Hendrik Antoon Lorentz (/ˈlɒrənts/; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the transformation equations underpinning Albert Einstein's theory of special relativity.
According to the biography published by the Nobel Foundation, "It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepared the ground for the fruitful reception of the new ideas based on the quantum theory." He received many honours and distinctions, including a term as chairman of the International Committee on Intellectual Cooperation, the forerunner of UNESCO, between 1925 and 1928.
Hendrik Antoon Lorentz
|Born||18 July 1853|
|Died||4 February 1928 (aged 74)|
|Alma mater||University of Leiden|
|Doctoral advisor||Pieter Rijke|
Hendrik Lorentz was born in Arnhem, Gelderland, Netherlands, the son of Gerrit Frederik Lorentz (1822–1893), a well-off nurseryman, and Geertruida van Ginkel (1826–1861). In 1862, after his mother's death, his father married Luberta Hupkes. Despite being raised as a Protestant, he was a freethinker in religious matters.[B 1] From 1866 to 1869, he attended the "Hogere Burger School" in Arnhem, a new type of public high school recently established by Johan Rudolph Thorbecke. His results in school were exemplary; not only did he excel in the physical sciences and mathematics, but also in English, French, and German. In 1870, he passed the exams in classical languages which were then required for admission to University.[B 2]
Lorentz studied physics and mathematics at the Leiden University, where he was strongly influenced by the teaching of astronomy professor Frederik Kaiser; it was his influence that led him to become a physicist. After earning a bachelor's degree, he returned to Arnhem in 1871 to teach night school classes in mathematics, but he continued his studies in Leiden in addition to his teaching position. In 1875, Lorentz earned a doctoral degree under Pieter Rijke on a thesis entitled "Over de theorie der terugkaatsing en breking van het licht" (On the theory of reflection and refraction of light), in which he refined the electromagnetic theory of James Clerk Maxwell.[B 2]
On 17 November 1877, only 24 years of age, Hendrik Antoon Lorentz was appointed to the newly established chair in theoretical physics at the University of Leiden. The position had initially been offered to Johan van der Waals, but he accepted a position at the Universiteit van Amsterdam.[B 2] On 25 January 1878, Lorentz delivered his inaugural lecture on "De moleculaire theoriën in de natuurkunde" (The molecular theories in physics). In 1881, he became member of the Royal Netherlands Academy of Arts and Sciences.
During the first twenty years in Leiden, Lorentz was primarily interested in the electromagnetic theory of electricity, magnetism, and light. After that, he extended his research to a much wider area while still focusing on theoretical physics. Lorentz made significant contributions to fields ranging from hydrodynamics to general relativity. His most important contributions were in the area of electromagnetism, the electron theory, and relativity.[B 2]
Lorentz theorized that atoms might consist of charged particles and suggested that the oscillations of these charged particles were the source of light. When a colleague and former student of Lorentz's, Pieter Zeeman, discovered the Zeeman effect in 1896, Lorentz supplied its theoretical interpretation. The experimental and theoretical work was honored with the Nobel prize in physics in 1902. Lorentz' name is now associated with the Lorentz-Lorenz formula, the Lorentz force, the Lorentzian distribution, and the Lorentz transformation.
In 1892 and 1895, Lorentz worked on describing electromagnetic phenomena (the propagation of light) in reference frames that move relative to the postulated luminiferous aether. He discovered that the transition from one to another reference frame could be simplified by using a new time variable that he called local time and which depended on universal time and the location under consideration. Although Lorentz did not give a detailed interpretation of the physical significance of local time, with it, he could explain the aberration of light and the result of the Fizeau experiment. In 1900 and 1904, Henri Poincaré called local time Lorentz's "most ingenious idea" and illustrated it by showing that clocks in moving frames are synchronized by exchanging light signals that are assumed to travel at the same speed against and with the motion of the frame (see Einstein synchronisation and Relativity of simultaneity). In 1892, with the attempt to explain the Michelson-Morley experiment, Lorentz also proposed that moving bodies contract in the direction of motion (see length contraction; George FitzGerald had already arrived at this conclusion in 1889).
