Re-evaluating Space-Time

  • A. J. ShortEmail author
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


Special relativity inspired a fundamental shift in our picture of reality, from a spatial state evolving in time to a static block universe. We will highlight some conceptual issues raised by the block universe viewpoint, particularly concerning its complexity, causality, and connection to quantum theory. In light of these issues, and inspired by recent results showing that relativity can emerge naturally in discrete space-time dynamics, we will explore whether the evolving state picture might be more natural after all.



AJS acknowledges support from the FQXi ‘Physics of What Happens’ grant program, via the SVCF.


  1. 1.
    A. Einstein, Zur Elektrodynamik bewegter Körper. Ann. Phys. 17, 891 (1905); English translation On the electrodynamics of moving bodies, G.B. Jeffery, W. Perrett (1923)Google Scholar
  2. 2.
    R. Arnowitt, S. Deser, C. Misner, Dynamical structure and definition of energy in general relativity. Phys. Rev. 116, 1322–1330 (1959)CrossRefzbMATHADSMathSciNetGoogle Scholar
  3. 3.
    A. Kolmogorov, On tables of random numbers. Sankhyā Ser. A 25, 369–375 (1963). MR 178484Google Scholar
  4. 4.
    I. Bialynicki-Birula, Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata. Phys. Rev. D 49, 6920 (1994)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    G.M. D’Ariano, A. Tosini, Emergence of space-time from topologically homogeneous causal networks. Stud. Hist. Phil. Sci. B: Stud. Hist. Phil. Mod. Phys. 44, 294-299 (2013)zbMATHADSMathSciNetGoogle Scholar
  6. 6.
    G.M. D’Ariano, P. Perinotti, Derivation of the Dirac equation from principles of information processing. Phys. Rev. A 90, 062106 (2014)CrossRefADSGoogle Scholar
  7. 7.
    A. Bisio, G.M. D’Ariano, A. Tosini, Quantum field as a quantum cellular automaton: the Dirac free evolution in one dimension. Ann. Phys. 354, 244 (2015)CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    G.M. D’Ariano, N. Mosco, P. Perinotti, A. Tosini, Path-integral solution of the one-dimensional Dirac quantum cellular automaton (2014). arXiv:1406.1021Google Scholar
  9. 9.
    G.M. D’Ariano, N. Mosco, P. Perinotti, A. Tosini, Discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions (2014). arXiv:1410.6032Google Scholar
  10. 10.
    A. Bisio, G.M. D’Ariano, P. Perinotti, Lorentz symmetry for 3d quantum cellular automata (2015). arXiv:1503.01017Google Scholar
  11. 11.
    T.C. Farrelly, A.J. Short, Discrete spacetime and relativistic quantum particles. Phys. Rev. A 89, 062109 (2014)CrossRefADSGoogle Scholar
  12. 12.
    T.C. Farrelly, A.J. Short, Causal fermions in discrete space-time. Phys. Rev. A 89, 012302 (2014)CrossRefADSGoogle Scholar
  13. 13.
    G.F. FitzGerald, The ether and the earth’s atmosphere. Science 13(328), 390 (1889)Google Scholar
  14. 14.
    H.A. Lorentz, The relative motion of the earth and the aether. Zittingsverlag Akad. V. Wet. 1, 74–79 (1892)Google Scholar
  15. 15.
    H. Minkowski, Raum und Zeit (English translation: space and time). Jahresberichte der Deutschen Mathematiker-Vereinigung, 75–88 (1909)Google Scholar
  16. 16.
    Y. Aharonov, P.G. Bergmann, J.L. Lebowitz, Time symmetry in the quantum process of measurement. Phys. Rev. B 134, 1410–1416, (1964)CrossRefzbMATHADSMathSciNetGoogle Scholar
  17. 17.
    J.-M.A. Allen, J. Barrett, D.C. Horsman, C.M. Lee, R.W. Spekkens, Quantum common causes and quantum causal models (2016). arXiv:1609.09487Google Scholar
  18. 18.
    G. Feinberg, Possibility of faster-than-light particles. Phys. Rev. 159, 1089–1105 (1967)CrossRefADSGoogle Scholar
  19. 19.
    K. Gödel, An example of a new type of cosmological solution of Einstein’s field equations of gravitation. Rev. Mod. Phys. 21, 447–450 (1949)CrossRefzbMATHADSMathSciNetGoogle Scholar
  20. 20.
    D.Z. Albert, Time and Chance (Harvard University Press, Harvard, 2003)Google Scholar
  21. 21.
    M. Tooley, Time, Tense, and Causation (Clarendon Press, Oxford, 1997)Google Scholar
  22. 22.
    H. Everett, Relative state formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957)CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    G.C. Ghirardi, A. Rimini, T. Weber, A model for a unified quantum description of macroscopic and microscopic systems, in Quantum Probability and Applications, ed. by L. Accardi et al. (Springer, Berlin, 1985)Google Scholar
  24. 24.
    D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables. I & II. Phys. Rev. 85, 166–193 (1952)zbMATHADSMathSciNetGoogle Scholar
  25. 25.
    R.B. Griffiths, Consistent histories and the interpretation of quantum mechanics. J. Stat. Phys. 36, 219–272 (1984)CrossRefzbMATHADSMathSciNetGoogle Scholar
  26. 26.
    S. Watanabe, Symmetry of physical laws. Part III. Prediction and retrodiction. Rev. Mod. Phys. 27(2), 179 (1955)Google Scholar
  27. 27.
    Y. Aharonov, P.G. Bergmann, J.L. Lebowitz, Time symmetry in the quantum process of measurement. Phys. Rev. B 134(6), 1410–1416 (1964)CrossRefzbMATHADSMathSciNetGoogle Scholar
  28. 28.
    Y. Aharonov, S. Popescu, J. Tollaksen, Each instant of time a new Universe (2013). arXiv:1305.1615Google Scholar
  29. 29.
    A. Kent, Path integrals and reality (2013). arXiv:1305.6565Google Scholar
  30. 30.
    A. Kent, Solution to the Lorentzian quantum reality problem. Phys. Rev. A 90, 012107 (2014)CrossRefADSGoogle Scholar
  31. 31.
    B.S. DeWitt, Quantum theory of gravity. I. The canonical theory. Phys. Rev. 160, 1113–1148 (1967)zbMATHGoogle Scholar
  32. 32.
    V. Giovannetti, S. Lloyd, L. Maccone, Quantum time. Phys. Rev. D 92, 045033 (2015)CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.H.H. Wills Physics LaboratoryUniversity of BristolBristolUK

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