Constraints on the universe as a numerical simulation

Abstract.

Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation and investigate potentially observable consequences. Among the observables that are considered are the muon g - 2 and the current differences between determinations of \( \alpha\), but the most stringent bound on the inverse lattice spacing of the universe, \( b^{-1}\gtrsim 10^{11}\) GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest-energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice.

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References

  1. 1

    N. Bostrom, Philos. Q. 53, 243 (2003)

    Article  Google Scholar 

  2. 2

    A.S. Kronfeld, arXiv:1209.3468 [physics.hist-ph] (2012)

  3. 3

    Z. Fodor, C. Hoelbling, Rev. Mod. Phys. 84, 449 (2012) arXiv:1203.4789 [hep-lat]

    Article  ADS  Google Scholar 

  4. 4

    S.R. Beane, arXiv:1206.5219 [hep-lat] (2012)

  5. 5

    T. Yamazaki, arXiv:1207.4277 [hep-lat]

  6. 6

    HAL QCD Collaboration (S. Aoki), arXiv:1206.5088 [hep-lat] (2012)

  7. 7

    S. Lloyd, Nature 406, 1047 (1999) arXiv:quant-ph/9908043

    Article  ADS  Google Scholar 

  8. 8

    S. Lloyd, arXiv:quant-ph/0501135 [quant-ph] (2005)

  9. 9

    K. Zuse, Rechnender Raum (Friedrich Vieweg and Sohn, Braunschweig, 1969)

  10. 10

    E. Fredkin, Physica D 45, 254 (1990)

    MathSciNet  Article  MATH  ADS  Google Scholar 

  11. 11

    S. Wolfram, A New Kind of Science (Wolfram Media, 2002) p. 1197

  12. 12

    G.'t Hooft, arXiv:1205.4107 [quant-ph] (2012)

  13. 13

    J. Church, Am. J. Math. 58, 435 (1936)

    MathSciNet  Article  Google Scholar 

  14. 14

    A. Turing, Proc. London Math. Soc. Ser. 2 442, 230 (1936)

    Google Scholar 

  15. 15

    D. Deutsch, Proc. R. Soc. London A 400, 97 (1985)

    MathSciNet  Article  MATH  ADS  Google Scholar 

  16. 16

    J. Barrow, Living in a Simulated Universe, edited by B. Carr (Cambridge University Press, 2008) Chapt. 27 Universe or Multiverse? pp. 481--486

  17. 17

    MILC Collaboration, http://physics.indiana.edu/~sg/milc.html

  18. 18

    J.B. Kogut, L. Susskind, Phys. Rev. D 11, 395 (1975)

    Article  ADS  Google Scholar 

  19. 19

    SPECTRUM Collaboration, http://usqcd.jlab.org/projects/AnisoGen/

  20. 20

    K.G. Wilson, Phys. Rev. D 10, 2445 (1974)

    Article  ADS  Google Scholar 

  21. 21

    B. Sheikholeslami, R. Wohlert, Nucl. Phys. B 259, 572 (1985)

    Article  ADS  Google Scholar 

  22. 22

    Hadron Spectrum Collaboration (H.-W. Lin et al.), Phys. Rev. D 79, 034502 (2009) arXiv:0810.3588 [hep-lat]

    Article  Google Scholar 

  23. 23

    V. Vinge, Science and Engineering in the Era of Cyberspace, edited by G.A. Landis (NASA Publication, 1993) CP-10129, Vision-21: Interdisciplinary, 115

  24. 24

    R. Kurzweil, The Singularity Is Near: When Humans Transcend Biology (Penguin Non-Classics, 2006) ISBN 0143037889

  25. 25

    S.R. Coleman, S.L. Glashow, Phys. Rev. D 59, 116008 (1999) arXiv:hep-ph/9812418

    Article  ADS  Google Scholar 

  26. 26

    O. Gagnon, G.D. Moore, Phys. Rev. D 70, 065002 (2004) arXiv:hep-ph/0404196 [hep-ph]

    Article  ADS  Google Scholar 

  27. 27

    J. Collins et al., Phys. Rev. Lett. 93, 191301 (2004) arXiv:gr-qc/0403053 [gr-qc]

    MathSciNet  Article  ADS  Google Scholar 

  28. 28

    S. Kachru et al., Phys. Rev. D 68, 046005 (2003) arXiv:hep-th/0301240 [hep-th]

    MathSciNet  Article  ADS  Google Scholar 

  29. 29

    L. Susskind, arXiv:hep-th/0302219 [hep-th] (2003)

  30. 30

    M.R. Douglas, JHEP 05, 046 (2003) arXiv:hep-th/0303194 [hep-th]