In 1899 and again in 1904, Lorentz added time dilation to his transformations and published what Poincaré in 1905 named Lorentz transformations. It was apparently unknown to Lorentz that Joseph Larmor had used identical transformations to describe orbiting electrons in 1897. Larmor's and Lorentz's equations look somewhat dissimilar, but they are algebraically equivalent to those presented by Poincaré and Einstein in 1905.[B 3] Lorentz's 1904 paper includes the covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well defined transformation properties. The paper clearly recognizes the significance of this formulation, namely that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. The 1904 paper includes a detailed discussion of the increase of the inertial mass of rapidly moving objects in a useless attempt to make momentum look exactly like Newtonian momentum; it was also an attempt to explain the length contraction as the accumulation of "stuff" onto mass making it slow and contract.
In 1905, Einstein would use many of the concepts, mathematical tools and results Lorentz discussed to write his paper entitled "On the Electrodynamics of Moving Bodies", known today as the theory of special relativity. Because Lorentz laid the fundamentals for the work by Einstein, this theory was originally called the Lorentz-Einstein theory.[B 4]
In 1906, Lorentz's electron theory received a full-fledged treatment in his lectures at Columbia University, published under the title The Theory of Electrons.
The increase of mass was the first prediction of Lorentz and Einstein to be tested, but some experiments by Kaufmann appeared to show a slightly different mass increase; this led Lorentz to the famous remark that he was "au bout de mon latin" ("at the end of my [knowledge of] Latin" = at his wit's end) The confirmation of his prediction had to wait until 1908 and later (see Kaufmann–Bucherer–Neumann experiments).
Lorentz published a series of papers dealing with what he called "Einstein's principle of relativity". For instance, in 1909, 1910, 1914. In his 1906 lectures published with additions in 1909 in the book "The theory of electrons" (updated in 1915), he spoke affirmatively of Einstein's theory:
It will be clear by what has been said that the impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the "true" times or the "true" lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, [...] I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena ... agree in the main with those which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. [...] It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced.
Though Lorentz still maintained that there is an (undetectable) aether in which resting clocks indicate the "true time":
1909: Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter.
1910: Provided that there is an aether, then under all systems x, y, z, t, one is preferred by the fact, that the coordinate axes as well as the clocks are resting in the aether. If one connects with this the idea (which I would abandon only reluctantly) that space and time are completely different things, and that there is a "true time" (simultaneity thus would be independent of the location, in agreement with the circumstance that we can have the idea of infinitely great velocities), then it can be easily seen that this true time should be indicated by clocks at rest in the aether. However, if the relativity principle had general validity in nature, one wouldn't be in the position to determine, whether the reference system just used is the preferred one. Then one comes to the same results, as if one (following Einstein and Minkowski) deny the existence of the aether and of true time, and to see all reference systems as equally valid. Which of these two ways of thinking one is following, can surely be left to the individual.
Lorentz also gave credit to Poincaré's contributions to relativity.
Indeed, for some of the physical quantities which enter the formulas, I did not indicate the transformation which suits best. That was done by Poincaré and then by Mr. Einstein and Minkowski [...] I did not succeed in obtaining the exact invariance of the equations [...] Poincaré, on the contrary, obtained a perfect invariance of the equations of electrodynamics, and he formulated the "postulate of relativity", terms which he was the first to employ. [...] Let us add that by correcting the imperfections of my work he never reproached me for them.
Lorentz was one of few scientists who supported Einstein's search for general relativity from the beginning – he wrote several research papers and discussed with Einstein personally and by letter.[B 5] For instance, he attempted to combine Einstein's formalism with Hamilton's principle (1915), and to reformulate it in a coordinate-free way (1916).[B 6] Lorentz wrote in 1919:
The total eclipse of the sun of May 29, resulted in a striking confirmation of the new theory of the universal attractive power of gravitation developed by Albert Einstein, and thus reinforced the conviction that the defining of this theory is one of the most important steps ever taken in the domain of natural science.
Einstein wrote of Lorentz:
1928: The enormous significance of his work consisted therein, that it forms the basis for the theory of atoms and for the general and special theories of relativity. The special theory was a more detailed expose of those concepts which are found in Lorentz's research of 1895.[B 7]
1953: For me personally he meant more than all the others I have met on my life's journey.[B 8]
Poincaré (1902) said of Lorentz's theory of electrodynamics:
The most satisfactory theory is that of Lorentz; it is unquestionably the theory that best explains the known facts, the one that throws into relief the greatest number of known relations ... it is due to Lorentz that the results of Fizeau on the optics of moving bodies, the laws of normal and abnormal dispersion and of absorption are connected with each other ... Look at the ease with which the new Zeeman phenomenon found its place, and even aided the classification of Faraday's magnetic rotation, which had defied all Maxwell's efforts.
