In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur; until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe was independent of one-dimensional time. However, in 1905, Albert Einstein based his seminal work on special relativity on two postulates: The laws of physics are invariant in all inertial systems; the logical consequence of taking these postulates together is the inseparable joining together of the four dimensions, hitherto assumed as independent, of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light has the same speed regardless of the frame of reference in which it is measured. Einstein framed his theory in terms of kinematics.
His theory was a breakthrough advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced, they were ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were difficult to fit into existing paradigms. In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve this flat spacetime to a Pseudo Riemannian manifold.
Non-relativistic classical mechanics treats time as a universal quantity of measurement, uniform throughout space and, separate from space. Classical mechanics assumes that time has a constant rate of passage, independent of the state of motion of an observer, or indeed of anything external. Furthermore, it assumes that space is Euclidean, to say, it assumes that space follows the geometry of common sense. In the context of special relativity, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity, in addition, provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. In ordinary space, a position is specified by three numbers, known as dimensions. In the Cartesian coordinate system, these are called x, y, z. A position in spacetime is called an event, requires four numbers to be specified: the three-dimensional location in space, plus the position in time.
Spacetime is thus four dimensional. An event is something that happens instantaneously at a single point in spacetime, represented by a set of coordinates x, y, z and t; the word "event" used in relativity should not be confused with the use of the word "event" in normal conversation, where it might refer to an "event" as something such as a concert, sporting event, or a battle. These are not mathematical "events" in the way the word is used in relativity, because they have finite durations and extents. Unlike the analogies used to explain events, such as firecrackers or lightning bolts, mathematical events have zero duration and represent a single point in spacetime; the path of a particle through spacetime can be considered to be a succession of events. The series of events can be linked together to form a line which represents a particle's progress through spacetime; that line is called the particle's world line. Mathematically, spacetime is a manifold, to say, it appears locally "flat" near each point in the same way that, at small enough scales, a globe appears flat.
An large scale factor, c relates distances measured in space with distances measured in time. The magnitude of this scale factor, along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe, noticeably different from what they might observe if the world were Euclidean, it was only with the advent of sensitive scientific measurements in the mid-1800s, such as the Fizeau experiment and the Michelson–Morley experiment, that puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space. In special relativity, an observer will, in most
Tests of general relativity
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, the gravitational redshift; the precession of Mercury was known. A program of more accurate tests starting in 1959 tested the various predictions of general relativity with a further degree of accuracy in the weak gravitational field limit limiting possible deviations from the theory. In the 1970s, additional tests began to be made, starting with Irwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the sun. Beginning in 1974, Hulse and others have studied the behaviour of binary pulsars experiencing much stronger gravitational fields than those found in the Solar System. Both in the weak field limit and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been well tested locally.
In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a black hole merger. This discovery, along with additional detections announced in June 2016 and June 2017, tested general relativity in the strong field limit, observing to date no deviations from theory. Albert Einstein proposed three tests of general relativity, subsequently called the classical tests of general relativity, in 1916: the perihelion precession of Mercury's orbit the deflection of light by the Sun the gravitational redshift of lightIn the letter to the London Times on November 28, 1919, he described the theory of relativity and thanked his English colleagues for their understanding and testing of his work, he mentioned three classical tests with comments: "The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up. Under Newtonian physics, a two-body system consisting of a lone object orbiting a spherical mass would trace out an ellipse with the center of mass of the system at a focus.
The point of closest approach, called the periapsis, is fixed. A number of effects in the Solar System cause the perihelia of planets to precess around the Sun; the principal cause is the presence of other planets. Another effect is solar oblateness. Mercury deviates from the precession predicted from these Newtonian effects; this anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in celestial mechanics, by Urbain Le Verrier. His reanalysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848 showed that the actual rate of the precession disagreed from that predicted from Newton's theory by 38″ per tropical century. A number of ad hoc and unsuccessful solutions were proposed, but they tended to introduce more problems. In general relativity, this remaining precession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime.
