Mathematical physics refers to the development of mathematical methods for application to problems in physics . The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics .
162-600: William Thomson, 1st Baron Kelvin (26 June 1824 – 17 December 1907) was a British mathematician, mathematical physicist and engineer. Born in Belfast, he was the professor of Natural Philosophy at the University of Glasgow for 53 years, where he undertook significant research and mathematical analysis of electricity, was instrumental in the formulation of the first and second laws of thermodynamics , and contributed significantly to unifying physics , which
324-795: A 126-ton schooner , the Lalla Rookh and used it as a base for entertaining friends and scientific colleagues. His maritime interests continued in 1871 when he was appointed to the Board of Enquiry into the sinking of HMS Captain . In June 1873, Thomson and Jenkin were on board the Hooper , bound for Lisbon with 2,500 miles (4,020 km) of cable when the cable developed a fault. An unscheduled 16-day stop-over in Madeira followed, and Thomson became good friends with Charles R. Blandy and his three daughters. On 2 May 1874 he set sail for Madeira on
486-538: A barrier to contain the emergence of Italian and German nation-states as well, in addition to containing France. But this reactionary balance of power, aimed at blocking German and Italian nationalism on the continent, was precarious. After Napoleon's final defeat in 1815, the surviving member states of the defunct Holy Roman Empire joined to form the German Confederation ( Deutscher Bund ) – a rather loose organization, especially because
648-405: A complete system of heliocentric cosmology anchored on the principle of vortex motion, Cartesian physics , whose widespread acceptance helped bring the demise of Aristotelian physics. Descartes used mathematical reasoning as a model for science, and developed analytic geometry , which in time allowed the plotting of locations in 3D space ( Cartesian coordinates ) and marking their progressions along
810-426: A copy of his paper, but when Joule eventually read it he wrote to Thomson on 6 October, claiming that his studies had demonstrated conversion of heat into work but that he was planning further experiments. Thomson replied on 27 October, revealing that he was planning his own experiments and hoping for a reconciliation of their two sides. Thomson returned to critique Carnot's original publication and read his analysis to
972-491: A distance —with a gravitational field . The gravitational field is Minkowski spacetime itself, the 4D topology of Einstein aether modeled on a Lorentzian manifold that "curves" geometrically, according to the Riemann curvature tensor . The concept of Newton's gravity: "two masses attract each other" replaced by the geometrical argument: "mass transform curvatures of spacetime and free falling particles with mass move along
1134-603: A fast-growing industrialized urban economic system. In previous centuries, the shortage of land meant that not everyone could marry, and marriages took place after age 25. The high birthrate was offset by a very high rate of infant mortality , plus periodic epidemics and harvest failures. After 1815, increased agricultural productivity meant a larger food supply, and a decline in famines, epidemics, and malnutrition. This allowed couples to marry earlier, and have more children. Arranged marriages became uncommon as young people were now allowed to choose their own marriage partners, subject to
1296-480: A form of the second law: It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. In the paper, Thomson supports the theory that heat was a form of motion but admits that he had been influenced only by the thought of Sir Humphry Davy and the experiments of Joule and Julius Robert von Mayer , maintaining that experimental demonstration of
1458-469: A framework of absolute space —hypothesized by Newton as a physically real entity of Euclidean geometric structure extending infinitely in all directions—while presuming absolute time , supposedly justifying knowledge of absolute motion, the object's motion with respect to absolute space. The principle of Galilean invariance/relativity was merely implicit in Newton's theory of motion. Having ostensibly reduced
1620-416: A geodesic curve in the spacetime" ( Riemannian geometry already existed before the 1850s, by mathematicians Carl Friedrich Gauss and Bernhard Riemann in search for intrinsic geometry and non-Euclidean geometry.), in the vicinity of either mass or energy. (Under special relativity—a special case of general relativity—even massless energy exerts gravitational effect by its mass equivalence locally "curving"
1782-480: A heuristic framework devised by Arnold Sommerfeld (1868–1951) and Niels Bohr (1885–1962), but this was soon replaced by the quantum mechanics developed by Max Born (1882–1970), Louis de Broglie (1892–1987), Werner Heisenberg (1901–1976), Paul Dirac (1902–1984), Erwin Schrödinger (1887–1961), Satyendra Nath Bose (1894–1974), and Wolfgang Pauli (1900–1958). This revolutionary theoretical framework
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#17327732807941944-629: A nation-state. However, the Confederation was not a 'loose' tie between the German states, as it was impossible to leave the Confederation, and as Confederation law stood above the law of the aligned states. The constitutional weakness of the Confederation lay in the principle of unanimity in the Diet and the limits of the Confederation's scope: it was essentially a military alliance to defend Germany against external attacks and internal riots. Ironically,
2106-575: A particle theory of light, the Dutch Christiaan Huygens (1629–1695) developed the wave theory of light, published in 1690. By 1804, Thomas Young 's double-slit experiment revealed an interference pattern, as though light were a wave, and thus Huygens's wave theory of light, as well as Huygens's inference that light waves were vibrations of the luminiferous aether , was accepted. Jean-Augustin Fresnel modeled hypothetical behavior of
2268-541: A political dimension to the army. In addition, the Diet oversaw the construction and maintenance of several German Federal Fortresses and collected funds annually from the member states for this purpose. Projections of army strength were published in 1835, but the work of forming the Army Corps did not commence until 1840 as a consequence of the Rhine Crisis . Money for the fortresses were determined by an act of
2430-513: A scale would be "quite independent of the physical properties of any specific substance." By employing such a "waterfall", Thomson postulated that a point would be reached at which no further heat (caloric) could be transferred, the point of absolute zero about which Guillaume Amontons had speculated in 1702. "Reflections on the Motive Power of Heat", published by Carnot in French in 1824,
2592-598: A second treaty, the Final Act of the Ministerial Conference to Complete and Consolidate the Organization of the German Confederation . This treaty was not concluded and signed by the parties until 15 May 1820. States joined the German Confederation by becoming parties to the second treaty. The states designated for inclusion in the Confederation were: In 1839, as compensation for the loss of part of
2754-542: A separate field, which includes the theory of phase transitions . It relies upon the Hamiltonian mechanics (or its quantum version) and it is closely related with the more mathematical ergodic theory and some parts of probability theory . There are increasing interactions between combinatorics and physics , in particular statistical physics. The usage of the term "mathematical physics" is sometimes idiosyncratic . Certain parts of mathematics that initially arose from
2916-469: A set of tables for its ready application. Mathematical physics There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in
3078-424: A third, more substantial P.Q.R. paper On the uniform motion of heat in homogeneous solid bodies, and its connection with the mathematical theory of electricity . In the paper he made remarkable connections between the mathematical theories of thermal conduction and electrostatics , an analogy that James Clerk Maxwell was ultimately to describe as one of the most valuable science-forming ideas . William's father
3240-690: A true state. Its territory comprised the parts of the German Confederation north of the river Main , plus Prussia's eastern territories and the Duchy of Schleswig , but excluded Austria and the other southern German states. Prussia's influence was widened by the Franco-Prussian War resulting in the proclamation of the German Empire at Versailles on 18 January 1871, which united the North German Federation with
3402-406: A veto by the parents. The upper and middle classes began to practice birth control , and a little later so too did the peasants. The population in 1800 was heavily rural, with only 8% of the people living in communities of 5,000 to 100,000 and another 2% living in cities of more than 100,000. In a heavily agrarian society, land ownership played a central role. Germany's nobles, especially those in
