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Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

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At the Frontier of Spacetime

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 183))

Abstract

We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density \(\chi ^{ijkl}= -\chi ^{jikl}= -\chi ^{ijlk}\) with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in \(\chi ^{ijkl}\), it can be derived from it.

Universally coupled, thus gravitational, scalar fields are still active players in contemporary theoretical physics. So, what is the relationship between the scalar of scalar-tensor theories, the dilaton and the inflaton? Clearly this is an unanswered and important question. The scalar field is still alive and active, if not always well, in current gravity research.

Carl H. Brans (1997)

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Notes

  1. 1.

    Carl Brans is one of the pioneers of the scalar-tensor theory of gravitation. This essay is dedicated to Carl on the occasion of his 80th birthday with all best wishes to him and his family. During the year of 1998, we had the privilege to host Carl, as an Alexander von Humboldt awardee, for several months at the University of Cologne. I remember with pleasure the many lively discussions we had on scalars, on structures of spacetime, on physics in general, and on various other topics.

  2. 2.

    We skip here the plethora of scalar mesons,

    $$\begin{aligned}&{\pi ^\pm ,\pi ^0,\eta ,f_0(500), \eta ' (958),f_0(980),a_0(980),...,} \\&K^\pm ,K^0,K^0_{S}, K^0_{L},K^*_0(1430), {D^\pm ,D^0,D^*_0 (2400)^0,D^\pm _s,...\,;} \end{aligned}$$

    they are all composed of two quarks. Thus, the scalar mesons do not belong to the fundamental particles.

  3. 3.

    Schuller et al. [90] took the \(\chi ^{ijkl}\)-tensor density, which arises so naturally in electrodynamics, called the tensor proportional to it “area metric”, and generalized it to n dimensions and to string theory. For reconstructing a volume element, they have, depending on the circumstances, two different recipes, like, for example, taking the sixth root of a determinant. From the point of view of 4-dimensional electrodynamics, the procedure of Schuller et al. looks contrived to us.

  4. 4.

    See [28, Sect. 28-8].

  5. 5.

    See [35, Sect. E.2.2].

  6. 6.

    See [35, Sect. E.2.3].

  7. 7.

    See [35, Sect. E.2.4].

  8. 8.

    See [35, Sect. E.2.5].

  9. 9.

    Here, in this context, \(\alpha \) is not the axion field!.

  10. 10.

    In the early 1980s, Ni [69] has shown the following: Suppressing the birefringence is a necessary and sufficient condition for a Lagrangian based constitutive tensor to be decomposable into metric+dilaton+axion in a weak gravitational field (weak violation of the Einstein equivalence principle), a remarkable result. Note that Ni assumed the existence of a metric. We, in (4.23), derived the metric from the electromagnetic response tensor density \(\chi ^{ijkl}\).

References

  1. P.A.R. Ade et al. [Polarbear Collaboration], Polarbear constraints on cosmic birefringence and primordial magnetic fields. Phys. Rev. D 92, 123509 (2015). arXiv.org:1509.02461

  2. D.N. Astrov, Magnetoelectric effect in chromium oxide. Sov. Phys. JETP 13, 729–733 (1961) (Zh. Eksp. Teor. Fiz. 40, 1035–1041 (1961))

    Google Scholar 

  3. P. Baekler, A. Favaro, Y. Itin, F.W. Hehl, The Kummer tensor density in electrodynamics and in gravity. Annals Phys. (NY) 349, 297–324 (2014). arXiv.org:1403.3467

    Google Scholar 

  4. A.B. Balakin, W.T. Ni, Non-minimal coupling of photons and axions. Class. Quant. Grav. 27, 055003 (2010). arXiv.org:0911.2946

    Google Scholar 

  5. A.O. Barut, R. Raçzka, Theory of Group Representations and Applications (PWN-Polish Scientific, Warsaw, 1977)

    MATH  Google Scholar 

  6. A.O. Barvinsky, A.Y. Kamenshchik, C. Kiefer, A.A. Starobinsky, C. Steinwachs, Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field. JCAP 0912, 003 (2009). arXiv.org:0904.1698

