What We Don’t Know About Time

Abstract

String theory has transformed our understanding of geometry, topology and space-time. Thus, for this special issue of Foundations of Physics commemorating “Forty Years of String Theory”, it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.

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References

  1. 1.

    Hawking, S.W.: The Chronology protection conjecture. Phys. Rev. D 46, 603–611 (1992)

    MathSciNet  ADS  Article  Google Scholar 

  2. 2.

    Hawking, S.W.: Quantum coherence and closed timelike curves. Phys. Rev. D 52, 5681–5686 (1995). arXiv:gr-qc/9502017

    MathSciNet  ADS  Article  Google Scholar 

  3. 3.

    Carroll, S.M., Chen, J.: Spontaneous inflation and the origin of the arrow of time. arXiv:hep-th/0410270

  4. 4.

    Price, H.: Cosmology, time’s arrow, and that old double standard. arXiv:gr-qc/9310022

  5. 5.

    Albrecht, A.: Cosmic inflation and the arrow of time. In: Barrow, J.D., et al. (ed.) Science and ultimate reality, pp. 363–401 (2002). arXiv:astro-ph/0210527

    Google Scholar 

  6. 6.

    Witten, E.: Perturbative gauge theory as a string theory in twistor space. Commun. Math. Phys. 252, 189–258 (2004). arXiv:hep-th/0312171

    MathSciNet  ADS  MATH  Article  Google Scholar 

  7. 7.

    Bars, I.: Survey of two time physics. Class. Quantum Gravity 18, 3113–3130 (2001). arXiv:hep-th/0008164

    MathSciNet  ADS  MATH  Article  Google Scholar 

  8. 8.

    Hull, C.M.: Timelike T duality, de Sitter space, large N gauge theories and topological field theory. J. High Energy Phys. 9807, 021 (1998). arXiv:hep-th/9806146

    MathSciNet  ADS  Article  Google Scholar 

  9. 9.

    Hull, C.M., Khuri, R.R.: Branes, times and dualities. Nucl. Phys. B 536, 219–244 (1998). arXiv:hep-th/9808069

    MathSciNet  ADS  Article  Google Scholar 

  10. 10.

    Hull, C.M.: Duality and the signature of space-time. J. High Energy Phys. 9811, 017 (1998). arXiv:hep-th/9807127

    MathSciNet  ADS  Article  Google Scholar 

  11. 11.

    Britto, R., Cachazo, F., Feng, B., Witten, E.: Direct proof of tree-level recursion relation in Yang-Mills theory. Phys. Rev. Lett. 94, 181602 (2005). arXiv:hep-th/0501052

    MathSciNet  ADS  Article  Google Scholar 

  12. 12.

    Kraus, P., Ooguri, H., Shenker, S.: Inside the horizon with AdS/CFT. Phys. Rev. D 67, 124022 (2003). arXiv:hep-th/0212277

    MathSciNet  ADS  Article  Google Scholar 

  13. 13.

    Fidkowski, L., Hubeny, V., Kleban, M., Shenker, S.: The black hole singularity in AdS/CFT. J. High Energy Phys. 0402, 014 (2004). arXiv:hep-th/0306170

    MathSciNet  ADS  Article  Google Scholar 

  14. 14.

    Levi, T.S., Ross, S.F.: Holography beyond the horizon and cosmic censorship. Phys. Rev. D 68, 044005 (2003). arXiv:hep-th/0304150

    MathSciNet  ADS  Article  Google Scholar 

  15. 15.

    Balasubramanian, V., Levi, T.S.: Beyond the veil: inner horizon instability and holography. Phys. Rev. D 70, 106005 (2004). arXiv:hep-th/0405048

    MathSciNet  ADS  Article  Google Scholar 

  16. 16.

    Bena, I., Bobev, N., Giusto, S., Ruef, C., Warner, N.P.: An infinite-dimensional family of black-hole microstate geometries. J. High Energy Phys. 1103, 022 (2011). arXiv:1006.3497 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  17. 17.

