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 :
124-595: The first postulate was first formulated by Galileo Galilei (see Galilean invariance ). Special relativity was described by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies". Maxwell's equations of electromagnetism appeared to be incompatible with Newtonian mechanics , and the Michelson–Morley experiment failed to detect the Earth's motion against
248-621: A book on the subject, encouraged by the election of Cardinal Maffeo Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the admonition of Galileo in 1616. Galileo's resulting book, Dialogue Concerning the Two Chief World Systems , was published in 1632, with formal authorization from the Inquisition and papal permission. Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in
372-602: A brief treatise entitled Sidereus Nuncius ( Starry Messenger ). On 30 November 1609, Galileo aimed his telescope at the Moon . While not being the first person to observe the Moon through a telescope (English mathematician Thomas Harriot had done so four months before but only saw a "strange spottednesse"), Galileo was the first to deduce the cause of the uneven waning as light occlusion from lunar mountains and craters . In his study, he also made topographical charts, estimating
496-634: A common origin because frames S and S' had been set up in standard configuration, so that t = 0 {\displaystyle t=0} when t ′ = 0. {\displaystyle t'=0.} Fig. 3-1c . Units in the primed axes have a different scale from units in the unprimed axes. From the Lorentz transformations, we observe that ( x ′ , c t ′ ) {\displaystyle (x',ct')} coordinates of ( 0 , 1 ) {\displaystyle (0,1)} in
620-611: A debate with Galileo, sending him an essay disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the action against Copernicanism that followed. Ingoli may have been commissioned by the Inquisition to write an expert opinion on the controversy, with the essay providing the basis for the Inquisition's actions. The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from Tycho Brahe's arguments, notably that heliocentrism would require
744-640: A derived principle, this article considers it to be the fundamental postulate of special relativity. The traditional two-postulate approach to special relativity is presented in innumerable college textbooks and popular presentations. Textbooks starting with the single postulate of Minkowski spacetime include those by Taylor and Wheeler and by Callahan. This is also the approach followed by the Misplaced Pages articles Spacetime and Minkowski diagram . Define an event to have spacetime coordinates ( t , x , y , z ) in system S and ( t ′ , x ′ , y ′ , z ′ ) in
868-518: A first observer O , and frame S ′ (pronounced "S prime" or "S dash") belongs to a second observer O ′ . Since there is no absolute reference frame in relativity theory, a concept of "moving" does not strictly exist, as everything may be moving with respect to some other reference frame. Instead, any two frames that move at the same speed in the same direction are said to be comoving . Therefore, S and S ′ are not comoving . The principle of relativity , which states that physical laws have
992-409: A friend of Galileo, included a realistic depiction of the Moon in one of his paintings; he probably used his own telescope to make the observation. On 7 January 1610, Galileo observed with his telescope what he described at the time as "three fixed stars, totally invisible by their smallness", all close to Jupiter, and lying on a straight line through it. Observations on subsequent nights showed that
1116-487: A genuinely pious Catholic, Galileo fathered three children out of wedlock with Marina Gamba . They had two daughters, Virginia (born 1600) and Livia (born 1601), and a son, Vincenzo (born 1606). Due to their illegitimate birth, Galileo considered the girls unmarriageable, if not posing problems of prohibitively expensive support or dowries, which would have been similar to Galileo's previous extensive financial problems with two of his sisters. Their only worthy alternative
1240-537: A lutenist and composer who added to Galileo's financial burdens for the rest of his life. Michelangelo was unable to contribute his fair share of their father's promised dowries to their brothers-in-law, who later attempted to seek legal remedies for payments due. Michelangelo also occasionally had to borrow funds from Galileo to support his musical endeavours and excursions. These financial burdens may have contributed to Galileo's early desire to develop inventions that would bring him additional income. When Galileo Galilei
1364-401: A method for measuring the apparent size of a star without a telescope. As described in his Dialogue Concerning the Two Chief World Systems , his method was to hang a thin rope in his line of sight to the star and measure the maximum distance from which it would wholly obscure the star. From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by
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#17327974451651488-568: A pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618 , which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body that had moved along a segment of a great circle at a constant distance from the earth, and since it moved in the sky more slowly than the Moon, it must be farther away than
1612-643: A powerful argument against both the Ptolemaic system and the geoheliocentric system of Tycho Brahe. A dispute over claimed priority in the discovery of sunspots, and in their interpretation, led Galileo to a long and bitter feud with the Jesuit Christoph Scheiner . In the middle was Mark Welser , to whom Scheiner had announced his discovery, and who asked Galileo for his opinion. Both of them were unaware of Johannes Fabricius ' earlier observation and publication of sunspots. Galileo observed
