⚛On Physics: On Electromagnetism (2010-)

"First, without a physical interpretation, a purely mathematical structure, here a Lie algebra, would have no empirical content. Second, if we interpret the Lie algebra in terms of physical structures, taking electromagnetic and weak currents as its representations, then we have physical content, but only at the phenomenological level. In order to understand the physical structures (the currents) properly, we have to move deeper onto the level of their constituents (hadrons or quarks) and their dynamics so that we can have a dynamic understanding of the behavior of the currents, and thus of many features of current algebra and of reasons why current algebra is so successful." (Tian Yu Cao,"From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism", 2010)

"The underlying idea of current algebra, light-cone current algebra included, was to exploit the broken symmetry of strong interactions. The idea was pursued through abstracting physical predictions, as the consequences of the symmetry and in the form of certain algebraic relations obeyed by weak and electromagnetic currents of hadrons to all orders in strong interactions, from some underlying mathematical field theoretical models of hadrons and their interactions, more specifically from models of quark fields universally coupled to a neutral gluon field." (Tian Yu Cao,"From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism", 2010)

"Rotations and translations are global symmetries: they apply uniformly across the whole of space and time. A rotation about some axis rotates every point in space through the same angle. Gauge symmetries are different: they are local symmetries, which can vary from point to point in space. In the case of electromagnetism, these local symmetries are changes of phase. A local oscillation of the electromagnetic field has both an amplitude (how big it is) and a phase (the time at which it reaches its peak)." (Ian Stewart, "Symmetry: A Very Short Introduction", 2013)

"The classical theories of space, time, and matter were brought to their peak in James Clerk Maxwell’s equations for electromagnetism. This elegant system of equations unified two of nature’s forces, previously thought to be distinct. In place of electricity and magnetism, there was a single electromagnetic field. A field pervades the whole of space, as if the universe were filled with some kind of invisible fluid. At each point of space we can measure the strength and direction of the field, as if that fluid were flowing in mathematical patterns. For some purposes the electromagnetic field can be split into two components, the electric field and the magnetic field. But a moving magnetic field creates an electric one, and conversely, so when it comes to dynamics, both fields must be combined into a single more complex one." (Ian Stewart, "Visions of Infinity", 2013)

"The invariance of physical laws with respect to position or orientation (i.e., the symmetry of space) gives rise to conservation laws for linear and angular momentum. Sometimes the implications of symmetry invariance are far more complicated or sophisticated than might at first be supposed; the invariance of the forces predicted by electromagnetic theory when measurements are made in observation frames moving uniformly at different speeds (inertial frames) was an important clue leading Einstein to the discovery of special relativity. With the advent of quantum mechanics, considerations of angular momentum and spin introduced new symmetry concepts into physics. These ideas have since catalyzed the modern development of particle theory." (George B Arfken et al, "Mathematical Methods for Physicists: A comprehensive guide", 2013)

"Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability - which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948." (Steven Weinberg, CERN Courier, [interview with Matthew Chalmers] 2017)

"Electromagnetism is the theory describing the interactions of electric and magnetic fields with matter based upon charges and currents. [...] Once delving a bit deeper into the theory of electromagnetism, it will become apparent that the use of tensors will help us significantly. In particular, when formulating Maxwell’s equations in the framework of special relativity, it will become clear that the electric and magnetic fields are different components of a rank two anti-symmetric tensor in four-dimensional space-time rather than vector fields in space that depend on time." (Mattias Blennow, "Mathematical Methods for Physics and Engineering", 2018)

"Euler’s formula - although deceptively simple - is actually staggeringly conceptually difficult to apprehend in its full glory, which is why so many mathematicians and scientists have failed to see its extraordinary scope, range, and ontology, so powerful and extensive as to render it the master equation of existence, from which the whole of mathematics and science can be derived, including general relativity, quantum mechanics, thermodynamics, electromagnetism and the strong and weak nuclear forces! It’s not called the God Equation for nothing. It is much more mysterious than any theistic God ever proposed." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

⚛On Physics: On Electromagnetism (2000-2009)

