James Clerk Maxwell Quotes (1831-1879)

“I have also cleared the electromagnetic theory of light from all unwarrantable assumption, so that we may safely determine the velocity of light by measuring the attraction between bodies kept at a given difference of potential, the value of which is known in electromagnetic measure.”

“I have also cleared the electromagnetic theory of light from all unwarrantable assumption, so that we may safely determine the velocity of light by measuring the attraction between bodies kept at a given difference of potential, the value of which is known in electromagnetic measure.”

“As for the atoms, they have been in far worse rows before they became naturalised in my brain, but they forget the days before, etc. At any rate the atoms are a very tough lot, and can stand a great deal of knocking about, and it is strange to find a number of them combining to form a man of feeling.”

“Heat may be generated and destroyed by certain processes, and this shows that heat is not a substance.”

“This identification of extension with substance runs through the whole of Descartes's works, and it forms one of the ultimate foundations of the system of Spinoza.”

“The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.”

“Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza.”

“Sir, I have received with much pleasure the tables of the satellites of Jupiter which you have been so kind as to send me, and I am encouraged by your interest in the Jovial system to ask you if you have made any special study of the apparent retardation of the eclipses as affected by the geocentric position of Jupiter. I am told that observations of this kind have been somewhat put out of fashion by other methods of determining quantities related to the velocity of light, but they afford the only method, so far as I know, of getting any estimate of the direction and magnitude of the velocity of the sun with respect to the luminiferous medium. Even if we were sure of the theory of aberration, we can only get differences of position of stars, and in the terrestrial methods of determining the velocity of light, the light comes back along the same path again, so that the velocity of the earth with respect to the ether would alter the time of the double passage by a quantity depending on the square of the ratio of the earth's velocity to that of light, and this is quite too small to be observed.”

“The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. ...mathematical theories of statical electricity, of magnetism, of the mechanical action between conductors carrying currents, and of the induction of currents have been formed. In these theories the force acting between the two bodies is treated with reference only to the condition of the bodies and their relative position, and without any express consideration of the surrounding medium. These theories assume, more or less explicitly, the existence of substances the particles of which have the property of acting on one another at a distance by attraction or repulsion. The most complete development of a theory of this kind is that of... MM. W. Weber and C. Neumann... The mechanical difficulties, however, which are involved in the assumption of particles acting at a distance with forces which depend on their velocities are such as to prevent me from considering this theory as an ultimate one... I have, therefore, preferred to seek an explanation of the fact in another direction, by supposing them to be produced by actions which go on in the surrounding medium as well as in the excited bodies, and endeavouring to explain the action between distant bodies without assuming the existence of forces capable of acting directly at sensible distances.”

“To prove the laws of motion by the law of gravitation would be an inversion of scientific order. We might as well prove the law of addition of numbers by the differential calculus.”

“Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza.”

“The first process... in the effectual study of science must be one of simplification and reduction of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis.”

“We cannot... regard Newton's statement as an appeal to experience and observation, but rather as a deduction of the third law of motion from the first.”

“He opened up a new field of mathematical physics by shewing how to deal mathematically with moving systems of innumerable molecules.”

“The primary property of matter was indeed distinctly announced by Descartes in what he calls the "First Law of Nature": "That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest."”

“Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza.”

“We have... used the word stress to denote the mutual action between two portions of matter. This word was borrowed from common language, and invested with a precise scientific meaning by the late Professor Rankine to whom we are indebted for several other valuable scientific terms.”

“It has been asserted that metaphysical speculation is a thing of the past and that physical science has extirpated it. The discussion of the categories of existence, however, does not appear to be in danger of coming to an end in our time, and the exercise of speculation continues as fascinating to every fresh mind as it was in the days of Thales.”

“According to Sir W. Thomson's theory of Vortex Atoms, the substance of which the molecule consists is a uniformly dense plenum, the properties of which are those of a perfect fluid, the molecule itself being nothing but a certain motion impressed on a portion of this fluid, and this motion is shewn, by a theorem due to Helmholtz, to be as indestructible as we believe a portion of matter to be.”

“According to Sir W. Thomson's theory of Vortex Atoms, the substance of which the molecule consists is a uniformly dense plenum, the properties of which are those of a perfect fluid, the molecule itself being nothing but a certain motion impressed on a portion of this fluid, and this motion is shewn, by a theorem due to Helmholtz, to be as indestructible as we believe a portion of matter to be.”

