The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation (...) is removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is (...) not fully satisfactory. This is a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory (...) presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature. (shrink)

Mathematical tradition has it that transformations characterized by a negative Jacobian determinant are referred to as improper transformations. The symmetry of a physical object corresponding to such an improper transformation becomes an improper symmetry. Improper symmetries have been successfully used for the purpose of crystal symmetry. The extension of these purely spatial symmetries to the domain of spacetime has led to a prejudicial use of light-cone properties, thus affecting adversely an unbiased symmetry classification. We pinpoint these (...) prejudicial procedures and trace their historical origin, while presenting an alternative that restores an unbiased treatment of improper spacetime symmetries. The applications discussed relate to recent developments in the symmetry classification of magnetic crystals and to the extension of Neumann's principle to the time domain. (shrink)

The televised Charlie Brown Christmas tale and its bawdy Peanuts characters taught me important lessons while growing up as the awkwardly drawn, “blockhead” sibling. This essay explores the down and dirty deities that reside in each of us, including Brown and Pig Pen, at once seen as contemporary symbols of the globally inter challenged-being and surprising instruments of sacred expression. Ruminations on the Bhagavad Gita, Immanuel Kant, Jessye Norman, bell hooks, and Thich Nhat Hahn encourage us to reimagine contexts for (...) power and authority, racial mistrust and injustice, and restoring our slumping spirits. (shrink)

This paper addresses the issue of the multiplicity of various grades of discernibility that can be defined in model theory. Building upon earlier works on the subject, I first expand the known logical categorizations of discernibility by introducing several symmetry-based concepts of discernibility, including one I call “witness symmetry-discernibility”. Then I argue that only grades of discernibility stronger than this one possess certain intuitive features necessary to individuate objects. Further downsizing of the set of non-equivalent grades of discernibility (...) can be achieved by stipulating that any relation of discernibility should be applied only to those pairs of objects which have been previously distinguished from the rest of the universe. Restricting discernibility to pairs of objects satisfying this condition gives an additional bonus in the form of restoring the transitivity of some types of indiscernibility which have been known to be non-transitive. (shrink)

In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and (...) exploit the notions of contingency and absoluteness in order to restore the symmetry of Hohfeldian modalities in accordance to the diagrams presented by Hohfeld. Interestingly, the investigation unveils three potestative squares defined at different levels of granularity (force, outcome and change) and allows us to further elaborate on the connections between deontic and potestative relations. (shrink)

The philosophy of mind concerns much about how novelty occurs in the world. The very recent progress in this field inspired by quantum mechanics indicates that symmetry restoration occurs in the mind at the moment when new creative thought arises. Symmetry restoration denotes the moment when one’s cognition leaves ordinary internalized mental schemes such as conceptual categories, heuristics, subjective theories, conventional thinking, or expectations. At this moment, fundamentally new, original thought may arise. We also predict that (...) in older age, symmetry restoration is less likely to occur as internalized mental schemes become more rigid in the elderly. Furthermore, the present study demonstrates that symmetry restoration may occur not only individually, in one’s mind, but also collectively, during collaborative creative activities, e.g. during small-group brainstorming sessions or creative improvisational performances. The possibility of collective symmetry restoration interacts well with the ideas in the field of relational ontology. Relational ontology highlights an important ontological role of relations. The ontological primacy is not given to individual entities, as in traditional metaphysics, but to relational structures and transformative relational processes (interactions). When accepting this assumption, we cannot imagine the situation when the actor’s mind could act absolutely independently and leave all of its relations as assumed in the compatibilist theory of free will. We argue that creative free action can be performed even in the case when the actor is entangled within their material, environmental, and social relational structures. (shrink)

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.

In this study, complex dynamics of Briggs–Rauscher reaction system is investigated analytically and numerically. First, the Briggs–Rauscher reaction system is reduced into a new nonlinear parametric oscillator. The Melnikov method is used to derive the condition of the appearance of horseshoe chaos in the cases ω = Ω and ω ≠ Ω. The performed numerical simulations confirm the obtained analytical predictions. Second, the prediction of coexisting attractors is investigated by solving numerically the new nonlinear parametric ordinary differential equation via the (...) fourth-order Runge–Kutta algorithm. As results, it is found that the new nonlinear chemical system displays various coexisting behaviors of symmetric and asymmetric attractors. In addition, the system presents a rich variety of bifurcations phenomena such as symmetry breaking, symmetry restoring, period doubling, reverse period doubling, period-m bubbles, reverse period-m bubbles, intermittency, and antimonotonicity. On the contrary, emerging chaotic band attractors and period-1, period-3, period-9, and period-m bubbles routes to chaos occur in this system. (shrink)

