Physics

"The first formulation of (part of) mechanics by means of a variational principle... is due to Maupertuis in 1746 in a paper called "Les lois du mouvement et du repos déduites d'un principe métaphysique" (Laws of motion and rest deduced from a metaphysical principle). Maupertuis had first introduced the principle of least action in optics in 1744. ...Through experimentation, he found that this quantity depends on mass, velocity, and distance. He called the product of the three factors "action" and accordingly expressed a "principle of the least quantity of action"..."

"From the expression for the atom of energy or quantum hv, where h is a constant and v is the frequency of the radiation, it is obvious that there exist as many different types of quanta of energy as there exist different frequencies of radiation. There is no unique type of quantum of energy in nature. That which is universal is not the quantum of energy hv, but the constant h. It can be shown that Planck's constant h is not a mere number; it represents some definite abstract mathematical entity, and that entity is action. We must assume, therefore, that there exist atoms of action in nature, just as there exist atoms of matter. ...we must possess a fairly thorough understanding of what is meant by action, as also of the part this important entity plays in science. ...the atomicity of action ...suggests that change is always discontinuous ...a series of jerks or jumps."

"Classical mechanics"

"I very much enjoyed your delightful explanation of the formation of meanders. It just happens that my wife had asked me about the “teacup phenomenon” a few days earlier, but I did not know a rational explanation. She says that she will never stir her tea again without thinking of you."

"The theoretical developments involving general relativity in the period prior to the renaissance made use of central principles of Einstein’s theory and of his s and methodology; the physicists who pursued these developments mostly did so, however, not to explore general relativity for its own sake but, rather, from an ulterior motive—the construction of some sort of successor theory. This goal they did not achieve. They did not consider general relativity itself to be a theory fundamental enough to warrant detailed theoretical study, nor did they believe that it held much empirical potential beyond what was already known. There was one central exception to this latter belief, and that is cosmology."

"In the early 1960s general relativity experienced a sudden revival in connection with astrophysical discoveries far removed from its original domain, which had essentially been confined to the solar system. The physicist Clifford Will coined the phrase “Renaissance of General Relativity” to describe the process through which general relativity became an internationally visible, highly active field of research in which theoretical explorations went hand in hand with new astrophysical discoveries such as s and the radiation. The systematic exploration of exact solutions, and the understanding of space-time singularities and of the physical reality of gravitational waves, all came only after the low-water-mark period, in the wake of the renaissance of general relativity."

"Although Einstein's general theory of relativity predicts that there can exist... a singularity in our past, it provides no reason why... a creation out of nothing should occur. ...There are ways of avoiding... a past singularity. If gravity were ever to become a repulsive... force in the distant past then the Universe need not have experienced a singular beginning."

"Einstein's general theory of relativity... was needed not because of conspicuous failures of Newton's theory... but because of inconsistencies between it and the requirements of electromagnetic theory, which Einstein had revised earlier in his special theory of relativity."

"Theory of relativity"

"Special relativity"

"Relativity Simply Explained"

"Albert Einstein"

"GTR has an extreme inner beauty and elegance; the construction of the GTR required the introduction of only one constant—the constant of gravitation. ...GTR produces the following: (1) Newton's law of gravitation, itself; (2) a foundation that enables one to apply Newton's law to the interaction of bodies surrounded by infinitely expanding matter; and (3) Friedmann's nonstationary cosmological model, including the prediction of the Hubble redshift for the spectra of distant objects. Only secondarily do we cite the three famous tests...—the precession of Mercury's perihelion, the deflection of a light beam passin near the Sun, and the variation of the frequency of light in a gravitational field."

"Thomas Matthews and prepared to... make some observations of a radio source they denoted 3C48... interested in... [the] visible light... on the night of September 26, 1960 they took a photographic plate of the area... Conventional wisdom... told them that they would find a cluster of galaxies... Instead... subsequent observations... and throughout 1961 showed... its spectrum of colors was highly unusual... its brightness and luminosity varied widely and rapidly... it was only "quasi" stellar. Hence the name quasi stellar radio source or ""... It was a remarkable year for general relativity, because it contained all the signs that a renaissance was about to begin. ...an era in which general relativity would become an active and exciting branch of physics, after almost a half century in the backwaters."

