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Relativity

Relativity

In physics, the term relativity is used in several, related contexts:
- Galileo first developed the principle of relativity, which is the postulate that the laws of physics are the same for all observers.
- Einstein's theory of relativity consists of special relativity and general relativity, which are built on the principle of relativity and the local constancy of the speed of light. In these theories space and time became unified as spacetime. In general relativity, the concept that this spacetime could be curved was introduced. This curved spacetime replaced Newton's force of gravity and the source of gravitation. The term "relativity" should not be confused with relativism. Much work has been done on the theory of relativity. It qualifies as objective science with very concrete, testable consequences, while the purpose of relativism is very different, namely to question all universal truths.

Other meanings

- Relativity is also the title of a Star Trek: Voyager Episode.
- Relativity was also a television series that aired on ABC from 1996 to 1997.

Galileo Galilei

Galileo Galilei (Pisa, February 15 1564 – Arcetri, January 8 1642), was an Italian physicist, astronomer, and philosopher who is closely associated with the scientific revolution. His achievements include improvements to the telescope, a variety of astronomical observations, the first law of motion and the second law of motion, and effective support for Copernicanism. He has been referred to as the "father of modern astronomy," as the "father of modern physics," and as "father of science." His experimental work is widely considered complementary to the writings of Francis Bacon in establishing the modern scientific method. Galileo's career coincided with that of Johannes Kepler. The work of Galileo is considered to be a significant break from that of Aristotle. In addition, his conflict with the Roman Catholic Church is taken as a major early example of the conflict of authority and freedom of thought, particularly with science, in Western society.

Galileo's Family & Early Careers

Galileo was born in Pisa, in the Tuscan region of Italy, the son of Vincenzo Galilei, a mathematician and musician born in Florence in 1520, and Giulia Ammannati, born in Pescia and married in 1563. Galileo was their first child. Although a devout Catholic, Galileo fathered three children out of wedlock. All were the children of Galileo and Marina Gamba. Because of their illegitimate birth, both girls were sent to the convent of San Matteo in Arcetri at early ages.
- Virginia (b. 1600) who took the name Maria Celeste upon entering a convent. Galileo's eldest child, the most beloved, and inherited her father's sharp mind. She died in 1634 on April second. She is buried with Galileo at the Basilica di Santa Croce di Firenze.
- Livia (b. 1601) took the name Suor Arcangela. Was sickly for most of her life at the convent.
- Vincenzio (b. 1606) was later legitimized and married Sestilia Bocchineri He was home schooled at a very young age. After that he attended the University of Pisa, but was forced to cease his study there for financial reasons. However, he was offered a position on its faculty in 1589 and taught mathematics. Soon after, he moved to the University of Padua, and served on its faculty teaching geometry, mechanics, and astronomy until 1610. During this time he explored science and made many landmark discoveries.

Experimental science

In the pantheon of the scientific revolution, Galileo takes a high position because of his pioneering use of quantitative experiments with results analyzed mathematically. There was no tradition of such methods in European thought at that time; the great experimentalist who immediately preceded Galileo, William Gilbert, did not use a quantitative approach. However, Galileo's father, Vincenzo Galilei, had performed experiments in which he discovered what may be the oldest known non-linear relation in physics, between the tension and the pitch of a stretched string. Galileo also contributed to the rejection of blind allegiance to authority (like the Church) or other thinkers (such as Aristotle) in matters of science and to the separation of science from philosophy or religion. These are the primary justifications for his description as the "father of science." In the 20th century some authorities challenged the reality of Galileo's experiments, in particular the distinguished French historian of science Alexandre Koyré. The experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, for instance, required accurate measurements of time, which appeared to be impossible with the technology of the 1600s. According to Koyré, the law was arrived at deductively, and the experiments were merely illustrative thought experiments. Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo (Settle, 1961), and the precision of the results was consistent with Galileo's report. Later research into Galileo's unpublished working papers from as early as 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law (Drake, 1973).

Astronomy

Contributions

Although the popular idea of Galileo inventing the telescope is inaccurate, he was one of the first people to use the telescope to observe the sky, and for a time was one of very few people able to make a good enough telescope for the purpose. Based on sketchy descriptions of telescopes invented in the Netherlands in 1608, Galileo made one with about 8x magnification, and then made improved models up to about 20x. On August 25, 1609, he demonstrated his first telescope to Venetian lawmakers. His work on the device also made for a profitable sideline with merchants who found it useful for their shipping businesses. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Sidereal Messenger). Sidereus Nuncius. This observation upset the notion that all celestial bodies must revolve around the Earth. Galileo published a full description in Sidereus Nuncius in March 1610.]] On January 7, 1610 Galileo discovered three of Jupiter's four largest satellites (moons): Io, Europa, and Callisto. Ganymede he discovered four nights later. He determined that these moons were orbiting the planet since they would appear and disappear; something he attributed to their movement behind Jupiter. He made additional observations of them in 1620. Later astronomers overruled Galileo's naming of these objects, changing his Medicean stars to Galilean satellites. The demonstration that a planet had smaller planets orbiting it was problematic for the orderly, comprehensive picture of the geocentric model of the universe, in which everything circled around the Earth. Galileo noted that Venus exhibited a full set of phases like the Moon. The heliocentric model of the solar system developed by Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun. By contrast, the geocentric model of Ptolemy predicted that only crescent and new phases would be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth. Galileo's observation of the phases of Venus proved that Venus orbited the Sun and lent support to (but did not prove) the heliocentric model. Galileo was one of the first Europeans to observe sunspots, although there is evidence that Chinese astronomers had done so before. The very existence of sunspots showed another difficulty with the unchanging perfection of the heavens as assumed in the older philosophy. And the annual variations in their motions, first noticed by Francesco Sizzi, presented great difficulties for either the geocentric system or that of Tycho Brahe. A dispute over priority in the discovery of sunspots led to a long and bitter feud with Christoph Scheiner; in fact, there can be little doubt that both of them were beaten by David Fabricius and his son Johannes. He was the first to report lunar mountains and craters, whose existence he deduced from the patterns of light and shadow on the Moon's surface. He even estimated the mountains' heights from these observations. This led him to the conclusion that the Moon was "rough and uneven, and just like the surface of the Earth itself", and not a perfect sphere as Aristotle had claimed. Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars, packed so densely that they appeared to be clouds from Earth. He also located many other stars too distant to be visible with the naked eye. Galileo observed the planet Neptune in 1612, but did not realize that it was a planet and took no particular notice of it. It appears in his notebooks as one of many unremarkable dim stars.

Modern claims of scientific errors and misconduct

Although Galileo is generally considered one of the first modern scientists, as evidenced by his position in the sunspot controversy, he is often said to have arrogantly considered himself to be the sole-propietor of the discoveries in astronomy. Furthermore, he never accepted Kepler's elliptical orbits for the planets, holding to the circular orbits of Copernicus, which still employed epicycles to account for irregularities in planetary motions. Concerning his theory on tides, Galileo attributed them to momentum despite his great knowledge of the ideas of relative motion and Kepler's better theories using the Moon as the cause. (Neither of these great scientists, however, had a workable physical theory of tides; this had to wait for the work of Newton) Galileo stated in his Dialogue that, if the Earth spins on its axis and is traveling at a certain speed around the Sun, parts of the Earth must travel "faster" at night and "slower" during the day. This, of course, is true in the Sun's frame of reference; but it is by no means adequate to explain the tides. Many commentators consider that Galileo developed this position simply to justify his own opinion because the theory was not based on any real scientific observations because if his theory was correct, there would be only one high tide per day and it would happen at noon. The fact that there are two daily high tides at Venice instead of one, and that they travel around the clock, Galileo and his contemporaries knew, but he dismissed as due to several secondary causes, such as the shape of the sea, its depth, and other things. Against the imputation that Galileo was guilty of some kind of deceit in making these arguments one may take the position of Albert Einstein, as one who had done original work in physics, that Galileo developed his "fascinating arguments" and accepted them too uncritically out of a desire for a physical proof of the motion of the Earth (Einstein, 1952)