    Bena, I., Warner, N.P.: Bubbling supertubes and foaming black holes. Phys. Rev. D 74, 066001 (2006). arXiv:hep-th/0505166

    MathSciNet  ADS  Article  Google Scholar 

  18. 18.

    Berglund, P., Gimon, E.G., Levi, T.S.: Supergravity microstates for BPS black holes and black rings. J. High Energy Phys. 0606, 007 (2006). arXiv:hep-th/0505167

    MathSciNet  ADS  Article  Google Scholar 

  19. 19.

    Gimon, E.G., Larsen, F., Simon, J.: Black holes in supergravity: the Non-BPS branch. J. High Energy Phys. 0801, 040 (2008). arXiv:0710.4967 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  20. 20.

    Lunin, O., Mathur, S.D.: Metric of the multiply wound rotating string. Nucl. Phys. B 610, 49–76 (2001). arXiv:hep-th/0105136

    MathSciNet  ADS  MATH  Article  Google Scholar 

  21. 21.

    Peet, A.W.: TASI lectures on black holes in string theory. arXiv:hep-th/0008241 and references therein

  22. 22.

    Johnson, C.V., Peet, A.W., Polchinski, J.: Gauge theory and the excision of repulson singularities. Phys. Rev. D 61, 086001 (2000). arXiv:hep-th/9911161

    MathSciNet  ADS  Article  Google Scholar 

  23. 23.

    Lin, H., Lunin, O., Maldacena, J.M.: Bubbling AdS space and 1/2 BPS geometries. J. High Energy Phys. 0410, 025 (2004). arXiv:hep-th/0409174

    MathSciNet  ADS  Article  Google Scholar 

  24. 24.

    Strominger, A.: Massless black holes and conifolds in string theory. Nucl. Phys. B 451, 96–108 (1995). arXiv:hep-th/9504090

    MathSciNet  ADS  MATH  Article  Google Scholar 

  25. 25.

    Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Commun. Math. Phys. 31, 161–170 (1973)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  26. 26.

    Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973)

    MathSciNet  ADS  Article  Google Scholar 

  27. 27.

    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975)

    MathSciNet  ADS  Article  Google Scholar 

  28. 28.

    Strominger, A., Vafa, C.: Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 379, 99–104 (1996). arXiv:hep-th/9601029

    MathSciNet  ADS  Article  Google Scholar 

  29. 29.

    Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460–2473 (1976)

    MathSciNet  ADS  Article  Google Scholar 

  30. 30.

    Balasubramanian, V., Czech, B.: Quantitative approaches to information recovery from black holes. Class. Quantum Gravity 28, 163001 (2011). arXiv:1102.3566 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  31. 31.

    Mathur, S.D.: Fuzzballs and the information paradox: a summary and conjectures. arXiv:0810.4525 [hep-th]

  32. 32.

    Mathur, S.D.: The Fuzzball proposal for black holes: an elementary review. Fortschr. Phys. 53, 793–827 (2005). arXiv:hep-th/0502050

    MathSciNet  MATH  Article  Google Scholar 

  33. 33.

    Balasubramanian, V., Marolf, D., Rozali, M.: Information recovery from black holes. Gen. Relativ. Gravit. 38, 1529–1536 (2006). arXiv:hep-th/0604045

    MathSciNet  ADS  MATH  Article  Google Scholar 

  34. 34.

    Balasubramanian, V., Czech, B., Hubeny, V.E., Larjo, K., Rangamani, M., Simon, J.: Typicality versus thermality: an analytic distinction. Gen. Relativ. Gravit. 40, 1863–1890 (2008). arXiv:hep-th/0701122

    MathSciNet  ADS  MATH  Article  Google Scholar 

  35. 35.

    Horowitz, G., Lawrence, A., Silverstein, E.: Insightful D-branes. J. High Energy Phys. 0907, 057 (2009). arXiv:0904.3922 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  36. 36.

    Balasubramanian, V., de Boer, J., Jejjala, V., Simon, J.: The library of Babel: on the origin of gravitational thermodynamics. J. High Energy Phys. 0512, 006 (2005). arXiv:hep-th/0508023

    ADS  Google Scholar 

  37. 37.

