In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of dispersive effects in the medium. Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems; the soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". A single, consensus definition of a soliton is difficult to find. Drazin & Johnson ascribe three properties to solitons: They are of permanent form. More formal definitions exist. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties. Dispersion and nonlinearity can interact to produce localized wave forms. Consider a pulse of light traveling in glass; this pulse can be thought of as consisting of light of several different frequencies.
Since glass shows dispersion, these different frequencies travel at different speeds and the shape of the pulse therefore changes over time. However the nonlinear Kerr effect occurs. If the pulse has just the right shape, the Kerr effect cancels the dispersion effect, the pulse's shape does not change over time, thus is a soliton. See soliton for a more detailed description. Many solvable models have soliton solutions, including the Korteweg–de Vries equation, the nonlinear Schrödinger equation, the coupled nonlinear Schrödinger equation, the sine-Gordon equation; the soliton solutions are obtained by means of the inverse scattering transform, owe their stability to the integrability of the field equations. The mathematical theory of these equations is a broad and active field of mathematical research; some types of tidal bore, a wave phenomenon of a few rivers including the River Severn, are'undular': a wavefront followed by a train of solitons. Other solitons occur as the undersea internal waves, initiated by seabed topography, that propagate on the oceanic pycnocline.
Atmospheric solitons exist, such as the morning glory cloud of the Gulf of Carpentaria, where pressure solitons traveling in a temperature inversion layer produce vast linear roll clouds. The recent and not accepted soliton model in neuroscience proposes to explain the signal conduction within neurons as pressure solitons. A topological soliton called a topological defect, is any solution of a set of partial differential equations, stable against decay to the "trivial solution". Soliton stability is due to topological constraints, rather than integrability of the field equations; the constraints arise always because the differential equations must obey a set of boundary conditions, the boundary has a nontrivial homotopy group, preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes. No continuous transformation maps a solution in one homotopy class to another; the solutions are distinct, maintain their integrity in the face of powerful forces.
Examples of topological solitons include the screw dislocation in a crystalline lattice, the Dirac string and the magnetic monopole in electromagnetism, the Skyrmion and the Wess–Zumino–Witten model in quantum field theory, the magnetic skyrmion in condensed matter physics, cosmic strings and domain walls in cosmology. In 1834, John Scott Russell describes his wave of translation; the discovery is described here in Scott Russell's own words: I was observing the motion of a boat, drawn along a narrow channel by a pair of horses, when the boat stopped – not so the mass of water in the channel which it had put in motion. I followed it on horseback, overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height, its height diminished, after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.
Scott Russell spent some time making theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties: The waves are stable, can travel over large distances The speed depends on the size of the wave, its width on the depth of water. Unlike normal waves they will never merge – so a small wave is overtaken by a large one, rather than the two combining. If a wave is too big for the depth of water, it splits into two, one big and one small. Scott Russell's experimental work
In physics, cryogenics is the production and behaviour of materials at low temperatures. A person who studies elements that have been subjected to cold temperatures is called a cryogenicist, it is not well-defined at what point on the temperature scale refrigeration ends and cryogenics begins, but scientists assume a gas to be cryogenic if it can be liquefied at or below −150 °C. The U. S. National Institute of Standards and Technology has chosen to consider the field of cryogenics as that involving temperatures below −180 °C; this is a logical dividing line, since the normal boiling points of the so-called permanent gases lie below −180 °C while the Freon refrigerants and other common refrigerants have boiling points above −180 °C. Discovery of superconducting materials with critical temperatures above the boiling point of liquid nitrogen has provided new interest in reliable, low cost methods of producing high temperature cryogenic refrigeration; the term "high temperature cryogenic" describes temperatures ranging from above the boiling point of liquid nitrogen, −195.79 °C, up to −50 °C, the defined upper limit of study referred to as cryogenics.
Cryogenicists use the Kelvin or Rankine temperature scale, both of which measure from absolute zero, rather than more usual scales such as Celsius or Fahrenheit, with their zeroes at arbitrary temperatures. Cryogenics The branches of engineering that involve the study of low temperatures, how to produce them, how materials behave at those temperatures. Cryobiology The branch of biology involving the study of the effects of low temperatures on organisms. Cryoconservation of animal genetic resources The conservation of genetic material with the intention of conserving a breed. Cryosurgery The branch of surgery applying cryogenic temperatures to destroy malignant tissue, e.g. cancer cells. Cryoelectronics The study of electronic phenomena at cryogenic temperatures. Examples include variable-range hopping. Cryotronics The practical application of cryoelectronics. Cryonics Cryopreserving humans and animals with the intention of future revival. "Cryogenics" is sometimes erroneously used to mean "Cryonics" in the press.