1736-502: A practical use for his discovery. Determining the east–west position of ships at sea required their clocks be synchronized with clocks at the prime meridian . Solving this longitude problem had great importance to safe navigation and large prizes were established by Spain and later Holland for its solution. Since eclipses of the moons he discovered were relatively frequent and their times could be predicted with great accuracy, they could be used to set shipboard clocks and Galileo applied for
1860-913: A reference frame moving at a velocity v on the x -axis with respect to that frame, S ′ . Then the Lorentz transformation specifies that these coordinates are related in the following way: t ′ = γ ( t − v x / c 2 ) x ′ = γ ( x − v t ) y ′ = y z ′ = z , {\displaystyle {\begin{aligned}t'&=\gamma \ (t-vx/c^{2})\\x'&=\gamma \ (x-vt)\\y'&=y\\z'&=z,\end{aligned}}} where γ = 1 1 − v 2 / c 2 {\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}
1984-416: A single unique moment and location in space relative to a reference frame: it is a "point" in spacetime . Since the speed of light is constant in relativity irrespective of the reference frame, pulses of light can be used to unambiguously measure distances and refer back to the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired. For example,
2108-523: A thing. Compounding this problem, other astronomers had difficulty confirming Galileo's observations. When he demonstrated the telescope in Bologna, the attendees struggled to see the moons. One of them, Martin Horky, noted that some fixed stars, such as Spica Virginis , appeared double through the telescope. He took this as evidence that the instrument was deceptive when viewing the heavens, casting doubt on
2232-400: Is a special case or specialization of concept B precisely if every instance of A is also an instance of B but not vice versa, or equivalently, if B is a generalization of A . A limiting case is a type of special case which is arrived at by taking some aspect of the concept to the extreme of what is permitted in the general case. If B is true, one can immediately deduce that A
2356-809: Is a property of the general Lorentz transform (also called the Poincaré transformation ), making it an isometry of spacetime. The general Lorentz transform extends the standard Lorentz transform (which deals with translations without rotation, that is, Lorentz boosts , in the x-direction) with all other translations , reflections , and rotations between any Cartesian inertial frame. Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( / ˌ ɡ æ l ɪ ˈ l eɪ oʊ ˌ ɡ æ l ɪ ˈ l eɪ / , US also / ˌ ɡ æ l ɪ ˈ l iː oʊ -/ ; Italian: [ɡaliˈlɛːo ɡaliˈlɛːi] ) or mononymously as Galileo ,
2480-551: Is always greater than 1, and ultimately it approaches infinity as β → 1. {\displaystyle \beta \to 1.} Fig. 3-1d . Since the speed of light is an invariant, the worldlines of two photons passing through the origin at time t ′ = 0 {\displaystyle t'=0} still plot as 45° diagonal lines. The primed coordinates of A {\displaystyle {\text{A}}} and B {\displaystyle {\text{B}}} are related to
2604-423: Is an invariant spacetime interval . Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy , as expressed in the mass–energy equivalence formula E = m c 2 {\displaystyle E=mc^{2}} , where c {\displaystyle c} is the speed of light in vacuum. It also explains how
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#17327974451652728-406: Is an observational perspective in space that is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes (so, at rest or constant velocity). In addition, a reference frame has the ability to determine measurements of the time of events using a "clock" (any reference device with uniform periodicity). An event is an occurrence that can be assigned
2852-659: Is built on the earlier work by Hendrik Lorentz and Henri Poincaré . The theory became essentially complete in 1907, with Hermann Minkowski 's papers on spacetime. The theory is "special" in that it only applies in the special case where the spacetime is "flat", that is, where the curvature of spacetime (a consequence of the energy–momentum tensor and representing gravity ) is negligible. To correctly accommodate gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some historical descriptions, does accommodate accelerations as well as accelerating frames of reference . Just as Galilean relativity
2976-502: Is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations (for the transition from one inertial system to any other arbitrarily chosen inertial system). This is a restricting principle for natural laws ... Thus many modern treatments of special relativity base it on the single postulate of universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime . Rather than considering universal Lorentz covariance to be
3100-410: Is horizontal and the t {\displaystyle t} (actually c t {\displaystyle ct} ) axis is vertical, which is the opposite of the usual convention in kinematics. The c t {\displaystyle ct} axis is scaled by a factor of c {\displaystyle c} so that both axes have common units of length. In the diagram shown,
3224-566: Is known as a Lorentz scalar . Writing the Lorentz transformation and its inverse in terms of coordinate differences, where one event has coordinates ( x 1 , t 1 ) and ( x ′ 1 , t ′ 1 ) , another event has coordinates ( x 2 , t 2 ) and ( x ′ 2 , t ′ 2 ) , and the differences are defined as we get If we take differentials instead of taking differences, we get Spacetime diagrams ( Minkowski diagrams ) are an extremely useful aid to visualizing how coordinates transform between different reference frames. Although it
3348-740: Is no absolute and well-defined state of rest (no privileged reference frames ), a principle now called Galileo's principle of relativity . Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics , including both the laws of mechanics and of electrodynamics . "Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of