Physics

Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the Classical mechanics developed by Sir Isaac Newton. He was a pioneer, at least in the European tradition, in performing rigorous experiments and insisting on a mathematical description of the laws of nature. One of the most famous stories about Galileo is that he dropped balls of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass (excluding the limited effect of air resistance). This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. Though the story of the tower first appeared in a biography by Galileo's pupil Vincenzo Viviani, it is not now generally accepted as true. However, Galileo did perform experiments involving rolling balls down inclined planes, which proved the same thing: falling or rolling objects (rolling is a slower version of falling, as long as the distribution of mass in the objects is the same) are accelerated independently of their mass. He determined the correct mathematical law for acceleration: the total distance covered, starting from rest, is proportional to the square of the time (This law is regarded as a predecessor to the many later scientific laws expressed in mathematical form.). He also concluded that objects retain their velocity unless a force -- often friction -- acts upon them, refuting the accepted Aristotelian hypothesis that objects "naturally" slow down and stop unless a force acts upon them. Galileo's Principle of Inertia stated: "A body moving on a level surface will continue in the same direction at constant speed unless disturbed." This principle was incorporated into Newton's laws of motion (1st law). Newton's laws of motion Galileo also noted that a pendulum's swings always take the same amount of time, independently of the amplitude. The story goes that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. While Galileo believed this equality of period to be exact, it is only an approximation appropriate to small amplitudes. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology below) In the early 1600s, Galileo and an assistant tried to measure the speed of light. They stood on different hilltops, each holding a shuttered lantern. Galileo would open his shutter, and, as soon as his assistant saw the flash, he would open his shutter. At a distance of less than a mile, Galileo could detect no delay in the round-trip time greater than when he and the assistant were only a few yards apart. While he could reach no conclusion on whether light propagated instantaneously, he recognized that the distance between the hilltops was perhaps too small for a good measurement. Galileo is lesser known for, yet still credited with being one of the first to understand sound frequency. After scraping a chisel at different speeds, he linked the pitch of sound to the spacing of the chisel's skips (frequency). In his 1632 Dialogue Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth's motion. (The original title for the book, in fact, described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition.) His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. Kepler and others correctly associated the Moon with an influence over the tides, based on empirical data; a proper physical theory of the tides, however, was not available until Newton. Galileo also put forward the basic principle of relativity, that the laws of physics are the same in any system that is moving at a constant speed in a straight line, regardless of its particular speed or direction. Hence, there is no absolute motion or absolute rest. This principle provided the basic framework for Newton's laws of motion and Einstein's theory of relativity.

Mathematics

While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analyses and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid's Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of Descartes, which a modern finds incomparably easier to follow. Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Technology

Galileo made a few contributions to what we now call technology as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo's physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things. In 1595–1598, Galileo devised and improved a "Geometric and Military Compass" suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolo Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations. About 1606–1607 (or possibly earlier), Galileo made a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube. In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons. In 1610, he used a telescope as a compound microscope, and he made improved microscopes in 1623 and after. This appears to be the first clearly documented use of the compound microscope. In 1612, having determined the orbital periods of Jupiter's satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for land surveys; for navigation, the first practical method was the chronometer of John Harrison. In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s. He created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen. ballpoint pen

Church controversy

:Main article: Trial of Galileo. Not long after Galileo began publishing his astronomical work in The Starry Messenger, his Copernican ideas came under attack as a possible heresy, violating the Biblical picture of the Earth as the center of the universe (as well as the accepted philosophical teachings of the time). By 1616 the attacks seemed to Galileo to have become dangerous, and he went to Rome to try to persuade the Church authorities not to ban the new teachings. The mission was a failure: in the end, Cardinal Bellarmine, acting on orders from the Pope, delivered him an order not hold or defend the idea that the Earth moves and the Sun stands still at the center. For the next several years Galileo stayed well away from the controversy. Toward 1630, however, he revived his project of writing a book on the subject, encouraged by the election of Pope Urban VIII. The book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition; there is dispute, however, concerning this license. Galileo was ordered to Rome to stand trial on suspicion of heresy in 1633. The sentence of the Inquisition was in three essential parts:
- Galileo was required to recant his heliocentric ideas, which were condemned as "formally heretical";.
- He was ordered imprisoned; the sentence was later commuted to house arrest.
- His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future. After a period with the friendly Archbishop Piccolomini in Siena, Galileo was allowed to return to his villa at Arcetri near Florence, where he spent the remainder of his life under house arrest.

Galileo's writings

Arcetri
- Two New Sciences 1638 Lowys Elzevir (Louis Elsevier) Leiden (in Italian, Discorsi e Dimostrazioni Matematiche, intorno á due nuoue scienze Leida, Appresso gli Elsevirii 1638)
- Dialogue Concerning the Two Chief World Systems 1632 (in Italian, Dialogo dei due massimi sistemi del mondo)
- The Starry Messenger 1610 Venice (in Latin, Sidereus Nuncius)
- Letter to Grand Duchess Christina

Writings on Galileo

- Galileo Galilei, an opera by Philip Glass
- Galileo a play by Bertolt Brecht

References

- Drake, Stillman (1953). Dialogue Concerning the Two Chief World Systems. Berkeley: University of California Press.
- Drake, Stillman (1957). Discoveries and Opinions of Galileo. New York: Doubleday & Company. ISBN 0-385-09239-3
- Drake, Stillman (1973). "Galileo's Discovery of the Law of Free Fall". Scientific American v. 228, #5, pp. 84-92.
- Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5
- Einstein, Albert (1952). Foreword to (Drake, 1953)
- Fantoli, Annibale (2003). Galileo — For Copernicanism and the Church, third English edition. Vatican Observatory Publications. ISBN 88-209-7427-4
- Fillmore, Charles (1931, 17th printing July 2004). Metaphysical Bible Dictionary. Unity Village, Missouri: Unity House. ISBN 0-871-59067-0
- Hellman, Hal (1988). Great Feuds in Science. Ten of the Liveliest Disputes Ever. New York: Wiley.
- Lessl, Thomas, "[http://www.catholiceducation.org/articles/apologetics/ap0138.html The Galileo Legend]". New Oxford Review, 27-33 (June 2000).
- Newall, Paula (2004). [http://www.galilean-library.org/hps.html "The Galileo Affair."]
- Settle, Thomas B. (1961). "An Experiment in the History of Science". Science, 133:19-23.
- Sobel, Dava. (1999). Galileo's Daughter. ISBN: 0-140-28055-3
- White, Andrew Dickson (1898). [http://www.santafe.edu/~shalizi/White/ A History of the Warfare of Science with Theology in Christendom]. New York 1898.

Named after Galileo

- The Galileo mission to Jupiter
- The Galilean moons of Jupiter
- Galileo Regio on Ganymede
- Galilaei crater on the Moon
- Galilaei crater on Mars
- Asteroid 697 Galilea (named on the occasion of the 300th anniversary of the discovery of the Galilean moons)
- Galileo (unit of acceleration)
- Galileo positioning system
- Galileo stadium in Miami, Florida

Notes

- Note 1: [http://www.lucidcafe.com/library/96feb/galileo.html Galileo, Lucid Cafe Feb '96]"

