Physics

"When the muscles of our bodies are excited... the fibres tend to shorten themselves and at the same time expand laterally. A state of stress is produced in the muscle, and the limb moves. This explanation of muscular action is by no means complete..."

"For similar reasons we may regard Faraday's conception of a state of stress in the electro-magnetic field as a method of explaining action at a distance by means of the continuous transmission of force, even though we do not know how the state of stress is produced."

"[T]he only kind of electro-magnetic disturbance which can be propagated through a non-conducting medium is a disturbance transverse to the direction of propagation, agreeing... with what we know about that disturbance which we call light."

"[O]ne of Faraday's most pregnant discoveries, that of the magnetic rotation of polarised light, enables us to proceed... Of two circularly polarised rays of light, precisely similar in configuration, but rotating in opposite directions, that ray is propagated with greater velocity which rotates in the same direction as the electricity of the magnetizing current."

"Thus every line of force preserves its identity during the whole course of its existence, though its shape and size may be altered to any extent."

"[E]very question relating to the forces acting on magnets or currents, or to the induction of currents in conducting circuits, may be solved by the consideration of Faraday's lines of force. In this place they can never be forgotten. By means of this new symbolism, Faraday defined with mathematical precision the whole theory of electro-magnetism, in language free from mathematical technicalities, and applicable to the most complicated and simplest cases."

"He observed that the motion which the magnetic and electric force tends to produce is invariably such a to shorten the lines of force and allow them to spread out laterally from each other. He thus preserved in the medium a state of stress, consisting of a tension, like that of a rope, in the direction of the lines of force, combined with a pressure in all directions at right angles to them."

"This is quite a new conception of action at a distance, reducing it to a phenomenon of the same kind as that action at a distance which is exerted by means of the tension of ropes and the pressure of rods."

"[E]ach individual line has a continuous existence in space and time. When a piece of steel becomes a magnet, or when an electric current begins to flow, the lines of force do not start into existence each in its own place, but as the strength increases new lines are developed within the magnet or current, and gradually grow outwards, so that the whole system expands from within, like in our former experiment."

"[T]he electro-magnetic theory of light will agree in every respect with the undulatory theory, and the work of Thomas Young and Fresnel will be established on a firmer basis than ever, when joined with that of Cavindish and Coulomb by the key-stone of the combined sciences of light and electricity—Faraday's great discovery of the electro-magnetic rotation of light."

"When Newton demonstrated that the force which acts on each of the heavenly bodies depends on its relative position with respect to the other bodies, the new theory met with violent opposition by the advanced philosophers... who described the doctrine of gravitation as a return to the exploded method of explaining everything by occult causes, attractive virtues, and the like. Newton... answered that he made no pretence of explaining the mechanism... To determine the mode in which their mutual action depends on their relative positions was a great step in science, and this Newton asserted he had made."

"The progress of science in Newton's time consisted in getting rid of the celestial machinery with which generations of astronomers had encumbered the heavens, and thus "sweeping cobwebs off the sky." Though the planets had already got rid of their crystal spheres, they were still swimming in the vortices of Descartes. Magnets were surrounded by effluvia, and electrified bodies by atmospheres, the properties of which resembled in no respect those of ordinary effluvias and atmospheres."

"[I]t was most essential that Newton's method should be extended to every branch of science to which it was applicable—that we should investigate the forces with which bodies act on each other... before attempting to explain how that force is transmitted. No men could be better fitted to apply themselves to the first part of the problem, than those who considered the second part quite unnecessary."

"But so far was Newton from asserting that bodies really act... over a distance, independently of anything in between them, that in a letter to Bentley... quoted by Faraday... he says:—"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must do if gravitation, in the sense of Epicurus, be essential and inherent in it... That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe that no man who has in philosophical matters a competent faculty of thinking can ever fall into it.""

"[A]s for those who introduce ætherial, or other media... without any direct evidence... or any clear understanding of how the media work... the less these men talk about their philosophical scruples about admitting action at a distance the better."

"The best way to prove that when one body pushes another it does not touch it, is to measure the distance between... Here are two glass lenses, one of which is pressed against another... By means of an electric light... a series of coloured rings is formed on the screen... first observed and first explained by Newton. The particular colour of any ring depends on the distance between the surfaces... [W]hat we call optical contact is not real contact. Optical contact indicates only that the distance between... is much less than a wavelength... Now it is possible to bring two pieces of glass so close together, that... they will adhere together so firmly, that when torn asunder the glass will break... Thus... bodies begin to press against each other whilst still at a measurable distance, and that even when pressed together with great force they are not in absolute contact... Why, then, say the advocates... should we continue to maintain the doctrine, founded only in the rough experience of a pre-scientific age, that matter cannot act where it is not, instead of admitting that all... contact essential to action were in reality cases of action at a distance... too small to be measured..."

