Theory of relativity

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Video simulation of the merger GW150914, showing spacetime distortion from gravity as the black holes orbit and merge

The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. [1] Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. [2] It applies to the cosmological and astrophysical realm, including astronomy. [3]

Contents

The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. [3] [4] [5] It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved 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. [3] [4] [5]

Development and acceptance

Albert Einstein published the theory of special relativity in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.

Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916. [3]

The term "theory of relativity" was based on the expression "relative theory" (German : Relativtheorie) used in 1906 by Planck, 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). [6] [7]

By the 1920s, the physics community understood and accepted special relativity. [8] It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics, and quantum mechanics.

By comparison, general relativity did not appear to be as useful, beyond making minor corrections to predictions of Newtonian gravitation theory. [3] It seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics seemed difficult and fully understandable only by a small number of people. Around 1960, general relativity became central to physics and astronomy. New mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. As astronomical phenomena were discovered, such as quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the first black hole candidates (1981), [3] the theory explained their attributes, and measurement of them further confirmed the theory.

Special relativity

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 and mathematicians, 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 any inertial frame of reference relative to one another (principle of relativity).
  2. The speed of light in vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source.

The resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment. Moreover, the theory has many surprising and counterintuitive consequences. Some of these are:

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.)

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. Einstein discussed his idea with mathematician Marcel Grossmann and they concluded that general relativity could be formulated in the context of Riemannian geometry which had been developed in the 1800s. [10] In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.

Some of the consequences of general relativity are:

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

Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it employs an analytic method, which means that the elements of this theory are not based on hypothesis but on empirical discovery. By observing natural processes, we understand their general characteristics, devise mathematical models to describe what we observed, and by analytical means we deduce the necessary conditions that have to be satisfied. Measurement of separate events must satisfy these conditions and match the theory's conclusions. [2]

Tests of special relativity

A diagram of the Michelson-Morley experiment Michelson-Morley experiment (en).svg
A diagram of the Michelson–Morley experiment

Relativity is a falsifiable theory: It 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. [12] 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 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 that 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. [13] [14]

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. The apparatus was sufficiently accurate to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881, [15] and again in 1887. [16] Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community. [14] In an attempt to salvage the aether paradigm, FitzGerald and Lorentz independently created an ad hoc hypothesis in which the length of material bodies changes according to their motion through the aether. [17] 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. [18] [19]

The Kennedy-Thorndike experiment shown with interference fringes. Kennedy-Thorndike experiment DE.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. [20] 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". [19] [21] 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. [18] [19]

The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938 [22] and with better accuracy in 1941. [23] 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. The strategy was to compare observed Doppler shifts with what was predicted by classical theory, 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. [18] [19]

Those classic experiments have been repeated many times with increased precision. Other experiments include, for instance, relativistic energy and momentum increase at high velocities, experimental testing of time dilation, and modern searches for Lorentz violations.[ citation needed ]

Tests of general relativity

General relativity has also been confirmed many times, the classic experiments being the perihelion precession of Mercury's orbit, the deflection of light by the Sun, and the gravitational redshift of light. Other tests confirmed the equivalence principle and frame dragging.

Modern applications

Far from being simply of theoretical interest, relativistic effects are important practical engineering concerns. Satellite-based measurement needs to take into account relativistic effects, as each satellite is in motion relative to an Earth-bound user, and is thus in a different frame of reference under the theory of relativity. Global positioning systems such as GPS, GLONASS, and Galileo, must account for all of the relativistic effects in order to work with precision, such as the consequences of the Earth's gravitational field. [24] This is also the case in the high-precision measurement of time. [25] Instruments ranging from electron microscopes to particle accelerators would not work if relativistic considerations were omitted. [26]

See also

Related Research Articles

<span class="mw-page-title-main">Luminiferous aether</span> Obsolete postulated medium for the propagation of light

Luminiferous aether or ether was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space, something that waves should not be able to do. The assumption of a spatial plenum of luminiferous aether, rather than a spatial vacuum, provided the theoretical medium that was required by wave theories of light.

<span class="mw-page-title-main">Special relativity</span> Theory of interwoven space and time by Albert Einstein

In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates:

  1. The laws of physics are invariant (identical) in all inertial frames of reference. This is known as the principle of relativity.
  2. The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance.
<span class="mw-page-title-main">Spacetime</span> Mathematical model combining space and time

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.

