Theory of relativity

This article is about the scientific concept. For philosophical or ontological theories about relativity, see Relativism. For the silent film, see The Einstein Theory of Relativity.

Two-dimensional projection of a three-dimensional analogy of spacetime curvature described in general relativity

The theory of relativity, or simply relativity, generally encompasses two theories of Albert Einstein: special relativity and general relativity. (The word relativity can also be used in the context an older theory, that of Galilean invariance).

Concepts introduced by the theories of relativity include:

• Measurements of various quantities are relative to the velocities of observers. In particular, space and time can dilate.
• Spacetime: space and time should be considered together and in relation to each other.
• The speed of light is nonetheless invariant, the same for all observers.

The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used by Max Planck in 1906, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper Alfred Bucherer used for the first time the expression "theory of relativity" (German: Relativitätstheorie).

Scope

The theory of relativity transformed theoretical physics and astronomy during the 20th century. When first published, relativity superseded a 200-year-old theory of mechanics stated by Isaac Newton.

The theory of relativity overturned the concept of motion from Newton's day, by positing that all motion is relative. Time was no longer uniform and absolute. Physics could no longer be understood as space by itself, and time by itself. Instead, an added dimension had to be taken into account with curved spacetime. Time now depended on velocity, and contraction became a fundamental consequence at appropriate speeds.

In the field of physics, relativity catalyzed and added an essential depth of knowledge to the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.

Two-theory view

The theory of relativity was representative of more than a single new physical theory. There are some explanations for this. First, special relativity was published in 1905, and the final form of general relativity was published in 1916.

Second, special relativity fits with and solves for elementary particles and their interactions, whereas general relativity solves for the cosmological and astrophysical realm (including astronomy).

Third, special relativity was widely accepted in the physics community by 1920. This theory rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics, and quantum mechanics. Conversely, general relativity did not appear to be as useful. There appeared to be little applicability for experimentalists as most applications were for astronomical scales. It seemed limited to only making minor corrections to predictions of Newtonian gravitation theory. Its impact was not apparent until the 1930s.

Finally, the mathematics of general relativity appeared to be incomprehensibly dense. Consequently, it was thought a small number of people in the world, at that time, could fully understand the theory in detail, but this was discredited by Richard Feynman on video recording available on YouTube. Then, at around 1960 a critical resurgence in interest occurred which has resulted in making general relativity central to physics and astronomy. New mathematical techniques applicable to the study of general relativity substantially streamlined calculations. From this, physically discernible concepts were isolated from the mathematical complexity. Also, the discovery of exotic astronomical phenomena in which general relativity was crucially relevant, helped to catalyze this resurgence. The astronomical phenomena included quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the discovery of the first black hole candidates (1971).

On the theory of relativity

Einstein stated that the theory of relativity belongs to the class of "principle-theories". As such it employs an analytic method. This means that the elements which comprise this theory are not based on hypothesis but on empirical discovery. The empirical discovery leads to understanding the general characteristics of natural processes. Mathematical models are then developed which separate the natural processes into theoretical-mathematical descriptions. Therefore, by analytical means the necessary conditions that have to be satisfied are deduced. Separate events must satisfy these conditions. Experience should then match the conclusions.

The special theory of relativity and the general theory of relativity are connected. As stated below, special theory of relativity applies to all inertial physical phenomena except gravity. The general theory provides the law of gravitation, and its relation to other forces of nature.

Special relativity

Main article: Special relativity

USSR stamp dedicated to Albert Einstein

Special relativity is a theory of the structure of spacetime. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:

1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory copes with experiment better than classical mechanics, e.g. in the Michelson–Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:

• Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
• Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
• Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
• Mass–energy equivalence: E = mc², energy and mass are equivalent and transmutable.
• Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism and introduction to special relativity).

General relativity

Main article: General relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion; an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and momentum within it.

Some of the consequences of general relativity are:

• Clocks run more slowly in deeper gravitational wells. This is called gravitational time dilation.
• Orbits precess in a way unexpected in Newton's theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars).
• Rays of light bend in the presence of a gravitational field.
• Rotating masses "drag along" the spacetime around them; a phenomenon termed "frame-dragging".
• The Universe is expanding, and the far parts of it are moving away from us faster than the speed of light.

Technically, general relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially.

Experimental evidence

Main articles: Tests of special relativity and Tests of general relativity

A diagram of the Michelson–Morley experiment

Like all falsifiable scientific theories, relativity makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation. The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the the Kennedy–Thorndike experiment, and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.

Maxwell's equations – the foundation of classical electromagnetism – describe light as a wave which moves with a characteristic velocity. The modern view is that light needs no medium of transmission, but Maxwell and his contemporaries were convinced that light waves were propagated in a medium, analogous to sound propagating in air, and ripples propagating on the surface of a pond. This hypothetical medium was called the luminiferous aether, at rest relative to the "fixed stars" and through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order (v/c) effects, and although observations of second-order effects (v²/c²) were possible in principle, Maxwell thought they were too small to be detected with then-current technology.

