History Of Physics

"Descartes subscribed to the doctrine of instantaneous propagation, but with him something new emerged: for his was the first uncompromisingly mechanical theory that asserted the instantaneous propagation of light in a material medium... Indeed, mechanical analogies had been used to explain optical phenomena long before Descartes, but the Cartesian theory was the first clearly to assert that light itself was nothing but a mechanical property of the luminous object and of the transmitting medium. It is for this reason that we may regard Descartes' theory of light as legitimate starting point of modern physical optics."

"Contemporary with Vitellio and Peccam was... Roger Bacon, a man of almost universal genius, and who wrote on almost every branch of science. He frequently quotes Alhazen on the subject of optics, and seems to have carefully studied his writings, as well as those of other Arabians, which were the fountains of natural knowledge in those days, and which had been introduced into Europe by means of the Moors in Spain. Notwithstanding the pains this great man took with the subject of opticks, it does not appear that, with respect to theory, he made any considerable advance upon what Alhazen had done before him."

"[W]ith regard to light, that it consists of vibrations was almost proved by the phenomena of , while those of polarisation showed the excursions of the particles to be perpendicular to the line of propogation; but the phenomena of dispersion, etc., require additional hypotheses which may be very complicated. Thus, the further progress of molecular speculation appears quite uncertain. If hypotheses are to be tried haphazard, or simply because they will suit certain phenomena, it will occupy the mathematical physicists of the world say half a century on the average to bring each theory to the test, and since the number of possible theories may go up into the trillion, only one of which can be true, we have little prospect of making further solid additions to the subject in our time."

"Thomas Young... attained equal eminence by his discoveries in connection with the undulatory theory of light, in which he was the first to assert the principle of interference, and that of transverse vibrations... The remarkable fact that Young, of whom Helmholtz says that he came a generation too soon, remained scientifically unrecognised and popularly almost unknown to his countrymen, has been explained by his unfortunate manner of expression and the peculiar channels through which his labours were announced to the world. ...[S]everal great names contributed, by the authority they commanded, to oppose Young's claims to originality and renown. Lord Brougham, shielded by the powerful anonymity of the ',' and ostentatiously parading the authority of Newton, submitted the views of Young to a ruthless and unfair criticism, the popular influence of which Young probably never overcame. The great authority on optics, Brewster, who has enriched that science by such a number of experiments and observations of the first importance, never really adopted the theories of Young and Fresnel."

"Helmholtz's invention of the ophthalmoscope in 1851 marks an epoch in ."

"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."

"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."

"There can be no doubt that light consists of the motion of a certain substance. For if we examine its production, we find that here on earth it is principally fire and flame which engender it, both of which contain beyond doubt bodies which are in rapid movement, since they dissolve and destroy many other bodies more solid than they: while if we regard its effects, we see that when light is accumulated, say by concave mirrors, it has the property of combustion just as fire has, that is to say, it disunites the parts of bodies, which is assuredly a proof of motion, at least in the true philosophy, in which the causes of all natural effects are conceived as mechanical causes. Which in my judgment must be accomplished or all hope of ever understanding physics is renounced."

"Perhaps the most striking example of the services which have been rendered to Science by the contemplation of various models, many or all of which have ultimately been found to be inadequate for complete representation, is to be found in the history of Optics. The various forms of the corpuscular theory, and of the wave theory, of Light were all attempts to represent the phenomena by models, the value of which had to be estimated by developing their Mathematical consequences, and comparing these consequences with the results of experiments. The adynamical theory of Fresnel, the elastic solid theory of the ether developed by Navier, Cauchy, Poisson, and Green, the labile ether theory developed by Cauchy and Kelvin, and the rotational ether theory of MacCullagh were all efforts of the kind... indicated; they were all successful in some greater or less degree in the representation of the phenomena, and they all stimulated Physicists to further efforts to obtain more minute knowledge of those phenomena. Even such an inadequate theory as that of Fresnel led to the very interesting observation by Humphry Lloyd of the phenomenon of conical refraction in crystals, as the result of the prediction by Rowan Hamilton that the phenomenon was a necessary consequence of the Mathematical fact that Fresnel's wave surface in a biaxal crystal possesses four conical points."