<span class="mw-page-title-main">Michelson–Morley experiment</span> 1887 investigation of the speed of light

The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by American physicists Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.

<span class="mw-page-title-main">Kennedy–Thorndike experiment</span> Modified form of the Michelson–Morley experiment, testing special relativity

The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental procedure, testing special relativity. The modification is to make one arm of the classical Michelson–Morley (MM) apparatus shorter than the other one. While the Michelson–Morley experiment showed that the speed of light is independent of the orientation of the apparatus, the Kennedy–Thorndike experiment showed that it is also independent of the velocity of the apparatus in different inertial frames. It also served as a test to indirectly verify time dilation – while the negative result of the Michelson–Morley experiment can be explained by length contraction alone, the negative result of the Kennedy–Thorndike experiment requires time dilation in addition to length contraction to explain why no phase shifts will be detected while the Earth moves around the Sun. The first direct confirmation of time dilation was achieved by the Ives–Stilwell experiment. Combining the results of those three experiments, the complete Lorentz transformation can be derived.

Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them, or a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.

<span class="mw-page-title-main">Length contraction</span> Contraction of length in the direction of propagation in Minkowski space

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.

The timeline of luminiferous aether or ether as a medium for propagating electromagnetic radiation begins in the 18th century. The aether was assumed to exist for much of the 19th century—until the Michelson–Morley experiment returned its famous null result. Further experiments were in general agreement with Michelson and Morley's result. By the 1920s, most scientists rejected the aether's existence.

Albert Einstein derived the theory of special relativity in 1905, from principle now called the postulates of special relativity. Einstein's formulation is said to only require two postulates, though his derivation implies a few more assumptions.

Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played an important role in its development and justification. The strength of the theory lies in its unique ability to correctly predict to high precision the outcome of an extremely diverse range of experiments. Repeats of many of those experiments are still being conducted with steadily increased precision, with modern experiments focusing on effects such as at the Planck scale and in the neutrino sector. Their results are consistent with the predictions of special relativity. Collections of various tests were given by Jakob Laub, Zhang, Mattingly, Clifford Will, and Roberts/Schleif.

In the 19th century, the theory of the luminiferous aether as the hypothetical medium for the propagation of light waves was widely discussed. The aether hypothesis arose because physicists of that era could not conceive of light waves propagating without a physical medium in which to do so. When experiments failed to detect the hypothesized luminiferous aether, physicists conceived explanations for the experiments' failure which preserved the hypothetical aether's existence.

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. 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.

In the history of physics, aether theories proposed the existence of a medium, a space-filling substance or field as a transmission medium for the propagation of electromagnetic or gravitational forces. Since the development of special relativity, theories using a substantial aether fell out of use in modern physics, and are now replaced by more abstract models.

What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century.

In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames.

<span class="mw-page-title-main">Relativity priority dispute</span> Issue in science history

Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Henri Poincaré and Hendrik Lorentz for special relativity, and to the work of David Hilbert, Carl F. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.

Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity.

When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed from the source to a mirror and back again to detector. Albert Einstein chose a synchronization convention that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention.

Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century, on scientific, pseudoscientific, philosophical, or ideological bases. Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now accepted by the scientific community.

<span class="mw-page-title-main">Timeline of special relativity and the speed of light</span>

This timeline describes the major developments, both experimental and theoretical, of:

