In contemplating the papersEinstein wrote in 1905, I often find myself wondering which of them is the most beautiful. ...My favorite ...is Einstein’s paper on the blackbody radiation. ...Einstein did not try to derive the Wien law. He simply accepted it as an empirical fact and asked what it meant. By a virtuoso bit of reasoning involving statistical mechanics (of which he was a master, having independently invented the subject over a three-year period beginning in 1902), he was able to show that... the radiation in the cavity was mathematically the same as that of a dilute gas of particles. As far as Einstein was concerned, this meant that this radiation was a dilute gas of particles—light quanta. ...He realized that if the energetic light quanta were to bombard, say, a metal surface, they would give up their energies in lump sums and thereby liberate electrons from the surface in a predictable way, something that is called the photoelectric effect. ...not many physicists were even interested in the subject of blackbody radiation ...Planck, who was interested, decided that Einstein’s paper was simply wrong.
If quantum mechanics is right, there is no way to get around the uncertainty principle. The reason that the electron’s probability wave spread so much after we confined it, Heisenberg would argue, is that its momentum became almost completely indeterminate. In a manner of speaking, it headed off in all directions.
Electrons and suchlike entities simply are, indeed they have always (or at least for eons) been, and they eventually made themselves known in the laboratory. It is nowadays fashionable to talk of non-human beings as though they act rather like people. The contemporary realist... might... find poetically congenial the evocative image of an electron as a tangible presence in the late nineteenth century laboratory, where, it might be said, they first learned to speak—or where, perhaps, they were no longer silenced.
Jed Z. Buchwald, Andrew Warwick (ed.), Histories of the Electron: The Birth of Microphysics (2004)
The power of the new quantum mechanics in giving us a better understanding of events on an atomic scale is becoming increasingly evident. The structure of the helium atom, the existence of half-quantum numbers in band spectra, the continuous spatial distribution of photo-electrons, and the phenomenon of radioactive disintegration, to mention only a few examples, are achievements of the new theory which had baffled the old.
Maxwell's equations had proved themselves incapable of accounting for dispersion. It appeared necessary to conceive of some structure for dielectrics which would act selectively, imposing different degrees of retardation on light waves of different frequencies. Lorentz achieved this result by assuming that electricity was atomic and that matter was constituted by more or less complicated groupings of these electric atoms or electrons.
Phenomena were accounted for by taking into consideration the frictional resistances that would interfere with rapid vibrations of the electrons. When these frictional resistances were weak, oscillatory disturbances, such as rays of light, could be propogated through the dielectric, which was then termed transparent (glass). When these frictional forces were considerable, the light ray was unable to set the electrons into vibration; its energy was consumed in the attempt, and as a result it could not proceed; the dielectric was then opaque (ebonite, sulphur).
In the case of conductors such as metals, the electrons were assumed to be very loosely held to their atoms so that the slightest difference of potential would tear them away and cause them to rush in the same direction, thereby producing an electric current. It was precisely because electrons in conductors were not tied down to fixed positions by elastic forces that they were incapable of vibrating; and so conductors were necessarily opaque to electromagnetic vibrations or to light. Conversely, it was because the electrons were all tied down to fixed positions in the dielectrics, that they could not rush along in one direction. As a result dielectrics were opaque to currents, and hence were non-conductors. According to these views of Lorentz, an electric current passing through matter was nothing but a rush of electrons.
The most precise experiments have proved the correctness of the Einsteinian laws of mechanics and...Bucherer's experiment proving the increase in mass of an electron in rapid motion is a case in point.
Very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of the electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein's theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation of Fitzgerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein's theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves.
One possibility in this direction is to regard, classically, an electron as the end of a single Faradayline of force. The electric field in this picture from discrete Faraday lines of force, which are to be treated as physical things, like strings. One has then to develop a dynamics for such a string like structure, and quantize it.... In such a theory a bare electron would be inconceivable, since one cannot imagine the end of a piece of string without having the string.
Matter in quantum mechanics is not an inert substance but an active agent, constantly making choices between alternative possibilities according to probabilistic laws. ...It appears that mind, as manifested by the capacity to make choices, is to some extent inherent in every electron. ...Our brains appear to be devices for the amplification of the mental component of the quantum choices made by molecules inside our heads. ...There is evidence from peculiar features of the laws of nature that the universe as a whole is hospitable to the growth of mind. ...an extension of the Anthropic Principle up to a universal scale.
In physics we have outgrown archer and apple-pie definitions of the fundamental symbols. To a request to explain what an electron really is supposed to be we can only answer, "It is part of the ABC of physics".