External links

- [http://www.newadvent.org/cathen/06342b.htm Galileo Galilei article at the Old Catholic Encyclopedia]
- [http://www.galilean-library.org/hps.html The Galileo Affair] by Paula Newall.
- [http://www.infidels.org/library/historical/andrew_white/Chapter3.html The Warfare of Science With Theology]
- [http://galileo.rice.edu/ The Galileo Project] at Rice University
- [http://www.pacifier.com/~tpope CCD Images through a Galilean Telescope] Modern recreation of what Galileo might have seen
- [http://wspace.danask.com/g/galileo_galilei.html about Galileo Galilei] at danask.com
- [http://www.mpiwg-berlin.mpg.de/Galileo_Prototype/MAIN.HTM Electronic representation of Galilei's notes on motion (MS. 72)]
- [http://www.firstthings.com/ftissues/ft0401/reviews/barr.html From Myth to History and Back] — Reviews of two books on Galileo
- [http://www.pbs.org/wgbh/nova/galileo/ PBS Nova Online: Galileo's Battle for the Heavens]
- [http://plato.stanford.edu/entries/galileo/ Stanford Encyclopedia of Philosophy entry]
- [http://www.galilean-library.org The Galilean Library], an educational site dedicated to Galileo
- [http://www.liberliber.it/biblioteca/g/galilei/ Galileo's writings in italian language], an italian site dedicated to free e-texts
- [http://www.newadvent.org/cathen/06342b.htm Galielo Galilei, in the Catholic Encyclopedia] found online on New Advent, an orthodox Catholic website Galilei Galilei Category:Astrologers Galilei Galilei Galilei Galilei Galilei als:Galileo Galilei ko:갈릴레오 갈릴레이 ja:ガリレオ・ガリレイ simple:Galileo Galilei th:กาลิเลโอ กาลิเลอี

Principle of relativity

Galilean relativity

Historically, the first principle of relativity that was formulated was a principle of relativity of uniform motion suggested by the observation that there doesn't seem to be a phenomenon in dynamics that will allow an observer to establish a zero point of velocity, nor a preferred direction. Every choice of a zero point of velocity, a choice necessary in order to perform a calculation, constitutes a choice of reference frame. All reference frames that move with respect to each other with constant velocity and in a straight line are called inertial reference frames. The circularity of this definition is a necessity, since there is no preferred inertial reference frame. In Galilean relativity, reference frames are related to each other in an intuitive way: to transform the velocity of an object from one frame to another, the vector representing the velocity of the object is added to the vector representing the velocity difference between the two reference frames. Such a transformation is called a Galilean transformation. The geometry of space is assumed to be Euclidian, and the measurement of time is assumed to be the same for all observers. Another way of formulating the observation that there is no phenomenon in dynamics that will allow an observer to establish a zero point of uniform velocity, is to state that the laws of motion are equally valid in all inertial reference frames. For example the following property of motion: the common center of mass of two objects will move in uniform motion and it will also remain in uniform motion when the two objects collide or bounce against each other. This is valid in all inertial reference frames.

Special relativity

If one assumes that both the Maxwell equations are valid, and that Galilean transformation is the appropriate transformation, then it should be possible to measure velocity absolutely. Poincaré and Einstein noticed that if one assumes that the Lorentz transformations are the appropriate transformations for transforming between inertial reference frames, then that constitutes a principle of relativity that is compatible with the Maxwell equations. Special relativity restored a principle of relativity in physics. The Maxwell equations had led to ether-theories, in which the nature of electrostatic and magnetic forces depend on the velocity of an object. Special relativity brought back the interpretation that in all inertial reference frames the same physics is going on. Thus there is no phenomenon that would allow an observer to pinpoint a zero point of velocity. The assumption that the Lorentz transformations are the appropriate transformations has vast implications. The intuitive assumption that clock time is universal has to be relinquished.

General relativity

When accelerated motion is involved, there are phenomena that will allow an observer to establish a zero point, there are phenomena that determine a preferred reference frame. For example the case of rotation: the astronomer Schwarzschild had noted that in the solar system the lines connecting the aphelia and perihelia of the planets do not rotate with respect to each other and with respect to the background of the fixed stars (apart from an unexplained precession of the perihelion of Mercury). Also it could be seen from astronomical observation of double stars that the lines connecting the aphelia and perihelia of those distant systems do not rotate either with respect to the overall background of the fixed stars. General relativity unifies the description of gravitation and the description of inertia. General relativity is a theory of gravitation that describes the properties of the mediator of gravitational interaction, in general relativity the mediator of gravitational interaction is deformation of space-time geometry. Gravitation is that the presence of mass and/or energy alters the rate of progression of time in the vicinity of that mass-energy. For an object to move inertially is to remain in the same Lorentz frame. To be accelerated by a force is to be accelerated with respect to the local Lorentz frame. If viewed sufficiently locally, the situations of being accelerated by a force and of gravitation being opposed by a force are fundamentally the same physics. (To be precise: it is completely the same only in the limit of infinitesimally small volumes of space-time.) The hypotenuse of the squares of the velocity and the narmal vector are inversely proportional to the gamma factor. At larger size-scales this equivalence does not hold. The deformation of space-time due to gravity decreases in proportion to the inverse square of the distance to the center of gravity. When viewed from a sufficiently large distance the local deformation of space-time due to gravitation is recognizable and thus can be accounted for as gravitation in a description that is based on as much relevant data as possible. Einstein's original aim was to show that a theory can be formulated in which the same type of relativity as in special relativity also holds for non-inertial motion. In the end, following where demands of consistency led him, Einstein formulated a theory that moves the descriptions of gravitation and inertia to a deeper level, and unifies them. The name 'general relativity' reflects Einstein's original aim, not the way it eventually was interpreted. Category:Relativity ja:相対性原理

Theory of relativity

Albert Einstein's theory of relativity is a set of two scientific theories in physics: special relativity and general relativity. These theories were conceived in order to explain the fact that electromagnetic waves do not conform to the Newtonian laws of motion. Electromagnetic waves were shown to move at a constant speed, independent of the motion of an observer. The core idea of both theories is that two observers who move relative to each other will measure different time and space intervals for the same events, but the content of physical law will be observed the same by both.

Special relativity

Einstein's 1905 paper, "On the Electrodynamics of Moving Bodies", introduced the special theory of relativity. Special relativity considers that observers in inertial reference frames, which are in uniform motion relative to one another, cannot perform any experiment to determine which one of them is in "absolute motion". The theory postulates that the speed of light in a vacuum will be the same for these observers (i.e. an observer invariant speed). One of the strengths of special relativity is that it can be derived from only a few premises:
- The speed of light in a vacuum is constant (specifically, 299,792,458 metres per second).
- The laws of physics are the same for all observers in inertial frames.

General relativity

General relativity was published by Einstein in 1916 (submitted as a series of lectures before the Prussian Academy of Sciences November 25 1915). General relativity is a geometrical theory which postulates that the presence of mass and energy "curves" spacetime, and this curvature affects the path of free particles (and even the path of light). It uses the mathematics of differential geometry and tensors in order to describe gravitation without the use of gravity. This theory considered all observers to be equivalent, not only those moving at a uniform speed.

References

External links

- [http://www.wired.com/news/space/0,2697,64505,00.html?tw=wn_tophead_1 Probe set to test theory of Relativity - Aug. 07, 2004]
- [http://relativity.livingreviews.org/ Living Reviews in Relativity] — An open access, peer-refereed, solely online physics journal publishing invited reviews covering all areas of relativity research.
- [http://www.mathpages.com/rr/rrtoc.htm Reflections on Relativity] — A complete online course on Relativity.
- [http://www.muppetlabs.com/~breadbox/txt/al.html Relativity explained in words of four letters or less]
- [http://www.sysmatrix.net/~kavs/kjs/briefingetr.html Briefing on Einstein's Theory of Relativity] — A terse dose of insight on the subject.
- [http://tprints.ecs.soton.ac.uk/40/01/Macroscopic_Spacetime_Shortcuts.pdf Evaluation of Manyfold spacetime short cuts from Relativity]
- [http://dir.salon.com/people/feature/2000/07/06/einstein/index.html Did Einstein cheat? - July 06, 2000]
- [http://wikisource.org/wiki/Relativity:_The_Special_and_General_Theory Relativity: The Special and General Theory] Category:Relativity ja:相対性理論 th:ทฤษฎีสัมพัทธภาพ

Special relativity

A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory [http://www.fourmilab.ch/etexts/einstein/specrel/www/ published] in 1905 by Albert Einstein. It replaced Newtonian notions of space and time and incorporated electromagnetism as represented by Maxwell's equations. The theory is called "special" because it applies the principle of relativity only to the "restricted" or "special" case of inertial reference frames in flat spacetime, where the effects of gravity can be ignored. Ten years later, Einstein published his general theory of relativity (general relativity, "GR") which incorporated these effects. For History and motivation, see the article: History of special relativity

Postulates

Main article: Postulates of special relativity 1. First postulate (principle of relativity) : The laws of electrodynamics and optics will be valid for all frames of reference in which the laws of mechanics hold good (non-accelerating frames). In other words: Every physical theory should look the same mathematically to every inertial observer; the laws of physics are independent of the state of inertial motion. 2. Second postulate (invariance of c) : Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body; here the velocity of light c is defined as the two-way velocity, determined with a single clock. In other words: The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, and does not depend on the velocity of the object emitting the light. An observer attempting to measure the speed of light's propagation will get the same answer no matter how the system's components are moving.