References

  1. ↑ Einstein A. (1916), Relativity: The Special and General Theory  (Translation 1920), New York: H. Holt and Company
  2. 1 2 Einstein, Albert (28 November 1919). "Time, Space, and Gravitation"  . The Times.
  3. 1 2 3 4 5 6 Will, Clifford M (2010). "Relativity". Grolier Multimedia Encyclopedia. Archived from the original on 21 May 2020. Retrieved 1 August 2010.
  4. 1 2 Will, Clifford M (2010). "Space-Time Continuum". Grolier Multimedia Encyclopedia. Retrieved 1 August 2010.[ permanent dead link ]
  5. 1 2 Will, Clifford M (2010). "Fitzgerald–Lorentz contraction". Grolier Multimedia Encyclopedia. Archived from the original on 25 January 2013. Retrieved 1 August 2010.
  6. ↑ Planck, Max (1906), "Die Kaufmannschen Messungen der Ablenkbarkeit der β-Strahlen in ihrer Bedeutung für die Dynamik der Elektronen (The Measurements of Kaufmann on the Deflectability of β-Rays in their Importance for the Dynamics of the Electrons)"  , Physikalische Zeitschrift, 7: 753–761
  7. ↑ Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN   978-0-201-04679-3
  8. ↑ Hey, Anthony J.G.; Walters, Patrick (2003). The New Quantum Universe (illustrated, revised ed.). Cambridge University Press. p. 227. Bibcode:2003nqu..book.....H. ISBN   978-0-521-56457-1.
  9. ↑ Greene, Brian. "The Theory of Relativity, Then and Now" . Retrieved 26 September 2015.
  10. ↑ Einstein, A.; Grossmann, M. (1913). "Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation" [Outline of a Generalized Theory of Relativity and of a Theory of Gravitation]. Zeitschrift für Mathematik und Physik. 62: 225–261.
  11. ↑ Feynman, Richard Phillips; Morínigo, Fernando B.; Wagner, William; Pines, David; Hatfield, Brian (2002). Feynman Lectures on Gravitation. West view Press. p. 68. ISBN   978-0-8133-4038-8.[ permanent dead link ], Lecture 5
  12. ↑ Roberts, T; Schleif, S; Dlugosz, JM, eds. (2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. University of California, Riverside . Retrieved 31 October 2010.
  13. ↑ Maxwell, James Clerk (1880), "On a Possible Mode of Detecting a Motion of the Solar System through the Luminiferous Ether"  , Nature, 21 (535): 314–315, Bibcode:1880Natur..21S.314., doi: 10.1038/021314c0
  14. 1 2 Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. pp.  111–113. ISBN   978-0-19-280672-7.
  15. ↑ Michelson, Albert A. (1881). "The Relative Motion of the Earth and the Luminiferous Ether"  . American Journal of Science. 22 (128): 120–129. Bibcode:1881AmJS...22..120M. doi:10.2475/ajs.s3-22.128.120. S2CID   130423116.
  16. ↑ Michelson, Albert A. & Morley, Edward W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether"  . American Journal of Science. 34 (203): 333–345. Bibcode:1887AmJS...34..333M. doi:10.2475/ajs.s3-34.203.333. S2CID   124333204.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  17. ↑ Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. p.  122. ISBN   978-0-19-280672-7.
  18. 1 2 3 Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 378–382. Bibcode:1949RvMP...21..378R. doi: 10.1103/RevModPhys.21.378 .
  19. 1 2 3 4 Taylor, Edwin F.; John Archibald Wheeler (1992). Spacetime physics: Introduction to Special Relativity (2nd ed.). New York: W.H. Freeman. pp.  84–88. ISBN   978-0-7167-2327-1.
  20. ↑ Kennedy, R.J.; Thorndike, E.M. (1932). "Experimental Establishment of the Relativity of Time" (PDF). Physical Review. 42 (3): 400–418. Bibcode:1932PhRv...42..400K. doi:10.1103/PhysRev.42.400. S2CID   121519138. Archived from the original (PDF) on 6 July 2020.
  21. ↑ Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 381. Bibcode:1949RvMP...21..378R. doi: 10.1103/revmodphys.21.378 .
  22. ↑ Ives, H.E.; Stilwell, G.R. (1938). "An experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America. 28 (7): 215. Bibcode:1938JOSA...28..215I. doi:10.1364/JOSA.28.000215.
  23. ↑ Ives, H.E.; Stilwell, G.R. (1941). "An experimental study of the rate of a moving atomic clock. II". Journal of the Optical Society of America. 31 (5): 369. Bibcode:1941JOSA...31..369I. doi:10.1364/JOSA.31.000369.
  24. ↑ Ashby, N. Relativity in the Global Positioning System. Living Rev. Relativ.6, 1 (2003). doi : 10.12942/lrr-2003-1 "Archived copy" (PDF). Archived from the original (PDF) on 5 November 2015. Retrieved 9 December 2015.{{cite web}}: CS1 maint: archived copy as title (link)
  25. ↑ Francis, S.; B. Ramsey; S. Stein; Leitner, J.; Moreau, J.M.; Burns, R.; Nelson, R.A.; Bartholomew, T.R.; Gifford, A. (2002). "Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (PDF). Proceedings 34th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting: 201–214. Archived from the original (PDF) on 17 February 2013. Retrieved 14 April 2013.
  26. ↑ Hey, Tony; Hey, Anthony J. G.; Walters, Patrick (1997). Einstein's Mirror (illustrated ed.). Cambridge University Press. p. x (preface). ISBN   978-0-521-43532-1.

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