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  1. Alexander Afriat, Is the World Made of Loops?
    In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...)
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  2. Grant Allen (1879). The Origin of the Sense of Symmetry. Mind 4 (15):301-316.
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  3. P. M. Allen & J. M. McGlade (1987). Evolutionary Drive: The Effect of Microscopic Diversity, Error Making, and Noise. [REVIEW] Foundations of Physics 17 (7):723-738.
    In order to model any macroscopic system, it is necessary to aggregate both spatially and taxonomically. If average processes are assumed, then kinetic equations of “population dynamics” can be derived. Much effort has gone into showing the important effects introduced by non-average effects (fluctuations) in generating symmetry-breaking transitions and creating structure and form. However, the effects of microscopic diversity have been largely neglected. We show that evolution will select for populations which retain “variability,” even though this is, at any given (...)
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  4. Valia Allori (forthcoming). Maxwell's Paradox: The Metaphysics of Classical Electrodynamics and its Time-Reversal Invariance. Analytica.
    In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that the (...)
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  5. J. Anandan (1999). Are There Dynamical Laws? Foundations of Physics 29 (11):1647-1672.
    The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to a final state then depends on the quantum geometry that is determined by symmetries, which may exist as relations between states in the absence of dynamical laws. This enables the experimentally well-confirmed quantum probabilities to be derived from the geometry of Hilbert (...)
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  6. J. Anandan (1980). On the Hypotheses Underlying Physical Geometry. Foundations of Physics 10 (7-8):601-629.
    The relationship between physics and geometry is examined in classical and quantum physics based on the view that the symmetry group of physics and the automorphism group of the geometry are the same. Examination of quantum phenomena reveals that the space-time manifold is not appropriate for quantum theory. A different conception of geometry for quantum theory on the group manifold, which may be an arbitrary Lie group, is proposed. This provides a unified description of gravity and gauge fields as well (...)
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  7. F. Antonuccio, S. Pinsky & S. Tsujimaru (2000). A Comment on the Light-Cone Vacuum in 1+1 Dimensional Super-Yang–Mills Theory. Foundations of Physics 30 (3):475-486.
    The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious “zero-mode” problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the gauge (...)
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  8. Jonas Rafael Becker Arenhart (2013). Weak Discernibility in Quantum Mechanics: Does It Save PII? Axiomathes 23 (3):461-484.
    The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning (...)
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  9. Franklin Shepard Axelrod (1972). The Principle of Symmetry: A Study in the History and Philosophy of Scientific Method. Dissertation, Boston University Graduate School
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  10. John C. Baez (2012). Division Algebras and Quantum Theory. Foundations of Physics 42 (7):819-855.
    Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the ‘three-fold way’. It (...)
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  11. David Baker (2011). Broken Symmetry and Spacetime. Philosophy of Science 78 (1):128-148.
    The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems forces us to adopt an unorthodox ontology. We must abandon the standard conception of the physical meaning of these symmetries, or else deny the attractive “liberal” notion of which physical quantities are significant. A third option, more attractive but less well understood, is to abandon the existing (Halvorson-Clifton) notion of intertranslatability for quantum theories.
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  12. David J. Baker & Hans Halvorson, How is Spontaneous Symmetry Breaking Possible?
    We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum (...)
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  13. David John Baker (2010). Symmetry and the Metaphysics of Physics. Philosophy Compass 5 (12):1157-1166.
    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.
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  14. David John Baker & Hans Halvorson (2013). How is Spontaneous Symmetry Breaking Possible? Understanding Wigner's Theorem in Light of Unitary Inequivalence. Studies in History and Philosophy of Science Part B 44 (4):464-469.
    We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...)
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  15. David John Baker, Hans Halvorson & Noel Swanson (2014). The Conventionality of Parastatistics. British Journal for the Philosophy of Science:axu018.
    Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don’t we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We (...)