Lack of an absolute reference frame

Special Relativity rejects the idea of any observable absolute ('unique' or 'special') frame of reference; rather physics must look the same to all observers travelling at a constant velocity (inertial frame). This 'principle of relativity' dates back to Galileo, and is incorporated into Newtonian Physics. In the late 19^th Century, some physicists suggested that the universe was filled with a substance known as "aether" (sometimes written "ether") which transmitted Electromagnetic waves. Aether constituted an absolute reference frame against which speeds could be measured. In other words, the aether was the only fixed or motionless thing in the universe. Aether had some wonderful properties: it was sufficiently elastic that it could support electromagnetic waves, those waves could interact with matter, yet it offered no resistance to bodies passing through it. It was also postulated that light arose from vibrations of the aether. The results of various experiments, including the Michelson-Morley experiment, suggested to some that the Earth was always 'stationary' relative to the Aether — something that is difficult to explain. For many, the most elegant solution was to discard the notion of Aether and an absolute frame, and to adopt Einstein's postulates.

Consequences

Main article: Consequences of Special Relativity Special relativity leads to different physical predictions than Galilean relativity when relative velocities become comparable to the speed of light. The speed of light is so much larger than anything humans encounter that some of the effects predicted by relativity are initially counter intuitive.
- The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames. (See Lorentz transformation equations)
- Two events that occur simultaneously in different places in one frame of reference may occur at different times in another frame of reference (lack of absolute simultaneity).
- The dimensions (e.g. length) of an object as measured by one observer may differ from the results of measurements of the same object made by another observer. (See Lorentz transformation equations)
- The twin paradox concerns a twin who flies off in a spaceship travelling near the speed of light. When he returns he discovers that his twin has aged much more rapidly than he has (or he aged more slowly).
- The ladder paradox involves a long ladder travelling near the speed of light and being contained within a smaller garage.

The Lorentz transformations of space and time

: Full article: Lorentz transformations Lorentz transformation") of a particle. The balls are placed at regular intervals of proper time along the world line. The solid diagonal lines are the light cones for the observer's current event, and intersect at that event. The small dots are other arbitrary events in the spacetime. For the observer's current instantaneous inertial frame of reference, the vertical direction indicates the time and the horizontal direction indicates distance.

