Physics Books

"[W]ithin the short span of a human life and with man's limited powers of memory, any stock of knowledge worthy of the name is unattainable except by the greatest mental economy. Science... may be regarded as a minimal problem... the completest possible presentment of facts with the least possible expenditure of thought."

"Nature does not begin with elements, as we are obliged to begin with them. It is certainly fortunate... that we can, from time to time, turn aside our eyes from the over powering unity of the All, and allow them to rest on individual details. But we should not omit, ultimately, to complete and correct our views by a thorough consideration of the things which for the time being we left out of account."

"When we reflect that the time-factor that enters into the is nothing more than... the measure of the distances (or angles of rotation) of the bodies of the universe, we see that even in the simplest case... apparently... the mutual action of only two masses, the neglecting of the rest of the world is impossible."

"The comportment of terrestrial bodies with respect to the earth is reducible to the comportment of the earth with respect to the remote heavenly bodies. If we were to assert that we knew more of moving objects than this their... experimentally-given comportment with respect to the celestial bodies, we should render ourselves culpable of a falsity. When... we say, that a body preserves unchanged its direction and velocity in space, our assertion is... an abbreviated reference to the entire universe. ...[S]uch ...is permitted the original author Newton, Descartes or Galileo] of the principle, because he knows... no difficulties stand in the way of carrying out its implied directions. But no remedy lies in his power, if difficulties of the kind mentioned present themselves; if, for example, the requisite, relatively fixed bodies are wanting."

"Let us... examine the point on which Newton, apparently with sound reasons, rests his distinction of absolute and relative motion. If the earth is affected with an absolute rotation about its axis, centrifugal forces are set up in the earth: it assumes an oblate form, the acceleration of gravity is diminished at the equator, the plane of Foucault's pendulum rotates, and so on. All these phenomena disappear if the earth is at rest and the other heavenly bodies are affected with absolute motion round it, such that the same relative rotation is produced. This is, indeed, the case, if we start ab initio from the idea of absolute space. But if we take our stand on the basis of facts, we shall find we have knowledge only of relative spaces and motions. Relatively, not considering the unknown and neglected medium of space, the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical. The universe is not twice given, with an earth at rest and an earth in motion; but only once, with its relative motions, alone determinable. It is, accordingly, not permitted us to say how things would be if the earth did not rotate. We may interpret the one case that is given us, in different ways. If, however, we so interpret it that we come into conflict with experience, our interpretation is... wrong. The principles of mechanics can, indeed, be so conceived, that even for relative rotations s arise."

"It might be... that... motion is determined by a medium... In such a case we should have to substitute this medium for Newton's absolute space. ...[I]t is easily demonstrable that the atmosphere is not this motion-determinative medium. We should, therefore, have to picture to ourselves some other medium, filling, say, all space, with respect to... which... we have at present no adequate knowledge. In itself such a state of things would not belong to the impossibilities. It is known, from recent hydrodynamical investigations, that a rigid body experiences resistance in a frictionless fluid only when its velocity changes. ...[T]his result is derived theoretically from the notion of inertia; but it might... also be regarded as the primitive fact from which we... start. ...[W]e might... hope to learn more in the future concerning this hypothetical medium; and from the point of view of science it would be in every respect a more valuable acquisition than the forlorn idea of absolute space."

"Newton has... acted contrary to his expressed intention only to investigate actual facts. No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs, that cannot be produced in experience. All our principles of mechanics are... experimental knowledge concerning the relative positions and motions of bodies. ...No one is warranted in extending these principles beyond the boundaries of experience. ...[S]uch an extension is meaningless, as no one possesses the requisite knowledge to make use of it."

"We arrive at the idea of time,—to express it briefly and popularly,—by the connection of that which is contained in... our memory with that which is contained in... our sense-perception. When we say that time flows on in a definite direction or sense, we mean that physical events generally (and therefore also physiological events) take place only in a definite sense. Differences of temperature, electrical differences, differences of level generally, if left to themselves, all grow less and not greater. ...In all this there is... a peculiar and profound connection of things. To demand at... present... a full elucidation of this matter, is to anticipate, in the manner of speculative philosophy, the results of all future special investigation, that is a perfect physical science."