The external world of physics has thus become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. ...that physical science is concerned with a world of shadows is one of the most significant of recent advances.
If to-day you ask a physicist what he has finally made out the æther or the electron to be, the answer will not be a description in terms of billiard balls or fly-wheels or anything concrete; he will point instead to a number of symbols and a set of mathematical equations which they satisfy. What do the symbols stand for? The mysterious reply is given that physics is indifferent to that; it has no means of probing beneath the symbolism. To understand the phenomena of the physical world it is necessary to know the equations which the symbols obey but not the nature of that which is being symbolised. ...this newer outlook has modified the challenge from the material to the spiritual world.
What quantum mechanics tells us, I believe, is surprising to say the least. It tells us that the basic components of objects – the particles, electrons, quarks etc. – cannot be thought of as "self-existent". The reality that they, and hence all objects, are components of is merely "empirical reality".
Bernard d'Espagnat, "Quantum weirdness: What we call 'reality' is just a state of mind", Guardian (20 March 2009)
Several of Thomson’s colleagues thought he was joking when he argued that the electron was smaller than the atom and was a constituent of every atom; to many scientists, the idea that there could exist matter smaller than the atom was inconceivable. Yet he was proved right.
Graham Farmelo, in The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (2009)
We have learned a lot from experience about how to handle some of the ways we fool ourselves. One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a little bit off because he had the incorrect value for the viscosity of air. It's interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan's, and the next one's a little bit bigger than that, and the next one's a little bit bigger than that, until finally they settle down to a number which is higher.
Why didn't they discover the new number was higher right away? It's a thing that scientists are ashamed of—this history—because it's apparent that people did things like this: When they got a number that was too high above Millikan's, they thought something must be wrong—and they would look for and find a reason why something might be wrong. When they got a number close to Millikan's value they didn't look so hard. And so they eliminated the numbers that were too far off, and did other things like that...
Richard Feynman, "Cargo Cult Science" (1974 California Institute of Technology commencement address)
And, just like it should in all stories about philosophers, it ended up in complete chaos. In all their previous discussions they hadn't even asked themselves whether such a simple object as a brick, much less an electron, is an "essential object."
It must have been one evening after midnight when I suddenly remembered my conversation with Einstein and particularly his statement, "It is the theory which decides what we can observe." I was immediately convinced that the key to the gate that had been closed for so long must be sought right here. ...We had always said so glibly that the path of the electron in the cloud chamber could be observed. But perhaps what we really observed was something much less. Perhaps we merely saw a series of discrete and ill-defined spots through which the electron had passed. ...The right question should therefore be: Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties?
A brief calculation after my return to the Institute showed that one could indeed represent such situations mathematically, and that the approximations are governed by what would later be called the uncertainty principle of quantum mechanics: the product of the uncertainties in the measured values of the position and momentum (i.e., the product of mass and velocity) cannot be smaller than Planck's constant. This formulation, I felt, established the much-needed bridge between the cloud chamber observations and the mathematics of quantum mechanics. True, it had still to be proved that any experiment whatsoever was bound to set up situations satisfying the uncertainty principle, but this struck me as plausible a priori, since the processes involved in the experiment or the observation had necessarily to satisfy the laws of quantum mechanics. On this presupposition, experiments are unlikely to produce situations that do not accord with quantum mechanics. "It is the theory which decides what we can observe." I resolved to prove this by calculations based on simple experiments during the next few days.
Clearly, if electric action is to be explained in mechanical terms, the mechanism must be supposed to be attached to the electric charges, and to move through space with them. It must extend through the whole of space, because the attraction and repulsion of an electron extend through the whole of space, and it must be the same for all directions in space. Further, as the pattern of events is unaltered by motion, the mechanism must be the same when the electron is in motion as when it is at rest. But experiment shows that an electron in motion exerts additional forces which are not the same for all directions in space; if we picture this electron as moving head-foremost through space, these forces surround it like a belt around its waist.
Thus direct experimental evidence shows that the forces exerted by an electron (or... any charged body) can neither be attributed to any mechanism attached to the body, nor through action transmitted through an ether or any medium surrounding the body. We have a perfect specification of the pattern of events written... in the language of mathematics, but this does not admit of interpretation in mechanical terms, or indeed in any terms other than those of mathematics.