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#17327732807943564-501: A village court which handled minor offenses. Inside the family, the patriarch made all the decisions and tried to arrange advantageous marriages for his children. Much of the villages' communal life centered around church services and holy days. In Prussia, the peasants drew lots to choose conscripts required by the army. The noblemen handled external relationships and politics for the villages under their control, and were not typically involved in daily activities or decisions. After 1815,
3726-524: A whole the reverse of concentration is gradually going on – I believe that no physical action can ever restore the heat emitted from the Sun, and that this source is not inexhaustible; also that the motions of the Earth and other planets are losing vis viva which is converted into heat; and that although some vis viva may be restored for instance to the earth by heat received from the sun, or by other means, that
3888-514: Is a tradition of mathematical analysis of nature that goes back to the ancient Greeks; examples include Euclid ( Optics ), Archimedes ( On the Equilibrium of Planes , On Floating Bodies ), and Ptolemy ( Optics , Harmonics ). Later, Islamic and Byzantine scholars built on these works, and these ultimately were reintroduced or became available to the West in the 12th century and during
4050-424: Is based on a probabilistic interpretation of states, and evolution and measurements in terms of self-adjoint operators on an infinite-dimensional vector space. That is called Hilbert space (introduced by mathematicians David Hilbert (1862–1943), Erhard Schmidt (1876–1959) and Frigyes Riesz (1880–1956) in search of generalization of Euclidean space and study of integral equations), and rigorously defined within
4212-413: Is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science , whatever the matter may be. Though eminent in the academic field, Thomson was obscure to the general public. In September 1852, he married childhood sweetheart Margaret Crum, daughter of Walter Crum ; but her health broke down on their honeymoon, and over
4374-623: The Zollverein . In 1834, the Prussian regime sought to stimulate wider trade advantages and industrialism by decree – a logical continuation of the program of Stein and Hardenberg less than two decades earlier. Historians have seen three Prussian goals: as a political tool to eliminate Austrian influence in Germany; as a way to improve the economies; and to strengthen Germany against potential French aggression while reducing
4536-534: The Great Eastern . Thomson introduced a new method of deep-sea depth sounding , in which a steel piano wire replaces the ordinary hand line. The wire glides so easily to the bottom that "flying soundings" can be taken while the ship is at full speed. Thomson added a pressure gauge to register the depth of the sinker. About the same time he revived the Sumner method of finding a ship's position, and calculated
4698-705: The Austrian Empire in 1866. The dispute over which had the inherent right to rule German lands ended in favour of Prussia, leading to the creation of the North German Confederation under Prussian leadership in 1867, to which the eastern portions of the Kingdom of Prussia were added. A number of South German states remained independent until they joined the North German Confederation, which was renamed and proclaimed as
4860-624: The British Association for the Advancement of Science annual meeting in Oxford . At that meeting, he heard James Prescott Joule making yet another of his, so far, ineffective attempts to discredit the caloric theory of heat and the theory of the heat engine built upon it by Sadi Carnot and Émile Clapeyron . Joule argued for the mutual convertibility of heat and mechanical work and for their mechanical equivalence. Thomson
5022-732: The Confederation of the Rhine in July 1806, joining sixteen of France's allies among the German states (including Bavaria and Württemberg ). After the Battle of Jena–Auerstedt of October 1806 in the War of the Fourth Coalition , various other German states, including Saxony and Westphalia, also joined the Confederation. Only Austria, Prussia, Danish Holstein , Swedish Pomerania , and
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5184-541: The Confederation of the Rhine , but this collapsed after his defeats in 1812 to 1815. The German Confederation had roughly the same boundaries as the Empire at the time of the French Revolution (less what is now Belgium ). It also kept intact most of Confederation's reconstituted member states and their boundaries. The member states , drastically reduced to 39 from more than 300 (see Kleinstaaterei ) under
5346-616: The County of Ayr . The title refers to the River Kelvin , which flows near his laboratory at the University of Glasgow's Gilmorehill home at Hillhead . Despite offers of elevated posts from several world-renowned universities, Kelvin refused to leave Glasgow, remaining until his retirement from that post in 1899. Active in industrial research and development, he was recruited around 1899 by George Eastman to serve as vice-chairman of
5508-548: The Federal Convention were binding for the member states). Additionally, the Confederation had been established for eternity and was impossible to dissolve (legally), with no member states being able to leave it and no new member being able to join without universal consent in the Federal Convention. On the other hand, the Confederation was weakened by its very structure and member states, partly because
5670-429: The French Revolution , where freedom of the individual and nation was asserted against privilege and custom. Representing a great variety of types and theories, they were largely a response to the disintegration of previous cultural patterns, coupled with new patterns of production, specifically the rise of industrial capitalism. However, the defeat of Napoleon enabled conservative and reactionary regimes such as those of
5832-579: The Habsburg monarchy in Austria, and the conservative notables of the small princely states and city-states in Germany. Meanwhile, demands for change from below had been fomenting due to the influence of the French Revolution. Throughout the German Confederation, Austrian influence was paramount, drawing the ire of the nationalist movements. Metternich considered nationalism, especially
5994-562: The Holy Roman Empire , were recognized as fully sovereign. The members pledged themselves to mutual defense, and joint maintenance of the fortresses at Mainz , the city of Luxembourg , Rastatt , Ulm , and Landau . The only organ of the Confederation was the Federal Assembly (officially Bundesversammlung , often called Bundestag ), which consisted of the delegates of the states' governments. There
6156-642: The King of the United Kingdom (until 1837) as King of Hanover were members of the German Confederation. Each of them had a vote in the Federal Assembly. At its foundation in 1815, four member states were ruled by foreign monarchs, as the King of Denmark was Duke of both Holstein and Saxe-Lauenburg. The four free cities of Bremen , Frankfurt , Hamburg , and Lübeck shared one vote in
6318-480: The Kingdom of Prussia were the largest and by far the most powerful members of the Confederation. Large parts of both countries were not included in the Confederation, because they had not been part of the former Holy Roman Empire, nor were the greater parts of their armed forces incorporated in the federal army. Austria and Prussia each had one vote in the Federal Assembly. Six other major states had one vote each in
6480-464: The Kingdom of Prussia , the Austrian Empire , and Tsarist Russia to survive, laying the groundwork for the Congress of Vienna and the alliance that strove to oppose radical demands for change ushered in by the French Revolution . With Austria 's position on the continent now intact and ostensibly secure under its reactionary premier Klemens von Metternich , the Habsburg empire would serve as
6642-524: The Lalla Rookh . As he approached the harbour, he signalled to the Blandy residence "Will you marry me?" and Fanny (Blandy's daughter Frances Anna Blandy) signalled back "Yes". Thomson married Fanny, 13 years his junior, on 24 June 1874. Over the period 1855 to 1867, Thomson collaborated with Peter Guthrie Tait on a textbook that founded the study of mechanics first on the mathematics of kinematics ,
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6804-517: The Renaissance . In the first decade of the 16th century, amateur astronomer Nicolaus Copernicus proposed heliocentrism , and published a treatise on it in 1543. He retained the Ptolemaic idea of epicycles , and merely sought to simplify astronomy by constructing simpler sets of epicyclic orbits. Epicycles consist of circles upon circles. According to Aristotelian physics , the circle was