  7. F. Bezrukov, M. Shaposhnikov, Inflation, LHC and the Higgs boson. Comptes Rendus Physique 16, 994–1002 (2015). http://dx.doi.org/10.1016/j.crhy.2015.08.005

    Google Scholar 

  8. M. Blagojević, Gravitation and Gauge Symmetries (IoP, Bristol, 2002)

    Book  MATH  Google Scholar 

  9. M. Blagojević, F.W. Hehl (eds.), Gauge Theories of Gravitation, a Reader with Commentaries (Imperial College Press, London, 2013)

    MATH  Google Scholar 

  10. C.H. Brans, Gravity and the tenacious scalar field, in On Einstein’s Path, Essays in Honor of E. Schucking, ed. by A. Harvey (Springer, New York, 1999), Chap. 9, pp. 121–138. arXiv.org:gr-qc/9705069

    Google Scholar 

  11. C.H. Brans, The roots of scalar-tensor theory: an approximate history, presented during the 1st Internat. Workshop on Gravitation and Cosmology, 31 May–4 Jun 2004, Santa Clara, Cuba 2004. arXiv.org:gr-qc/0506063

  12. C. Brans, R.H. Dicke, Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. C.G. Callan Jr., S.R. Coleman, R. Jackiw, A new improved energy-momentum tensor. Annals Phys. (NY) 59, 42–73 (1970)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. O. Castillo-Felisola, C. Corral, S. Kovalenko, I. Schmidt, V.E. Lyubovitskij, Axions in gravity with torsion. Phys. Rev. D 91, 085017 (2015). arXiv.org:1502.03694

  15. J.M. Charap, W. Tait, A gauge theory of the Weyl group. Proc. R. Soc. Lond. A 340, 249–262 (1974)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. C.M. Chen, J.M. Nester, R.S. Tung, Gravitational energy for GR and Poincaré gauge theories: a covariant Hamiltonian approach. Int. J. Mod. Phys. D 24, 1530026 (2015). arXiv.org:1507.07300

    Google Scholar 

  17. D.H. Delphenich, On linear electromagnetic constitutive laws that define almost-complex structures. Annalen Phys. (Berlin) 16, 207–217 (2007). arXiv.org:gr-qc/0610031

    Google Scholar 

  18. D.H. Delphenich, Pre-metric Electromagnetism, electronic book, 410 pp. http://www.neo-classical-physics.info/ (2009)

  19. D. Delphenich, Pre-metric electromagnetism as a path to unification. arXiv.org:1512.05183

  20. R.H. Dicke, The Theoretical Significance of Experimental Relativity (Blackie & Son, London, 1964)

    Google Scholar 

  21. P. Di Vecchia, R. Marotta, M. Mojaza, J. Nohle, The story of the two dilatons (2015). arXiv.org:1512.03316

  22. A. Einstein, Eine neue formale Deutung der Maxwellschen Feldgleichungen der Elektrodynamik (A New Formal Interpretation of Maxwell’s Field Equations of Electrodynamics) (Sitzungsber. Königl. Preuss. Akad. Wiss., Berlin, 1916), pp. 184–188; see also A.J. Kox et al. (eds.), The Collected Papers of Albert Einstein, vol. 6 (Princeton University Press, Princeton, 1996), pp. 263–269

    Google Scholar 

  23. A. Einstein, The Meaning of Relativity, 5th edn. (Princeton University Press, Princeton, 1955) (first published in 1922)

    Google Scholar 

  24. A. Favaro, Recent advances in classical electromagnetic theory. Ph.D. thesis, Imperial College London (2012)

    Google Scholar 

  25. A. Favaro, Private communication (2015)

    Google Scholar 

  26. A. Favaro, L. Bergamin, The non-birefringent limit of all linear, skewonless media and its unique light-cone structure. Annalen Phys. (Berlin) 523, 383–401 (2011). arXiv.org:1008.2343