Einstein showed that general relativity agrees with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity. Although earlier measurements of planetary orbits were made using conventional telescopes, more accurate measurements are now made with radar; the total observed precession of Mercury is 574.10″±0.65 per century relative to the inertial ICRF. This precession can be attributed to the following causes: The correction by 42.98″ is 3/2 multiple of classical prediction with PPN parameters γ = β = 1. Thus the effect can be explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation. In general relativity the perihelion shift σ, expressed in radians per revolution, is given by: σ = 24 π 3 L 2 T 2 c 2, where L is the semi-major axis, T is the orbital period, c is the speed of light, e is the orbital eccentricity; the other planets experience perihelion shifts as well, since they are farther from the Sun and have longer periods, their shifts are lower, could not be observed until long after Mercury's.
For example, the perihelion shift of Earth's orbit due to general relativity is of 3.84″ per century, Venus's is 8.62″. Both values have now been measured, with results in good agreement with theory; the periapsis shift has now been measured for binary pulsar systems, with PSR 1913+16 amounting to 4.2º per year. These observations are consistent with general relativity, it i
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is conceived in three linear dimensions, although modern physicists consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime; the concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Debates concerning the nature and the mode of existence of space date back to antiquity. Many of these classical philosophical questions were discussed in the Renaissance and reformulated in the 17th century during the early development of classical mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another.
In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. The metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition". In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space. Galilean and Cartesian theories about space and motion are at the foundation of the Scientific Revolution, understood to have culminated with the publication of Newton's Principia in 1687.
Newton's theories about space and time helped. While his theory of space is considered the most influential in Physics, it emerged from his predecessors' ideas about the same; as one of the pioneers of modern science, Galilei revised the established Aristotelian and Ptolemaic ideas about a geocentric cosmos. He backed the Copernican theory that the universe was heliocentric, with a stationary sun at the center and the planets—including the Earth—revolving around the sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galilei wanted to prove instead that the sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galilei, celestial bodies, including the Earth, were inclined to move in circles; this view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging. Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by natural laws.
In other words, he sought a metaphysical foundation or a mechanical explanation for his theories about matter and motion. Cartesian space was Euclidean in structure—infinite and flat, it was defined as that. The Cartesian notion of space is linked to his theories about the nature of the body and matter, he is famously known for his "cogito ergo sum", or the idea that we can only be certain of the fact that we can doubt, therefore think and therefore exist. His theories belong to the rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the empiricists believe, he posited a clear distinction between the body and mind, referred to as the Cartesian dualism. Following Galilei and Descartes, during the seventeenth century the philosophy of space and time revolved around the ideas of Gottfried Leibniz, a German philosopher–mathematician, Isaac Newton, who set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together".
Unoccupied regions are those that could have objects in them, thus spatial relations with other places. For Leibniz space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete. Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes alike except for the location of the material world in
In astronomy, a syzygy is a straight-line configuration of three or more celestial bodies in a gravitational system. The word is used in reference to the Sun and either the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses occur at times of syzygy, as do occultations; the term is applied when the Sun and Moon are in conjunction or opposition. The word syzygy is used to describe interesting configurations of astronomical objects in general. For example, one such case occurred on March 21, 1894, around 23:00 GMT, when Mercury transited the Sun as would have been seen from Venus, Mercury and Venus both transited the Sun as seen from Saturn, it is used to describe situations when all the planets are on the same side of the Sun although they are not in a straight line, such as on March 10, 1982. On June 3, 2014, the Curiosity rover on Mars observed the planet Mercury transiting the Sun, marking the first time a planetary transit has been observed from a celestial body besides Earth.
Syzygy sometimes results in transit, or eclipse. An occultation occurs when an larger body passes in front of an smaller one. A transit occurs. In the combined case where the smaller body transits the larger, an occultation is termed a secondary eclipse. An eclipse occurs when a body or disappears from view, either by an occultation, as with a solar eclipse, or by passing into the shadow of another body, as with a lunar eclipse. Transits and occultations of the Sun by Earth's Moon are called solar eclipses regardless of whether the Sun is or covered. By extension, transits of the Sun by a satellite of a planet may be called eclipses, as with the transits of Phobos and Deimos shown on NASA's JPL photojournal, as may the passage of a satellite into the planet's shadow, as with this eclipse of Phobos; the term eclipse is used more for bodies passing in front of one another. For example, a NASA Astronomy Picture of the Day refers to the Moon eclipsing and occulting Saturn interchangeably; as electromagnetic rays are somewhat bent by gravitation, when they pass by a heavy mass they are bent.