6966-688: The Royal Society of Edinburgh in January 1849, still convinced that the theory was fundamentally sound. However, though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's. In February 1851 he sat down to articulate his new thinking. He was uncertain of how to frame his theory, and the paper went through several drafts before he settled on an attempt to reconcile Carnot and Joule. During his rewriting, he seems to have considered ideas that would subsequently give rise to
7128-471: The University of Berlin , founded in 1810, became the world's leading university. Von Ranke , for example, professionalized history and set the world standard for historiography. By the 1830s, mathematics, physics, chemistry, and biology had emerged with world class science, led by Alexander von Humboldt (1769–1859) in natural science and Carl Friedrich Gauss (1777–1855) in mathematics. Young intellectuals often turned to politics, but their support for
7290-463: The University of Glasgow , not out of any precociousness; the university provided many of the facilities of an elementary school for able pupils, and this was a typical starting age. In school, he showed a keen interest in the classics along with his natural interest in the sciences. At age 12 he won a prize for translating Lucian of Samosata's Dialogues of the Gods from Ancient Greek to English. In
7452-456: The heat death paradox (Kelvin's paradox) in 1862, which uses the second law of thermodynamics to disprove the possibility of an infinitely old universe; this paradox was later extended by William Rankine . In final publication, Thomson retreated from a radical departure and declared "the whole theory of the motive power of heat is founded on ... two ... propositions, due respectively to Joule, and to Carnot and Clausius." Thomson went on to state
7614-511: The province of Luxemburg to Belgium, the Duchy of Limburg was created and became a member of the German Confederation (held by the Netherlands jointly with Luxembourg) until the dissolution of 1866. In 1867 the duchy was declared to be an "integral part of the Kingdom of the Netherlands". The cities of Maastricht and Venlo were not included in the Confederation. The Austrian Empire and
7776-425: The second law of thermodynamics . In Carnot's theory, lost heat was absolutely lost, but Thomson contended that it was " lost to man irrecoverably; but not lost in the material world". Moreover, his theological beliefs led Thomson to extrapolate the second law to the cosmos, originating the idea of universal heat death . I believe the tendency in the material world is for motion to become diffused, and that as
7938-399: The transatlantic telegraph project , he was knighted in 1866 by Queen Victoria , becoming Sir William Thomson. He had extensive maritime interests and worked on the mariner's compass , which previously had limited reliability. Kelvin was ennobled in 1892 in recognition of his achievements in thermodynamics, and of his opposition to Irish Home Rule , becoming Baron Kelvin, of Largs in
8100-567: The " German Empire " in 1871, as the unified Germany (aside from Austria) with the Prussian king as emperor (Kaiser) after the victory over French Emperor Napoleon III in the Franco-Prussian War of 1870. Most historians have judged the Confederation to have been weak and ineffective, as well as an obstacle to the creation of a German nation-state. This weakness was part of its design, as the European Great Powers , including Prussia and especially Austria, did not want it to become
8262-609: The "continental" mathematics resisted by a British establishment still working in the shadow of Sir Isaac Newton . Unsurprisingly, Fourier's work had been attacked by domestic mathematicians, Philip Kelland authoring a critical book. The book motivated Thomson to write his first published scientific paper under the pseudonym P.Q.R. , defending Fourier, which was submitted to The Cambridge Mathematical Journal by his father. A second P.Q.R. paper followed almost immediately. While on holiday with his family in Lamlash in 1841, he wrote
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#17327732807948424-552: The 1880s, there was a prominent paradox that an observer within Maxwell's electromagnetic field measured it at approximately constant speed, regardless of the observer's speed relative to other objects within the electromagnetic field. Thus, although the observer's speed was continually lost relative to the electromagnetic field, it was preserved relative to other objects in the electromagnetic field. And yet no violation of Galilean invariance within physical interactions among objects
8586-786: The Assembly, but rarely deployed ambassadors itself. During the revolution of 1848/49 the Federal Assembly was inactive. It transferred its powers to the Provisorische Zentralgewalt , the revolutionary German Central Government of the Frankfurt National Assembly . After crushing the revolution and illegally disbanding the National Assembly, the Prussian King failed to create a German nation state by himself. The Federal Assembly
8748-469: The Carnot–Clapeyron theory further through his dissatisfaction that the gas thermometer provided only an operational definition of temperature. He proposed an absolute temperature scale in which "a unit of heat descending from a body A at the temperature T ° of this scale, to a body B at the temperature ( T −1)°, would give out the same mechanical effect [work] , whatever be the number T ." Such
8910-631: The Confederate Diet in that year. By 1846, Luxemburg still had not formed its own contingent, and Prussia was rebuffed for offering to supply 1,450 men to garrison the Luxemburg fortress that should have been supplied by Waldeck and the two Lippes. In that same year, it was decided that a common symbol for the Federal Army should be the old Imperial two-headed eagle, but without crown, scepter, or sword, as any of those devices encroached on
9072-606: The Confederation into a unified German federal state with a liberal constitution (usually called the Frankfurt Constitution in English). The Federal Convention was dissolved on 12 July 1848, but was re-established in 1850 after the revolution was crushed by Austria, Prussia, and other states. The Confederation was finally dissolved after the victory of the Kingdom of Prussia in the Seven Weeks' War over
9234-707: The East called Junkers , dominated not only the localities, but also the Prussian court , and especially the Prussian army . Increasingly after 1815, a centralized Prussian government based in Berlin took over the powers of the nobles, which in terms of control over the peasantry had been almost absolute. They retained control of the judicial system on their estates until 1848, as well as control of hunting and game laws. They paid no land tax until 1861 and kept their police authority until 1872, and controlled church affairs into
9396-620: The Federal Assembly. The 23 remaining states (at its formation in 1815) shared five votes in the Federal Assembly: There were therefore 17 votes in the Federal Assembly. The rules of the Confederation provided for three different types of military interventions: Other military conflicts were foreign to the confederation ( bundesfremd ). An example is Austria's oppression of the uprising in Northern Italy in 1848 and 1849, as these Austrian territories lay outside of
9558-595: The Federal Assembly: the Kingdom of Bavaria , the Kingdom of Saxony , the Kingdom of Württemberg , the Electorate of Hesse , the Grand Duchy of Baden , and the Grand Duchy of Hesse . Three foreign monarchs ruled member states: the King of Denmark as Duke of Holstein and Duke of Saxe-Lauenburg ; the King of the Netherlands as Grand Duke of Luxembourg and (from 1839) Duke of Limburg ; and
9720-687: The French-occupied Principality of Erfurt stayed outside the Confederation of the Rhine. The War of the Sixth Coalition from 1812 to winter 1814 saw the defeat of Napoleon and the liberation of Germany. In June 1814, the famous German patriot Heinrich vom Stein created the Central Managing Authority for Germany ( Zentralverwaltungsbehörde ) in Frankfurt to replace the defunct Confederation of
9882-693: The Kelvin–Joule effect, and the published results did much to bring about general acceptance of Joule's work and the kinetic theory . Thomson published more than 650 scientific papers and applied for 70 patents (not all were issued). Regarding science, Thomson wrote the following: In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge
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#173277328079410044-446: The Keplerian celestial laws of motion as well as Galilean terrestrial laws of motion to a unifying force, Newton achieved great mathematical rigor, but with theoretical laxity. In the 18th century, the Swiss Daniel Bernoulli (1700–1782) made contributions to fluid dynamics , and vibrating strings . The Swiss Leonhard Euler (1707–1783) did special work in variational calculus , dynamics, fluid dynamics, and other areas. Also notable
