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Explanation, the Progress of Physical Theories and Computer Simulations

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From Quantum to Classical

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 204))

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Abstract

The items in the title are in many ways related to each other when approaching the question of explanation in physics. In Duhem’s terms, a physical theory can never “explain” the world in the sense of leading to a metaphysical reality, but the better the theory becomes in describing and predicting phenomena, the nearer it comes to a “natural classification” which is in fact a way to put the question of explanation. This opens the room among others for following the effect of the progress of theories on explanation. This, however, also depends on our ability of exploring the theories and their phenomenology “from first principles” (without further assumptions or approximations)—which in contemporary physics is a key word for computer simulations. Computer simulations also provide the possibility to test the relations between theories defined at different scales. Finally, using methods from machine learning in combination with computer simulations may allow finding relevant correlations in the data produced in a numerical analysis and thus a grasp on the internal connections in the theory providing the “right concepts” for understanding and explanation. I shall here propose a certain view of the problem of explanation in physics with emphasis on the physics of fundamental phenomena and also discuss the role of computers in modern natural science under this perspective.

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Notes

  1. 1.

    Forschungsstätte der Evangelischen Studiengemeinschaft (Protestant Institute for Interdisciplinary Research), Heidelberg.

  2. 2.

    Joos et al. [32].

  3. 3.

    Blanchard et al. (Eds.) [9].

  4. 4.

    I.-O. Stamatescu in Ferrari and Stamatescu (Eds.) [22] and in Seiler and Stamatescu (Eds.) [48].

  5. 5.

    Scheibe [44].

  6. 6.

    Cassirer [15].

  7. 7.

    A. Einstein, “Reply to criticisms”, in Cushing [18], p. 357. This is not “against philosophy”, this just means that physics needs its free space to do its job.

  8. 8.

    Salmon [43].

  9. 9.

    Hempel [28].

  10. 10.

    See, e.g. Thagard [50].

  11. 11.

    See, e.g. Churchland [16].

  12. 12.

    Duhem, “La theorie physique, son objet et sa structure” (1908), english translation [20].

  13. 13.

    A discussion of the understanding of “natural classification” as assumed in the following will be given in Sect. 2.3. For the moment I shall only refer to Duhem [20], Chapt. 2 with the suggestion that the order provided by an accomplished theory tends to be “the reflex of an ontological order”.

  14. 14.

    There are of course also other notions of explanation as related to the context, to other understanding of causation or to particular phenomena—cf. for instance P. Weingarten, M. Massimi in proceedings of the AIPS Conference 2016, “Mechanistic Explanation” (to appear). For a general discussion see Woodward [55].

  15. 15.

    This implies of course theory and mathematics and can be very complex—the “cosmic distance ladder”, for instance, belongs to the empirical part of cosmology but it implies both observation and theoretical models.

  16. 16.

    H. von Helmholtz, “Die Tatsachen in der Wahrnehmung” (1878) in [27].

  17. 17.

    H. von Helmholtz [27]. In modern terms his argument can be described as IBE (inference to the best explanation)….

  18. 18.

    Tegmark [49] and related papers. This perspective can appear as the logical completion of a certain form of “structural realism” which appeals to mathematical physicists such as Poincaré and Weyl and which cuts short the question why, say, equations and the objects they both define and refer to should have different ontological status.

  19. 19.

    See Bohm and Hiley [12], also Bell [5].

  20. 20.

    For a comprehensive account see ’t Hooft [51].

  21. 21.

    In fact this interaction reaches also the meta-theoretical level when comparing different theories, cf Barth [4].

  22. 22.

    Or indicates a structure which can be deployed when asked for.

  23. 23.

    “… es muss also etwas in mir geben, das nicht nur zu der Sache führt, sondern sie auch ausdrückt.” see Leibniz, Quid sit idea”, in C.I. Gerhardt (Ed), vol. VII, p. 263 sq. [24].

  24. 24.

    In Ferrari and Stamatescu (Eds.) (2002) [22].

  25. 25.

