Holism and structuralism in U(1) gauge theory

After decades of neglect philosophers of physics have discovered gauge theories--arguably the paradigm of modern field physics--as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism--in the eyes of its proponents the best suited realist position towards modern physics--has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories--in particular U(1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov-Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed.

[1]  A. Hey,et al.  Gauge Theories in Particle Physics: A Practical Introduction: Volume 2 Non-Abelian Gauge Theories: Qcd and the Electoweak Theory , 2004 .

[2]  W. Drechsler,et al.  Fiber bundle techniques in gauge theories , 1977 .

[3]  Quantum Analogies: A Reply to Maudlin , 1999, Philosophy of Science.

[4]  John D. Norton,et al.  Must Evidence Underdetermine Theory , 2003 .

[5]  Simon Saunders,et al.  Critical Notice: Tian Yu Cao's “The Conceptual Development of 20th Century Field Theories” , 2003, Synthese.

[6]  T. Maudlin.  Healey on the Aharonov-Bohm Effect , 1998, Philosophy of Science.

[7]  R. Znajek,et al.  General relativity and gravitation : one hundred years after the birth of Albert Einstein , 1980 .

[8]  GAUGE THEORIES OF THE FORCES BETWEEN ELEMENTARY PARTICLES. (GERMAN TRANSLATION) , 1980 .

[9]  John Earman.  Gauge Matters , 2002, Philosophy of Science.

[10]  D. Bohm,et al.  Significance of Electromagnetic Potentials in the Quantum Theory , 1959 .

[11]  D. Howard.  Einstein on locality and separability , 1985 .

[12]  Elena Castellani.  Interpreting bodies : classical and quantum objects in modern physics , 1998 .

[13]  L. Laudan.  A Confutation of Convergent Realism , 1981, Philosophy of Science.

[14]  On the Reality of Gauge Potentials , 2001, Philosophy of Science.

[15]  Craig Callender,et al.  Physics Meets Philosophy at the Planck Scale , 2001 .

[16]  J. Worrall.  Structural Realism: The Best of Both Worlds?* , 1989 .

[17]  藤川 和男.  I. J. R. Aitchison and A. J. G. Hey: Gauge Theories in Particle Physics; A Practical Introduction, Adam Hilger, Bristol, 1982, xvi+342ぺージ, 23.5×15.5cm, 8,990円(Graduate Student Series in Physics). , 1982 .

[18]  H. Brown.  Aspects of Objectivity in Quantum Mechanics , 1998 .

[19]  Robert W. Batterman,et al.  Falling Cats, Parallel Parking, and Polarized Light , 2003 .

[20]  F. Wilczek,et al.  Geometric Phases in Physics , 1989 .

[21]  Chuang Liu.  Gauge gravity and the unification of natural forces , 2003 .

[22]  John D. Norton,et al.  What Price Spacetime Substantivalism? The Hole Story , 1987, The British Journal for the Philosophy of Science.

[23]  Gordon Belot,et al.  Symmetry and gauge freedom , 2003 .

[24]  R. Healey.  Holism and Nonseparability , 1991 .

[25]  H. Lyre.  The Principles of Gauging , 2001, Philosophy of Science.

[26]  Tian Yu Cao,et al.  Conceptual Developments of 20th Century Field Theories , 2019 .

[27]  H. Lyre,et al.  Curve It, Gauge It, or Leave It? Practical Underdetermination in Gravitational Theories , 2003 .

[28]  K. Brading,et al.  Symmetries in physics: philosophical reflections , 2003, quant-ph/0301097.

[29]  A. Alexandrova.  The British Journal for the Philosophy of Science , 1965, Nature.

[30]  L. O'raifeartaigh,et al.  The Dawning of Gauge Theory , 2020 .

[31]  D. Malament,et al.  Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics , 2002 .

[32]  Jeremy Butterfield,et al.  From Physics to Philosophy: Index of subjects , 1999 .