10206-412: The Rhine. However, plenipotentiaries gathered at the Congress of Vienna were determined to create a weaker union of German states than that envisaged by Stein. The German Confederation was created by the 9th Act of the Congress of Vienna on 8 June 1815 after being alluded to in Article 6 of the 1814 Treaty of Paris , ending the War of the Sixth Coalition. The Confederation was formally created by
10368-404: The Second Schleswig War (or Deutsch-Dänischer Krieg in German). As Schleswig and Denmark were not member states, this war was foreign to the Confederation. The Confederation took no part in this war. A federal intervention confronted for example the raid of the revolutionaries in Baden in April 1848. In June 1866, the Federal Convention decided to takes measures against Prussia. This decision
10530-442: The War of 1866 proved its ineffectiveness, as it was unable to combine the federal troops in order to fight the Prussian secession. The War of the Third Coalition lasted from about 1803 to 1806. Following defeat at the Battle of Austerlitz by the French under Napoleon in December 1805, Holy Roman Emperor Francis II abdicated, and the Empire was dissolved on 6 August 1806. The resulting Treaty of Pressburg established
10692-426: The academic year 1839/1840, Thomson won the class prize in astronomy for his "Essay on the figure of the Earth" which showed an early facility for mathematical analysis and creativity. His physics tutor at this time was his namesake, David Thomson . Throughout his life, he would work on the problems raised in the essay as a coping strategy during times of personal stress. On the title page of this essay Thomson wrote
10854-440: The access he was given unsatisfactory, and the Agamemnon had to return home following a disastrous storm in June 1858. In London, the board was about to abandon the project and mitigate their losses by selling the cable. Thomson, Cyrus West Field and Curtis M. Lampson argued for another attempt and prevailed, Thomson insisting that the technical problems were tractable. Though employed in an advisory capacity, Thomson had, during
11016-410: The adulation. Thomson, along with the other principals of the project, was knighted on 10 November 1866. To exploit his inventions for signalling on long submarine cables, Thomson entered into a partnership with C. F. Varley and Fleeming Jenkin . In conjunction with the latter, he also devised an automatic curb sender , a kind of telegraph key for sending messages on a cable. Thomson took part in
11178-735: The aether. The English physicist Michael Faraday introduced the theoretical concept of a field—not action at a distance. Mid-19th century, the Scottish James Clerk Maxwell (1831–1879) reduced electricity and magnetism to Maxwell's electromagnetic field theory, whittled down by others to the four Maxwell's equations . Initially, optics was found consequent of Maxwell's field. Later, radiation and then today's known electromagnetic spectrum were found also consequent of this electromagnetic field. The English physicist Lord Rayleigh [1842–1919] worked on sound . The Irishmen William Rowan Hamilton (1805–1865), George Gabriel Stokes (1819–1903) and Lord Kelvin (1824–1907) produced several major works: Stokes
11340-423: The armed forces of a state. For example, Prussia's army consisted of nine Army Corps but contributed only three to the German Federal Army. The strength of the mobilized German Federal Army was projected to total 303,484 men in 1835 and 391,634 men in 1860, with the individual states providing the following figures: Between 1806 and 1815, Napoleon organized the German states, aside from Prussia and Austria, into
11502-467: The atmospheric electric field. Thomson's water dropper electrometer was used for measuring the atmospheric electric field at Kew Observatory and Eskdalemuir Observatory for many years, and one was still in use operationally at the Kakioka Observatory in Japan until early 2021. Thomson may have unwittingly observed atmospheric electrical effects caused by the Carrington event (a significant geomagnetic storm) in early September 1859. Between 1870 and 1890
11664-645: The attention of the project's undertakers. In December 1856, he was elected to the board of directors of the Atlantic Telegraph Company. Thomson became scientific adviser to a team with Whitehouse as chief electrician and Sir Charles Tilston Bright as chief engineer, but Whitehouse had his way with the specification, supported by Faraday and Samuel F. B. Morse . Thomson sailed on board the cable-laying ship HMS Agamemnon in August 1857, with Whitehouse confined to land owing to illness, but
11826-410: The axiomatic modern version by John von Neumann in his celebrated book Mathematical Foundations of Quantum Mechanics , where he built up a relevant part of modern functional analysis on Hilbert spaces, the spectral theory (introduced by David Hilbert who investigated quadratic forms with infinitely many variables. Many years later, it had been revealed that his spectral theory is associated with
11988-413: The blending of some mathematical aspect and theoretical physics aspect. Although related to theoretical physics , mathematical physics in this sense emphasizes the mathematical rigour of the similar type as found in mathematics. On the other hand, theoretical physics emphasizes the links to observations and experimental physics , which often requires theoretical physicists (and mathematical physicists in
12150-669: The board of the British company Kodak Limited, affiliated with Eastman Kodak . In 1904 he became chancellor of the University of Glasgow . Kelvin resided in Netherhall, a redstone mansion in Largs , which he built in the 1870s and where he died in 1907. The Hunterian Museum at the University of Glasgow has a permanent exhibition on the work of Kelvin, which includes many of his original papers, instruments, and other artefacts, including his smoking pipe. Thomson's father, James Thomson ,
12312-475: The board that using purer copper for replacing the lost section of cable would improve data capacity, that he first made a difference to the execution of the project. The board insisted that Thomson join the 1858 cable-laying expedition, without any financial compensation, and take an active part in the project. In return, Thomson secured a trial for his mirror galvanometer, which the board had been unenthusiastic about, alongside Whitehouse's equipment. Thomson found
12474-682: The boys were tutored in French in Paris. Much of Thomson's life during the mid-1840s was spent in Germany and the Netherlands . Language study was given a high priority. His sister, Anna Thomson, was the mother of physicist James Thomson Bottomley FRSE. Thomson attended the Royal Belfast Academical Institution, where his father was a professor in the university department. In 1834, aged 10, he began studying at
12636-445: The cable must be "abandoned as being practically and commercially impossible". Thomson attacked Whitehouse's contention in a letter to the popular Athenaeum magazine, pitching himself into the public eye. Thomson recommended a larger conductor with a larger cross section of insulation . He thought Whitehouse no fool and suspected that he might have the practical skill to make the existing design work. Thomson's work had attracted
12798-459: The cable-laying expedition of the SS ; Great Eastern , but the voyage was dogged by technical problems. The cable was lost after 1,200 miles (1,900 km) had been laid, and the project was abandoned. A further attempt in 1866 laid a new cable in two weeks, and then recovered and completed the 1865 cable. The enterprise was feted as a triumph by the public, and Thomson enjoyed a large share of
12960-444: The celebrated Henri Victor Regnault , at Paris; but in 1846 he was appointed to the chair of natural philosophy in the University of Glasgow. At age 22 he found himself wearing the gown of a professor in one of the oldest universities in the country and lecturing to the class of which he was a first year student a few years before. By 1847, Thomson had already gained a reputation as a precocious and maverick scientist when he attended
13122-618: The confederation's borders. During the existence of the Confederation, there was only one federal war: the war against Denmark beginning with the Schleswig-Holstein uprising in 1848 (the First Schleswig War ). The conflict became a federal war when the Bundestag demanded from Denmark to withdraw its troops from Schleswig (April 12) and recognized the revolutionary of Schleswig-Holstein (April 22). The confederation
13284-439: The context of physics) and Newton's method to solve problems in mathematics and physics. He was extremely successful in his application of calculus and other methods to the study of motion. Newton's theory of motion, culminating in his Philosophiæ Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ) in 1687, modeled three Galilean laws of motion along with Newton's law of universal gravitation on
13446-491: The conversion of heat into work was still outstanding. As soon as Joule read the paper he wrote to Thomson with his comments and questions. Thus began a fruitful, though largely epistolary, collaboration between the two men, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856, its discoveries including the Joule–Thomson effect , sometimes called