If we wish to visualize... processes pictorially, no single picture is available, and the best we can do is to construct a number of imperfect pictures, each representing one, but only one, aspect of the complete set of phenomena. For instance, if a shower of electrons is shot on to a zinc sulfide screen, a number of flashes are produced—one for each electron—and we may picture the electrons as bullet-like projectiles hitting a target. But if the same shower is made to pass near a suspended magnet, this is found to be deflected as the electrons go by. The electrons may now be pictured as octopus-like structures with tentacles or 'tubes of force' sticking out from it in every direction.
It would, however, be wrong to think of an electron as a bullet-like structure with tentacles sticking out from its surface. We can calculate the mass of the bullet, and also the mass of the tentacles. The two masses are found to be identical, each agreeing with the known mass of the electron. Thus we cannot take the electron to be bullet plus tentacles... we must take it to be bullet or tentacles. The two pictures do not depict two different parts of the electron, but two different aspects of the electron. They are not additive but alternative; as one comes into play, the other must disappear.
Actually the situation is even more complicated, since a separate tentacle picture is needed for each speed of motion of the electron, the speed being measured relative to the suspended magnet or other object on which the moving electron is to act. ...When the electron is at rest, the tentacles stick out equally in all directions. But an electron which is at rest relative to one magnet may be in motion relative to another, and to discuss the action of the electron on this second magnet we must picture it as having a belt of tentacles round its waist. This shows that we must have a different picture for every speed of relative motion, so that the total number of pictures is infinite, and we cannot form the picture we need unless we know the speed of the electron relative to the object it is about to meet.
It is clear... that the electrons—those minute particles whose size is to that of a bacillus as the size of a bacillus is to, say, the whole earth, and whose properties we may yet measure with the greatest precision— that these electrons are one of the most important foundations of our whole world structure.
Today we know that on the sub-atomic level the fate of an electron or a whole atom is not determined by its past. But this discovery has not led to any basically new departure in the philosophy of nature, only to a state of bewildered embarrassment, a further retreat of physics into a language of even more abstract symbolism. Yet if causality has broken down and events are not rigidly governed by the pushes and pressures of the past, may they not be influenced in some manner by the "pull" of the future—which is a manner of saying that "purpose" may be a concrete physical factor in the evolution of the universe, both on the organic and unorganic levels. In the relativistic cosmos, gravitation is a result of the curvature and creases in space which continually tend to straighten themselves out—which, as Whittaker remarked, "is a statement so completely teleological that it certainly would have delighted the hearts of the schoolmen."
In the Easter holidays of 1881 Helmholtz went to London with his wife at the invitation of the Chemical Society to give a Lecture in the place 'in which the great investigator Faraday, whose memory was to be honoured, had so often surprised his admiring audience by his revelations of the unsuspected secrets of nature.'
His discourse on 'The Recent Development of Faraday's Ideas on Electricity' ranks from its form and content among the most beautiful and profound of his Addresses. ...Commencing with an historical review of the development of Electrodynamics, which culminated in a brilliant exposition of the Faraday-Maxwell Theory, he for the first time gave a connected account of the relation between electrical and chemical forces... To arrive at an understanding of the relations between electrical forces and chemical affinity, he shows from the phenomena of electrolytic dissociation how we are to picture the ponderable atoms as bound up with electricity. He concludes from the assumption that ions are charged with electricity, that a wandering group of atoms invariably carries the same charge of electricity with it, and that electricity itself is composed of definite elementary particles which behave like the atoms of electricity.
According to the view... on the Continent, matter... included electrical corpuscles in instantaneous interaction. This approach... goes back to André-Marie Ampère and Ottaviano Mossotti in the 1830s, and can be found in a rudimentary form as early as 1759, in... Franz Æpinus. Later in the nineteenth century it was greatly developed by several German physicists, including Rudolf Clausius, Wilhelm Weber, and Karl-Friedrich Zöllner. In these theories, hypothetical electrical particles were considered to be the fundamental constituents of both matter and ether. ...with the increasing popularity of Maxwellianfield theory (where electrical particles have no place), the theories were given up by most physicists. ...
In 1874 Stoney proposed the "electrine" as a unit electrical charge, and in 1891 he introduced the "electron" as a measure of an atomic unit charge. ...Helmholtz argued the cause of "atoms of electricity" in his Faraday Lecture of 1881. The Stoney-Helmholtz electron could be both a positive and a negative charge and was... conceived as a unit quantity of electricity rather than a particle residing in all forms of matter. ...Stoney associated his electron not only with electrolysis but also with the emission of light. In 1891 he suggested that electrons rotating in molecules or atoms might be responsible for spectral lines...
Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (1999)
It being assumed as the basis for this New View that Electricity is the only element in nature which has weight, we have immediately to notice certain consequences of the assumption which are inevitable...
3. The attraction of common matter for electricity cannot be the cause of gravitation, because bodies gravitate when neither electrically plus nor minus; in which neutral state, owing to the definite nature of electrical attraction, the electricity of no one body attracts the common matter of any other body.
4. On a supposition that particles, or atoms, of electricity attract one another, instead of being mutually repulsive, as is taught by preceding theories, then the quantity of electricity in each chemical atom acting on the universal electricity would confer on all chemical atoms gravitating forces represented by their respective equivalent numbers.
Richard Laming, A New View of Electrical Action Based Upon the Only Ponderable Element in Nature, and Allotted to Atoms in Quantities that are Definite (1858) Vol. 1-2
Let it be granted,
lst. That electricity consists of parts, or particles, of a spherical form; that the whole of the terrestrial electricity is attracted at all distances by and around the particles of terrestrial common matter, they also being of a spherical form; and that the quantity of electricity attracted by each common particle is definite and unalterable.
2ndly. That each particle of common matter attracts each of the electrical particles which constitute its equivalent with a force which varies in some inverse ratio of the distances.
3rdly. That each particle of common matter attracts any portion of its electrical equivalent that may have been removed to an abnormal distance from it with a force which varies as the squares of the numbers of electrical particles contained in that portion.
Richard Laming, A New View of Electrical Action Based Upon the Only Ponderable Element in Nature, and Allotted to Atoms in Quantities that are Definite (1858) Vol. 1-2
The facts of chemical physics point to electrification being distributed in an atomic manner, so that an atom of electricity, say an electron, has the same claims to separate and permanent existence as an atom of matter. The fundamental question then is, how far the conception of separate isolated electrons, pervading the aether of free space, can provide an explanation of electrodynamic and optical phenomena. ...Whatever view one may entertain as to the presence of qualities other than electric in the atom, all are I think now-a-days agreed that the electron is there. And whatever view one may have as to the validity and sufficiency of an æther with simple rotational elasticity, the formal equations to which that theory leads for free space are just those equations of Maxwell which Hertz's experimental work has fully verified. The problem of electrodynamics is then that of the free æther, whose properties are represented analytically by these acknowledged equations, disturbed by the action of the electrons of material atoms moving about in it. The original Amperean electrodynamics, proceeding by consideration of elements of current, has not proved valid or sufficient in matters involving electric radiation, or even ordinary electrodynamic force. A most successful modification of it was that proposed by Weber in which elements of current were replaced, as the fundamental object of consideration, by moving electric particles which acted on each other at a distance according to a law of force involving their velocities. This theory was, however, shown long ago by Lord Kelvin and Professor von Helmholtz to be untenable on account of its violating the principles of the modern theory of energy; now, of course, direct action at a distance is altogether out of court. The present question is whether a theory of electrons which act on each other, not directly according to a law of force, but mediately by propagation of the effect across the intervening æther, suffices to avoid the discrepancies of earlier theories and give a consistent account of electrical and optical phenomena; and it is maintained that the answer is altogether in the affirmative.
J. Larmor, On the Theory of Moving Electrons and Electric Charges (Aug, 1896) Philosophical Magazine and Journal of ScienceVol. XLII, (July-Dec, 1896) No. CCLV, pp. 201-203
One has been led to the conception of electrons, i.e. of extremely small particles, charged with electricity, which are present in immense numbers in all ponderable bodies, and by whose distribution and motions we endeavor to explain all electric and optical phenomena that are not confined to the free ether. ...according to our modern views, the electrons in a conducting body, or at least a certain part of them, are supposed to be in a free state, so that they can obey an electric force by which the positive particles are driven in one, and the negative electrons in the opposite direction. In the case of a non-conducting substance, on the contrary, we shall assume that the electrons are bound to certain positions of equilibrium. If, in a metallic wire, the electrons of one kind, say the negative ones, are travelling in one direction, and perhaps those of the opposite kind in the opposite direction, we have to do with a current of conduction, such as may lead to a state in which a body connected to one end of the wire has an excess of either positive or negative electrons. This excess, the charge of the body as a whole, will, in the state of equilibrium and if the body consists of a conducting substance, be found in a very thin layer at its surface.