"September 1959 to September 1960—a year with great portents for Einstein's general theory of relativity. ...a paper by Robert V. Pound and Glen A. Rebka, Jr. ...entitled "Apparent Weight of Photons"... described the first successful laboratory measurement of the... gravitational red shift of light... A few months later, in June 1960... there appeared a paper by... Roger Penrose... "A Approach to General Relativity." ...[which] outlined a very elegant and streamlined technique for solving certain problems in general relativity. ...Later that summer ... ...[put] the finishing touches on his Ph.D. thesis ..."Mach's Principle and a Varying Gravitational Constant." ...[which] presented the equations for ...an alternative to Einstein's ...a "scaler-tensor" theory of gravity ...[eventually] known as the ."

"... I don’t see any reason why anyone today would take Einstein’s general theory of relativity seriously as the foundation of a quantum theory of gravitation, if by Einstein’s theory is meant the theory with a Lagrangian density given by just the term {\sqrt{g} R / 16 \pi G}. It seems to me there’s no reason in the world to suppose that the Lagrangian does not contain all the higher terms with more factors of the curvature and/or more derivatives, all of which are suppressed by inverse powers of the Planck mass, and of course don’t show up at any energy far below the Planck mass, much less in astronomy or particle physics. Why would anyone suppose that these higher terms are absent?"

"Despite the weakness of the early experimental evidence for general relativity, Einstein’s theory became the standard textbook theory of gravitation in the 1920s and retained that position from then on, even while the various eclipse expeditions of the 1920s and 1930s were reporting at best equivocal evidence for the theory. … Perhaps all of us were just gullible and lucky, but I do not think that is the real explanation. I believe that the general acceptance of general relativity was due in large part to the attractions of the theory itself—in short, to its beauty."

"In the past, the thesis that this conversation is eternal sometimes provoked a few chuckles, but then I realised that it was worth remembering that Einstein's relativity, although with a logic very different from mine, says that future and past events are no less real than present ones. So much so that when Popper spoke with Einstein, he called him Parmenides. Interviewer: The English physicist Julian Barbour asserts that time does not exist and that events are like postcards hanging on a clothesline, all present at the same time... Severino: Yes, he slightly varied the image that Popper used with Einstein of frames wrapped in a reel. But neither of them can explain the camera or the movement of the gaze that passes from one postcard to another. To do so requires a logic [...] that science cannot provide. In general, science believes that the mind is a special thing among things. This is where the theory of experience, which scientists tend to neglect, comes into play. Experience is the transcendental mind; it does not enter or exit a field of vision but is the place where everything enters and exits. To understand what the unwinding of the frames or the gaze that flows over the postcards is, we need to introduce the concept of transcendental consciousness, which was glimpsed in some way by idealism, that is, the place within which the eternal occurs. The so-called becoming of the world cannot be the beginning of being and the cessation of being, but is the appearing and disappearing of the eternal in that transcendental consciousness."

"Einstein asked himself a question... how can the sun and the Earth "attract" each other without touching..? ...[H]e imagined that the sun and the Earth each modified the space and time that surrounded them, just as a body in water displaces the water... This modification of the structure of time influences in turn the movement of the bodies, causing them to "fall" toward one another. ...The Earth is a large mass and slows down time in its vicinity. ...If things fall, it is due to this slowing of time. ...Where time passes uniformly, in interplanetary space, things do not fall. ...[H]ere on ...our planet, the movement of things inclines naturally toward where time passes more slowly, as when we run ...into the sea and the resistance of the water on our legs makes us fall headfirst... [T]ime passes more slowly for your feet than it does for your head."

"The great triumph of the theory of relativity lies in its absorbing the universal force of gravitation into one geometric structure... Einstein's achievements would be substantially as great even though it were not for... observational tests."

"It thus characterizes not only the gravitational field but also the behaviour of measuring rods and clocks, i.e. the metric of the four-dimensional world which contains the geometry of ordinary three-dimensional space as a special case. This fusion of two previously quite disconnected subjects—metric and gravitation—must be considered as the most beautiful achievement of the general theory of relativity."