13608-774: The curved geometry construction to model 3D space together with the 1D axis of time by treating the temporal axis like a fourth spatial dimension—altogether 4D spacetime—and declared the imminent demise of the separation of space and time. Einstein initially called this "superfluous learnedness", but later used Minkowski spacetime with great elegance in his general theory of relativity , extending invariance to all reference frames—whether perceived as inertial or as accelerated—and credited this to Minkowski, by then deceased. General relativity replaces Cartesian coordinates with Gaussian coordinates , and replaces Newton's claimed empty yet Euclidean space traversed instantly by Newton's vector of hypothetical gravitational force—an instant action at
13770-456: The curved geometry, replacing rectilinear axis by curved ones. Gauss also introduced another key tool of modern physics, the curvature. Gauss's work was limited to two dimensions. Extending it to three or more dimensions introduced a lot of complexity, with the need of the (not yet invented) tensors. It was Riemman the one in charge to extend curved geometry to N dimensions. In 1908, Einstein's former mathematics professor Hermann Minkowski , applied
13932-435: The description of motion without regard to force . The text developed dynamics in various areas but with constant attention to energy as a unifying principle. A second edition appeared in 1879, expanded to two separately bound parts. The textbook set a standard for early education in mathematical physics . Thomson made significant contributions to atmospheric electricity for the relatively short time for which he worked on
14094-459: The development of physics are not, in fact, considered parts of mathematical physics, while other closely related fields are. For example, ordinary differential equations and symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and Hamiltonian mechanics belong to mathematical physics. John Herapath used the term for the title of his 1847 text on "mathematical principles of natural philosophy",
14256-440: The development of quantum mechanics and some aspects of functional analysis parallel each other in many ways. The mathematical study of quantum mechanics , quantum field theory , and quantum statistical mechanics has motivated results in operator algebras . The attempt to construct a rigorous mathematical formulation of quantum field theory has also brought about some progress in fields such as representation theory . There
14418-521: The early 20th century. To help the nobility avoid indebtedness, Berlin set up a credit institution to provide capital loans in 1809, and extended the loan network to peasants in 1849. When the German Empire was established in 1871, the nobility controlled the army and the Navy, the bureaucracy, and the royal court; they generally set governmental policies. Peasants continued to center their lives in
14580-495: The electromagnetic field's invariance and Galilean invariance by discarding all hypotheses concerning aether, including the existence of aether itself. Refuting the framework of Newton's theory— absolute space and absolute time —special relativity refers to relative space and relative time , whereby length contracts and time dilates along the travel pathway of an object. Cartesian coordinates arbitrarily used rectilinear coordinates. Gauss, inspired by Descartes' work, introduced
14742-452: The equations of Kepler's laws of planetary motion . An enthusiastic atomist, Galileo Galilei in his 1623 book The Assayer asserted that the "book of nature is written in mathematics". His 1632 book, about his telescopic observations, supported heliocentrism. Having introduced experimentation, Galileo then refuted geocentric cosmology by refuting Aristotelian physics itself. Galileo's 1638 book Discourse on Two New Sciences established
14904-425: The failed Revolution of 1848 forced many into exile. The population of the German Confederation (excluding Austria) grew 60% from 1815 to 1865, from 21,000,000 to 34,000,000. The era saw the demographic transition take place in Germany. It was a transition from high birth rates and high death rates to low birth and death rates as the country developed from a pre-industrial to a modernized agriculture and supported
15066-555: The fields of electromagnetism , waves, fluids , and sound. In the United States, the pioneering work of Josiah Willard Gibbs (1839–1903) became the basis for statistical mechanics . Fundamental theoretical results in this area were achieved by the German Ludwig Boltzmann (1844–1906). Together, these individuals laid the foundations of electromagnetic theory, fluid dynamics, and statistical mechanics. By
15228-414: The first theoretical physicist and one of the founders of modern mathematical physics. The prevailing framework for science in the 16th and early 17th centuries was one borrowed from Ancient Greek mathematics , where geometrical shapes formed the building blocks to describe and think about space, and time was often thought as a separate entity. With the introduction of algebra into geometry, and with it
15390-429: The first mathematical development of Michael Faraday 's idea that electric induction takes place through an intervening medium, or " dielectric ", and not by some incomprehensible "action at a distance". He also devised the mathematical technique of electrical images, which became a powerful agent in solving problems of electrostatics , the science which deals with the forces between electrically charged bodies at rest. It
15552-461: The flow of time. Christiaan Huygens , a talented mathematician and physicist and older contemporary of Newton, was the first to successfully idealize a physical problem by a set of parameters in his Horologium Oscillatorum (1673), and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon in Traité de la Lumière (1690). For these reasons, he is considered
15714-506: The following lines from Alexander Pope 's " An Essay on Man ". These lines inspired Thomson to understand the natural world using the power and method of science: Go, wondrous creature! mount where Science guides; Go measure earth, weigh air, and state the tides; Instruct the planets in what orbs to run, Correct old Time, and regulate the sun; Thomson became intrigued with Joseph Fourier's Théorie analytique de la chaleur ( The Analytical Theory of Heat ) and committed himself to study
15876-607: The forces of the old order against those inspired by the French Revolution and the Rights of Man. The breakdown of the competition was, roughly, the emerging capitalist bourgeoisie and petit-bourgeoisie (engaged mostly in commerce, trade, and industry), and the growing (and increasingly radicalized) industrial working class ; and the other side associated with landowning aristocracy or military aristocracy (the Junker s ) in Prussia,
16038-520: The forces unleashed by the French Revolution were seemingly under control after the Vienna Congress, the conflict between conservative forces and liberal nationalists was only deferred at best. The era until the failed 1848 revolution, in which these tensions built up, is commonly referred to as Vormärz ("pre-March"), in reference to the outbreak of riots in March 1848. This conflict pitted
16200-556: The form of the nationalistic and liberal democratic college fraternities known as the Burschenschaften . The Wartburg Festival in 1817 celebrated Martin Luther as a proto-German nationalist, linking Lutheranism to German nationalism, and helping arouse religious sentiments for the cause of German nationhood. The festival culminated in the burning of several books and other items that symbolized reactionary attitudes. One item
16362-806: The formulation of modern theories in physics, including field theory and quantum mechanics. The French mathematical physicist Joseph Fourier (1768 – 1830) introduced the notion of Fourier series to solve the heat equation , giving rise to a new approach to solving partial differential equations by means of integral transforms . Into the early 19th century, following mathematicians in France, Germany and England had contributed to mathematical physics. The French Pierre-Simon Laplace (1749–1827) made paramount contributions to mathematical astronomy , potential theory . Siméon Denis Poisson (1781–1840) worked in analytical mechanics and potential theory . In Germany, Carl Friedrich Gauss (1777–1855) made key contributions to
16524-423: The foundation for Prussia's future military might by professionalizing the military and decreeing universal military conscription . In order to industrialize Prussia, working within the framework provided by the old aristocratic institutions, land reforms were enacted to break the monopoly of the Junker s on land ownership, thereby also abolishing, among other things, the feudal practice of serfdom . Although