"Accordingly, we find in his Optical Queries, and in his letters to Boyle, that Newton had very early made the attempt to account for gravitation by means of the pressure of a medium, and that the reason he did not publish these investigations "proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.""

"The mathematicians saw in this experiment nothing but a method of exhibiting at one view the direction in different places of the resultant two forces, one directed to each pole of the magnet; a somewhat complicated result of a simple law of force."

"Why... should we not admit that the familiar mode of communicating motion by pushing and pulling... is the type and exemplification of all action between bodies, even in case in which we can observe nothing between..."

"Here for instance is a kind of attraction which Professor Guthrie has made us familiar. A disk is set in vibtration, and is then brought near a light suspended body, which immediately begins to move towards the disk as if by an invisible cord. ...Sir W. Thomson has pointed out that in a moving fluid the pressure is least where the velocity is greatest. The velocity of the vibratory motion of the air is greatest near the disk. Hence the pressure of the air on the suspended body is less on the side nearest the disk... the body yields to the greater pressuire, and moves toward the disk. The disk, therefore, does not act where it is not. It sets the air next to it in motion by pushing it, this motion is communicated to more and more distant portions of the air in turn, and thus the pressure on opposite sides of the suspended body rendered unequal, and it moves toward the disk in consequence of excess pressure. The force is therefore the force of the old school—a case of vis a tergo—a shove from behind."

"But the advocates... maintain that even when the action is apparently the pressure of contiguous portions of matter... that a space always intervenes between... that so far from action at a distance being impossible, it is the only kind of action which ever occurs, and that the favorite old vis a tergo... exists only in the imagination of schoolmen."

"The advocates of the doctrine of action at a distance, however... say... Do we not see an instance of action at a distance in the case of a magnet... Besides this, Newton's law of gravitation... asserts not only that the heavenly bodies act ... across immense intervals of space... on one another with precisely the same force as if the strata beneath which each is buried [were] non-existant. If any medium takes part... it must surely make some difference whether the space... contains nothing but this medium, or whether it is occupied by the dense matter of the earth or of the sun."

"The mode in which Faraday was accustomed to look at phenomena of this kind differs from that adapted by many modern inquirers, and my special aim will be to enable you to place yourselves at Faraday's point of view, and to point out the scientific value of that conception of lines of force which, in his hands, became the key to the science of electricity. ..."

"But Faraday, by a series of steps as remarkable for their geometrical definiteness as for their speculative ingenuity, imparted to his conception of these lines of force a clearness and precision far in advance of that with which the mathematicians could then invest their new formulæ."

"The doctrine of direct action at a distance... was first asserted by , in his preface to the Principia... According to Cotes, it is by experience that we learn that all bodies gravitate. We do not learn in any other way that they are extended, movable, or solid. Gravitation, therefore, has as much right to be considered an essential property of matter..."

"The question is that of the transmission of force. We see two bodies at a distance from each other exert a mutual influence on each other's motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else?"

"Faraday's lines of force are not to be considered merely as individuals, but as forming a system, drawn in space in a definite manner so that the number of lines which pass through an area, say of one square inch, indicates the intensity of the force acting through the area. Thus the lines of force become definite in number. The strength of a magnetic pole is measured by the number of lines which proceed from it; the electro-tonic state of a circuit is measured by the number of lines which pass through it."

"And when the Newtonian philosophy gained ground in Europe, it was the opinion of Cotes rather than that of Newton that became most prevalent, till at last Boscovich propounded his theory, that matter is a congeries of mathematical points, each endowed with the power of attracting or repelling the others according to fixed laws. In his world, matter is unextended, and contact is impossible. He did not forget, however, to endow his mathematical points with inertia."

"I must ask you to go over very old ground, and to turn your attention to a question which has been raised again and again ever since man began to think."

"... Where was the particle just before I made the measurement? There are three plausible answers to this question, and they serve to characterize the main schools of thought regarding quantum indeterminacy: ... realist ... orthodox ... agnostic ... Until fairly recently, all three positions (realist, orthodox, and agnostic) had their partisans. But in 1964 John Bell astonished the physics community by showing that it makes an observable difference whether the particle had a precise (though unknown) position prior to the measurement, or not. Bell's discovery effectively eliminated agnosticism as a viable option ..."