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  16. Yuri Balashov (2002). What is a Law of Nature? The Broken-Symmetry Story. Southern Journal of Philosophy 40 (4):459-473.
    I argue that the contemporary interplay of cosmology and particle physics in their joint effort to understand the processes at work during the first moments of the big bang has important implications for understanding the nature of lawhood. I focus on the phenomenon of spontaneous symmetry breaking responsible for generating the masses of certain particles. This phenomenon presents problems for the currently fashionable Dretske-Tooley-Armstrong theory and strongly favors a rival nomic ontology of causal powers.
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  17. J. Balog & P. Hraskó (1981). Thomas Precession and the Operational Meaning of the Lorentz-Group Elements. Foundations of Physics 11 (11-12):873-880.
    When space-reflection and time-reversal symmetries are broken, the Thomas precession formulas derived by Thomas' method and from the BMT equation differ from each other. This apparent contradiction is resolved by pointing out that the breakdown of discrete symmetries may lead to a change in the operational meaning of the Lorentz-group elements.
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  18. Sorin Bangu (2008). Reifying Mathematics? Prediction and Symmetry Classification. Studies in History and Philosophy of Science Part B 39 (2):239-258.
    In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised by (...)
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  19. Umberto Bartocci & Marco Mamone Capria (1991). Symmetries and Asymmetries in Classical and Relativistic Electrodynamics. Foundations of Physics 21 (7):787-801.
    By a comparison between Maxwell's electrodynamics classically interpreted (MT) and relativistic electrodynamics (RED), this paper discusses whether the “asymmetries” in MT mentioned by A. Einstein in his 1905 relativity paper are only of a conceptual nature or rather involve specific empirical claims. It is shown that in fact MT predicts strongly asymmetric behaviour for very simple interactions, and an analysis is made of the extent of the “symmetry” achieved by means of relativistic postulates. A “low” velocity experiment is suggested which (...)
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  20. A. O. Barut (1987). Irreversibility, Organization, and Self-Organization in Quantum Electrodynamics. Foundations of Physics 17 (6):549-559.
    QED is a fundamental microscopic theory satisfying all the conservation laws and discrete symmetries C, P, T. Yet, dissipative phenomena, organization, and self-organization occur even at this basic microscopic two-body level. How these processes come about and how they are described in QED is discussed. A possible new phase of QED due to self-energy effects leading to self-organization is predicted.
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  21. A. O. Barut, P. Budinich, J. Niederle & R. Raçzka (1994). Conformal Space-Times—The Arenas of Physics and Cosmology. Foundations of Physics 24 (11):1461-1494.
    The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the implications of global compactified space-times for (...)
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  22. Jacob D. Bekenstein (1986). Gravitation and Spontaneous Symmetry Breaking. Foundations of Physics 16 (5):409-422.
    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 (...)
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  23. Michael Belie (2003). Breaking Rules1. In Neil A. Manson (ed.), God and Design: The Teleological Argument and Modern Science. Routledge 277.
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  24. Gordon Belot, Symmetry and Equivalence.
    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 (in the sense of being equally well- or ill-suited to represent any given situation, relative to any reasonable interpretation). 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 (...)
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  25. Gordon Belot (2005). Dust, Time and Symmetry. British Journal for the Philosophy of Science 56 (2):255 - 291.
    Two symmetry arguments are discussed, each purporting to show that there is no more room for a preferred division of spacetime into instants of time in general relativistic cosmology than in Minkowski spacetime. The first argument is due to Gödel, and concerns the symmetries of his famous rotating cosmologies. The second turns upon the symmetries of a certain space of relativistic possibilities. Both arguments are found wanting. Introduction Symmetry arguments Gödel's argument 3.1 Time in special relativity 3.2 Time in the (...)
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  26. Darrin W. Belousek (2000). Statistics, Symmetry, and (In)Distinguishability in Bohmian Mechanics. Foundations of Physics 30 (1):153-164.
