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A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.

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In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde M_4 $$ \end{document}.

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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 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)

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It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a (...) related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (shrink)

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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)

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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)

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This important study makes a convincing case for its thesis that the dramatic form of Shakespeare's plays corresponds to that of a natural system evolving to a more complex state while undergoing symmetry breaking. Drawing upon such key concepts of chaos theory as global agency and self-similarity, the book constructs a methodology which illuminates many problematic aspects of agency in the selected comedies, tragedies, and histories it examines. Each of these genres is shown to reflect the paradoxical dynamics of a (...) chaotic system. This fresh «systems perspective» offers a serious challenge to the structuralist assumptions underlying many current literary approaches. (shrink)

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William Lynch has persistently questioned the politics underlying my appeal to science and technology studies’ flagship symmetry principle. He believes that it licenses the worst features of the ‘post-truth condition’. I respond in two parts, the first facing the future and the second facing the past. In the first part, I argue that the symmetry principle will be crucial in decisions that society will increasingly need to make concerning the inclusion of animals and machines on grounds of sentience, consciousness, intelligence, (...) etc. In the second part, I argue that the symmetry principle has been in fact at the core of the ‘justice as fairness’ idea that has been at the core of both liberal and socialist democracies. Difficulties start once the means of expression and communication are made widely available and the standards of fairness are subject to continual questioning and renegotiation. (shrink)

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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..

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We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.In 2+1 dimensional spacetime, a velocity of the particle and spin tensor are dependent to each other and the chirality can not be introduced. (...) The free particle has 7 constants of motion: The momentum three vector, the charge, the energy in proper time, the scalar constant spin or magnetic polarization and the two components of total angular momentum. Two component electric polarizations oscillate with Zitterbewegung frequency.In 1+1 dimensional spacetime we have an independent velocity vector and a scalar spin tensor. The free particle has 5 integrals of motion: The momentum two vector, the charge, the energy in proper time, and the scalar total angular momentum. The normal component of the velocity or the scalar electric polarization oscillates with Zitterbewegung frequency.In 3+1 dimensional spacetime, the particle has an independent velocity vector, spin tensor and chirality. The free particle has 12 integrals of motion: The momentum four vector, the charge, the energy in proper time or mass, the three vector spin or magnetic polarizations and three components of total angular momentum. The parallel component of velocity into momentum and the normal components of the spin tensor or the spin three vector are constants of motion for the free particle. The chirality and electric polarizations oscillate with the Zitterbewegung frequency. The system is superintegrable in all dimensions. (shrink)

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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)

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Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this (...) overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries. (shrink)

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This volume brings together a collection of essays on the history and philosophy of probability and statistics by one of the eminent scholars in these subjects. Written over the last fifteen years, they fall into three broad categories. The first deals with the use of symmetry arguments in inductive probability, in particular, their use in deriving rules of succession. The second group deals with four outstanding individuals who made lasting contributions to probability and statistics in very different ways: Frank Ramsey, (...) R. A. Fisher, Alan Turing, and Abraham de Moivre. The last group of essays deals with the problem of 'predicting the unpredictable' - making predictions when the range of possible outcomes is unknown in advance. The essays weave together the history and philosophy of these subjects and document the fascination that they have exercised for more than three centuries. (shrink)

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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)

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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)

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The effect of prism adaptation on movement is typically reduced when the movement at test (prisms off) differs on some dimension from the movement at training (prisms on). Some adaptation is latent, however, and only revealed through further testing in which the movement at training is fully reinstated. Applying a nonlinear attractor dynamic model (Frank, Blau, & Turvey, 2009) to available data (Blau, Stephen, Carello, & Turvey, 2009), we provide evidence for a causal link between the latent (or secondary) aftereffect (...) and an additive force term that is known to account for symmetry breaking. The evidence is discussed in respect to the hypothesis that recalibration aftereffects reflect memory principles (encoding specificity, transfer-appropriate processing) oriented to time-translation invariance—when later testing conserves the conditions of earlier training. Forgetting or reduced adaptation effects follow from the loss of this invariance and are reversed by its reinstatement. (shrink)

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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)

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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)

