Hendrik Lorentz

Hendrik Antoon Lorentz

Hendrik Antoon Lorentz (July 18, 1853 – February 4, 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 which formed the basis of the special relativity theory of Albert Einstein. He was Chairman of the International Committee on Intellectual Cooperation from 1925 to his death.

Quotes

• Briefly, everything occurs as if the Earth were at rest.
  • On the Influence of the Earth’s Motion of Luminiferous Phenomena, in A. Miller’s Albert Einstein’s Special Theory of Relativity, p. 20

• Let there be in every material particle several material points charged with electricity, of which, however, only one be movable, and have the charge e and the mass μ.
  • As quoted by Walter Kaufmann, "The Development of the Electron Idea" (Nov. 8, 1901) The Electrician Vol. 48 pp. 95-97. Lecture delivered before the 73rd Naturforscher Versammlung at Hamburg. From the Physikalische Zeitshrift, of October 1, 1901.

The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (1916)

• One has been led to the conception of electrons, i.e. of extremely small particles, charged with electricity, which are present in immense numbers in all ponderable bodies, and by whose distribution and motions we endeavor to explain all electric and optical phenomena that are not confined to the free ether. ...according to our modern views, the electrons in a conducting body, or at least a certain part of them, are supposed to be in a free state, so that they can obey an electric force by which the positive particles are driven in one, and the negative electrons in the opposite direction. In the case of a non-conducting substance, on the contrary, we shall assume that the electrons are bound to certain positions of equilibrium. If, in a metallic wire, the electrons of one kind, say the negative ones, are travelling in one direction, and perhaps those of the opposite kind in the opposite direction, we have to do with a current of conduction, such as may lead to a state in which a body connected to one end of the wire has an excess of either positive or negative electrons. This excess, the charge of the body as a whole, will, in the state of equilibrium and if the body consists of a conducting substance, be found in a very thin layer at its surface.
  In a ponderable dielectric there can likewise be a motion of the electrons. Indeed, though we shall think of each of them as haying a definite position of equilibrium, we shall not suppose them to be wholly immovable. They can be displaced by an electric force exerted by the ether, which we conceive to penetrate all ponderable matter... the displacement will immediately give rise to a new force by which the particle is pulled back towards its original position, and which we may therefore appropriately distinguish by the name of elastic force. The motion of the electrons in non-conducting bodies, such as glass and sulphur, kept by the elastic force within certain bounds, together with the change of the dielectric displacement in the ether itself, now constitutes what Maxwell called the displacement current. A substance in which the electrons are shifted to new positions is said to be electrically polarized.
  Again, under the influence of the elastic forces, the electrons can vibrate about their positions of equilibrium. In doing so, and perhaps also on account of other more irregular motions, they become the centres of waves that travel outwards in the surrounding ether and can be observed as light if the frequency is high enough. In this manner we can account for the emission of light and heat. As to the opposite phenomenon, that of absorption, this is explained by considering the vibrations that are communicated to the electrons by the periodic forces existing in an incident beam of light. If the motion of the electrons thus set vibrating does not go on undisturbed, but is converted in one way or another into the irregular agitation which we call heat, it is clear that part of the incident energy will be stored up in the body, in other terms [words] that there is a certain absorption. Nor is it the absorption alone that can be accounted for by a communication of motion to the electrons. This optical resonance, as it may in many cases be termed, can likewise make itself felt even if there is no resistance at all, so that the body is perfectly transparent. In this case also, the electrons contained within the molecules will be set in motion, and though no vibratory energy is lost, the oscillating particles will exert an influence on the velocity with which the vibrations are propagated through the body. By taking account of this reaction of the electrons we are enabled to establish an electromagnetic theory of the refrangibility of light, in its relation to the wave-length and the state of the matter, and to form a mental picture of the beautiful and varied phenomena of double refraction and circular polarization.
  On the other hand, the theory of the motion of electrons in metallic bodies has been developed to a considerable extent. ...important results that have been reached by Riecke, Drude and J. J. Thomson... the free electrons in these bodies partake of the heat-motion of the molecules of ordinary matter, travelling in all directions with such velocities that the mean kinetic energy of each of them is equal to that of a gaseous molecule at the same temperature. If we further suppose the electrons to strike over and over again against metallic atoms, so that they describe irregular zigzag-lines, we can make clear to ourselves the reason that metals are at the same time good conductors of heat and of electricity, and that, as a general rule, in the series of the metals, the two conductivities change in nearly the same ratio. The larger the number of free electrons, and the longer the time that elapses between two successive encounters, the greater will be the conductivity for heat as well as that for electricity.
  • Ch. I General principles. Theory of free electrons.