    This paper continues an earlier work by considering in what sense and to what extent identical Bohmian-mechanical particles in many-particle systems can be considered indistinguishable. We conclude that while whether identical Bohmian-mechanical particles ace considered to be “statistically (in)distinguishable” is a matter of theory choice underdetermined by logic and experiment, such particles are in any case “physically distinguishable.”.
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  27. Darrin W. Belousek (2000). Statistics, Symmetry, and the Conventionality of Indistinguishability in Quantum Mechanics. Foundations of Physics 30 (1):1-34.
    The question to be addressed is, In what sense and to what extent do quantum statistics for, and the standard formal quantum-mechanical description of, systems of many identical particles entail that identical quantum particles are indistinguishable? This paper argues that whether or not we consider identical quantum particles as indistinguishable is a matter of theory choice underdetermined by logic and experiment.
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  28. Yemima Ben-Menahem (2012). Symmetry and Causation. Iyyun 61:193-218.
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  29. Carl M. Bender & H. F. Jones (2000). Effective Potential for Mathcal{P}Mathcal{T}-Symmetric Quantum Field Theories. Foundations of Physics 30 (3):393-411.
    Recently, a class of $\mathcal{P}\mathcal{T}$ -invariant scalar quantum field theories described by the non-Hermitian Lagrangian $\mathcal{L}$ = $ \frac{1}{2} $ (∂ϕ) 2 +gϕ 2 (iϕ)ε was studied. It was found that there are two regions of ε. For ε<0 the $\mathcal{P}\mathcal{T}$ -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For ε≥0 the $\mathcal{P}\mathcal{T}$ -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle (...)
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  30. Fedde Benedictus (2011). D.E. Neuenschwander: Emmy Noether's Wonderful Theorem. [REVIEW] Foundations of Physics 41 (9):1491-1492.
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  31. M. K. Bennett & D. J. Foulis (1995). Phi-Symmetric Effect Algebras. Foundations of Physics 25 (12):1699-1722.
    The notion of a Sasaki projectionon an orthomodular lattice is generalized to a mapping Φ: E × E → E, where E is an effect algebra. If E is lattice ordered and Φ is symmetric, then E is called a Φ-symmetric effect algebra.This paper launches a study of such effect algebras. In particular, it is shown that every interval effect algebra with a lattice-ordered ambient group is Φ-symmetric, and its group is the one constructed by Ravindran in his proof that (...)
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  32. Alvin K. Benson (1978). Self-Consistent Selection of a Superconducting Representation for the BCS Model. Foundations of Physics 8 (9-10):653-666.
    Taking the BCS Hamiltonian written in second-quantized form, a modified form of Umezawa's self-consistent field theory method is applied, and a unitarily nonequivalent representation is selected in which the Hamiltonian obviously describes a superconducting system. This result is not at all obvious, since the original Hamiltonian is completely symmetric, and there is no reason a priori for expecting it to describe an asymmetric superconducting configuration. All higher order terms are accounted for, and in doing so, one finds the existence of (...)
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  33. Alvin K. Benson (1978). Microscopic Mechanism for the Macroscopic Asymmetry of Superconductivity. Foundations of Physics 8 (11-12):893-904.
    Some of the physical implications involved in self-consistently selecting a superconducting (nonequivalent) representation for the BCS Hamiltonian are developed and discussed. This is done by comparing the phase symmetry of our system in original variables with that same symmetry when written in terms of physical variables. It is shown explicitly that Goldstone's theorem is satisfied and that dynamical rearrangement of symmetry has taken place in going from original to physical variables. Thus, it is found that the original phase symmetry transformation (...)
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  34. A. N. Bernal, M. P. López & M. Sánchez (2002). Fundamental Units of Length and Time. Foundations of Physics 32 (1):77-108.
    Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime, at least in the non-quantum case. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.