The slope of the world line (deviation from being vertical) is the velocity of the particle on that section of the world line. So at a bend in the world line the particle is being accelerated. Note how the view of spacetime changes when the observer accelerates, changing the instantaneous inertial frame of reference. These changes are governed by the Lorentz transformations. Also note that:
• the balls on the world line before/after future/past accelerations are more spaced out due to time dilation.
• events which were simultaneous before an acceleration are at different times afterwards (due to the relativity of simultaneity),
• events pass through the light cone lines due to the progression of proper time, but not due to the change of views caused by the accelerations,and
• the world line always remains within the future and past light cones of the current event.]] Einstein has said that all of the consequences of Special Relativity can be found from examination of the Lorentz transformations. Relativity theory depends on "reference frames". A reference frame is a point in space at rest, or in uniform motion, from which a position can be measured along 3 spatial axes. In addition, a reference frame has a clock, moving with the reference frame allowing the measurement of the time of events. An event is an occurrence that can be assigned a single unique time and location in space relative to a reference frame: It is a "point" in space-time. For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four space-time coordinates: The time of occurrence and its 3-dimensional spatial location from a reference point. Let's call this reference frame $S$ . In relativity theory we often want to calculate the position of a point from a different reference point. Suppose we have a second reference frame $S'$ , whose spatial axes and clock exactly coincide with that of $S$ at time zero, but it is moving at a constant velocity $v$ with respect to $S$ along the $x$ axes. As we shall see, since there is no absolute reference frame in Relativity, a concept of 'moving' doesn't strictly exist, everything is always moving with respect to some other reference frame. Instead, in relativity theory any two frames $S$ and $S'$ are said to be comoving. Let's define the event to have space-time coordinates $(t, x, y, z)$ in system $S$ and $(t', x', y', z')$ in $S'$ . Then the Lorentz transformation specifies that these coordinates are related in the following way: : $t' = \gamma \left(t - \frac \right)$ : $x' = \gamma (x - v t)\,$ : $y' = y\,$ : $z' = z\,$ where $\gamma \equiv \frac$ is called the Lorentz factor and $c$ is the speed of light in a vacuum. As we can see the $y$ and $z$ coordinates are unaffected, but the $x$ and $t$ axes are mixed up by the transformation. In fact they are a form of rotation.
Lorentz Contraction and Time Dilation
Multiplying through we get: : $t' = \gamma t - \gamma \frac$ : $x' = \gamma x - \gamma v t\,$ Examination of the first term of the equation for $x'$ in the Lorentz transformation shows that all positions $x$ in one frame are multiplied by gamma, a number greater than one, to calculate the spatial interval in the second comoving frame. This may be correctly interpreted as a physical contraction of any object from full sized, and at rest in one frame, to the second frame in which it is moving. This is termed Lorentz Contraction. Similarly, in the equation for time $t'$ , $t$ is multiplied by gamma in the second comoving frame. This may be interpreted as time proceeding more slowly when an object is moving relative to another frame of reference. This is termed Time Dilation. It might be expected that since one frame seems contracted, from the contracted frame of reference, the other would seem expanded; and similar effects with time. However since the Lorentz equations are symmetrical with respect to opposite relative speed, each frame sees the other as equally contracted and time dilated. These effects are not merely appearances; the time in the different frame of references essentially do travel at different rates to each other and the lengths of objects really are physically changed whilst in relative motion. If this symmetry seems paradoxical, consider that two observers can only communicate at the speed of light or less. See also the Twin Paradox.
Simultaneity
Special relativity holds that events that are simultaneous in one frame of reference need not be simultaneous in another frame of reference. Simultaneity can be seen by considering the second term of the expanded Lorentz equation for $t'$ . Here as the velocity $v$ varies two events move forwards or backwards in time relative to each other if they are physically separated in space. This can be observed in Diagram 1; some events may be observed moving from the past to the future and back again as acceleration between reference frames occurs and time passes. Lack of simultaneity implies that, for example, the two ends of a rod in a comoving frame actually are not equally old — so for example, a cast radioactive rod would be older and have lower activity at the trailing edge than the leading edge. Indeed, lack of simultaneity explains why Lorentz Contraction occurs — the rod is partially tilted in time as it accelerates giving a foreshortening in the spatial dimension.
Causality
simultaneous In diagram 2 the interval AB is 'time-like'; i.e., there is a frame of reference in which event A and event B occur at the same location in space, separated only by occurring at different times. If A precedes B in that frame, then A precedes B in all frames. It is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the cause and B the effect). The interval AC in the diagram is 'space-like'; i.e., there is a frame of reference in which event A and event C occur simultaneously, separated only in space. However there are also frames in which A precedes C (as shown) and frames in which C precedes A. Barring some way of traveling faster than light, it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no direct causal connection between A and C. However many points in spacetime would be in the light cone of both C and A and can be causally related to either or both of these events, and similarly both C and A could have been caused by an earlier event. Since the set of points of spacetime that is in any events light cone is completely independent of reference frame, then causality is absolutely assured.
Addition of velocities
If the observer in $S$ sees an object moving along the $x$ axis at velocity $w$ then the observer in the $S'$ system will see the object moving with velocity $w'$ where : $w'=\frac$ . This equation can be derived from the space and time transformations above. Notice that if the object is moving at the speed of light in the $S$ system (i.e. $w=c$ ), then it will also be moving at the speed of light in the $S'$ system. Also, if both $w$ and $v$ are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities: $w'=w-v$ .
Mass, momentum, and energy
In addition to modifying notions of space and time, special relativity forces one to reconsider the concepts of mass, momentum, and energy, all of which are important constructs in Newtonian mechanics. Special relativity shows, in fact, that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. There are a couple of (equivalent) ways to define momentum and energy in SR. One method uses conservation laws. If these laws are to remain valid in SR they must be true in every possible reference frame. However, if one does some simple thought experiments using the Newtonian definitions of momentum and energy one sees that these quantities are not conserved in SR. One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities. It is these new definitions which are taken as the correct ones for momentum and energy in SR. Given an object of invariant mass m₀ traveling at velocity u the energy and momentum are given by : $E = \gamma m_0 c^2 \,\!$ : $p = \gamma m_0 u \,\!$ where γ (the Lorentz factor) is given by : $\gamma = \frac \,\!$ and c is the speed of light. The term γ occurs frequently in relativity, and comes from the Lorentz transformation equations. The energy and momentum can be related through the formula : $E^2 - (p c)^2 = (m_0 c^2)^2 \,\!$ which is referred to as the relativistic energy-momentum equation. These equations can be more succinctly stated using the four-momentum $P^a$ and the four-velocity $U^a$ as : $P^a = m_0 U^a$ which can be viewed as a relativistic analogue of Newton's second law. For velocities much smaller than those of light γ can be approximated using a Taylor series expansion and one finds that : $E \approx m_0 c^2 + \begin \frac \end m_0 u^2 \,\!$ : $p \approx m_0 u \,\!$ Barring the first term in the energy expression (discussed below), these formulas agree exactly with the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. Looking at the above formulas for energy, one sees that when an object is at rest (u = 0 and γ = 1) there is a non-zero energy remaining: : $E = m_0 c^2 \,\!$ This energy is referred to as rest energy. The rest energy does not cause any conflict with the Newtonian theory because it is a constant and, as far as kinetic energy is concerned, it is only differences in energy which are meaningful. Taking this formula at face value, we see that in relativity, mass is simply another form of energy. In 1927 Einstein remarked about special relativity: Under this theory mass is not an unalterable magnitude, but a magnitude dependent on (and, indeed, identical with) the amount of energy. [http://www.pbs.org/wgbh/nova/newton/einstein.html] This formula becomes important when one measures the masses of different atomic nuclei. By looking at the difference in masses, one can predict which nuclei have extra stored energy which can be released by nuclear reactions, providing important information which was useful in the development of the nuclear bomb. The implications of this formula on 20th century life have made it one of the most famous equations in all of science.
Relativistic mass
Introductory physics courses and some older textbooks on special relativity sometimes define a relativistic mass which increases as the velocity of a body increases. According to the geometric interpretation of special relativity, this is often depreciated and the term 'mass' is reserved to mean 'rest mass' and is thus independent of the inertial frame, i.e., invariant. Using the relativistic mass definition, the mass of an object may vary depending on the observer's inertial frame in the same way that other properties such as its length may do so. Defining such a quantity may sometimes be useful in that doing so simplifies a calculation by restricting it to a specific frame. For example, consider a body with an invariant mass m₀ moving at some velocity relative to an observer's reference system. That observer defines the relativistic mass of that body as: : $m = \gamma m_0\!$ "Relativistic mass" should not be confused with the "longitudinal" and "transverse mass" definitions that were used around 1900 and that were based on an inconsistent application of the laws of Newton: those used F=ma for a variable mass, while relativistic mass corresponds to Newton's dynamic mass in which p=mv and F=dp/dt. Note also that the body does not actually become more massive in its proper frame, since the relativistic mass is only different for an observer in a different frame. The only mass that is frame independent is the invariant mass. When using the relativistic mass, the used reference frame should be specified if it isn't already obvious or implied. It also goes almost without saying that the increase in relativistic mass does not come from an increased number of atoms in the object. Instead, each atom, indeed each subatomic particle increases its relativistic mass as the object accelerates. Physics textbooks sometimes use the relativistic mass as it allows the students to utilize their knowledge of Newtonian physics to gain some intuitive grasp of relativity in their frame of choice (usually their own!). "Relativistic mass" is also consistent with the concepts "time dilation" and "length contraction".
The geometry of space-time
SR uses a 'flat' 4-dimensional Minkowski space, which is an example of a space-time. This space, however, is very similar to the standard 3 dimensional Euclidean space, and fortunately by that fact, very easy to work with. The differential of distance(ds) in cartesian 3D space is defined as: : $ds^2 = dx_1^2 + dx_2^2 + dx_3^2$ where $(dx_1,dx_2,dx_3)$ are the differentials of the three spatial dimensions. In the geometry of special relativity, a fourth dimension, time, is added, with units of c, so that the equation for the differential of distance becomes: : $ds^2 = dx_1^2 + dx_2^2 + dx_3^2 - c^2 dt^2$ In many situations it may be convenient to treat time as imaginary (e.g. it may simplify equations), in which case $t$ in the above equation is replaced by $i.t'$ , and the metric becomes : $ds^2 = dx_1^2 + dx_2^2 + dx_3^2 + c^2(dt')^2$ If we reduce the spatial dimensions to 2, so that we can represent the physics in a 3-D space : $ds^2 = dx_1^2 + dx_2^2 - c^2 dt^2$ We see that the null geodesics lie along a dual-cone: image:sr1.jpg defined by the equation : $ds^2 = 0 = dx_1^2 + dx_2^2 - c^2 dt^2$ or : $dx_1^2 + dx_2^2 = c^2 dt^2$ Which is the equation of a circle with r=c
- dt. If we extend this to three spatial dimensions, the null geodesics are continuous concentric spheres, with radius = distance = c×(±time). image:sr3.jpg : $ds^2 = 0 = dx_1^2 + dx_2^2 + dx_3^2 - c^2 dt^2$ : $dx_1^2 + dx_2^2 + dx_3^2 = c^2 dt^2$ This null dual-cone represents the "line of sight" of a point in space. That is, when we look at the stars and say "The light from that star which I am receiving is X years old.", we are looking down this line of sight: a null geodesic. We are looking at an event $d = \sqrt$ meters away and d/c seconds in the past. For this reason the null dual cone is also known as the 'light cone'. (The point in the lower left of the picture below represents the star, the origin represents the observer, and the line represents the null geodesic "line of sight".) image:sr1.jpg The cone in the −t region is the information that the point is 'receiving', while the cone in the +t section is the information that the point is 'sending'. The geometry of Minkowski space can be depicted using Minkowski diagrams, which are also useful in understanding many of the thought-experiments in special relativity.
Relativity and unifying Electromagnetism
The magnetic field generated by a moving charge disappears and becomes a purely electrostatic field in a comoving frame of reference. As electric and magnetic fields are reference frame dependent and thus intertwined, one speaks of electromagnetic fields. Special relativity provides the transformation rules for how an electromagnetic field in one inertial frame appears in another inertial frame.
Status
Main article: Status of special relativity Special relativity is accurate only when gravitational effects are negligible or very weak; otherwise, it must be replaced by general relativity. At very small scales, such as at the Planck length and below, it is also possible that special relativity breaks down, due to the effects of quantum gravity. However, at macroscopic scales and in the absence of strong gravitational fields, special relativity is now universally accepted by the physics community and experimental results which appear to contradict it are widely believed to be due to unreproducible experimental error. Because of the freedom one has to select how one defines units of length and time in physics, it is possible to make one of the two postulates of relativity a tautological consequence of the definitions, but one cannot do this for both postulates simultaneously, as when combined they have consequences which are independent of one's choice of definition of length and time. Special relativity is mathematically self-consistent, and is also compatible with all modern physical theories, most notably quantum field theory, string theory, and general relativity (in the limiting case of negligible gravitational fields). However special relativity is incompatible with several earlier theories, most notably Newtonian mechanics. See Status of special relativity for a more detailed discussion. A few key experiments can be mentioned that led to special relativity:
- The Trouton-Noble experiment showed that the torque on a capacitor is independent on position and inertial reference frame — such experiments led to the first postulate
- The famous Michelson-Morley experiment demonstrated the directional invariance of the two-way speed of light — "the speed of light" as defined in the second postulate. A number of experiments have been conducted to test special relativity against rival theories. These include:
- Kaufman's experiment — electron deflection in exact accordance with Lorentz-Einstein prediction
- Hamar experiment — no "ether flow obstruction"
- Kennedy-Thorndike experiment — time dilation in accordance with Lorentz transformations
- Rossi-Hall experiment — relativistic effects on a fast-moving particle's half-life
- Experiments to test emitter theory demonstrated that the speed of light is independent of the speed of the emitter. In addition, particle accelerators run almost every day somewhere in the world, and routinely accelerate and measure the properties of particles moving at near lightspeed. Many effects seen in particle accelerators are highly consistent with relativity theory and are deeply inconsistent with the earlier Newtonian mechanics.
See also
:People: Arthur Eddington | Albert Einstein | Hendrik Lorentz | Hermann Minkowski | Bernhard Riemann | Henri Poincaré | Alexander MacFarlane | Harry Bateman | Robert S. Shankland :Relativity: Theory of relativity | principle of relativity | general relativity | frame of reference | inertial frame of reference | Lorentz transformations :Physics: Newtonian Mechanics | spacetime | speed of light | simultaneity | cosmology | Doppler effect | relativistic Euler equations | Aether drag hypothesis :Math: Minkowski space | four-vector | world line | light cone | Lorentz group | Poincaré group | geometry | tensors | split-complex number :Philosophy: actualism | convensionalism | formalism
External links

