Publication: Quantum-gravity and minimum length
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1995-01-20
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World Scientific Publ Co Pte Ltd
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Abstract
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.
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© World Scientific Publ Co Pte Ltd
I am very grateful to Jonathan Halliwell and Max Bañados for fruitful discussions and suggestions and for a critical reading of the manuscript. I also thank Alex Mikovi´c and Roya Mohayaee for useful conversations. The author was supported by a joint fellowship from the Ministerio de Educación y Ciencia (Spain) and the British Council.
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[1] C. J. Isham, gr-qc/9310031, IC-TP/93-94/1 (1993). Prima facie questions in quantum gravity.
[2] V. B. Berestetskiĭ, E. M. Lifshitz and L. P. Pitaevskiĭ, Relativistic Quantum Theory (Pergamon, xford, 1971).
[3] W. Heisenberg, Z. Phys. 110, 251 (1938). The limits of the applicability of quantum theory up to now. [4] T. D. Newton and E. P. Wigner, Rev. Mod. Phys. 21, 400 (1949). Localized states for elementary systems.
[5] J. A. Wheeler, in Relativity, Groups and Topology, eds. B. S. DeWitt and C. DeWitt (Gordon and Breach, London, 1964). Geometrodynamics and the issue of the final state.
[6] M. A. Markov, Preprint P-0187 of the Inst. Nucl. Res., Moscow (1980). On quantum violation of topology in small spatial regions.
[7] M. A. Markov, Preprint P-0208 of the Inst. Nucl. Res., Moscow (1981). On the maximon and the concept of elementary particle.
[8] H.-H. Borzeszkowski and H.-J. Treder, The Meaning of Quantum Gravity (Reidel, Dordrecht, 1988).
[9] T. Padmanabhan, T. R. Seshadri and T. P. Singh, Int. J. Mod. Phys. A1, 486 (1986). Uncertainty principle and the quantum fluctuations of the Schwarzschild light cones.
[10] V. Daftardar and N. Dadhich, Int. J. Mod. Phys. A1, 731 (1986). Uncertainty principle and the quantum fluctuation of the light cones in the static space-times.
[11] Chung-I Kuo and L. H. Ford, Phys. Rev D47, 4510 (1993). Semiclassical gravity theory and quantum fluctuations.
[12] C. A. Mead, Phys. Rev. 135, B849 (1964). Possible connection between gravitation and fundamental length.
[13] N. Itzhaki, Phys. Lett. B328, 274 (1994). Time measurement in quantum gravity.
[14] T. Padmanabhan, Ann. Phys. (NY) 165, 38 (1985). Physical significance of Planck’s length.
[15] T. Padmanabhan, Gen. Rel. Grav. 17, 215 (1985). Planck length as the lower bound to all physical length scales. [16] T. Padmanabhan, Class. Q. Grav. 3, 911 (1986). Role of general relativity in uncertainty principle.
[17] T. Padmanabhan, Class. Q. Grav. 4, L107 (1987). Limitations on the operational defi- nition of space-time events and quantum gravity.
[18] J. Greensite, Phys. Lett. B255, 375 (1991). Is there a minimum length in D = 4 lattice quantum gravity?
[19] J. V. Narlikar and T. Padmanabhan, Phys. Rep. 100, 151 (1983). Quantum cosmology via path integrals.
[20] B. A. Berg, B. Krishnan, M. Katoot, Nucl. Phys. B404, 359 (1993). Asymptotic freedom and Euclidean quantum gravity.
[21] B. A. Berg, B. Krishnan, Phys. Lett. B318, 59 (1993). Phase structure of SU(2) lattice gauge theory with quantum gravity.
[22] G. Feinberg, R. Friedberg, T. D. Lee, H. C. Ren, Nucl. Phys. B245, 343 (1984). Lattice gravity near the continuum limit.
[23] M. Kato, Phys. Lett. B245, 43 (1990). Particle theories with minimum observable length and open string theory. [24] K. Konishi, G. Paffuti and P. Provero, Phys. Lett. B234, 276 (1990). Minimum physical length and the generalized uncertainty principle in string theory.
[25] G. Veneziano, Europhys. Lett. 2, 199 (1986). A stringy nature needs just two constants.
[26] D. Amati, M. Ciafaloni and G. Veneziano, Phys. Lett. B216, 41 (1989). Can spacetime be probed below the string size?
[27] T. Yoneya, Mod. Phys. Lett. A4, 1587 (1989). On the interpretation of minimal length in string theories.
[28] R. Guida, K. Konishi and P. Provero, Mod. Phys. Lett. A6, 1487 (1991). On the short distance behaviour of string theory.
[29] P. F. Mende, hep-th/9210001, Brown-HET-875 (1992). String theory at short distance and the principle of equivalence.
[30] A. Strominger, hep-th/9110011, UCSB-TH-91-41 (1991). Quantum gravity and string theory: what we have learned.
[31] V. P. Nair, A. Shapere, A. Strominger and F. Wilczek, Nucl. Phys. B287, 402 (1987). Compactification of the twisted heterotic string.