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  35. Review author[S.]: J. D. Bernal (1955). Symmetry. British Journal for the Philosophy of Science 5 (20):335-341.
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  36. Sinem Binicioǧlu, M. Ali Can, Alexander A. Klyachko & Alexander S. Shumovsky (2007). Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement. [REVIEW] Foundations of Physics 37 (8):1253-1277.
    Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach (...)
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  37. Robert C. Bishop, Quantum Time Arrows, Semigroups and Time-Reversal in Scattering.
    Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be (...)
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  38. Marcel Bodea (2002). An Epistemological Investigation Of The Concept Of Symmetry In Physics. Studia Philosophica 1.
    The symmetry – one of the most important concepts of natural science - in physical theory expressed the invariance of some structural feature of the physical world under some transformation. A number of important physical principles stipulate that some physical quantity is conserved. Usually the symmetry is connected with space-time theory, but the impact of the symmetry theory can be traced in solid-state physics, quantum chemistry, theory of elementary particles as well as many other scientific branches. A very important mathematical (...)
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  39. Petar Bojanić (2010). The Figures of (a) Symmetry:'Pirates' and the World as a Closed Commercial State. Theoria 53 (4):5-14.
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  40. Rodney Bomford (1999). The Symmetry of God. Monograph Collection (Matt - Pseudo).
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  41. H. -H. V. Borzeszkowski & H. -J. Treder (1997). Mach's Principle and Hidden Matter. Foundations of Physics 27 (4):595-603.
    According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor $\hat \Theta _{ik}$ satisfying the relation $\hat \Theta _{i;k}^k = 0$ . The tensor $\hat \Theta _{ik}$ is formed from the Einstein-Cartan torsion field given by the anholonomy objects, (...)
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  42. Timothy H. Boyer (2010). Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation. Foundations of Physics 40 (8):1102-1116.
    It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. (...)
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  43. Timothy H. Boyer (1989). Conformal Symmetry of Classical Electromagnetic Zero-Point Radiation. Foundations of Physics 19 (4):349-365.
    The two-point correlation functions of classical electromagnetic zero-point radiation fields are evaluated in four-vector notation. The manifestly Lorentz-covariant expressions are then shown to be invariant under scale transformations and under the conformal transformations of Bateman and Cunningham. As a preliminary to the electromagnetic work, analogous results are obtained for a scalar Gaussian random classical field with a Lorentz-invariant spectrum.
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  44. Katherine Bracing & Harvey R. Brown (2003). Symmetries and Noether's Theorems. In Katherine A. Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press 89.
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  45. Katherine Brading (2002). Symmetries, Conservation Laws, and Noether's Variational Problem.
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  46. Katherine A. Brading & Elena Castellani (eds.) (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press.
    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, (...)
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  47. Katherine Brading & Elena Castellani, Symmetries and Invariances in Classical Physics.
    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 (...)
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  48. Harvey R. Brown & Peter Holland, Dynamical Versus Variational Symmetries: Understanding Noether's First Theorem.
    It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Specific attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.
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  49. Harvey R. Brown & Peter Holland, Simple Applications of Noether's First Theorem in Quantum Mechanics and Electromagnetism.
    Internal global symmetries exist for the free non-relativistic Schrodinger particle, whose associated Noether charges---the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate---are exhibited. Analogous symmetries in classical electromagnetism are also demonstrated.
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  50. Harvey R. Brown & Roland Sypel (1995). On the Meaning of the Relativity Principle and Other Symmetries. International Studies in the Philosophy of Science 9 (3):235 – 253.
    Abstract The historical evolution of the principle of relativity from Galileo to Einstein is briefly traced, and purported difficulties with Einstein's formulation of the principle are examined and dismissed. This formulation is then compared to a precise version formulated recently in the geometrical language of spacetime theories. We claim that the recent version is both logically puzzling and fails to capture a crucial physical insight contained in the earlier formulations. The implications of this claim for the modern treatment of general (...)
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