"[W]e are not restricted to any one definite measure, all being interconnected."

"It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things..."

"[A]ll things in the world are connected with one another and depend on one another, and...we... and all our thoughts are... a part of nature."

"Time... appears to be some particular and independent thing, on the progress of which the position of the pendulum depends, while the things that we resort to for comparison and choose at random appear to play a wholly collateral part."

"Newton... [with respect to "Absolute, true, and mathematical time... duration" and to "Relative, apparent, and commone time"] stood under the influence of the view of mediæval philosophy, as though he had grown unfaithful to his resolve to investigate only actual facts."

"The principle of the parallelogram of forces, at which Stevinus arrived and employed, (yet without expressly formulating it,) consists... of following truth. If a body A (Fig. 26) is acted by two forces whose directions coincide with the AB and AC, and whose magnitudes are proportional the lengths AB and AC, these two forces produce the same effect as a single force, which acts in the direction of the diagonal AD of the parallelogram ABCD and is proportional to that diagonal."

"[E]very enlightening progress made in science is accompanied with a certain feeling of disillusionment. We discover that that which appeared wonderful to us is no more wonderful than other things which we know instinctively and regard as self-evident; nay, that the contrary would be much more wonderful; that everywhere the same fact expresses itself. Our puzzle turns out then to be a puzzle no more; it vanishes into nothingness, and takes its place among the shadows of history."

"We now propose to enter more minutely into subject of our inquiries, and at the same time, without making the history of mechanics the chief topic discussion, to consider its historical development so far as this is requisite to an understanding of the present state of mechanical science... Apart from the consideration that we cannot afford to neglect the great incentives that it is in our power to derive from the foremost intellects of all epochs, incentives which taken as a whole are more fruitful than the greatest men of the present day are able to offer, there is no grander, no more intellectually elevating spectacle than that of the utterances of the fundamental investigators in their gigantic power. Possessed as yet of no methods, for these were created by their labors, and are only rendered comprehensible to us by their performances, they grapple with and subjugate the object of their inquiry, and imprint upon it the forms of conceptual thought. They that know the entire course of the development of science, will, as a matter of course, judge more freely and more correctly of the significance of any present scientific movement than they, who limited in their views, to the age in which their own lives have been spent, contemplate merely the momentary trend that the course of intellectual events takes at the present moment."

"In the infinite variety of nature many ordinary events occur; while others appear uncommon, perplexing, astonishing, or even contradictory to the ordinary run of things. As long as this is the case we do not possess a well-settled and unitary conception of nature. Thence is imposed the task of... seeking out... those elements that are the same, and... ever present. By this means, on the one hand, the most economical and briefest description and communication are rendered possible; and on the other, when once a person has acquired the skill of recognising these permanent elements throughout the greatest range and variety of phenomena... this ability leads to a comprehensive, compact, consistent, and facile conception of the facts. When... we are everywhere able to detect the same few simple elements, combining in the ordinary manner, then they appear to us as things... familiar... in the phenomena, we feel at home with them, they no longer perplex us, they are explained. It is a process of adaptation of thoughts to facts with which we are here concerned."

"[I]t is necessary to make a distinction between mechanical experience and mechanical science... If we carefully examine the ancient Egyptian and Assyrian monuments, we shall find there pictorial representations of many kinds of implements and mechanical contrivances... long before theory was dreamed of, implements, machines, mechanical experiences, and mechanical knowledge were abundant."

"Regard for the true endeavor of philosophy, that of guiding into one common stream the many rills of knowledge, will not be found wanting in my work, although it takes a determined stand against the encroachments of metaphysical methods."

"The elucidations which I here offer are, in part, substantially contained in my treatise, Die Geschichte und die Wurzel des Satzcs von der Erhaltung der Arbeit (...1872). At a later date nearly the same views were expressed by Kirchhoff (Vorlesungen über mathematische Physik: Mechanik, Leipsic, 1874) and by Helmholtz (Die Thatsachen in der Wahrnehmung, Berlin, 1879), and have since become commonplace enough. Still the matter, as I conceive it, does not seem to have been exhausted, and I cannot deem my exposition to be at all superfluous."