16686-507: The geometry of the four, unified dimensions of space and time.) Another revolutionary development of the 20th century was quantum theory , which emerged from the seminal contributions of Max Planck (1856–1947) (on black-body radiation ) and Einstein's work on the photoelectric effect . In 1912, a mathematician Henri Poincare published Sur la théorie des quanta . He introduced the first non-naïve definition of quantization in this paper. The development of early quantum physics followed by
16848-718: The idea of a coordinate system, time and space could now be though as axes belonging to the same plane. This essential mathematical framework is at the base of all modern physics and used in all further mathematical frameworks developed in next centuries. By the middle of the 17th century, important concepts such as the fundamental theorem of calculus (proved in 1668 by Scottish mathematician James Gregory ) and finding extrema and minima of functions via differentiation using Fermat's theorem (by French mathematician Pierre de Fermat ) were already known before Leibniz and Newton. Isaac Newton (1642–1727) developed calculus (although Gottfried Wilhelm Leibniz developed similar concepts outside
17010-422: The individual sovereignty of the states. King Frederick William IV of Prussia was among those who derided the "disarmed imperial eagle" as a national symbol. The German Federal Army was divided into ten Army Corps (later expanded to include a Reserve Corps). However, the Army Corps were not exclusive to the German Confederation but composed from the national armies of the member states, and did not include all of
17172-542: The law of equal free fall as well as the principles of inertial motion, founding the central concepts of what would become today's classical mechanics . By the Galilean law of inertia as well as the principle of Galilean invariance , also called Galilean relativity, for any object experiencing inertia, there is empirical justification for knowing only that it is at relative rest or relative motion—rest or motion with respect to another object. René Descartes developed
17334-752: The laying of the French Atlantic submarine communications cable of 1869, and with Jenkin was engineer of the Western and Brazilian and Platino-Brazilian cables, assisted by vacation student James Alfred Ewing . He was present at the laying of the Pará to Pernambuco section of the Brazilian coast cables in 1873. Thomson's wife, Margaret, died on 17 June 1870, and he resolved to make changes in his life. Already addicted to seafaring, in September he purchased
17496-457: The lead of Thomson and Tait, the branch of topology called knot theory was developed. Thomson's initiative in this complex study that continues to inspire new mathematics has led to persistence of the topic in history of science . Thomson was an enthusiastic yachtsman, his interest in all things relating to the sea perhaps arising from, or fostered by, his experiences on the Agamemnon and
17658-609: The liberal press, and seriously restricted academic freedom . German artists and intellectuals, heavily influenced by the French Revolution, turned to Romanticism . At the universities, high-powered professors developed international reputations, especially in the humanities led by history and philology, which brought a new historical perspective to the study of political history, theology, philosophy, language, and literature. With Georg Wilhelm Friedrich Hegel (1770–1831) in philosophy, Friedrich Schleiermacher (1768–1834) in theology and Leopold von Ranke (1795–1886) in history,
17820-442: The loss cannot be precisely compensated and I think it probable that it is under-compensated. Compensation would require a creative act or an act possessing similar power , resulting in a rejuvenating universe (as Thomson had previously compared universal heat death to a clock running slower and slower, although he was unsure whether it would eventually reach thermodynamic equilibrium and stop for ever ). Thomson also formulated
17982-430: The mathematical fields of linear algebra , the spectral theory of operators , operator algebras and, more broadly, functional analysis . Nonrelativistic quantum mechanics includes Schrödinger operators, and it has connections to atomic and molecular physics . Quantum information theory is another subspecialty. The special and general theories of relativity require a rather different type of mathematics. This
18144-430: The more general sense) to use heuristic , intuitive , or approximate arguments. Such arguments are not considered rigorous by mathematicians. Such mathematical physicists primarily expand and elucidate physical theories . Because of the required level of mathematical rigour, these researchers often deal with questions that theoretical physicists have considered to be already solved. However, they can sometimes show that
18306-474: The most important decisions in the Federal Convention required unanimity and the purpose of the Confederation was limited to only security matters. On top of that, the functioning of the Confederation depended on the cooperation of the two most populous member states, Austria and Prussia which in reality were often in opposition . The German revolutions of 1848–1849 , motivated by liberal, democratic, socialist, and nationalist sentiments, attempted to transform
18468-541: The nationalist youth movement, the most pressing danger: German nationalism might not only repudiate Austrian dominance of the Confederation, but also stimulate nationalist sentiment within the Austrian Empire itself. In a multi-national polyglot state in which Slavs and Magyars outnumbered the Germans, the prospects of Czech, Slovak, Hungarian, Polish, Serb, or Croatian sentiment along with middle class liberalism
18630-608: The need for administrative, economic, and social reforms to improve the efficiency of the bureaucracy and encourage practical merit-based education. Inspired by the Napoleonic organization of German and Italian principalities, the Prussian Reform Movement led by Karl August von Hardenberg and Count Stein was conservative, enacted to preserve aristocratic privilege while modernizing institutions. Outside Prussia, industrialization progressed slowly, and
18792-419: The next 17 years Thomson was distracted by her suffering. On 16 October 1854, George Gabriel Stokes wrote to Thomson to try to re-interest him in work by asking his opinion on some experiments of Faraday on the proposed transatlantic telegraph cable . Faraday had demonstrated how the construction of a cable would limit the rate at which messages could be sent—in modern terms, the bandwidth . Thomson jumped at
18954-525: The perfect form of motion, and was the intrinsic motion of Aristotle's fifth element —the quintessence or universal essence known in Greek as aether for the English pure air —that was the pure substance beyond the sublunary sphere , and thus was celestial entities' pure composition. The German Johannes Kepler [1571–1630], Tycho Brahe 's assistant, modified Copernican orbits to ellipses , formalized in
19116-694: The presence of constraints). Both formulations are embodied in analytical mechanics and lead to an understanding of the deep interplay between the notions of symmetry and conserved quantities during the dynamical evolution of mechanical systems, as embodied within the most elementary formulation of Noether's theorem . These approaches and ideas have been extended to other areas of physics, such as statistical mechanics , continuum mechanics , classical field theory , and quantum field theory . Moreover, they have provided multiple examples and ideas in differential geometry (e.g., several notions in symplectic geometry and vector bundles ). Within mathematics proper,
19278-522: The previous solution was incomplete, incorrect, or simply too naïve. Issues about attempts to infer the second law of thermodynamics from statistical mechanics are examples. Other examples concern the subtleties involved with synchronisation procedures in special and general relativity ( Sagnac effect and Einstein synchronisation ). The effort to put physical theories on a mathematically rigorous footing not only developed physics but also has influenced developments of some mathematical areas. For example,
19440-532: The principle of Galilean invariance across all inertial frames of reference , while Newton's theory of motion was spared. Austrian theoretical physicist and philosopher Ernst Mach criticized Newton's postulated absolute space. Mathematician Jules-Henri Poincaré (1854–1912) questioned even absolute time. In 1905, Pierre Duhem published a devastating criticism of the foundation of Newton's theory of motion. Also in 1905, Albert Einstein (1879–1955) published his special theory of relativity , newly explaining both
19602-410: The problem and published his response that month. He expressed his results in terms of the data rate that could be achieved and the economic consequences in terms of the potential revenue of the transatlantic undertaking. In a further 1855 analysis, Thomson stressed the impact that the design of the cable would have on its profitability. Thomson contended that the signalling speed through a given cable