It will be Lorentz's main claim to fame that he demonstrated that the fundamental equations of electromagnetism also allow of a group of transformations that enables them to resume the same form when a transition is made from one reference system to another. This group differs fundamentally from the above group as regards transformations of space and time.''
Lorentz was chairman of the first Solvay Conference held in Brussels in the autumn of 1911. Shortly after the conference, Poincaré wrote an essay on quantum physics which gives an indication of Lorentz's status at the time:
... at every moment [the twenty physicists from different countries] could be heard talking of the [quantum mechanics] which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was the mechanics of Lorentz, the one dealing with the principle of relativity; the one which, hardly five years ago, seemed to be the height of boldness.
In 1910, Lorentz decided to reorganize his life. His teaching and management duties at Leiden University were taking up too much of his time, leaving him little time for research. In 1912, he resigned from his chair of theoretical physics to become curator of the "Physics Cabinet" at Teylers Museum in Haarlem. He remained connected to Leiden University as an external professor, and his "Monday morning lectures" on new developments in theoretical physics soon became legendary.[B 2]
Lorentz initially asked Einstein to succeed him as professor of theoretical physics at Leiden. However, Einstein could not accept because he had just accepted a position at ETH Zurich. Einstein had no regrets in this matter, since the prospect of having to fill Lorentz's shoes made him shiver. Instead Lorentz appointed Paul Ehrenfest as his successor in the chair of theoretical physics at the Leiden University, who would found the Institute for Theoretical Physics which would become known as the Lorentz Institute.[B 2]
After World War I, Lorentz was one of the driving forces behind the founding of the "Wetenschappelijke Commissie van Advies en Onderzoek in het Belang van Volkswelvaart en Weerbaarheid", a committee which was to harness the scientific potential united in the Royal Netherlands Academy of Arts and Sciences (KNAW) for solving civil problems such as food shortage which had resulted from the war. Lorentz was appointed chair of the committee. However, despite the best efforts of many of the participants the committee would harvest little success. The only exception being that it ultimately resulted in the founding of TNO, the Netherlands Organisation for Applied Scientific Research.[B 2]
Lorentz was also asked by the Dutch government to chair a committee to calculate some of the effects of the proposed Afsluitdijk (Enclosure Dam) flood control dam on water levels in the Waddenzee. Hydraulic engineering was mainly an empirical science at that time, but the disturbance of the tidal flow caused by the Afsluitdijk was so unprecedented that the empirical rules could not be trusted. Originally Lorentz was only supposed to have a coordinating role in the committee, but it quickly became apparent that Lorentz was the only physicist to have any fundamental traction on the problem. In the period 1918 till 1926, Lorentz invested a large portion of his time in the problem. Lorentz proposed to start from the basic hydrodynamic equations of motion and solve the problem numerically. This was feasible for a "human computer", because of the quasi-one-dimensional nature of the water flow in the Waddenzee. The Afsluitdijk was completed in 1932, and the predictions of Lorentz and his committee turned out to be remarkably accurate.[B 11][B 2] One of the two sets of locks in the Afsluitdijk was named after him.
In 1881, Lorentz married Aletta Catharina Kaiser. Her father was J.W. Kaiser, a professor at the Academy of Fine Arts. He was the Director of the museum which later became the well-known Rijksmuseum (National Gallery). He also was the designer of the first postage stamps of The Netherlands.
There were two daughters, and one son from this marriage.
In January 1928, Lorentz became seriously ill, and died shortly after on February 4.[B 2] The respect in which he was held in the Netherlands is apparent from Owen Willans Richardson's description of his funeral:
The funeral took place at Haarlem at noon on Friday, February 10. At the stroke of twelve the State telegraph and telephone services of Holland were suspended for three minutes as a revered tribute to the greatest man the Netherlands has produced in our time. It was attended by many colleagues and distinguished physicists from foreign countries. The President, Sir Ernest Rutherford, represented the Royal Society and made an appreciative oration by the graveside.— O. W. Richardson[B 12]
Unique 1928 film footage of the funeral procession with a lead carriage followed by ten mourners, followed by a carriage with the coffin, followed in turn by at least four more carriages, passing by a crowd at the Grote Markt, Haarlem from the Zijlstraat to the Smedestraat, and then back again through the Grote Houtstraat towards the Barteljorisstraat, on the way to the "Algemene Begraafplaats" at the Kleverlaan (northern Haarlem cemetery) has been digitized on YouTube.[B 13] Einstein gave a eulogy at a memorial service at Leiden University.