    Google Scholar 

  27. A. Favaro, F.W. Hehl, Light propagation in local and linear media: Fresnel-Kummer wave surfaces with 16 singular points. Phys. Rev. A 93, 013844 (2016). arXiv.org:1510.05566

  28. R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol.II: Mainly Electromagnetism and Matter (Addison-Wesley, Reading, 4th Printing 1969)

    Google Scholar 

  29. D.Z. Freedman, A. Van Proeyen, Supergravity (Cambridge University Press, Cambridge, 2012)

    Book  MATH  Google Scholar 

  30. Y. Fujii, K. Maeda, The Scalar-Tensor Theory of Gravitation (Cambridge University Press, Cambridge, 2003)

    MATH  Google Scholar 

  31. D. Giulini, The rich structure of Minkowski space, in Minkowski Spacetime: A Hundred Years Later, ed. by V. Petkov. Fundamental Theories of Physics (Springer), vol. 165, pp. 83–132 (2010). arXiv.org:0802.4345

    Google Scholar 

  32. H. Goenner, Some remarks on the genesis of scalar-tensor theories. Gen. Rel. Grav. 44, 2077–2097 (2012). arXiv.org:1204.3455

    Google Scholar 

  33. Z. Haghani, N. Khosravi, S. Shahidi, The Weyl-Cartan Gauss-Bonnet gravity, Class. Quant. Grav. 32, 215016 (2015). arXiv.org:1410.2412

    Google Scholar 

  34. F.W. Hehl, J.D. McCrea, E.W. Mielke, Y. Ne’eman, Progress in metric-affine gauge theories of gravity with local scale invariance. Found. Phys. 19, 1075–1100 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  35. F.W. Hehl, Yu.N Obukhov, Foundations of Classical Electrodynamics: Charge, Flux, and Metric (Birkhäuser, Boston, 2003)

    Google Scholar 

  36. F.W. Hehl, Yu.N. Obukhov, Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme. Lecture Notes in Physics (Springer), vol. 702, pp. 163–187 (2006). arXiv.org:gr-qc/0508024

  37. F.W. Hehl, Yu.N. Obukhov, J.P. Rivera, H. Schmid, Relativistic nature of a magnetoelectric modulus of Cr\(_{2}\) O\(_{3}\) crystals: a four-dimensional pseudoscalar and its measurement. Phys. Rev. A 77, 022106 (2008). arXiv.org:0707.4407

  38. Y. Itin, No-birefringence conditions for spacetime. Phys. Rev. D 72, 087502 (2005). arXiv.org:hep-th/0508144

  39. Y. Itin, Photon propagator for axion electrodynamics. Phys. Rev. D 76, 087505 (2007). arXiv.org:0709.1637

  40. Y. Itin, On light propagation in premetric electrodynamics. Covariant dispersion relation. J. Phys. A 42, 475402 (2009). arXiv.org:0903.5520

  41. Y. Itin, Dispersion relation for anisotropic media. Phys. Lett. A 374, 1113–1116 (2010). arXiv.org:0908.0922

  42. Y. Itin, Y. Friedman, Backwards on Minkowski’s road. From 4D to 3D Maxwellian electromagnetism. Annalen Phys. (Berlin) 17, 769–786 (2008). arXiv.org:0807.2625

    Google Scholar 

  43. Y. Itin, F.W. Hehl, Is the Lorentz signature of the metric of space-time electromagnetic in origin? Annals Phys. (NY) 312, 60–83 (2004). arXiv.org:gr-qc/0401016

    Google Scholar 

  44. Y. Itin, C. Lämmerzahl, V. Perlick, Finsler-type modification of the Coulomb law. Phys. Rev. D 90, 124057 (2014). arXiv.org:1411.2670

  45. H.A. Kastrup, On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics. Annalen Phys. (Berlin) 17, 631–690 (2008). arXiv.org:0808.2730

