The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behaviour under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not (...) occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature. (shrink)

In this paper, I want to draw attention to a connection between rigid designation with its consequence that we are able to stipulate worlds and haecceitism, the doctrine that we have possible worlds alike in all qualitative features which nonetheless are metaphysically different, in that two individuals can have all their qualitative features swapped while remaining the same individuals. I shall argue that stipulation leads to haecceitism, which in turn depends upon commitment to haecceity ("primitive thisness"). Haecceitism is, I (...) claim, an unattractive doctrine, but there is one powerful argument for it, drawn from the desire to make sense of observed frequencies of probabilistic events in terms of possible configurations of phase spaces which may be taken to be a form of possible world. However, by paying close attention to classical and quantum statistics, we see that this argument fails. (shrink)

This article compares treatments of the Stern–Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector but we cannot explain why there are only two locations where the electron is ever found. Using non-relativistic or relativistic quantum (...) mechanics, we can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum but we cannot explain another feature that could be explained within any of the other theories. (shrink)

The rigid recoil of a crystal is the accepted mechanism for the Mössbauer effect. It’s at odds with the special theory of relativity which does not allow perfectly rigid bodies. The standard model of particle physics which includes QED should not allow any signals to be transmitted faster than the speed of light. If perturbation theory can be used, then the X-ray emitted in a Mössbauer decay must come from a single nuclear decay vertex at which the (...) 4-momentum is exactly conserved in a Feynman diagram. Then the 4-momentum of the final state Mössbauer nucleus must be slightly off the mass shell. This off-shell behavior would be followed by subsequent diffusion of momentum throughout the crystal to bring the nucleus back onto the mass shell and the crystal to a final relaxed state in which it moves rigidly with the appropriate recoil velocity. This mechanism explains the Mössbauer effect at the microscopic level and reconciles it with relativity. Because off-mass-shell quantum mechanics is required, the on-mass-shell theories developed originally for the Mössbauer effect are inadequate. Another possibility is that that the recoil response involves a non-perturbative effect in the standard model which could allow for a non-local instantaneous momentum transfer between the crystal and the decay, as proposed for example by Preparata and others in super-radiance theory. The recoil time of the crystal is probably not instantaneous, and if it could be measured, one could distinguish between various theories. An experiment is proposed in this paper to measure this time. The idea is to measure the total energy radiated due to bremsstrahlung from a charged Mössbauer crystal which has experienced a recoil. Using Larmor’s formula, along with corrections to it, allows one to design an experiment. The favored idea is to use many small nano-spheres of Mössbauer-active metals, whose outer surfaces are charged. The energy radiated then varies as the charge squared divided by the recoil time. This can then be measured with the extreme sensitivity available in Mössbauer experiments. If it turns out that experiments prove the need for off-mass-shell theory, then this would have profound implications for all of condensed matter physics. It would mean that an off-mass-shell theory like those considered by Stueckelberg, Horwitz, Piron, Greenberger, and many others are required to describe nature. The inclusion of these would be a major shift in the foundations. It would mean that there are new dynamic variables—the rest masses of particles. The ability to measure the diffusion relaxation time should prove useful also in chemical analysis, and provide a new class of analytical methods for material science. This problem is also interesting because the Mössbauer effect is a phenomenon where the solid-state environment dramatically and indisputably influences the probability of a nuclear process. (shrink)

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients (...) are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed. (shrink)

The influential Berkeley theoretical physicist Geoffrey Chew renounced the reigning approach to the study of subatomic particles in the early 1960s. The standard approach relied on a rigid division between elementary and composite particles. Partly on the basis of his new interpretation of Feynman diagrams, Chew called instead for a “nuclear democracy” that would erase this division, treating all nuclear particles on an equal footing. In developing his rival approach, which came to dominate studies of the strong nuclear force (...) throughout the 1960s, Chew drew on intellectual resources culled from his own political activities and his attempts to reform how graduate students in physics would be trained. (shrink)

We may now ask the question: In what historical perspective should we place the work of Richard Goldschmidt? There is no doubt that in the period 1910–1950 Goldschmidt was an important and prolific figure in the history of biology in general, and of genetics in particular. His textbook on physiological genetics, published in 1938, was an amazing compendium of ideas put forward in the previous half-century about how genes influence physiology and development. His earlier studies on the genetic and geographic (...) distribution of the various species and races of Lymantria contributed soundly to an understanding of the inheritance and development of sex, as well as the genetics of speciation. He was a curious mixture of the experimentalist, empiricist, and theorizer, who could grasp both the large and the small at once and wrap them into the same integrated and coherent package.In insisting on trying to relate genetics to development, Goldschmidt was continually forced to speculate and to forsake experimental fact for generalized theory. In refusing to reconcile a physiological and developmental conception with a corpuscular theory of the gene, he forced himself to substitute for a large body of experimentally verified evidence, vague and general speculations which did not lead in any precise direction. L. C. Dunn summarizes succinctly the effect of Goldschmidt's thinking on the development of genetic theory: Although Goldschmidt's ideas had a considerable influence in directing attention to the developmental processes intervening between genes and characters, they did not lead to the establishment of a general theory of development in genetical terms. In fact, at the end of the period, as signalized by Goldschmidt's book of 1938 [Physiological Gentics] doubt remained whether there was a field with a defined problem which could be identified as developmental genetics.Yet the frequency with which Goldschmidt is cited by later writers suggests that there is a more positive side to his contribution than this. The early Mendelians had recognized the genic constitution of organisms and the Drosophila workers had uncovered in detail the chromosomal mechanism of heredity. These great discoveries were of classical character, solidly based on a multitude of well established facts. By themselves, however, they would not have been sufficient to place genetics in the central position within biology which it was to assume. Beyond the “static” analysis of gene transmission an insight was needed into the dynamic role of genes in cellular physiology, biochemistry, and development. Goldschmidt recognized this aspect and outlined in brilliant generalizations a physiological theory of genetics. Necessarily the prophetic nature of this achievement — romantic in the sense of Ostwald's classification of great scientists and their discoveries — transcended its factual basis. It was the audacity of the theoretician unimpeded by the still scanty data which gave a new focus to biological thought.Some have called Goldschmidt an “obstructionist” in the history of genetics—one whose efforts were largely directed toward useless and continual criticism — challenge for the sake of challenge. As this line of argument goes, time wasted answering Goldschmidt's poorly conceived criticisms could have been better used to pursue new lines of thought within the classical gene theory. Sometimes historians are upbraided for studying the work of such “obstructionists,” or even the work of those whose ideas have later proved to be inadequate. This argument misses the point of history and the lessons which it can teach. Perhaps Goldschmidt did take the time of a number of the classical geneticists who tried to answer his objections to the gene theory; and perhaps many of his own ideas about genes were, by today's view, “wrong.” These are always easier judgments to make by hindsight than at the moment. But that is not the point. Goldschmidt had a considerable influence on his contemporaries, and to dismiss him as an obstructionist because his opponents later proved to be more nearly right, distorts history and obscures significant questions which we might well be asking. It might be valuable to know why Goldschmidt felt compelled to be an iconoclast —and how that impulse, psychological in orgin, led him to overlook critical items of evidence which his opponents considered more carefully. It might also be valuable to try and understand how a contemporary of Goldschmidt or. Morgan really viewed the gene theory — what were its strong and weak point? Such questions are not readily answered by studying the work of only those men who were correct by later standards.Answers to some of the above questions can be gleaned from this study of Goldschmidt — though the first, and most psychologically oriented, question is largely untouched here.On the one hand, Goldschmidt forced classical geneticists to reexamine the foundation of their ideas about the nature, inviolability, and even physical dimensions of genes. He also kept alive the very real problems of gene physiology and its relations to development — a relationship that was given less attention by the Drosophila school in their pursuit of the transmission process. On a broader level he emphasized to the biological community a principle that was in danger of being lost in the enthusiasm surrounding the expansion of the Mendelian-chromosome theory. The point was that all theories in science are transient, logical constructs which should not be held as sacred. Time and again, as the history of science has shown, theories become rigid structures which retard new modes of thought. From Goldschmidt's perspective, the gene theory was in danger of performing just that function, for it was preventing workers from viewing the gene in a functional as well as a structural light.On the other hand, examining the work of critics (or even of outright “obstructionists”) gives the historian an opportunity to observe how the more established community of scholars at some point in time reacts to challenges of its cherished ideas. The fact that many workers in his own day (such as Beadle, Luria, Delbruck, Sturtevant, Bridges, and others), as well as most geneticists today, saw Goldschmidt as having been largely “obstructionist” is useful historical (and/or sociological) data. Clearly, as this paper has tried to show, Goldschmidt's ideas were not all obstructionist, and his viewpoint that genes must be considered functionally was one which was clearly valid, premature as it may have been from an experimental and technique point of view. Perhaps Goldschmidt's major fault was that he developed alternative theories which were not easily testable. Nonetheless, his challenge to a fundamental and established idea brought forth a reaction from many members of the genetic community which indicates how unwilling they were to reconsider the formalized theory on which their work was based. While many of Goldschmidt's criticisms — and particularly his way of making them — arose out of his own idiosyncrasies, they were also a product of his times. His view of the nature of theory-construction, and his rejection of old-style reductionism and mechanism, were part of a growing awareness within the world scientific community that explanations based on reducing complex phenomena to ultimate particles or units were clearly inadequate. The success of the Mendelian-chromosome theory had obscured that fact for many geneticists, but to Goldschmidt it was a point that could not be allowed to pass unnoticed. (shrink)

