Electromagnetism

"The subject of electric oscillation announced in a remarkable paper of Henry in 1842 and threshed out in its main features by Kelvin in 1856, followed by Kirchhoff's treatment of the transmission of oscillations along a wire (1857), has become of discriminating importance between Maxwell's theory of the electric field and the other equally profound theories of an earlier date. These crucial experiments contributed by Hertz (1887, et seq.) showed that electromagnetic waves move with the velocity of light, and like it are capable of being reflected, refracted, brought to interference and polarized. A year later Hertz (1888) worked out the distribution of the vectors in the space surrounding the oscillatory source. ...Some doubt was thrown on the details of Hertz's results by Sarasin and de la Rive's phenomenon of multiple resonance (1890), but this was soon explained away as the necessary result of the occurrence of damped oscillations by Poincaré (1891), by Bjerknes (1891) and others."

"Maxwell in particular noted that the phenomena of electromagnetism did not fit into the scheme of Newtonian mechanics. Whereas it had been thought that only the distance between two objects determined the force one exerted on the other, electric charges in motion, such as are met with in electric currents, were found to produce effects not encountered when charges are at rest. Celestial bodies will only attract each other; electric charges at rest will either attract or repel... they will exert forces only in the direction of the connecting straight line. Oersted discovered that an electric current (...charges in motion) will exert a force on a magnetic needle at right angles to the connecting straight line. Previous observations in astronomy had tended to show that the force between two bodies depended only on their instantaneous configuration, but Hertz showed by experiment that electromagnetic disturbances propagate as waves, at a finite rate of speed. Hence the force experienced by one body can be understood and explained only in terms of the history of the other."

"Maxwell succeeded in casting all known electromagnetic effects into a mathematical form that has endured to this day... known as Maxwell's field equations. Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space ('). Faraday and Maxwell regarded the effect on an electrically charged body as giving rise to stresses in its immediate surroundings. These in turn produce stresses in ever widening circles, gradually diminishing... These stresses... thought of as capable of existence in otherwise empty space, are called fields... intermediaries between material particles and which assume the burden of Newton's action at a distance."

"Faraday was the first scientist to realise the enormous importance of the electromagnetic field. He saw in it a reality of a new category differing from matter. It was capable of transmitting effects from place to place, and was not to be likened to a mere mathematical fiction such as the gravitational field was then assumed to be. In his opinion, the phenomena of electricity and magnetism should be approached via the field rather than via the charged bodies and currents. In other words, according to Faraday, when a current was flowing along a wire, the most important aspect of the phenomenon lay not in the current itself but in the fields of electric and magnetic force distributed throughout space in the current's vicinity. It is this elevation of the field to a position of preeminence that is often called the pure physics of the field. Faraday was not a mathematician and was unable to co-ordinate the phenomena he foresaw in a mathematical way, and derive the full benefit from his ideas. Before dying, however, he entrusted this task to his colleague Maxwell; and one of the most astonishing theories of science, eclipsed only in recent years by Einstein's theory of relativity, was the outcome."

"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:"

"The... weak force... couples to both s and s, 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."

"Classical mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems, including the 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."

"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."

"After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the bases of experience or according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the stand-point of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest."

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

"How can s be produced in the center of the sun and how can they be detected in laboratories here on earth if they are subject neither to the nor to the electromagnetic one? Another force, the so-called weak force, is responsible. The does participate in that interaction, along with the electron."

"The color gauge theory postulates the existence of eight massless particles, sometimes called s, that are the carriers of the just as the photon is the carrier of the electromagnetic force."

"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."

"There are many, many "why" questions. Also a number of 'how' questions. What is the mechanism that causes the weak interactions to be weak and the electromagnetic interactions not weak?"

"In 1933 Enrico Fermi suggested that beta radioactivity, and the manner in which the neutron spontaneously decayed, could be described using a formalsm similar to that developed by Dirac for the electromagnetic force, but 10-10 times weaker. With its range of only about 1/1,000th the diameter of the nucleus, it could not play a role in binding the nucleus, but it could affect individual s. The fact that the metastable particles exhibited the same characteristic time of 10-10 second indicated that this weak force acted on many types of particles. ...a 'characteristic time' ...being the time for an interaction across a nucleus 3 fm in diameter; an event taking place in a shorter time [than 10-23 seconds for the strong force] has 'no meaning'. ...For electromagnetic interactions, the strength is 10-3 of the strong force, and so the characteristic time is longer (10-20 [seconds]); this is roughly the time for a photon to cross an atom."