    Balasubramanian, V., Czech, B., Larjo, K., Marolf, D., Simon, J.: Quantum geometry and gravitational entropy. J. High Energy Phys. 0712, 067 (2007). arXiv:0705.4431 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  38. 38.

    Susskind, L.: String theory and the principles of black hole complementarity. Phys. Rev. Lett. 71, 2367–2368 (1993). arXiv:hep-th/9307168

    MathSciNet  ADS  MATH  Article  Google Scholar 

  39. 39.

    Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998). arXiv:hep-th/9711200

    MathSciNet  ADS  MATH  Google Scholar 

  40. 40.

    Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105–114 (1998). arXiv:hep-th/9802109

    MathSciNet  ADS  Article  Google Scholar 

  41. 41.

    Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998). arXiv:hep-th/9802150

    MathSciNet  ADS  MATH  Google Scholar 

  42. 42.

    Balasubramanian, V., Kraus, P.: Space-time and the holographic renormalization group. Phys. Rev. Lett. 83, 3605–3608 (1999). arXiv:hep-th/9903190

    MathSciNet  ADS  MATH  Article  Google Scholar 

  43. 43.

    Henningson, M., Skenderis, K.: The holographic Weyl anomaly. J. High Energy Phys. 9807, 023 (1998). arXiv:hep-th/9806087

    MathSciNet  ADS  Article  Google Scholar 

  44. 44.

    Skenderis, K.: Lecture notes on holographic renormalization. Class. Quantum Gravity 19, 5849–5876 (2002). arXiv:hep-th/0209067

    MathSciNet  MATH  Article  Google Scholar 

  45. 45.

    de Boer, J., Verlinde, E.P., Verlinde, H.L.: On the holographic renormalization group. J. High Energy Phys. 0008, 003 (2000). arXiv:hep-th/9912012

    Article  Google Scholar 

  46. 46.

    Banks, T., Fischler, W., Shenker, S.H., Susskind, L.: M theory as a matrix model: a conjecture. Phys. Rev. D 55, 5112–5128 (1997). arXiv:hep-th/9610043

    MathSciNet  ADS  Article  Google Scholar 

  47. 47.

    Van Raamsdonk, M.: Building up space-time with quantum entanglement. Gen. Relativ. Gravit. 42, 2323–2329 (2010). arXiv:1005.3035 [hep-th]

    ADS  MATH  Article  Google Scholar 

  48. 48.

    Van Raamsdonk, M.: Comments on quantum gravity and entanglement. arXiv:0907.2939 [hep-th]

  49. 49.

    Jacobson, T.: Thermodynamics of space-time: the Einstein equation of state. Phys. Rev. Lett. 75, 1260–1263 (1995). arXiv:gr-qc/9504004

    MathSciNet  ADS  MATH  Article  Google Scholar 

  50. 50.

    Verlinde, E.P.: On the origin of gravity and the laws of Newton. J. High Energy Phys. 1104, 029 (2011). arXiv:1001.0785 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  51. 51.

    Bombelli, L., Lee, J., Meyer, D., Sorkin, R.: Space-time as a causal set. Phys. Rev. Lett. 59, 521–524 (1987)

    MathSciNet  ADS  Article  Google Scholar 

  52. 52.

    Konopka, T., Markopoulou, F., Smolin, L.: Quantum gravity. arXiv:hep-th/0611197

  53. 53.

    Konopka, T., Markopoulou, F., Severini, S.: Quantum gravity: a model of emergent locality. Phys. Rev. D 77, 104029 (2008). arXiv:0801.0861 [hep-th]

    MathSciNet  ADS  Article  Google Scholar 

  54. 54.

    Balasubramanian, V., Kraus, P., Lawrence, A.E.: Bulk versus boundary dynamics in anti-de Sitter space-time. Phys. Rev. D 59, 046003 (1999). arXiv:hep-th/9805171

    MathSciNet  ADS  Article  Google Scholar 

  55. 55.