The discovery of the Higgs particle required a signal of 5σ significance. The rigid application of that condition is a convention that disregards more specific aspects of the given experiment. In particular, it does not account for the characteristics of the look elsewhere effect in the individual experimental context. The paper relates this aspect of data analysis to the question as to what extent theoretical reasoning should be admitted to play a role in the assessment of the significance (...) of empirical data. (shrink)

The clock hypothesis of relativity theory equates the proper time experienced by a point particle along a timelike curve with the length of that curve as determined by the metric. Is it possible to prove that particular types of clocks satisfy the clock hypothesis, thus genuinely measure proper time, at least approximately? Because most real clocks would be enormously complicated to study in this connection, focusing attention on an idealized light clock is attractive. The present paper extends and generalized (...) partial results along these lines with a theorem showing that, for any timelike curve in any spacetime, there is a light clock that measures the curve’s length as accurately and regularly as one wishes. (shrink)

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a (...) connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c 2 , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems. (shrink)

We have lived under the hegemony of the reductionistic scientific worldview since Galileo, Newton, and Laplace. In this view, the universe is meaningless, as Stephen Weinberg famously said, and organisms and a court of law are "nothing but" particles in morion. This scientific view is inadequate. Physicists are beginning to abandon reductionism in favor of emergence. Emergence, both epistemological and ontological, embraces the emergence of life and of agency. With agency comes meaning, value, and doing, beyond mere happenings. More organisms (...) are conscious. None of this violates any laws of physics, but it cannot be reduced to physics. Emergence is real, and the tiger chasing the gazelle are real parts of the real universe. We live, therefore, in an emergent universe. This emergence often is entirely unpredictable beforehand, from the evolution of novel functionalities in organisms to the evolution of the economy and human history. We are surrounded on all sides by a creativity that cannot even be prestated. Thus we have the first glimmerings of a new scientific worldview, beyond reductionism. In our universe emergence is real, and there is ceaseless, stunning creativity that has given rise to our biosphere, our humanity, and our history. We are partial co-creators of this emergent creativity. It is our choice whether we use the God word. I believe it is wise to do so. God can be our shared name for the true creativity in the natural universe. Such a view invites a new sense of the sacred, as those aspects of the creativity in the universe that we deem worthy of holding sacred. We are not logically forced to this view. Yet a global civilization, hopefully persistently diverse and creative, is emerging. I believe we need a shared view of God, a fully natural God, to orient our lives. We need a shared view of the sacred that is open to slow evolution, because rigidity in our view of the sacred violates how our most precious values evolve and invites ethical hegemony. We need a shared global ethic beyond our materialism. I believe a sense of God as the natural, awesome creativity in the universe can help us construct the sacred and a global ethic to help shape the global civilization toward what we choose with the best of our limited wisdom. (shrink)

The ontology of the "tractatus", In terms of which objects are characterized as propertyless simples, Is coherent provided wittgenstein is not mistakenly taken to be a constructive atomist building complexes from simples. A geometrical model is given to illustrate this. It is also shown that an ontology like that of the "tractus" removes much of the conceptual puzzlement of modern particle physics and has implications for current debates about realism, Possible worlds and rigid designators.