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a composite (...) object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions. (shrink)

The problem of explanatory non-symmetries provides the strongest reason to abandon the view that laws can figure in explanations without causal underpinnings. I argue that this problem can be overcome. The solution that I propose starts from noticing the importance of conditions of application when laws do explanatory work, and I go on to develop a notion of nomological dependence that can tackle the non-symmetry problem. The strategy is to show how a strong notion of counterfactual dependence as guaranteed (...) by the laws is a plausible account of what we aim towards when we give law-based explanations. The aim of this project is not to deny that causal relations can do explanatory work but to restore laws of nature as capable of being explanatory even in the absence of any knowledge of causal underpinnings. (shrink)

This paper explores how insights from two-dimensional semantics can be brought to bear on debates surrounding (realist) metaethical naturalism. It defends two central claims. (1) A plausible principle of 2-D symmetry for normative terms provides us with reason to reject standard forms of synthetic metaethical naturalism. (2) Moore's Open Question Argument can be powerfully revived within the framework of 2-D semantics. I approach these issues by diagnosing how Attitudinal Semanticists' use of 2-D semantics--to account for moral objectivity--goes wrong. I (...) argue that their "rigidification" strategy doesn't resolve, but merely pushes under the rug, the fundamental concerns that robust moral realists have with Attitudinal Semantics. These concerns re-emerge when we consider the intuitive symmetry between the primary and secondary intensions of normative terms. Attempts to restore symmetry via super-rigidity are subsequently shown to pose "Open Question" problems for (realist) metaethical naturalism more broadly. (shrink)

The Kansas-Nebraska Act of 1854 officially opened the Great Plains to westward settlement, and the public survey of 1855 by Charles A. Manners and Joseph Ledlie along the Sixth Principal Meridian established the grid by which the uncharted expanse of the Great Plains was brought into scale. The mechanical act performed by land surveyors is believed by photographer Joe Deal to be powerfully similar to the artistic act of making a photograph.To Deal, both acts are about establishing a frame around (...) a vast scene that suggests no definite boundaries of its own. Thus, when approaching his own photographs of the Great Plains, Deal viewed his photography as a form of reenactment, a method of understanding how it felt to contain the Great Plains in smaller, more measurable units. In West and West, Deal, who was born and raised in Kansas, revisited the Kansas-Nebraska territory and applied his photographic understanding of the landscape grid and horizon line to illuminate the sense of infinite space that transcends the reality of the survey. As Deal writes in his concluding essay: “If the square, as employed in the surveys of public lands, could function like a telescope, framing smaller and smaller sections of the plains down to a transect, it can also be used as a window, equilaterally divided by the horizon, that begins with a finite section of the earth and sky and restores them in the imagination to the vastness that now exists as an idea: the landscape that is contained within the perfect symmetry of the square implies infinity.” The stunning photographs in West and West present the Great Plains from a rare perspective. From this vantage point, Deal is able to distill and contemplate its expanse. (shrink)

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations (...) for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use (...) the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket, or is covariance sufficient? A graviton mass breaks the gauge symmetry, but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail. (shrink)

