Advertisement

Erkenntnis

, Volume 84, Issue 3, pp 585–615 | Cite as

Philosophical Issues Concerning Phase Transitions and Anyons: Emergence, Reduction, and Explanatory Fictions

  • Elay ShechEmail author
Article

Abstract

Various claims regarding intertheoretic reduction, weak and strong notions of emergence, and explanatory fictions have been made in the context of first-order thermodynamic phase transitions. By appealing to John Norton’s recent distinction between approximation and idealization, I argue that the case study of anyons and fractional statistics, which has received little attention in the philosophy of science literature, is more hospitable to such claims. In doing so, I also identify three novel roles that explanatory fictions fulfill in science. Furthermore, I scrutinize the claim that anyons, as they are ostensibly manifested in the fractional quantum Hall effect, are emergent entities and urge caution. Consequently, it is suggested that a particular notion of strong emergence signals the need for the development of novel physical–mathematical research programs.

Notes

Acknowledgements

I gratefully acknowledge useful discussion with Jonathan Bain, Tom Lancaster, Robin Hendry, and Olivier Sartenear. Previous versions of this paper were presented at the “Emergence and the Limit: A Workshop in Philosophy of Physics” at London School of Economics on 11/25/2016, “Workshop on Symmetry and Symmetry Breaking in Fundamental Physics” at Paris Centre for Quantum Computing on 12/02/2016, and “Scale and the Sciences: A One-day Workshop” at The Institute for advanced Study at Durham University on 12/07/2016 7. I thank the participants for helpful comments. Thanks also to Narin Shech and Isabel Ranner for assistance with figures and editing. This work was produced as part of a Senior Research Fellowship at Durham University generously funded by the Institute for Advanced Study.