In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid (...) spheres should be eternal, as has been erroneously assumed, especially since the time of Newton. (shrink)

This paper shows that, in Newtonian mechanics, unstable three-dimensional rigid bodies must exist. Laraudogoitia recently provided examples of one- and two-dimensional homogeneous unstable rigid bodies, conjecturing the instability would persist for three-dimensional bodies in four-dimensional space. My result proves that, if one admits non homogeneous balls or hollow spheres, then the conjecture is true without having to resort to tetra-dimensionality. Furthermore, I show that instability also holds for at least certain simple classes of elastic bodies. Altogether, the laws (...) of classical dynamics actually lead to the existence of unstable material bodies belonging to the three types of entities accepted therein: point particles, rigid bodies and continuous deformable bodies. A whole range of forms of indeterminism which, until now, has not been considered in the literature. I end with a new conjecture on the connection existing between all these forms of instability and the dimensionality of space. (shrink)

continent. 1.3 (2011): 149-155. The world is teeming. Anything can happen. John Cage, “Silence” 1 Autonomy means that although something is part of something else, or related to it in some way, it has its own “law” or “tendency” (Greek, nomos ). In their book on life sciences, Medawar and Medawar state, “Organs and tissues…are composed of cells which…have a high measure of autonomy.”2 Autonomy also has ethical and political valences. De Grazia writes, “In Kant's enormously influential moral philosophy, autonomy (...) , or freedom from the causal determinism of nature, became prominent in justifying the human use of animals.”3 One of the oldest uses of autonomy in English is a description of the French civil war from the late sixteenth century: “Others of the…rebellion entred in counsell, whether they ought to admit the King vpon reasonable conditions, specially hauing their autonomy.”4 Life, and in particular human life, and in particular human politics, is well served by the usages of autonomy . What about the rest of reality, however? Should it be thought of, if it's even considered real and mind-independent, as pure stuff for the manipulation or decorative tastes of truly autonomous beings? We tend to think of things such as paperweights and iPhones as mere tools of human design and human use. To use them is to cause them to exist as fully and properly as they can. But according to Martin Heidegger, when a tool such as a paperweight is used, it disappears, or withdraws ( Entzug ). We are preoccupied with copying the page that the paperweight is holding down. We are concerned with an essay deadline, and the paperweight simply disappears into this general project. If the paperweight slips, or if the iPhone freezes, we might notice it. All of a sudden it becomes vorhanden (present-at-hand) rather than zuhanden (ready-to-hand).5 Yet Heidegger is unable to draw a meaningful distinction between what happens to a paperweight when it slips from the book I'm copying from and what happens to the paperweight when it presses on the still resilient pages of the thick paperback itself. Further still and related to this point, even when I am using the paperweight as part of some general task, I am not using the entirety of the paperweight as such. My project itself selects a thin slice of paperweight-being for the purposes of holding down a book. Even when it is zuhanden the paperweight is withdrawn. Graham Harman is the architect of this way of thinking.6 Harman discovered a gigantic coral reef of withdrawn entities beneath the Heideggerian submarine of Da-sein, which itself is operating at an ontological depth way below the choppy surface of philosophy, beset by the winds of epistemology, and infested with the sharks of materialism, idealism, empiricism and most of the other isms that have defined what is and what isn't for the last several hundred years. At a moment when the term ontology was left alone like a piece of well chewed old chewing gum that no one wants to have anything to do with, object-oriented ontology (OOO) has put it back on the table. The coral reef isn't going anywhere and once you have discovered it, you can't un-discover it. And it seems to be teeming with strange facts. The first fact is that the entities in the reef—we call them “objects” somewhat provocatively—constitute all there is: from doughnuts to dogfish to the Dog Star to Dobermans to Snoop Dogg. People, plastic clothes pegs, piranhas and particles are all objects. And they are all pretty much the same, at this depth. There is not much of a distinction between life and non-life (as there isn't in contemporary life science). And there is not much of a distinction between intelligence and non-intelligence (as there is in contemporary artificial intelligence theory). A lot of these distinctions are made by humans, for humans (anthropocentrism). And the concept autonomy has come into play in policing such distinctions. In this essay I shall to try to liberate autonomy for the sake of nonhumans. I shall do so by parsing carefully the title, which is taken from Hakim Bey's work The Temporary Autonomous Zone .8 First we shall explore the term autonomous . Then we shall explore what the full meaning of zone is. Finally, we shall investigate what temporary means. Each of these terms is of great value. An object withdraws from access. This means that its very own parts can't access it. Since an object's parts can't fully express the object, the object is not reducible to its parts. OOO is anti-reductionist. But OOO is also anti-holist. An object can't be reduced to its “whole” either, “reduced upwards” as it were. The whole is not greater than the sum of its parts. So we have a strange irreductionist situation in which an object is reducible neither to its parts nor to its whole. A coral reef is made of coral, fish, seaweed, plankton and so on. But one of these things on its own doesn't embody part of a reef. Yet the reef just is an assemblage of these particular parts. You can't find a coral reef in a parking lot. In this way, the vibrant realness of a reef is kept safe both from its parts and from its whole. Moreover, the reef is safe from being mistaken for a parking lot. Objects can't be reduced to tiny Lego bricks such as atoms that can be reused in other things. Nor can be reduced upwards into instantiations of a global process. A coral reef is an expression of the biosphere or of evolution, yes; but so is this sentence, and we ought to be able to distinguish between coral reefs and sentences in English. The preceding facts go under the heading of undermining . Any attempt to undermine an object—in thought, or with a gun, or with heat, or with the ravages of time or global warming—will not get at the withdrawn essence of the object. By essence is meant something very different from essentialism . This is because essentialism depends upon some aspect of an object that OOO holds to be a mere appearance of that object, an appearance-for some object. This reduction to appearance holds even if that object for which the appearance occurs is the object itself! Even a coral reef can't grasp its essential coral reefness. In essentialism, a superficial appearance is taken for the essence of a thing, or of things in general. In thinking essentialism we may be able to discern another way of avoiding OOO. This is what Harman has christened overmining .? The overminer decides that some things are more real than others: say for example human perception. Then the overminer decides that other things are only granted realness status by somehow coming into the purview of the more real entity. When I measure a photon, when I see a coral reef, it becomes what it is. But when I measure a photon, I never measure the actual photon. Indeed, since at the quantum scale to measure means “to hit with a photon or an electron beam” (or