"For [...] small things, there must be something else. There is. We call it the electric interaction (more generally, the electromagnetic interaction), and it arises from an endowment of matter known as the electric charge. Standing still, an electrically charged particle throws up an electric potential to which other charged particles can respond.Electric or magnetic, charge gives rise to both. Whether we say 'electric potential' (because we perceive a charge to be at rest) or "magnetic potential" (because we perceive a charge to be in motion), the difference lies solely in our point of view. The source is one. From the world of mass we descend [...] into the world of charge, ready to see our most familiar surroundings in a new light. Let there be electric charge." (Michael Munowitz, "Knowing: The Nature of Physical Law", 2005)

"We divide math up into separate areas (analysis, mechanics, algebra, geometry, electromagnetism, number theory, quantum mechanics, etc.) to clarify the study of each part; but the equally valuable activity of integrating the components into a working whole is all too often neglected. Without it, the stated aim of ‘taking something apart to see how it ticks’ degenerates imperceptibly into ‘taking it apart to ensure it never ticks again’." (Miles Reid & Balazs Szendröi, "Geometry and Topology", 2005)

"In formal terms, the ground state energy (vacuum energy) of the electromagnetic quantum field is infinite. This causes mathematical trouble in quantum electrodynamics." Eberhard Zeidler, "Quantum Field Theory II: Quantum Electrodynamics", 2006)

"Topology is rooted in Maxwell’s theory on the electromagnetic field." (Eberhard Zeidler, "Quantum Field Theory I: Basics in Mathematics and Physics", 2006)

"In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But... these transformations do not leave Maxwell's equations invariant. Pondering this, the mathematicians Henri Poincaré and Hermann Minkowski were led to a new view of the symmetries of space and time, on a purely mathematical level. If they had described these symmetries in physical terms, they would have beaten Einstein to relativity, but they avoided physical speculations. They did understand that symmetries in the laws of electromagnetism do not affect space and time independently but mix them up. The mathematical scheme describing these intertwined changes is known as the Lorentz group, after the physicist, Hendrik Lorentz." (Ian Stewart, "Why Beauty Is Truth: The History of Symmetry", 2008)

"The abstractions of Einstein's curved space and time gave rise to analogies and pictures that played a new explanatory role. Space and time gave way to space-time, visible light was augmented by images across the rest of the electromagnetic spectrum, and we realise d that we could see back towards the apparent beginnings of time." (John D Barrow,"Cosmic Imagery: Key Images in the History of Science", 2008)

"There’s matter, like the electron; antimatter, like the positron; and then there are things that are neither matter nor antimatter. The most familiar example of something that is beyond substance is electromagnetic radiation. All electromagnetic radiation, from gamma rays through X-rays and ultra-violet to visible light, infra red, and radio waves, consists of photons of different energies. Matter and antimatter can cancel one another out, their annihilation leaving non-substance in the form of photons; if the conditions are right this sequence can happen in reverse where photons turn into pieces of matter and antimatter." (Frank Close, "Antimatter", 2009)

⚛On Physics: On Electromagnetism (1975-1999)

"Electromagnetic fields [...] are neither charged nor magnetized and thus cannot contribute to their own source. The general theory does reveal a new feature of electromagnetic fields... Since they have energy, they produce gravitational effects and thus affect the structure of space-time, which, in turn, means that an electromagnetic field can affect the motion of non-charged matter." (Nancy Nersessian, "Faraday to Einstein: Constructing Meaning in Scientific Theories", 1984)

"The [...] weak force [...] couples to both quarks and leptons, and is very short-ranged due to the large rest mass of the messenger quanta involved. Its effective strength is usually many orders of magnitude weaker than electromagnetism, and its action can cause particles to change identity, as when a neutron decays. Unlike the electromagnetic and strong forces, the weak force violates parity conservation." (Paul Davies, "Forces of Nature", 1986)