The word cryogenics stems from Greek κρύο – "cold" + γονική – "having to do with production". Cryogenic fluids with their boiling point in kelvins. Liquefied gases, such as liquid nitrogen and liquid helium, are used in many cryogenic applications. Liquid nitrogen is the most used element in cryogenics and is purchasable around the world. Liquid helium is commonly used and allows for the lowest attainable temperatures to be reached; these liquids may be stored in Dewar flasks, which are double-walled containers with a high vacuum between the walls to reduce heat transfer into the liquid. Typical laboratory Dewar flasks are spherical, made of glass and protected in a metal outer container. Dewar flasks for cold liquids such as liquid helium have another double-walled container filled with liquid nitrogen. Dewar flasks are named after James Dewar, the man who first liquefied hydrogen. Thermos bottles are smaller vacuum flasks fitted in a protective casing. Cryogenic barcode labels are used to mark Dewar flasks containing these liquids, will not frost over down to −195 degrees Celsius.
Cryogenic transfer pumps are the pumps used on LNG piers to transfer liquefied natural gas from LNG carriers to LNG storage tanks, as are cryogenic valves. The field of cryogenics advanced during World War II when scientists found that metals frozen to low temperatures showed more resistance to wear. Based on this theory of cryogenic hardening, the commercial cryogenic processing industry was founded in 1966 by Ed Busch. With a background in the heat treating industry, Busch founded a company in Detroit called CryoTech in 1966 which merged with 300 Below in 1999 to become the world's largest and oldest commercial cryogenic processing company. Busch experimented with the possibility of increasing the life of metal tools to anywhere between 200% and 400% of the original life expectancy using cryogenic tempering instead of heat treating; this evolved in the late 1990s into the treatment of other parts. Cryogens, such as liquid nitrogen, are further used for specialty chilling and freezing applications.
Some chemical reactions, like those used to produce the active ingredients for the popular statin drugs, must occur at low temperatures of −100 °C. Special cryogenic chemical reactors are used to remove reaction heat and provide a low temperature environment; the freezing of foods and biotechnology products, like vaccines, requires nitrogen in blast freezing or immersion freezing systems. Certain soft or elastic materials become hard and brittle at low temperatures, which makes cryogenic milling an option for some materials that cannot be milled at higher temperatures. Cryogenic processing is not a substitute for heat treatment, but rather an extension of the heating–quenching–tempering cycle; when an item is quenched, the final temperature is ambient. The only reason for this is. There is nothing metallurgically significant about ambient temperature; the cryogenic process continues this action from ambient temperature down to −320 °F. In most instances the cryogenic cycle is followed by a heat tempering procedure.
As all alloys do not have the same chemical constituents, the tempering procedure varies according to the material's chemical composition, t
Vacuum is space devoid of matter. The word stems from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists discuss ideal test results that would occur in a perfect vacuum, which they sometimes call "vacuum" or free space, use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure; the Latin term in vacuo is used to describe an object, surrounded by a vacuum. The quality of a partial vacuum refers to how it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. Much higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry and engineering, operate below one trillionth of atmospheric pressure, can reach around 100 particles/cm3.
Outer space is an higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space. According to modern understanding if all matter could be removed from a volume, it would still not be "empty" due to vacuum fluctuations, dark energy, transiting gamma rays, cosmic rays and other phenomena in quantum physics. In the study of electromagnetism in the 19th century, vacuum was thought to be filled with a medium called aether. In modern particle physics, the vacuum state is considered the ground state of a field. Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Evangelista Torricelli produced the first laboratory vacuum in 1643, other experimental techniques were developed as a result of his theories of atmospheric pressure. A torricellian vacuum is created by filling a tall glass container closed at one end with mercury, inverting it in a bowl to contain the mercury.
Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes, a wide array of vacuum technology has since become available. The recent development of human spaceflight has raised interest in the impact of vacuum on human health, on life forms in general; the word vacuum comes from Latin, meaning'an empty space, void', noun use of neuter of vacuus, meaning "empty", related to vacare, meaning "be empty". Vacuum is one of the few words in the English language that contains two consecutive letters'u'. There has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, which posited void and atom as the fundamental explanatory elements of physics. Following Plato the abstract concept of a featureless void faced considerable skepticism: it could not be apprehended by the senses, it could not, provide additional explanatory power beyond the physical volume with which it was commensurate and, by definition, it was quite nothing at all, which cannot rightly be said to exist.