whatever), measurement, perception ( aisthesis ), and doing become the same. What I “see” are deflections, tracks in a diffusion cloud chamber or interference patterns. Far from underwriting a world of pure illusion where the mind is king, quantum theory is one of the very first truly rigorous realisms, thinking its objects as irreducibly resistant to full comprehension, by anything.9 So far we have made objects safe from being swallowed up by larger objects and broken down into smaller objects—undermining. And so far we have made objects safe from being mere projections or reflections of some supervenient entity—overmining. That's quite a degree of autonomy. Everything in the coral reef, from the fish to a single coral lifeform to a tiny plankton, is autonomous. But so is the coral reef itself. So are the heads of the coral, a community of tiny polyps. So is each individual head. Each object is like one of Leibniz's monads, in that each one contains a potentially infinite regress of other objects; and around each object, there is a potentially infinite progress of objects, as numerous multiverse theories are now also arguing. But the infinity, the uncountability, is more radical than Leibniz, since there is nothing stopping a group of objects from being an object, just as a coral reef is something like a society of corals. Each object is “a little world made cunningly” (John Donne).10 We are indeed approaching something like the political valance of autonomy . The existence of an object is irreducibly a matter of coexistence. Objects contain other objects, and are contained “in” other objects. Let us, however, explore further the ramifications of the autonomy of objects. We will see that this mereological approach (based on the study of parts) only gets at part of the astonishing autonomy of things. Yet there are some more things to be said about mereology before we move on. Consider the fact that since objects can't be undermined or overmined, it means that there is strictly no bottom object . There is no object to which all other objects can be reduced, so that we can say everything we want to say about them, hypothetically at least, based on the behavior of the bottom object. The idea that we could is roughly E.O Wilson's theory of consilience .11 Likewise, there is no object from which all things can be produced, no top object . Objects are not emanations from some primordial One or from a prime mover. There might be a god, or gods. Suppose there were. In an OOO universe even a god would not know the essential ins and outs of a piece of coral. Unlike even some forms of atheism, the existence of god (or nonexistence) doesn't matter very much for OOO. If you really want to be an atheist, you might consider giving OOO a spin. If there is no top object and no bottom object, neither is there a middle object . That is, there is no such thing as a space, or time, “in” which objects float. There is no environment distinct from objects. There is no Nature (I capitalize the word to reinforce a sense of its deceptive artificiality). There is no world, if by world we mean a kind of “rope” that connects things together.12 All such connections must be emergent properties of objects themselves. And this of course is well in line with post-Einsteinian physics, in which spacetime just is the product of objects, and which may even be an emergent property of a certain scale of object larger than 10?¹?cm).13 Objects don't sit in a box of space or time. It's the other way around: space and time emanate from objects. How does this happen? OOO tries to produce an explanation from objects themselves. Indeed, the ideal situation would be to rely on just one single object. Otherwise we are stuck with a reality in which objects require other entities to function, which would result in some kind of undermining or overmining. We shall see that we have all the fuel we need “inside” one object to have time and space, and even causality. We shall discover that rather than being some kind of machinery or operating system that underlies objects, causality itself is a phenomenon that floats ontologically “in front of” them. In so doing, we will move from the notion of autonomy and begin approaching a full exploration of the notion of zone , which was promised at the outset of this essay. Since an object is withdrawn, even “from itself,” it is a self-contradictory being. It is itself and not-itself, or in a slightly more expanded version, there is a rift between essence and appearance within an object (as well as “between” them). This rift can't be the same as the clichéd split between substance and accidents , which is the default ontology. On this view, things are like somewhat boring cupcakes with somewhat less boring sugar sprinkles on them of different colors and shapes. But on the OOO view, what is called substance is just another limited slice of an object, a way of apprehending something that is ontologically fathoms deeper. What is called substance and what is called accidence are just on the side of what this essay calls appearance. The rift (Greek, chorismos ) between essence and appearance means that an object presents us with something like what in logic is known as the Liar: some version of the sentence “This sentence is false.” The sentence is true, which means that it is a lie, which means that it is false. Or the sentence is false, which means that it is telling the truth, which means that it is true. Now logic since Aristotle has tried desperately to quarantine such beasts in small backwaters and side streets so that they don't act too provocatively.14 But if OOO holds, then at least one very significant thing in the universe is both itself and not-itself: the object. An object is p ? ¬p. To cope with this fact, we shall need some kind of paraconsistent or even fully dialetheic logic, one that is not allergic to dialetheias (double-truthed things). Yet if we accept that objects are dialetheic, p ? ¬p, we can derive all kinds of things easily from objects. Consider the fact of motion. If objects only occupy one location “in” space at any “one” time, then Zeno's paradoxes will apply to trying to think how an object moves. Yet motion seems like a basic, simple fact of our world. Either everything is just an illusion and nothing really moves at all (Parmenides). Or objects are here and not-here “at the same time.”15 This latter possibility provides the basic setup for all the motion we could wish for. Objects are not “in” time and space. Rather, they “time” (a verb) and “space.” They produce time and space. It would be better to think these verbs as intransitive rather than transitive, in the manner of dance or revolt . They emanate from objects, yet they are not the object. “How can we know the dancer from the dance?” (Yeats).16 The point being, that for there to be a question, there must be a distinction—or there must not be (p ? ¬p).17 It becomes impossible to tell: “What constitutes pretense is that, in the end, you don't know whether it's pretense or not.”18 In this notion of the emergence of time and space from an object we can begin to understand the term zone . Zone can mean belt , something that winds around something else. We talk of temperate zones and war zones. A zone is a place where a certain action is taking place: the zone winds around, it radiates heat, bullets fly, armies are defeated. To speak of an autonomous zone is to speak of a place that a certain political act has carved out of some other entity. Cynically, Tibet is called TAR, the Tibetan Autonomous Region, for this very reason. In this phrase, Region tries to emulate zone : it sounds as if the place has its own rules, but of course, it is very much under the control of China. What action is taking place? “[N]ot something that just is what it is, here and now, without mystery, but something like a quest…a tone on its way calling forth echoes and responses…water seeking its liquidity in the sunlight rippling across the cypresses in the back of the garden.”19 If as suggested earlier there is no functional