In a ponderable dielectric there can likewise be a motion of the electrons. Indeed, though we shall think of each of them as haying a definite position of equilibrium, we shall not suppose them to be wholly immovable. They can be displaced by an electric force exerted by the ether, which we conceive to penetrate all ponderable matter... the displacement will immediately give rise to a new force by which the particle is pulled back towards its original position, and which we may therefore appropriately distinguish by the name of elastic force. The motion of the electrons in non-conducting bodies, such as glass and sulphur, kept by the elastic force within certain bounds, together with the change of the dielectric displacement in the ether itself, now constitutes what Maxwell called the displacement current. A substance in which the electrons are shifted to new positions is said to be electrically polarized.
Again, under the influence of the elastic forces, the electrons can vibrate about their positions of equilibrium. In doing so, and perhaps also on account of other more irregular motions, they become the centres of waves that travel outwards in the surrounding ether and can be observed as light if the frequency is high enough. In this manner we can account for the emission of light and heat. As to the opposite phenomenon, that of absorption, this is explained by considering the vibrations that are communicated to the electrons by the periodic forces existing in an incident beam of light. If the motion of the electrons thus set vibrating does not go on undisturbed, but is converted in one way or another into the irregular agitation which we call heat, it is clear that part of the incident energy will be stored up in the body, in other terms [words] that there is a certain absorption. Nor is it the absorption alone that can be accounted for by a communication of motion to the electrons. This optical resonance, as it may in many cases be termed, can likewise make itself felt even if there is no resistance at all, so that the body is perfectly transparent. In this case also, the electrons contained within the molecules will be set in motion, and though no vibratory energy is lost, the oscillating particles will exert an influence on the velocity with which the vibrations are propagated through the body. By taking account of this reaction of the electrons we are enabled to establish an electromagnetic theory of the refrangibility of light, in its relation to the wave-length and the state of the matter, and to form a mental picture of the beautiful and varied phenomena of double refraction and circular polarization.
On the other hand, the theory of the motion of electrons in metallic bodies has been developed to a considerable extent. ...important results that have been reached by Riecke, Drude and J. J. Thomson... the free electrons in these bodies partake of the heat-motion of the molecules of ordinary matter, travelling in all directions with such velocities that the mean kinetic energy of each of them is equal to that of a gaseous molecule at the same temperature. If we further suppose the electrons to strike over and over again against metallic atoms, so that they describe irregular zigzag-lines, we can make clear to ourselves the reason that metals are at the same time good conductors of heat and of electricity, and that, as a general rule, in the series of the metals, the two conductivities change in nearly the same ratio. The larger the number of free electrons, and the longer the time that elapses between two successive encounters, the greater will be the conductivity for heat as well as that for electricity.
H. A. Lorentz has found out the Relativity theorem and has created the Relativity postulate as a hypothesis that electrons and matter suffer contractions in consequence of their motion according to a certain law. A. Einstein has brought out the point very clearly, that this postulate is not an artificial hypothesis but is rather a new way of comprehending the time-concept, which is forced upon us by observation of natural phenomena.
Hermann Minkowski, The Fundamental Equations for Electromagnetic Processes in Moving Bodies (1907) Tr. Meghnad Saha (1920)
The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity.
Heisenberg's name will always be associated with his theory of quantum mechanics, published in 1925, when he was only 23 years old. For this theory and the applications of it which resulted especially in the discovery of allotropic forms of hydrogen, Heisenberg was awarded the Nobel Prize for Physics for 1932.
His new theory was based only on what can be observed, that is to say, on the radiation emitted by the atom. We cannot, he said, always assign to an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits postulated by Niels Bohr actually exist. Mechanical quantities, such as position, velocity, etc. should be represented, not by ordinary numbers, but by abstract mathematical structures called "matrices" and he formulated his new theory in terms of matrix equations.
If we ask, for instance, whether the position of the electron remains the same, we must say 'no'; if we ask whether the electron's position changes with time, we must say 'no'; if we ask whether the electron is at rest, we must say 'no'; if we ask whether it is in motion, we must say 'no'. The Buddha has given such answers when interrogated as to the conditions of a man's self after his death; but they are not familiar answers for the tradition of seventeenth and eighteenth century science.
In his standoff with Dr. Ramsay of Harvard last fall, Dr. Leggett suggested that his colleagues should consider the merits of the latter theory. "Why should we think of an electron as being in two states at once but not a cat, when the theory is ostensibly the same in both cases?" Dr. Leggett asked.
Dr. Ramsay said that Dr. Leggett had missed the point. How the wave function mutates is not what you calculate. "What you calculate is the prediction of a measurement," he said.
