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
A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth; the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way. For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and radiates into outer space. All occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime, for some stars by supernova nucleosynthesis when it explodes.
Near the end of its life, a star can contain degenerate matter. Astronomers can determine the mass, age and many other properties of a star by observing its motion through space, its luminosity, spectrum respectively; the total mass of a star is the main factor. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement. A plot of the temperature of many stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram. Plotting a particular star on that diagram allows the age and evolutionary state of that star to be determined. A star's life begins with the gravitational collapse of a gaseous nebula of material composed of hydrogen, along with helium and trace amounts of heavier elements; when the stellar core is sufficiently dense, hydrogen becomes converted into helium through nuclear fusion, releasing energy in the process. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective heat transfer processes.
The star's internal pressure prevents it from collapsing further under its own gravity. A star with mass greater than 0.4 times the Sun's will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements in shells around the core; as the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled as new stars. Meanwhile, the core becomes a stellar remnant: a white dwarf, a neutron star, or if it is sufficiently massive a black hole. Binary and multi-star systems consist of two or more stars that are gravitationally bound and move around each other in stable orbits; when two such stars have a close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, such as a star cluster or a galaxy. Stars have been important to civilizations throughout the world, they have used for celestial navigation and orientation.
Many ancient astronomers believed that stars were permanently affixed to a heavenly sphere and that they were immutable. By convention, astronomers grouped stars into constellations and used them to track the motions of the planets and the inferred position of the Sun; the motion of the Sun against the background stars was used to create calendars, which could be used to regulate agricultural practices. The Gregorian calendar used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to its local star, the Sun; the oldest dated star chart was the result of ancient Egyptian astronomy in 1534 BC. The earliest known star catalogues were compiled by the ancient Babylonian astronomers of Mesopotamia in the late 2nd millennium BC, during the Kassite Period; the first star catalogue in Greek astronomy was created by Aristillus in 300 BC, with the help of Timocharis. The star catalog of Hipparchus included 1020 stars, was used to assemble Ptolemy's star catalogue.
Hipparchus is known for the discovery of the first recorded nova. Many of the constellations and star names in use today derive from Greek astronomy. In spite of the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. In 185 AD, they were the first to observe and write about a supernova, now known as the SN 185; the brightest stellar event in recorded history was the SN 1006 supernova, observed in 1006 and written about by the Egyptian astronomer Ali ibn Ridwan and several Chinese astronomers. The SN 1054 supernova, which gave birth to the Crab Nebula, was observed by Chinese and Islamic astronomers. Medieval Islamic astronomers gave Arabic names to many stars that are still used today and they invented numerous astronomical instruments that could compute the positions of the stars, they built the first large observatory research institutes for the purpose of producing Zij star catalogues. Among these, the Book of Fixed Stars was written by the Persian astronomer Abd al-Rahman al-Sufi, who observed a number of stars, star clusters and galaxies.
According to A. Zahoor, in the 11th century, the Persian polymath scholar Abu Rayhan Biruni described the Milky
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
A neutron star is the collapsed core of a giant star which before collapse had a total of between 10 and 29 solar masses. Neutron stars are the smallest and densest stars, not counting hypothetical quark stars and strange stars. Neutron stars have a radius of the order of a mass lower than a 2.16 solar masses. They result from the supernova explosion of a massive star, combined with gravitational collapse, that compresses the core past white dwarf star density to that of atomic nuclei. Once formed, they no longer generate heat, cool over time. Most of the basic models for these objects imply that neutron stars are composed entirely of neutrons. Neutron stars are supported against further collapse by neutron degeneracy pressure, a phenomenon described by the Pauli exclusion principle, just as white dwarfs are supported against collapse by electron degeneracy pressure; however neutron degeneracy pressure is not sufficient to hold up an object beyond 0.7M☉ and repulsive nuclear forces play a larger role in supporting more massive neutron stars.
If the remnant star has a mass exceeding the Tolman–Oppenheimer–Volkoff limit, it continues collapsing to form a black hole. Neutron stars that can be observed are hot and have a surface temperature of around 600000 K, they are so dense that a normal-sized matchbox containing neutron-star material would have a weight of 3 billion metric tons, the same weight as a 0.5 cubic kilometre chunk of the Earth. Their magnetic fields are between 1015 times stronger than Earth's magnetic field; the gravitational field at the neutron star's surface is about 2×1011 times that of Earth's gravitational field. As the star's core collapses, its rotation rate increases as a result of conservation of angular momentum, hence newly formed neutron stars rotate at up to several hundred times per second; some neutron stars emit beams of electromagnetic radiation. Indeed, the discovery of pulsars by Jocelyn Bell Burnell in 1967 was the first observational suggestion that neutron stars exist; the radiation from pulsars is thought to be emitted from regions near their magnetic poles.