Thus, the heavy mass acts as a form of gravitational lens. If the light source, the diffracting mass and the observer stand in a line, one sees what is termed as an Einstein ring. Syzygy causes the bimonthly phenomena of neap tides. At the new and full moon, the Sun and Moon are in syzygy, their tidal forces act to reinforce each other, the ocean both rises higher and falls lower than the average. Conversely, at the first and third quarter, the Sun and Moon are at right angles, their tidal forces counteract each other, the tidal range is smaller than average. Tidal variation can be measured in the earth's crust, this may affect the frequency of earthquakes
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present; the relation is specified by the Einstein field equations, a system of partial differential equations. Some predictions of general relativity differ from those of classical physics concerning the passage of time, the geometry of space, the motion of bodies in free fall, the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay; the predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date.
Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes; the bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO.
In addition, general relativity is the basis of current cosmological models of a expanding universe. Acknowledged as a theory of extraordinary beauty, general relativity has been described as the most beautiful of all existing physical theories. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations; these equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, form the core of Einstein's general theory of relativity. The Einstein field equations are nonlinear and difficult to solve.
Einstein used approximation methods in working out initial predictions of the theory. But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric; this solution laid the groundwork for the description of the final stages of gravitational collapse, the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, which resulted in the Reissner–Nordström solution, now associated with electrically charged black holes. In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption. By 1929, the work of Hubble and others had shown that our universe is expanding; this is described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant.
Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an hot and dense earlier state. Einstein declared the cosmological constant the biggest blunder of his life. During that period, general relativity remained something of a curiosity among physical theories, it was superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters. A 1919 expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919, making Einstein famous, yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between 1960 and 1975, now known as the golden age of general relativity. Physicists began to understand the concept of a black hole, to identify quasars as one of these objects' astrophysical manifestations.
More precise solar system tests confirmed the theory's predictive power, relativistic cosmology, became amenable to direct observational tests. Over the years, general relativity has acqui
In physics, redshift is a phenomenon where electromagnetic radiation from an object undergoes an increase in wavelength. Whether or not the radiation is visible, "redshift" means an increase in wavelength, equivalent to a decrease in wave frequency and photon energy, in accordance with the wave and quantum theories of light. Neither the emitted nor perceived light is red. Examples of redshifting are a gamma ray perceived as an X-ray, or visible light perceived as radio waves; the opposite of a redshift is energy increases. However, redshift is a more common term and sometimes blueshift is referred to as negative redshift. There are three main causes of red in astronomy and cosmology: Objects move apart in space; this is an example of the Doppler effect. Space itself expands; this is known as cosmological redshift. All sufficiently distant light sources show redshift corresponding to the rate of increase in their distance from Earth, known as Hubble's Law. Gravitational redshift is a relativistic effect observed due to strong gravitational fields, which distort spacetime and exert a force on light and other particles.
Knowledge of redshifts and blueshifts has been used to develop several terrestrial technologies such as Doppler radar and radar guns. Redshifts are seen in the spectroscopic observations of astronomical objects, its value is represented by the letter z. A special relativistic redshift formula can be used to calculate the redshift of a nearby object when spacetime is flat. However, in many contexts, such as black holes and Big Bang cosmology, redshifts must be calculated using general relativity. Special relativistic and cosmological redshifts can be understood under the umbrella of frame transformation laws. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; the history of the subject began with the development in the 19th century of wave mechanics and the exploration of phenomena associated with the Doppler effect. The effect is named after Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842.
The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot in 1845. Doppler predicted that the phenomenon should apply to all waves, in particular suggested that the varying colors of stars could be attributed to their motion with respect to the Earth. Before this was verified, however, it was found that stellar colors were due to a star's temperature, not motion. Only was Doppler vindicated by verified redshift observations; the first Doppler redshift was described by French physicist Hippolyte Fizeau in 1848, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red. In 1887, Vogel and Scheiner discovered the annual Doppler effect, the yearly change in the Doppler shift of stars located near the ecliptic due to the orbital velocity of the Earth.