“That celebrated traveller Humboldt was profoundly impressed with the scientific value of a combined effort to be made by the observers of all nations, to obtain accurate measurements of the magnetism of the earth; and we owe it mainly to his enthusiasm for science... that not only private men of science, but the governments of most of the civilised nations... were induced to take part in the enterprise.”

“The properties of bodies were investigated by several distinguished French mathematicians on the hypothesis that they are systems of molecules in equilibrium. The somewhat unsatisfactory nature of the results... produced... a reaction in favour of the opposite method of treating bodies as if they were... continuous. This method, in the hands of Green, Stokes, and others, has led to results the value of which does not at all depend on what theory we adopt as to the ultimate constitution of bodies.”

“The properties of bodies were investigated by several distinguished French mathematicians on the hypothesis that they are systems of molecules in equilibrium. The somewhat unsatisfactory nature of the results... produced... a reaction in favour of the opposite method of treating bodies as if they were... continuous. This method, in the hands of Green, Stokes, and others, has led to results the value of which does not at all depend on what theory we adopt as to the ultimate constitution of bodies.”

“The experimental investigation by which Ampère established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of electricity.' It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.”

“It is to Gauss, to the Magnetic Union, and to magnetic observers in general, that we owe our deliverance from that absurd method of estimating forces by a variable standard which prevailed so long even among men of science. It was Gauss who first based the practical measurement of magnetic force (and therefore of every other force) on those long established principles, which, though they are embodied in every dynamical equation, have been so generally set aside, that these very equations, though correctly given... are usually explained... by assuming, in addition to the variable standard of force, a variable, and therefore illegal, standard of mass.”

“In a memoir presented to the Royal Society of Göttingen in 1858, but afterwards withdrawn, and only published in Poggendorff's Annalen in 1867, after the death of the author, Bernhard Riemann]deduces the phenomena of the induction of electric currents from a modified form of Poisson's equationfrac{mathrm{d^2}V}{mathrm{d}x^2} + frac{mathrm{d^2}V}{mathrm{d}y^2} + frac{mathrm{d^2}V}{mathrm{d}z^2} + 4 pi rho= frac{1}{a^2} frac{mathrm{d^2}V}{mathrm{d}t^2}where V is the electrostatic potential and a velocity. This equation is of the same form as those which express the propagation of waves and other disturbances in elastic media. The author, however, seems to avoid making explicit mention of any medium through which the propagation takes place. The mathematical investigation given by Riemann has been examined by Clausius, who does not admit the soundness of the mathematical processes, and shews that the hypothesis that potential is propogated like light does not lead either to the formula of Weber, or to the known laws of electrodynamics.”

“Pisarro explained the Neo-Impressionist theories to his dealer Durand-Ruel in a letter written towards the end of 1886. He stressed the importance of Seurat's role as inventor of the theory, and described the new function of colour, which replaced the mechanical mixtures of pigments with optical mixtures, where colours partially fused in the spectator's eye. The component parts of each optical colour mixture were to be painted in separate touches so that they retained their colour purity. When colours were mixed on the palette, they could only be combined with close neighbors on the colour circle, so as to avoid excessive dulling of the hues. Pissaro noted that the great colour theorists who had influenced Seurat's thinking were Chevreul, the Scott Maxwell, and the American Ogden Rood. Optical colour mixtures, they argued, were more luminous than mixed pigments.”

“The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...historians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown.”