References

  1. Ando, T., Fowler, A. B., & Stern, F. (1982). Electronic properties of two-dimensional systems. Reviews of Modern Physics, 54, 437–672.CrossRefGoogle Scholar
  2. Arovas, D., Schrieffer, J. R., & Wilczek, F. (1984). Fractional statistics and the quantum Hall effect. Physical Review Letters, 53, 722–723.CrossRefGoogle Scholar
  3. Artin, E. (1947). Theory of braids. Annals of Mathematics, 48(1), 101–126.CrossRefGoogle Scholar
  4. Bain, J. (2013). Emergence in effective field theories. European Journal for Philosophy of Science, 3, 257–273.CrossRefGoogle Scholar
  5. Bain, J. (2016). Emergence and mechanism in the fractional quantum Hall effect. Studies in History and Philosophy of Modern Physics, 56, 27–38. CrossRefGoogle Scholar
  6. Baker, D. J., Halvorson, H., & Swanson, N. (2015). The conventionality of parastatistics. British Journal for the Philosophy of Science, 66(4), 929–976.CrossRefGoogle Scholar
  7. Bangu, S. (2009). Understanding thermodynamic singularities: phase transitions, date and phenomena. Philosophy of Science, 76, 488–505.CrossRefGoogle Scholar
  8. Bangu, S. (2011). On the role of bridge laws in intertheoretic relations. Philosophy of Science, 78(5), 1108–1119.CrossRefGoogle Scholar
  9. Bangu, S. (2015a). Neither weak, no strong? Emergence and functional reduction. In B. Falkenburg & M. Morrison (Eds.), Why more is different: Philosophical issues in condensed matter physics and complex systems (pp. 153–164). Heidelberg: Springer.CrossRefGoogle Scholar
  10. Bangu, S. (2015b). Why does water boil? Fictions in scientific explanation. In U. Mäki., I. Votsis., S. Ruphy. & G. Schurz (Eds.), Recent developments in the philosophy of science: EPSA13 Helsinki. European studies in philosophy of science (Vol. 1, pp. 319–330). Cham: Springer.Google Scholar
  11. Batterman, R. (2002). The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence. London: Oxford University Press.Google Scholar
  12. Batterman, R. (2005). Critical phenomena and breaking drops: Infinite idealizations in physics. Studies in History and Philosophy of Modern Physics, 36, 225–244.CrossRefGoogle Scholar
  13. Batterman, R., & Rice, C. (2014). Minimal model explanations. Philosophy of Science, 81(3), 349–376.CrossRefGoogle Scholar
  14. Blythe, R. A., & Evans, M. R. (2003). The Lee–Yang theory of equilibrium and nonequilibrium phase transitions. The Brazilian Journal of Physics, 33(3), 464–475.CrossRefGoogle Scholar
  15. Bokulich, A. (2008). Re-examining the quantum-classical relation: Beyond reductionism and pluralism. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Borrmann, P., Mülken, O., & Harting, J. (2000). Classification of phase transitions in small systems. Physical Review Letters, 84, 3511–3514.CrossRefGoogle Scholar
  17. Butterfield, J. (2011). Less is different: Emergence and reduction reconciled. Foundations of Physics, 41(6), 1065–1135.CrossRefGoogle Scholar
  18. Camino, F. E., Zhou, W., & Goldman, V. J. (2005). Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics. Physical Review B, 72, 075342.CrossRefGoogle Scholar
  19. Chakraborty, T., & Pietilinen, P. (1995). The quantum Hall effects. Berlin: Springer.CrossRefGoogle Scholar
  20. Chalmers, D. J. (2006). Strong and weak emergences. In P. Clayton & P. Davies (Eds.), The re-emergence of emergence: The emergentist hypothesis from science to religion (pp. 244–257). Oxford: Oxford University Press.Google Scholar
  21. Chomaz, P., Gulminelli, F., & Duflot, V. (2001). Topology of event distributions as a generalized definition of phase transitions in finite systems. Physical Review E, 64, 046114.CrossRefGoogle Scholar
  22. Compagner, A. (1989). Thermodynamics as the continuum limit of statistical mechanics. American Journal of Physics, 57, 106–117.CrossRefGoogle Scholar
  23. Earman, J. (2010). Understanding permutation invariance in quantum mechanics. Unpublished manuscript.Google Scholar
  24. Earman, J. (2017). The role of idealizations in the Aharonov–Bohm effect. Synthese.  https://doi.org/10.1007/s11229-017-1522-9.CrossRefGoogle Scholar
