Book contents
- Frontmatter
- Contents
- List of contributors
- 1 The problem with quantum gravity
- 2 A dialogue on the nature of gravity
- 3 Effective theories and modifications of gravity
- 4 The small-scale structure of spacetime
- 5 Ultraviolet divergences in supersymmetric theories
- 6 Cosmological quantum billiards
- 7 Progress in RNS string theory and pure spinors
- 8 Recent trends in superstring phenomenology
- 9 Emergent spacetime
- 10 Loop quantum gravity
- 11 Loop quantum gravity and cosmology
- 12 The microscopic dynamics of quantum space as a group field theory
- 13 Causal dynamical triangulations and the quest for quantum gravity
- 14 Proper time is stochastic time in 2D quantum gravity
- 15 Logic is to the quantum as geometry is to gravity
- 16 Causal sets: discreteness without symmetry breaking
- 17 The Big Bang, quantum gravity and black-hole information loss
- 18 Conversations in string theory
- Index
- References
16 - Causal sets: discreteness without symmetry breaking
Published online by Cambridge University Press: 05 August 2012
By
Book contents
- Frontmatter
- Contents
- List of contributors
- 1 The problem with quantum gravity
- 2 A dialogue on the nature of gravity
- 3 Effective theories and modifications of gravity
- 4 The small-scale structure of spacetime
- 5 Ultraviolet divergences in supersymmetric theories
- 6 Cosmological quantum billiards
- 7 Progress in RNS string theory and pure spinors
- 8 Recent trends in superstring phenomenology
- 9 Emergent spacetime
- 10 Loop quantum gravity
- 11 Loop quantum gravity and cosmology
- 12 The microscopic dynamics of quantum space as a group field theory
- 13 Causal dynamical triangulations and the quest for quantum gravity
- 14 Proper time is stochastic time in 2D quantum gravity
- 15 Logic is to the quantum as geometry is to gravity
- 16 Causal sets: discreteness without symmetry breaking
- 17 The Big Bang, quantum gravity and black-hole information loss
- 18 Conversations in string theory
- Index
- References
Summary
Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One proposed application of causal sets is to use them as the histories in a quantum sum-over-histories, i.e. to construct a quantum theory of spacetime. It is expected by many that quantum gravity will introduce some kind of ‘fuzziness’, uncertainty and perhaps discreteness into spacetime, and generic effects of this fuzziness are currently being sought. Applied as a model of discrete spacetime, causal sets can be used to construct simple phenomenological models which allow us to understand some of the consequences of this general expectation.
Introduction: seeing atoms with the naked eye
At present, one of the most important tasks in theoretical physics is to understand the nature of spacetime at the Planck scale. Various indications from our current most successful theories point to this scale: quantum effects are to be expected to invalidate the general theory of relativity here. What should replace our current best understanding of spacetime? This question remains controversial as no theory of quantum gravity can yet be claimed to be complete. For example, some researchers are convinced that the kinematical structure used to replace the continuous manifolds of GR should be discrete, but others do not adhere to this requirement. George Ellis' great contribution to our understanding of spacetime, and his interest in the issue of spacetime discreteness, make this a very appropriate topic for these proceedings.
Information
- Type
- Chapter
- Information
- Foundations of Space and TimeReflections on Quantum Gravity, pp. 385 - 409Publisher: Cambridge University PressPrint publication year: 2012
References
[1], On the transmission of light through an atmosphere containing small particles in suspension, in Scientific Papers by Lord Rayleigh, Vol. 4, pp. 247–405, New York: Dover, 1899/1964.
[2], Eur. J. Phys. 26, 183 (2005).
[3], , and , Phys. Rev. Lett. 59, 521 (1987).
[4] (2010), 1001.4041.
[5], The causal set approach to quantum gravity, in Approaches to Quantum Gravity: Towards a New Understanding of Space and Time, edited by , Cambridge University Press, 2006, gr-qc/0601121.
[7], AIP Conf. Proc. 861, 79 (2006).
[8] (2005), gr-qc/0508109.
[9], (2003), gr-qc/0309009.
[10], First steps with causal sets, in Proceedings of the Ninth Italian Conference on General Relativity and Gravitational Physics, Capri, Italy, September 1990, edited by et al., pp. 68–90, World Scientific, Singapore, 1991.
[11], Space-time and causal sets, in Relativity and Gravitation: Classical and Quantum, Proceedings of the SILARG VII Conference, Cocoyoc, Mexico, December 1990, edited by et al., pp. 150–73, World Scientific, Singapore, 1991.
[12], Stud. Hist. Philos. Mod. Phys. 36, 291 (2005), hep-th/0504037.
[13], Int. J. Theor. Phys. 36, 2759 (1997), gr-qc/9706002.
[14] (1989), gr-qc/9511063.
[15] and , J. Math. Phys. 50, 012503 (2009), 0708.1721.
[16] (2007), 0708.2481.
[17] (2010), 1001.4188.
[18], and , J. Math. Phys. 17, 174 (1976).
[19], J. Math. Phys. 18, 1399 (1977).
[20], CERN-TH-2538.
[21], Talk given at 8th Conference on General Relativity and Gravitation, Waterloo, Canada, August 7–12, 1977.
[22] and , Phys. Lett. A141, 226 (1989).
[23], PhD thesis, MIT, 1988.
[24], Phys. Rev. D67, 024034 (2003), gr-qc/0207103.
[25] and , Phys. Rev. Lett. 66, 260 (1991).
[26], and (2005), gr-qc/0512073.
[27] and , Class. Quant. Grav. 26, 155013 (2009), 0810.1768.
[28], and , J. Math. Phys. 48, 032501 (2007), gr-qc/0604124.
[29], and , Class. Quant. Grav. 26, 175008 (2009), 0902.0434.
[30] and (2010), 1001.2725.
[31] and , Trans. Amer. Math. Society 205, 205 (1975).
[32], , , and , Class. Quant. Grav. 16, 3457 (1999), gr-qc/9901063.
[33], Nucl. Phys. B144, 349 (1978).
[34], and , Mod. Phys. Lett. A19, 1829 (2004), gr-qc/0311055.
[35], and (2006), gr-qc/0605006.
[36], J. Phys. Conf. Ser. 174, 012020 (2009), 0901.4009.
[37] (2008), 0806.0339.
[38], and (2005), astro-ph/0505267.
[39], , and (2010), 1003.0878.
[40], , , and , Phys. Rev. Lett. 93, 191301 (2004), gr-qc/0403053.
[41] and , Phys. Rev. Lett. 91, 179101 (2003), gr-qc/0306113.
[42], Phys. Rev. D80, 025011 (2009), 0902.0590.
[43] (2007), gr-qc/0703099.
[44] and , Phys. Rev. D61, 024002 (2000), gr-qc/9904062.
[45] and (2005), gr-qc/0504066.
[46], , , and , Phys. Rev. D67, 084031 (2003), gr-qc/0210061.
[47] and (2005), gr-qc/0504069.
[48], Int. J. Theor. Phys. 39, 1731 (2000), gr-qc/0003043.
[49], , and , Phys. Rev. D63, 084026 (2001), gr-qc/0009063.
[50] and , J. Math. Phys. 44, 1666 (2003), gr-qc/0209020.
[51] and , Phys. Rev. D63, 104011 (2001), gr-qc/0003117.
[52] and , Random Struct. Algorithms 36, 218 (2010).
[53] and (2009), 0909.4771.
[54], and (2009), 0906.3947.
[55], Mod. Phys. Lett. A9, 3119 (1994), gr-qc/9401003.
[56], Space-time quantum mechanics and the quantum mechanics of space-time, in Proceedings of the Les Houches Summer School on Gravitation and Quantizations, Les Houches, France, 6 July — 1 August 1992, edited by and , North-Holland, 1995, gr-qc/9304006.
[57], and (2010), 1002.0589.
[58], and , Class. Quant. Grav. 25, 105025 (2008), 0706.0375.
[59] (2009), 0911.1479.
[60], and , J. Comb. Theory, Ser.A 73, 193 (1996).
[61], , and , Phys. Rev. D69, 103523 (2004), astro-ph/0209274.
[62], Braz. J. Phys. 35, 280 (2005), gr-qc/0503057.
[63] and , Phys. Rev. D74, 106001 (2006), astro-ph/0607485.
[64], and , Phys. Rev. D79, 124047 (2009), 0810.5591.
[65], and (2010), 1001.4545.
[66], Class. Quant. Grav. 25, 202001 (2008), 0806.3083.
[67], Phys. Rev. Lett. 103, 180401 (2009), 0909.0944.
[68] and , Astrophys. J. 585, L77 (2003), astro-ph/0301184.
[69] (2004), gr-qc/0402009.
[70], Class. Quant. Grav. 20, 3107 (2003), astro-ph/0302333.
[71], and , Astrophys. J. 591, L87 (2003), astro-ph/0302372.
[72], and , Phys. Rev. Lett. 96, 051301 (2006), gr-qc/0508121.
[73], and , Discreteness and the transmission of light from distant sources, in preparation.
[74], Proceedings of the Royal Society of Edinburgh VI, 94 (1867), http://zapatopi.net/kelvin/papers/on_vortex_atoms.html.
Accessibility standard: Unknown
Accessibility compliance for the PDF of this book is currently unknown
and may be updated in the future.
- 2
- Cited by