If the magnetic poles do not coincide with the rotational axis of the neutron star, the emission beam will sweep the sky, when seen from a distance, if the observer is somewhere in the path of the beam, it will appear as pulses of radiation coming from a fixed point in space. The fastest-spinning neutron star known is PSR J1748-2446ad, rotating at a rate of 716 times a second or 43,000 revolutions per minute, giving a linear speed at the surface on the order of 0.24 c. There are thought to be around 100 million neutron stars in the Milky Way, a figure obtained by estimating the number of stars that have undergone supernova explosions. However, most are old and cold, neutron stars can only be detected in certain instances, such as if they are a pulsar or part of a binary system. Slow-rotating and non-accreting neutron stars are undetectable. Soft gamma repeaters are conjectured to be a type of neutron star with strong magnetic fields, known as magnetars, or alternatively, neutron stars with fossil disks around them.
Neutron stars in binary systems can undergo accretion which makes the system bright in X-rays while the material falling onto the neutron star can form hotspots that rotate in and out of view in identified X-ray pulsar systems. Additionally, such accretion can "recycle" old pulsars and cause them to gain mass and spin-up to fast rotation rates, forming the so-called millisecond pulsars; these binary systems will continue to evolve, the companions can become compact objects such as white dwarfs or neutron stars themselves, though other possibilities include a complete destruction of the companion through ablation or merger. The merger of binary neutron stars may be the source of short-duration gamma-ray bursts and are strong sources of gravitational waves. In 2017, a direct detection of the gravitational waves from such an event was made, gravitational waves have been indirectly detected in a system where two neutron stars orbit each other. In October 2018, astronomers reported that GRB 150101B, a gamma-ray burst event detected in 2015, may be directly related to the historic GW170817 and associated with the merger of two neutron stars.
The similarities between the two events, in terms of gamma ray, optical and x-ray emissions, as well as to the nature of the associated host galaxies, are "striking", suggesting the two separate events may both be the result of the merger of neutron stars, both may be a kilonova, which may be more common in the universe than understood, according to the researchers. Any main-sequence star with an initial mass of above 8 times the mass of the sun has the potential to produce a neutron star; as the star evolves away from the main sequence, subsequent nuclear burning produces an iron-rich core. When all nuclear fuel in the core has been exhausted, the core must be supported by degeneracy pressure alone. Further deposits of mass from shell burning cause the core to exceed the Chandrasekhar limit. Electron-deg
Cambridge University Press
Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the world's oldest publishing house and the second-largest university press in the world, it holds letters patent as the Queen's Printer. The press mission is "to further the University's mission by disseminating knowledge in the pursuit of education and research at the highest international levels of excellence". Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. With a global sales presence, publishing hubs, offices in more than 40 countries, it publishes over 50,000 titles by authors from over 100 countries, its publishing includes academic journals, reference works and English language teaching and learning publications. Cambridge University Press is a charitable enterprise that transfers part of its annual surplus back to the university. Cambridge University Press is both the oldest publishing house in the world and the oldest university press.
It originated from letters patent granted to the University of Cambridge by Henry VIII in 1534, has been producing books continuously since the first University Press book was printed. Cambridge is one of the two privileged presses. Authors published by Cambridge have included John Milton, William Harvey, Isaac Newton, Bertrand Russell, Stephen Hawking. University printing began in Cambridge when the first practising University Printer, Thomas Thomas, set up a printing house on the site of what became the Senate House lawn – a few yards from where the press's bookshop now stands. In those days, the Stationers' Company in London jealously guarded its monopoly of printing, which explains the delay between the date of the university's letters patent and the printing of the first book. In 1591, Thomas's successor, John Legate, printed the first Cambridge Bible, an octavo edition of the popular Geneva Bible; the London Stationers objected strenuously. The university's response was to point out the provision in its charter to print "all manner of books".
Thus began the press's tradition of publishing the Bible, a tradition that has endured for over four centuries, beginning with the Geneva Bible, continuing with the Authorized Version, the Revised Version, the New English Bible and the Revised English Bible. The restrictions and compromises forced upon Cambridge by the dispute with the London Stationers did not come to an end until the scholar Richard Bentley was given the power to set up a'new-style press' in 1696. In July 1697 the Duke of Somerset made a loan of £200 to the university "towards the printing house and presse" and James Halman, Registrary of the University, lent £100 for the same purpose, it was in Bentley's time, in 1698, that a body of senior scholars was appointed to be responsible to the university for the press's affairs. The Press Syndicate's publishing committee still meets and its role still includes the review and approval of the press's planned output. John Baskerville became University Printer in the mid-eighteenth century.
Baskerville's concern was the production of the finest possible books using his own type-design and printing techniques. Baskerville wrote, "The importance of the work demands all my attention. Caxton would have found nothing to surprise him if he had walked into the press's printing house in the eighteenth century: all the type was still being set by hand. A technological breakthrough was badly needed, it came when Lord Stanhope perfected the making of stereotype plates; this involved making a mould of the whole surface of a page of type and casting plates from that mould. The press was the first to use this technique, in 1805 produced the technically successful and much-reprinted Cambridge Stereotype Bible. By the 1850s the press was using steam-powered machine presses, employing two to three hundred people, occupying several buildings in the Silver Street and Mill Lane area, including the one that the press still occupies, the Pitt Building, built for the press and in honour of William Pitt the Younger.