The Michelson–Morley experiment was designed to detect second order effects of the "aether wind" – the motion of the aether relative to the earth. Michelson designed an instrument called the Michelson interferometer to accomplish this. It comprised a light source, two highly reflective mirrors, a half silvered mirror, and a detector. Light emitted by a sodium lamp was split by the half-silvered mirror and sent along two paths of equal length at right angles to each other. Light moving along these paths was reflected by the two mirrors multiple times, eventually traveling 22 m before returning to the half silvered mirror where they were recombined and sent to the detector. The detector measured the interference pattern which resulted from the recombined beams. If the aether existed, its velocity relative to the earth should change with the time of day and the season, as earth rotated and orbited the sun. Consequently, the travel time for light along the direction of the aether wind should be different than that of light moving at right angles to the wind. Changes in the interference pattern, if observed, would be an indication of the relative difference in travel times. Michelson and Morley floated the interferometer on a pool of mercury and slowly rotated it while looking for changes in the interference patter, and repeated the procedure at thee-month intervals. The apparatus was more than accurate enough to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881, and again in 1887. Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community. In an attempt to salvage the aether paradigm, Fitzgerald and Lorentz independently created an ad hoc hypothesis in which motion the length of material bodies changes according to their motion through the aether. This was the origin of Fitzgerald-Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result of the Michelson–Morley experiment is that the round-trip travel time for light is isotropic (independent of direction), but the result alone is not enough to discount the theory of the aether or validate the predictions of special relativity.

File:Kennedy-Thorndike experiment.svg

The Kennedy–Thorndike experiment shown with interference fringes.

While the Michelson–Morley experiment showed that the velocity of light is isotropic, it said nothing about how the magnitude of the velocity changed (if at all) in different inertial frames. The Kennedy–Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy and Edward Thorndike. They used an interferometer similar to the one used by Michelson and Morley, except the arms were about 16 cm different in length. They used a mercury lamp for a light source, and took great pains to ensure the stability of the detector: The interferometer was mounted on a plate of quartz, which has a very low coefficient of thermal expansion, and was enclosed in a vacuum chamber. The vacuum chamber was surrounded by a water jacket whose temperature was maintained within ±0.001 °C. The water jacket was enclosed in two nested darkrooms whose temperatures were also very precisely maintained. As in the Michelson–Morley experiment, the interferometer produced a pattern of bright and dark fringes at the detector. Changes in the fringe pattern (a phase shift) would indicate changes in the travel time for light along the arms in different inertial frames as as Earth orbits the sun. In order to carry out the experiment, Kennedy and Thorndike would have had to run the apparatus continually for six months, but this was not feasible at the time. Instead, they ran the machine at intervals ranging from eight days to one month, with separations of three months between successive runs. They obtained a null result, and concluded that "there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit". That possibility was thought to be too coincidental to provide an acceptable explanation, so from the null result of their experiment it was concluded that the round-trip time for light is the same in all inertial reference frames.

The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938 and with better accuracy in 1941. It was designed to test the transverse Doppler effect – the redshift of light from a moving source in a direction perpendicular to its velocity – which had been predicted by Einstein in 1905. This effect is extremely difficult to directly detect and interpret, so Ives and Stilwell measured the longitudinal Doppler effect and looked for discrepancies between what was predicted by classical theory and special relativity. Specifically, they measured the blueshift and redshift of light emitted by canal rays – beams of positive ions – as they moved past a detector. According to classical electromagnetism, the difference in the observed redshift and blueshift frequences should be inversely proportional to the difference between the speed of light and the speed of the light source. According to special relativity, there should be a slight redshift correction to both of those frequencies. The strategy of the Ives–Stilwell experiment was to average the observed red and blue-shits, and look for a Lorentz factor correction. Such a correction was observed, from which was concluded that the frequency of a moving atomic clock is altered according to special relativity.

History

Main articles: History of special relativity and History of general relativity

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others.

General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915.

Minority views

Einstein's contemporaries did not all accept his new theories at once. However, the theory of relativity is now considered as a cornerstone of modern physics, see Criticism of relativity theory.

Although it is widely acknowledged that Einstein was the creator of relativity in its modern understanding, some believe that others deserve credit for it, see Relativity priority dispute.

See also

• General relativity references
• Special relativity references

Further reading

• Bergmann, Peter G. (1976). Introduction to the Theory of Relativity. Dover Publications. ISBN 0-486-63282-2.
• Brian, Denis (1995). Einstein: a life. New York: J. Wiley. ISBN 0471114596.
• Einstein, Albert (2005). Relativity: The Special and General Theory (The masterpiece science ed. ed.). New York: Pi Press. ISBN 0131862618. {{cite book}}: |edition= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Einstien, Albert (1979). Albert Einstein, Autobiographical Notes (A Centennial ed. ed.). La Salle, Ill.: Open Court Publishing Co. ISBN 0875483526. {{cite book}}: |edition= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Einstien, Albert (2009). Einstein's Essays in Science (Dover ed. ed.). Mineola, N.Y.: Dover Publications. ISBN 9780486470115. {{cite book}}: |edition= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Einstien, Albert (1956) [1922]. The Meaning of Relativity (5 ed.). Princeton University Press. {{cite book}}: Cite has empty unknown parameter: |1= (help)
• Ohanian, Hans C. (2008). Einstein's Mistakes: The Human Failings of Genius (1st ed. ed.). New York: W.W. Norton & Co. ISBN 9780393062939. {{cite book}}: |edition= has extra text (help)
• Russell, Bertrand (1969). The ABC of Relativity (3rd rev. ed ed.). London: Allen & Unwin. ISBN 0045210012. {{cite book}}: |edition= has extra text (help)
• Stephen, Hawking (2005). A Briefer History of Time. New York, NY: Bantam Dell. ISBN 9780553804362. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Brockman, John, ed. (2006). My Einstein (1. ed. ed.). New York: Pantheon Books. ISBN 0375423451. {{cite book}}: |edition= has extra text (help)

External links

• Theory of relativity at Curlie
• Relativity Milestones: Timeline of Notable Relativity Scientists and Contributions