    “Wir machen uns innere Scheinbilder oder Symbole der äußeren Gegenstände, und zwar machen wir sie von solcher Art, daß die denknotwendigen Folgen der Bilder stets Bilder seien von den naturnotwendigen Folgen der abgebildeten Gegenstände …” [30]. Notice that this parallels Leibniz’ conception, which is also worth mentioning: “Dass eine Idee von Dingen in uns ist, heißt deshalb nichts anderes, als dass Gott, Urheber gleichermaßen der Dinge wie des Geistes, diese Fähigkeit des Denkens dem Geist eingeprägt hat, damit 〈derselbe〉 aus seinen Tätigkeiten dasjenige ableiten kann, was vollkommen demjenigen entspricht, was aus den Dingen folgt.“ in C.I. Gerhardt (Ed), vol. VII, p. 263 sq. [24].

  26. 26.

    Articles in Ferrari and Stamatescu (Eds.) [22].

  27. 27.

    W. Heisenberg, in Scheibe and Süssman (1973), p. 140 [45].

  28. 28.

    For an actual assessment see Seiler and Stamatescu (Eds.) (2007) [22].

  29. 29.

    The SM are in fact a collection of partial QFTs without complete unification, GRT and partial models.

  30. 30.

    A succinct presentation of the features and the general implications of quantum theory including most of the themes discussed here is Kiefer [34], see also Kiefer [33] for a brief introduction and discussion of the main quantum effects.

  31. 31.

    In fact eQED is not really a fundamental object in the theory. The fundamental objects in QFT are the quantum fields, in which the fundamental relations of the theory (local interactions) are expressed. Particles are special manifestations of the fields. We also have unstable particles and resonances (e.g., Higgs boson!) and we observe a continuous transition between what we understand by particle and by just signal (enhancement) in a collision cross section. See also Falkenburg [21].

  32. 32.

    The notion “closed” as used here is rather sloppy and does not imply that the dynamics may not lead to “unphysical” situations, such as singularities and divergences. Sometimes these can be tamed by supplementary procedures, as in QFT, but they also can be of a more fundamental nature, as in CM, ED or GRT and signal the need for an overriding theory.

  33. 33.

    This accumulation was the ground on which Maxwell's ED could be established, but the latter is not just the sum of these partial laws. Accumulation and jumps are strongly intercorrelated, a modern example is the development of the SME.

  34. 34.

    Theoretical (e.g., the divergent self energy of electrons) as well as empirical (e.g. the stability of matter) in ED.

  35. 35.

    Barnes [3], Aristotle, JB 53::Analytica posteriora I 2 71b.

  36. 36.

    Cassirer [15], p. 189.

  37. 37.

    This concept was hypothesized following the empirical observation of conservation laws (e.g. charge conservation) and other correlations between observations. It led to a powerful theoretical constructive principle. It is not a genuine symmetry but has rather the status of a covariance since physical information is normally carried by gauge invariant quantities.

  38. 38.

    A relativistic QM cannot be established as a consistent theory see e.g. Wachter [53]. This makes clear that one cannot simply add a new hypothesis to an old theory but one must build up a new, closed theoretical scheme “incorporating” the former. In the case at hand it means going from particles to fields as fundamental with particles as a manifestation of these.

  39. 39.

    We can, however, on the basis of a given theoretical scheme valid at a high energy scale derive effective theories at lower scales by the “renormalization group” procedure which allows to redefine the theory for adequate applications there.

  40. 40.

    For a brief overview see Rettler and Bailey [42].

  41. 41.

    For a transcendental perspective see Bitbol et al. [8].

  42. 42.

    “[wir meinen] etwas zu wissen, wenn wir glauben, sowohl die Ursache zu kennen, aufgrund derer ein Ding ist (und zu wissen, dass diese seine Ursache ist), als auch, dass es nicht anders sein kann” Barnes [3], Aristotle, JB 52: Analytica posteriora I 2 71b.

  43. 43.

    Cf. Duhem [20], Ch. II, & 4. This and other statements in Ch. II and at other places suggest that the “instrumentalism” positioning of Duhem may need a more refined discussion, as also hinted at in Ariew [2], see also the article of Karl-Norbert Ihmig in Ferrari and Stamatescu (Eds.) [22].

  44. 44.