Lorentz is considered one of the prime representatives of the "Second Dutch Golden Age", a period of several decades surrounding 1900 in which in the natural sciences in the Netherlands flourished.[B 2]
Richardson describes Lorentz as:
M. J. Klein (1967) wrote of Lorentz's reputation in the 1920s:
In addition to the Nobel prize, Lorentz received a great many honours for his outstanding work. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1905. The Society awarded him their Rumford Medal in 1908 and their Copley Medal in 1918. He was elected an Honorary Member of the Netherlands Chemical Society in 1912.
Many papers by Lorentz (mostly in English) are available for online viewing in the Proceedings of the Royal Netherlands Academy of Arts and Science, Amsterdam.
Although he grew up in Protestant circles, he was a freethinker in religious matters; he regularly attended the local French church to improve his French.
In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. It is also called the radiation reaction force or the self force.
The formula predates the theory of special relativity and is not valid at velocities on the order of the speed of light. Its relativistic generalization is called the "Abraham–Lorentz–Dirac force". Both of these are in the domain of classical physics, not quantum physics, and therefore may not be valid at distances of roughly the Compton wavelength or below. There is, however, an analogue of the formula that is both fully quantum and relativistic, called the "Abraham–Lorentz–Dirac–Langevin equation".The force is proportional to the square of the object's charge, times the jerk (rate of change of acceleration) that it is experiencing. The force points in the direction of the jerk. For example, in a cyclotron, where the jerk points opposite to the velocity, the radiation reaction is directed opposite to the velocity of the particle, providing a braking action.
It was thought that the solution of the Abraham–Lorentz force problem predicts that signals from the future affect the present, thus challenging intuition of cause and effect (retrocausality). For example, there are pathological solutions using the Abraham–Lorentz–Dirac equation in which a particle accelerates in advance of the application of a force, so-called pre-acceleration solutions. One resolution of this problem was discussed by Yaghjian and is further discussed by Rohrlich and Medina.Hugo Tetrode
Hugo Martin Tetrode (7 March 1895, in Amsterdam – 18 January 1931, in Amstelveen) was a Dutch theoretical physicist who contributed to statistical physics, early quantum theory and quantum mechanics.
In 1912, Tetrode developed the Sackur–Tetrode equation, a quantum mechanical expression of the entropy of an ideal gas. Otto Sackur derived this equation independently around the same time. The Sackur–Tetrode constant, S0/R, is a fundamental physical constant representing the translational contribution to the entropy of an ideal gas at a temperature of 1 K and pressure of 100 kPa, where R is the gas constant.
From Amsterdam, Tetrode corresponded with Albert Einstein, Hendrik Lorentz and Paul Ehrenfest on quantum mechanics and wrote several influential papers on quantum mechanics which were published in the German physics journal Zeitschrift für Physik. In particular, the Machian notion that elementary particles only act on other elementary particles and not themselves was a key idea in the formulation of the Wheeler–Feynman Time symmetric theory.Length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.Lorentz-violating electrodynamics
Searches for Lorentz violation involving photons are among the best tests of relativity. Examples range from modern versions of the classic Michelson-Morley experiment that utilize highly stable electromagnetic resonant cavities to searches for tiny deviations from c in the speed of light emitted by distant astrophysical sources. Due to the extreme distances involved, astrophysical studies have achieved sensitivities on the order of parts in 1038.Lorentz (crater)
Lorentz is a huge lunar impact crater that lies just beyond the northwest limb of the Moon, in a region that is brought into sight of the Earth during favorable librations. This formation is nearly as large as the Mare Nectaris on the near side of the Moon, although it has not been submerged by lava as have the lunar mare. Sections of the crater floor are, however, relatively level, particularly an arc along the western rim. But this last region is still marked by a number of tiny craterlets. The remainder of the interior is rough and irregular, and marked with a multitude of impacts.
Lorentz contains a prominent crater pairing, with Nernst located just to the north of Lorentz's midpoint, and Röntgen attached to the southeastern rim of Nernst. Lying across the southern rim of Lorentz is Laue, and Avicenna lies across the northwestern rim. Near the more indeterminate eastern rim of Lorentz is Aston.Lorentz Institute
The Lorentz Institute (Dutch: Instituut-Lorentz) was established in 1921 and is the oldest institute for theoretical physics in The Netherlands. Together with the experimental physics groups in the Kamerlingh Onnes Laboratory and the Huygens Laboratory, it makes up the Leiden Institute of Physics. The Instituut-Lorentz participates in two research schools, the Casimir Research School (jointly with Delft University of Technology) and the Dutch Research School of Theoretical Physics.Lorentz Medal
Lorentz Medal is a distinction awarded every four years by the Royal Netherlands Academy of Arts and Sciences. It was established in 1925 on the occasion of the 50th anniversary of the doctorate of Hendrik Lorentz. The medal is given for important contributions to theoretical physics, though in the past there have been some experimentalists among its recipients.Many of the award winners later received a Nobel Prize.Lorentz covariance
In relativistic physics, Lorentz symmetry, named after Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:
A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e., they transform under the trivial representation).