"The number of those actively engaged in research in general relativity ... remain[ed] small in the 1930s, 1940s, and early 1950s. ... once said to me, 'You only had to know what your six best friends were doing and you would know what was happening in general relativity.' ...However, in the 1930s a new element... briefly attracted attention, then stayed... quiescent for a quarter of a century. ...J. Robert Oppenheimer and... decided to study the relative influence of nuclear and gravitational influences in s. ...Their work attracted... Richard Chase Tolman. ...there appeared in 1939, a pair of papers, one by Tolman on the static solution of Einstein's field equations for fluid spheres... and one... by Oppenheimer and ... In this paper, the foundations are laid for a general relativistic theory of . ...Half a year later, the paper... by Oppenheimer and came out... Thus began the physics of s..."

"The theory of gravitational fields, constructed on the basis of the theory of relativity, is called the general theory of relativity. It was established by Einstein (and finally formulated by him in 1915), and represents probably the most beautiful of all existing physical theories. It is remarkable that it was developed by Einstein in a purely deductive manner and only later was substantiated by astronomical observations."

"A scientific theory is usually felt to be better than its predecessors not only in the sense that it is a better instrument for discovering and solving puzzles but also because it is somehow a better representation of what nature is really like. One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is “really there.” Perhaps there is some other way of salvaging the notion of ‘truth’ for application to whole theories, but this one will not do. There is, I think, no theory-independent way to reconstruct phrases like ‘really there’; the notion of a match between the ontology of a theory and its “real” counterpart in nature now seems to me illusive in principle. Besides, as a historian, I am impressed with the implausability of the view. I do not doubt, for example, that Newton’s mechanics improves on Aristotle’s and that Einstein’s improves on Newton’s as instruments for puzzle-solving. But I can see in their succession no coherent direction of ontological development. On the contrary, in some important respects, though by no means in all, Einstein’s general theory of relativity is closer to Aristotle’s than either of them is to Newton’s."

"The other constraint in our choice of concepts... lies in Einstein's call for frugality and simplicity. ...the aim of any good theoretical system is "the greatest possible sparsity of the logically independent elements (basic concepts and axioms)." Any redundancy or elaboration must be avoided, for "it is the grand object of all theory to make these irreducible elements as simple and as few in number as possible." For example, it was, in his view, "an unsatisfactory feature of classical mechanics that in its fundamental laws the same mass appears in two different roles, namely as an inertial mass in the laws of motion, and as a gravitational mass in the law of gravitation." The equivalence of these two interpretations of mass signaled to him a truth which needed to be stated as a basic axiom (in General Relativity Theory), rather than saddling the theory with a proliferation which did not seem to be inherent in phenomena."

"To begin with the difference between my conception and Newton's law of gravitation: Please imagine the earth removed, and in its place suspended a box as big as a room or a whole house and inside a man naturally floating in the centre, there being no for force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenly jerked to one side, which is scientifically termed 'difform motion,' as opposed to 'uniform motion.' The person would then naturally reach bottom on the opposite side. The result would consequently be the same as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difform motion will in every case produce the same effects as gravitation. I have applied this new idea to every kind of difform motion and have thus developed mathematical formulas which I am convinced give more precise results than those based on Newton's theory. Newton's formulas, however, are such close approximations that it was difficult to find by observation any obvious disagreement with experience."

"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity [is most obvious] lies nearest at hand; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."

"Oh leave the Wise our measures to collate One thing at least is certain, light has weight One thing is certain, and the rest debate— Light rays, when near the Sun, do not go straight."

"I might say that my recent work has been very much concerned with Einstein’s general relativity, and I believe that the times and the distances which are to be used in Einstein’s general relativity are not the same as the times and distances which would be provided by atomic clocks. There are good theoretical reasons for believing that that is so and for believing that gravitational forces are getting weaker, compared to electric forces, as the world gets older."

"General relativity was considered by Einstein as his most important discovery... a new theory of gravitation bringing in a very powerful kind of symmetry. This symmetry is of importance in physics only where gravitational fields occur, while the symmetry previously... of special relativity, is of importance in all physics. So that this further symmetry... although it is such a wonderful mathematical theory, does not have the big effect on physics."

"There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of his relativity—which was probably the greatest scientific discovery that was ever made."

"Up to the early 1950s, general relativity was a little-frequented subject, amongst physicists—a theory that had to be praised, but that could be safely ignored. ...Its supporting evidence was sparse, questionable, and unstable: essentially it reduced to the changing experimental verdicts on the three notorious tests."

"Differential geometry originally sneaked into theoretical physics through Einstein's theory of general relativity."