Aristotle believed that no void could occur because the denser surrounding material continuum would fill any incipient rarity that might give rise to a void. In his Physics, book IV, Aristotle offered numerous arguments against the void: for example, that motion through a medium which offered no impediment could continue ad infinitum, there being no reason that something would come to rest anywhere in particular. Although Lucretius argued for the existence of vacuum in the first century BC and Hero of Alexandria tried unsuccessfully to create an artificial vacuum in the first century AD, it was European scholars such as Roger Bacon, Blasius of Parma and Walter Burley in the 13th and 14th century who focused considerable attention on these issues. Following Stoic physics in this instance, scholars from the 14th century onward departed from the Aristotelian perspective in favor of a supernatural void beyond the confines of the cosmos itself, a conclusion acknowledged by the 17th century, which helped to segregate natural and theological concerns.
Two thousand years after Plato, René Descartes proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void and atom. Although Descartes agreed with the contemporary position, that a vacuum does not occur in nature, the success of his namesake coordinate system and more implicitly, the spatial–corporeal component of his metaphysics would come to define the philosophically modern notion of empty space as a quantified extension of volume. By the ancient definition however, directional information and magnitude were conceptually distinct. In the medieval Middle Eastern world, the physicist and Islamic scholar, Al-Farabi, conducted a small experiment concerning the existence of vacuum, in which he investigated handheld plungers in water, he concluded that air's volume can expand to fill available space, he suggested that the concept of perfect vacuum was incoherent. However, according to Nader El-Bizri, the physicist Ibn al-Haytham and the Mu'tazili theologians disagreed with Aristotle and Al-Farabi, they supported the existence of a void.
Using geometry, Ibn al-Haytham mathematically demonstrated that place is the imagined three-dimensional void between the inner surfaces of a containing body. According to Ahmad Dallal, Abū Rayhān al-Bīrūnī states that "there is no observable
Starlings are small to medium-sized passerine birds in the family Sturnidae. The name "Sturnidae" comes from the Latin word for sturnus. Many Asian species the larger ones, are called mynas, many African species are known as glossy starlings because of their iridescent plumage. Starlings are native to Europe and Africa, as well as northern Australia and the islands of the tropical Pacific. Several European and Asian species have been introduced to these areas as well as North America and New Zealand, where they compete for habitats with native birds and are considered to be invasive species; the starling species familiar to most people in Europe and North America is the common starling, throughout much of Asia and the Pacific, the common myna is indeed common. Starlings have strong feet, their flight is strong and direct, they are gregarious, their preferred habitat is open country, they eat insects and fruit. Several species live around human habitation and are omnivores. Many species search for prey such as grubs by "open-bill probing", that is, forcefully opening the bill after inserting it into a crevice, thus expanding the hole and exposing the prey.
Plumage of many species is dark with a metallic sheen. Most species lay blue or white eggs. Starlings have diverse and complex vocalizations and have been known to embed sounds from their surroundings into their own calls, including car alarms and human speech patterns; the birds can recognize particular individuals by their calls and are the subject of research into the evolution of human language. Starlings are medium-sized passerines; the shortest-bodied species is Kenrick's starling, at 15 centimetres, but the lightest-weight species is Abbott's starling, 34 grams. The largest starling, going on standard measurements and weight, is the Nias hill myna; this species can measure up to 36 cm and, in domestication they can weigh up to 400 g. Rivalling the prior species in bulk if not dimensions, the mynas of the genus Mino are large the yellow-faced and long-tailed mynas; the longest species in the family is the white-necked myna, which can measure up to 50 cm, although around 60% in this magpie-like species is comprised by its long tail.
There is less sexual dimorphism in plumage, with only 25 species showing such differences between the two sexes. The plumage of the starling is brightly coloured due to iridescence; some species of Asian starling have crests or erectile feathers on the crest. Other ornamentation includes brightly coloured bare areas on the face; these colours can be derived from pigments, or, as in the Bali starling, structural colour, caused by light scattering off parallel collagen fibres. The irises of many species are yellow, although those of younger birds are much darker. Starlings inhabit a wide range of habitats from the Arctic Circle to the Equator. In fact the only habitat they do not occupy is the driest sandy deserts; the family is absent from the Americas and from large parts of Australia but is present over the majority of Europe and Asia. The genus Aplonis has spread across the islands of the Pacific reaching Polynesia and Micronesia, it is a species of this genus, the only starling found in northern Australia.