"Returning to electromagnetic waves. Maxwell's inimitable theory of displacement was for long generally regarded as a speculation. There was, for many years, an almost complete dearth of interest in the unverified parts of Maxwell's theory. Prof. Fitzgerald... was the most prominent of the very few materialists... who appeared to have a solid faith in the electromagnetic theory of the ether; thinking about it and endeavouring to arrive at an idea of the nature of diverging electromagnetic waves, and how to produce them, and to calculate the loss of energy by radiation. An important step was then made by Poynting, establishing the formula for the flow of energy. Still, however, the theory wanted experimental proof. Three years ago electromagnetic waves were nowhere. Shortly after, they were everywhere. This was due to a very remarkable and unexpected event, no less than the experimental discovery by Hertz... of the veritable actuality of electromagnetic waves in the ether. And it never rains but it pours; for whilst Hertz with his resonating circuit was working in Germany... Lodge was doing in some respects similar work in England, in connection with the theory of lightning conductors. These researches, followed by the numerous others of Fitzgerald and Trouton, J. J. Thomson, &c., have dealt a death blow to the electrodynamic speculations of the Weber-Clausius type (to mention only the first and one of the last) and have given to Maxwell's theory just what was wanted in its higher parts, more experimental basis. The interest excited has been immense, and the theorist can now write about electromagnetic waves without incurring the reproach that he is working out a mere paper theory."

"Newton's system was for a long time considered as final and the task... seemed simply to be an expansion.... The first difficulty arose in the discussion of the electromagnetic field in... Faraday and Maxwell. In Newtonian mechanics the gravitational force had been considered as given... In the work of Faraday and Maxwell... the field of force... became the object of the investigation... they tried to set up equations of motion for the fields, not primarily for the bodies... This change led back to a point of view...held... before Newton. An action could... be transferred... only when the two bodies touched... Newton had introduce a very new and strange hypothesis by assuming a force that acted over a long distance. Now in the theory of fields... action is transferred from one point to a neighboring point... in terms of differential equations. ...the description of the s... by Maxwell's equations seemed a satisfactory solution of the problem of force. ...The axioms and definitions of Newton had referred to bodies and their motion; but with Maxwell the fields... seemed to have acquired the same degree of reality as the bodies in Newton's theory. This view... was not easily accepted.; and to avoid such a change in the concept of reality... many physicists believed that Maxwell's equations actually referred to the deformations of an elastic medium... the ether... the medium was so light and thin that it could penetrate into other matter and could not be seen or felt. ...[H]owever ...it could not explain the complete absence of any longitudinal light waves."

"The third closed system of concepts and axioms has its origin in the phenomena of electricity and magnetism and has reached its final form in the first decade of the twentieth century through the work of Lorentz, Einstein and Minkowski. It comprises electrodynamics, special relativity, optics, magnetism, and one may include the de Broglie theory of matter waves of all different sorts of elementary particles, but not the wave theory of Schrodinger."

"In the autumn of 1878 [Heinrich Hertz] came to Berlin and it was as an university student there in the physical laboratory under my control that I first made his acquaintance. ...In Germany at that time the laws of electromagnetics were deduced by most physicists from the hypothesis of W. Weber, who sought to trace back electric and magnetic phenomena to a modification of Newton's assumption of direct forces acting at a distance and in a straight line. With increasing distance these forces diminish in accordance with the same laws as those assigned by Newton to the force of gravitation, and held by Coulomb to apply to the action between pairs of electrified particles. The force was directly proportional to the product of the two quantities of electricity, and inversely proportional to the square of their distance apart; like quantities produced repulsion, unlike quantities attraction. Furthermore, in Weber's hypothesis it was assumed that this force was propagated through infinite space instantaneously, and with infinite velocity. The only difference between the views of W. Weber and of Coulomb consisted in this—that Weber assumed that the magnitude of the force between the two quantities of electricity might be affected by the velocity with which the two quantities approached towards or receded from one another, and also by the acceleration of such velocity. Side by side with Weber's theory there existed a number of others, all of which... regarded the magnitude of the force expressed by Coulomb's law as being modified by the influence of some component of the velocity... Such theories were advanced by F. E. Neumann, by his son C. Neumann, by Riemann, Grassmann, and subsequently by Clausius. Magnetised molecules were regarded as the axes of circular electric currents, in accordance with an analogy between their external effects previously discovered by Ampère. This plentiful crop of hypotheses had become very unmanageable, and in dealing with them it was necessary to go through complicated calculations, resolutions of forces into their components in various directions, and so on. So at that time the domain of electromagnetics had become a pathless wilderness. Observed facts and deductions from exceedingly doubtful theories were inextricably mixed up together. With the object of clearing up this confusion I had set myself the task of surveying the region of electromagnetics, and of working out the distinctive consequences of the various theories, in order, wherever... possible, to decide between them by suitable experiments."

"It's of no use whatsoever. This is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there."

"It is electromagnetism... in all its many forms, that has been so basic, that haunts us and guides us [in the development of transistor electronics]."

"An electric field can be described by four field quantities ... The electric field intensity \overrightarrow{E} is the vector field used in electrostatics when charge is at rest in free space and is defined as the electric force on a test charge. The electric displacement vector \overrightarrow{D} (also called the electric flux density or displacement flux) is a vector field used in studying the electric fields inside material objects. Similarly, magnetic field intensity \overrightarrow{H} is a vector needed in discussing magnetic phenomena, that is the field generated at a point in free space by steady or time-varying electric currents in a source; it is related to the magnetic force acting on a moving charge. The magnetic flux density \overrightarrow{B} is useful in the investigation of the magnetic fields within material objects where the material modifies the field intensity."