- [http://cosmo.nyu.edu/hogg/sr/ The Hogg Notes on Special Relativity] A good introduction to special relativity at the undergraduate level.
- [http://www.everythingimportant.org/relativity/special.pdf Beneath the Foundations of Spacetime] Special relativity can be derived with moving rulers in such a way that the astonishing connection between space and time can be clearly understood.
- [http://www.magen.co.uk/calculator.html Relativity calculator] Geometric calculations of relativistic problems such as the addition of velocities. Note that it is Java-based and can take several minutes to load using a 56k modem.
- [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Special_relativity.html Relativity in its Historical Context] The discovery of special relativity was inevitable, given the momentous discoveries that preceded it.
- [http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf Nothing but Relativity] There are many ways to derive the Lorentz transformation without invoking Einstein's constancy of light postulate. The path preferred in this paper restates a simple, established approach.
- [http://www.mathpages.com/rr/rrtoc.htm Reflections on Relativity] A complete online book on relativity with an extensive bibliography.
- [http://www.phys.vt.edu/~takeuchi/relativity/notes Special Relativity Lecture Notes] is a standard introduction to special relativity containing illustrative explanations based on drawings and spacetime diagrams from Virginia Polytechnic Institute and State University.
- [http://www.mathpreprints.com/math/Preprint/paultrr/20040119/1/Evaluation_of_Brane_World_Mach_Principles.pdf Brane World Mach Principles and the Michelson-Morley experiment]
- [http://fr.wikipedia.org/wiki/Relativit%C3%A9_restreinte#Petites_exp.C3.A9riences_de_pens.C3.A9e Petites expériences de pensée] : five interesting thought experiments about special relativity quoted in the French Language Wikipedia.
- [http://spoirier.lautre.net/en/relativity.htm Special relativity theory made intuitive] A new approach to explain the theoretical meaning of Special Relativity from an intuitive geometrical viewpoint
- [http://www2.slac.stanford.edu/vvc/theory/relativity.html Special Relativity] Stanford University, Helen Quinn, 2003
- , by Albert Einstein
- [http://www.motionmountain.net/C-2-CLSC.pdf Special Relativity] This is chapter two of Christoph Schiller's 1000 page walk through the whole of physics, from classical mechanics to relativity, electrodynamics, thermodynamics, quantum theory, nuclear physics and unification. 61 pages.
- [http://www.guardian.co.uk/life/science/story/0,12996,1456747,00.html "Why Einstein may have got it wrong"] by David Adam, The Guardian, April 11, 2005.
- [http://www.anu.edu.au/Physics/Savage/TEE/ Through Einstein's Eyes] The Australian National University. Relativistic visual effects explained with movies and images.
- [http://gregegan.customer.netspace.net.au/FOUNDATIONS/01/found01.html Greg Egan's Foundations].
- [http://3quarksdaily.blogs.com/3quarksdaily/2005/06/monday_musing_s.html Short Essay Explaining Special Relativity] by S. Abbas Raza of [http://3quarksdaily.com 3 Quarks Daily]
- [http://www.phys.unsw.edu.au/einsteinlight Einstein Light] An [http://www.sciam.com/article.cfm?chanID=sa004&articleID=0005CFF9-524F-1340-924F83414B7F0000 award]-winning, non-technical introduction (film clips and demonstrations) supported by dozens of pages of further explanations and animations, at levels with or without mathematics.
- [http://www.cell-action.com/einstein/index.html Enlightening Ideas] a humoristic animation about the special relativity for the general public, Yannick Mahé, 2005
- [http://arxiv.org/PS_cache/physics/pdf/0504/0504110.pdf On the abuse and use of relativistic mass October 21, 2005 ]
References

Textbooks

- Einstein, Albert. "Relativity — The Special and the General Theory", Routledge Classics 1993 ISBN 0-415-25538-4
- Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman Company. ISBN 0716743450
- Schutz, Bernard F. A First Course in General Relativity, Cambridge University Press. ISBN 0521277035
- Taylor, Edwin, and Wheeler, John (1992). Spacetime physics (2nd ed.). W.H. Freeman and Company. ISBN 0716723271
- Einstein, Albert (1996). The Meaning of Relativity. Fine Communications. ISBN 1567311369
- Geroch, Robert (1981). General Relativity From A to B. University of Chicago Press. ISBN 0226288641
Journal articles

- [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the Electrodynamics of Moving Bodies], A. Einstein, Annalen der Physik, 17:891, June 30, 1905 (in English translation)
- Wolf, Peter and Gerard, Petit. "Satellite test of Special Relativity using the Global Positioning System," Physics Review A 56 (6), 4405-4409 (1997).
- Will, Clifford M. "Clock synchronization and isotropy of the one-way speed of light," Physics Review D 45, 403-411 (1992).
- Alvager et al., "Test of the Second Postulate of Special Relativity in the GeV region," Physics Letters 12, 260 (1964).
- ko:특수 상대성 이론 ja:特殊相対性理論 simple:Special relativity

Speed of light

. The effect is due to electrons moving faster than the speed at which light moves in water.]] The speed of light in a vacuum is defined to be exactly 299,792,458 metres per second (or 1,079,252,848.8 km/h, which is approximately 186,282.397 miles per second, or 670,616,629.4 miles per hour). This value is denoted by the letter c, reputedly from the Latin celeritas, "speed", and also known as Einstein's constant. Note that this speed is a definition, not a measurement; in fact, the fundamental SI unit of distance, the metre, is defined in terms of the speed of light: it is the distance light travels in a vacuum in 1/299,792,458 of a second. The speed of light through a transparent medium (that is, not in vacuum) is less than c; the ratio of c to this speed is called the refractive index of the medium. "Speed of light" is sometimes abbreviated SOL.