• 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.e., the principle that the equations by means of which physical phenomena may be described are not altered in form when we change the axes of coordinates for others having a uniform motion of translation relatively to the original system.
  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... 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.
  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 vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. ...it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether.
  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.
  • Ch. V Optical Phenomena in Moving Bodies.

Theory of Relativity: A Concise Statement (1920)

Originally published in The Nieuwe Rotterdamsche Courant (November 19, 1919)

• Einstein's theory has the very highest degree of æsthetic merit: every lover of the beautiful must wish it to be true. It gives a vast unified survey of the operations of nature, with a technical simplicity in the critical assumptions which makes the wealth of deductions astonishing. It is a case of an advance arrived at by pure theory: the whole effect of Einstein's work is to make physics more philosophical (in a good sense), and to restore some of that intellectual unity which belonged to the great scientific systems of the seventeenth and eighteenth centuries, but which was lost through increasing specialization and the overwhelming mass of detailed knowledge. In some ways our age is not a good one to live in, but for those who are interested in physics there are great compensations.

• I cannot refrain... from expressing my surprise that, according to the report in The Times there should be so much complaint about the difficulty of understanding the new theory. It is evident that Einstein's little book "About the Special and the General Theory of Relativity in Plain Terms," did not find its way into England during wartime. Any one reading it will, in my opinion, come to the conclusion that the basic ideas of the theory are really clear and simple; it is only to be regretted that it was impossible to avoid clothing them in pretty involved mathematical terms, but we must not worry about that. ...
  The Newtonian theory remains in its full value as the first great step, without which one cannot imagine the development of astronomy and without which the second step, that has now been made, would hardly have been possible. It remains, moreover, as the first, and in most cases, sufficient, approximation. It is true that, according to Einstein's theory, because it leaves us entirely free as to the way in which we wish to represent the phenomena, we can imagine an idea of the solar system in which the planets follow paths of peculiar form and the rays of light shine along sharply bent lines—think of a twisted and distorted planetarium—but in every case where we apply it to concrete questions we shall so arrange it that the planets describe almost exact ellipses and the rays of light almost straight lines.
  It is not necessary to give up entirely even the ether. ...according to the Einstein theory, gravitation itself does not spread instantaneously, but with a velocity that at the first estimate may be compared with that of light. ...In my opinion it is not impossible that in the future this road, indeed abandoned at present, will once more be followed with good results, if only because it can lead to the thinking out of new experimental tests. Einstein's theory need not keep us from so doing; only the ideas about the ether must accord with it.

Quotes about Lorentz

• The term relativity refers to time and space. According to Galileo and Newton, time and space were absolute entities, and the moving systems of the universe were dependent on this absolute time and space. On this conception was built the science of mechanics. The resulting formulas sufficed for all motions of a slow nature; it was found, however, that they would not conform to the rapid motions apparent in electrodynamics.
  This led the Dutch professor Lorentz, and myself to develop the theory of special relativity. Briefly, it discards absolute time and space and makes them in every instance relative to moving systems. By this theory all phenomena in electrodynamics, as well as mechanics, hitherto irreducible by the old formulæ—and there are multitudes—were satisfactorily explained.
  • Albert Einstein, as quoted in Hendrik Antoon Lorentz, The Einstein Theory of Relativity: A Concise Statement (1920)

• Lorentz made an important addition to his original theory. He introduced changes in time. Clocks, he said, would be slowed down by the ether wind, and in just such a way as to make the velocity of light always measure 299,800 meters per second.
  • Martin Gardner, Relativity Simply Explained (1962) Ch. 2 The Michelson-Morley Experiment.

• 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.
  • Nobel Lectures, Physics 1901-1921 (1967) Elsevier Publishing Company, Amsterdam & Les Prix Nobel, as quoted in "Hendrik A. Lorentz - Biographical"

• At the anniversary meeting of the Royal Society on November 30 medals were presented by the president Sir J. J. Thomson... The characterization of the work of the medallists as printed in Nature was as follows:
  The Copley Medal is awarded to Hendrik Antoon Lorentz, For. Mem. R. S. Lorentz is generally recognized as one of the most distinguished mathematical physicists of the present time. His researches have covered many fields of investigation, but his principal work deals with the theory of electrons and the constitution of matter considered as an electro-dynamic problem. When Zeeman had discovered the effect of magnets on spectroscopic lines, he perceived at once the theoretical bearing of the effect, which led to the discovery of the circular polarization of the components of the lines split up by magnetic force. Lorentz's name is also associated with that of Fitzgerald in the independent explanation of the Michelson Morley effect, from which far-reaching consequences have been derived. An important optical relationship between the density of a medium and its index of refraction (independently by L. Lorentz [Lorenz]) was published in 1878, and he has been an active and fruitful investigator ever since.
  • "The Medallists of the Royal Society," (Dec. 27, 1918) Science, Vol. 48, pp. 637-638