    Google Scholar 

  46. R.M. Kiehn, G.P. Kiehn, J.B. Roberds, Parity and time-reversal symmetry breaking, singular solutions, and Fresnel surfaces. Phys. Rev. A 43, 5665–5671 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  47. W. Kopczyński, J.D. McCrea, F.W. Hehl, The Weyl group and its currents. Phys. Lett. A 128, 313–317 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  48. V.A. Kostelecký, N. Russell, J. Tasson, Constraints on torsion from bounds on Lorentz violation. Phys. Rev. Lett. 100, 111102 (2008). arXiv.org:0712.4393

  49. K. Küpfmüller, W. Mathis, A. Reibiger, Theoretische Elektrotechnik, 19th edn. (Springer Vieweg, Berlin, 2013)

    Book  Google Scholar 

  50. C. Lämmerzahl, F.W. Hehl, Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics. Phys. Rev. D 70, 105022 (2004). arXiv.org:gr-qc/0409072

  51. C. Lämmerzahl, V. Perlick, W. Hasse, Observable effects in a class of spherically symmetric static Finsler spacetimes. Phys. Rev. D 86, 104042 (2012). arXiv.org:1208.0619

  52. O.L. de Lange, R.E. Raab, Multipole theory and the Hehl-Obukhov decomposition of the electromagnetic constitutive tensor. J. Math. Phys. 56, 053502 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. A. Lasenby, M. Hobson, Scale-invariant gauge theories of gravity: theoretical foundations (2015). arXiv.org:1510.06699

  54. I.V. Lindell, Electromagnetic wave equation in differential-form representation. Progr. Electromagn. Res. (PIER) 54, 321–333 (2005)

    Article  Google Scholar 

  55. I.V. Lindell, Multiforms, Dyadics, and Electromagnetic Media, IEEE Press, Wiley, Hoboken, 2015)

    Google Scholar 

  56. I.V. Lindell, Plane-wave propagation in electromagnetic PQ medium. Progr. Electromagn. Res. (PIER) 154, 23–33 (2015)

    Article  Google Scholar 

  57. I.V. Lindell, A. Favaro, Decomposition of electromagnetic Q and P media. Progr. Electromagn. Res. B (PIER B) 63, 79–93 (2015)

    Article  Google Scholar 

  58. I.V. Lindell, A. Sihvola, Perfect electromagnetic conductor. J. Electromagn. Waves Appl. 19, 861–869 (2005). arXiv.org:physics/0503232

    Google Scholar 

  59. J. Łopuszánski, An Introduction to Symmetry and Supersymmetry in Quantum Field Theory (World Scientific, Singapore, 1991)

    Google Scholar 

  60. E.W. Mielke, Spontaneously broken topological \(SL(5, R)\) gauge theory with standard gravity emerging. Phys. Rev. D 83, 044004 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  61. E.W. Mielke, Weak equivalence principle from a spontaneously broken gauge theory of gravity. Phys. Lett. B 702, 187–190 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  62. E.W. Mielke, Symmetry breaking in topological quantum gravity. Int. J. Mod. Phys. D 22, 1330009 (2013)

    Article  ADS  MATH  Google Scholar 

  63. E.W. Mielke, F.W. Hehl, J.D. McCrea, Belinfante type invariance of the Noether identities in a Riemannian and a Weitzenböck spacetime. Phys. Lett. A 140, 368–372 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  64. E.W. Mielke, E.S. Romero, Cosmological evolution of a torsion-induced quintaxion. Phys. Rev. D 73, 043521 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  65. V. Mukhanov, Physics Colloquium, University of Bonn on 2013 May 17

    Google Scholar 

  66. Y. Nakayama, Scale invariance vs conformal invariance. Phys. Rep. 569, 1–93 (2015). arXiv.org:1302.0884

    Google Scholar 

  67. W.-T. Ni, A Non-metric Theory of Gravity, (Montana State University, Bozeman, 1973). http://astrod.wikispaces.com/

  68. W.-T. Ni, Equivalence principles and electromagnetism. Phys. Rev. Lett. 38, 301–304 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  69. W.-T. Ni, Equivalence principles and precision experiments, in Precision Measurement and Fundamental Constants II, ed. by B.N. Taylor, W.D. Phillips. Natl. Bur. Stand. (US) Spec. Publ. 617, 647–651 (1984). http://astrod.wikispaces.com/