"I have not in every case been able to avoid the use of the abbreviated and precise terminology of mathematics. To do so would have been to sacrifice matter to form; for the language of everyday life has not yet grown to be sufficiently accurate for the purposes of so exact a science as mechanics."

"The gist and kernel of mechanical ideas has in almost every case grown up in the investigation of very simple and special cases of mechanical processes; and the analysis of the history of the discussions concerning these cases must ever remain the method at once the most effective and the most natural for laying this gist and kernel bare. Indeed, it is not too much to say that it is the only way in which a real comprehension of the general upshot of mechanics is to be attained."

"An instinctive, irreflective knowledge of the processes of nature will doubtless always precede the scientific, conscious apprehension, or investigation, of phenomena. The former is the outcome of the relation in which the processes of nature stand to the satisfaction of our wants."

"The history of the development of mechanics, is... indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed."

"That branch of physics which is at once the oldest and the simplest and which is therefore as introductory to other departments of this science, is concerned with the motions and equilibrium masses. It bears the name of mechanics."

"The new apparatus for the illustration of the subject, here figured and described, were designed entirely by me and constructed by Mr. F. Hajek... In less immediate connection with the text stand the fac-simile reproductions of old originals in my possession. The quaint and naive traits of the great inquirers, which find in them their expression, have always exerted upon me a refreshing influence in my studies, and I have desired that my readers should share this pleasure with me."

"The questions here dealt with have occupied me since my earliest youth, when my interest for them was powerfully stimulated by the beautiful introductions of Lagrange to... his Analytic Mechanics, as well as by the lucid and lively tract of Jolly, Principien der Mechanik (...1852). If Duehring's estimable work, Kritische Geschichte der Principien der Mechanik (...1873), did not particularly influence me, it was that at the time of its appearance, my ideas had been... published. ...[T]he reader will... find many points of agreement between Dühring's criticisms and those here expressed."

"As stated repeatedly in this book, John von Neumann's Mathematical Foundations of Quantum Mechanics was an extraordinarily influential work. It is important to recall that the language most commonly used to describe and discuss the measurement process in terms of a collapse or projection of the wave function essentially originates with this classic work. It was von Neumann who so clearly distinguished (in the mathematical sense) between the continuous time-symmetric quantum mechanical equations of motion and the discontinuous, time-asymmetric measurement process. Although much of his contribution to the development of the theory was made broadly within the boundaries of the Copenhagen view, he stepped beyond those boundaries in his interpretation of quantum measurement."

"There are (at least) two possible ways to formulate precisely (i.e. mathematically) elementary QM. The eldest one, historically speaking, is due to von Neumann in essence, and is formulated using the language of Hilbert spaces and the spectral theory of unbounded operators. A more recent and mature formulation was developed by several authors in the attempt to solve quantum field theory problems in mathematical physics. … The newer formulation can be considered an extension of the former one, in a very precise sense that we shall not go into here, also by virtue of the novel physical context it introduces and by the possibility of treating physical systems with infinitely many degrees of freedom, i.e. quantum fields. In particular, this second formulation makes precise sense of the demand for locality and covariance of relativistic quantum field theories, and allows to extend quantum field theories to a curved spacetime."

"The physicists didn't want to be bothered with the idea that maybe quantum theory is only provisional. A horn of plenty had been spilled before them, and every physicist could find something to apply quantum mechanics to. They were pleased to think that this great mathematician had shown it was so. Yet the Von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It's not just flawed, it's silly. If you look at the assumptions made, it does not hold up for a moment. It's the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they're nonsense. You may quote me on that: The proof of Von Neumann is not merely false but foolish!"

"Thus the formal proof of von Neumann does not justify his informal conclusion: 'It is therefore not, as is often assumed, a question of reinterpretation of quantum mechanics - the present system of quantum mechanics would have to be objectively false in order that another description of the elementary process than the statistical one be possible.' It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made."