"If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. …in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg […] The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies] - so they all tend to converge, as desired." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"Strong, weak and electromagnetic interaction are evidently part of a grand unified theory. These temperatures are today quite inaccessible. They were achieved only in the earliest moments of the Big Bang. Since then, the universe has congealed, losing its symmetry." (Sheldon L Glashow, "The Charm of Physics", 1991)

"Einstein was thus faced with the following apparent problem. Either give up the principle of relativity, which appears to make physics possible by saying that the laws of physics are independent of where you measure them, as long as you are in a state of uniform motion; or give up Maxwell’s beautiful theory of electromagnetism and electromagnetic waves. In a truly revolutionary move, he chose to give up neither. [...] It is a testimony to his boldness and creativity not that he chose to throw out existing laws that clearly worked, but rather that he found a creative way to live within their framework. So creative, in fact, that it sounds nuts." (Lawrence M Krauss, "Fear of Physics: A Guide for the Perplexed", 1993)

"The problems associated with the initial singularity of the universe bring us to what is called the theory of everything. It is an all-encompassing theory that would completely explain me origin of the universe and everything in it. It would bring together general relativity and quantum mechanics, and explain everything there is to know about the elementary particles of the universe, and the four basic forces of nature (gravitational, electromagnetic, weak, and strong nuclear forces). Furthermore, it would explain the basic laws of nature and the fundamental constants of nature such as the speed of light and Planck's constant." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"The reason general relativity cannot be unified with electromagnetic theory seems to be related to its nonlinearity. To unify the two fields properly we have to construct a "quantized" version of relativity; in other words, we have to quantize it, and so far no one has." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

On Physics: On Electromagnetism (1925-1949)

"The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light – a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions." (A.A. Michelson, "Studies in Optics", 1927)

"The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma." (Arthur S Eddington, "Science and the Unseen World", 1929)

"Classical mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems, including the electromagnetic field in interaction with matter. The underlying ideas and the laws governing their application form a simple and elegant scheme, which one would be inclined to think could not be seriously modified without having all its attractive features spout. Nevertheless it has been found possible to set up a new scheme, called quantum mechanics, which is more suitable for the description of phenomena on the atomic scale and which is in some respects more elegant and satisfying than the classical scheme. This possibility is due to the changes which the new scheme involves being of a very profound character and not clashing with the features of the classical theory that make it so attractive, as a result of which all these features can be incorporated in the new scheme." (Paul Dirac, "The Principles of Quantum Mechanics", 1930)

"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. So far this transformation from the force to the potential, from the action at a distance to the field, is only a purely mathematical operation." (Willem de Sitter,"Kosmos", 1932)

"Two points should be specially emphasized in connection with the general theory of relativity. First, it is a purely physical theory, invented to explain empirical physical facts, especially the identity of gravitational and inertial mass, and to coordinate and harmonize different chapters of physical theory, especially mechanics and electromagnetic theory. It has nothing metaphysical about it. Its importance from a metaphysical or philosophical point of view is that it aids us to distinguish in the observed phenomena what is absolute, or due to the reality behind the phenomena, from what is relative, i.e. due to the observer.S econd, it is a pure generalization, or abstraction, like Newton's system of mechanics and law of gravitation. It contains no hypothesis, as contrasted with the atomic theory or the theory of quanta, which are based on hypothesis. It may be considered as the logical sequence and completion of Newton's Principia. The science of mechanics was founded by Archimedes, who had a clear conception of the relativity of motion, and may be called the first relativist. Galileo, who was inspired by the reading of the works of Archimedes, took the subject up where his great predecessor had left it. His fundamental discovery is the law of inertia, which is the backbone of Newton's classical system of mechanics, and retains the same central position in Einstein's relativistic system. Thus one continuous line of thought can be traced through the development of our insight into the mechanical processes of nature... characterized by the sequence [...] Archimedes, Galileo, Newton, Einstein." (Willem de Sitter, "The Astronomical Aspect of the Theory of Relativity", 1933)

"The electromagnetic field theory is, for the modern physicist, as real as the chair on which he sits." (Leopold Infeld, "The Evolution of Physics, Field and Ether", 1938)