Asian species are most common in evergreen forests. In contrast to this, African species are more to be found in open woodlands and savannah; the high diversity of species found in Asia and Africa is not matched by Europe, which has one widespread species and two more restricted species. The European starling is both widespread and catholic in its habitat, occupying most types of open habitat. Like many other starling species it has adapted to human-modified habitat, including farmland, orchards and urban areas; some species of starling are migratory, either like the Shelley's starling, which breeds in Ethiopia and northern Somalia and migrates to Kenya and southern Somalia, or the white-shouldered starling, migratory in part of its range but is resident in others. The European starling was purposefully introduced to North America in 1890–1891 by the American Acclimatization Society, an organization dedicated to introducing European flora and fauna into North America for cultural and economic reasons.
Eugene Schieffelin, chairman at the time decided all birds mentioned by William Shakespeare should be in North America. A hundred of them were released from New York's Central Park; the starlings are a social family. Most species associate in flocks of varying sizes throughout the year. A flock of starlings is called a murmuration; these flocks may include other species of starlings and sometimes species from other families. This sociality is evident in their roosting behaviour. Starlings imitate a variety of avian species and have a repertoire of about 15–20 distinct imitations, they imitate a f
Pyotr Leonidovich Kapitsa or Peter Kapitza (Russian: Пётр Леони́дович Капи́ца, Romanian: Petre Capiţa was a leading Soviet physicist and Nobel laureate, best known for his work in low-temperature physics. Kapitsa was born in Kronstadt, Russian Empire, to Bessarabian-Volhynian-born parents Leonid Petrovich Kapitsa, a military engineer who constructed fortifications, Olga Ieronimovna Kapitsa from a noble Polish Stebnicki family. Besides Russian, the Kapitsa family spoke Romanian. Kapitsa's studies were interrupted by the First World War, in which he served as an ambulance driver for two years on the Polish front, he graduated from the Petrograd Polytechnical Institute in 1918. His wife and two children died in the flu epidemic of 1918-19, he subsequently studied in Britain, working for over ten years with Ernest Rutherford in the Cavendish Laboratory at the University of Cambridge, founding the influential Kapitza club. He was the first director of the Mond Laboratory in Cambridge. In the 1920s he originated techniques for creating ultrastrong magnetic fields by injecting high current for brief periods into specially constructed air-core electromagnets.
In 1928 he discovered the linear dependence of resistivity on magnetic field strength in various metals for strong magnetic fields. In 1934 Kapitsa returned to Russia to visit his parents but the Soviet Union prevented him from travelling back to Great Britain; as his equipment for high-magnetic field research remained in Cambridge, he changed the direction of his research to the study of low temperature phenomena, beginning with a critical analysis of the existing methods for achieving low temperatures. In 1934 he developed original apparatus for making significant quantities of liquid helium. Kapitsa formed the Institute for Physical Problems, in part using equipment which the Soviet government bought from the Mond Laboratory in Cambridge. In Russia, Kapitsa began a series of experiments to study liquid helium, leading to the discovery in 1937 of its superfluidity, he reported the properties of this new state of matter in a series of papers, for which he was awarded the Nobel Prize in Physics "for basic inventions and discoveries in the area of low-temperature physics".
In 1939 he developed a new method for liquefaction of air with a low-pressure cycle using a special high-efficiency expansion turbine. During World War II he was assigned to head the Department of Oxygen Industry attached to the USSR Council of Ministers, where he developed his low-pressure expansion techniques for industrial purposes, he invented high power microwave generators and discovered a new kind of continuous high pressure plasma discharge with electron temperatures over 1,000,000 K. In November 1945, Kapitsa quarreled with Lavrentiy Beria, head of the NKVD and in charge of the Soviet atomic bomb project, writing to Joseph Stalin about Beria's ignorance of physics and his arrogance. Stalin backed Kapitsa. Kapitsa refused to meet Beria: "If you want to speak to me come to the Institute." Stalin offered to meet Kapitsa. After the war, a group of prominent Soviet scientists lobbied the government to create a new technical university, the Moscow Institute of Physics and Technology. Kapitsa taught there for many years.