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The time-scale dynamic equations play an important role in modeling complex dynamical processes. In this paper, the Mei symmetry and new conserved quantities of time-scale Birkhoff’s equations are studied. The definition and criterion of the Mei symmetry of the Birkhoffian system on time scales are given. The conditions and forms of new conserved quantities which are found from the Mei symmetry of the system are derived. As a special case, the Mei symmetry of time-scale Hamilton canonical equations is discussed and (...) new conserved quantities for the Hamiltonian system on time scales are derived. Two examples are given to illustrate the application of results. (shrink)

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Can recognition theories distinguish legitimate from illegitimate claims to recognition put forward by social movements? This paper identifies an under-theorised problem of recognition theories: in viewing struggles for recognition as a force for social progress in the mould of the New Social Movements of the 1960s and 1970s, existing accounts have trouble identifying and ruling out illegitimate claims to recognition as formulated by contemporary counter-movements like white supremacists or men’s rights activists. I refer to this issue as the symmetry problem (...) of recognition since it amounts to difficulties in identifying grounds for excluding illegitimate claims to recognition that do not also symmetrically justify the exclusion of legitimate ones (and vice versa). I argue that criteria for telling apart legitimate from illegitimate claims to recognition need to include interpretation issues as a dimension of analysis, which consequently requires incorporating democratic deliberation as a necessary component of recognition theory. (shrink)

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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)

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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.

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Dispositional essentialists ultimately appeal to dispositional essences in order to provide (a) an explanation of the conservation of physical quantities and (b) identity conditions for fundamental physical properties. This paper aims to offer alternative suggestions based on symmetry considerations and exhibits their consequences for the thesis of dispositional essentialism.

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Judgments of symmetry lay at the heart of the classical theory of probability. It was by direct appeal to the symmetries exhibited by the processes underlying simple games of chance that the earliest theorists of probability were able to justify the initial assumptions of equiprobability which allowed them to compute the probabilities of more complex events using combinatorial methods, i.e., by simply counting cases. Nevertheless, in spite of the role that symmetry played in the earliest writings on the subject, in (...) light of the fact it is only in highly contrived settings that a direct appeal to symmetries can suffice to determine the probabilities of events, many philosophers have been led to conclude that the concept of symmetry itself has, at best, a limited role to play in a general theory of probability. In this essay, I argue that this view of the matter is mistaken, and that judgments of symmetry, in fact, have an indispensible role to play in all probabilistic reasoning. In chapter 1, I provide a detailed account of symmetry-based reasoning and argue against the view that the judgments of relevance on which such reasoning is based must be construed in subjective terms if symmetry-based reasoning is to be applied to deterministic processes. In chapter 2, I argue that the two most plausible proposals for how to avoid an appeal to symmetry in the assignment of probabilities (viz., those which are based on a priori principles of epistemic conservatism or the observed frequencies of events) must themselves rely on implicit assumptions of symmetry if they are to defend themselves against the charges of incoherency and arbitrariness. In chapter 3, I consider a decision-theoretic example of symmetry-based reasoning, in which the appeal to symmetry arises in the context of an agent's choice of a deliberative methodology. In this context, the principle of symmetry amounts to the requirement that the agent avoid adopting a biased deliberative methodology, i.e., one which treats two equally legitimate sources of information differently. In the specific context of the exchange paradox, I propose an account of how biased information is to be handled, which, despite suffering from some important defects, does, I believe, capture some of our general intuitions about how a rational agent ought to adjust his expectations to correct for the effects of bias. (shrink)

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Symmetry is at the heart of our understanding of matter. This book tells the fascinating story of the constituents of matter from a common symmetry perspective. The standard model of elementary particles and the periodic table of chemical elements have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. -/- The purpose of Shattered Symmetry is to share the admiration for the power (...) and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. Along the way the theory of symmetry groups is gradually introduced with special emphasis on its use as a classification tool and its graphical representations. This is applied to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires us to leave the common ground of linear algebras and explore the potential of non-linearity. (shrink)

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Proceedings of the 11th Interdisciplinary Symmetry Congress-Festival of the International Society for the Interdisciplinary Study of Symmetry. Special Theme: “Tradition and Innovation in Symmetry - Katachi”.