difference between substance and accidence; if there is no difference between perceiving and doing; if there is no real difference between sentience and non-sentience—then causality itself is a strange, ultimately nonlocal aesthetic phenomenon. A phenomenon, moreover, that emanates from objects themselves, wavering in front of them like the astonishingly beautiful real illusion conjured in this quotation of Alphonso Lingis. Lingis's sentence does what it says, casting a compelling, mysterious spell, the spell of causality, like a demonic force field. A real illusion: if we knew it was an illusion, if it were just an illusion, it would cease to waver. It would not be an illusion at all. We would be in the real of noncontradiction. Since it is like an illusion, we can never be sure: “What constitutes pretense…” A zone is what Lingis calls a level . A zone is not entirely a matter of “free will”: this concept has already beaten down most objects into abject submission. Objects are far more threateningly autonomous, and sensually autonomous, than the Kantian version of autonomy cited in the first paragraph of this essay. A zone is not studiously decided upon by an earnest committee before it goes into action. One of its predominant features is that it is already happening . We find ourselves in it, all of a sudden, in the late afternoon as the shadows lengthen around a city square, giving rise to an uncanny sensation of having been here before. Objects emit zones. Wherever I find myself a zone is already happening, an autonomous zone. It is the nonautonomous zones that are impositions on what is already the case. Or rather, these zones are autonomous zones that exclude and police. They are brittle. Every object is autonomous, but some objects try to maintain themselves through rigidity and brittleness, like (and such as) a police state. Paradoxically, the more rigidly one tries to exclude contradiction, the more virulent become the dialetheias that are possible. I can get around “This sentence is false” by imagining that there are metalanguages that explain what counts as a sentence. Then I can decide that this isn't a real sentence. This is basically Alfred Tarski's strategy, since he invented the notion of metalanguage specifically to cope with dialetheias.20 For example we might claim that sentences such as “This sentence is false” are neither true nor false. But then you can imagine a strengthened version of the Liar such as: “This sentence is not true”; or “This sentence is neither true nor false.” And we can go on adding to the strengthened Liar if the counter-attack tries to build immunity by specifying some fourth thing that a sentence can be besides true, false, and neither true nor false: “This sentence is false, or neither true nor false, or the fourth thing.” And so on.21 It seems as if language becomes more brittle the more it tries to police the Liars of this world. Why? I believe that this increasing brittleness is a symptom of a deep fact about reality. What is this deep fact? Simply that there are objects, that these objects are withdrawn, and that they are walking contradictions. This means indeed that (as Lacan put it) “there is no metalanguage,” since a metalanguage would function as a “middle object” that gave coherency and evenness to the others.22 Since there is no metalanguage, there is no rising above the disturbing illusory play of causality. This may even have political implications: no global critique is therefore possible, and attempts to smooth out or totalize are doomed to fail. To think the zone is to think the notion of temporary , which we shall now begin to discuss in greater detail. The zone is not in time: rather it “times.” But because a zone is an emanation of an object, it is based on a wavering fragility, since objects are p ? ¬p. When an object is born, that means that it has broken free of some other object. An object can be born because it and other objects are fragile. If not, no movement would be possible. Objects contain the seeds of their own destruction, a dialetheic sentence that says something like “This sentence cannot be proved.” Kurt Gödel argues that every true system of propositions contains at least one sentence that the system cannot prove. In order to be true, the system must have a minimum incoherence. To be real, it has to be fragile. Imagine a record player. Now imagine a record called I Cannot Be Played on This Record Player . When you play it on this record player, it produces sympathetic vibrations that cause the record player to shudder apart. No matter how many defense mechanisms you build in, there will always be the possibility of at least one record that destroys the record player.23 That is what being physical is. An object is inherently fragile because it is both itself and not-itself. When the rift between appearance and essence collapses, that is called destruction, ending, death. When an object breaks, several new objects are born. An opera singer sings a loud note in tune with the resonant frequency of a wine glass. (See the movie included below.) The singing is a zone, an autonomous level of intensity, opening a rift between appearance and essence. The glass ripples—for a moment it is nakedly a glass and a not-glass—almost as if it were having an orgasm, a little death. It is caught in the rift of the singing. Then its structure can't handle the coherence of the sound waves, and it breaks. It is incoherence and inconsistency that is the mark of existence, not consistency and noncontradiction. When things break or die, they become coherent. Essence disappears into appearance. I become the memories of friends. A glass becomes a dancing wave. Instantly, there are glass fragments, new temporary autonomous zones. The fragments have broken free from the glass. They are no longer its parts, but emanate their own time and space, becoming perhaps accidental weapons as they bury themselves in my flesh. Thus Hakim Bey's instructions on creating temporary autonomous zones oscillate disturbingly between performance art and politics, circus clowning and revolution. To play with the aesthetic is to play with causality, to rip from the sensual ether emanating from things new regions, new zones. Anarchist politics is the creation of fresh objects in a reality without a top or a bottom object, or for that matter a middle object: Everything in nature is perfectly real including consciousness, there's absolutely nothing to worry about. Not only have the chains of the Law been broken, they never existed; demons never guarded the stars, the Empire never got started, Eros never grew a beard. … There is no becoming, no revolution, no struggle, no path; already you're the monarch of your own skin—your inviolable freedom waits to be completed only by the love of other monarchs: a politics of dream, urgent as the blueness of sky.24 Bey imagines that this is because chaos is a primordial “undifferentiated oneness-of-being.” A Parmenides or a Spinoza or a Laruelle would read this a certain way. Individual objects, or decisions to talk about this rather than that, are just maggot-like things crawling around on the surface of the giant cheese of oneness.25 Yet he also describes chaos as “Primordial uncarved block, sole worshipful monster, inert & spontaneous, more ultraviolet than any mythology.” This image is of an inconsistent object, not of an undifferentiated field. An object, indeed, that can be distinguished from other things. If not, then the first part of The Temporary Autonomous Zone , subtitled “The Broadsheets of Ontological Anarchism,” is a kind of onto-theology. Onto-theology proclaims that some things are more real than others. Bey, however, is writing poetically, and thus ambiguously. We are at liberty to read “undifferentiated oneness-of-being” as something like the irreducibility of a thing to its parts and so forth (undermining and overmining). This certainly seems closer to the language in the following paragraph: “There is no becoming … already you're the monarch of your own skin.”26 On this