  70. W.-T. Ni, Dilaton field and cosmic wave propagation. Phys. Lett. A 378, 3413–3418 (2014). arXiv.org:1410.0126

    Google Scholar 

  71. W.T. Ni, Spacetime structure and asymmetric metric from the premetric formulation of electromagnetism. Phys. Lett. A 379, 1297–1303 (2015). arXiv.org:1411.0460

    Google Scholar 

  72. W.-T. Ni, S.-S. Pan, H.-C. Yeh, L.-S. Hou, J. Wan, Search for an axionlike spin coupling using a paramagnetic salt with a dc SQUID. Phys. Rev. Lett. 82, 2439 (1999)

    Article  ADS  Google Scholar 

  73. Yu.N. Obukhov, Poincaré gauge gravity: Selected topics. Int. J. Geom. Meth. Mod. Phys. 3, 95–138 (2006). arXiv.org:gr-qc/0601090

    Google Scholar 

  74. Y.N. Obukhov, T. Fukui, G.F. Rubilar, Wave propagation in linear electrodynamics. Phys. Rev. D 62, 044050 (2000). arXiv.org:gr-qc/0005018

  75. Yu.N. Obukhov, F.W. Hehl, On possible skewon effects on light propagation. Phys. Rev. D 70, 125015 (2004). arXiv.org:physics/0409155

  76. Yu.N. Obukhov, D. Puetzfeld, Equations of motion in scalar-tensor theories of gravity: a covariant multipolar approach. Phys. Rev. D 90, 104041 (2014). arXiv.org:1404.6977

  77. Yu.N. Obukhov, G.F. Rubilar, Fresnel analysis of the wave propagation in nonlinear electrodynamics. Phys. Rev. D 66, 024042 (2002). arXiv.org:gr-qc/0204028

  78. V. Perlick, On the hyperbolicity of Maxwell’s equations with a local constitutive law. J. Math. Phys. 52, 042903 (2011). arXiv:1011.2536

    Article  ADS  MathSciNet  MATH  Google Scholar 

  79. V. Perlick, Private communication (2015)

    Google Scholar 

  80. E.J. Post, Formal Structure of Electromagnetics—General Covariance and Electromagnetics (North Holland, Amsterdam, 1962) (Dover, Mineola, 1997)

    Google Scholar 

  81. D. Puetzfeld, Y.N. Obukhov, Equations of motion in metric-affine gravity: a covariant unified framework. Phys. Rev. D 90, 084034 (2014). arXiv:1408.5669

    Article  ADS  Google Scholar 

  82. D. Puetzfeld, Y.N. Obukhov, Equivalence principle in scalar-tensor gravity. Phys. Rev. D 92, 081502(R) (2015). arXiv.org:1505.01285

  83. R.E. Raab, A.H. Sihvola, On the existence of linear non-reciprocal bi-isotropic (NRBI) media. J. Phys. A 30, 1335–1344 (1997)

    Article  ADS  MATH  Google Scholar 

  84. G.F. Rubilar, Linear pre-metric electrodynamics and deduction of the light cone. Annalen Phys. (Berlin) 11, 717–782 (2002). arXiv.org:0706.2193

    Google Scholar 

  85. C. Schaefer, Einführung in Die Theoretische Physik, vol.3, Part 1 (de Gruyter, Berlin, 1932)

    Google Scholar 

  86. E. Scholz, Higgs and gravitational scalar fields together induce Weyl gauge. Gen. Rel. Grav. 47(7) (2015). arXiv.org:1407.6811

  87. E. Scholz, MOND-like acceleration in integrable Weyl geometric gravity. Found. Phys. 46, 176–208 (2016). arXiv.org:1412.0430