"Faraday, Maxwell, Larmor and a great number of others tried to explain electromagnetic action on these lines, but all attempts failed, and it began to seem impossible that any properties of ether could explain the observed pattern of events." (James Jeans, "Physics and Philosophy", 1942)

"Then the theory of relativity came and explained the cause of the failure. Electric action requires time to travel from one point of space to another, the simplest instance of this being the finite speed of travel of light […] Thus electromagnetic action may be said to travel through space and time jointly. But by filling space and space alone [excluding time] with an ether, the pictorial representations had all supposed a clear-cut distinction between space and time." (James H Jeans, "Physics and Philosophy", 1942)

"It is as dangerous for people unaccustomed to handling words and unacquainted with their technique to tinker about with these heavily-charged nuclei of emotional power as it would be for me to burst into a laboratory and play about with a powerful electromagnet or other machine highly charged with electrical force." (Dorothy L Sayers, "Unpopular Opinions", 1946)

"In the development of electromagnetic theory, there has been a continual and significant trend, which in a way has set the pattern for the development of all of theoretical physics. This has been the trend away from the concept known as "action at a distance" toward the concept of field theory." (John C Slater & Nathaniel H Frank, "Electromagnetism", 1947)

"The first forces brought into mathematical formulation were gravitational forces, as seen in planetary motion. Next were elastic forces. Then followed electric and magnetic forces... Their [electric and magnetic forces] study was mostly a product of the nineteenth century. [...] electromagnetic forces are of a far wider application than was first supposed. It has become evident that, instead of being active only in electrostatic and electromagnetic applications such as the telegraph, dynamo, and radio, the forces between the nuclei and electrons of single atoms, the chemical forces between atoms and molecules, the forces of cohesion and elasticity holding solids together, are all of an electric nature. [...] electromagnetic theory [...] carries us rather far into the structure of matter [...] The equations underlying the theory, Maxwell's equations, are relatively simple, but not nearly so simple as Newton's Newton's laws of motion." (John C Slater & Nathaniel H Frank, "Electromagnetism", 1947)

"This fact, that all charges are integral multiples of a fundamental unit, is still one of the unexplained puzzles of fundamental physics. It does not in any way contradict electromagnetic theory, but it is not predicted by it, and until we have a more fundamental theory that explains it, we shall not feel that we really understand electromagnetic phenomena thoroughly. Presumably its explanation will not come until we understand quantum theory more thoroughly than we do at present." (John C Slater & Nathaniel H Frank, "Electromagnetism", 1947)

"Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about electromagnetism. In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

On Physics: On Electromagnetism (1950-1974)

"[...] even in a temporal description of nature given by a relational theory of time. However, a theory, like the special theory of relativity, that denies the existence of an infinitely fast causal chain, deprives the concept of absolute simultaneity of its physical meaning even within a single inertial system. [...]  But since the metrical concept of velocity presupposes that we know the meaning of a transit time and since such a time, in turn, depends on a prior criterion of clock synchronization or simultaneity, we must first formulate the limiting property of electromagnetic chains [the fastest causal chain] without using the concept of simultaneity of noncoincident events." (Adolf Grünbaum, "Logical and philosophical foundations of the special theory of relativity", American Journal of Physics 23, 1955)

"There is nothing in the world except empty curved space. Matter, charge, electromagnetism, and other fields are only manifestations of the curvature of space." (John A Wheeler, 1957)

"In essence, the curvature in space created by the electromagnetic field is the electromagnetic field; and this curvature can in principle be detected by purely geometric measurements." (Kip Thorne, "The Dynamics of Space-Time", 1963) 

"It requires a much higher degree of imagination to understand the electromagnetic field than to understand invisible angels. […] I speak of the E and B fields and wave my arms and you may imagine that I can see them […] [but] I cannot really make a picture that is even nearly like the true waves." (Richard Feynman, "The Feynman Lectures on Physics", 1964)