“In order to appreciate the nature of Maxwell's contributions , let us recall how matters stood in his day. ...Faraday's law of induction ...states that a variable magnetic field generates an electric field. Maxwell, however, considered that this law, standing alone, lacked symmetry; so he formulated the hypothesis that conversely a variable electric field should generate a magnetic one, and proceeded to construct his theory... no experimental results could be claimed to have justified any such assumption... His celebrated equations of electromagnetics represented, therefore, the results of experiment, supplemented by this additional hypothetical assumption. The advisability of making this hypothesis was accentuated when it was found to ensure the law of conservation of electricity. ...In the particular case of free space in which only fields but no charges or currents are present, Maxwell's equations of electromagnetics, termed field-equations (since they describe the state of the electromagnetic field), can be written: {| style="margin-left: auto; margin-right: auto; border: none;" |- | (1) operatorname{div},mathbf{E} = 0 |  |   (3) operatorname{div},mathbf{H} = 0 |- | (2) operatorname{curl},mathbf{E} = -frac{1}{c} {dmathbf{H} over dt} |  |   (4) operatorname{curl},mathbf{H} = -frac{1}{c} {dmathbf{E} over dt} |} where E represents electric field intensity, H magnetic field density, t denotes time, and c a most important constant... (2) represents Faraday's law of induction, while (4) constitutes the hypothetical law postulated by Maxwell... Prior to Maxwell's investigations the fourth equation would have been written "curl H = 0"...From his field equations, Maxwell... was able to deduce the two additional ones: {| style="margin-left: auto; margin-right: auto; border: none;" |- | (5) bigtriangleup,mathbf{E} = frac{1}{c^2} {d^2mathbf{H} over dt^2} |  |   (6) bigtriangleup,mathbf{H} = frac{1}{c^2} {d^2mathbf{E} over dt^2} |} ...these last two equations connote that varying electric and magnetic intensities will be propagated through the ether in wave form with a velocity c... This discovery removed all possibility of action at a distance, since the field perturbations now appeared to be propagated from place to place with a finite velocity. It was... of interest to determine the precise value of c. ...Physicists ...were unable, in Maxwell's day, to devise a means of performing such delicate experiments. ...Maxwell remarked that it would be given by the ratio of the magnitude of any electric charge, measured in terms of electrostatic units (based on electricity), and then of electromagnetic units (based on magnetism). If two magnetic poles of equal strength, situated in empty space... one centimetre apart, attract or repel each other with a force of one dyne, either pole is said to represent one unit of magnetic pole strength in the electromagnetic system of units. Owing to the interconnections between magnetism and electricity, we can deduce therefrom the unit of electric charge also in the electromagnetic system. Likewise, if two electric charges of equal strength... in empty space at a distance of one centimetre apart, attract or repel each other with a force of one dyne, either charge is said to represent one unit of electric charge in the electrostatic system of units. From this we can derive the unit of magnetic pole strength in the electrostatic system. Precise measurements... then proved that the value of this ratio was about 186,000 miles per second; whence it became necessary to assume that periodic perturbations in the strains and stresses of the field would be propagated in the form of waves moving through the ether with this particular speed. But this velocity was precisely that of light waves propagated through the luminiferous ether.”

“The first clear sign of a breakdown in communication between physics and mathematics was the extraordinary lack of interest among mathematicians in James Clerk Maxwell's discovery of the laws of electromagnetism. Maxwell discovered his equations, which describe the behavior of electric and magnetic fields under the most general conditions, in the year 1861, and published a clear and definitive statement of them in 1865. This was the great event of nineteenth century physics, achieving for electricity and magnetism what Newton had achieved for gravitation two hundred years earlier. Maxwell's equations contained, among other things, the explanation of light as an electromagnetic phenomenon, and the basic principles of electric power transmission and radio technology. ...But in addition to their physical applications, Maxwell's equations had abstract mathematical qualities which were profoundly new and important. Maxwell's theory was formulated in terms of a new style of mathematical concept, a tensor field extending throughout space and time and obeying coupled partial differential equations of peculiar symmetry. ...If they had taken Maxwell's equations to heart as Euler took Newton's, they would have discovered, among other things, Einstein's theory of special relativity, the theory of topological groups and their linear representations, and probably large pieces of the theory of hyperbolic differential equations and functional analysis. A great part of twentieth century physics and mathematics could have been created in the nineteenth century, simply by exploring to the end the mathematical concepts to which Maxwell's equations naturally lead.”

“If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz. The lion's share in this revolution fell to Clerk Maxwell. He showed that the whole of what was then known about light and electro-magnetic phenomena was expressed in his well known double system of differential equations, in which the electric and magnetic fields appear as the dependent variables. Maxwell did, indeed try to explain, or justify, these equations by intellectual constructions. But... the equations alone appeared as the essential thing and the strength of the fields as the ultimate entities, not to be reduced to anything else.”

“'''From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.”

“What does distinguish Maxwell to a great degree is a strong intuition, rising at times to divination, which goes hand in hand with rich power of imagination. For the latter quality much evidence can be cited: his predilection for diagrams, his use of roll-curves [Rollkui'Ven], of stereoscopic figures, of reciprocal force-planes [Kraefteplaenen].”

