has an absolute meaning. If a light beam is thought of as a train racing at a speed of 300,000 kilometers per second, then no matter how fast an observer flies in a rocket ship alongside this light-train, the light-train will always be moving 300,000 kilometers per second faster than the rocket ship.

Scientists, quite confused, proposed that there was an absolute standard of rest, an ether filling space, and that somehow this ether explains why Galilean relativity breaks down. This ether had originally been proposed as the medium that carries the electromagnetic waves. In 1887, experiments by scientists Albert A. Michelson and Edward Williams Morley revealed no evidence of this ether. Meanwhile, the Irish physicist George Francis FitzGerald (1889) and the Dutch physicist Hendrik Antoon Lorentz (1899) worked out the correct equations of transformation between inertial frames. A proper understanding of these equations was lacking, however.

Einstein dismissed the ether conjecture and reaffirmed that the laws of physics should appear the same in all inertial reference frames; excepting the velocity of light, all velocities are again relative. Still, there was a twist. In order to account for the fact that the speed of light is the same in any inertial frame, Einstein proposed that measurements of both length and time are different for observers in different inertial frames. Observer A will find that objects in Observer B’s inertial frame shrink in the direction of relative motion and that Observer B’s wristwatch runs slower than Observer A’s. Observer B will, with equal justification, say that objects in Observer A’s inertial reference frame appear shorter in the direction of motion and that Observer A’s wristwatch appears to be running slower. This theory is now referred to as special relativity. Special relativity Relativity;special

Another profound consequence of special relativity is that it is impossible to accelerate a body from rest or from sublight velocities up to the speed of light. The equations that Einstein derived predict that it would take an infinite amount of energy to do so. The faster a body is moving, the harder it is to accelerate the body further. A popular interpretation is that the mass of an object increases as it gains velocity, becoming infinitely massive as the speed of light is reached. More generally, mass is merely another form of energy and can be converted back and forth.

Unfortunately, the conclusion that nothing can be accelerated past the speed of light conflicted with the then-current understanding of gravitation. Gravitation theories According to Newton, given two objects with a gravitational force between them, if one of the objects is moved slightly, the other object instantly feels a shift in the gravitational force between them. The line of force between the two objects is always a straight line connecting them. Aided by the insights of special relativity, Einstein realized that information on the movement of the first object cannot travel instantly to the second. At the fastest, this information may travel at the speed of light. The line of force between two objects must curve if one of the objects experiences a push. There must be a lag time before the second object realizes the first has moved. The reconciliation between special relativity and gravitation forms Einstein’s theory of general relativity.

After Einstein had made some first steps toward the general theory, between 1905 and 1907, mathematical difficulties and an increasing interest in the new quantum physics caused him to defer work on gravitation. Between 1905 and 1911, he made stunning contributions to statistical and quantum physics. Then, between 1912 and 1913, he returned to the study of gravitation, collaborating with his old school friend Marcel Grossman. Although their theory proved incorrect, Grossman, a mathematician, introduced Einstein to differential geometry, essential to the mastering of curved space. Finally, in the summer of 1915, Einstein discovered his errors. After furious work, he presented his general theory in its final form on November 25, 1915. (David Hilbert, Hilbert, David a mathematician, discovered the errors at the same time Einstein did and presented the fundamental equation only five days before Einstein; however, the physical principles behind the general theory and the vision of its existence are usually credited to Einstein.)

The resolution of the conflict between special relativity and Newtonian gravitation came in the form of gravity waves, which carry information about the motion of masses at the speed of light in much the same way electromagnetic waves carry information about the motion of electrical charges. Far-off objects thus do not instantly perceive changes in the position of a nearby object, but must wait for gravity waves from the nearby object to reach them.

There is more than one way to formulate a theory of gravity waves, however. Einstein made one further assumption (partly inspired by the assertion of Austrian physicist and philosopher Ernst Mach) that all motions possess only relative meaning, not simply inertial (constant velocity) motion. Einstein required that physical laws should appear the same regardless of frame of reference, even one accelerated under the influence of gravitational fields. Yet again there was a twist, this time requiring a generalization of what is meant by inertial motion and a revolution in the concept of the structure of space and time.

Significance

Both general relativity and special relativity revolutionized ideas about the structure of space and time. Special relativity introduced the concept of four-dimensional space-time, wherein measurements of the spatial dimensions of an object cannot be made independent of a measurement of the temporal dimension—that is, the velocity with which the object is moving to or away from the observer. Objects that move away very quickly will shrink along the direction of motion.