view, there is no difference between art and politics: “When ugliness, poor design & stupid waste are forced upon you, turn Luddite, throw your shoe in the works, retaliate.” Since Romanticism this has been the war cry of the vanguard artist.27 To say to is to fall prey to the tired axioms of the avant-garde, and we think we know how the game goes. But OOO is not simply a way to advocate “new and improved” versions of this shock-the-bourgeoisie boredom. Bey's text is certainly full enough of that. Rather, since causality as such is aesthetic, and since nonhumans are not that different from humans, the new approach would be to form aesthetic–causal alliances with nonhumans. These alliances would have to resist becoming brittle, whether that brittleness is right wing (authoritarianism) or left wing (the endless maze of critique). No “ism,” especially not the ultimate forms, nihilism and cynicism, is in any sense effective at this point. All forms of brittleness are based on the mistaken assumption that there is a metalanguage and that therefore “Anything you can do, I can do meta.” I will not be listing any approaches here, as Bey does. Such lists and manifestos belong to the vanguardism that no longer works. Why? Not because of some marvelous revolution in human consciousness, but because nonhumans have so successfully impinged upon human social, psychic and aesthetic space. It is the time after the end of the world. That happened in 1945, when a thin layer of radioactive materials was deposited in Earth's crust. Geology now calls it this era the Anthropocene . Ironically, this period, named after humans, is the moment at which even the most thick headed of us make decisive contact with nonhumans, from mercury in our blood to manta rays to magnesium. Richard Dawkins, Pat Robertson and Lady Gaga all have to deal with global warming and mass extinction, somehow. We now live in an Age of Asymmetry marked by a skewed, spiraling relationship between vast knowledge and vast nonhuman things—both become vaster and vaster because of one another and for the same reasons.28 This means that coming up with the perfect attitude or the perfect aesthetic prescription just won't work any more. Even the most hardened anthropocentrist now has to pay through the nose for basic food supplies, and has to use more sunscreen. Whether he knows it or acknowledges it, he is already acting with regard towards nonhumans. There is nothing special to think, no special critique that will get rid of the stains of coexistence. The problem won't fit into the well-established modern boxes, which is why the “mystical,” “spiritual” quality of Bey's prose is welcome. Of course, when I put it this way, you may immediately close off and decide that I am talking about perfect attitudes after all, or something outside of politics, or other ways that the radical left marshals to police its thinking of the nonhuman. Because that is what is really at stake in all this: the nonhuman in its coexistence with the human—bosons, gods, clouds, spirits, lifeforms, experiences, the sunlight rippling across the cypresses. Bey begins to get at this in a Latour litany in the second part of The Temporary Autonomous Zone , “The Assassins”: Pomegranate, mulberry, persimmon, the erotic melancholy of cypresses, membrane-pink shirazi roses, braziers of meccan aloes & benzoin, stiff shafts of ottoman tulips, carpets spread like make-believe gardens on actual lawns—a pavilion set with a mosaic of calligrammes—a willow, a stream with watercress—a fountain crystalled underneath with geometry— the metaphysical scandal of bathing odalisques, of wet brown cupbearers hide-&-seeking in the foliage—“water, greenery, beautiful faces.”29 This will be conveniently dismissed as orientalism. If we're never allowed to escape the crumbling prison of modernity for fear of imperialism there is truly no hope. In a similar way, the fear of anthropocentrism and anthropomorphism is very often staged from a place that just is anthropocentrism .30 Critique turns into ressentiment . An object radiates a zone that is aesthetic and therefore causal. Because objects “time” they are temporary. Not because they exist “in” time that eventually gets the better of them. Their very existence implies the possibility of their non-existence. Since objects are not consistent, they can cease to exist. But nothing, no one, will ever be able to insert a blade between appearance and existence, even thought there is a rift there. Now that's what I call autonomy. NOTES 1. John Cage, Silence: Lectures and Writings (Middletown, CT: Wesleyan University Press, 1973), 96. 2. P. B. Medawar and J. S. Medawar, The Life Science: Current Ideas in Biology (London: Wildwood House, 1977), 8. 3. David DeGrazia, Animal Rights: A Very Short Introduction (Oxford: Oxford University Press, 2002), 5. 4. Antony Colynet, A True History of the Civil Warres in France (London, 1591), 480. 5. Martin Heidegger, Being and Time , tr. Joan Stambaugh (Albany, N.Y: State University of New York Press, 1996) 62–71. 6. Graham Harman, Tool-Being: Heidegger and the Metaphysics of Objects (Peru, IL: Open Court, 2002). 7. Hakim Bey, The Temporary Autonomous Zone (Brooklyn: Autonomedia, 1991). 8. Graham Harman, The Quadruple Object (Ripley: Zero Books, 2011), 7–18. 9. This is not the place to get into an argument about quantum theory, but I have argued that quanta also do not endorse a world that I can't speak about because it is only real when measured. This world is that of the reigning Standard Model proposed by Niels Bohr and challenged by De Broglie and Bohm (and now the cosmologist Valentini, among others). See Timothy Morton, “Here Comes Everything: The Promise of Object-Oriented Ontology,” Qui Parle 19.2 (Spring–Summer, 2011), 163–190. 10. John Donne, Holy Sonnets 15, in The Major Works: Including Songs and Sonnets and Sermons , ed. John Carey (Oxford: Oxford University Press, 2009). 11. Edward O. Wilson, Consilience: The Unity of Knowledge (New York: Knopf, 1998). 12. Martin Heidegger, What Is a Thing? (Washington: Regnery, 1968), 243. 13. Albert Einstein, Relativity: The Special and the General Theory (London: Penguin, 2006); Petr Horava, “Quantum Gravity at a Lifshitz Point,” arXiv:0901.3775v2 [hep-th]. 14. Graham Priest, In Contradiction (Oxford University Press, 2006), passim: the most notable recent quarantine officers have been Tarski, Russell, and Frege. 15. Priest, In Contradiction , 172–181. 16. William Butler Yeats, “Among School Children,” Collected Poems , ed. Richard J. Finneran (New York: Scribner, 1996). 17. Paul de Man, “Semiology and Rhetoric,” Diacritics 3.3 (Autumn, 1973), 27–33 (30). 18. Jacques Lacan, Le seminaire, Livre III: Les psychoses (Paris: Editions de Seuil, 1981), 48. See Slavoj Zizek, The Parallax View (Cambridge, Mass.: MIT Press, 2006), 206. 19. Alphonso Lingis, The Imperative (Bloomington: Indiana University Press, 1998), 29. 20. Priest, In Contradiction , 9–27. 21. See Graham Priest and Francesco Berto, “ Dialetheism ,” The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), ed. Edward N. Zalta. 22. Jacques Lacan, Écrits: A Selection , tr. Alan Sheridan (London: Tavistock, 1977), 311. 23. The analogy can be found at length in Douglas Hofstadter, “Contracrostipunctus,” Gödel, Escher, Bach: An Eternal Golden Braid (New York: Basic Books, 1999), 75–81. 24. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 25. This is closest to the language of François Laruelle in Philosophies of Difference: A Critical Introduction to Non-Philosophy (New York: Continuum, 2011) 179. 26. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 27. Peter Bürger, Theory of the Avant Garde (Minneapolis: University of Minnesota Press, 1984). 28. For further discussion see Timothy Morton, “From Modernity to the Anthropocene: Ecology and Art in the Age of Asymmetry,” The International Social Science Journal 209 (forthcoming). 29. Bey, “ The Assassins ,” Temporary Autonomous Zone . 30. Timothy Morton, The Ecological Thought (Cambridge, Mass.: Harvard University Press, 2010), 75–76. (shrink)