  25. Emch, G. (2006). Quantum statistical physics. In Butterfield, J., & Earman, J. (Eds.), Philosophy of physics, part B, a volume of the handbook of the philosophy of science (pp. 1075–1182). North Holland.Google Scholar
  26. Ezawa, Z. F. (2013). Quantum Hall effects: Recent theoretical and experimental developments. Singapore: World Scientific.CrossRefGoogle Scholar
  27. Fadell, E., & Neuwirth, L. (1962). Configuration Spaces. Mathematica Scandinavica, 10, 111–118.CrossRefGoogle Scholar
  28. Falkenburg, B. (2015). How do quasi-particles exist? In B. Falkenburg & M. Morrison (Eds.), Why more is different: Philosophical issues in condensed matter physics and complex systems (pp. 227–249). Heidelberg: Springer.CrossRefGoogle Scholar
  29. Fox, R., & Neuwirth, L. (1962). The braid groups. Mathematica Scandinavica, 10, 119–126.CrossRefGoogle Scholar
  30. Fradkin, E. (2013). Field theories of condensed matter physics (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  31. Franzosi, R., & Pettini, M. (2004). Theorem on the origin of phase transitions. Physical Review Letters, 92, 060601.CrossRefGoogle Scholar
  32. Franzosi, R., Pettini, M., & Spinelli, L. (2000). Topology and phase transitions: Paradigmatic evidence. Physical Review Letters, 84, 2774–2777.CrossRefGoogle Scholar
  33. Gelfert, A. (2016). How to do science with models: A philosophical primer. Cham: Springer.CrossRefGoogle Scholar
  34. Gross, D. H. E., & Votyakov, E. V. (2000). Phase transitions in “small” systems. The European Physical Journal B—Condensed Matter and Complex Systems, 15, 115–126.CrossRefGoogle Scholar
  35. Guay, A., & Sartenaer, O. (2016a). A new look at emergence. Or when after is different. European Journal for Philosophy of Science, 6, 297–322.CrossRefGoogle Scholar
  36. Guay, A., & Sartenaer, O. (2016b). Emergent quasiparticles. Or how to get a rich physics from a sober metaphysics. In: O. Bueno, R. Chen, & M. B. Fagan (Eds.), Individuation across experimental and theoretical sciences. Oxford: Oxford University Press. http://hdl.handle.net/2078.1/179059.
  37. Halliday, D., Resnick, R., & Walker, J. (2011). Fundamental of physics (9th ed.). Hoboken, NJ: Wiley.Google Scholar
  38. Hempel, C. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: Free Press.Google Scholar
  39. Hendry, R. F. (2010). Ontological reduction and molecular structure. Studies in History and Philosophy of Modern Physics, 41, 183–191.CrossRefGoogle Scholar
  40. Huang, Wung-Hong. (1995). Boson-fermion transmutation and the statistics of anyons. Physical Review E, 51(4), 3729–3730.CrossRefGoogle Scholar
  41. Jain, J. (1989). Composite-fermion approach for the fractional quantum Hall effect. Physical Review Letters, 63, 199–202.CrossRefGoogle Scholar
  42. Jian, C.-M., & Qi, X.-L. (2014). Layer construction of 3D topological states and string braiding statistics. Physical Review X, 4, 041043.CrossRefGoogle Scholar
  43. Jiang, S., Mesaros, A., & Ran, Y. (2014). Generalized modular transformations in (3 + 1)D topologically ordered phases and triple linking invariant of loop braiding. Physical Review X, 4, 031048.CrossRefGoogle Scholar
  44. Kadanoff, L. P. (2000). Statistical physics: Statics, dynamics and renormalization. Singapore: World Scientific.CrossRefGoogle Scholar
  45. Khare, A. (2005). Fractional statistics and quantum theory. New Jersey: World Scientific.CrossRefGoogle Scholar
  46. Kim, J. (1998). Mind in a physical world. Cambridge: MIT Press.CrossRefGoogle Scholar
  47. Kim, J. (1999). Making sense of emergence. Philosophical Studies, 95, 3–36.CrossRefGoogle Scholar
  48. Kim, J. (2006). Emergence: Core ideas and issues. Synthese, 151(3), 347–354.CrossRefGoogle Scholar
  49. Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531.CrossRefGoogle Scholar
  50. Klitzing, K. V., Dorda, G., & Pepper, M. (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Physical Review Letters, 45, 494.CrossRefGoogle Scholar