3472-605: Is not as easy to perform exact computations using them as directly invoking the Lorentz transformations, their main power is their ability to provide an intuitive grasp of the results of a relativistic scenario. To draw a spacetime diagram, begin by considering two Galilean reference frames, S and S′, in standard configuration, as shown in Fig. 2-1. Fig. 3-1a . Draw the x {\displaystyle x} and t {\displaystyle t} axes of frame S. The x {\displaystyle x} axis
3596-424: Is now accepted to be an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields , that is, at a sufficiently small scale (e.g., when tidal forces are negligible) and in conditions of free fall . But general relativity incorporates non-Euclidean geometry to represent gravitational effects as
3720-457: Is proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible. Even so, the Newtonian model is still valid as a simple and accurate approximation at low velocities (relative to the speed of light), for example, everyday motions on Earth. Special relativity has a wide range of consequences that have been experimentally verified. These include
3844-429: Is the Lorentz factor and c is the speed of light in vacuum, and the velocity v of S ′ , relative to S , is parallel to the x -axis. For simplicity, the y and z coordinates are unaffected; only the x and t coordinates are transformed. These Lorentz transformations form a one-parameter group of linear mappings , that parameter being called rapidity . Solving the four transformation equations above for
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3968-483: The c t ′ {\displaystyle ct'} and x ′ {\displaystyle x'} axes are tilted from the unprimed axes by an angle α = tan − 1 ( β ) , {\displaystyle \alpha =\tan ^{-1}(\beta ),} where β = v / c . {\displaystyle \beta =v/c.} The primed and unprimed axes share
4092-555: The Dialogue , his final interrogation, in July 1633, concluded with his being threatened with torture if he did not tell the truth, but he maintained his denial despite the threat. The sentence of the Inquisition was delivered on 22 June. It was in three essential parts: According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered
4216-584: The Duchy of Florence ) on 15 February 1564, the first of six children of Vincenzo Galilei , a leading lutenist , composer, and music theorist , and Giulia Ammannati , the daughter of a prominent merchant, who had married two years earlier in 1562, when he was 42, and she was 24. Galileo became an accomplished lutenist himself and would have learned early from his father a skepticism for established authority. Three of Galileo's five siblings survived infancy. The youngest, Michelangelo (or Michelagnolo), also became
4340-636: The Florentine Academy , he presented two lectures, On the Shape, Location, and Size of Dante's Inferno , in an attempt to propose a rigorous cosmological model of Dante's hell . Being inspired by the artistic tradition of the city and the works of the Renaissance artists , Galileo acquired an aesthetic mentality . While a young teacher at the Accademia, he began a lifelong friendship with
4464-600: The Milky Way , previously believed to be nebulous , and found it to be a multitude of stars packed so densely that they appeared from Earth to be clouds. He located many other stars too distant to be visible to the naked eye. He observed the double star Mizar in Ursa Major in 1617. In the Starry Messenger , Galileo reported that stars appeared as mere blazes of light, essentially unaltered in appearance by
4588-574: The Roman Inquisition by Father Niccolò Lorini , who claimed that Galileo and his followers were attempting to reinterpret the Bible, which was seen as a violation of the Council of Trent and looked dangerously like Protestantism . Lorini specifically cited Galileo's letter to Castelli. Galileo went to Rome to defend himself and his ideas. At the start of 1616, Francesco Ingoli initiated
4712-563: 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. In Ptolemy's geocentric model , it was impossible for any of the planets' orbits to intersect the spherical shell carrying the Sun. Traditionally, the orbit of Venus was placed entirely on the near side of the Sun, where it could exhibit only crescent and new phases. It
4836-524: The Tychonic , Capellan and Extended Capellan models, each either with or without a daily rotating Earth. These all explained the phases of Venus without the 'refutation' of full heliocentrism's prediction of stellar parallax. Galileo's discovery of the phases of Venus was thus his most empirically practically influential contribution to the two-stage transition from full geocentrism to full heliocentrism via geo-heliocentrism. In 1610, Galileo also observed
4960-410: The isotropy and homogeneity of space and the independence of measuring rods and clocks from their past history. Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations. But the most common set of postulates remains those employed by Einstein in his original paper. A more mathematical statement of
5084-566: The relativity of simultaneity , length contraction , time dilation , the relativistic velocity addition formula, the relativistic Doppler effect , relativistic mass , a universal speed limit , mass–energy equivalence , the speed of causality and the Thomas precession . It has, for example, replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there
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5208-535: The thermometer , and, in 1586, published a small book on the design of a hydrostatic balance he had invented (which first brought him to the attention of the scholarly world). Galileo also studied disegno , a term encompassing fine art, and, in 1588, obtained the position of instructor in the Accademia delle Arti del Disegno in Florence, teaching perspective and chiaroscuro . In the same year, upon invitation by
5332-548: The Aristotelian belief in the immutability of the heavens. Perhaps based only on descriptions of the first practical telescope which Hans Lippershey tried to patent in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnification. He later made improved versions with up to about 30x magnification. With a Galilean telescope , the observer could see magnified, upright images on