"David J. Griffiths, Introduction to Quantum Mechanics (2nd ed., 2016), pp. 3–4"

"One of the fundamental concepts of mechanics is that of a particle. By this we mean a body whose dimensions may be neglected in describing its motion. The possibility of so doing depends, of course, on the conditions of the problem concerned. For example, the planets may be regarded as particles in considering their motion about the Sun, but not in considering their rotation about their axes."

"There were two things that especially attracted me to the ideas of renormalization and quantum field theory. One of them was that the requirement that a physical theory be renormalizable is a precise and rational criterion of simplicity. In a sense, this requirement had been used long before the advent of renormalization theory. When Dirac wrote down the Dirac equation in 1928 he could have added an extra ‘Pauli’ term ... which would have given the electron an arbitrary anomalous magnetic moment. Dirac could (and perhaps did) say ‘I won’t add this term because it’s ugly and complicated and there’s no need for it.’ I think that in physics this approach generally makes good strategies but bad rationales. It’s often a good strategy to study simple theories before you study complicated theories because it’s easier to see how they work, but the purpose of physics is to find out why nature is the way it is, and simplicity by itself is I think never the answer. But renormalizability was a condition of simplicity which was being imposed for what seemed after Dyson’s 1949 papers ... like a rational reason, and it explained not only why the electron has the magnetic moment it has, but also (together with gauge symmetries) all the detailed features of the standard model of weak, electromagnetic, and strong, interactions, aside from some numerical parameters. The other thing I liked about quantum field theory during this period of tremendous optimism was that it offered a clear answer to the ancient question of what we mean by an elementary particle: it is simply a particle whose field appears in the Lagrangian. It doesn’t matter if it’s stable, unstable, heavy, light — if its field appears in the Lagrangian then it’s elementary, otherwise it’s composite."

"In the history of Science it is possible to find many cases in which the tendency of Mathematics to express itself in the most abstract forms has proved to be of ultimate service in the physical order of ideas. Perhaps the most striking example is to be found in the development of abstract Dynamics. The greatest treatise which the world has seen, on this subject, is Lagrange's Mécanique Analytique, published in 1788. ...conceived in the purely abstract Mathematical spirit ...Lagrange's idea of reducing the investigation of the motion of a dynamical system to a form dependent upon a single function of the of the system was further developed by Hamilton and Jacobi into forms in which the equations of motion of a system represent the conditions for a stationary value of an integral of a single function. The extension by Routh and Helmholtz to the case in which "ignored co-ordinates" are taken into account, was a long step in the direction of the desirable unification which would be obtained if the notion of potential energy were removed by means of its interpretation as dependent upon the kinetic energy of concealed motions included in the dynamical system. The whole scheme of abstract Dynamics thus developed upon the basis of Lagrange's work has been of immense value in theoretical Physics, and particularly in statistical Mechanics... But the most striking use of Lagrange's conception of generalized co-ordinates was made by Clerk Maxwell, who in this order of ideas, and inspired on the physical side by... Faraday, conceived and developed his dynamical theory of the Electromagnetic field, and obtained his celebrated equations. The form of Maxwell's equations enabled him to perceive that oscillations could be propagated in the electromagnetic field with the velocity of light, and suggested to him the Electromagnetic theory of light. Heinrich Herz, under the direct inspiration of Maxwell's ideas, demonstrated the possibility of setting up electromagnetic waves differing from those of light only in respect of their enormously greater length. We thus see that Lagrange's work... was an essential link in a chain of investigation of which one result... gladdens the heart of the practical man, viz. wireless telegraphy."

"Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible—in statistics by the use of the principle of virtual velocities, in dynamics by the use of . This led... to generalized coordinates and to the equation of motion in their "Lagrangian" form... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis."

"The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians. Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of ."

"When the position of every point of a material system can be determined in terms of any independent variables n in number, the system is said to possess n degrees of freedom, and the n independent variables are called the generalised coordinates. The choice of the particular independent variables is perfectly arbitrary, and may be varied indefinitely, but the number of degrees of freedom cannot be either increased or diminished."

"When the body degenerates into a material straight line the number of degrees of freedom is reduced to five; and when this straight line is constrained to move parallel to some fixed plane the number of degrees of freedom is still further reduced to four."

"In a rigid body free to move in any manner there are six degrees of freedom, and the generalised coordinates most frequently chosen in this case are the three rectangular coordinates of some point in the body and three angular coordinates determining the orientation of the body about that point, generally the angles θ, φ, ψ of ordinary occurrence in rigid dynamical problems."