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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)

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Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in (...) triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations. (shrink)

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The modal ontological argument (MOA) proceeds from God’s possible existence to God’s actual existence. A prominent objection to the MOA is that it suffers from a symmetry problem: an exactly parallel modal ontological argument can be given for God's non-existence. Several attempts have been made to break the symmetry between the arguments. This draft is a mostly comprehensive survey of those attempts. -/- The draft was initially written as a supplement to the 2024 Summer edition of the SEP entry on (...) Ontological Arguments. However, the draft is not included in the SEP entry. (shrink)

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Molecules have more or less symmetric and complex structures which can be defined in the mathematical framework of topology, group theory, dynamical systems theory, and quantum mechanics. But symmetry and complexity are by no means only theoretical concepts of research. Modern computer aided visualizations show real forms of matter which nevertheless depend on the technical standards of observation, computation, and representation. Furthermore, symmetry and complexity are fundamental interdisciplinary concepts of research inspiring the natural sciences since the antiquity.

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We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being \ rather than \ itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is (...) obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided. (shrink)

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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)

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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)

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Symmetry permeates our existence from end to end. It was born in space and on Earth long before the emergence of human civilization - the Solar system is proof of this. After man began conscious existence, he became imbued with natural symmetry in space and time. He also began to create symmetrically arranged things in his environment and events in his behavior. In the end, symmetry has become integral to human life, society, and our consciousness.

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Whether designing animals, insects, or plants, Nature draws upon symmetry and periodicity to play a fundamental role in defining the body plan. When implemented with the proper chemical mechanisms, these principles guide our bodies from single-celled embryos to bilaterally symmetric creatures with intricate periodic structures, such as the spine and rib cage. The properties of symmetry and periodicity also appear to be fundamental to visual perception. We will show that this is no coincidence, but is a consequence of the fact (...) that these properties are generated by the same underlying phenomenon, standing wave patterns formed from harmonic resonances. The symmetry in life forms arises from chemical harmonic resonances, whereas the symmetry in visual perception arises from harmonic resonances in the visual system. We will show that harmonic resonances have very interesting properties for the representation of geometrical form that make them eminently suitable for encoding geometric form for body plans as well as for visual perception. In particular, we will show that by being simultaneously invariant to perspective transformation and robust to deformation, such resonant representations have fundamental advantages over more traditional techniques. (shrink)

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A drastic resolution of the quantum paradoxes is proposed, combining (I) von Neumann's postulate that collapse of the state vector is due to the act of observation, and (II) my reinterpretation of von Neumann's quantal irreversibility as an equivalence between wave retardation and entropy increase, both being “factlike” rather than “lawlike” (Mehlberg). This entails a coupling of the two de jure symmetries between (I) retarded and (II) advanced waves, and between Aristotle's information as (I) learning and (II) willing awareness. Symmetric (...) acceptance of cognizance as a source of retarted waves, and of will as a sink of advanced waves, is submitted as a central “paradox” of the Copernican or Einsteinian sort, out of which new light is shed upon previously known paradoxes, such as the EPR paradox, Schrödinger's cat, and Wigner's friend. Parapsychology is thus found to creep into the picture. (shrink)

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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)

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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.

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Here I respond to Anthony Brueckner and John Martin Fischer’s “The Evil of Death: A Reply to Yi.” They developed an influential strategy in defense of the deprivation account of death’s badness against the Lucretian symmetry problem. The core of their argument consists in the claim that it is rational for us to welcome future intrinsic goods while being indifferent to past intrinsic goods. Previously, I argued that their approach is compatible with the evil of late birth insofar as an (...) earlier birth would have generated more goods in the future. In reply, Brueckner and Fischer argue that my critique fails to appreciate an important aspect of their thought experiment, which aims only to show that the deprivation of past goods per se is not bad for us. Thus, purportedly, my critique poses no threat to their view. Here I argue that since the deprivation account explains the evil of death with recourse to how one’s life would have fared had one lived longer, it ought to respond to the symmetry problem with reference to how one’s life would have fared had one been born earlier. However, it is not generally true that the life one would have had with an earlier birth is not preferable to one’s actual life, because in many cases such a life would contain more future goods. (shrink)

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Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a carefully coded expression of our experience then its effectiveness is quite reasonable. Its effectiveness is built into its design. We consider group theory, the logic of symmetry. We examine the premise that symmetry is identity; that group theory encodes our experience of identification. To decide whether group theory describes the world in such an elemental way we catalogue (...) the detailed correspondence between elements of the physical world and elements of the formalism. Providing an unequivocal match between concept and mathematical statement completes the case. It makes effectiveness appear reasonable. The case that symmetry is identity is a strong one but it is not complete. The further validation required suggests that unexpected entities might be describable by the irreducible representations of group theory. (shrink)

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The primary goal of this paper is to distinguish binding from reflexivity in domains where they appear to overlap. In so doing I will argue that Principles A and B of the Binding Theory are symmetric in the domains to which they apply. This symmetry derives from a deeper unity that permits us to dispense with Principles A and B and replace them with interpretive principles that distinguish reflexivity and binding.