5456-598: The Church, the majority of educated people subscribed to the Aristotelian geocentric view that the Earth is the centre of the Universe and the orbit of all heavenly bodies, or Tycho Brahe's new system blending geocentrism with heliocentrism. Opposition to heliocentrism and Galileo's writings on it combined religious and scientific objections. Religious opposition to heliocentrism arose from biblical passages implying
5580-669: The Earth—it was what is commonly known as a terrestrial telescope or a spyglass. He could also use it to observe the sky; for a time he was one of those who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated one of his early telescopes, with a magnification of about 8x or 9x, to Venetian lawmakers. His telescopes were also a profitable sideline for Galileo, who sold them to merchants who found them useful both at sea and as items of trade. He published his initial telescopic astronomical observations in March 1610 in
5704-714: The Florentine painter Cigoli . In 1589, he was appointed to the chair of mathematics in Pisa. In 1591, his father died, and he was entrusted with the care of his younger brother Michelagnolo . In 1592, he moved to the University of Padua where he taught geometry, mechanics , and astronomy until 1610. During this period, Galileo made significant discoveries in both pure fundamental science (for example, kinematics of motion and astronomy) as well as practical applied science (for example, strength of materials and pioneering
5828-475: The Moon. Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on Comets , published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci , although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures that are now known to be mistaken. (The correct approach to
5952-556: The Pope and the Jesuits , who had both strongly supported Galileo up until this point. He was tried by the Inquisition, found "vehemently suspect of heresy", and forced to recant. He spent the rest of his life under house arrest. During this time, he wrote Two New Sciences (1638), primarily concerning kinematics and the strength of materials . Galileo was born in Pisa (then part of
6076-469: The S and S' frames. Fig. 3-1b . Draw the x ′ {\displaystyle x'} and c t ′ {\displaystyle ct'} axes of frame S'. The c t ′ {\displaystyle ct'} axis represents the worldline of the origin of the S' coordinate system as measured in frame S. In this figure, v = c / 2. {\displaystyle v=c/2.} Both
6200-611: The Sun or even the orbit of the Earth. It would not be until much later that astronomers realized the apparent magnitudes of stars were caused by an optical phenomenon called the airy disk , and were functions of their brightness rather than true physical size (see Magnitude#History ). Galileo defended heliocentrism based on his astronomical observations of 1609 . In December 1613, the Grand Duchess Christina of Florence confronted one of Galileo's friends and followers, Benedetto Castelli , with biblical objections to
6324-511: The Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea . The reference to tides was removed from the title by order of the Inquisition. For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of
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#17327974451656448-634: The book, and to be careful not to advocate heliocentrism. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian geocentric view in Dialogue Concerning the Two Chief World Systems , was often caught in his own errors and sometimes came across as a fool. Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher ( Simplicius in Latin, "Simplicio" in Italian),
6572-410: The chandelier took the same amount of time to swing back and forth, no matter how far it was swinging. When he returned home, he set up two pendulums of equal length and swung one with a large sweep and the other with a small sweep and found that they kept time together. It was not until the work of Christiaan Huygens , almost one hundred years later, that the tautochrone nature of a swinging pendulum
6696-406: The condemned opinions, and initially he denied even defending them. However, he was eventually persuaded to admit that, contrary to his true intention, a reader of his Dialogue could well have obtained the impression that it was intended to be a defence of Copernicanism. In view of Galileo's rather implausible denial that he had ever held Copernican ideas after 1616 or ever intended to defend them in
6820-485: The existence of the moons. Christopher Clavius 's observatory in Rome confirmed the observations and, although unsure how to interpret them, gave Galileo a hero's welcome when he visited the next year. Galileo continued to observe the satellites over the next eighteen months, and by mid-1611, he had obtained remarkably accurate estimates for their periods—a feat which Johannes Kepler had believed impossible. Galileo saw
6944-503: The explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four spacetime coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S . In relativity theory, we often want to calculate the coordinates of an event from differing reference frames. The equations that relate measurements made in different frames are called transformation equations . To gain insight into how
7068-461: The fixed nature of the Earth. Scientific opposition came from Brahe, who argued that if heliocentrism were true, an annual stellar parallax should be observed, though none was at the time. Aristarchus and Copernicus had correctly postulated that parallax was negligible because the stars were so distant. However, Brahe countered that since stars appear to have measurable angular size , if the stars were that distant, they would have to be far larger than
