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",^[16] known today as the special theory of relativity. Because Lorentz laid the fundamentals for the work by Einstein, this theory was originally called the Lorentz–Einstein theory.^[17]

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)^[18] 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,^{[19][failed verification]} 1910,^[20][21] 1914.^[22] 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:^[19]

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.^[19]
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.^[20]

Lorentz also gave credit to Poincaré's contributions to relativity.^[23]

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.^[24] For instance, he attempted to combine Einstein's formalism with Hamilton's principle (1915),^[25] and to reformulate it in a coordinate-free way (1916).^[26][27] Lorentz wrote in 1919:^[28]

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.

Lorentz gave a series of lectures in the fall of 1926 at Cornell University on the new quantum mechanics; in these he presented Erwin Schrödinger's wave mechanics.^[29]

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.^[5]

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.^[5]

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.^[5]

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.^[30] 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.^[31][5] 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.

Dr. Geertruida Luberta Lorentz, the eldest daughter, was a physicist. She married Professor Wander Johannes de Haas, who was the Director of the Cryogenic Laboratory at the University of Leiden.^[32]

In January 1928, Lorentz became seriously ill, and died shortly after on 4 February.^[5] 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^[33]

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.^[34] Amongst others, the funeral was attended by Albert Einstein and Marie Curie.^[35]

Lorentz is considered one of the prime representatives of the "Second Dutch Golden Age", a period of several decades surrounding 1900 in which the natural sciences flourished in the Netherlands.^[5]

Richardson describes Lorentz as:

A man of remarkable intellectual powers. Although steeped in his own investigation of the moment, he always seemed to have in his immediate grasp its ramifications into every corner of the universe. The singular clearness of his writings provides a striking reflection of his wonderful powers in this respect. He possessed and successfully employed the mental vivacity which is necessary to follow the interplay of discussion, the insight which is required to extract those statements which illuminate the real difficulties, and the wisdom to lead the discussion among fruitful channels, and he did this so skillfully that the process was hardly perceptible.^[33]

M. J. Klein (1967) wrote of Lorentz's reputation in the 1920s:

For many years physicists had always been eager "to hear what Lorentz will say about it" when a new theory was advanced, and, even at seventy-two, he did not disappoint them.^[36]

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.^[37]
1953: For me personally he meant more than all the others I have met on my life's journey.^[38]

Poincaré (1902) said of Lorentz's theory of electrodynamics:^[39]

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.

Paul Langevin (1911) said of Lorentz:^[40]

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:^[41]

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 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.^[1] 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.^[42] He was an International Member of the American Philosophical Society, the United States National Academy of Sciences, and the American Academy of Arts and Sciences.^[43][44][45]

MOTORES ELÉCTRICOS. Ley de LORENTZ

La fuerza magnética está descrita por la ley de la Ley de Lorentz:

Fuerza de Lorentz 

Una cantidad fija de carga q que se mueve a una velocidad constante v en un campo magnético uniforme B, experimenta una fuerza F, perpendicular tanto a la velocidad  v como al campo B

Hendrik Antoon Lorentz, 1921

A veces queremos encontrar la fuerza que actúa sobre un alambre de longitud L por el que pasa una corriente I que se encuentra dentro de un campo magnético. Podemos lograrlo al reordenar la expresión previa. Si recordamos que la velocidad es la distancia dividida entre el tiempo, y puesto que la corriente I es la cantidad de carga que fluye por unidad de tiempo, entonces

q.v.B = q.(L/t).B = (q/t).L.B = I.L.B

Así obtenemos otra expresión para la Fuerza de Lorentz:

 

Estas fuerzas se pueden utilizar para provocar un PAR DE FUERZAS que hagan girar una espira, siendo este efecto el principio de funcionamiento de los motores eléctricos.

Par de fuerzas de Lorentz sobre una espira

Motor CC

Examen hasta aquí

El valor del momento de fuerza viene dado por el producto de la fuerza por la distancia que separa ambas líneas de acción:

A continuación, se sustituye la fuerza por su valor, teniendo en cuenta que la intensidad y el campo magnético son siempre perpendiculares. Después se reorganizan los términos de la expresión:

Ahora, el producto de la longitud de la espira por su anchura da como resultado la superficie de la misma. Con ésto se obtiene una expresión que es independiente de la forma de la espira, y sólo influye su superficie:

Y, ya para acabar, se transforma esta igualdad en un producto vectorial si se considera la superficie como un vector cuyo módulo es el valor de superficie, dirección perpendicular al plano de la espira y sentido definido por la regla de la mano derecha según el sentido de la intensidad, previamente invertida:

Con lo cual, además, tenemos la dirección del momento de giro como un vector, y nuevamente por la regla de la mano derecha este vector indica el sentido de giro. Cuando hay varias espiras, la expresión se multiplica por el número de las mismas:

 

 

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