"The history of science is not restricted to the enumeration of successful investigations. It has to tell of unsuccessful inquiries, and to explain why some of the ablest men have failed to find the key of knowledge, and how the reputation of others has only given a firmer footing to the errors into which they fell."

"It has been asserted that metaphysical speculation is a thing of the past and that physical science has extirpated it. The discussion of the categories of existence, however, does not appear to be in danger of coming to an end in our time, and the exercise of speculation continues as fascinating to every fresh mind as it was in the days of Thales."

"According to Sir W. Thomson's theory of Vortex Atoms, the substance of which the molecule consists is a uniformly dense plenum, the properties of which are those of a perfect fluid, the molecule itself being nothing but a certain motion impressed on a portion of this fluid, and this motion is shewn, by a theorem due to Helmholtz, to be as indestructible as we believe a portion of matter to be. If a theory of this kind is true, or even if it is conceivable, our idea of matter may have been introduced into our minds through our experience of those systems of vortices which we call bodies, but which are not substances, but motions of a substance; and yet the idea which we have thus acquired of matter, as a substance possessing inertia, may be truly applicable to that fluid of which the vortices are the motion, but of whose existence, apart from the vortical motion of some of its parts, our experience gives us no evidence whatever."

"We may be mistaken. No one has as yet seen or handled an individual molecule, and our molecular hypothesis may, in its turn, be supplanted by some new theory of the constitution of matter; but the idea of the existence of unnumbered individual things, all alike and all unchangeable, is one which cannot enter the human mind and remain without fruit. But what if these molecules, indestructible as they are, turn out to be not substances themselves, but mere affections of some other substance?"

"There are innumerable other molecules, whose constants are not approximately, but absolutely identical with those of the first molecule, and this whether they are found on the earth, in the sun, or in the fixed stars. By what process of evolution the philosophers of the future will attempt to account for this identity in the properties of such a multitude of bodies, each of them unchangeable in magnitude, and some of them separated from others by distances which Astronomy attempts in vain to measure, I cannot conjecture. My mind is limited in its power of speculation, and I am forced to believe that these molecules must have been made as they are from the beginning of their existence. ...we cannot ascribe either their existence or the identity of their properties to the operation of any of those causes which we call natural. Is it true then that our scientific speculations have really penetrated beneath the visible appearance of things which seem to be subject to generation and corruption and reached the entrance of that world of order and perfection which continues this day as it was created perfect in number and measure and weight?"

"The properties of bodies were investigated by several distinguished French mathematicians on the hypothesis that they are systems of molecules in equilibrium. The somewhat unsatisfactory nature of the results... produced... a reaction in favour of the opposite method of treating bodies as if they were... continuous. This method, in the hands of Green, Stokes, and others, has led to results the value of which does not at all depend on what theory we adopt as to the ultimate constitution of bodies."

"Two theories of the constitution of bodies have struggled for victory with various fortunes since the earliest ages of speculation: one is the theory of a universal plenum, the other is that of atoms and void. The theory of the plenum is associated with the doctrine of mathematical continuity, and its mathematical methods are those of the Differential Calculus, which is the appropriate expression of the relations of continuous quantity. The theory of atoms and void leads us to attach more importance to the doctrines of integral numbers and definite proportions; but, in applying dynamical principles to the motion of immense numbers of atoms, the limitation of our faculties forces us to abandon the attempt to express the exact history of each atom, and to be content with estimating the average condition of a group of atoms large enough to be visible. This method... which I may call the statistical method, and which in the present state of our knowledge is the only available method of studying the properties of real bodies, involves an abandonment of strict dynamical principles, and an adoption of the mathematical methods belonging to the theory of probability. ...If the actual history of Science had been different, and if the scientific doctrines most familiar to us had been those which must be expressed in this way, it is possible that we might have considered the existence of a certain kind of contingency a self evident truth, and treated the doctrine of philosophical necessity as a mere sophism."