In contrast with Kant's "Theory of Beauty" his "Analytics of the Sublime" has till now been paid meager systematic attention. This essay on the architectonics of the sublime proves three theses. (1) Beauty and sublime are not experiences of two different object classes, but of two contrary moods of mind. (2) Kant's exposition of the "mathematical-sublime" is based on not immediately evident premises. But these difficulties concerning the "comprehensio aesthetica" can be explained retrospectively from the "dynamical-sublime". For only in view (...) of a symbolically threatening nature its mere "extensively" immeasurable oversize is apperceived asan "intensively" overwhelming power, which evokes the feeling of reluctance. And even the (strictly thought) absurd idea of a "totallygiven infinity" is the playing retort of the imaginative power, by which a reversal of the proportions, a belittling of nature, and the restoration of pleasure is accomplished. (3) The symmetry of the fourmoments of judgment is novel, but plausible. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:OSCAR WILDE AND POSTSTRUCTURALISM by Guy Willoughby Towards the beginning ofthe hugely entertaining and provocative manifesto called "The Critic as Artist" (1890),1 Oscar Wilde causes the well-named discipulus Ernest to inquire of the suave magister, Gilbert: "But what are the two supreme and highest arts?" The prompt answer takes us to the heart ofWilde's aesthetic priorities: "Life and Literature," says Gilbert: "Life and the perfect expression of life" (p. (...) 1016). The aim of this discussion is, first, to consider the terms of Oscar Wilde's aesthetics; second, to relate them to tendencies in contemporary theory. I will be arguing, in sum, that the ideas entertained in his essays, and demonstrated in his fictions, have suggestive implications for our practices today—particularly in die light of a gathering rapprochement across the range of cultural study. The abiding theme ofOscar Wilde's writings is his insistence throughout not merely on art's primacy, but on the vital importance ofaesthetic criteria to life itself. In de Profundü (1897), that extraordinary attempt at self-definition, the author claims that it is only by conceiving of one's existence as an art-statement, as a dynamic convergence of forces extending in time and place, that trial, humiliation, and reversal—the shocks the flesh is heir to—can be imaginatively subsumed into a composite whole. He summed up the argument of the apologia thus to André Gide: "My life is like a work of art; an artist never starts the 316 Guy Willoughby317 same thing twice... or if he does, it's that he hasn't succeeded. My life before prison was as successful as possible. Now it's something that's over."2 Accordingly, he ascribes in de Profundis the greatest value to the frank acceptance of all one's deeds and susceptibilities, no matter how vicious or unlovely: "to reject one's experiences is to arrest one's development," he writes. "Whatever is realised is right" (p. 916). It is noteworthy, furthermore, that Wilde oudines this same argument under varying conditions throughout his work as essayist, story-teller, and playwright. In his wry but delicately tuned fairy tales, the most successful heroes and heroines are those who—like the litde Nightingale, the young King, or the Star-Child—manage to transform their lives into images of complex, artistic unity, suggestive of the radical power of the imagination. As the author ofde Profundis was to remark: "every work of art is the conversion of an idea into an image. Every single human being should be the fulfilment of a prophecy" (p. 928). Likewise, the elegant rhetorical strategies of Wilde's two critical dialogues announce art's power to starde and provoke its spectators into new attitudes, and—in particular—to suggest a transference ofaesthetic criteria to life itself. Artistic appreciation develops "that sense of form which is the basis of creative no less than of critical achievement," which may then be profitably applied to one's disparate experience: "it is form that creates not merely the critical temperament, but also the aesthetic instinct, that unerring instinct that reveals to one all things under their conditions of beauty" ("The Critic as Artist," p. 1052). It is only by cultivating a flexible, formalist oudook that a cramping and static Weltanschauung may be avoided; ethical distinctions too must be recast, if a successful life-as-artwork is to be sustained. Thus, writes Wilde, "Ethics, like natural selection, makes existence possible. Aesthetics, like sexual selection, makes life lovely and wonderful, fills it with new forms, and gives it progress, variety and change" (p. 1058). Moreover, the critical or aesthetic impulse—and the point of Wilde's essay is that the terms are interchangeable—has overall a vital cosmopolitan function; it will heal all human divisions, "by insisting on the unity of the human mind in the variety of its forms" (p. 1057). If we transfer aesthetic criteria from art to life, therefore, we will discover a new raison d'être in a skeptical age; we will understand that our apprehension of symmetry in art offers a motive for restoring a novel order to our own lives, singly and together. So it will be that "form [will... (shrink)

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature Tc below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T (...) function. The conservation of energy is spontaneously violated for T>Tc, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures. (shrink)