    Referred to by I. Kant in The critique of practical reason, Ch.III, also as “physico-mechanical connections in nature” in The critique of pure reason, Appendix.

  45. 45.

    We can, for instance, derive classical behaviour as a certain QM effect (Decoherence), see Joos et al. [32] and Sect. 2.7.

  46. 46.

    This is of course an important discussion which, however, is beyond the aim of this essay. In ED, for instance, we should consider also the electromagnetic fields as “natural kinds” and possibly also the potentials because of their role, say, in quantisation. This would imply, however, redefining identity, classes, etc. taking into account gauge transformations and then adapt our discussion on their relative character considering the progress of theories. For a succinct overview of the philosophy of science discussion hereto see Bird and Tobin [7]. Here however we shall only retain the observation that natural kinds just as natural classification have the same conditional status as the theories and their symbols, see Sect. 2.1, and are also bound in the process of evolving the physical knowledge and should be empirically and theoretically well defined at each level.

  47. 47.

    “Particle” is a powerful concept in promoting hypotheses, so for instance it dominates the search for “dark matter”. See also Falkenburg [21].

  48. 48.

    In a brief section Feynman [23], II, 20–9 discusses the deficiency of the imagination in science while finding intellectual beauty in the wave equation due to the regularities and further developments it suggests. If we take this over to understanding it says that it is not the direct imagination which counts but the multitude of relations implied by a symbol.

  49. 49.

    W. Heisenberg, “The concept of understanding in theoretical physics”, in Blum [10] CIII, p. 335. Notice that “right concepts” and “natural kinds” need not be related.

  50. 50.

    Bell [5].

  51. 51.

    See I.-O. Stamatescu, Appendix 4, in Joos et al. [32].

  52. 52.

    Cf. the note on relativistic QM (footnote 38).

  53. 53.

    A metaphysics based on complex numbers is proposed, for instance, in the “Ur-model” of v. Weizsäcker [52], extrapolated to a universal Ansatz for everything in Görnitz and Görnitz [25].

  54. 54.

    Joos et al. [32]. There exist of course macroscopic quantum effects unaffected by decoherence such as superconductivity, laser, transistors with many practical applications.

  55. 55.

    The hypothesis that quantum effects are at work in our brains, may be problematic since under the typical working conditions there (temperature, external influences) decoherence may be expected to destroy local quantum coherence. In an evolutionary perspective there seems to be no necessity for a quantum organ, see Hepp and Koch [29].

  56. 56.

    There are macroscopic quantum effects which in a sense can belong to daily experience, such as superconductivity, or which by enhancement produce macroscopic effects, such as nuclear energy. And of course X-rays, LED, MRT, etc. They prove that the world is fundamentally quantum at all levels but the genuine quantum character is not direct enough to help us build quantum intuitions, and their interpretation remains abstract—the more so that QM itself does not offer us a clear and consistent interpretation for its most fundamental rules, e.g. measurement (albeit when using classical concepts …).

  57. 57.

    There is very much literature on this subject—see, e.g., the bibliography in our mentioned book on decoherence, [32], Therefore I shall only mention some of the earliest studies hereto which also have a direct connection with our discussion here: Zeh [57], Joos and Zeh [31, 32], Zurek [58].

  58. 58.

    This is not the interpretational structure mentioned in Sect. 2.1 but the attempt to provide a metaphysics for QM.

  59. 59.

    See, for instance, Zeh [57] and the discussion in Joos et al. [32].

  60. 60.

    See e.g. Joos et al. [32].

  61. 61.

    Wigner [54].

  62. 62.

    To what extent does QM comply with this understanding of lawfulness is an outstanding question—between the incompleteness criticism (Einstein), the claim of universality of statistical laws (Schrödinger), the denial of the need for space–time description (Anschauung; Heisenberg, Cassirer), ….

  63. 63.

    See, e.g., the exciting discussion in Penrose [40].

  64. 64.

    The mathematical-symbolic schemes of classical physics, for instance, provide keys for developing symbols for the newer theories.

  65. 65.

    See, e.g., Bourbaki [13].

  66. 66.