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According to the orthodox view, one can appeal to the symmetries of a theory in order to show that it is impossible to measure the properties that are not invariant under such symmetries. For example, it is widely believed that the fact that boosts are symmetries of Newtonian mechanics entails that it is impossible to measure states of absolute motion in a Newtonian world (these states vary under boosts). This paper offers an overview of the various ways by which philosophers (...) have spelled out the connection between the symmetries of a theory and the alleged impossibility of measuring some properties (the variant ones). The paper will use the case of absolute motion as a case study, and will discuss a recent unorthodox view according to which this kind of motion can actually be measured in Newtonian mechanics. The paper ends by considering some avenues by which the discussion can be further developed. (shrink)

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In this paper I focus on the impact on structuralism of the quantum treatment of objects in terms of symmetry groups and, in particular, on the question as to how we might eliminate, or better, reconceptualise such objects in structural terms. With regard to the former, both Cassirer and Eddington not only explicitly and famously tied their structuralism to the development of group theory but also drew on the quantum treatment in order to further their structuralist aims and here I (...) sketch the relevant history with an eye on what lessons might be drawn. With regard to the latter, Ladyman has explicitly cited Castellani's work on the group-theoretical constitution of quantum objects and I indicate both how such an approach needs to be understood if it is to mesh with Ladyman's 'ontic' form of structural realism and how it might accommodate permutation symmetry through a consideration of Huggett's recent account. (shrink)

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Crazily, Christopher Norris seems to think sociology is at war with philosophy; it is not. I respond to his hostile comments on the sociology of scientific knowledge, which was inspired by Wittgenstein, by explaining the need for symmetry in the explanation of scientific knowledge, methodological relativism, elective modernism and a number of other issues.

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IN THIS PAPER, I observe a set of symmetries exposed by examining cases of excused blameworthiness and mitigated praiseworthiness, and argue that a prominent contemporary approach to explaining moral responsibility is ill-suited to explaining why the symmetry obtains. The view I have in mind has a distinctive explanatory strategy: an agent S’s being responsible, on this view, is to be explained in terms of the appropriateness of holding S responsible. This explanatory strategy, whatever its other merits, cannot adequately explain the (...) symmetry. In light of my arguments here, this view faces a challenge: it can either give up its distinctive explanatory strategy, or else fail to capture the symmetry. While failure to accommodate the symmetrical observation is not grounds for rejecting this view, it does count as a significant cost, one that ought to be recognized and addressed. (shrink)

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In this paper I attempt mainly to elucidate the claim, advanced by Woorward, that the key notion to characterize physical laws is that of invariance. I draw a distinction betwen two levels of invariance in order to elaborate that thesis. I maintain that distinctive marks of the nomic status of basic laws of physics are either that they hold invariantly, within a domain of applivation, or that they fulfill some principles of symmetry. The fomer mark relatesd to the manner in (...) which physical systems change invariantly whereas the latter concerns to the invariance of the laws themselves. This view contrats with the traditional philosophical thesis that physical laws are true universal statements with a necessary character which differentiate then from accidental true generalizations, which are contingent. (shrink)

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The paper discusses the invariance view of reality: a view inspired by the relativity and quantum theory. It is an attempt to show that both versions of Structural Realism (epistemological and ontological) are already embedded in the invariance view but in each case the invariance view introduces important modifications. From the invariance view we naturally arrive at a consideration of symmetries and structures. It is often claimed that there is a strong connection between invariance and reality, established by symmetries. The (...) invariance view seems to render frame-invariant properties real, while frame-specific properties are illusory. But on a perspectival, yet observer-free view of frame-specific realities they too must be regarded as real although supervenient on frame-invariant realities. Invariance and perspectivalism are thus two faces of symmetries. Symmetries also elucidate structures. Because of this recognition, the invariance view is more comprehensive than Structural Realism. Referring to broken symmetries and coherence considerations, the paper concludes that at least some symmetries are ontological, not just epistemological constraints. (shrink)

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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)

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