Originally published in 1904, Whittaker’s A Treatise on the Analytical Dynamics of Particles and Rigid Bodies soon became a classic of the subject and has remained in print for most of these 108 years. In this paper, we follow the book as it develops from a report that Whittaker wrote for the British Society for the Advancement of Science to its influence on Dirac’s version of quantum mechanics in the 1920s and beyond.

The Fermi energy at 0°K is evaluated for electrons confined to cubical and spherical rigid-walled boxes of equal volume, respectively, in the Sommerfeld approximation. Due primarily to large differences in single-particle degeneracies, Fermi energies compared for equal numbers of particles in these two configurations are found to be unequal. Approximate expressions of the Fermi energy in the large particle-number limit for the spherical case reveal that it agrees in form with the Fermi energy for the cubical configuration. (...) The finite cylindrical box is also examined and it is found that for fixed number of particles and fixed volume, the Fermi energy varies as the two characteristic lengths of the box are changed. Experimental corroboration of the theory is suggested through measurement of the work function for equal-volume micrometallic samples in the different geometries. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem (...) without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in (...) the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light. (shrink)

This paper continues an earlier investigation into the philosophical tradition of Vienna Indeterminism until the formation of the Vienna Circle in 1929. It focuses in particular on how Philipp Frank and Richard von Mises were able to contemplate genuine indeterminism in physics before the advent of quantum mechanics. On this account, all apparently deterministic laws could well be the macroscopic limit of indeterministic basic laws valid for the single mirco-events. Philosophically Vienna Indeterminism was launched by Mach's redefinition of causality in (...) terms of functional dependencies. This severed the rigid bond between causality and empirical realism characteristic of the Kantian conception and made possible to adjust the ontology according to the needs of a single theory. The debates between Max Planck and Franz Serafin Exner teach that the indeterminism issue was also a struggle about Boltzmann's philosophical legacy between Vienna and Berlin. Quite in line with Mach's firm empiricism, Vienna Indeterminists rejected any final decision between determinism and indeterminism on the metaphysical level. Once the frequency interpretation had won favor, the empiricist stance, moreover, permitted them to consider mass phenomena as generic observational facts coordinated to statistical collectives and to treat them on a par with moving point particles. The only condition imposed on this ontology was the uniqueness of this coordination, a condition that could be viewed as a late heir of Mach's principle of unique determination which had complemented his relational ontology. (shrink)

The ontologies of scientific theories include a variety of objects: point-mass particles, rigid rods, frictionless planes, flat and curved spacetimes, perfectly spherical planets, continuous fluids, ideal gases, nonidentical but indistinguishable electrons, atoms, quarks and gluons, strong and weak nuclear forces, ideally rational agents, and so on. But the scientific community currently regards only some of these objects as real. According to Paul Teller, a group sometimes can be justified in regarding competing ontologies as real and the ontologies we are (...) justified in regarding as real are inexact, because the theories that give those ontologies characterize what things are like rather than what they are. In this paper, I argue that Teller's view is incomplete and suggest that one way to remove this incompleteness is to adopt a criterion for when we are justified in regarding a theory's ontology as real that is based upon a theory's comparative degree of confirmation. I argue that this criterion is prima-facie plausible and that Teller's view is false if this criterion is correct. (shrink)

Engineering Dynamics spans the full range of mechanics problems, from one-dimensional particle kinematics to three-dimensional rigid-body dynamics, including an introduction to Lagrange's and Kane's methods. It skillfully blends an easy-to-read, conversational style with careful attention to the physics and mathematics of engineering dynamics, and emphasizes the formal systematic notation students need to solve problems correctly and succeed in more advanced courses.

The conditions are outlined under which the body construction of annelids could have been transformed into that of arthropods. As an adaptation to a vagile life and an uptake of food by filtering particles from the sediment, the body was more and more flattened. Thus lateral protrusions, the subsequent pleurotergites, developed, and the parapodia were shifted to a more ventral position and could differentiate into the branched limbs typical for arthropods. This is the condition under which parts of the body (...) wall were kept immobile, so that they could become sclerotized in the form of rigid plates. (shrink)

This paper presents three interesting consequences that follow from admitting an ontology of rigid bodies in classical mechanics. First, it shows that some of the most characteristic properties of supertasks based on binary collisions between particles, such as the possibility of indeterminism or the non-conservation of energy, persist in the presence of gravitational interaction. This makes them gravitational supertasks radically different from those that have appeared in the literature to date. Second, Sect. 6 proves that the role of gravitation (...) in supertasks of this kind may be highly non-trivial. Third,, the gravitational supertasks found in the first part enable us to show that indeterminism of classical mechanics with gravitation is much more general than has been supposed until now. This result is especially interesting from the philosophical viewpoint, as it links the scope of indeterminism in a theory like classical mechanics directly with the nature of its ontological hypotheses. (shrink)

The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta ofevents as its fundamental description. The evolution of the events, as functions of (...) a universal invariant world, or historical, time, traces out the world lines that represent the phenomena (e.g., particles) which are observed in the laboratory. The positions in time of each of the events, i.e., the time of their potential detection, are, in this framework, controlled by this universal parameter τ, the time at which they are generated (and may proceed in the positive or negative sense). We find that the notion of thestate of a system requires generalization; at any given τ, it involves information about the system at timest(τ) ≠ τ. The correlation of what may be measured att(τ) with what is generated at τ is necessarily quite rigid, and is related covariantly to the spacelike correlations found in interference experiments. We find, furthermore, that interaction with Maxwell electromagnetism leads back to a static picture of the world, with no real evolution. As a consequence of this result, and the requirement of gauge invariance for the quantum mechanical evolution equation, we conclude that electromagnetism is described by a pre-Maxwell field, whose τ-integral (or asymptotic behavior as τ → ∞) may be identified with the Maxwell field. We therefore consider the world of events in space time, interacting through τ-dependent pre-Maxwell fields, as far as electrodynamics is concerned, as the objective dynamical reality. Our perception of the world, through laboratory detectors and our eyes, are based onintegration over τ over intervals sufficiently large to obtain an aposteriori description of the phenomena which coincides with the Maxwell theory. Fundamental notions, such as the conservation of charge, rest on this construction. The decomposition of the common notion of time into two essentially different aspects, one associated with an unvarying flow, and the second with direct observation subject to dynamical modification, has profound philosophical consequences, of which we are able to explore here only a few. (shrink)

We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them (...) are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation. (shrink)

This book is a contribution to both the study of the logical and philosophical foundations of physics, and the investigation of applied formal axiomatic systems. Basri uses the techniques of logic and set theory in order to construct a rigorous physical theory whose theorems turn out to be those of the general theory of relativity or else arbitrarily close approximations thereof. Whether Basri's approach turns out to be fruitful for the analysis of foundational problems in physics remains to be seen, (...) but he has clearly rendered an important service in providing at least one rigorously unified way of talking about such things as particles, events, signals, clocks, rigid measuring instruments, etc. A novel feature of the book is that the basis of Basri's system is rather phenomenalistic: he uses primitives like "the class of unbiased human observers" and "the class of simultaneous sensations of observer H." The obvious philosophical problems about perception and the external world which are consequent upon this sort of approach are not treated by Basri, but he is certainly not to be faulted on this account. There are, however, a number of errors and imprecisions in the underlying logistic system, some of which are more serious than others. But in general, this book deserves to be read and its thesis considered by all students interested in serious and responsible efforts in the philosophy of physics.—H. P. K. (shrink)

In this fascinating work, Scott Soames offers a new conception of the relationship between linguistic meaning and assertions made by utterances. He gives meanings of proper names and natural kind predicates and explains their use in attitude ascriptions. He also demonstrates the irrelevance of rigid designation in understanding why theoretical identities containing such predicates are necessary, if true.

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

A paradigmatic case of rigidity for singular terms is that of proper names. And it would seem that a paradigmatic case of rigidity for general terms is that of natural kind terms. However, many philosophers think that rigidity cannot be extended from singular terms to general terms. The reason for this is that rigidity appears to become trivial when such terms are considered: natural kind terms come out as rigid, but so do all other general terms, and in particular (...) all descriptive general terms. This paper offers an account of rigidity for natural kind terms which does not trivialise in this way. On this account, natural kind terms are de jure obstinately rigid designators and other general terms, such as descriptive general terms, are not. (shrink)

I have been told that for some twenty minutes after reading this paper Kripke believed I had shown that proper names could be non-rigid designators. (Then, apparently, he found a crucial error in the set-up.) I take great pride in this (alleged) fact.

