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Foundations of Physics

, Volume 47, Issue 5, pp 625–639 | Cite as

Quantum Inflation of Classical Shapes

  • Tim KoslowskiEmail author
Article
  • 136 Downloads

Abstract

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization.

Keywords

Shape dynamics Quantum effect Inflation Bohmian trajectory 

Notes

Acknowledgements

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a grant to the University of New Brunswick and by the Foundational Questions Institute through Grant FQXi-RFP3-1339. I am very grateful for an invitation to the 2013 “Haunted Workshop” in Tepoztlan, Mexico, where discussions with Ward Struyve and Daniel Sudarsky raised the question about quantum corrections to classical shape dynamics cosmology was raised. It was also at this workshop where Ward Struyve introduced me to detail about Bohmian mechanics.

References

  1. 1.
    Anderson, E., Barbour, J., Foster, B.Z., Kelleher, B., Murchadha, N.O.: The physical gravitational degrees of freedom. Class. Quantum Gravity 22, 1795 (2005)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Barbour, J.: Shape dynamics: an introduction. arXiv:1105.0183
  3. 3.
    Barbour, J.: The Definition of Mach’s Principle. Found. Phys. 40, 1263 (2010). arXiv:1007.3368
  4. 4.
    Gomes, H., Gryb, S., Koslowski, T.: Einstein gravity as a 3D conformally invariant theory. Class. Quantum Gravity 28, 045005 (2011). arXiv:1010.2481
  5. 5.
    Gomes, H., Koslowski, T.: The Link between General Relativity and Shape Dynamics. Class. Quantum Gravity 29, 075009 (2012). arXiv:1101.5974
  6. 6.
    Gomes, H., Koslowski, T.: Coupling shape dynamics to matter gives spacetime. Gen. Relativ. Gravit. 44, 1539 (2012). arXiv:1110.3837
  7. 7.
    Gomes, H., Koslowski, T.: Frequently asked questions about Shape Dynamics. Found. Phys. 43, 1428 (2013). arXiv:1211.5878
  8. 8.
    Koslowski, T.A.: Observable equivalence between General Relativity and Shape Dynamics. arXiv:1203.6688
  9. 9.
    Koslowski, T.A.: Shape dynamics and effective field theory. Int. J. Mod. Phys. A 28, 1330017 (2013). arXiv:1305.1487
  10. 10.
    Bojowald, M.: Loop quantum cosmology. Living Rev. Relativ. 11, 4 (2008)ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    Arnowitt, R.L., Deser, S., Misner, C.W.: The dynamics of general relativity. Gen. Relativ. Gravit. 40, 1997 (2008)ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    Dirac, P.A.M.: The theory of gravitation in Hamiltonian form. Proc. R. Soc. Lond. A 246(1246), 333343 (1958)MathSciNetGoogle Scholar
  13. 13.
    Dirac, P.A.M.: Fixation of coordinates in the Hamiltonian theory of gravitation. Phys. Rev. 114, 924930 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    York, J.W.: Role of conformal three geometry in the dynamics of gravitation. Phys. Rev. Lett. 28, 10821085 (1972)CrossRefGoogle Scholar
  15. 15.
    York, J.W.: Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial value problem of general relativity. J. Math. Phys. 14, 456 (1973)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Anderson, E.: The problem of time in quantum gravity. arXiv:1009.2157
  17. 17.
    Barbour, J.B., Bertotti, B.: Mach’s principle and the structure of dynamical theories. Proc. R. Soc. Lond. A 382, 295 (1982)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Barbour, J., Lostaglio, M., Mercati, F.: Scale anomaly as the origin of time. Gen. Relativ. Gravit. 45, 911 (2013). arXiv:1301.6173
  19. 19.
    Barbour, J., Koslowski, T., Mercati, F.: The solution to the problem of time in shape dynamics. Class. Quantum Gravity 31, 155001 (2014). arXiv:1302.6264
  20. 20.
    Bohm, D.: A suggested interpretation in terms of ’Hidden Variables’: part I and part II. Phys. Rev. 85, 166179, 180193 (1952)Google Scholar
  21. 21.
    Allori, A., Dürr, D., Goldstein, S., Zanghi, N.: Seven steps towards the classical world. J. Opt. B Quantum Semiclassical Opt. 4, S482 (2002) arXiv:quant-ph/0112005
  22. 22.
    Barbour, J., Koslowski, T., Mercati, F.: A gravitational origin of the arrows of time. arXiv:1310.5167
  23. 23.
    Rovelli, C.: Quantum Gravity. University Press, Cambridge, UK (2004)CrossRefzbMATHGoogle Scholar
  24. 24.
    Bojowald, M., Hoehn, P., Tsobanjan, A.: An Effective approach to the problem of time. Class. Quantum Gravity 28, 035006 (2011). [arXiv:1009.5953 [gr-qc]]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Moncrief, V.: Reduction of the Einstein equations in (2+1)-dimensions to a Hamiltonian system over Teichmuller space. J. Math. Phys. 30, 2907 (1989)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Budd, T., Koslowski, T.: Shape dynamics in 2+1 dimensions. Gen. Relativ. Gravit. 44, 1615 (2012). arXiv:1107.1287
  27. 27.
    Struyve, W., Valentini, A.: De Broglie–Bohm guidance equations for arbitrary Hamiltonians. J. Phys. A 42, 035301 (2009). [arXiv:0808.0290]ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de MéxicoMexcio CityMexico

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