19764-426: The representatives of the member states. The most important issues had to be decided on unanimously. The Convention was presided over by the representative of Austria. This was a formality, however, as the Confederation did not have a head of state, since it was not a state. The Confederation, on the one hand, was a strong alliance between its member states because federal law was superior to state law (the decisions of
19926-407: The scope at that time being "the causes of heat, gaseous elasticity, gravitation, and other great phenomena of nature". The term "mathematical physics" is sometimes used to denote research aimed at studying and solving problems in physics or thought experiments within a mathematically rigorous framework. In this sense, mathematical physics covers a very broad academic realm distinguished only by
20088-595: The southern German states. All the constituent states of the former German Confederation became part of the Kaiserreich in 1871, except Austria, Luxembourg , the Duchy of Limburg , and Liechtenstein . The late 18th century was a period of political, economic, intellectual, and cultural reforms, the Enlightenment (represented by figures such as Locke , Rousseau , Voltaire , and Adam Smith ), but also involving early Romanticism , and climaxing with
20250-499: The spectrum of the hydrogen atom. He was surprised by this application.) in particular. Paul Dirac used algebraic constructions to produce a relativistic model for the electron , predicting its magnetic moment and the existence of its antiparticle, the positron . Prominent contributors to the 20th century's mathematical physics include (ordered by birth date): German Confederation The German Confederation ( German : Deutscher Bund [ˌdɔʏtʃɐ ˈbʊnt] )
20412-464: The subject, around 1859. He developed several instruments for measuring the atmospheric electric field, using some of the electrometers he had initially developed for telegraph work, which he tested at Glasgow and whilst on holiday on Arran. His measurements on Arran were sufficiently rigorous and well-calibrated that they could be used to deduce air pollution from the Glasgow area, through its effects on
20574-589: The theoretical foundations of electricity , magnetism , mechanics , and fluid dynamics . In England, George Green (1793–1841) published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828, which in addition to its significant contributions to mathematics made early progress towards laying down the mathematical foundations of electricity and magnetism. A couple of decades ahead of Newton's publication of
20736-681: The theory of partial differential equation , variational calculus , Fourier analysis , potential theory , and vector analysis are perhaps most closely associated with mathematical physics. These fields were developed intensively from the second half of the 18th century (by, for example, D'Alembert , Euler , and Lagrange ) until the 1930s. Physical applications of these developments include hydrodynamics , celestial mechanics , continuum mechanics , elasticity theory , acoustics , thermodynamics , electricity , magnetism , and aerodynamics . The theory of atomic spectra (and, later, quantum mechanics ) developed almost concurrently with some parts of
20898-651: The two great rivals, the Austrian Empire and the Kingdom of Prussia , each feared domination by the other. In Prussia the Hohenzollern rulers forged a centralized state. By the time of the Napoleonic Wars, Prussia, grounded in the virtues of its established military aristocracy (the Junkers ) and stratified by rigid hierarchical lines, had been surpassed militarily and economically by France. After 1807, Prussia's defeats by Napoleonic France highlighted
21060-413: The urban population grew rapidly, due primarily to the influx of young people from the rural areas. Berlin grew from 172,000 people in 1800 to 826,000 in 1870; Hamburg grew from 130,000 to 290,000; Munich from 40,000 to 269,000; Breslau (now Wrocław ) from 60,000 to 208,000; Dresden from 60,000 to 177,000; Königsberg (now Kaliningrad ) from 55,000 to 112,000. Offsetting this growth, there
21222-463: The village, where they were members of a corporate body and helped manage community resources and monitor community life. In the East, they were serfs who were bound prominently to parcels of land. In most of Germany, farming was handled by tenant farmers who paid rents and obligatory services to the landlord, who was typically a nobleman. Peasant leaders supervised the fields and ditches and grazing rights, maintained public order and morals, and supported
21384-554: The vortex atom theory, which purported that an atom was a vortex in the aether , was popular among British physicists and mathematicians. Thomson pioneered the theory, which was distinct from the 17th century vortex theory of René Descartes in that Thomson was thinking in terms of a unitary continuum theory, whereas Descartes was thinking in terms of three different types of matter, each relating respectively to emission, transmission, and reflection of light. About 60 scientific papers were written by approximately 25 scientists. Following
21546-457: The voyage ended after 380 miles (610 km) when the cable parted. Thomson contributed to the effort by publishing in the Engineer the whole theory of the stresses involved in the laying of a submarine communications cable , showing when the line is running out of the ship, at a constant speed in a uniform depth of water, it sinks in a slant or straight incline from the point where it enters
21708-425: The voyages, developed a real engineer's instincts and skill at practical problem-solving under pressure, often taking the lead in dealing with emergencies and being unafraid to assist in manual work. A cable was completed on 5 August. Thomson's fears were realised when Whitehouse's apparatus proved insufficiently sensitive and had to be replaced by Thomson's mirror galvanometer. Whitehouse continued to maintain that it
21870-406: The water to that where it touches the bottom. Thomson developed a complete system for operating a submarine telegraph that was capable of sending a character every 3.5 seconds. He patented the key elements of his system, the mirror galvanometer and the siphon recorder , in 1858. Whitehouse still felt able to ignore Thomson's many suggestions and proposals. It was not until Thomson convinced
22032-504: The year of Lord Kelvin's birth, used −267 as an estimate of the absolute zero temperature. Thomson used data published by Regnault to calibrate his scale against established measurements. In his publication, Thomson wrote: ... The conversion of heat (or caloric ) into mechanical effect is probably impossible, certainly undiscovered —But a footnote signalled his first doubts about the caloric theory, referring to Joule's very remarkable discoveries . Surprisingly, Thomson did not send Joule
22194-459: Was group theory , which played an important role in both quantum field theory and differential geometry . This was, however, gradually supplemented by topology and functional analysis in the mathematical description of cosmological as well as quantum field theory phenomena. In the mathematical description of these physical areas, some concepts in homological algebra and category theory are also important. Statistical mechanics forms
22356-546: Was a book by August von Kotzebue . In 1819, Kotzebue was accused of spying for Russia, and then murdered by a theological student, Karl Ludwig Sand , who was executed for the crime. Sand belonged to a militant nationalist faction of the Burschenschaften . Metternich used the murder as a pretext to issue the Carlsbad Decrees of 1819, which dissolved the Burschenschaften , cracked down on
22518-498: Was a leader in optics and fluid dynamics; Kelvin made substantial discoveries in thermodynamics ; Hamilton did notable work on analytical mechanics , discovering a new and powerful approach nowadays known as Hamiltonian mechanics . Very relevant contributions to this approach are due to his German colleague mathematician Carl Gustav Jacobi (1804–1851) in particular referring to canonical transformations . The German Hermann von Helmholtz (1821–1894) made substantial contributions in
22680-525: Was a teacher of mathematics and engineering at the Royal Belfast Academical Institution and the son of a farmer. James Thomson married Margaret Gardner in 1817 and, of their children, four boys and two girls survived infancy. Margaret Thomson died in 1830 when William was six years old. William and his elder brother James were tutored at home by their father while the younger boys were tutored by their elder sisters. James
22842-482: Was able to make a generous provision for his favourite son's education and, in 1841, installed him, with extensive letters of introduction and ample accommodation, at Peterhouse, Cambridge . While at Cambridge, Thomson was active in sports, athletics and sculling , winning the Colquhoun Sculls in 1843. He took a lively interest in the classics, music, and literature; but the real love of his intellectual life