"We must never forget that it is principles, not phenomena,—the interpretation, not the mere knowledge of facts,—which are the objects of enquiry to the natural philosopher. As truth is single, and consistent with itself, a principle may be as completely and as plainly elucidated by the most familiar and simple fact, as by the most imposing and uncommon phenomenon. The colours which glitter on a soap-bubble are the immediate consequence of a principle the most important from the variety of phenomena it explains, and the most beautiful, from its simplicity and compendious neatness, in the whole science of optics. If the nature of periodical colours can be made intelligible by the contemplation of such a trivial object, from that moment it becomes a noble instrument in the eye of correct judgment; and to blow a large, regular, and durable soap-bubble may become the serious and praise-worthy endeavour of a sage, while children stand round and scoff, or children of a larger growth hold up their hands in astonishment at such waste of time and trouble. To the natural philosopher there is no natural object unimportant or trifling. From the least of nature's works he may learn the greatest lessons."

"To complete the theory of reflexion and on the undulatory hypothesis, it will be necessary to show what becomes of those oblique portions of the secondary waves, diverging in all directions from every point of the reflecting or refracting surfaces... which do not conspire to form the principal wave. But to understand this, we must enter on the doctrine of the interference of the rays of light,—a doctrine we owe almost entirely to the ingenuity of Dr. Young, though some of its features may be pretty distinctly traced in the writings of Hooke, (the most ingenious man, perhaps, of his age,) and though Newton himself occasionally indulged in speculations bearing a certain relation to it. But the unpursued speculations of Newton, and the appercus of Hooke, however distinct, must not be put in competition, and, indeed, ought scarcely to be mentioned with the elegant, simple, and comprehensive theory of Young,—a theory which, if not founded in nature, is certainly one of the happiest fictions that the genius of man has yet invented to group together natural phenomena, as well as the most fortunate in the support it has unexpectedly received from whole classes of new phenomena, which at their first discovery seemed in irreconcileable opposition to it. It is, in fact, in all its applications and details one succession of felicities insomuch that we may almost be induced to say, if it be not true, it deserves to be so. The limits of this Essay, we fear, will hardly allow us to do it justice."

"Newton's proof of the law of refraction is based on an erroneous notion that light travels faster in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature."

"The result of my work has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the s which Monsieur Descartes has established."

"[T]he explanation of the rectilinear propagation of light from the standpoint of the wave theory presents difficulties. To overcome these difficulties Huygens made the supposition that every point P which is reached by a light-wave may be conceived as the source of elementary light-waves, but that these elementary waves produce an appreciable effect only upon the surface of their envelope. ...Fresnel replaced Huygens' arbitrary assumption that only the envelope of the elementary waves produces appreciable light effects by the principle that the elementary waves in their criss-crossing influence one another in accordance with the principle of interference. Light ought then to appear not only upon the enveloping surface, but everywhere where the elementary waves reinforce one another; on the other hand, there should be darkness wherever they destroy one another. ...[I]t is possible to deduce from this Fresnel-Huygens principle not only the laws of diffraction, but also those of straight-line propagation, reflection, and refraction."

"The wave theory furnishes the simplest possible explanation of interference phenomena. On the other hand it has considerable difficulty in explaining the rectilinear propagation of light. In this respect the analogy between sound and light seems to break down, for sound does not travel in straight lines. ...This analogy between sound and light presents still further contradictions when polarization phenomena are under consideration. It was these contradictions which prevented for a long time the general recognition of the wave theory in spite of the simple explanation which it offers of interference. The difficulties were not removed until a too close analogy between sound and light was given up."

"Kepler's theory of vision introduced the concept of optical images that is the basis of modern ."

"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 , 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)."

"Mohammedan science made a great advance on that of the Greeks... [in] optics, and this was very largely a by-product of medicine. Optics comes much more in the doctor's province, especially in tropical and sub-tropical countries where there is a prevalence of eye diseases ...This goes right back to the ns, who were doing ...cataract operations, between 2000 and 2500 BC. Therefore... they introduced into science something ...which the Greeks did not have ...the lens. The Greeks ...knew that the mirror could focus the rays—that was due to Archimedes—but they did not have any lenses."

"It is manifest that everything in the world, whether it be substance or accident, produces rays in its own manner like a star... Everything that has actual existence in the world of the elements emits rays in every direction, which fill the whole world."

"The spectrum of the sun was first observed, in 1666, by Newton, who allowed light coming from a small round opening in a shutter to pass through a glass prism. This spectrum was most impure; and a pure spectrum was not obtained until, in 1802, Wollaston repeated Newton's experiment, replacing the round opening by a slit parallel to the edge of the prism. He observed several dark lines crossing the spectrum, which limited, as he thought, the different spectral colors."