7192-485: The fourth on 13 January. Galileo named the group of four the Medicean stars , in honour of his future patron, Cosimo II de' Medici, Grand Duke of Tuscany , and Cosimo's three brothers. Later astronomers, however, renamed them Galilean satellites in honour of their discoverer. These satellites were independently discovered by Simon Marius on 8 January 1610 and are now called Io , Europa , Ganymede , and Callisto ,
7316-403: The geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space . As long as the universe can be modeled as a pseudo-Riemannian manifold , a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime . Galileo Galilei had already postulated that there
7440-525: The gridlines are spaced one unit distance apart. The 45° diagonal lines represent the worldlines of two photons passing through the origin at time t = 0. {\displaystyle t=0.} The slope of these worldlines is 1 because the photons advance one unit in space per unit of time. Two events, A {\displaystyle {\text{A}}} and B , {\displaystyle {\text{B}},} have been plotted on this graph so that their coordinates may be compared in
7564-453: The heights of the mountains. The Moon was not what was long thought to have been a translucent and perfect sphere, as Aristotle claimed, and hardly the first "planet", an "eternal pearl to magnificently ascend into the heavenly empyrian", as put forth by Dante . Galileo is sometimes credited with the discovery of the lunar libration in latitude in 1632, although Thomas Harriot or William Gilbert may have done so before. The painter Cigoli,
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#17327974451657688-402: The hypothesized luminiferous aether . These led to the development of the Lorentz transformations , by Hendrik Lorentz , which adjust distances and times for moving objects. Special relativity corrects the hitherto laws of mechanics to handle situations involving all motions and especially those at a speed close to that of light (known as relativistic velocities ). Today, special relativity
7812-415: The implicitly assumed concepts of absolute simultaneity and synchronization across non-comoving frames. The form of Δ s 2 {\displaystyle \Delta s^{2}} , being the difference of the squared time lapse and the squared spatial distance, demonstrates a fundamental discrepancy between Euclidean and spacetime distances. The invariance of this interval
7936-530: The legal heir of Galileo and married Sestilia Bocchineri. Although Galileo seriously considered the priesthood as a young man, at his father's urging he instead enrolled in 1580 at the University of Pisa for a medical degree. He was influenced by the lectures of Girolamo Borro and Francesco Buonamici of Florence. In 1581, when he was studying medicine, he noticed a swinging chandelier , which air currents shifted about to swing in larger and smaller arcs. To him, it seemed, by comparison with his heartbeat, that
8060-430: The mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincaré group of symmetry transformations. Einstein later derived these transformations from his axioms. Many of Einstein's papers present derivations of the Lorentz transformation based upon these two principles. Reference frames play a crucial role in relativity theory. The term reference frame as used here
8184-419: The most assured, regardless of the exact validity of the (then) known laws of either mechanics or electrodynamics. These propositions were the constancy of the speed of light in vacuum and the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as: The constancy of
8308-495: The motion of the Earth. Prompted by this incident, Galileo wrote a letter to Castelli in which he argued that heliocentrism was actually not contrary to biblical texts and that the Bible was an authority on faith and morals, not science. This letter was not published but circulated widely. Two years later, Galileo wrote a letter to Christina that expanded his arguments previously made in eight pages to forty pages. By 1615, Galileo's writings on heliocentrism had been submitted to
8432-456: The name "Simplicio" in Italian also has the connotation of "simpleton". This portrayal of Simplicio made Dialogue Concerning the Two Chief World Systems appear as an advocacy book: an attack on Aristotelian geocentrism and defence of the Copernican theory. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. However, the Pope did not take
8556-432: The names given by Marius in his Mundus Iovialis published in 1614. Galileo's observations of the satellites of Jupiter caused controversy in astronomy: a planet with smaller planets orbiting it did not conform to the principles of Aristotelian cosmology , which held that all heavenly bodies should circle the Earth, and many astronomers and philosophers initially refused to believe that Galileo could have discovered such
8680-535: The opinion that the sun stands still at the centre of the world and the Earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing." The decree of the Congregation of the Index banned Copernicus's De Revolutionibus and other heliocentric works until correction. For the next decade, Galileo stayed well away from the controversy. He revived his project of writing
8804-540: The painting, Stillman Drake wrote "there is no doubt now that the famous words were already attributed to Galileo before his death". However, an intensive investigation by astrophysicist Mario Livio has revealed that said painting is most probably a copy of an 1837 painting by the Flemish painter Roman-Eugene Van Maldeghem. After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena ), Galileo
8928-476: The phenomena of electricity and magnetism are related. A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations . Time and space cannot be defined separately from each other (as was previously thought to be the case). Rather, space and time are interwoven into a single continuum known as "spacetime" . Events that occur at
9052-473: The planet Saturn , and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn's rings were directly oriented to Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him. Galileo observed the planet Neptune in 1612. It appears in his notebooks as one of many unremarkable dim stars. He did not realise that it