"If it's a cat, I can guarantee you will get that it's alive or dead," Dr. Ramsay said. David Gross, a recent Nobel winner and director of the Kavli Institute for Theoretical Physics in Santa Barbara, leapt into the free-for-all, saying that 80 years had not been enough time for the new concepts to sink in. "We're just too young. We should wait until 2200 when quantum mechanics is taught in kindergarten."
Dennis Overbye, "Quantum Trickery: Testing Einstein's Strangest Theory", The New York Times (Dec. 27, 2005)
J. J. Thomson was about to make the most significant find of the late nineteenth century... Thompson had been investigating the nature of cathode rays. He was convinced that they were some kind of electrified particles and, to prove his theory, began testing their behavior in electric or magnetic fields. By measuring both the extent to which such fields deflected them and their electric charge, he discovered that cathode rays consisted of very small negatively charged particles whose mass was about eighteen hundred times smaller than the lightest known substance—the hydrogen atom. ...He initially named these tiny carriers of electricity "corpuscles." Later they would become known as "electrons." The corpuscles were, in fact, the first subatomic particles to be found...
Dianna Preston, Before the Fallout from Marie Curie to Hiroshima (2005).
The theory that the atoms of matter are all built up of some simple fundamental unit or protyle has been advanced at various times by prominent chemists and physicists. One of the earliest hypotheses of this kind was that due to Prout, who supposed that all the elements were built up of hydrogen. This general point of view has received strong support from observations that the properties of elements vary in a periodic manner with their atomic weight. This is exemplified by the classification of the elements according to the well-known periodic law. In order to explain the electrical and optical properties of matter, it was generally supposed that the atom consisted of a number of positively and negatively charged particles, held in equilibrium by electrical forces. The properties of such electrical atoms were early studied by Larmor and Lorentz.
The first point that arises is the atom. I was brought up to look at the atom as a nice hard fellow, red or grey in colour, according to taste. In order to explain the facts, however, the atom cannot be regarded as a sphere of material, but rather as a sort of wave motion of a peculiar kind. The theory of wave-mechanics, however bizarre it may appear... has the astonishing virtue that it works, and works in detail, so that it is now possible to understand and explain things which looked almost impossible in earlier days. One of the problems encountered is the relation between the electron, an atom and the radiation produced by them jointly; the new mechanics states the type of radiation emitted with correct numerical relations. When applied to the periodic table, a competent and laborious mathematician can predict the periodic law from first principles.
[When I joined the Institute for Advanced Study in Princeton] I did this in the hope that by rubbing elbows with those great atomic physicists and mathematicians I would learn something about living matters. But as soon as I revealed that in any living system there are more than two electrons, the physicists would not speak to me. With all their computers they could not say what the third electron might do. The remarkable thing is that it knows exactly what to do. So that little electron knows something that all the wise men of Princeton don't, and this can only be something very simple.
I think you and Uhlenbeck have been very lucky to get your spinning electron published and talked about before Pauli heard of it. It appears that more than a year ago Kronig believed in the spinning electron and worked out something; the first person he showed it to was Pauli. Pauli ridiculed the whole thing so much that the first person became also the last and no one else heard anything of it. Which all goes to show that the infallibility of the Deity does not extend to his self-styled vicar on earth.
The electron: may it never be of any use to anybody!
J. J. Thomson, popular toast or slogan at his Cavendish Laboratory in the early 1900s, as quoted in Proceedings of the Royal Institution of Great Britain, Volume 35 (1951), p. 251.
A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. ...But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.
Hermann Weyl, Space—Time—Matter, Preface (1950) 1st American Printing of 4th Edition (1922); tr. Henry L. Brose; orig. title: Raum, Zeit, Materie (1918)
The reason universities have students is so they can teach the professors, and Feynman was one of the best. Through some wonderful freak of fate, I ended up with him assigned to me. He had what so many people with a purely mathematical background lack: he had a feel for the physical world. He had worked in a paint factory, I think, in the summertime before he came to Princeton.
I was very enthusiastic about the idea that in the world there are nothing but particles, with Dirac thinking that the electron is the basic particle, and that if you could understand the interaction between electron and electron, then everything else will follow, everything else would be subsidiary to that simple picture. The idea of an electromagnetic field traveling through space, that's just talk. The real thing is that this electron does something, and later that electron, affected by it, does something. Action at a distance. And we found we could express that in consistent mathematical language, although we didn't get a chance to write it up until after the war.
Thomson's lecture drew from Fitz Gerald the suggestion that "we are dealing with free electrons in these cathode rays"—a remark the point of which will become more evident when we come to consider the direction in which the Maxwellian theory was being developed at this time.