  51. Laidlaw, M. G., & DeWitt, C. M. (1971). Feyman functional integrals for system of indistinguishable particles. Physical Review D, 3, 1375–1378.CrossRefGoogle Scholar
  52. Lancaster, T., & Blundell, S. (2014). Quantum field theory for the gifted amateur. Oxford: Oxford University Press.CrossRefGoogle Scholar
  53. Lancaster, T., & Pexton, M. (2015). Reduction and emergence in the fractional quantum Hall state. Studies in History and Philosophy of Modern Physics, 52, 343–357.CrossRefGoogle Scholar
  54. Landsman, N. P. (2016). Quantization and superselection III: Mutliply connected spaces and indistinguishable particles. Reviews in Mathematical Physics, 28, 1650019.CrossRefGoogle Scholar
  55. Lanford, O. (1975). Time evolution of large classical systems. In J. Moser (Ed.), Dynamical systems, theory and applications: Lecture notes in theoretical physics (Vol. 38, pp. 1–111). Heidelberg: Springer.CrossRefGoogle Scholar
  56. Lanford, O. (1981). The hard sphere gas in the Boltzmann–Grad limit. Physica A, 106, 70–76.CrossRefGoogle Scholar
  57. Laughlin, R. (1983). Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations. Physical Review Letters, 50, 1395–1398.CrossRefGoogle Scholar
  58. Laughlin, R. B. (1999). Nobel lecture: fractional quantization. Reviews of Modern Physics, 71, 863–874.CrossRefGoogle Scholar
  59. Laughlin, R. B. (2005). A different universe: Reinventing physics from the bottom down. New York: Basic Books.Google Scholar
  60. Le Bellac, M., Mortessagne, F., & Batrouni, G. G. (2004). Equilibrium and non-equilibrium statistical thermodynamics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  61. Lederer, P. (2015). The quantum Hall effects: Philosophical approach. Studies in History and Philosophy of Modern Physics, 50, 25–42.CrossRefGoogle Scholar
  62. Leinaas, J. M., & Myrheim, J. (1977). On the theory of identical particles. Nuovo Cimento, 37B, 1–23.CrossRefGoogle Scholar
  63. Masenes, L., & Oppenheim, J. (2017). A general derivation and quantification of the third law of thermodynamics. Nature Communications, 8, 14538.CrossRefGoogle Scholar
  64. McMullin, E. (1985). Galilean Idealization. Studies in the History and Philosophy of Science, 16, 247–273.CrossRefGoogle Scholar
  65. Menon, T., & Callender, C. (2013). Turn and face the strange… Ch-ch-changes: Philosophical questions raised by phase transitions. In R. Batterman (Ed.), The oxford handbook to philosophy of physics (pp. 189–223). Oxford: Oxford University Press.Google Scholar
  66. Messiah, A. M. (1962). Quantum mechanics. New York, NY: Wiley.Google Scholar
  67. Messiah, A. M., & Greenberg, O. W. (1964). Symmetrization postulate and its experimental foundation. Physical Review B, 136, 248–267.CrossRefGoogle Scholar
  68. Mitchell, S. D. (2012). Emergence: Logical, functional and dynamical. Synthese, 185, 171–186.CrossRefGoogle Scholar
  69. Morandi, G. (1992). The role of topology in classical and quantum mechanics. Berlin: Springer.CrossRefGoogle Scholar
  70. Morrison, M. (2012). Emergent physics and micro-ontology. Philosophy of Science, 79, 141–166.CrossRefGoogle Scholar
  71. Naaijkens, P. (2015). Kitaev’s quantum double model from a local quantum physics point of view. In R. Brunetti et al. (Eds.), Advances in algebraic quantum field theory (p. 365). New York: Springer.CrossRefGoogle Scholar
  72. Nagel, E. (1961). The structure of science. New York: Harcourt, Brace and World.CrossRefGoogle Scholar
  73. Norton, J. D. (2012). Approximations and Idealizations: Why the difference matters. Philosophy of Science, 79, 207–232.CrossRefGoogle Scholar
  74. O’Connor, T., & Wong, H. Y. (2005). The metaphysics of emergence. Noûs, 39(658), 678.Google Scholar
  75. Rueger, A. (2000). Physical emergence, diachronic and synchronic. Synthese, 124, 297–322.CrossRefGoogle Scholar
  76. Ruelle, D. (1999/2007). Statistical mechanics: Rigorous results. Repr. Singapore: World Scientific.Google Scholar
  77. Ruelle, D. (2004). Thermodynamic formalism (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  78. Salmon, W. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press.Google Scholar