9176-421: The positions of these "stars" relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars . On 10 January, Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days, he concluded that they were orbiting Jupiter: he had discovered three of Jupiter's four largest moons . He discovered
9300-447: The possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results ... How, then, could such a universal principle be found?" Albert Einstein: Autobiographical Notes Einstein discerned two fundamental propositions that seemed to be
9424-466: The previous decade, Barberini, the future Urban VIII, had come down on the side of Galileo and the Lincean Academy . Galileo's dispute with Grassi permanently alienated many Jesuits, and Galileo and his friends were convinced that they were responsible for bringing about his later condemnation, although supporting evidence for this is not conclusive. At the time of Galileo's conflict with
9548-401: The primed coordinate system transform to ( β γ , γ ) {\displaystyle (\beta \gamma ,\gamma )} in the unprimed coordinate system. Likewise, ( x ′ , c t ′ ) {\displaystyle (x',ct')} coordinates of ( 1 , 0 ) {\displaystyle (1,0)} in
9672-448: The primed coordinate system transform to ( γ , β γ ) {\displaystyle (\gamma ,\beta \gamma )} in the unprimed system. Draw gridlines parallel with the c t ′ {\displaystyle ct'} axis through points ( k γ , k β γ ) {\displaystyle (k\gamma ,k\beta \gamma )} as measured in
9796-428: The principle of relativity made later by Einstein, which introduces the concept of simplicity not mentioned above is: Special principle of relativity : If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K ′ moving in uniform translation relatively to K . Henri Poincaré provided
9920-478: The prizes. Observing the moons from a ship proved too difficult, but the method was used for land surveys, including the remapping of France. From September 1610, Galileo observed that Venus exhibits a full set of phases similar to that of the Moon . The heliocentric model of the Solar System developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around
10044-472: The properties of the pendulum and " hydrostatic balances". He was one of the earliest Renaissance developers of the thermoscope and the inventor of various military compasses . With an improved telescope he built, he observed the stars of the Milky Way , the phases of Venus , the four largest satellites of Jupiter , Saturn's rings , lunar craters and sunspots . He also built an early microscope . Galileo's championing of Copernican heliocentrism
10168-502: The pseudonym Lothario Sarsio Sigensano, purporting to be one of his own pupils. The Assayer was Galileo's devastating reply to the Astronomical Balance . It has been widely recognized as a masterpiece of polemical literature, in which "Sarsi's" arguments are subjected to withering scorn. It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII , to whom it had been dedicated. In Rome, in
10292-488: The rebellious phrase " And yet it moves ". There was a claim that a 1640s painting by the Spanish painter Bartolomé Esteban Murillo or an artist of his school, in which the words were hidden until restoration work in 1911, depicts an imprisoned Galileo apparently gazing at the words "E pur si muove" written on the wall of his dungeon. The earliest known written account of the legend dates to a century after his death. Based on
10416-415: The result of several secondary causes including the shape of the sea, its depth, and other factors. Albert Einstein later expressed the opinion that Galileo developed his "fascinating arguments" and accepted them uncritically out of a desire for physical proof of the motion of the Earth. Galileo also dismissed the idea, known from antiquity and by his contemporary Johannes Kepler, that the Moon caused
10540-420: The same form in each inertial reference frame , dates back to Galileo , and was incorporated into Newtonian physics. But in the late 19th century the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance they called " aether ", which, they postulated, would act as the medium through which these waves, or vibrations, propagated (in many respects similar to
10664-411: The same laws of physics. In particular, the speed of light in vacuum is always measured to be c , even when measured by multiple systems that are moving at different (but constant) velocities. From the principle of relativity alone without assuming the constancy of the speed of light (i.e., using the isotropy of space and the symmetry implied by the principle of special relativity) it can be shown that
10788-657: The same position in space. While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. This asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane , but the frames are actually equivalent. The consequences of special relativity can be derived from the Lorentz transformation equations. These transformations, and hence special relativity, lead to different physical predictions than those of Newtonian mechanics at all relative velocities, and most pronounced when relative velocities become comparable to
10912-406: The same time for one observer can occur at different times for another. Until several years later when Einstein developed general relativity , which introduced a curved spacetime to incorporate gravity, the phrase "special relativity" was not used. A translation sometimes used is "restricted relativity"; "special" really means "special case". Some of the work of Albert Einstein in special relativity
11036-443: The sense of Holy Scripture". The Inquisition found that the idea of the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth, it is at least erroneous in faith". Pope Paul V instructed Cardinal Bellarmine to deliver this finding to Galileo, and to order him to abandon heliocentrism. On 26 February, Galileo was called to Bellarmine's residence and ordered "to abandon completely ...