Since it appears that all negative electricity is made up of equal particles and since it is very probable that any atom can be exactly neutral it follows that the amount of positive electricity in any atom must be an exact multiple of the charge of one negative electron. This makes it probable that positive electricity is also made up of equal parts, but so far they have not been obtained free.
"The Development of the Electron Idea" (Nov. 8, 1901)
Walter Kaufmann, The ElectricianVol. 48 pp. 95-97. Lecture delivered before the 73rd Naturforscher Versammlung at Hamburg. From the Physikalische Zeitshrift, of October 1, 1901.
It is not an unusual phenomenon in the history of science that views which were once considered antiquated and out of date suddenly come into favor again, though in a more or less modified form. An extremely interesting case of this kind is presented by the revolution in our ideas of electric phenomena which has taken place within the last 10 years...
The modern theory of electrical and allied optical phenomena... [i.e.,] the "electron theory," means practically a return to views as laid down in the sixties and seventies by Wilhelm Weber and Zöllner, but modified by the results of Maxwell's and Hertz's researches. W. Weber imagined electric phenomena as the actions of elementary electrical particles—so called "electric atoms"—whose mutual influence depended not only upon their positions but also upon their relative velocities and accelerations. Although Weber succeeded by means of his hypothesis in completely describing the electrodynamical phenomena known at his time, and even in giving a quantitatively useful explanation of the correspondence between electric and thermal conduction in metals, as well as Ampère's molecular currents in magnets, still his theory was far from becoming the common property of physicists of his day. The reason for this negative success may be sought for in the fact that most of the laws of electrodynamics when expressed from the standpoint of pure phenomenology in the shape of differential equations, are much more simple and convenient than Weber's formulæ. In addition, Weber makes no attempt to calculate the size of his electrical atoms and to test the result... And, finally, the work of Faraday and Maxwell brought about a general feeling that in electric and magnetic phenomena a finite rate of propagation would have to take the place of action at a distance. This demand was already put forward by Gauss in letter to Weber in 1845...
Maxwell's treatises, begun in 1861-62 and concluded in 1873 in his famous "Treatise on Electricity and Magnetism," as well as the brilliant experimental confirmation of Maxwell's results by H. Hertz from 1887, seemed calculated to deprive Weber's views of the last vestige of vitality. ...Maxwell's formulæ, wholly void as they were of atomistic conceptions, represented the fundamental electrical phenomena just as well as the old conceptions based upon action at a distance, and the newly-discovered Hertzian waves could only be represented by Maxwell's theory.
...this brilliant success had at first blinded physicists with regard to the insufficiency of Maxwell's theory in... optical phenomena. According to Maxwell... the vibrations of light were not mechanical, but electrical vibrations of the ether, and the two constants by which Maxwell defined the electric and magnetic behaviour of every body (the dielectric constant and the magnetic permeability) had also to be the determining elements in its refractive power. Although the condition demanded by Maxwell—of the refractive power varying as the square root of the dielectric constant—was well fulfilled in a number of bodies, yet... many bodies, notably water, showed... enormous deviations... To this was added the dependence of the refractive index upon the colour [frequency], for which the original theory gave no explanation whatever.
Already in 1880... H. A. Lorentz showed that the foundations of an electromagnetic theory of dispersion could be laid in a manner quite analogous to the mechanical theory, by regarding every molecule as the origin of electric vibrations of a definite period. He says:—"Let there be in every material particle several material points charged with electricity, of which, however, only one be movable, and have the charge e and the mass μ." Lorentz derives the equations of dispersion from this fundamental assumption of vibrating charged particles.
The next question is: What reason have we for assuming presence of electric particles in every transparent body? The answer is furnished by a set of phenomena which hardly fitted into Maxwellian theory, and which was, therefore, almost always in accordance with the old views. I refer to the phenomena of electrolysis. When the electric current traverses an electrolyte, then, according to Faraday's law, every unit of current deposits chemically equivalent masses at the electrode. We may, therefore, assume that every chemical equivalent of an ion wandering in electrolyte is attached to definite and unchangeable positive or negative quantity of electricity.