    This is of course a relevant issue in the philosophy of physics. For a nice example of using modern mathematical tools at the meta-theoretical level see, e.g., Barth [4].

  67. 67.

    Or “regulative principles”—not to be understood as constitutive (cf. I. Kant, The Critique of Pure Reason, Appendix).

  68. 68.

    The name “gauge symmetry” is slightly misleading (cf footnote 37), nevertheless this concept proved to be very rich and extremely useful both in developing and in analysing theories.

  69. 69.

    For a few references; Churchland [16], Churchland and Sejnowsk [17], Boden [11].

  70. 70.

    Thagard [50].

  71. 71.

    McCulloch and Pitts [38].

  72. 72.

    Dreitlein [19].

  73. 73.

    The capacity of a system to take all allowed configurations.

  74. 74.

    Mlodinov and Stamatescu [39].

  75. 75.

    Kühn and Stamatescu [35], Kühn et al. (Eds.) [36].

  76. 76.

    Kühn and Stamatescu [37, 48].

  77. 77.

    Schmidt and Stamatescu [47].

  78. 78.

    An interesting discussion of the stability properties of the solar system can be found in Petterson [41].

  79. 79.

    See Stamatescu and Kühn et al. (Eds.) [36].

  80. 80.

    Non-standard logics can also be represented in binary logic.

  81. 81.

    McCulloch and Pitts [38].

  82. 82.

    There are a number of approaches in this field which mix analogue (cold atoms, optical lattices, etc.) and digital features in various combinations.

  83. 83.

    Cf. Scherzer et al. [46] and references therein. For a review see Berger et al. [6].

  84. 84.

    Of course one uses simulations also for processes, hypotheses, etc. as far as these can be formalized.

  85. 85.

    Wunderlich et al. [56] and further publication of the Neuromorphic Computer Group at the University of Heidelberg. Neuromorphic computers are “hybride” (analog-digital) machines with some millions of Hodkgin-Huxley neurons in variable architectures.

  86. 86.

    For an introduction and review see Carleo et al. [14].

  87. 87.

    For partial assessments see e.g. Altman et al. [1], Grambling and Horowitz [26].

Abbreviations

CM:

Classical mechanics

CSM:

Classical statistical mechanics

CS:

Complex systems theory

ED:

Classical electrodynamics

GRT:

General relativity theory

QED:

Quantum electrodynamics

QFT:

Quantum field theory

LFT:

Lattice field theory

QG:

Quantum gravity (in spe)

QM:

Quantum mechanics (in the text used sometimes as paradigm for quantum theories in general)

SM:

Standard model: SME (of elementary particles), SMC (of cosmology)

SRT:

Special relativity theory

SST:

Solid state theory

Th:

Thermodynamics

References

  1. E. Altman et al., Quantum Simulators: Architectures an Opportunities. PRX Quantum 2, 017003 (2021), arXiv:1912.06939v2 [Quantum-ph]A (2019)

  2. R. Ariew, Pierre Duhem (2020). https://plato.stanford.edu/archives/fall2020/entries/duhem/

  3. J. Barnes, Aristoteles: Eine Einführung (Reclam, Stuttgart, 1992)

    Google Scholar 

  4. L. Barth, A mathematical framework to compare classical field theories (2019). arXiv:1910.08614

  5. J.S. Bell, Speakable and unspeakable in quantum mechanics: collected papers in quantum philosophy (Cambridge Univ. Press, Cambridge, UK, 2004)

    Book  Google Scholar 

  6. C.E. Berger et al., Complex Langevin and other aproaches to the sign problem in quantum manybody physics. Phys. Rep. 892(2021), 1–54 (2021). https://doi.org/10.1016/j.physrep.20200.9.002

    Article  ADS  MathSciNet  Google Scholar 

  7. A. Bird , E. Tobin, Natural kinds (2018). https://plato.stanford.edu/archives/spr2018/entries/natural-kinds/

  8. M. Bitbol et al. (eds.), Constituting Objectivity (Springer, Berlin, Heidelberg, New York, 2009)

    Google Scholar 

  9. Blanchard et al. (Eds.) Decoherence, Theoretical, Experimental and Conceptual Problems, Springer, Berlin, Heidelberg, New York w York (1998)