11160-502: The smaller sizes were not small enough to answer Tycho's argument. Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide such evidence. This theory was so important to him that he originally intended to call his Dialogue Concerning
11284-445: The spacetime coordinates measured by observers in different reference frames compare with each other, it is useful to work with a simplified setup with frames in a standard configuration . With care, this allows simplification of the math with no loss of generality in the conclusions that are reached. In Fig. 2-1, two Galilean reference frames (i.e., conventional 3-space frames) are displayed in relative motion. Frame S belongs to
11408-462: The spacetime transformations between inertial frames are either Euclidean, Galilean, or Lorentzian. In the Lorentzian case, one can then obtain relativistic interval conservation and a certain finite limiting speed. Experiments suggest that this speed is the speed of light in vacuum. Einstein consistently based the derivation of Lorentz invariance (the essential core of special relativity) on just
11532-414: The spacing between c t ′ {\displaystyle ct'} units equals ( 1 + β 2 ) / ( 1 − β 2 ) {\textstyle {\sqrt {(1+\beta ^{2})/(1-\beta ^{2})}}} times the spacing between c t {\displaystyle ct} units, as measured in frame S. This ratio
11656-602: The speed of light was motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether . There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment. In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance. The derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions ( made in almost all theories of physics ), including
11780-463: The speed of light. The speed of light is so much larger than anything most humans encounter that some of the effects predicted by relativity are initially counterintuitive . In Galilean relativity, an object's length ( Δ r {\displaystyle \Delta r} ) and the temporal separation between two events ( Δ t {\displaystyle \Delta t} ) are independent invariants,
11904-436: The star at his viewing point. In his Dialogue , he reported that he had found the apparent diameter of a star of first magnitude to be no more than 5 arcseconds , and that of one of sixth magnitude to be about / 6 arcseconds. Like most astronomers of his day, Galileo did not recognise that the apparent sizes of stars that he measured were spurious, caused by diffraction and atmospheric distortion, and did not represent
12028-422: The stars as they appeared to be much larger than the Sun. The essay also included four theological arguments, but Ingoli suggested Galileo focus on the physical and mathematical arguments, and he did not mention Galileo's biblical ideas. In February 1616, an Inquisitorial commission declared heliocentrism to be "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places
12152-588: The study of comets had been proposed at the time by Tycho Brahe.) In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christoph Scheiner , and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work. The Jesuits were offended, and Grassi soon replied with a polemical tract of his own, The Astronomical and Philosophical Balance , under
12276-588: The surname "Galilei") derives from the Latin "Galilaeus", meaning "of Galilee ". The biblical roots of Galileo's name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair , one of Galileo's opponents, the Dominican priest Tommaso Caccini , delivered against Galileo a controversial and influential sermon . In it he made a point of quoting Acts 1:11 : "Ye men of Galilee, why stand ye gazing up into heaven?". Despite being
12400-560: The suspected public ridicule lightly, nor the Copernican advocacy. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings in September 1632. He finally arrived in February 1633 and was brought before inquisitor Vincenzo Maculani to be charged . Throughout his trial, Galileo steadfastly maintained that since 1616 he had faithfully kept his promise not to hold any of
12524-573: The telescope). His multiple interests included the study of astrology , which at the time was a discipline tied to the studies of mathematics, astronomy and medicine. Tycho Brahe and others had observed the supernova of 1572 . Ottavio Brenzoni's letter of 15 January 1605 to Galileo brought the 1572 supernova and the less bright nova of 1601 to Galileo's notice. Galileo observed and discussed Kepler's Supernova in 1604. Since these new stars displayed no detectable diurnal parallax , Galileo concluded that they were distant stars, and, therefore, disproved
12648-440: The telescope, and contrasted them to planets, which the telescope revealed to be discs. But shortly thereafter, in his Letters on Sunspots , he reported that the telescope revealed the shapes of both stars and planets to be "quite round". From that point forward, he continued to report that telescopes showed the roundness of stars, and that stars seen through the telescope measured a few seconds of arc in diameter. He also devised
12772-693: The tides in 1616, addressed to Cardinal Orsini . 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. If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about 12 hours apart. Galileo dismissed this anomaly as
12896-528: The tides—Galileo also took no interest in Kepler's elliptical orbits of the planets . Galileo continued to argue in favour of his theory of tides, considering it the ultimate proof of Earth's motion. In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi , professor of mathematics at the Jesuit Collegio Romano . It began as a dispute over the nature of comets, but by
13020-573: The time Galileo had published The Assayer ( Il Saggiatore ) in 1623, his last salvo in the dispute, it had become a much wider controversy over the very nature of science itself. The title page of the book describes Galileo as a philosopher and "Matematico Primario" of the Grand Duke of Tuscany. Because The Assayer contains such a wealth of Galileo's ideas on how science should be practised, it has been referred to as his scientific manifesto. Early in 1619, Father Grassi had anonymously published
13144-535: The time, surnames were optional in Italy, and his first name had the same origin as his sometimes-family name, Galilei. Both his given and family name ultimately derived from an ancestor, Galileo Bonaiuti , an important physician, professor, and politician in Florence in the 15th century. Galileo Bonaiuti was buried in the same church, the Basilica of Santa Croce in Florence , where about 200 years later, Galileo Galilei
13268-520: The true sizes of stars. However, Galileo's values were much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Brahe, and enabled Galileo to counter anti-Copernican arguments such as those made by Tycho that these stars would have to be absurdly large for their annual parallaxes to be undetectable. Other astronomers such as Simon Marius, Giovanni Battista Riccioli , and Martinus Hortensius made similar measurements of stars, and Marius and Riccioli concluded
