Physicists From Scotland

"Maxwell's equations have had a greater impact on human history than any ten presidents."

"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."

"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 law\nabla \cdot \mathbf{D} = \rho_\mathrm{v}it says that electric charges produce electric fields. This bit is Ampere's law\mathbf{\nabla} \times \mathbf{H} = \mathbf{J}it says that a electric currents produce magnetic fields. Faraday's law\nabla \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 . The thought experiment is simply to consider a rapidly oscillating current with a break in the circuit, a ... 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."

"He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yesterday's work, lest he fall into despair; nor to-morrow's, lest he become a visionary—not that which ends with the day, which is a worldly work; nor yet that only which remains to eternity, for by it he cannot shape his actions. Happy is the man who can recognise in the work of to-day a connected portion of the work of life and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises because the present is given him for a possession. Thus ought Man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible; nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it."

"He achieved greatness unequalled."

"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]."

"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."

"The work of James Clerk Maxwell changed the world forever."

"The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field."

"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."

"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 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 s 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."

"In the study of electricity and magnetism we may consider phenomena in which conditions do not vary as time passes by; the electric charges and the magnets remain at rest, and the currents flowing in fixed wires do not vary in intensity. Conditions are then termed stationary [static]; it is as though time played no part. The laws which govern this type of phenomena were discovered empirically over a century ago, and were expressed mathematically in terms of spatial vectors. The problem of ascertaining how electric and magnetic phenomena would behave when conditions ceased to be stationary was one that could not be predicted; further experimental research was necessary before the general laws could be obtained. Even so, the difficulties were considerable, and it needed Maxwell's genius to establish the laws from the incomplete array of experimental evidence then at hand. All this work extended over nearly a century; it was slow and laborious. Yet, had men realised that our world was one of four-dimensional Minkowskian space-time, and not one of separate space and time, things would have been different. By extending the well-known stationary laws to four-dimensional space-time, through the mere addition of time components to the various trios of space ones, we should have written out inadvertently the laws governing varying fields, or, in other words, we should have constructed Maxwell's celebrated equations. Electromagnetic induction, discovered experimentally by Faraday, the additional electrical term introduced tentatively by Maxwell, radio waves, everything in the electromagnetics of the field, could have been foreseen at one stroke of the pen. A century of painstaking effort could have been saved. We are assuming that a four-dimensional vector calculus would have been in existence; but this is purely a mathematical question."

"In order to appreciate the nature of Maxwell's contributions , let us recall how matters stood in his day. ... ...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:"

"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."

"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."

"But listen, what harmony holy Is mingling its notes with our own! The discord is vanishing slowly, And melts in that dominant tone. And they that have heard it can never Return to confusion again, Their voices are music for ever, And join in the mystical strain."