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element (...) of a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Imitation, Violence, and ExchangeGirard and MaussPer Bjørnar Grande (bio)RECIPROCAL VIOLENCE AND THE DESIRE FOR WHAT THE OTHER DESIRESIn this article, I would like to draw attention to the potentially violent outcome of exchange interactions between individuals and groups. Both Girard and Mauss examine violence in a wider social and political process.1 According to Mauss, the smallest difference, such as a lack of reciprocity, may evoke a desire for retribution. (...) Understanding reactions when there is a lack of symmetry, real or illusory, can give us an important insight into the generative mechanisms behind violence. This is why traditional societies tried, often very successfully, to protect individuals through prohibitions and taboos. These prohibitions and taboos were directed against any kind of activity that could possibly result in violent rivalries among the population. The killing of adulterers, thieves, and foreigners can be seen as a way of ridding society of people perceived as having undesirable traits and ridding it of the potential imitation of their bad desires. In this way, a society's violence may function in a protective [End Page 221] and anti-mimetic way. The violence against transgressors is a kind of mimetic anti-mimesis, a way of telling people to follow the rules of society so that they will become mimetically immune to the forces that threaten society.Violent victimizing appears to fulfill a generative function by preventing transgressions, moral cleansing, and restoration of peace. At the same time, however, it bears (unconsciously for the participants) a similarity to what one wishes to expel, namely, the feared violence and negative influence of the person or persons who are victimized. Despite attempts to expel violent transgressions, the attempts themselves are quite similar to the violence they are trying to exorcise. Both Freud and Girard argue that those who conduct a rite of sacrifice are projecting onto the sacrificial victim qualities that reflect some of their own innermost concerns.2 Sacrificial violence, seen from a modern, nonsacrificial standpoint, is a kind of suicide. By killing the other, one also kills something in oneself.In demolishing the victim they are symbolically annihilating aspects of themselves. What is destroyed is destructiveness itself: the feelings of violence and hostility that lie behind attempts to carry out violent activities. Such feelings are antithetical to the ties of friendship that bond a community together, and feelings of violence towards one's peers and associates must be banished if a closely knit community—such as a tribal brotherhood, a spiritual fellowship, or a modern nation—is to survive.3Modern societies are full of these projections of one's own desires onto the other, which expose the modern variant of what is sacrifice, and which are often less physically but instead psychologically violent, yet still victimizing in their attitude of projecting. Terms such as "imitation," "identification," and "comparison" do not have to turn out to be violent—even when a great deal of competition is involved. In this respect, I disagree with some Girardians who claim that imitative desire must be violent and who look back to an insight going back to Heraclitus that violence is the source of all.4 The all-decisive factor is the gradual shift from competition to rivalry, from being allies to becoming enemies. The transition from being competitive friends to rivals comes as a result of imitation. Seen in this way, imitative desire is the generative force behind violence, the snake that turns friends and lovers into rivals.This Freudian act of projection resembles an act of doubling, an intense mimesis of the other that creates doubles. From a Girardian perspective, it is the clash of desire that leads to doubling, and later to violence.5 The imitation of each other's desires will sooner or later cause some kind of violence.6 This doubling does not only have to involve two people; it can be groups, even countries. [End Page 222] But the effect is always negative. Raymund Schwager explains it in the following terms:Whoever is desirous has to expect that the others will too. Whoever succumbs to rivalry arouses the same passion in others. Whoever resorts to violence is imitated in his or... (shrink)

Myofascial Pain Syndrome is somatic pain due to muscular tension associated with muscular-skeletal imbalance. The pain and discomfort of the patient is not simply due to some isolated tension, but in the dynamic relationships between related structures. As the body adjusts to reestablish balance and symmetry, the tension and pain in one area “diagonalizes,” creating a tense correlate along a diagonal axis. This diagonalization of tension exacerbates and perpetuates the initial condition of pain and dysfunction. The purpose of this (...) paper is to argue that there are moral and social analogues to MFPS with their own forms of diagonalized asymmetry. Following the Aristotelian model of virtue and vice, whereby moral traits and dispositions become vice as a result of a loss of balance in conduct, and George Herbert Mead’s social psychology, which describes the self in terms of dynamic interrelation and co-operation of multiple sub-selves, I maintain that otherwise positive strengths in personal character, when overemphasized or exaggerated, can be juxtaposed to analogous weaknesses in related areas of personal health and conduct. I will argue that the descriptive analogy of MFPS has a corollary set of prescriptions for restoring balance in a moral subject. (shrink)

It is widely held among philosophers that the conservation of energy is true and important, and widely held among philosophers of science that conservation laws and symmetries are tied together by Noether's first theorem. However, beneath the surface of such consensus lie two slights to Noether's first theorem. First, there is a 325+-year controversy about mind-body interaction in relation to the conservation of energy and momentum, with occasional reversals of opinion. The currently popular Leibnizian view, dominant since the late 19th (...) century, claims to find an objection to broadly Cartesian views in their implication of energy non-conservation. Here energy conservation is viewed as an oracle, an unchallengeable black box. But Noether's first theorem and its converse show that conservation and symmetry of the laws stand or fall together. Absent some basis for expecting conservation in brains that has a claim on the Cartesian, the objection is circular. An empirically based argument is possible, but is a different argument with little force except insofar as it is rooted in neuroscience. Second, General Relativity has a 100+-year-long controversy about whether gravitational energy exists and is objectively localized. The usual view is that gravitational energy exists but is not objectively localized, though some deny its existence. Without positive answers to both questions, generally applicable conservation laws do not exist: energy is not conserved. This conclusion is startling in itself and a problem for conserved quantity theories of causation. Yet Noether's first theorem applies to General Relativity, which has uncountably many symmetries of its laws and so has conservation laws, indeed uncountably many of them. Many authors downplay these laws due to their quirky properties; some authors even attempt to explain the laws' supposed nonexistence in terms of an absence of symmetries of the geometry, which is a distraction. Thus Noether's first theorem is widely ignored, left uninterpreted, or distorted in relation to General Relativity. Taking the theorem seriously seems possible, however, restoring the conservation of energy, or rather, energies. How do these controversies relate? One sometimes finds claims that General Relativity's supposed lack of conservation laws answers Leibniz on behalf of Descartes. Taking seriously the superabundance of formal conservation laws in General Relativity, however, suggests that General Relativity resists mind-to-body causation. This conclusion can be proven apart from interpretive controversies. The resistance is, however, finite and tends to be swamped by larger world-view considerations. (shrink)