From 1957, he was a member of the presidium of the Soviet Academy of Sciences and at his death in 1984 was the only presidium member, not a member of the Communist Party. In 1966, Kapitsa was allowed to visit Cambridge to receive Prize. While dining at his old college, Trinity, he found, he asked to borrow one, but a college servant asked him when be last dined at high table, "Thirty-two years" replied Kapitza. Within moments the servant-returned, not with any gown, but Kapitsa's own. In 1978, Kapitsa won the Nobel Prize in Physics "for his basic inventions and discoveries in the area of low-temperature physics" and was cited for his long term role as a leader in the development of this area, he shared the prize with Arno Allan Penzias and Robert Woodrow Wilson, who won for discovering the cosmic microwave background. Kapitsa resistance is the thermal resistance at the interface between a solid; the Kapitsa–Dirac effect is a quantum mechanical effect consisting of the diffraction of electrons by a standing wave of light.
In fluid dynamics, the Kapitza number is a dimensionless number characterizing the flow of thin films of fluid down an incline. Kapitsa was married in 1927 to Anna Alekseevna Krylova, daughter of applied mathematician A. N. Krylov, they had two sons and Andrey. Sergey Kapitsa was a demographer, he was the host of the popular and long-running Russian scientific TV show Evident, but Incredible. Andrey Kapitsa was a geographer, he was credited with the discovery and naming of Lake Vostok, the largest subglacial lake in Antarctica, which lies 4,000 meters below the continent's ice cap. A minor planet, 3437 Kapitsa, discovered by Soviet astronomer Lyudmila Georgievna Karachkina in 1982, is named after him, he was elected a Fellow of the Royal Society in 1929. In 1958 he was elected a Member of the German Academy of Sciences Leopoldina. Bipolar battery Kapitza's pendulum
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars and light—are brought toward one another. On Earth, gravity gives weight to physical objects, the Moon's gravity causes the ocean tides; the gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars – and for the stars to group together into galaxies – so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker on farther objects. Gravity is most described by the general theory of relativity which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass; the most extreme example of this curvature of spacetime is a black hole, from which nothing—not light—can escape once past the black hole's event horizon. However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravity is the weakest of the four fundamental forces of physics 1038 times weaker than the strong force, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant force at the macroscopic scale, is the cause of the formation and trajectory of astronomical bodies. For example, gravity causes the Earth and the other planets to orbit the Sun, it causes the Moon to orbit the Earth, causes the formation of tides, the formation and evolution of the Solar System and galaxies; the earliest instance of gravity in the Universe in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a unknown manner. Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework with the other three forces of physics, are a current area of research.
Archimedes discovered the center of gravity of a triangle. He postulated that if the centers of gravity of two equal weights wasn't the same, it would be located in the middle of the line that joins them; the Roman architect and engineer Vitruvius in De Architectura postulated that gravity of an object didn't depend on weight but its "nature". Aryabhata first identified the force to explain why objects are not thrown out when the earth rotates. Brahmagupta described gravity as an attractive force and used the term "gruhtvaakarshan" for gravity. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous experiment dropping balls from the Tower of Pisa, with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects; this was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass fall more in an atmosphere.
Galileo's work set the stage for the formulation of Newton's theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; the equation is the following: F = G m 1 m 2 r 2 Where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.
A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for under Newton's theory, but all searches for another perturbing body had been fruitless; the issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century. Although Newton's theory has been superseded by Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize and predict natural phenomena. This is in contrast to experimental physics; the advancement of science depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous aether. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect an experimental result lacking a theoretical formulation. A physical theory is a model of physical events, it is judged by the extent. The quality of a physical theory is judged on its ability to make new predictions which can be verified by new observations.
A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results without deep physical understanding.
"Modelers" appear much like phenomenologists, but try to model speculative theories that have certain desirable features, or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories, because developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, reinterpret or generalise extant theories, or create new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled. Theoretical problems that need computational investigation are the concern of computational physics. Theoretical advances may consist in setting aside old, incorrect paradigms or may be an alternative model that provides answers that are more accurate or that can be more applied. In the latter case, a correspondence principle will be required to recover the known result. Sometimes though, advances may proceed along different paths. For example, an correct theory may need some conceptual or factual revisions.
However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle. Physical theories become accepted if they are able to make correct predictions and no incorrect ones; the theory should have, at least as a secondary objective, a certain economy and elegance, a notion sometimes called "Occam's razor" after the 13th-century English philosopher William of Occam, in which the simpler of two theories that describe the same matter just as adequately is preferred. They are more to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method. Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories. Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, continued by Plato and Aristotle, whose views held sway for a millennium. During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar and rhetoric and of the Quadrivium like arithmetic, geometry and astronomy.
During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon. As the Scientific Revolution gathered pace, the concepts of matter, space and causality began to acquire the form we know today, other sciences spun off from the rubric of natural philosophy, thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe.