Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that this differs from Kolmogorov complexity [3], which only captures compressibility. The Kolmogorov complexity would generally be small for a block-universe as one could write a compact program to generate it by iterating the physical laws on the initial state.
- 2.
- 3.
A similar alternative is the ‘moving spotlight’ view of time. In this picture the entire block universe exists, but in addition a particular spatial slice representing an objective present is ’highlighted’, and this highlight evolves up the block universe. However, this view seems to suffer from almost all of the disadvantages of the block universe, as well as those of a preferred frame.
- 4.
Or more generally that operators localised in a spatial region only evolve into operators on a slightly larger region.
References
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)
R. Arnowitt, S. Deser, C. Misner, Dynamical structure and definition of energy in general relativity. Phys. Rev. 116, 1322–1330 (1959)
A. Kolmogorov, On tables of random numbers. Sankhyā Ser. A 25, 369–375 (1963). MR 178484
I. Bialynicki-Birula, Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata. Phys. Rev. D 49, 6920 (1994)
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)
G.M. D’Ariano, P. Perinotti, Derivation of the Dirac equation from principles of information processing. Phys. Rev. A 90, 062106 (2014)
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)
G.M. D’Ariano, N. Mosco, P. Perinotti, A. Tosini, Path-integral solution of the one-dimensional Dirac quantum cellular automaton (2014). arXiv:1406.1021
G.M. D’Ariano, N. Mosco, P. Perinotti, A. Tosini, Discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions (2014). arXiv:1410.6032
A. Bisio, G.M. D’Ariano, P. Perinotti, Lorentz symmetry for 3d quantum cellular automata (2015). arXiv:1503.01017
T.C. Farrelly, A.J. Short, Discrete spacetime and relativistic quantum particles. Phys. Rev. A 89, 062109 (2014)
T.C. Farrelly, A.J. Short, Causal fermions in discrete space-time. Phys. Rev. A 89, 012302 (2014)
G.F. FitzGerald, The ether and the earth’s atmosphere. Science 13(328), 390 (1889)
H.A. Lorentz, The relative motion of the earth and the aether. Zittingsverlag Akad. V. Wet. 1, 74–79 (1892)
H. Minkowski, Raum und Zeit (English translation: space and time). Jahresberichte der Deutschen Mathematiker-Vereinigung, 75–88 (1909)
Y. Aharonov, P.G. Bergmann, J.L. Lebowitz, Time symmetry in the quantum process of measurement. Phys. Rev. B 134, 1410–1416, (1964)
J.-M.A. Allen, J. Barrett, D.C. Horsman, C.M. Lee, R.W. Spekkens, Quantum common causes and quantum causal models (2016). arXiv:1609.09487
G. Feinberg, Possibility of faster-than-light particles. Phys. Rev. 159, 1089–1105 (1967)
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)
D.Z. Albert, Time and Chance (Harvard University Press, Harvard, 2003)
M. Tooley, Time, Tense, and Causation (Clarendon Press, Oxford, 1997)
H. Everett, Relative state formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957)
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)
D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables. I & II. Phys. Rev. 85, 166–193 (1952)
R.B. Griffiths, Consistent histories and the interpretation of quantum mechanics. J. Stat. Phys. 36, 219–272 (1984)
S. Watanabe, Symmetry of physical laws. Part III. Prediction and retrodiction. Rev. Mod. Phys. 27(2), 179 (1955)
Y. Aharonov, P.G. Bergmann, J.L. Lebowitz, Time symmetry in the quantum process of measurement. Phys. Rev. B 134(6), 1410–1416 (1964)
Y. Aharonov, S. Popescu, J. Tollaksen, Each instant of time a new Universe (2013). arXiv:1305.1615
A. Kent, Path integrals and reality (2013). arXiv:1305.6565
A. Kent, Solution to the Lorentzian quantum reality problem. Phys. Rev. A 90, 012107 (2014)
B.S. DeWitt, Quantum theory of gravity. I. The canonical theory. Phys. Rev. 160, 1113–1148 (1967)
V. Giovannetti, S. Lloyd, L. Maccone, Quantum time. Phys. Rev. D 92, 045033 (2015)
Acknowledgements
AJS acknowledges support from the FQXi ‘Physics of What Happens’ grant program, via the SVCF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Short, A.J. (2017). Re-evaluating Space-Time. In: Renner, R., Stupar, S. (eds) Time in Physics. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68655-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-68655-4_4
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-68654-7
Online ISBN: 978-3-319-68655-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)