In 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors. The earliest occurrence of the term red-shift in print appears to be by American astronomer Walter S. Adams in 1908, in which he mentions "Two methods of investigating that nature of the nebular red-shift"; the word does not appear unhyphenated until about 1934 by Willem de Sitter indicating that up to that point its German equivalent, was more used. Beginning with observations in 1912, Vesto Slipher discovered that most spiral galaxies mostly thought to be spiral nebulae, had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years he wrote a review in the journal Popular Astronomy. In it he states that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km showed the means available, capable of investigating not only the spectra of the spirals but their velocities as well."
Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable "positive" velocities. Subsequently, Edwin Hubble discovered an approximate relationship between the redshifts of such "nebulae" and the distances to them with the formulation of his eponymous Hubble's law; these observations corroborated Alexander Friedmann's 1922 work, in which he derived the Friedmann-Lemaître equations. They are today considered strong evidence for the Big Bang theory; the spectrum of light that comes from a single source can be measured. To determine the redshift, one searches for features in the spectrum such as absorption lines, emission lines, or other variations in light intensity. If found, these featur
Time is the indefinite continued progress of existence and events that occur in irreversible succession through the past, in the present, the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, to quantify rates of change of quantities in material reality or in the conscious experience. Time is referred to as a fourth dimension, along with three spatial dimensions. Time has long been an important subject of study in religion and science, but defining it in a manner applicable to all fields without circularity has eluded scholars. Diverse fields such as business, sports, the sciences, the performing arts all incorporate some notion of time into their respective measuring systems. Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities.
Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event constitutes one standard unit such as the second, is useful in the conduct of both advanced experiments and everyday affairs of life; the operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Temporal measurement has occupied scientists and technologists, was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, the beat of a heart.
The international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is of significant social importance, having economic value as well as personal value, due to an awareness of the limited time in each day and in human life spans. Speaking, methods of temporal measurement, or chronometry, take two distinct forms: the calendar, a mathematical tool for organising intervals of time, the clock, a physical mechanism that counts the passage of time. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day. Personal electronic devices display both calendars and clocks simultaneously; the number that marks the occurrence of a specified event as to hour or date is obtained by counting from a fiducial epoch – a central reference point. Artifacts from the Paleolithic suggest that the moon was used to reckon time as early as 6,000 years ago. Lunar calendars were among the first to appear, with years of either 13 lunar months.
Without intercalation to add days or months to some years, seasons drift in a calendar based on twelve lunar months. Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year and a year of just twelve lunar months; the numbers twelve and thirteen came to feature prominently in many cultures, at least due to this relationship of months to years. Other early forms of calendars originated in Mesoamerica in ancient Mayan civilization; these calendars were religiously and astronomically based, with 18 months in a year and 20 days in a month, plus five epagomenal days at the end of the year. The reforms of Julius Caesar in 45 BC put the Roman world on a solar calendar; this Julian calendar was faulty in that its intercalation still allowed the astronomical solstices and equinoxes to advance against it by about 11 minutes per year. Pope Gregory XIII introduced a correction in 1582. During the French Revolution, a new clock and calendar were invented in attempt to de-Christianize time and create a more rational system in order to replace the Gregorian calendar.
The French Republican Calendar's days consisted of ten hours of a hundred minutes of a hundred seconds, which marked a deviation from the 12-based duodecimal system used in many other devices by many cultures. The system was abolished in 1806. A large variety of devices have been invented to measure time; the study of these devices is called horology. An Egyptian device that dates to c. 1500 BC, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a nonlinear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so. A sundial uses a gnomon to cast a shadow on a set of markings calibrated to the hour; the position of the shadow marks the hour in local time. The idea to separate the day into smaller parts is credited to Egyptians because of their sundials, which operated on a duodecimal system; the importance of the number 12 is due to the number of lunar cycles in a year and the number of stars used to count the passage of night.
The most precise timekeeping device of the ancient