We propose a new quantum ontology, in which properties are the fundamental building blocks. In this property ontology physical systems are defined as bundles of type-properties. Not all elements of such bundles are associated with definite case-properties, and this accommodates the Kochen and Specker theorem and contextuality. Moreover, we do not attribute an identity to the type-properties, which gives rise to a novel form of the bundle theory. There are no “particles” in the sense of classical individuals in this ontology, (...) although the behavior of such individuals is mimicked in some circumstances. This picture leads in a natural way to the symmetrization postulates for systems of many “identical particles”. (shrink)

This volume brings together eleven essays by the distinguished philosopher of science, Peter Achinstein. The unifying theme is the nature of the philosophical problems surrounding the postulation of unobservable entities such as light waves, molecules, and electrons. How, if at all, is it possible to confirm scientific hypotheses about "unobservables"? Achinstein examines this question as it arose in actual scientific practice in three nineteenth-century episodes: the debate between particle and wave theorists of light, Maxwell's kinetic theory of gases, and (...) J.J. Thomson's discovery of the electron. The book contains three parts, each devoted to one of these topics, beginning with an essay presenting the historical background of the episode and an introduction to the philosophical issues. There is an illuminating evaluation of various scientific methodologies, including hypothetico-deductivism, inductivism, and the method of independent warrant which combines features of the first two. Achinstein assesses the philosophical validity of both nineteenth-century and modern answers to questions about unobservables, and presents and defends his own solutions. (shrink)

The phenomenon of rigid designation - in particular, de jure rigidity - is typically treated metaphysically. The picture is: reference is gained in a way that puts no constraints on what an object in other worlds, or counterfactual situations must be like, in order to be the referent of that term, other than 'being this thing'. This allows 'pure metaphysical' investigation into, and discovery of 'the nature' of the referent. It is argued that this presupposes a 'privileged' ontology, of (...) a sort that is far from obvious. An alternative picture of rigidity is sketched, terms have associated criteria of identity and criteria of application for counterfactual situations. A term is rigid when these coincide. Aside from being a better account of rigidity, it also undermines the picture of rigid terms allowing us to 'metaphysically' investigate the nature of the referent: matters of identity and essence for the referent are settled by these semantic constraints (though it can be done in a way that allows are a posteriori necessities). (shrink)

For an expression to be rigid means that it refers to one and the same thing with respect to any possible situation. But how is this in turn to be understood? An example will help us work through the definition. Take a word like ‘Aristotle.’ That word is a proper name; and proper names are a clear case of a type of word that refers. ‘Aristotle’ refers to a particular person, the last great philosopher of antiquity; in general, a (...) name refers to the thing of which it is the name. To continue working through the definition of rigidity, we need to make sense of referring with respect to. It is tempting, for example, but mistaken, to understand a word's referring with respect to a possible situation as it's being used, in that situation, to refer to something. (shrink)

In Naming and Necessity Kripke argues 'intuitively' that names are rigid. Unlike Kripke, Ben-Yami first introduces and justifies the Principle of the Independence of Reference (PIR), according to which the reference of a name is independent of what is said in the rest of the sentence containing it. Ben-Yami then derives rigidity, or something close to it, from the PIR. Additional aspects of the use of names and other expressions in modal contexts, explained by the PIR but not by (...) the rigidity claim, are then discussed. Ben-Yami next examines a difficulty in accepted definitions of rigidity, stemming from the fact that the same name can be used to name different particulars. This difficulty might force us to adopt a revised form of the rigidity claim. (shrink)

Kripke defines a rigid designator as one that designates the same object in every possible world in which that object exists. He argues that proper names are rigid. So also, he claims, are various natural kind terms. But we wonder how they could be. These terms are general and it is not obvious that they designate at all. It has been proposed that these kind terms rigidly designate abstract objects. This proposal has been criticized because all terms then (...) seem to come out rigid, thus trivializing rigidity. The paper starts with further criticisms of this proposal aimed particularly at a recent version given by LaPorte. The paper goes on to develop and defend an alternative proposal presented briefly in Devitt and Sterelny (1999): instead of taking those natural kind terms to rigidly designate an object we take them to rigidly apply to the members of their extensions. Schwartz has rightly insisted that a notion of rigidity must do some theoretical work if it is to be interesting. The paper argues that rigid application for kind terms does the same primary work as rigid designation for singular terms, the work of refuting description theories of some terms; and it does the same secondary work, of explaining certain modal phenomena (with one exception). (shrink)

It is generally assumed that rigidity plays a key role in explaining the necessary a posteriori status of identity statements, both between proper names and between natural kind terms. However, while the notion of rigid designation is well defined for singular terms, there is no generally accepted definition of what it is for a general term to be rigid. In this paper I argue that the most common view, according to which rigid general terms are the ones (...) which designate the same kind in all possible worlds, fails to deliver a posteriori necessities. I also present an alternative view, on which the work of explaining a posteriori necessities is not done by rigidity, but by a related metasemantic notion, which I call actuality - dependence. (shrink)

In this paper I examine two ways of defining the rigidity of general terms. First I discuss the view that rigid general terms express essential properties. I argue that the view is ultimately unsatisfactory, although not on the basis of the standard objections raised against it. I then discuss the characterisation in terms of sameness of designation in every possible world. I defend that view from two objections but I argue that the approach, although basically right, should be interpreted (...) cautiously. (shrink)

Rigid designators for concrete objects and for properties -- On the coherence of the distinction -- On whether the distinction assigns to rigidity the right role -- A uniform treatment of property designators as singular terms -- Rigid appliers -- Rigidity - associated arguments in support of theoretical identity statements: on their significance and the cost of its philosophical resources -- The skeptical argument impugning psychophysical identity statements: on its significance and the cost of its philosophical resources -- (...) The skeptical argument further examined: on resources, allegedly overlooked, for confirming psychological identities. (shrink)

Rigid expressionism is the view that all natural kind terms and many other kind terms are rigid designators. Rigid expressionists embrace the ‘overgeneralization’ of rigidity, since they hold that not just natural kind terms but all unstructured kind terms are rigid designators. Unfortunately overgeneralization remains a defeating problem for rigid expressionism. It runs together natural kind terms and nominal kind terms in a way that enforces a false semantic uniformity. The Kripke/putnam view of natural kind (...) terms minus the claim of rigidity is correct, but a traditional descriptivist theory is appropriate for nominal kind terms. None of them should be thought of as either rigid or non-rigid, however. (shrink)