"Descartes's theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of was, however, called in question by his fellow-countryman Pierre de Fermat... and a controversy ensued which was kept up by the Cartesians long after the death of their master. Fermat eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated in the form, "Nature always acts by the shortest course." From it the law of reflection can readily be derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces. In order to obtain the law of refraction, Fermat assumed that "the resistance of the media is different," and applied his "method of maxima and minima" to find the paths which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution. "The result of my work," he writes, "has been the most extraordinary, the most unforeseen and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established." His surprise was all the greater, as he had supposed light to move more slowly in dense than in rare media, whereas Descartes had... been obliged to make the contrary supposition."

"In order to receive in the eye all the light diffracted through a narrow opening, and to see the phenomena strongly magnified; still more in order to directly measure the inflection of the light, I placed in front of the objective of a -telescope a screen in which there was a narrow vertical opening which could be made wider or narrower by means of a screw. By means of a heliostat I threw sunlight into a darkened room through a narrow slit so that it fell upon this screen, through whose opening the light was therefore diffracted. I could then observe through the telescope the phenomena produced by the diffraction, magnified, and yet seen with sufficient brightness; and at the same time I could measure the angles of inflection of the light by means of the theodolite."

"If sunlight is admitted into a darkened room through a small opening and falls upon a dark screen some distance away, which has a narrow aperture, and if the light which passes through this slit is allowed to fall upon a white surface or a piece of ground-glass placed a short distance behind the screen, one sees... that the illuminated portion of the white surface is larger than the narrow slit in the screen, and that it has colored edges—in short, that the light through the slit is inflected or diffracted. The narrower the openings, so much the greater is the inflection. The shadow of every body which is placed in a beam of sunlight entering a darkened room through a small opening is bounded by fringes of color which are, moreover, for any given distance of the surface on which the shadow is received, of the same size for bodies of all kinds of matter. The shadow of a narrow object, such as a hair, has, in addition to the outer fringes, others within the shadow, which change with the thickness of the hair, but in other respects are similar to the outer ones. Since the colored fringes are very small, and since most of the light is lost through absorption at the surface on which the shadow is cast, no great accuracy could be expected with the methods which have been used up to this time to observe diffraction phenomena; and this is all the more true because by these methods it is impossible to measure the angles of inflection of the light which alone can make us acquainted with the laws of diffraction. Up to the present, these angles from which the path of the diffracted light can be learned have been calculated from the dimensions of the colored bands and their distance from the diffracting body; but assumptions have been made which... do not agree with the truth, and which, therefore, give false results."

"All experiments in which the eye of the investigator is provided with good optical instruments are distinguished, as is well known, by a high degree of precision; and some of the most important discoveries could not have been made without these instruments. Up to the present time, in experiments on diffraction there has been no instrument, except a magnifying-glass, which could be used with profit; and this may perhaps be one of the reasons why in this field of physical optics we are so backward, and why we know so little of the laws of this modification of light. ...[I]t is most to be desired that these laws should be exactly known; and this is specially so because a knowledge of them makes the nature of light itself better known at the same time."

"There are many persons... whom we should astonish, and possibly enrage, by asserting... that we could cause darkness by means of light, that silence could be produced by sound, or cold by heat. ...[B]y throwing a second stone into the water we form another series of undulations which are mutually destroyed when they encounter each other. It is the same with the peculiar fluid which, existing throughout space, is thrown in a state of undulation by incandescent bodies; by opposing one set of waves to another we obtain rest as a result. This fact was first observed by Grimaldi in 1665 and Dr. Thomas Young was the first to offer an explanation. Fresnel used it with great success at the beginning of the century to demonstrate the truth of the undulatory theory, by showing that it could not be explained by any other."

"A short time after the invention of the telescope and the consequent discovery of Jupiter's satellites, Römer... was engaged in a series of observations... to determine the time which one of these bodies took to revolve round its planet. The method employed by Römer was to observe the successive s of the satellite and to notice the interval that elapsed between each of them. But it at last happened that the interval between the two occultations, which was about forty five hours, became prolonged by periods of 8, 13, and 16 minutes, during that half of the year when the earth was receding from the planet, while it became proportionally cut short during [earth's approach]. Römer was struck by a happy idea he suspected instantly that... an interval of time sufficiently long [was required] to allow the light that had left the satellite immediately after its disappearance to reach the eye of the observer. ...[T]he farther off the earth was from the satellite the longer was the interval of time between its disappearance and that of the arrival of the last portions of its light upon the earth ...It was thus that Römer explained the difference between the calculated and observed time of the occultation and he saw that he was on the threshold of a great discovery. ...he saw that light propagated itself through space with a certain velocity and that the fact... just mentioned furnished the precise means of measuring it. Thus the occultation of the satellite was retarded one second for every 185,000 miles that the earth is distant from Jupiter; the reason being that a ray of light takes a second to travel this distance... because the velocity of light is... 185,000 miles per second."