“I want to talk about thought experiments and how they can work, and I want to do that by talking about my favorite example which is Maxwell's equations, the laws of electromagnetism. Again, these are more equations, but it's ok because they're on a T-shirt. So these laws govern the behavior of electric and magnetic fields, but actually, when Maxwell was a boy... there was a missing term. ...When Maxwell got into the field these were the equations, and they had been discovered experimentally, and I want to say a little bit about them. So this bit here is Gauss's lawnabla cdot mathbf{D} = rho_mathrm{v}it says that electric charges produce electric fields. This bit is Ampere's lawmathbf{nabla} times mathbf{H} = mathbf{J}it says that a electric currents produce magnetic fields. Faraday's lawnabla times mathbf{E} = -frac{partial mathbf{B}} {partial t}says that oscillating magnetic fields can also produce electric fields... These were discovered and confirmed by a tremendous amount of data. They were consistent with all known measurements/observations of electromagnetism in Maxwell's day, but there are a problem, and the problem was exposed by a thought experiment. The thought experiment is simply to consider a rapidly oscillating current with a break in the circuit, a capacitor... and the problem is that if you use those equations to calculate the magnetic field next to the capacitor you don't get definite answer, you get two different answers, depending on how you use the equations. So there is something wrong. Even without doing this experiment you know that there is something wrong with those equations, and from this clue and a lot more reasoning... Maxwell was able to figure out that he could fix this by adding one more term [to Ampere's law]...nabla times mathbf{H} = mathbf{J} +frac{partial mathbf{D}} {partial t}and with this the equations are mathematically and physically well posed. They give unambiguous answers to questions like the one I mentioned. Now, Maxwell got a huge bonus because... Faraday's law says that an oscillating magnetic field produces an electric field. Maxwell's new term says that an oscillating electric field produces a magnetic field. So each can produce the other, and so you can get a disturbance which is self-sustaining, and which doesn't just sustain... but moves... Faraday, Maxwell, Faraday, Maxwell... you get a self-sustaining disturbance which moves at a velocity that you get from the equations, and the velocity is the speed of light. So Maxwell got a huge bonus for understanding the unification of electricity and magnetism. He understood the nature of light! When I first heard about this in high school I thought this was the coolest thing, and I still do. It's what we're all trying to do.”

“One reason for the success of Maxwell's teaching texts, and those of Thomson and Tait, is that they were... expounding in clear and persuasive language the new understanding in basic physics that their authors had been responsible for developing... In a way, Maxwell's contributions to the great ninth edition of the Encyclopaedia Britannica were a natural development of his zeal for teaching. They covered Atom, Attraction, Capillary action, Constitution of bodies, Diagrams, Diffusion, Ether, Faraday, Harmonic analysis, and Physical sciences. ...Maxwell deserves to be remembered as one of the nineteenth century's notable pedagogues. ...His expertise was built upon understanding, enthusiasm, hard work, and experience.”

“In electromagnetism... the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as "singularities" in the field.”

“Maxwell's importance in the history of scientific thought is comparable to Einstein's (whom he inspired) and to Newton's (whose influence he curtailed)”

“In a famous memoir, Clerk Maxwell showed nearly a hundred years ago that Saturn's rings would be unstable if they were solid, and that they must consist of a swarm of separate bodies. In a system of particles rotating about a centre of gravitational attraction the innermost particles will rotate more rapidly than the outermost, in order to counteract the stronger gravitational pull towards the centre. In studying the problem of Galactic rotation we are almost entirely dependent on the determination of velocities in the line of sight, which can be measured spectroscopically by the Doppler effect. ...On the theory of Galactic rotation stars which are further from the centre than the sun will tend, in general, to move more slowly, i.e. relative to the sun they will lag behind, whereas stars nearer to the centre will race ahead.”

“Changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields. Thus the fields can animate one another in turn, giving birth to self-reproducing disturbances that travel at the speed of light. Ever since Maxwell, we understand that these disturbances are what light is.”

“[I]n the mid-19th century math seemed... useless for physicists pondering the complexities of molecular motions in gases. ...How could anyone grasp the inner workings of a mass of molecules too numerous to count and too small to be seen? Yet... Maxwell found a way, by using statistics—mathematical descriptions of large groups of molecules. ...Maxwell got the idea to use statistics in physics from social scientists applying math to society!”