  79. Santos, G. C. (2015). Ontological emergence: How is that possible? Towards a new relational ontology. Foundations of Science, 20(4), 429–446.CrossRefGoogle Scholar
  80. Shech, E. (2013). What is the ‘paradox of phase transitions?’. Philosophy of Science, 80, 1170–1181.CrossRefGoogle Scholar
  81. Shech, E. (2015). Two approaches to fractional statistics in the quantum Hall effect: Idealizations and the curious case of the anyon. Foundations of Physics, 45(9), 1063–1110.CrossRefGoogle Scholar
  82. Shech, E. (2016). Fiction, depiction, and the complementarity thesis in art and science. The Monist, 99(3), 311–332.CrossRefGoogle Scholar
  83. Shech, E. (2017). Idealizations, essential self-adjointness, and minimal model explanation in the Aharonov–Bohm effect. Synthese.  https://doi.org/10.1007/s11229-017-1428-6.CrossRefGoogle Scholar
  84. Shech, E. (2018). Infinitesimal idealization, easy road nominalism, and fractional quantum statistics. Synthese.  https://doi.org/10.1007/s11229-018-1680-4.CrossRefGoogle Scholar
  85. Shech, E., & Gelfert, A. (2016). The exploratory role of idealizations and limiting cases in models. http://philsci-archive.pitt.edu/13338/.
  86. Stamerjohanns, H., Oliver Mülken, O., & Borrmann, P. (2002). Deceptive signals of phase transitions in small magnetic clusters. Physical Review Letters, 88(5), 053401–053414.CrossRefGoogle Scholar
  87. Stanley, H. E. (1971). Introduction to phase transitions and critical phenomena. New York and Oxford: Oxford University Press.Google Scholar
  88. Stern, A. (2008). Anyons and the quantum Hall effect-a pedagogical review. Annalen der Physik, 323, 204–249.Google Scholar
  89. Suarez, M. (Ed.). (2009). Fictions in science: Essays on idealization and modeling. London: Routledge.Google Scholar
  90. Tsui, D. C., Stormer, H. L., & Gossard, A. C. (1982). Two-dimensional magnetotransport in the extreme quantum limit. Physical Review Letters, 48(22), 1559.CrossRefGoogle Scholar
  91. Wales, D. J., & Berry, R. S. (1994). Coexistence in finite systems. Physical Review Letters, 73, 2875–2878.CrossRefGoogle Scholar
  92. Wang, C., & Levin, M. (2014). Braiding statistics of loop excitations in three dimensions. Physical Review Letters, 113, 080403.CrossRefGoogle Scholar
  93. Wang, J. C., & Wen, X.-G. (2015). NonAbelian string and particle braiding in topological order: Modular SL(3,\( {\mathbb{Z}} \)) representation and (3 + 1)-dimensional twisted gauge theory. Physical Review B, 91, 035134.Google Scholar
  94. Weisberg, M. (2013). Simulation and similarity: Using models to understand the world. New York: Oxford University Press.CrossRefGoogle Scholar
  95. Wen, X.-G. (1990). Topological orders in rigid states. International Journal of Modern Physics B, 4, 239–271.CrossRefGoogle Scholar
  96. Wen, X.-G. (2004). Quantum field theory of many-body systems. Oxford: Oxford University Press.Google Scholar
  97. Wilczek, F. (1982). Quantum mechanics of fractional-spin particles. Physical Review Letters, 49, 957–959.CrossRefGoogle Scholar
  98. Wilczek, F. (Ed.). (1990). Fractional statistics and anyon superconductivity. Singapore: World Scientific.Google Scholar
  99. Winsberg, E. (2009). A function for fictions: Expanding the scope of science. In M. Suárez (Ed.), Fictions in science (pp. 179–192). London: Routledge.Google Scholar
  100. Yang, C. N., & Lee, T. D. (1952). Statistical theory of equations of state and phase transitions. I. Theory of condensation. Physical Review, 97, 404.CrossRefGoogle Scholar
  101. Zee, A. (1995). Quantum Hall fluids. In H. Geyer (Ed.), Field theory, topology, and condensed matter physics (pp. 99–153). Berlin: Springer.CrossRefGoogle Scholar
  102. Zhang, S.-C., Hansson, T., & Kivelson, S. (1989). Effective-field-theory model for the fractional quantum Hall effect. Physical Review Letters, 62, 82–85.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Auburn UniversityAuburnUSA

Personalised recommendations