"We can say with every confidence that "the Providence which shapes our ends," knows our wants better than we do ourselves, and bestows on us the things we ought to have asked for instead of those we have asked for. We shall find a very simple proof of this in the history of the discovery of the velocity of light."

"[T]he complementary of any colour is that which is necessary to make white light. ...The impression left by the setting sun is of this character. At first, while the eye is open, the image is black, then brownish red, with a light blue border; but if the eye be shut suddenly, it becomes green, with a red border, the brilliancy of colour being apparently in proportion to the strength of the impression. These spectra may be perceived for a long time, if the eye is gently rubbed with the finger now and then. Some eyes are more impressionable in this respect than others, and Beyle gives an instance of an individual who saw the spectrum of the sun for years, whenever he looked at a bright object. A modern instance of this occurred lately to an amateur astronomer who was looking at an eclipse of the sun. He unfortunately used a glass that was not sufficiently smoked and the image... remained on his retina for months after. This... afforded an instance of the necessity of attention in order to see any object, for after the first few days he only became sensible of [it] when his attention was called to it by some accidental circumstance. These facts were so inexplicable to Locke that he consulted Newton on the subject, and was surprised to learn that the great philosopher himself had suffered for several months from a sun-spectrum in the eye."

"The phenomena of ocular spectra and complementary colours... forms a curious chapter in the history of those illusions which take their origin in the eye... [A]fter looking fixedly at a bright light or a striking colour for a few moments the eye preserves an impression of the object for a certain time. A very light window looked at intently for several seconds will leave the impression of its cross bars on the retina for several minutes, the colour of the image changing at every movement of the eye. The same effect may be observed when looking at the setting sun, or a flaring gas light. If the light at which we look is coloured we shall see the complementary colour in the impression left on the retina. Sir David Brewster was one of the first to notice and experiment upon these very interesting facts."

"Euler at first hesitated to confide in Dollond's experiments; but he was assured of their correctness by Clairaut, who had throughout paid great attention to the subject; and those two great mathematicians, as well as D'Alembert, proceeded to investigate mathematical formulæ which might be useful in the application of the discovery. The remainder of the deductions, which were founded upon the laws of dispersion of various refractive substances, belongs rather to the history of art than of science. Dollond used at first, for his achromatic object-glass, a lens of crown-glass, and one of flint-glass; afterwards, two lenses of the former substance, including between them one of the latter. He also adjusted the curvatures of his lenses in such a way as to correct imperfections arising from the spherical form of the glasses, as well as the fault of colour. Afterwards Blair, and more recently Mr. Barlow, have used fluid media along with glass lenses, in order to produce improved object-glasses; and various mathematicians, as Sir J. Herschel and Professor Airy among ourselves, have simplified and extended the investigation of the formulæ which determine the best combinations of lenses in the object-glasses and eye-glasses of telescopes, both with reference to spherical and chromatic aberrations."

", in 1757, repeated Newton's experiment, and obtained an opposite result. He found that when an object was seen through two prisms, one of glass and one of water, of such angles that it did not appear displaced by refraction, it was coloured. Hence it followed that, without being coloured, the rays might be made to undergo refraction; and that thus, substituting lenses for prisms, a combination might be formed, which should produce an image without colouring it, and make the construction of an achromatic telescope possible."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"This book tells the story of the researches that are traditionally lumped together under the label "radiation theory" and revolving, loosely speaking around the familiar heat-and-light exchange (hot bodies emit light and radiate; the absorption of light, especially sunlight, is warming)."

"These days it is common knowledge that short waves are more powerful than long ones, as the very short ones, known as x-rays, damage living tissues. It took half-a-century to learn this fact: it was one of the great discoveries of young Albert Einstein of 1905. When he announced it leading researchers found it most incredible..."