"Einstein['s] 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. ..."

"Velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of 'MM'. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

"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."

"That light is not itself a substance may be proved from the phenomenon of interference. A beam of light from a single source is divided by certain optical methods into two parts, and these, after travelling by different paths, are made to reunite and fall upon a screen. If either half of the beam is stopped, the other falls on the screen and illuminates it, but if both are allowed to pass, the screen in certain places becomes dark, and thus shows that the two portions of light have destroyed each other. Now, we cannot suppose that two bodies when put together can annihilate each other; therefore light cannot be a substance. ... What we have proved is that one portion of light can be the exact opposite of another portion... Such quantities are the measures, not of substances, but always of processes taking place in a substance. We therefore conclude that light is... a process going on in a substance... so that when the two portions [of light] are combined no process goes on at all. ...the light is extinguished when the difference of the length of the paths is an odd multiple of... a half wave-length. ...we see on the screen a set of fringes consisting of dark lines at equal intervals, with bright bands of graduated intensity between them. ...if the two rays are polarized ...when the two planes of polarization are parallel the phenomena of interference appear as above ...As the plane turns ...light bands become less distinct ...at right angles ...illumination of the screen becomes uniform, and no trace of interference can be discovered. ...The process may, however, be an electromagnetic one ...the electric displacement and the magnetic disturbance are perpendicular to each other, either ...supposed to be in the plane of polarization."

"In a memoir... in 1858... published in... 1867, after the death of the author, Bernhard Riemann deduces the phenomena of the induction of electric currents from a modified form of \frac{\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."

"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."

"[T]he work of a number of theoretical physicists in the 1960s culminated in the electroweak theory that is designed to unify electromagnetism and the weak force... This theory is sometimes called the 'GWS Theory', from... Sheldon Glashow, Steven Weinberg and Abdus Salam... The main feature of the theory is that at extremely high temperatures the electromagnetic and weak forces are two components of a single force, the electroweak force. The symmetry between the two forces would only be apparent at temperatures of trillions of degrees... in the Big Bang. At lower temperatures... electromagnetism remains a long range force, but the weak force takes on the characteristics of... a very weak force that acts over extremely short distances. ...But the theory is dependent on the existence of the Higgs particle..."

"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 . Standing still, an electrically charged particle throws up an 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 "" (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."

"In this corner, static electricity: the spark... In that corner, magnetism: the trusty realignment of the compass needle. Two different forces? No. The difference is only superficial, because both interactions arise from a single source, the electric charge. An electrostatic field comes about from charges at rest, and the magnetic field comes about from charges in motion. And since motion and rest are merely matters of opinion, who is to say which is which?"

"[W]hat shall we say, then, to a nuclear event such as... beta decay... in which a neutron turns into a proton and also shoots out an electron together with an antineutrino? ...Coming from within... is the weak interaction. Not in all nuclei, but certainly in many... the weak interaction sometimes subverts the neutrons and protons bound otherwise so strongly. It takes only a change in flavor. The weak force, with the weak interaction charges as the source, transforms a into an and hence a into a . At the same time, an electron and antineutrino spring loose... The strong force plays no part here, since neither the electron nor the antineutrino carries a strong interaction charge. Electrically neutral, the antineutrino escapes the electromagnetic force as well. ...the weak force ...allows a neutron to decay into a proton, electron, and antineutrino. The four particles all carry weak interaction charges, and their common endowment makes them all actors in a single play."

"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."

"Weyl considered an aspect about general relativity... the nonpreservation of direction in a curved space. ...[He] decided to consider the possibility that length was also not preserved. ...To effect this change mathematically, Weyl had to make a slight modification in the structure of general relativity. He assumed that in addition to the usual metric (set of numbers or variables) that described the gravitational field, there was another one related to length. ...amazingly when the result was analyzed Maxwell's equations mysteriously appeared. It almost seemed as if a bit of magic had occurred and scientists quickly became interested in the miracle. ...but with detailed analysis the theory was shown to be flawed. Einstein was the first to put his finger on the flaw. ...Weyl soon acknowledged the flaw and laid his theory to rest. It may have been a failure (actually it was not an entire failure; a similar idea is used today in modern field theory), but it did accomplish something important: it got people interested in the possibility that the electromagnetic and gravitational field could be unified. Einstein soon began working on an alternative theory, as did others."

"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 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."

"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."

"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, , 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 ."

"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."

"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."

"[T]here does not seem to be definite experimental evidence to indicate that the electronic mass is entirely electromagnetic."

"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 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."

"One of the things that excited me so much about quantum chromodynamics, after the work of Gross and Wilczek and Politzer, was that it seemed to provide a rational explanation for what had always been mysterious to me — the fact that there were symmetries, like parity conservation, charge conjugation invariance, and strangeness conservation, that were very good symmetries of the strong and electromagnetic interactions — as far as we knew exact — and yet were not respected by the weak interactions. Why should nature have ... symmetries that are symmetries of part of nature but not other parts of nature?"

"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."

"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 . 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."

"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."