Overview

According to standard modern physical theory, all electromagnetic radiation, including visible light, propagates (or moves) at a constant speed in a vacuum, commonly known as the speed of light, which is a physical constant denoted as c. This speed c is also the speed of propagation of gravity in the theory of general relativity. One consequence of the laws of electromagnetism (such as Maxwell's equations) is that the speed c of electromagnetic radiation does not depend on the velocity of the object emitting the radiation; thus for instance the light emitted from a rapidly moving light source would travel at the same speed as the light coming from a stationary light source (although the colour, frequency, energy, and momentum of the light will be shifted, which is called the relativistic Doppler effect). If one combines this observation with the principle of relativity, one concludes that all observers will measure the speed of light in vacuum as being the same, regardless of the reference frame of the observer or the velocity of the object emitting the light. Because of this, one can view c as a fundamental physical constant. This fact can then be used as a basis for the theory of special relativity. It is worth noting that it is the constant speed c, rather than light itself, which is fundamental to special relativity; thus if light is somehow manipulated to travel at more or less than c, this will not directly affect the theory of special relativity. Observers travelling at large velocities will find that distances and times are distorted ("dilated") in accordance with the Lorentz transforms; however, the transforms distort times and distances in such a way that the speed of light remains constant. A person travelling near the speed of light would also find that colours of lights ahead were blue shifted and of those behind were red shifted. If information could travel faster than c in one reference frame, causality would be violated: in some other reference frames, the information would be received before it had been sent, so the 'cause' could be observed after the 'effect'. Due to special relativity's time dilation, the ratio between an external observer's perceived time and the time perceived by an observer moving closer and closer to the speed of light approaches zero. If something could move faster than light, this ratio would not be a real number. Such a violation of causality has never been observed. real number and those that are not.]] To put it another way, information propagates to and from a point from regions defined by a light cone. The interval AB in the diagram to the right is 'time-like' (that is, there is a frame of reference in which event A and event B occur at the same location in space, separated only by their occurring at different times, and if A precedes B in that frame then A precedes B in all frames: there is no frame of reference in which event A and event B occur simultaneously). Thus, it is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the 'cause' and B the 'effect'). On the other hand, the interval AC in the diagram to the right is 'space-like' (that is, there is a frame of reference in which event A and event C occur simultaneously, separated only in space; see simultaneity). However, there are also frames in which A precedes C (as shown) or in which C precedes A. Barring some way of travelling faster than light, it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C. According to the currently prevailing definition, adopted in 1983, the speed of light is exactly 299,792,458 metres per second (approximately 3 × 10⁸ metres per second, or about thirty centimetres (one foot) per nanosecond). The value of

c

defines the permittivity of free space (

\epsilon_0

) in SI units as: :

\varepsilon_0 = 10^/4\pi c^2 \quad \mathrm

The permeability of free space (

\mu_0

) is not dependent on

c

and is defined in SI units as: :

\mu_0 = 4\,\pi\, 10^ \quad \mathrm

. These constants appear in Maxwell's equations, which describe electromagnetism, and are related by: :

c= \frac

Astronomical distances are sometimes measured in light years (the distance that light would travel in one year, roughly 9.46 × 10¹² kilometres or about 5.88 × 10¹² miles) especially in popularised texts.

Communications

The speed of light is of relevance to communications. For example, given that the equatorial circumference of the Earth is 40,075 km and

c

, the theoretical shortest amount of time for a piece of information to travel half the globe is 0.067 second. The actual transit time is longer, in part because the speed of light is slower by about 30% in an optical fibre and straight lines rarely occur in global communications situations, but also because delays are created when the signal passes through an electronic switch or signal regenerator. A typical time as of 2004 for an Australia or Japan to US computer-to-computer ping is 0.18 second. The speed of light additionally affects wireless communications design. The finite speed of light became quite apparent to everybody following the communication of Houston ground control and Neil Armstrong when he became the first man to set foot on the Moon: For every question, Houston had to wait nearly 3 seconds for the answer to arrive, and would have to do so even if the astronauts replied immediately. (See animation.) Similarly, instantaneous remote control of an interplanetary spacecraft is impossible, in the sense that the time it takes, for example, for the earth-based controllers to become aware of a problem, plus the time it takes for the spacecraft to receive their response, can be some hours. The speed of light can also be of concern on short distances. In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 GHz, a signal can only travel a maximum of 300 mm in a single cycle. Processors must therefore be placed close to each other to minimise communication latencies. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips.

Physics

Constant velocity from all reference frames

It is important to realise that the speed of light is not a "speed limit" in the conventional sense. An observer chasing a beam of light will measure it moving away from him at the same speed as a stationary observer. This leads to some unusual consequences for velocities. Most individuals are accustomed to the addition rule of velocities: if two cars approach each other from opposite directions, each travelling at a speed of 50 kilometres per hour (31 miles per hour), one expects that each car will perceive the other as approaching at a combined speed of 50 + 50 = 100 km/h (62 mph) to a very high degree of accuracy. At velocities at or approaching the speed of light, however, it becomes clear from experimental results that this rule does not apply. Two spaceships approaching each other, each travelling at 90% the speed of light relative to some third observer between them, do not perceive each other as approaching at 90% + 90% = 180% the speed of light; instead they each perceive the other as approaching at slightly less than 99.5% the speed of light. This last result is given by the Einstein velocity addition formula: :

u =  \,\!

where v and w are the speeds of the spaceships as observed by the third observer, and u is the speed of either space ship as observed by the other. Contrary to one's usual intuitions, regardless of the speed at which one observer is moving relative to another observer, both will measure the speed of an incoming light beam as the same constant value, the speed of light. The above equation was derived by Albert Einstein from his theory of special relativity, which takes the principle of relativity as a main premise. This principle (originally proposed by Galileo Galilei) requires physical laws to act in the same way in all reference frames. As Maxwell's equations directly give a speed of light, it should be the same for every observer—a consequence which sounded obviously wrong to the 19th century physicists, who assumed that the speed of light given by Maxwell's theory is valid relative to the luminiferous aether. But the Michelson-Morley experiment, arguably the most famous and useful failed experiment in the history of physics, could not find this aether, suggesting instead that the speed of light is constant in all frames of reference. Although it is uncertain whether Einstein knew the results of the Michelson-Morley experiment, he took the speed of light being constant as a given fact, understood it as reaffirming Galilei's principle of relativity, and deduced the consequences, now known as the theory of special relativity which includes the counter-intuitive addition formula above.

Interaction with transparent materials

special relativity, as demonstrated by this prism (in the case of a prism splitting white light into a spectrum of colours, the refraction is known as dispersion).]] In passing through materials, light is slowed to less than c by the ratio called the refractive index of the material. The speed of light in air is only slightly less than

c

. Denser media, such as water and glass, can slow light much more, to fractions such as 3/4 and 2/3 of c. This reduction in speed is also responsible for bending of light at an interface between two materials with different indices, a phenomenon known as refraction. Since the speed of light in a material depends on the refractive index, and the refractive index depends on the frequency of the light, light at different frequencies travels at different speeds through the same material. This can cause distortion of electromagnetic waves that consist of multiple frequencies, called dispersion. Note that the speed of light referred to is the observed or measured speed in some medium and not the true speed of light (as observed in vacuum). On the microscopic scale, considering electromagnetic radiation to be like a particle, refraction is caused by continual absorption and re-emission of the photons that compose the light by the atoms or molecules through which it is passing. In some sense, the light itself travels only through the vacuum existing between these atoms, and is impeded by the atoms. The process of absorption and re-emission itself takes time thereby creating the impression that the light itself has undergone delay (i.e. loss of speed) between entry and exit from the medium in question. It may be noted, that once the light has emerged from the medium it changes back to its original speed and this is without gaining any energy. This can mean only one thing - that the light's speed itself was never altered in the first place. Alternatively, considering electromagnetic radiation to be like a wave, the charges of each atom (primarily the electrons) interfere with the electric and magnetic fields of the radiation, slowing its progress.