Under the stewardship of C. J. Clay, University Printer from 1854 to 1882, the press increased the size and scale of its academic and educational publishing operation. An important factor in this increase was the inauguration of its list of schoolbooks. During Clay's administration, the press undertook a sizeable co-publishing venture with Oxford: the Revised Version of the Bible, begun in 1870 and completed in 1885, it was in this period as well that the Syndics of the press turned down what became the Oxford English Dictionary—a proposal for, brought to Cambridge by James Murray before he turned to Oxford. The appointment of R. T. Wright as Secretary of the Press Syndicate in 1892 marked the beginning of the press's development as a modern publishing business with a defined editorial policy and administrative structure, it was Wright who devised the plan for one of the most distinctive Cambridge contributions to publishing—the Cambridge Histories. The Cambridge Modern History was published
A white dwarf called a degenerate dwarf, is a stellar core remnant composed of electron-degenerate matter. A white dwarf is dense: its mass is comparable to that of the Sun, while its volume is comparable to that of Earth. A white dwarf's faint luminosity comes from the emission of stored thermal energy; the nearest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. There are thought to be eight white dwarfs among the hundred star systems nearest the Sun; the unusual faintness of white dwarfs was first recognized in 1910. The name white dwarf was coined by Willem Luyten in 1922. White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star, that of about 10 solar masses; this includes over 97% of the other stars in the Milky Way. § 1. After the hydrogen-fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant during which it fuses helium to carbon and oxygen in its core by the triple-alpha process.
If a red giant has insufficient mass to generate the core temperatures required to fuse carbon, an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, the remnant white dwarf. White dwarfs are composed of carbon and oxygen. If the mass of the progenitor is between 8 and 10.5 solar masses, the core temperature will be sufficient to fuse carbon but not neon, in which case an oxygen–neon–magnesium white dwarf may form. Stars of low mass will not be able to fuse helium, hence, a helium white dwarf may form by mass loss in binary systems; the material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the heat generated by fusion against gravitational collapse, but is supported only by electron degeneracy pressure, causing it to be dense; the physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit—approximately 1.44 times of M☉—beyond which it cannot be supported by electron degeneracy pressure.
A carbon-oxygen white dwarf that approaches this mass limit by mass transfer from a companion star, may explode as a type Ia supernova via a process known as carbon detonation. A white dwarf is hot when it forms, but because it has no source of energy, it will cool as it radiates its energy; this means that its radiation, which has a high color temperature, will lessen and redden with time. Over a long time, a white dwarf will cool and its material will begin to crystallize, starting with the core; the star's low temperature means it will no longer emit significant heat or light, it will become a cold black dwarf. Because the length of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the universe, it is thought that no black dwarfs yet exist; the oldest white dwarfs still radiate at temperatures of a few thousand kelvins. The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C.
The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783. In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. In 1939, Russell looked back on the discovery:, p. 1 I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars—including comparison stars—which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, I discussed; this piece of routine work proved fruitful—it led to the discovery that all the stars of faint absolute magnitude were of spectral class M. In conversation on this subject, I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B. Characteristically, he sent a note to the Observatory office and before long the answer came that the spectrum of this star was A.
I knew enough about it in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a pretty rule of stellar characteristics; the spectral type of 40 Eridani B was described in 1914 by Walter Adams. The white dwarf companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius and Procyon were changing their positions periodically. In 1844 he predicted that both stars had unseen companions: If we were to regard Sirius and Procyon as double stars, the change of their motions would not surprise us.
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure; some of these derive from a unit of force divided by a unit of area. Pressure may be expressed in terms of standard atmospheric pressure. Manometric units such as the centimetre of water, millimetre of mercury, inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer. Pressure is the amount of force applied at right angles to the surface of an object per unit area; the symbol for it is p or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is used; the usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, on writing style. Mathematically: p = F A, where: p is the pressure, F is the magnitude of the normal force, A is the area of the surface on contact.
Pressure is a scalar quantity. It relates the vector surface element with the normal force acting on it; the pressure is the scalar proportionality constant that relates the two normal vectors: d F n = − p d A = − p n d A. The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward; the equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect to say "the pressure is directed in such or such direction"; the pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same. Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point.
It is a fundamental parameter in thermodynamics, it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre; this name for the unit was added in 1971. Other units of pressure, such as pounds per square inch and bar, are in common use; the CGS unit of pressure is 0.1 Pa.. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre and the like without properly identifying the force units, but using the names kilogram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2. Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume, it is therefore related to energy density and may be expressed in units such as joules per cubic metre. Mathematically: p =; some meteorologists prefer the hectopascal for atmospheric air pressure, equivalent to the older unit millibar. Similar pressures are given in kilopascals in most other fields, where the hecto- prefix is used.
The inch of mercury is still used in the United States. Oceanographers measure underwater pressure in decibars because pressure in the ocean increases by one decibar per metre depth; the standard atmosphere is an established constant. It is equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa; because pressure is measured by its ability to displace a column of liquid in a manometer, pressures are expressed as a depth of a particular fluid. The most common choices are water; the pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column