In his Faraday Memorial Address of 1881 Helmholtz points out that Faraday's law necessarily implies the existence of electric atoms. For since the charged chemical atoms called by ions (i.e., wanderers) are liberated at the electrodes as neutral bodies, there must be a giving up of the charges or a partial exchange with charges of opposite sign. During this process, which cannot instantaneous, the charges must, therefore, be capable of existence during a short time at least. It obviously suggests itself to regard this always uniform unit charge as an elementary quantity of electricity, as an "electric atom." And when a neutral molecule—say NaCl—splits up in +Na and -CI when dissolved in water, it is most probable that both the sodium and the chlorine atom had their charges beforehand, and that these charges were not appreciable [apparent] because they were equal and opposite. But if we consider a ray of light traversing a crystal of salt, the charges and the atoms they accompany must be thrown into vibrations, and must influence the propagation of the light. It is, therefore, the electrolytic valency charges which we have to regard as the electric particles vibrating a transparent body, and whose attractive forces, as Helmholtz showed, probably constituted the greatest part of the forces of chemical affinity.
Now, although the plans of the edifice of the electromagnetic theory of light were laid in 1880 by H. A. Lorentz, and even indicated much earlier by W. Weber, a full 10 years were required before the discoveries of Heinrich Hertz gave the impetus to collect the building stones and work them into shape. In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney by the now universally accepted name of electron. The result of these calculations is important, as showing that it does not clash with other experimental data. Thus, H. Ebert proved that the amplitude of an electron in luminous sodium vapour need only be a small fraction of a molecular diameter in order to excite a radiation of the absolute intensity determined by E. Wiedemann. The way of determining the amount of electricity contained in the electron is very simple. The quantity of electricity required for the electrolytic evolution of 1 cubic cm. of any monatomic gas is divided by Loschmidt's number—i.e., the number of gas molecules contained in 1 cubic cm. Considering the uncertainty of this number, it can only be said that one electron contains about 10-10 electrostatic units. The value of this number would be very questionable but for the circumstance that a whole series of other methods... tend to very similar values.
While it thus became clear that the supposition of vibrating ionic charges was compatible with observed phenomena as regards the order of magnitude, two works appeared... which completed the edifice of the electromagnetic theory of light. Of these works, that of Helmholtz only deals with the special question of the dispersion of light in absorbing media, while the other, due to H. A. Lorentz, goes much further. It shows how the assumption of vibrating charged particles in transparent bodies eliminates all the difficulties in the way of an adequate explanation of the propagation of light in moving bodies, such as the aberration of stellar light. Lorentz's theory leaves Maxwell's theory untouched as regards the free ether. A material body influences the optical and electrical processes only by virtue of the electric charges contained in it, while in the interspaces filled with ether everything remains unhanged. Maxwell's "dielectric constant" therefore disappears as a fundamental conception in Lorentz's theory. It becomes a derived conception, and it is immediately seen that for rapid electric oscillations, in which the inertia of the vibrating charges enters into consideration, it has no significance. The same applies mutatis mutandis, to the magnetic permeability.
In view of the facility with which Lorentz's theory explains the dispersion and observation phenomena, a direct proof of its truth was hardly required. But that was also forthcoming. In 1896 a pupil of Lorentz, P. Zeeman, discovered a phenomenon whose existence Faraday had vainly sought for in 1862. If a luminous vapour, say a sodium flame, is brought into a strong magnetic field, the spectrum lines of the vapour show peculiar changes, consisting of a doubling or trebling, according to the line of vision. These changes are predicted by Lorentz's theory. The Zeeman phenomenon further permitted a determination of the inert mass connected with the vibrating charges, and then a striking result was obtained: the vibrating electron is always negatively charged, while the positive charge is stationary. The ratio of charge to mass is that of 17 million electromagnetic units to 1 gramme, and since 1 gramme of hydrogen only contains 9,650 units, it follows that the mass attached to the vibrating electron is only about 1/2000th part of the hydrogen atom. The original and almost tacit assumption that the whole ion—i.e., the chemical atom plus its valency charge—was in oscillation must, therefore, be abandoned. We must suppose that the charge, just as is the case in electrolysis, has also an independent mobility in the light-emitting molecule, and that the mass concerned in the Zeeman phenomenon is that of the electron itself.
We thus arrive at a view which nearly coincides with the old conception of Weber, but with the important difference that instead of a direct action at a distance we have an action transmitted by the ether, and further, that we have now a perfectly distinct numerical estimate of the magnitude of the electric atoms. Another difference from Weber is this: Weber assumed at haphazard that the positive particles were the more mobile. Now, in accordance with the Zeeman effect, we must give the negative particles that property. It has been found that in other electron phenomena also, it is always the negative electron which appears as the freely mobile one. Whence this curious one-sidedness comes, whether it will some day be possible to prove the existence of a free positive electron, or whether we must substitute a unitarian theory for the dualistic theory of electricity, we must leave to future developments.