• In deriving... the energy of the moving electron, it was assumed that the field of the moving electron is the same as that of the stationary electron. This is, however, only the case if the electron moves slowly, because when a Faraday tube is moved it tends to set itself at right angles to the direction of motion. The tubes constituting the electron therefore tend to crowd together in a plane perpendicular to the direction of motion of the electron. The result is an increase in the inertia or mass of the electron, because more work must be done to move a Faraday tube parallel to itself than along its own direction, just as it is harder to move a log of wood in the water parallel to itself than to move it endwise. This increase in the mass of the electron only becomes appreciable when it moves with a speed greater than about one-tenth that of light... The mass of the electron is measured by the ratio of the force to the acceleration to which it gives rise. According to the theory of Abraham and Lorentz the electron has two masses: the longitudinal mass, when it is accelerated in the direction of motion, and the transverse mass, when it is accelerated perpendicular to the direction of motion of the electron. If m represents the mass of the slow moving electron, then the longitudinal and transverse masses m₁ and m₂ are given by

${\frac {m_{1}}{m}}={\frac {1}{(1-{\frac {v^{2}}{c^{2}}})^{\frac {3}{2}}}};$

${\frac {m_{2}}{m}}={\frac {1}{(1-{\frac {v^{2}}{c^{2}}})^{\frac {1}{2}}}};$

where c is the speed of light. It is seen that as the speed of the electron approaches that of light its electromagnetic mass tends to become infinitely large. The transverse mass of the highspeed electron for various speeds has been determined by Kaufmann and Bucherer. Their experiments verify the above expression for the transverse mass. From this it would seem that the mass of the electron is entirely electromagnetic. Later developments of the Theory of Relativity have rendered this conclusion somewhat questionable, so that there does not seem to be definite experimental evidence to indicate that the electronic mass is entirely electromagnetic.

• Hendrik Johannes Van der Bijl, The Thermionic Vacuum Tube and Its Applications (1920) p. 8.

"The Development of the Electron Idea" (Nov. 8, 1901)

Walter Kaufmann, The Electrician Vol. 48 pp. 95-97. Lecture delivered before the 73rd Naturforscher Versammlung at Hamburg. From the Physikalische Zeitshrift, of October 1, 1901.

• Already in 1880, at a time when nobody in Germany yet believed in Maxwell's electromagnetic theory of light, H. A. Lorentz showed that the foundations of an electromagnetic theory of dispersion could be laid in a manner quite analogous to the mechanical theory, by regarding every molecule as the origin of electric vibrations of a definite period. He says:—"Let there be in every material particle several material points charged with electricity, of which, however, only one be movable, and have the charge e and the mass μ." Lorentz derives the equations of dispersion from this fundamental assumption of vibrating charged particles.
  • Ref: Amsterdam Akad. Versl. 18; Wied. Ann., 9, 641, 1880.

• According to Maxwell... the vibrations of light were not mechanical, but electrical vibrations of the ether, and the two constants by which Maxwell defined the electric and magnetic behaviour of every body (the dielectric constant and the magnetic permeability) had also to be the determining elements in its refractive power. Although the condition demanded by Maxwell—of the refractive power varying as the square root of the dielectric constant—was well fulfilled in a number of bodies, yet... many bodies, notably water, showed such enormous deviations that they sufficed to prove the inadequacy of the theory in its original form. To this was added the dependence of the refractive index upon the colour [frequency], for which the original theory gave no explanation whatever. ...
  Now, although the plans of the edifice of the electromagnetic theory of light were laid in 1880 by H. A. Lorentz, and even indicated much earlier by W. Weber, a full 10 years were required before the discoveries of Heinrich Hertz gave the impetus to collect the building stones and work them into shape. In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney by the now universally accepted name of electron. ...H. Ebert proved that the amplitude of an electron in luminous sodium vapour need only be a small fraction of a molecular diameter in order to excite a radiation of the absolute intensity determined by E. Wiedemann. The way of determining the amount of electricity contained in the electron is very simple. The quantity of electricity required for the electrolytic evolution of 1 cubic cm. of any monatomic gas is divided by Loschmidt's number—i.e., the number of gas molecules contained in 1 cubic cm. ...
  While it thus became clear that the supposition of vibrating ionic charges was compatible with observed phenomena as regards the order of magnitude, two works appeared, independent of each other, which completed the edifice of the electromagnetic theory of light. Of these works, that of Helmholtz only deals with the special question of the dispersion of light in absorbing media, while the other, due to H. A. Lorentz, goes much further. It shows how the assumption of vibrating charged particles in transparent bodies eliminates all the difficulties in the way of an adequate explanation of the propagation of light in moving bodies, such as the aberration of stellar light. Lorentz's theory leaves Maxwell's theory untouched as regards the free ether. A material body influences the optical and electrical processes only by virtue of the electric charges contained in it, while in the interspaces filled with ether everything remains unchanged. Maxwell's "dielectric constant" therefore disappears as a fundamental conception in Lorentz's theory. It becomes a derived conception, and it is immediately seen that for rapid electric oscillations, in which the inertia of the vibrating charges enters into consideration, it has no significance. The same applies mutatis mutandis, to the magnetic permeability.