"As related by Archimedes in the "sand-counter", Aristarchus advanced the bold hypothesis that the earth rotates in a circle about the sun. Most astronomers rejected this... as Archimedes tells us also. [I]n view of the status of mechanics at the time, there are weighty arguments against the motion of the earth... already found in Aristotle and, developed more fully, in Ptolemy. If the earth had such an enormously rapid motion, says Ptolemy, then everything that was not clinched to and riveted to the earth, would fall behind and would therefore appear to fly off in the opposite direction. Clouds... would be overtaken by the rotation of the earth and would lag behind. ...[T]here is nothing to be said against this since the Greeks did not know the law of inertia and required a force to account for every motion. If the earth does not drag the clouds along, they have to lag behind. We do not know how Aristarchus met these arguments."

"The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force."

"On the law of inertia (next to that of the permanence of substance) the possibility of a natural science proper entirely rests. The opposite of the first, and therefore the death of all natural philosophy, would be hylozoism. From the same conception of inertia as that of mere lifelessness, it follows... that it does not signify a positive effort to maintain its state. Only living beings can be termed inert in this latter sense, inasmuch as they have a conception of another state, which they dread and strive against with all their might."

"Law I. Every body perseveres in its state of rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces. ...the motion of a cannon ball is retarded, but this arises from an action between the projectile and the air which surrounds it, whereby the ball experiences a force in the direction opposite to its relative motion, while the air, pushed forward by an equal force, is itself set in motion... But our conviction of the truth of this law may be greatly strengthened by considering what is involved in a denial of it. ...Let us in the first place suppose the law to be that the velocity diminishes at a certain [extremely slow] rate... The velocity referred to in this hypothetical law can only be the velocity referred to a point absolutely at rest... the point of reference. ...If, when referred to a certain point, the body appears to be moving northward with diminishing velocity, we have only to refer it to another point moving northward with a uniform velocity greater than that of the body, and it will appear to be moving southward with increasing velocity. Hence the hypothetical law is without meaning unless we admit the possibility of defining absolute rest and absolute velocity. Even if we admit this as a possibility, the hypothetical law, if found to be true, might be interpreted, not as a contradiction of Newton's law, but as evidence of the resisting action of some medium in space. To take another case. Suppose the law to be that a body, not acted on by any force, ceases at once to move. This is not only contradicted by experience, but it leads to a definition of absolute rest as the state which a body assumes as soon as it is freed from the action of external forces. It may thus be shown that the denial of Newton's law is in contradiction to the only system of consistent doctrine about space and time which the human mind has been able to form."

"The idea that inertia is an acquired property is old, generally going under the name of “”. According to it, inertia is due to the interaction of bodies with some omnipresent medium. Ideas along this line differ on what the medium is, and on the nature of the interaction. But if indeed such is the origin of inertia, then inertia is not some property of ultimate fundamentality, but can take different forms depending on where we are in parameter space of the body with respect to signposts and boundary stones defined by the characteristics of the medium."

"The inertia of matter is and means nothing but its lifelessness, as matter in itself. Life means the capacity of a substance, to act from an internal principle, determining a finite substance to change, and a material substance to rest or motion, as change of its state. ...Thus all matter as such is lifeless. The proposition of inertia says so much and no more. If we seek the cause of any change of matter whatsoever in life, we shall have to seek it at once in another substance, distinct from matter, although bound up with it."

"The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line."

"Second law of mechanics.—All change of matter has an external cause. (Every body remains in its state of rest or motion in the same direction and with the same velocity, if not compelled by an external cause to forsake this state.) Demonstration. (From universal metaphysics the proposition that all change has a cause, is laid at the foundation; here it only remains to be proved of matter, that its change must always have an external cause. ... this cause cannot be internal for matter has no absolutely internal determinations and grounds of determination. ... Observation. This mechanical law can only be called the law of inertia (lex inertiæ)..."

"[O]ne of the most interesting aspects in Fabri's physics is the wholehearted adoption of the important principle of conservation of rectilinear motion (...CRM) - a direct result of an impetus which... tends to conserve itself in the absence of obstacles or hindrences, and the possibility of motion in a vacuum... CRM is often referred to as "inertia", but this problematic term is both anachronistic and misleading. The word... (...meaning "laziness") was first utilized in a physical sense by Johannes Kepler, to mean a tendency of bodies to come to rest once they are set in motion... It was subsequently used, in a different sense - meaning the reluctance of bodies in rest to be set in motion - by Descartes... and even by Fabri himself. This notion, as... expressed in Newton's first law... could be regarded merely as a "less important aspect of inertia" than in his second law... it is also clear that the classical (or Newtonian) concept cannot be fully expressed and understood without Newton's third law and his concept of force..."

"The law of inertia has no known origin."

"[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path."