"If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston.""

"In the long debate about action at a distance versus contact action we also find a concern with the effective individuation of particles and subsystems and with distant action. Belief in contact action goes back to Aristotle and Eudoxes, based on the self-evident regulative principle that a thing cannot act where it is not. For them, causal explanations were essential for true science. For Descartes too, there could be no vacuum and what may appear to be empty is actually filled with an aether. After the Principia, there were basically two camps on the "gravity dilemma." The one, among whose members were the Cartesians, Leibniz, and Huygens, maintained that an ether was required to allow any intelligible explanation of gravitational phenomena. The other, notably represented by Newton's ally... , took gravity to be evidence for God's action. ...God is everywhere and, hence, "instantaneous" action... is no mystery. The basic motivating factor in demanding contact action was that of intelligibility. Maxwell put the matter quite succinctly when he argued for "a force of the old school—a case of vis a tergo—a shove from behind."

"What is the 'means' by which the non-local connection is actualized? ...[S]ome possible responses ...(1) The connection is mediated ...by particles or fields that propogate at superliminal fields. ...(2) The connection propogates backward in time. ...(3) Physical space has more than three spatial dimensions. ...(4) [P]hysical space is not simply connected. ... Option (2) violates the Principle of Causality. ... Based on the results of tests of Bell-type inequalities... non-local connections have at least the features... (a) not decreasing with distance; (b) cannot be shielded against; and (c) are highly selective in what they effect. The[se] features are consistent with Option (4)..."

"The results of experiments on Bell-type arrangements have forced the conceptual issue of quantum non-locality into focus. ...[A]ny physically adequate quantum theory must violate the Principle of Locality. Yet the idea... still sits uncomfortably with most of us. ...The kind of non-locality... has been described as 'benign' since it cannot be used for any kind of signalling... and therefore does not explicitly violate Special Relativity. It is fortunate that parts of the universe do not constantly exhibit non-local behaviors so that we can continue to use established scientific methods to investigate the world. However... non-locality does not necessitate a causality."

"Quantum mechanics has an axiomatic structure, exposed by von Neumann, Dirac and others. The axioms... tell us that every state of a system corresponds to a vector in a complex , every physical observable corresponds to linear hermitian operator acting on that Hilbert space, etc. ...Special relativity can be deduced... from two axioms: the equivalence of inertial reference frames, and the constancy of the speed of light. Both axioms have clear physical meaning. By contrast, the numerous axioms of quantum mechanics have [none]... the new axioms are hardly more natural than the old. offers hope... a remarkable property of... nonlocality. ...Bell showed, quantum correlations could not arise in any theory in which all variables obey relativistic causality. On the other hand, quantum correlations themselves obey relativistic causality—we cannot exploit quantum correlations to transmit signals at superliminal speeds (ar at any speed). That quantum mechanics combines nonlocality and causality is wondrous... Shimony has aptly called the nonlocality manifest in quantum correlations "passion at a distance"... [and] has raised the question whether nonlocality and causality can peacefully coexist in any other theory besides quantum mechanics."

"[T]he view that the ultimate theory... should be more in accord with the fundamental principles of quantum theory need not imply that such a theory will be any form of quantum theory currently known, such as quantum mechanics or quantum field theory. ...[These] are far from complete or free of deficiencies even within their proper scope. Some new or perhaps now unimaginable theories and very likely new principles may be required to approach the ultimate constitution of nature. Will these theories retain the locality principle? My Bayesian bet would be that this will more likely than not to be the case, but one cannot be certain."

"The principle of locality states that no instantaneous transmission of physical influences between spatially separated physical systems ("action at a distance") is allowed, or... that physical systems can only be physically influenced by their immediate environment. ...[The] broader principle states that any possible definitive determinations concerning any given system—its physical state; the application of technology (such as a measurement, which, rather than a prediction, definitely determines a physical state of a quantum system); the falsifiability of claims concerning quantum systems, and so forth—is local."

"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 be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. 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 no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent is material or immaterial, I have left to the consideration of my readers."

"Descartes' objective was comprehensibility—to make the workings of nature completely transparent. Locality was essential to this goal. Objects interacted strictly locally: they moved in straight lines until they collided; only then did they change course. Like Democritus and Aristotle, Descartes offered no real evidence for this principle."