• In view of the facility with which Lorentz's theory explains the dispersion and observation phenomena, a direct proof of its truth was hardly required. But that was also forthcoming. In 1896 a pupil of Lorentz, P. Zeeman, discovered a phenomenon whose existence Faraday had vainly sought for in 1862. If a luminous vapour, say a sodium flame, is brought into a strong magnetic field, the spectrum lines of the vapour show peculiar changes, consisting of a doubling or trebling, according to the line of vision. These changes are predicted by Lorentz's theory. The Zeeman phenomenon further permitted a determination of the inert mass connected with the vibrating charges, and then a striking result was obtained: the vibrating electron is always negatively charged, while the positive charge is stationary. ...The original and almost tacit assumption that the whole ion—i.e., the chemical atom plus its valency charge—was in oscillation must, therefore, be abandoned. We must suppose that the charge, just as is the case in electrolysis, has also an independent mobility in the light-emitting molecule, and that the mass concerned in the Zeeman phenomenon is that of the electron itself.

The Evolution of Scientific Thought from Newton to Einstein (1927)

A. D'Abro (Book copy @archive.org)

• Maxwell's equations had proved themselves incapable of accounting for dispersion. It appeared necessary to conceive of some structure for dielectrics which would act selectively, imposing different degrees of retardation on light waves of different frequencies. Lorentz achieved this result by assuming that electricity was atomic and that matter was constituted by more or less complicated groupings of these electric atoms or electrons.
  Phenomena were accounted for by taking into consideration the frictional resistances that would interfere with rapid vibrations of the electrons. When these frictional resistances were weak, oscillatory disturbances, such as rays of light, could be propagated through the dielectric, which was then termed transparent (glass). When these frictional forces were considerable, the light ray was unable to set the electrons into vibration; its energy was consumed in the attempt, and as a result it could not proceed; the dielectric was then opaque (ebonite, sulphur).
  In the case of conductors such as metals, the electrons were assumed to be very loosely held to their atoms so that the slightest difference of potential would tear them away and cause them to rush in the same direction, thereby producing an electric current. It was precisely because electrons in conductors were not tied down to fixed positions by elastic forces that they were incapable of vibrating; and so conductors were necessarily opaque to electromagnetic vibrations or to light. Conversely, it was because the electrons were all tied down to fixed positions in the dielectrics, that they could not rush along in one direction. As a result dielectrics were opaque to currents, and hence were non-conductors. According to these views of Lorentz, an electric current passing through matter was nothing but a rush of electrons.
  • p. 130

• Lorentz accepted what appeared to him to be inevitable, and asserted that the time had come to recognize that nature seemed to have entered into some giant conspiracy to defraud us of a knowledge of our velocity through the ether. Accordingly, he laid down his celebrated principle of correlation, according to which adjustments were so regulated in nature that the velocity of our planet through the ether could never be detected, however precise our measurements.
  Lorentz applied his mathematical talents to the discovery of the necessary adjustments which would have to exist in nature for this correlation to be satisfied completely so far as electrodynamics and optics were concerned. ...He succeeded in establishing the transformations which would be in harmony with the invariance of the electrodynamic equations, and he found these to differ perceptibly with the classical ones; although reducing to the latter in the case of low velocities. The new transformations constitute the celebrated Lorentz transformations. ...
  These transformations expressed the existence of two separate phenomena: first, the Fitzgerald contraction of bodies moving through the ether... and secondly, a new phenomenon consisting in the slowing down (with increase in velocity through the ether) of the rate of time-flow as applying to electromagnetic processes. ...For psychological reasons, however, imbued with the spirit of classical science, Lorentz was unable to realise the importance of his discovery; and he never succeeded in ridding himself of his belief in the absoluteness of time. For him, and also for Larmor, who contributed to these discoveries, this new species of variable duration, depending as it did on the motion through the ether of the Galilean frame, was not real time. It was a species of "local time"—a distortion of real time—the time which the observer in the moving frame would live and sense.
  And so Lorentz assumed that these new transformations applied only to purely electromagnetic quantities, and no reference was made to their being applicable to mechanical phenomena as well. Though, as a result of these transformations, the velocity of light proved to have always the same invariant value through all Galilean frames when measured by the observer in the frame, no suspicion was cast on the classical formula for the composition of the velocities of material bodies; and this in spite of the fact that the two circumstances were mutually incompatible.
  • pp. 134-137