    Google Scholar 

  88. J.A. Schouten, Tensor Analysis for Physicists, corr. 2nd edn. (Clarendon Press, Oxford, 1959) (Dover, New York, 1989)

    Google Scholar 

  89. E. Schrödinger, Space-Time Structure (Cambridge University Press, Cambridge, 1954)

    MATH  Google Scholar 

  90. F.P. Schuller, C. Witte, M.N.R. Wohlfarth, Causal structure and algebraic classification of area metric spacetimes in four dimensions. Ann. Phys. (NY) 325, 1853–1883 (2010). arXiv.org:0908.1016

  91. A. Serdyukov, I. Semchenko, S. Tretyakov, A. Sihvola, Electromagnetics of Bi-anisotropic Materials. Theory and Applications (Gordon and Breach, Amsterdam, 2001)

    Google Scholar 

  92. E. Shamonina, L. Solymar, Metamaterials: How the subject started. Metamaterials 1, 12–18 (2007)

    Article  ADS  Google Scholar 

  93. A. Sihvola, I.V. Lindell, Perfect electromagnetic conductor medium. Ann. Phys. (Berlin) 17, 787–802 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  94. A. Sihvola, Private communication (2015)

    Google Scholar 

  95. E. Tonti, The Mathematical Structure of Classical and Relativistic Physics: a general classification diagram (Birkhäuser/Springer, New York, 2013)

    Book  MATH  Google Scholar 

  96. C. Truesdell, R.A. Toupin, The classical field theories, in Encyclopedia of Physics, vol. III/1, ed. by S. Flügge (Springer, Berlin, 1960), pp. 226–793

    Google Scholar 

  97. V. Vennin, J. Martin, C. Ringeval, Cosmic inflation and model comparison. Comptes Rendus Physique 16, 960–968 (2015)

    Article  ADS  Google Scholar 

  98. S. Weinberg, The Quantum Theory of Fields. Volume II: Modern Applications (Cambridge University Press, Cambridge, 1996)

    Google Scholar 

  99. F. Wilczek, Two applications of axion electrodynamics. Phys. Rev. Lett. 58, 1799–1802 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  100. P. Russer, Electromagnetics, Microware Circuit and Antenna Design for Communications Engineering, 2nd edn. (Artech House, Norwood, MA, 2006)

    Google Scholar 

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Acknowledgments

This project was partly supported by the German-Israeli Research Foundation (GIF) by the grant GIF/No. 1078-107.14/2009. I am grateful to Claus Kiefer (Cologne) for helpful remarks re Higgs cosmology, to Yuri Obukhov (Moscow) re questions of torsion and of the Hadamard method, to Helmut Rumpf (Vienna) re the Mukhanov bound of \(10^{-29}\,\mathrm{{m}}\), and to Volker Perlick (Bremen) re gravity versus electromagnetism and what is more fundamental. I would like to thank Ari Sihvola and Ismo Lindell (both Espoo/Helsinki) and Alberto Favaro (London) for the permission to use the image in Fig.2. Many useful comments on a draft of this paper were supplied by Hubert Goenner (Göttingen), Yakov Itin (Jerusalem), Claus Lämmerzahl (Bremen), Ecardo Mielke (Mexico City), Wei-Tou Ni (Hsinchu), Erhard Scholz (Wuppertal), Frederic Schuller (Erlangen), and Dirk Puetzfeld (Bremen). I am grateful to Alan Kostelecký (Bloomington) for a last-minute exchange of emails.

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  1. Institute for Theoretical Physics, University of Cologne, 50923, Cologne, Germany

    Friedrich W. Hehl

  2. Department of Physics and Astronomy, University of Missouri, Columbia, MO, 65211, USA

    Friedrich W. Hehl

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    Torsten Asselmeyer-Maluga

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Hehl, F.W. (2016). Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior. In: Asselmeyer-Maluga, T. (eds) At the Frontier of Spacetime. Fundamental Theories of Physics, vol 183. Springer, Cham. https://doi.org/10.1007/978-3-319-31299-6_4

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