[33]  Constitution of objects in classical mechanics and in quantum mechanics , 1995 .

[34]  Richard Healey,et al.  Nonlocality and the Aharonov-Bohm Effect , 1997, Philosophy of Science.

[35]  A. Nounou.  Symmetries in Physics: A fourth way to the Aharonov–Bohm effect , 2003 .

[36]  Richard Healey,et al.  Holism in philosophy of mind and philosophy of physics , 2003 .

[37]  T. Cao.  Conceptual Foundations of Quantum Field Theory , 2004 .

[38]  Andrzej Trautman,et al.  Fiber Bundles Gauge Fields and Gravitation , 1980 .

[39]  Joseph Samuel,et al.  THE AHARONOV-BOHM EFFECT , 1994 .

[40]  S. French,et al.  Symmetries in Physics: Understanding permutation symmetry , 2003 .

[41]  H. Lyre,et al.  A versus B! Topological nonseparability and the Aharonov-Bohm effect , 2001 .

[42]  B. Dewitt.  Quantum Theory without Electromagnetic Potentials , 1962 .

[43]  Understanding Electromagnetism , 2005 .

[44]  Jeeva Anandan,et al.  The geometric phase , 1992, Nature.

[45]  James Ladyman,et al.  Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure , 2003, Synthese.

[46]  The Gauge Argument , 2000, Philosophy of Science.

[47]  Sunny Y. Auyang,et al.  How Is Quantum Field Theory Possible , 1995 .

[48]  R. Persaud.  Philosophy of science , 1992, The Lancet.

[49]  J. Earman.  Tracking down gauge: an ode to the constrained Hamiltonian formalism , 2003 .

[50]  J. Ladyman.  What is Structural Realism , 1998 .

[51]  J. Earman,et al.  Pre-socratic quantum gravity , 2001 .

[52]  S. Leeds.  Gauges: Aharonov, Bohm, Yang, Healey , 1999, Philosophy of Science.

[53]  Michael Redhead.  Symmetries in Physics: The interpretation of gauge symmetry , 2003 .

[54]  Michael Redhead.  Quantum field theory and the philosopher , 1999 .

[55]  Mauro Dorato,et al.  Substantivalism, Relationism, and Structural Spacetime Realism , 2000 .

[56]  K. Brading,et al.  Are Gauge Symmetry Transformations Observable? , 2004, The British Journal for the Philosophy of Science.

[57]  Andrew Wayne,et al.  Ontological Aspects of Quantum Field Theory , 2002 .

[58]  A. Fine,et al.  Gauge theory, anomalies and global geometry: The interplay of physics and mathematics , 1997 .

[59]  Gauge theories and holisms , 2004 .

[60]  Christopher A. Martin.  Gauge Principles, Gauge Arguments and the Logic of Nature , 2002, Philosophy of Science.

[61]  Akira Tonomura,et al.  The Quantum World Unveiled by Electron Waves , 1998 .

[62]  Paul Teller,et al.  Relational Holism and Quantum Mechanics1 , 1986, The British Journal for the Philosophy of Science.

[63]  John C. Baez,et al.  Knots and quantum gravity , 1994 .

[64]  F. Wilczek.  Quantum Field Theory , 1998, hep-th/9803075.

[65]  Chuang Liu.  The Aharonow—Bohm Effect and the Reality of Wave Packets , 1994, The British Journal for the Philosophy of Science.

[66]  Peter Kosso.  The Empirical Status of Symmetries in Physics , 2000, The British Journal for the Philosophy of Science.

[67]  Marc Henneaux,et al.  Quantization of Gauge Systems , 1992 .

[68]  R. L. Christiansen,et al.  Yellowstone Park as a Window on the Earth's Interior , 1980 .

[69]  M. P. Ryan,et al.  Directions in General Relativity , 2005 .

[70]  Elena Castellani.  Galilean Particles: An Example of Constitution of Objects , 1998 .

[71]  The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity , 1999, gr-qc/9908048.