"The development of quantum mechanics in the beginning of the twentieth century was a unique intellectual adventure, which obliged scientists and philosophers to change radically the concepts they used to describe the world. After these heroic efforts, it became possible to understand the stability of matter, the mechanical and thermal properties of materials, the interaction of radiation and matter, and many other properties of the microscopic world that had been impossible to understand with classical physics. A few decades later, that conceptual revolution enabled a technological revolution, at the root of our information-based society. It is indeed with the quantum mechanical understanding of the structure and properties of matter that physicists and engineers were able to invent and develop the transistor and the laser—two key technologies that permit the high-bandwidth circulation of information, as well as many other scientific and commercial applications."

"The realization of the importance of entanglement and the clarification of the quantum description of single objects have been at the root of a second quantum revolution, and the John Bell was its prophet."

"The blackbody oven embodied an... instance of radiation interacting with matter. ...Planck first... derived an empirical equation to fit the data. ...His more ambitious aim now was to find a theoretical entropy-energy connection applicable to the blackbody problem. ...Ludwig Boltzmann interpreted the second law of thermodynamics as a "probability law." If the relative probability or disorder for the state of the system was W, he concluded, then the entropy S of the system in that state was proportional to the logarithm of W,S ∝ lnW ...Plank applied this to the blackbody problem by writingS = k lnW (1)for the total entropy of the vibrating molecules... "resonators"—in the blackbody oven's walls... k is now called Boltzmann's constant. ...Boltzmann's theory taught the lesson that conceivably—but against astronomically unfavorable odds—any macroscopic process can reverse... contradicting the second law of thermodynamics. Boltzmann's conclusions seemed fantastic to Planck, but by 1900 he was becoming increasingly desparate, even reckless... The counting procedure Planck used to calculate the disorder W... was borrowed from... Boltzmann's theoretical techniques. He considered... that the total energy of the resonators was made up of small indivisible "elements," each one of magnitude ε. It was then possible to evaluate W as a count of the number of ways a certain number of energy elements could be distributed to a certain number of resonators... His argument would not succeed unless he assumed that the energy ε of the elements was proportional to the frequency with which the resonators vibrated, ε ∝ v, or ε = hv, with h the proportionality constant."

"The second quantum revolution... was the term coined by... Alain Aspect to describe the changes in physics, the beginnings of which date back to the 1960s. ...he brought together two different threads. The first one embraced the emergence of the awareness of the importance of... entanglement. ...It started a conceptual revolution, including the perspective of building quantum computers... The second thread derives from physicists' ability to isolate, control, and observe single quantum systems such as electrons, neutrons and atoms. Finally these threads merged into a new field of research entitled quantum information. In Aspect's formulation... he posited two quantum revolutions taking place in the twentieth century. The first one, in the first half of the century, created the scientific theory that describes the behavior of atoms, radiation, and their interactions. The second one occurred in the second half and is still evolving... intellectual aspects... arose from the renewal of research on the foundations of quantum physics."

"Intuitively, Planck knew that his work was as important as Newton's in paving a new physics, as he privately confided to his son in 1901. Because of his own conservative beliefs, Planck felt stymied by the revolutionary nature of his own ideas... In truth, Planck was only underestimating the importance of his work, if anything. In retrospect... it started a revolution in science—the quantum revolution—compared to which the Copernican revolution pales."

"The development of the quantum ideas themselves occurred in discrete jumps, quantum leaps of the creative insights of a few people."

"The start of the revolution that produced the old quantum theory is moved from the end of 1900 to 1906... The preceding crisis...resulted from the difficulties in reconciling Planck's derivation with the tenets of classical physics. Planck's change in vocabulary—from "resonator" to "oscillator" and from "element" to "quantum"—is the central symptom of incommensurability. It signals the changed meaning of the quantity hv from a mental subdivision of the energy continuum to a physically separable atom of energy. That my critics continue to apply the term "energy quantum" to pre-1906 papers and lectures in which Planck consistently used "energy element" reveals something of the difficulty of reversing the gestalt switch that took place during that year and those which followed. ...Boltzmann's probabilistic derivation of the entropy of a gas ...illustrates the problem to which the concept of paradigm was a response. The derivation was not reduced to rules but instead served as a model to be applied by means of analogy. As a result, when its application was transferred from gases to radiation, Planck and Lorentz could invent different analogies with which to effect change."

"Quantum mechanics is revolutionary because it overturned scientific concepts that seemed to be so obvious and so well confirmed by experience that they were beyond reasonable question, but it is an incomplete because we still do not know precisely where quantum mechanics will lead us—nor even why it must be true!"