"Thermostatics, which even now is usually called thermodynamics, has an unfortunate history and a cancerous tradition. It arose in a chaos of metaphysical and indeed irrational controversy, the traces of which drip their poison even today. As compared with the older science of mechanics and the younger science of electromagnetism, its mathematical structure is meager. Though claims for its breadth of application are often extravagant, the examples from which its principles usually are inferred are most special, and extensive mathematical developments based on fundamental equations, such as typify mechanics and electromagnetism, are wanting. The logical standards acceptable in thermostatics fail to meet the criteria of other exact sciences [...]." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Let us consider, for a moment, the world as described by the physicist. It consists of a number of fundamental particles which, if shot through their own space, appear as waves, and are thus [...] of the same laminated structure as pearls or onions, and other wave forms called electromagnetic which it is convenient, by Occam’s razor, to consider as travelling through space with a standard velocity. All these appear bound by certain natural laws which indicate the form of their relationship." (G Spencer-Brown, "Laws of Form", 1969)

On Physics: On Electromagnetism (1900-1924)

"By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy (and statements concerning the form of the energy) alone." (Hermann Minkowski, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies", 1907)

"It would be very unsatisfactory if the new way of looking at the time-concept, which permits a Lorentz transformation, were to be confined to a single part of Physics." (Hermann Minkowski, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies", 1907)

"Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively." (Oliver Heaviside, "Electromagnetic Theory", 1912)

"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." (Hendrik Lorentz, "The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat", 1916)

"A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory." (Albert Einstein, "The Meaning of Relativity", 1922)

"Before the development of the theory of relativity it was known the principle of energy and momentum could be expressed in a differential form for the electromagnetic field. The four-dimensional formulation of these principles leads to an important conception, that of the energy tensor, which is important of the further development of the theory of relativity." (Albert Einstein, "The Meaning of Relativity", 1922)

"First, the physicists in the persons of Faraday and Maxwell, proposed the 'electromagnetic field' in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematicians, […] secretly undermined belief in the evidence of Euclidean Geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope and entailing a deeper vision. This revolution was promoted essentially by the thought of one man, Albert Einstein." (Hermann Weyl," Space, Time, Matter", 1922)

"When Faraday filled space with quivering lines of force, he was bringing mathematics into electricity. When Maxwell stated his famous laws about the electromagnetic field it was mathematics. The relativity theory of Einstein which makes gravity a fiction, and reduces the mechanics of the universe to geometry, is mathematical research." (James B Shaw, "The Spirit of Research", The Monist No. 4, 1922)

On Physics: On Electromagnetism (-1899)

"My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force [...] I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards. From the determination by Kohlrausch and Weber of the numerical relation between the statical and magnetic effects of electricity, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations." (James C Maxwell, [Letter to Michael Faraday] 1861) 

"The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit. This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws." (James C Maxwell, "A Dynamical Theory of the Electromagnetic Field", 1865)

"The theory I propose may therefore be called a theory of the Electromagnetic Field because it has to do with the space in the neighbourhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in the space there is matter in motion, by which the observed electromagnetic phenomena are produced." (James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field", 1865)

"What, then, is light according to the electromagnetic theory? It consists of alternate and opposite rapidly recurring transverse magnetic disturbances, accompanied with electric displacements, the direction of the electric displacement being at the right angles to the magnetic disturbance, and both at right angles to the direction of the ray." (James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field", 1865)

"Faraday is, and must always remain, the father of that enlarged science of electromagnetism." (James C Maxwell, "Faraday", Nature, 1873)

"The experimental investigation by which Ampere 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." (James C Maxwell, "A Treatise on Electricity and Magnetism", 1873)

"One of the chief peculiarities of this treatise is the doctrine that the true electric current, on which the electromagnetic phenomena depend, is not the same thing as the current of conduction, but that the time-variation of the electric displacement must [also] be taken into account [...]" (James C Maxwell, "A Treatise on Electricity and Magnetism" 1881)

"This maze of symbols, electric and magnetic potential, vector potential, electric force, current, displacement, magnetic force, and induction, have been practically reduced to two, electric and magnetic force." (George F Fitzgerald, The Electrician, [bookmreview] 1893)