    Balasubramanian, V., Kraus, P., Lawrence, A.E., Trivedi, S.P.: Holographic probes of anti-de Sitter space-times. Phys. Rev. D 59, 104021 (1999). arXiv:hep-th/9808017

    MathSciNet  ADS  Article  Google Scholar 

  56. 56.

    Balasubramanian, V., Kraus, P.: A stress tensor for anti-de Sitter gravity. Commun. Math. Phys. 208, 413–428 (1999). arXiv:hep-th/9902121

    MathSciNet  ADS  MATH  Article  Google Scholar 

  57. 57.

    Balasubramanian, V., Gopakumar, R., Larsen, F.: Gauge theory, geometry and the large N limit. Nucl. Phys. B 526, 415–431 (1998). arXiv:hep-th/9712077

    MathSciNet  ADS  MATH  Article  Google Scholar 

  58. 58.

    Polchinski, J.: M theory and the light cone. Prog. Theor. Phys. Suppl. 134, 158–170 (1999). arXiv:hep-th/9903165

    MathSciNet  ADS  Article  Google Scholar 

  59. 59.

    Strominger, A.: The dS/CFT correspondence. J. High Energy Phys. 0110, 034 (2001). arXiv:hep-th/0106113

    MathSciNet  ADS  Article  Google Scholar 

  60. 60.

    Balasubramanian, V., de Boer, J., Minic, D.: Mass, entropy and holography in asymptotically de Sitter spaces. Phys. Rev. D 65, 123508 (2002). arXiv:hep-th/0110108

    MathSciNet  ADS  Article  Google Scholar 

  61. 61.

    Balasubramanian, V., de Boer, J., Minic, D.: Notes on de Sitter space and holography. Class. Quantum Gravity 19, 5655–5700 (2002). arXiv:hep-th/0207245

    MATH  Article  Google Scholar 

  62. 62.

    Bousso, R., Maloney, A., Strominger, A.: Conformal vacua and entropy in de Sitter space. Phys. Rev. D 65, 104039 (2002). arXiv:hep-th/0112218

    MathSciNet  ADS  Article  Google Scholar 

  63. 63.

    Polchinski, J.: Dirichlet branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724–4727 (1995). arXiv:hep-th/9510017

    MathSciNet  ADS  MATH  Article  Google Scholar 

  64. 64.

    Gutperle, M., Strominger, A.: Space-like branes. J. High Energy Phys. 0204, 018 (2002). arXiv:hep-th/0202210

    MathSciNet  ADS  Article  Google Scholar 

  65. 65.

    Jones, G., Maloney, A., Strominger, A.: Nonsingular solutions for S-branes. Phys. Rev. D 69, 126008 (2004). arXiv:hep-th/0403050

    MathSciNet  ADS  Article  Google Scholar 

  66. 66.

    Sen, A.: Rolling tachyon. J. High Energy Phys. 0204, 048 (2002). arXiv:hep-th/0203211

    ADS  Article  Google Scholar 

  67. 67.

    Larsen, F., Naqvi, A., Terashima, S.: Rolling tachyons and decaying branes. J. High Energy Phys. 0302, 039 (2003). arXiv:hep-th/0212248

    MathSciNet  ADS  Article  Google Scholar 

  68. 68.

    Lambert, N.D., Liu, H., Maldacena, J.M.: Closed strings from decaying D-branes. J. High Energy Phys. 0703, 014 (2007). arXiv:hep-th/0303139

    MathSciNet  ADS  Article  Google Scholar 

  69. 69.

    Gaiotto, D., Itzhaki, N., Rastelli, L.: Closed strings as imaginary D-branes. Nucl. Phys. B 688, 70–100 (2004). arXiv:hep-th/0304192

    MathSciNet  ADS  MATH  Article  Google Scholar 

  70. 70.

    Balasubramanian, V., Keski-Vakkuri, E., Kraus, P., Naqvi, A.: String scattering from decaying branes. Commun. Math. Phys. 257, 363–394 (2005). arXiv:hep-th/0404039

    MathSciNet  ADS  MATH  Article  Google Scholar 

  71. 71.