"Faster-than-light" observations and experiments

It has long been known theoretically that it is possible for the group velocity of light to exceed c. One recent experiment made the group velocity of laser beams travel for extremely short distances through caesium atoms at 300 times c. However, it is not possible to use this technique to transfer information faster than c: the velocity of information transfer depends on the front velocity (the speed at which the first rise of a pulse above zero moves forward) and the product of the group velocity and the front velocity is equal to the square of the normal speed of light in the material. Exceeding the group velocity of light in this manner is comparable to exceeding the speed of sound by arranging people in a distantly spaced line, and asking them all to shout "I'm here!", one after another with short intervals, each one timing it by looking at their own wristwatch so they don't have to wait until they hear the previous person shouting. The speed of light may also appear to be exceeded in some phenomena involving evanescent waves, such as tunnelling. Experiments indicate that the phase velocity of evanescent waves may exceed c; however, it would appear that neither the group velocity nor the front velocity exceed c, so, again, it is not possible for information to be transmitted faster than c. In some interpretations of quantum mechanics, quantum effects may be transmitted at speeds greater than c (indeed, action at a distance has long been perceived as a problem with quantum mechanics: see EPR paradox). For example, the quantum states of two particles can be entangled, so the state of one particle fixes the state of the other particle (say, one must have spin +½ and the other must have spin −½). Until the particles are observed, they exist in a superposition of two quantum states, (+½, −½) and (−½, +½). If the particles are separated and one of them is observed to determine its quantum state then the quantum state of the second particle is determined automatically. If, as in some interpretations of quantum mechanics, one presumes that the information about the quantum state is local to one particle, then one must conclude that second particle takes up its quantum state instantaneously, as soon as the first observation is carried out. However, it is impossible to control which quantum state the first particle will take on when it is observed, so no information can be transmitted in this manner. The laws of physics also appear to prevent information from being transferred through more clever ways and this has led to the formulation of rules such as the no-cloning theorem. So-called superluminal motion is also seen in certain astronomical objects, such as the jets of radio galaxies and quasars. However, these jets are not actually moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and at a small angle to the line of sight. Although it may sound paradoxical, it is possible for shock waves to be formed with electromagnetic radiation. As a charged particle travels through an insulating medium, it disrupts the local electromagnetic field in the medium. Electrons in the atoms of the medium will be displaced and polarised by the passing field of the charged particle, and photons are emitted as the electrons in the medium restore themselves to equilibrium after the disruption has passed. (In a conductor, the disruption can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves travel, the photons constructively interfere and intensify the observed radiation. The result (analogous to a sonic boom) is known as Cherenkov radiation. The ability to communicate or travel faster-than-light is a popular topic in science fiction. Particles that travel faster than light, dubbed tachyons, have been proposed by particle physicists but have yet to be observed. Some physicists, notably João Magueijo and John Moffat, have proposed that in the past light travelled much faster than the current speed of light. This theory is called variable speed of light (VSL) and its supporters claim that it has the ability to explain many cosmological puzzles better than its rival, the inflation model of the universe. However, it has yet to gain wide acceptance.

Light-slowing experiments

universe, are due to the slower speed of light in a medium (water, in this case).]] In a sense, any light travelling through a medium other than a vacuum travels below

c

as a result of refraction. However, certain materials have an exceptionally high refractive index: in particular, the optical density of a Bose-Einstein condensate can be very high. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light beam to about 17 metres per second, and, in 2001, they were able to momentarily stop a beam. In 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light by directing it into a mass of hot rubidium gas, the atoms of which, in Lukin's words, behaved "like tiny mirrors", due to an interference pattern in two "control" beams.

History

Until relatively recent times, the speed of light was largely a matter of conjecture. Empedocles maintained that light was something in motion, and therefore there had to be some time elapsed in travelling. Aristotle said that, on the contrary, "light is due to the presence of something, but it is not a movement". Furthermore, if light had a finite speed, it would have to be very great; Aristotle asserted "the strain upon our powers of belief is too great" to believe this. One of the ancient theories of vision is that light is emitted from the eye, instead of being reflected into the eye from another source. On this theory, Heron of Alexandria advanced the argument that the speed of light must be infinite, since distant objects such as stars appear immediately when one opens one's eyes.

Medieval and early modern theories

The Islamic philosophers Avicenna and Alhazen believed that light has a finite speed, although most philosophers agreed with Aristotle on this point. The Aryan school of philosophy in ancient India also held the speed of light to be finite. The 14th century philosopher Sayana wrote the following comment on verse 1.50 of the Rig Veda: :"Thus it is remembered: [O Sun] you who traverse 2202 yojanas in half a nimesa." According to some, this refers to the speed of light. It is not known exactly how long a yojana and a nimesa is, but this value is possibly accurate to within 1% (Kak, 1998), though by adopting other possible values of these units the accuracy of the statement can be reduced to a factor of 4. Johannes Kepler believed that the speed of light is infinite since empty space presents no obstacle to it. Francis Bacon argued that the speed of light is not necessarily infinite, since something can travel too fast to be perceived. René Descartes argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light is infinite. In fact, Descartes was convinced that if the speed of light were finite, his whole system of philosophy would be demolished.

Measurement of the speed of light

Isaac Beeckman, a friend of Descartes, proposed an experiment (1629) in which one would observe the flash of a cannon reflecting off a mirror about one mile away. Galileo proposed an experiment (1638), with an apparent claim to have performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. Descartes criticised this experiment as superfluous, in that the observation of eclipses, which had more power to detect a finite speed, gave a negative result. This experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile. No delay was observed. Robert Hooke explained the negative results as Galileo had: by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great. The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer, who was studying the motions of Jupiter's satellite Io with a telescope. It is possible to time the revolution of Io because it is entering/exiting Jupiter's shadow at regular intervals. Rømer observed that Io revolved around Jupiter once every 42.5 hours when Earth was closest to Jupiter. He also observed that, as Earth and Jupiter moved apart, Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart, as a result of the extra time it took for light to cross the extra distance between the planets, which had accumulated in the interval between one signal and the next. Similarly, about half a year later, Io's entries into the shadow happened more frequently, as Earth and Jupiter were now drawing closer together. On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the astronomical unit); the modern estimate is closer to 16 minutes and 40 seconds. Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by Christiaan Huygens, who estimated the speed of light to be 1000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), well below the currently accepted value, but still very much faster than any physical phenomenon then known. Isaac Newton also accepted the finite speed. In his book "Opticks" he, in fact, reports the more accurate value of 16 minutes per diameter, which it seems he inferred for himself (whether from Rømer's data, or otherwise, is not known). The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. And later observations also showed the effect with the three other Galilean moons, where it was more difficult to observe, thus laying to rest some further objections that had been raised. Even if, by these observations, the finite speed of light may not have been established to everyone's satisfaction (notably Jean-Dominique Cassini's), after the observations of James Bradley (1728), the hypothesis of infinite speed was considered discredited. Bradley deduced that starlight falling on the Earth should appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit to the speed of light. This "aberration of light", as it is called, was observed to be about 1/200 of a degree. Bradley calculated the speed of light as about 185,000 miles per second (298,000 kilometres per second). This is only slightly less than the currently accepted value. The aberration effect has been studied extensively over the succeeding centuries, notably by Friedrich Georg Wilhelm Struve and Magnus Nyren. Magnus Nyren The first successful measurement of the speed of light using an earthbound apparatus was carried out by Hippolyte Fizeau in 1849. Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror several thousand metres away. On the way from the source to the mirror, the beam passed through a rotating cog wheel. At a certain rate of rotation, the beam could pass through one gap on the way out and another on the way back. But at slightly higher or lower rates, the beam would strike a tooth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 kilometres per second. Fizeau's method was later refined by Marie Alfred Cornu (1872) and Joseph Perrotin (1900). Leon Foucault improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estima