General relativity introduces the idea that space-time Space-time[Space time] is curved; that is, the presence of mass or other forms of energy distorts space-time, in much the same way that a bowling ball placed on a trampoline distorts the surface of the trampoline. What appears as gravitational force is not, within general relativity, a force at all; it is simply the motion of bodies in curved space-time along paths as nearly straight as possible. Thus the motion of Earth around the Sun, which appears in three dimensions as a circular orbit, in curved four-dimensional space-time is actually a straight line. Thus a marble placed on the trampoline holding the bowling ball will roll toward the bowling ball, not because it is gravitationally attracted to the bowling ball but because the trampoline is not flat. Einstein generalized the concept of an inertial frame to curved space-time.

One of the most important results of this generalization is a proof of the equivalence of inertial and gravitational mass, which had puzzled scientists since the time of Newton. Inertial mass is the resistance a body gives to force. A larger inertial mass means it is harder to accelerate a body to a given speed. Gravitational mass is a measure of a body’s gravitational force field. The larger the gravitational mass, the more strongly it feels the gravitational force of other mass. Since motion in a gravitational field is a generalized inertial motion in curved space-time, there is no gravitational force, per se, in general relativity. Hence there is actually only inertial mass, no gravitational mass.

Predictions based on general relativity, now confirmed by experiment, include the bending of light rays on passing massive celestial objects, the shift of light frequency in a gravitational field (the gravitational redshift), an additional rotation of the elliptical orbit of Mercury around the Sun (the precession of the perihelion of Mercury), the existence of black holes Black holes (regions of such enormous mass density that even light cannot escape), and the expansion of the universe.

Light rays bend toward massive objects because space is deformed around them, and the light rays simply follow the straightest contours of space-time by them. A black hole occurs when the deformation of space is so great that the light ray is continually bent toward the gravitational source, never able to escape. Light frequencies shift in the neighborhood of strong gravitational fields because the passage of time is also distorted by the deformation of space-time. Wristwatches, for example, appear to run slower in strong gravitational fields. (Light cycles through phases much like a common alternating current electrical outlet. Its frequency is hence a measure of time, much like a wristwatch with a variable-speed second hand.) The additional rotation of the elliptical orbit of Mercury and the expansion of the universe come from analysis of Einstein’s new equations of motion.

There is also a practical significance to general relativity in the field of satellite communications, because measurements of time and space are different when observed from high-altitude satellites compared with when observed on the surface of the earth. For example, highly accurate satellite-based navigation systems would send oceangoing ships off course by several kilometers if relativistic corrections were not taken into account. General relativity Relativity;general Physics;general relativity

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Bergmann, Peter G. The Riddle of Gravitation. Rev. ed. Mineola, N.Y.: Dover, 1993. A clear, full presentation of gravitation from the ancient Greeks through special and general relativity and the consequences of quantum mechanics. No mathematical background is required. Many illustrations and diagrams. Helpful bibliography, glossary, and index.
  • citation-type="booksimple"

    xlink:type="simple">Einstein, Albert. Relativity: The Special and General Theory. Translated by Robert W. Lawson. Reprint. New York: Routledge, 2001. An intelligible and elegantly written explanation of Einstein’s theory, but fairly demanding for the average reader. Knowledge of high school-level algebra helpful but not essential. Includes diagrams, index, and bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Gamow, George. Biography of Physics. New York: Harper & Row, 1961. Chapter 6 is devoted to relativity. Chatty, with amusing anecdotes, helpful diagrams, and a few equations. Presents basic ideas, but no discussion of black holes or quantum effects. Fairly light reading.
  • citation-type="booksimple"

    xlink:type="simple">Hawking, Stephen A. A Brief History of Time. 10th anniversary ed. New York: Bantam Books, 1996. Clear and well organized, with vivid explanations of basic principles; excellent for the nonspecialist. The first two chapters provide historical background and describe the major concepts of relativity. Succeeding chapters deal with black holes, quantum effects, particle physics, time, and the unification of physical laws. Includes helpful diagrams, glossary, and index.
  • citation-type="booksimple"

    xlink:type="simple">Pais, Abraham. Subtle Is the Lord: The Science and the Life of Albert Einstein. 1982. Reprint. New York: Oxford University Press, 2005. Meticulously referenced biography of Einstein. Features detailed chronology of Einstein’s life, good subject index, and exhaustive name index.

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