    Balasubramanian, V., Jokela, N., Keski-Vakkuri, E., Majumder, J.: A thermodynamic interpretation of time for rolling tachyons. Phys. Rev. D 75, 063515 (2007). arXiv:hep-th/0612090

    ADS  Article  Google Scholar 

  72. 72.

    Czech, B., Rozali, M., Balasubramanian, V.: In progress

  73. 73.

    Witten, E.: Instability of the Kaluza-Klein vacuum. Nucl. Phys. B 195, 481 (1982)

    ADS  Article  Google Scholar 

  74. 74.

    Balasubramanian, V., Ross, S.F.: The dual of nothing. Phys. Rev. D 66, 086002 (2002). arXiv:hep-th/0205290

    MathSciNet  ADS  Article  Google Scholar 

  75. 75.

    Balasubramanian, V., Larjo, K., Simon, J.: Much ado about nothing. Class. Quantum Gravity 22, 4149–4170 (2005). arXiv:hep-th/0502111

    MathSciNet  ADS  MATH  Article  Google Scholar 

  76. 76.

    Banados, M., Gomberoff, A., Martinez, C.: Anti-de Sitter space and black holes. Class. Quantum Gravity 15, 3575–3598 (1998). arXiv:hep-th/9805087

    MathSciNet  ADS  MATH  Article  Google Scholar 

  77. 77.

    He, J., Rozali, M.: On bubbles of nothing in AdS/CFT. J. High Energy Phys. 0709, 089 (2007). arXiv:hep-th/0703220 [HEP-TH]

    MathSciNet  ADS  Article  Google Scholar 

  78. 78.

    Horowitz, G.T., Silverstein, E.: The inside story: quasilocal tachyons and black holes. Phys. Rev. D 73, 064016 (2006). arXiv:hep-th/0601032

    MathSciNet  ADS  Article  Google Scholar 

  79. 79.

    Khoury, J., Ovrut, B.A., Steinhardt, P.J., Turok, N.: The ekpyrotic universe: colliding branes and the origin of the hot big bang. Phys. Rev. D 64, 123522 (2001). arXiv:hep-th/0103239

    MathSciNet  ADS  Article  Google Scholar 

  80. 80.

    Balasubramanian, V., Ross, S.F.: Holographic particle detection. Phys. Rev. D 61, 044007 (2000). arXiv:hep-th/9906226

    MathSciNet  ADS  Article  Google Scholar 

  81. 81.

    Liu, H., Moore, G.W., Seiberg, N.: Strings in a time dependent orbifold. J. High Energy Phys. 0206, 045 (2002). arXiv:hep-th/0204168

    MathSciNet  ADS  Article  Google Scholar 

  82. 82.

    Simon, J.: The geometry of null rotation identifications. J. High Energy Phys. 0206, 001 (2002). arXiv:hep-th/0203201

    ADS  Article  Google Scholar 

  83. 83.

    Craps, B., Sethi, S., Verlinde, E.P.: A matrix big bang. J. High Energy Phys. 0510, 005 (2005). arXiv:hep-th/0506180

    MathSciNet  ADS  Article  Google Scholar 

  84. 84.

    Craps, B., Evnin, O.: Light-like big bang singularities in string and matrix theories. arXiv:1103.5911 [hep-th], to appear in Class. Quant. Gravity

  85. 85.

    Carroll, S.M.: What if time really exists? arXiv:0811.3772 [gr-qc]

  86. 86.

    Markopoulou, F.: Space does not exist, so time can. arXiv:0909.1861 [gr-qc]

  87. 87.

    Rovelli, C.: Forget time. arXiv:0903.3832 [gr-qc]

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Correspondence to Vijay Balasubramanian.

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Balasubramanian, V. What We Don’t Know About Time. Found Phys 43, 101–114 (2013). https://doi.org/10.1007/s10701-011-9591-y

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Keywords

  • String theory
  • Time