    Article  ADS  Google Scholar 

  31. 31

    T. Appelquist, arXiv:1204.6000 [hep-ph] (2012)

  32. 32

    S. Hsu, A. Zee, Mod. Phys. Lett. A 21, 1495 (2006) arXiv:physics/0510102 [physics]

    Article  ADS  Google Scholar 

  33. 33

    K. Symanzik, Nucl. Phys. B 226, 187 (1983)

    MathSciNet  Article  ADS  Google Scholar 

  34. 34

    K. Symanzik, Nucl. Phys. B 226, 205 (1983)

    MathSciNet  Article  ADS  Google Scholar 

  35. 35

    G. Aslanyan, A.V. Manohar, JCAP 06, 003 (2012) arXiv:1104.0015 [astro-ph.CO]

    Article  ADS  Google Scholar 

  36. 36

    P. Jizba et al., Phys. Rev. D 81, 084030 (2010) arXiv:0912.2253 [hep-th]

    Article  ADS  Google Scholar 

  37. 37

    D.B. Kaplan, S. Sun, Phys. Rev. Lett. 108, 181807 (2012) arXiv:1112.0302 [hep-ph]

    Article  ADS  Google Scholar 

  38. 38

    M. Lüscher, P. Weisz, Commun. Math. Phys. 97, 59 (1985)

    Article  MATH  ADS  Google Scholar 

  39. 39

    P.J. Mohr, arXiv:1203.5425 [physics.atom-ph] (2012)

  40. 40

    R. Bouchendira et al., Phys. Rev. Lett. 106, 080801 (2011)

    Article  ADS  Google Scholar 

  41. 41

    D. Colladay, V.A. Kostelecký, Phys. Rev. D 55, 6760 (1997)

    Article  ADS  Google Scholar 

  42. 42

    R.C. Myers, M. Pospelov, Phys. Rev. Lett. 90, 211601 (2003) arXiv:hep-ph/0301124 [hep-ph]

    MathSciNet  Article  ADS  Google Scholar 

  43. 43

    S.M. Carroll et al., Phys. Rev. D 41, 1231 (1990)

    Article  ADS  Google Scholar 

  44. 44

    P. Laurent et al., Phys. Rev. D 83, 121301 (2011) arXiv:1106.1068 [astro-ph.HE]

    Article  ADS  Google Scholar 

  45. 45

    L. Maccione et al., JCAP 04, 022 (2009) arXiv:0902.1756 [astro-ph.HE]

    Article  ADS  Google Scholar 

  46. 46

    I. Motie, S.-S. Xue, Int. J. Mod. Phys. A 27, 1250104 (2012) arXiv:1206.0709 [hep-ph]

    Article  ADS  Google Scholar 

  47. 47

    S.-S. Xue, Phys. Lett. B 706, 213 (2011) arXiv:1110.1317 [hep-ph]

    Article  ADS  Google Scholar 

  48. 48

    OPERA Collaboration (T. Adam), arXiv:1109.4897 [hep-ex] (2011)

  49. 49

    S.R. Coleman, S.L. Glashow, Phys. Lett. B 405, 149 (1997) arXiv:hep-ph/9703240 [hep-ph]

    Article  Google Scholar 

  50. 50

    K. Greisen, Phys. Rev. Lett. 16, 748 (1966)

    Article  ADS  Google Scholar 

  51. 51

    G. Zatsepin, V. Kuzmin, JETP Lett. 4, 78 (1966)

    ADS  Google Scholar 

  52. 52

    Pierre Auger Collaboration (J. Abraham et al.), Phys. Lett. B 685, 239 (2010) arXiv:1002.1975 [astro-ph.HE]

    Article  ADS  Google Scholar 

  53. 53

    HiRes Collaboration (P. Sokolsky et al.), PoS ICHEP2010, 444 (2010) arXiv:1010.2690 [astro-ph.HE]

    Google Scholar 

Download references

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Correspondence to Silas R. Beane.

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Communicated by U.-G. Meißner

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Beane, S.R., Davoudi, Z. & J. Savage, M. Constraints on the universe as a numerical simulation. Eur. Phys. J. A 50, 148 (2014). https://doi.org/10.1140/epja/i2014-14148-0

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Keywords

  • Dispersion Relation
  • Lattice Spacing
  • Wilson Action
  • Strong Nuclear Force
  • Universe Simulation