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is (...) no such concept. The present paper arrives at a cautiously pessimistic conclusion. (shrink)

Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and (...) philosophy of science, the volume is a valuable reference for students and researchers. (shrink)

Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such (...) as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic. (shrink)

Machine generated contents note: 1 Introduction 1 -- 2 Central themes and critical issues 10 -- Introduction 10 -- Core themes 11 -- Differences which have surfaced in the move from -- margins to mainstream 15 -- The claims of restorative justice: a brief examination 21 -- Some limitations of restorative justice 25 -- Some dangers of restorative justice 29 -- Debunking restorative justice 32 -- 3 Reviving restorative justice traditions 36 -- The rebirth of an ancient practice 36 -- (...) Pre-modem criminal justice 37 -- The renaissance of native justice traditions 43 -- Navajo peacemaking 44 -- Can one characterise ancient and indigenous -- justice as restorative? 47 -- Can one revive restorative justice traditions? 49 -- Conclusion: did restorative justice ever die? 59 -- 4 Healing the victim 62 -- Introduction 62 -- The experiences and needs of victims 64 -- The inadequacy of punitive justice for the victim 67 -- Victim reforms 70 -- Restitution from the offender 74 -- Beyond restitution: restoring victims 76 -- Restorative justice or 'clubbing together'? 78 -- Using victims to rehabilitate offenders 81 -- Paternalism towards victims 83 -- Balancing the needs of the victim with those of society 84 -- 5 A restorative approach to offenders 87 -- Introduction 87 -- Restorative justice as an alternative to retributive justice 88 -- Restorative justice as an alternative to treatment 94 -- The goals and methods of restorative justice in relation -- to offenders 95 -- An alternative to punishment or an alternative form of -- punishment? 106 -- An alternative to treatment? 111 -- 6 Shame, apology and forgiveness 114 -- Introduction 114 -- Restorative cautioning 115 -- The psychological routes of restorative conferencing 116 -- The idea of reintegrative shaming 118 -- Some questions about shaming 123 -- Apology and forgiveness 132 -- 7 Mediation, participation and the role of community 136 -- Introduction: handling criminal conflicts 136 -- The rationale for the restorative justice process 140 -- Achieving restorative goals 141 -- Moral development and the strengthening of community 144 -- The role of community 151 -- 8 The future of restorative justice 161 -- Introduction 161 -- Implementing restorative justice: the paths less likely 163 -- The implementation of restorative techniques 166 -- Restorative justice and the pattern of penal control 169 -- The future of restorative justice research 170 -- Appendix to chapter 3: the theological roots of judicial -- punishment 172. (shrink)

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of (...) the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics. (shrink)

The classical field theories that underlie the quantum treatments of the electromagnetic, weak, and strong forces share a peculiar feature: specifying the initial state of the field determines the evolution of some degrees of freedom of the theory while leaving the evolution of some others wholly arbitrary. This strongly suggests that some of the variables of the standard state space lack physical content-intuitively, the space of states of such a theory is of higher dimension than the corresponding space of genuine (...) physical possibilities. The structure of such theories can helpfully be characterized in terms of the action of symmetry groups on their space of states; and the conceptual problems surrounding their strange behavior can be sharpened in light of the observation that it is usually possible to eliminate the redundant variables associated with these symmetries-which turn out to be precisely those variables whose evolution is unconstrained by the dynamical laws of the theory. This paper discusses this approach, uses it to frame questions about the interpretation of classical gauge theories, and to reflect (pessimistically) on our prospects of reaching satisfactory answers to these questions. (shrink)

I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures (...) all of the structure of classical mereology. (shrink)

The widely held picture of dynamical symmetry as surplus structure in a physical theory has many metaphysical applications. Here, I focus on its relevance to the question of which quantities in a theory represent fundamental natural properties.