    Google Scholar 

  10. Blum, W. et al. (Eds.), Werner Heisenberg. Gesammelte Werke, Piper, München (1989)

    Google Scholar 

  11. M. Boden (ed.), The philosophy of Artificial Intelligence (Oxford University Press, Oxford, 1990)

    Google Scholar 

  12. D. Bohm, B.J. Hiley, The Undivided Universe: Ontological Interpretation of Quantum Theory (Chapman & Hall, Routledge, 1993)

    Google Scholar 

  13. N. Bourbaki, (group work pseudonym), (1939–1980), Eléments de mathématique, Hermann, Chemnitz

    Google Scholar 

  14. Carleo, G. et al.Machine Learning and the physical sciences. Rev. Mod. Phys. 91.045002 (2019). arXiv:1903.10563 [physics.comp-ph]

  15. E. Cassirer, Zur Modernen Physik, Wissenschaftliche Buchgesellschaft, Darmstadt (1987)

    Google Scholar 

  16. P.M. Churchland, A Neurocomputational Perspective: The Nature ef Mind and the Structure of Science (MIT Press Cambridge, MA, 1989)

    Google Scholar 

  17. P.S. Churchland, T.J. Sejnowski, The Computational Brain (MIT Univ. Press, Cambridge, MA, 1992)

    Book  Google Scholar 

  18. J.T. Cushing, Philosophical Concepts in Physics (Cambridge Univ. Press, Cambridge, UK, 1998)

    Book  Google Scholar 

  19. J. Dreitlein, The unreasonable effectiveness of computer Physics. Found. Phys. 23, 923 (1993)

    Article  ADS  Google Scholar 

  20. P. Duhem, The Aim and Structure of Physical Theory (Princeton University Press, Princeton, NJ, 1954)

    Book  Google Scholar 

  21. B. Falkenburg, Particle Metaphysics, Springer, Berlin, Heidelberg, New York (2007)

    Google Scholar 

  22. M. Ferrari, I.-O. Stamatescu (eds.), Symbol and physical knowledge (Springer, Berlin, Heidelberg, New York, 2002)

    Google Scholar 

  23. R. Feynman, P., Leighton, R. B., Sands, M., The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1964)

    Google Scholar 

  24. C.I. Gerhardt, (Ed.), G.W. Leibniz: Sämtliche Schriften und Briefe, Berlin Verlag, Berlin (1849)

    Google Scholar 

  25. T. Görnitz, B. Görnitz, Von der Quantenphysik zum Bewusstsein, Springer, Berlin, Heidelberg, New York (2016)

    Google Scholar 

  26. E. Grambling, M. Horowitz, Quantum Computing: Progress and Prospects, The National Academy Press, https://doi.org/10.17226/25196.Grumbling, E (2019)

  27. H. von Helmholtz, Philosophische Vorträge und Aufsätze (Akademie Verlag, Berlin, 1971)

    Book  Google Scholar 

  28. C. Hempel, Aspects of Scientific Explanation (Free Press, New York, NY, 1965)

    Google Scholar 

  29. K. Hepp, C. Koch, Nature 440, 611 (2006)

    Article  ADS  Google Scholar 

  30. H. Hertz, Die Prinzipien der Mechanik (Akademische Verlaganstalt, Leipzig, 1894)

    MATH  Google Scholar 

  31. E. Joos, H.D. Zeh, The emergence of classical properties through interaction with the environment. Z. Phys. B 59, 223–243 (1985)

    Article  ADS  Google Scholar 

  32. E. Joos , et al., Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd Edn. Springer, Berlin, Heidelberg, New York (2003)