13392-420: The two basic principles of: relativity and invariance of the speed of light. He wrote: The insight fundamental for the special theory of relativity is this: The assumptions relativity and light speed invariance are compatible if relations of a new type ("Lorentz transformation") are postulated for the conversion of coordinates and times of events ... The universal principle of the special theory of relativity
13516-408: The unprimed coordinates through the Lorentz transformations and could be approximately measured from the graph (assuming that it has been plotted accurately enough), but the real merit of a Minkowski diagram is its granting us a geometric view of the scenario. For example, in this figure, we observe that the two timelike-separated events that had different x-coordinates in the unprimed frame are now at
13640-565: The unprimed coordinates yields the inverse Lorentz transformation: t = γ ( t ′ + v x ′ / c 2 ) x = γ ( x ′ + v t ′ ) y = y ′ z = z ′ . {\displaystyle {\begin{aligned}t&=\gamma (t'+vx'/c^{2})\\x&=\gamma (x'+vt')\\y&=y'\\z&=z'.\end{aligned}}} This shows that
13764-408: The unprimed frame is moving with the velocity − v , as measured in the primed frame. There is nothing special about the x -axis. The transformation can apply to the y - or z -axis, or indeed in any direction parallel to the motion (which are warped by the γ factor) and perpendicular; see the article Lorentz transformation for details. A quantity that is invariant under Lorentz transformations
13888-476: The unprimed frame, where k {\displaystyle k} is an integer. Likewise, draw gridlines parallel with the x ′ {\displaystyle x'} axis through ( k β γ , k γ ) {\displaystyle (k\beta \gamma ,k\gamma )} as measured in the unprimed frame. Using the Pythagorean theorem, we observe that
14012-745: The values of which do not change when observed from different frames of reference. In special relativity, however, the interweaving of spatial and temporal coordinates generates the concept of an invariant interval , denoted as Δ s 2 {\displaystyle \Delta s^{2}} : Δ s 2 = def c 2 Δ t 2 − ( Δ x 2 + Δ y 2 + Δ z 2 ) {\displaystyle \Delta s^{2}\;{\overset {\text{def}}{=}}\;c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2})} The interweaving of space and time revokes
14136-446: The way sound propagates through air). The aether was thought to be an absolute reference frame against which all speeds could be measured, and could be considered fixed and motionless relative to Earth or some other fixed reference point. The aether was supposed to be sufficiently elastic to support electromagnetic waves, while those waves could interact with matter, yet offering no resistance to bodies passing through it (its one property
14260-508: Was a Florentine astronomer , physicist and engineer, sometimes described as a polymath . He was born in the city of Pisa , then part of the Duchy of Florence . Galileo has been called the father of observational astronomy , modern-era classical physics, the scientific method , and modern science . Galileo studied speed and velocity , gravity and free fall , the principle of relativity , inertia , projectile motion and also worked in applied science and technology, describing
14384-419: Was a planet, but he did note its motion relative to the stars before losing track of it. Galileo made naked-eye and telescopic studies of sunspots . Their existence raised another difficulty with the unchanging perfection of the heavens as posited in orthodox Aristotelian celestial physics. An apparent annual variation in their trajectories, observed by Francesco Sizzi and others in 1612–1613, also provided
14508-514: Was allowed to return to his villa at Arcetri near Florence in 1634, where he spent part of his life under house arrest. Galileo was ordered to read the Seven Penitential Psalms once a week for the next three years. However, his daughter Maria Celeste relieved him of the burden after securing ecclesiastical permission to take it upon herself. Special case In logic , especially as applied in mathematics , concept A
14632-542: Was also buried. When he did refer to himself with more than one name, it was sometimes as Galileo Galilei Linceo, a reference to his being a member of the Accademia dei Lincei , an elite science organization founded in the Papal States . It was common for mid-16th century Tuscan families to name the eldest son after the parents' surname. Hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name "Galileo" (and thence
14756-416: Was also possible to place it entirely on the far side of the Sun, where it could exhibit only gibbous and full phases. After Galileo's telescopic observations of the crescent, gibbous and full phases of Venus, the Ptolemaic model became untenable. In the early 17th century, as a result of his discovery, the great majority of astronomers converted to one of the various geo-heliocentric planetary models, such as
14880-485: Was eight, his family moved to Florence , but he was left under the care of Muzio Tedaldi for two years. When Galileo was ten, he left Pisa to join his family in Florence, where he came under the tutelage of Jacopo Borghini. He was educated, particularly in logic, from 1575 to 1578 in the Vallombrosa Abbey , about 30 km southeast of Florence. Galileo tended to refer to himself only by his first name. At
15004-542: Was met with opposition from within the Catholic Church and from some astronomers. The matter was investigated by the Roman Inquisition in 1615, which concluded that his opinions contradicted accepted Biblical interpretations. Galileo later defended his views in Dialogue Concerning the Two Chief World Systems (1632), which appeared to attack and ridicule Pope Urban VIII , thus alienating both
15128-462: Was that it allowed electromagnetic waves to propagate). The results of various experiments, including the Michelson–Morley experiment in 1887 (subsequently verified with more accurate and innovative experiments), led to the theory of special relativity, by showing that the aether did not exist. Einstein's solution was to discard the notion of an aether and the absolute state of rest. In relativity, any reference frame moving with uniform motion will observe
15252-465: Was the religious life. Both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence . Livia took the name Sister Arcangela and was ill for most of her life. Vincenzo was later legitimised as
15376-399: Was used to create an accurate timepiece. Up to this point, Galileo had deliberately been kept away from mathematics, since a physician earned a higher income than a mathematician. However, after accidentally attending a lecture on geometry, he talked his reluctant father into letting him study mathematics and natural philosophy instead of medicine. He created a thermoscope , a forerunner of
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