An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame. This condition is a requirement according to the principle of relativity; i.e., all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Both covariant and contravariant four-vectors can be Lorentz covariant quantities.
Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance.Lorentz factor
The Lorentz factor or Lorentz term is the factor by which time, length, and relativistic mass change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.Due to its ubiquity, it is generally denoted γ (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as Γ (Greek uppercase-gamma) rather than γ.Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of
(in SI units). Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a charged particle which might be traveling near the speed of light (relativistic form of the Lorentz force).
Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865. Hendrik Lorentz arrived in a complete derivation in 1895, identifying the contribution of the electric force a few years after Oliver Heaviside correctly identified the contribution of the magnetic force.Lorentz group
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz.
For example, the following laws, equations, and theories respect Lorentz symmetry:
The kinematical laws of special relativity
Maxwell's field equations in the theory of electromagnetism
The Dirac equation in the theory of the electron
The Standard model of particle physicsThe Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature. In general relativity physics, in cases involving small enough regions of spacetime where gravitational variances are negligible, physical laws are Lorentz invariant in the same manner as that of special relativity physics.Lorentz scalar
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of vectors, or from contracting tensors of the theory. While the components of vectors and tensors are in general altered under Lorentz transformations, Lorentz scalars remain unchanged.
A Lorentz scalar is not always immediately seen to be an invariant scalar in the mathematical sense, but the resulting scalar value is invariant under any basis transformation applied to the vector space, on which the considered theory is based. A simple Lorentz scalar in Minkowski spacetime is the spacetime distance ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation. Other examples of Lorentz scalars are the "length" of 4-velocities (see below), or the Ricci curvature in a point in spacetime from General relativity, which is a contraction of the Riemann curvature tensor there.Lorentz surface
In mathematics, a Lorentz surface is a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue of a Riemann surface in indefinite signature.Lorentz–Heaviside units
Lorentz–Heaviside units (or Heaviside–Lorentz units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant ε0 and magnetic constant µ0 do not appear, having been incorporated implicitly into the unit system and electromagnetic equations. Lorentz–Heaviside units may be regarded as normalizing ε0 = 1 and µ0 = 1, while at the same time revising Maxwell's equations to use the speed of light c instead.Lorentz–Heaviside units, like SI units but unlike Gaussian units, are rationalized, meaning that there are no factors of 4π appearing explicitly in Maxwell's equations. The fact that these units are rationalized partly explains their appeal in quantum field theory: the Lagrangian underlying the theory does not have any factors of 4π in these units. Consequently, Lorentz–Heaviside units differ by factors of √4π in the definitions of the electric and magnetic fields and of electric charge. They are often used in relativistic calculations, and are the unit of choice in High Energy Physics (particle physics). They are particularly convenient when performing calculations in spatial dimensions greater than three such as in string theory.Pieter Zeeman
Pieter Zeeman (Dutch: [ˈzeːmɑn]; 25 May 1865 – 9 October 1943) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect.Rayleigh–Lorentz pendulum
Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of the slow variation of frequency, it is shown that the ratio of average energy to frequency is constant.Zonnemaire
Zonnemaire is a village in the Dutch province of Zeeland. It is a part of the municipality of Schouwen-Duiveland, and lies about 19 kilometres (12 mi) southwest of Hellevoetsluis.
Zonnemaire was a separate municipality until 1961, when it was merged with Brouwershaven.In 2001, the village of Zonnemaire had 330 inhabitants. The built-up area of the village was 0.092 km2, and contained 151 residences.
The statistical area "Zonnemaire", which also can include the surrounding countryside, has a population of around 1,040.Zonnemaire was named after Sonnemare, the water between the former islands of Bommenede and Schouwen.
Zonnemaire is the birthplace of Pieter Zeeman, who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect.
Recipients of the Copley Medal (1901–1950)
Nobel Prize laureates from The Netherlands
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