If the tiles of a mosaic are arranged symmetrically, then the image those tiles constitute must be symmetric as well. This paper formulates and defends the general principle at work in this case: roughly, that a symmetry cannot ground an asymmetry. It is argued that the principle supports strong objections to four metaphysical views: qualitativism, relationalism, the tenseless or ‘B’ theory of time, and comparativism. A response to these objections is developed which appeals to fragmentalism, the view that reality (...) contains facts which are incompatible with one another. But fragmentalism might be thought too bizarre to tolerate, and if it is, then the objections developed in this paper may well be fatal. (shrink)

Fearful Symmetry brings the incredible discoveries of contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters in (...) the intellectual history of humankind. (shrink)

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only (...) from those epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning1.1 A rough introduction to symmetry1.2 The symmetry-to-reality inference1.3 Two questions1.4 Two answers1.5 Preliminary clarifications2 Against Redundancy2.1 Redundancy2.2 Is absolute velocity redundant?2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection4.1 The epistemic approach4.2 The Occamist norm4.3 From symmetry to detection5 The Meaning of ‘Symmetry’5.1 A framework5.2 Formal definitions5.3 Ontic definitions6 Epistemic Definitions6.1 Taking observation seriously6.2 How things look6.3 Observation sentences6.4 Observational equivalence7 Symmetry as an Epistemic Notion 7.1 Observational equivalence and metaphysics7.2 The Occamist norm revisted7.3 Consequences8 Conclusion. (shrink)

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These (...) predictions were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price. (shrink)

Many important explanations in physics are based on ideas and assumptions about symmetries, but little has been said about the nature of such explanations. This chapter aims to fill this lacuna, arguing that various symmetry explanations can be naturally captured in the spirit of the counterfactual-dependence account of Woodward, liberalized from its causal trappings. From the perspective of this account symmetries explain by providing modal information about an explanatory dependence, by showing how the explanandum would have been different, had (...) the facts about an explanatory symmetry been different. Furthermore, the authors argue that such explanatory dependencies need not be causal. (shrink)

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.

A survey of the main themes and arguments concerning symmetry and invariance in physics and philosophy of physics.

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of (...) the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity. (shrink)

The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the (...) class='Hi'>symmetry issue is the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)

Imagine that we are on a train playing with some mechanical systems. Why can’t we detect any differences in their behavior when the train is parked versus when it is moving uniformly? The standard answer is that boosts are symmetries of Newtonian systems. In this paper, I use the case of a spring to argue that this answer is problematic because symmetries are neither sufficient nor necessary for preserving its behavior. I also develop a new answer according to which boosts (...) preserve the relational properties on which the behavior of a system depends, even when they are not symmetries. (shrink)

James Henry Collin recently developed a new symmetry breaker favouring the ontological argument’s possibility premiss over that of the reverse ontological argument. The symmetry breaker amounts to an undercutting defeater for the reverse possibility premiss based on Kripkean cases of a posteriori necessity. I argue, however, that symmetry re-arises in two forms. First, I challenge the purported asymmetry in epistemic entitlements to the original and reverse possibility premisses. Second, relevantly similar Kripkean cases equally undercut the original possibility (...) premiss. (shrink)

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not (...) generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic. (shrink)

We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries. Overall, the account meshes well with standard treatments of symmetries. But the distinction between the common core and the dual theories prompts a distinction between three kinds of symmetry: which we call ‘stipulated’, ‘accidental’ and ‘proper’.

It is often said in physics that if two models of a theory are related by a symmetry, then the two models provide (or could provide) two different representations of the very same situation, alike the case of two maps of different color for the very same city. It is also said that the situations represented by two models of a theory are indiscernible in some ways when the models in question are related by a symmetry of the (...) theory, just like the situation in the interior of the cabin of a train when the train is at rest in the station is empirically indiscernible from the situation in the interior when the train is moving uniformly (in classical mechanics, these two situations are represented by two models related by a boost). In recent years, philosophers of physics have focused a lot of attention in developing various principles that aim to elucidate these and similar remarks on symmetries, models, physical equivalence, and representation that are widespread in physics practice. The goal of the current article is to provide a critical review of these principles, and suggest a new framework for thinking about these kinds of questions. One important upshot of the paper is that questions of indiscernibility, and questions of the representational capacity of models, must be distinguished from one another. (shrink)