"In the brief period between 1900 and 1935 there occurred one of the most astonishing outbursts of scientific creativity in all of history. ...no other historical era has crammed so much scientific creativity, so many discoveries of new ideas and techniques, into so few years. Although a few outstanding individuals dominate... they were assisted in their work by an army of talented scientists and technicians."

"In the years 1925 and 1926 modern quantum theory came into being fully fledged. These anni mirabiles remain an episode of great significance in the folk memory of the theoretical physics community... Werner Heisenberg had been struggling to understand the details of atomic spectra. ...Heisenberg's discovery came to be known as matrix mechanics. ...In 1925 matrices were... mathematically exotic to the average theoretical physicist... Prince Louis de Broglie... made the bold suggestion that if undulating light also showed particle-like properties... one should expect particles such as electrons to manifest wavelike properties... by generalizing the Planck formula. The latter had made the particlelike property of energy proportional to the wavelike property of frequency. De Broglie suggested that... particlelike... momentum... should analogously be related to... wavelength, with Planck's universal constant again... These equivalences provided... for translating from particles to waves, and vice versa. In 1924, de Broglie laid out these ideas in his doctoral thesis. ...To attain a full dynamical theory, a further generalization... allowed the incorporation of interactions... This is the problem that Schrödinger succeeded in solving. Early in 1926 he published the famous equation... led to its discovery by exploiting an analogy drawn from optics."

"The quantum revolution describes our deepest insight, so far, into the physical structure of nature. It is comparable only with the Copernican revolution, switching from a finally oriented anthropomorphic description of physical phenomena to one using general laws with initial or boundary conditions, connected with the names Kepler, Galileo, and Newton, or with the change from tangible mass points as basic structures to Faraday's and Maxwell's field concepts and, shortly before quantum theory, with the relativization of space and time by the lonely genius Einstein."

"Quantum mechanics, created early this century in response to certain experimental facts which were inexplicable according to previously held ideas (...'classical physics'), caused three great revolutions. In the first place it opened up a completely new set range of phenomena to which the methods of physics could be applied. ...The second revolution was the apparent breakdown of determinism, which had always been an unquestioned ingredient and an inescapable prediction of classical physics. ...The outcome of any particular experiment is not, even in principle, predictable, but is chosen at random from a set of possibilities; all that can be predicted is the probability of particular results when the experiment is repeated many times. ...even if we had complete knowledge of the initial state... The third revolution ...challenged the basic belief, implicit in all science and indeed in almost the whole of human thinking, that there exists an objective reality ...that does not depend for its existence on its being observed."

"In Newton's time only two kinds of force were available for quantitative investigation. One was the force of gravity; the other the forces of push and pull encountered in everyday life... Newton endeavored to construct a general theory of all forces, both those known in his time and those that might be discovered and investigated later. He intended his theory of gravitation to be one example that he himself could work out fully... Newton formulated his celebrated three laws: (1) In the absence of force, a body will continue at rest or in its present state of uniform rectilinear motion. (2) In the presence of force, a body will be accelerated in the direction of that force, the product of its mass by its acceleration being equal to the force (f = ma). (3) To every force there corresponds an equal counterforce, acting in a direction opposite to that of the force... According to the third law, then, each planet exerts an attractive counterforce to the sun, accelerating it toward the planet... a relatively small acceleration, because the mass of the sun so vastly exceeds... every planet..."

"The foundational achievement of classical mechanics is to establish that the first point is faulty. It is fruitful, in that framework, to allow a broader concept of the character of physical reality. To know the state of a system of particles, one must know not only their positions, but also their velocities and their masses. Armed with that information, classical mechanics predicts the system’s future evolution completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity."

"Newtonian mechanics does not apply to all situations. If the speeds of the interacting bodies are very large —an appreciable fraction of the speed of light —we must replace Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. If the interacting bodies are on the scale of atomic structure (for example, they might be electrons in an atom), we must replace Newtonian mechanics with quantum mechanics. Physicists now view Newtonian mechanics as a special case of these two more comprehensive theories. Still, it is a very important special case because it applies to the motion of objects ranging in size from the very small (almost on the scale of atomic structure) to astronomical (galaxies and clusters of galaxies)."

"Newton did not show the cause of the apple falling, but he shewed a similitude between the apple and the stars. By doing so he turned old facts into new knowledge; and was well content if he could bring diverse phenomenon under "two or three Principles of Motion" even "though the Causes of these Principles were not yet discovered.""