"The generation that grew up with Newtonian gravity found the theory entirely natural. For millennia, natural philosophers recoiled from nonlocality; in the eighteenth century, they embraced it. ...And no sooner did scholars get used to Newtonian nonlocality when along came another U-turn and a new generation went back to thinking that the world had to be—just had to be—local, thereby setting up our present predicament. ...Naturalistic explanations tend to be local. In our experience, when you want something to move... you need to go over and push on it... Thales suggested that earthquakes occur [not by the arbitrary will of gods, but] because the land is floating on a subterranean ocean... occasionally rocking back and forth. The cause is in direct contact with the effect. ...The concept of space was the atomists' [e.g., Democritus and Lucretius] creation. ...matter needs a venue to exist and move. ...If atoms were the athletes and space the playing field, locality was the rulebook. ...The atomists held that atoms interact only by direct contact."

"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. 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? 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. ... 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..."

"In fact every theory in the history of physics before quantum theory was EPR-local. So the discovery that the world is not EPR-local (i.e. that any physical theory that makes accurate predictions cannot be EPR-local) would mark a radical break in the history of physics."

"[L]ocality... reflects our ability to construct the "big picture" like a jigsaw puzzle, starting with a description of the most basic interactions among elementary particles."

"To soothe the theologians, who in his time were pressing so hardly upon Galileo, Descartes was content to say that the operation by which God maintains the world is similar to that by which he created it; so that, if it had pleased him, instead of creating it instantaneously, to allow these laws of evolution to operate, the result would have been what we now see. He began by assuming space to be occupied by perfectly homogeneous and continuous matter. He then supposed this solid substance to be divided into parcels of various shape and size, each of them animated by motion in various directions. These would observe the laws of motion as Descartes defines them:—1. Each would maintain its own condition of rest or motion or magnitude, until altered by contact with another. 2. In such contact the gain or loss of motion to one body would be exactly compensated by the loss or gain to another—the total quantity of motion in the world remaining invariable. 3. Owing to constant contacts, motion would be usually in curved lines, the moving body tending always to follow the tangent to the curve. The result after a period of time would be the differentiation of primitive matter into three kinds. The moving portions of matter, by constant attrition, would be for the most part converted into spheroidal molecules of various sizes. Some larger masses of irregular shape would amalgamate into solid masses; the finer particles rubbed off from the molecules would insert themselves between them, vibrating with far more rapid motion than they. This vibrating ethereal substance would collect towards the centre of a vortex, and form a sun or star: round it would revolve aërial matter, and plunged amidst this, at various distances, the solid masses of the planets. How by degrees yet further differentiation took place... so that the various metals and crystals arose, and finally plant life, and animal life... is described in the Principia and in the Treatise on Man."

"Classical electrodynamics is generally understood to be the paradigm of a local and causal physical theory. ...[A] theory with real fields realistically appears to be a local theory. ...But what, exactly, is it for a theory to be local or nonlocal? ...Informally, locality principles are often introduced in causal terms. Newtonian graviational theory... is said to be nonlocal because it allows action-at-a-distance, while the theory of special relativity is often said to imply the locality condition that there can be no superliminal causal propogation. According to a widespread view, however, the notion of causation should have no place in fundamental physics... Thus, Bertrand Russell famously argued that in the advanced sciences the notion of functional dependency has replaced that of causation... "a relic of a bygone age..." ...Russell was wrong. ...I will appeal to Dirac's classical theory of the electron ....the most promising candidate for a fully consistent theory of classical charged particles, is causally nonlocal. ...[T]he theory allows for forces to act where they are not and for superliminal causal propogation."

"Frans van Luteren (1991), in his extensive... study of conceptions of gravity in the eighteenth and nineteenth centuries, demonstrates that a quest for intelligibility was uppermost for several physicists who attempted [to challenge the absolute non-locality doctrine with] ether-type explanations for action-at-a-distance."

"For several centuries, there has been a strong feeling that nonlocal theories are not acceptable in physics. ...Newton felt very uneasy about action-at-a-distance and... Einstein regarded it as 'spooky'. But... one can see nothing basically irrational about such an idea. Rather it seems to be most reasonable to keep an open mind on the subject and therefore allow oneself to explore this possibility. If the price of avoiding nonlocality is to make an intuitive explanation impossible, one has to ask whether the cost is not too great."