    Google Scholar 

  33. C. Kiefer, Quantentheorie, S. Fischer, Frankfurt Main (2002)

    Google Scholar 

  34. C. Kiefer, Der Quantenkosmos, S. Fischer, Frankfurt Main (2008)

    Google Scholar 

  35. R. Kühn, I.-O. Stamatescu, J. Phys. A Math. Gen. 32, 5479 (1999)

    Article  Google Scholar 

  36. R. Kühn et al. (eds.), Adaptivity and Learning (Springer, Berlin, Heidelberg, 2003)

    Google Scholar 

  37. R. Kühn , I.-O. Stamatescu, Biol. Cybernetics 97 (2007) 99 and 101 (2009) 40

    Google Scholar 

  38. W.S. McCulloch, W.A. Pitts, Bull. Math. Biophysics 5, 1151 (1943)

    Article  Google Scholar 

  39. L. Mlodinow, I.-O. Stamatescu, Internat. J. Comput. Inform.Sci. 14, 201 (1985)

    Google Scholar 

  40. R. Penrose, The emperor’s New Mind (Oxford University Press, Oxford, 1989)

    Book  Google Scholar 

  41. I. Petterson, Newton's Clock – Chaos in the Solar System, Henry Holt and Co, New York, NY (1993)

    Google Scholar 

  42. B. Rettler, A.M. Bailey, Object (2017).https://plato.stanford.edu/win2017/entries/object/

  43. W.C. Salmon, Causality and Explanation (Oxford University Press, Oxford, 1998)

    Book  Google Scholar 

  44. E. Scheibe, Die Philosophie der Physiker, C.H. Beck (2007)

    Google Scholar 

  45. E. Scheibe, G. Süssman (Hrsgb.), Einheit und Vielfalt, Goettingen (1973)

    Google Scholar 

  46. M. Scherzer et al. Deconfinement phase transition line with the Complex Langevin equation up to mu/T ~5. Phys. Rev. D 102, 014515, arXiv:2004.05372 (2020)

  47. M. G. Schmidt, I.-O. Stamatescu, Matter determinants in background fields using random walk world line loops on the lattice. Mod. Physics Letters A 18(22), https://doi.org/10.1142/S0217732303011204, arXiv:hep-lat/0209120 (2004)

  48. E. Seiler, I.-O. Stamatescu (eds.), Approaches to Fundamental Physics (Springer, Berlin, Heidelberg, New York, 2007)

    MATH  Google Scholar 

  49. M. Tegmark, The mathematical universe. Found. Phys. 38(2), 101–150 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  50. P. Thagard, Computational Philosophy of Science (MIT Press, Cambridge, MA, 1988)

    Book  Google Scholar 

  51. G. 't Hooft, The Cellular Automaton Interpretation of Quantum Mechanics, Springer Open (2016)

    Google Scholar 

  52. C.F. von Weizsäcker, Aufbau der Physik (Springer, Berlin, Heidelberg, New York, 1985)

    MATH  Google Scholar 

  53. A. Wachter, Relativistic Quantum Mechanics (Springer, Berlin, Heidelberg, New York, 2011)

    Book  Google Scholar 

  54. E.P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences. Pure Appl. Math. 13, 1–14 (1960)

    Google Scholar 

  55. J. Woodward, Scientific Explanation (2021). https://plato.stanford.edu/archives/spr2021/entries/scientific-explanation/

  56. T. Wunderlich et al., Demonstrating advantages of neuromorphic computing: a pilot study. Frontiers in Neurophysics (2019). https://doi.org/10.3389/fnins.2019.00260

    Article  Google Scholar 

  57. H.D. Zeh, On the interpretation of measurement in quantum theory. Found. Phys. 1, 69–76 (1970)

    Article  ADS  Google Scholar 

  58. W.H. Zurek, Environment induced superselection rules. Phys. Rev. D 26, 1862–1880 (1982)

    Google Scholar 

  59. W.H. Zurek, Decoherence and the transition from quantum to classical. Physics Today 44, 36–44 (1991)

    Google Scholar 

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  1. Institut für Theoretische Physik, Universität Heidelberg, 69120, Heidelberg, Germany

    Ion-Olimpiu Stamatescu

  2. Forschungsstätte der Evangelischen Studiengemeinschaft, 69118, Heidelberg, Germany

    Ion-Olimpiu Stamatescu

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    Claus Kiefer

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Stamatescu, IO. (2022). Explanation, the Progress of Physical Theories and Computer Simulations. In: Kiefer, C. (eds) From Quantum to Classical. Fundamental Theories of Physics, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-030-88781-0_12

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