"We cannot enter into full sympathy with these lower phases of our nature without losing some of that antipathy to them which is our surest safeguard against a reversion to a meaner type, and we gladly return to the company of those illustrious men who by aspiring to noble ends, whether intellectual or practical, have risen above the region of storms into a clearer atmosphere, where there is no misrepresentation of opinion, nor ambiguity of expression, but where one mind comes into closest contact with another at the point where both approach nearest to the truth."

"The history of the development, whether normal or abnormal, of ideas is of all subjects that in which we, as thinking men, take the deepest interest. But when the action of the mind passes out of the intellectual stage, in which truth and error are the alternatives, into the more violently emotional states of anger and passion, malice and envy, fury and madness; the student of science, though he is obliged to recognise the powerful influence which these wild forces have exercised on mankind, is perhaps in some measure disqualified from pursuing the study of this part of human nature."

"It is true that the history of science is very different from the science of history. We are not studying or attempting to study the working of those blind forces which, we are told, are operating on crowds of obscure people, shaking principalities and powers, and compelling reasonable men to bring events to pass in an order laid down by philosophers. The men whose names are found in the history of science are not mere hypothetical constituents of a crowd, to be reasoned upon only in masses. We recognise them as men like ourselves, and their actions and thoughts, being more free from the influence of passion, and recorded more accurately than those of other men, are all the better materials for the study of the calmer parts of human nature."

"It is not so long ago since any man who devoted himself to geometry, or to any science requiring continued application, was looked upon as necessarily a misanthrope, who must have abandoned all human interests, and betaken himself to abstractions so far removed from the world of life and action that he has become insensible alike to the attractions of pleasure and to the claims of duty. In the present day, men of science are not looked upon with the same awe or with the same suspicion. They are supposed to be in league with the material spirit of the age, and to form a kind of advanced Radical party among men of learning."

"There is a narrow professional spirit which may grow up among men of science, just as it does among men who practise any other special business. But surely a University is the very place where we should be able to overcome this tendency of men to become, as it were, granulated into small worlds, which are all the more worldly for their very smallness. We lose the advantage of having men of varied pursuits collected into one body, if we do not endeavour to imbibe some of the spirit even of those whose special branch of learning is different from our own."

"It must be one of our most constant aims to maintain a living connexion between our work and the other liberal studies of Cambridge, whether literary, philological, historical or philosophical."

"There may be some mathematicians who pursue their studies entirely for their own sake. Most men, however, think that the chief use of mathematics is found in the interpretation of nature. Now a man who studies a piece of mathematics in order to understand some natural phenomenon which he has seen, or to calculate the best arrangement of some experiment which he means to make, is likely to meet with far less distraction of mind than if his sole aim had been to sharpen his mind for the successful practice of the Law, or to obtain a high place in the Mathematical Tripos."

"A man whose soul is in his work always makes more progress than one whose aim is something not immediately connected with his occupation. In the latter case the very motive of which he makes use to stimulate his flagging powers becomes the means of distracting his mind from the work before him."

"Now in the case of study, a great part of our fatigue often arises, not from those mental efforts by which we obtain the mastery of the subject, but from those which are spent in recalling our wandering thoughts; and these efforts of attention would be much less fatiguing if the disturbing force of mental distraction could be removed."

"When we have overcome these difficulties, and successfully bridged over the gulph between the abstract and the concrete... we have acquired the rudiment of a permanent mental endowment. When, by a repetition of efforts of this kind, we have more fully developed the scientific faculty, the exercise of this faculty in detecting scientific principles in nature, and in directing practice by theory, is no longer irksome, but becomes an unfailing source of enjoyment, to which we return so often, that at last even our careless thoughts begin to run in a scientific channel."

"It is not till we attempt to bring the theoretical part of our training into contact with the practical that we begin to experience the full effect of what Faraday has called "mental inertia"—not only the difficulty of recognising, among the concrete objects before us, the abstract relation which we have learned from books, but the distracting pain of wrenching the mind away from the symbols to the objects, and from the objects back to the symbols. This however is the price we have to pay for new ideas."

"The knowledge of physical science obtained by the combined use of mathematical analysis and experimental research will be of a more solid, available, and enduring kind than that possessed by the mere mathematician or the mere experimenter."