• The classical or Galilean transformations were $x'=x-vt,y'=y,z'=z,t'=t,$ where $v$ was the velocity of the frame with respect to a frame at rest in the ether, hence with respect to the ether itself; this velocity being directed along the $x$ axis and the two frames being assumed to have coincided at the initial instant $t=0$. Under the same conditions the Lorentz transformations were $x'=\beta (x-vt),y'=y,z'=z;t'=\beta (t-{\frac {vx}{c^{2}}})$  where  $\beta ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$
  • Footnote p. 136

• When... in such experiments as that of Trouton and Noble, mechanical and purely electromagnetic effects were indissolubly connected, a large measure of obscurity was involved. Lorentz, however, succeeded in extricating himself from his difficulties and in accounting for all the negative experiments; but he was compelled to appeal to additional hypotheses, such as a modification in those elastic forces which cause electrons to vibrate in transparent bodies (Rayleigh and Brace experiments). In a similar way it was possible to explain the negative result of the Trouton and Noble experiment. ...we can understand the numerous difficulties into which Lorenz's theory was leading us. We knew very little about the constitution of matter, and here, in Lorentz's theory, we were compelled to account for negative experiments by taking this unknown constitution of matter into consideration.
  ...this accumulation of hypotheses postulated ad hoc makes it painfully artificial. ...Even if we admitted that all matter were electronically constituted, and that the constituent electrons became flattened as a result of their motion through the ether, it was still impossible to conceive of an identical flattening of all bodies, whether rigid or soft, unless we assumed that an appropriate adjustment had also taken place in the other factors entering into the constitution of matter (elastic forces, etc.).
  • p. 137

• Lorentz, thanks to his mathematical knowledge, realised that something much deeper was at the root of all the trouble and that more radical means would have to be adopted. Accordingly, he proceeded to tackle the very foundations of science, namely, the space and time transformations which had endured for centuries. But Lorentz only proceeded in a half-hearted way and did not have the courage to push his discoveries to their logical conclusion, contenting himself with patching up rather than reconstructing. Einstein... took the bull by the horns, abandoned the classical structure, and proceeded to build up an entirely new edifice, superbly coherent and free from all artificial support and scaffoldings.
  • p. 139

• The most precise experiments have proved the correctness of the Einsteinian laws of mechanics and...Bucherer's experiment proving the increase in mass of an electron in rapid motion is a case in point.
  Very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of the electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein's theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation of Fitzgerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein's theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves.
  Furthermore, the fact that this increase in mass of matter in motion is now due to relative motion and not to motion through the stagnant ether, as in Lorentz's theory, changes the entire outlook considerably. According to Lorentz, the electron really increased in mass, since its motion through the ether remained a reality. According to Einstein, the electron increases in mass only in so far as it is in relative motion with respect to the observer. Were the observer to be attached to the flying electron no increase in mass would exist; it would be the electron left behind which would now appear to have suffered the increase. Thus mass follows distance, duration and electromagnetic field in being a relative and having no definite magnitude of itself and being essentially dependent on the conditions of observation.
  Owing to the general validity of the Lorentz-Einstein transformations, it becomes permissible to apply them to all manner of phenomena.. ...temperature, pressure and many other physical magnitudes turned out to be relatives. ...entropy, electric charge and the velocity of light in vacuo were absolutes transcending the observer's motion. ...a number of other entities are found to be absolutes, the most important of which is that abstract mathematical quantity called the Einsteinian interval, which plays so important a part in the fabric of the new objective world of science, the world of four-dimensional space-time.
  • pp. 159-160

Also see

• Theory of relativity

External links

• A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein (1927) @archive.org
• H.A. Lorentz, The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (1916)
• H.A. Lorentz, The Einstein Theory of Relativity: A Concise Statement (1920)
• Publications of H.A. Lorentz @Lorentz Institute for Theoretical Physics