23004-624: Was an association of 39 predominantly German-speaking sovereign states in Central Europe . It was created by the Congress of Vienna in 1815 as a replacement of the former Holy Roman Empire , which had been dissolved in 1806 as a result of the Napoleonic Wars . The Confederation had only one organ, the Bundesversammlung , or Federal Convention (also Federal Assembly or Confederate Diet). The Convention consisted of
23166-468: Was certainly horrifying to the monarchist landed aristocracy. Figures like August Heinrich Hoffmann von Fallersleben , Ludwig Uhland , Georg Herwegh , Heinrich Heine , Georg Büchner , Ludwig Börne , and Bettina von Arnim rose in the Vormärz era. Father Friedrich Jahn 's gymnastic associations exposed middle class German youth to nationalist and democratic ideas, which took
23328-495: Was detected. As Maxwell's electromagnetic field was modeled as oscillations of the aether , physicists inferred that motion within the aether resulted in aether drift , shifting the electromagnetic field, explaining the observer's missing speed relative to it. The Galilean transformation had been the mathematical process used to translate the positions in one reference frame to predictions of positions in another reference frame, all plotted on Cartesian coordinates , but this process
23490-538: Was established by the Board of Trade and the Atlantic Telegraph Company. Most of the blame for the cable's failure was found to rest with Whitehouse. The committee found that, though underwater cables were notorious in their lack of reliability , most of the problems arose from known and avoidable causes. Thomson was appointed one of a five-member committee to recommend a specification for a new cable. The committee reported in October 1863. In July 1865, Thomson sailed on
23652-416: Was extensive emigration, especially to the United States. Emigration totaled 480,000 in the 1840s, 1,200,000 in the 1850s, and 780,000 in the 1860s. Despite its name and intention, the German Confederation was not entirely populated by Germans; many people of other ethnic groups lived within its borders: Further efforts to improve the confederation began in 1834 with the establishment of a customs union ,
23814-526: Was held back because of political disunity, conflicts of interest between the nobility and merchants, and the continued existence of the guild system, which discouraged competition and innovation. While this kept the middle class at bay, affording the old order a measure of stability not seen in France, Prussia's vulnerability to Napoleon's military proved to many among the old order that a fragile, divided, and traditionalist Germany would be easy prey for its cohesive and industrializing neighbor. The reforms laid
23976-500: Was his equipment that was providing the service and started to engage in desperate measures to remedy some of the problems. He fatally damaged the cable by applying 2,000 volts . When the cable failed completely Whitehouse was dismissed, though Thomson objected and was reprimanded by the board for his interference. Thomson subsequently regretted that he had acquiesced too readily to many of Whitehouse's proposals and had not challenged him with sufficient vigour. A joint committee of inquiry
24138-470: Was intended to benefit from the major share of his father's encouragement, affection and financial support and was prepared for a career in engineering. In 1832, his father was appointed professor of mathematics at Glasgow , and the family moved there in October 1833. The Thomson children were introduced to a broader cosmopolitan experience than their father's rural upbringing, spending mid-1839 in London, and
24300-428: Was intrigued but sceptical. Though he felt that Joule's results demanded theoretical explanation, he retreated into an even deeper commitment to the Carnot–Clapeyron school. He predicted that the melting point of ice must fall with pressure , otherwise its expansion on freezing could be exploited in a perpetuum mobile . Experimental confirmation in his laboratory did much to bolster his beliefs. In 1848, he extended
24462-602: Was inversely proportional to the square of the length of the cable. Thomson's results were disputed at a meeting of the British Association in 1856 by Wildman Whitehouse , the electrician of the Atlantic Telegraph Company . Whitehouse had possibly misinterpreted the results of his own experiments but was doubtless feeling financial pressure as plans for the cable were already well under way. He believed that Thomson's calculations implied that
24624-443: Was known before his work, Kelvin determined its correct value as approximately −273.15 degrees Celsius or −459.67 degrees Fahrenheit . The Joule–Thomson effect is also named in his honour. Kelvin worked closely with mathematics professor Hugh Blackburn in his work. He also had a career as an electrical telegraph engineer and inventor which propelled him into the public eye and earned him wealth, fame, and honours. For his work on
24786-648: Was no head of state, but the Austrian delegate presided over the Assembly (according to the Bundesakte). Austria did not have extra powers, but consequently the Austrian delegate was called Präsidialgesandther and Austria the Präsidialmacht (presiding power). The Assembly met in Frankfurt. The Confederation was enabled to accept and deploy ambassadors. It allowed ambassadors of the European powers to
24948-506: Was partly in response to his encouragement that Faraday undertook the research in September 1845 that led to the discovery of the Faraday effect , which established that light and magnetic (and thus electric) phenomena were related. He was elected a fellow of St. Peter's (as Peterhouse was often called at the time) in June 1845. On gaining the fellowship, he spent some time in the laboratory of
25110-526: Was replaced by Lorentz transformation , modeled by the Dutch Hendrik Lorentz [1853–1928]. In 1887, experimentalists Michelson and Morley failed to detect aether drift, however. It was hypothesized that motion into the aether prompted aether's shortening, too, as modeled in the Lorentz contraction . It was hypothesized that the aether thus kept Maxwell's electromagnetic field aligned with
25272-633: Was revived in 1850 on Austrian initiative, but only fully reinstalled in the Summer of 1851. Rivalry between Prussia and Austria grew more and more, especially after 1859. The Confederation was dissolved in 1866 after the Austro-Prussian War , and was succeeded in 1866 by the Prussian-dominated North German Confederation . Unlike the German Confederation, the North German Confederation was in fact
25434-438: Was supposed to collectively defend the German Confederation from external enemies, primarily France. Successive laws passed by the Confederate Diet set the form and function of the army, as well as contribution limits of the member states. The Diet had the power to declare war and was responsible for appointing a supreme commander of the army and commanders of the individual army corps. This made mobilization extremely slow and added
25596-404: Was technically not a federal execution for a lack of time to observe the actual procedure. Prussia had violated, according to the majority of the convention, federal law by sending its troops to Holstein. The decision led to the war in summer 1866 that ended with the dissolution of the confederation ( known as Seven Weeks War or by other names ). The German Federal Army ( Deutsches Bundesheer )
25758-545: Was the Italian-born Frenchman, Joseph-Louis Lagrange (1736–1813) for work in analytical mechanics : he formulated Lagrangian mechanics ) and variational methods. A major contribution to the formulation of Analytical Dynamics called Hamiltonian dynamics was also made by the Irish physicist, astronomer and mathematician, William Rowan Hamilton (1805–1865). Hamiltonian dynamics had played an important role in
25920-434: Was the pursuit of science. The study of mathematics, physics, and in particular, of electricity, had captivated his imagination. In 1845 Thomson graduated as second wrangler . He also won the first Smith's Prize , which, unlike the tripos , is a test of original research. Robert Leslie Ellis , one of the examiners, is said to have declared to another examiner "You and I are just about fit to mend his pens." In 1845, he gave
26082-523: Was then in its infancy of development as an emerging academic discipline. He received the Royal Society 's Copley Medal in 1883 and served as its president from 1890 to 1895. In 1892, he became the first scientist to be elevated to the House of Lords . Absolute temperatures are stated in units of kelvin in Lord Kelvin's honour. While the existence of a coldest possible temperature, absolute zero ,
26244-499: Was transformed into the German Empire of 1848 . Prussia was de facto the most important member state conducting the war for Germany. There are several examples for federal executions and especially federal interventions. In 1863, the Confederation ordered a federal execution against the duke of Holstein (the Danish king). Federal troops occupied Holstein which was a member state. After this, Austria and Prussia declared war on Denmark,
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