[32] R. Brandenberger and L. Vafa, Nucl. Phys. B316, 391 (1989). Superstrings in the early universe.
[33] Y. I. Kogan, JETP Lett. 45, 709 (1987). Vortices on the world sheet and string’s critical dynamics.
[34] Y. I. Kogan, Mod. Phys. Lett. A6, 501 (1991). The R → α ′/R spacetime duality from the 2+1 point of view.
[35] P. S. Aspinwall, B. R. Greene, D. R. Morrison, Nucl. Phys. B420, 184 (1994). Measuring small distances in N = 2 sigma models.
[36] P. S. Aspinwall, hep-th/9404060, IASSNS-HEP-94-19 (1994). Minimum distances in nontrivial string target spaces.
[37] I. Klebanov and L. Susskind, Nucl. Phys. B309, 175 (1988). Continuum string theories from discrete field theories.
[38] D. Gross and P. F. Mende, Phys. Lett. B197, 129 (1987). The high energy behaviour of string scattering amplitudes.
[39] D. Gross and P. F. Mende, Nucl. Phys. B303, 407 (1988). String theory beyond the Planck scale.
[40] J. J. Atick and E. Witten, Nucl. Phys. B310, 291 (1988). The Hagedorn transition and the number of degrees of freedom of string theory.
[41] C. Rovelli and L. Smolin, Phys. Rev. Lett. 61, 1155 (1988). Knot theory and quantum gravity.
[42] C. Rovelli and L. Smolin, Nucl. Phys. B331, 80 (1990). Loop space representation of quantum gravity.
[43] C. Rovelli, Class. Q. Grav. 8, 1613 (1991). Ashtekar formulation of general relativity and loop space nonperturbative quantum gravity: a report.
[44] L. Smolin, in Quantum Gravity and Cosmology, eds. J. Pérez-Mercader et al. (World Scientific, Singapore, 1992). Recent developments in nonperturbative quantum gravity.
[45] C. Rovelli, Class. Q. Grav. 8, 317 (1991). Quantum reference systems.
[46] A. Ashtekar, C. Rovelli and L. Smolin, Phys. Rev. Lett. 69, 237 (1992). Weaving a lassical metric with quantum threads.
[47] C. Rovelli, Nucl. Phys. B405, 797 (1993). A generally covariant quantum field theory and a prediction on quantum measurements of geometry.
[48] J. D. Bekenstein, Lett. Nuovo Cim. 11, 467 (1974). The quantum mass spectrum of the Kerr black hole.
[49] V. F. Mukhanov, JETP Lett. 44, 63 (1986). Are black holes quantized?
[50] Y. I. Kogan, JETP Lett. 44, 267 (1986). Quantization of the black hole mass in string theory.
[51] J. GarcÃa-Bellido, hep-th/9302127, SU-ITP-93-4, IEM-FT-68/93 (1993). Quantum black holes.
[52] Y. Peleg, hep-th/9307057, BRX-TH-350 (1993). Quantum dust holes. A statistical mechanics derivation of black hole thermodynamics.
[53] M. Maggiore, Phys. Lett. B304, 65 (1993). A generalized uncertainty principle in quantum gravity.
[54] J. Preskill, P. Schwarz, A. Shapere, S. Trivedi and F. Wilczek, Mod. Phys. Lett. A6, 2353 (1991). Limitations on the statistical description of black holes.
[55] S. Deser, Rev. Mod. Phys. 29, 417 (1957). General relativity and the divergence problem in quantum field theory.
[56] T. D. Lee, Phys. Lett. B122, 217 (1983). Can time be a discrete variable?
[57] T. Padmanabhan, Phys. Rev. Lett. 60, 2229 (1988). Acceptable density perturbations from inflation due to quantum gravitational damping.
[58] C. A. Mead, Phys. Rev. 143, 990 (1966). Observable consequences of fundamental length hypotheses.
[59] P. F. González-DÃaz, Lett. Nuovo Cim. 41, 481 (1984). Small-distance derivatives.
[60] P. K. Townsend, Phys. Rev. D15, 2795 (1977). Small-scale structure of spacetime as the origin of the gravitational constant.
[61] M. Maggiore, Phys. Rev. D49, 5182 (1993). Quantum groups, gravity and the generalized uncertainty principle.
[62] M. Maggiore, Phys. Lett. B319, 83 (1993). The algebraic structure of the generalized uncertainty principle.
[63] A. Kempf, hep-th/9311147, DAMTP-93-65 (1993). Uncertainty relation in quantum mechanics with group symmetry.
[64] A. Kempf, S. Majid, hep-th/9405067, DAMTP-94-33 (1994). Quantum field theory with non-zero minimal uncertainties in positions and momenta.
[65] N. Bohr and L. Rosenfeld, Det. Kgl. Danske Videnskabernes Selskab., Math.-fys. Medd. 12, 8 (1933); in Selected Papers of León Rosenfeld, eds. Cohen and Stachel (Reidel, Dordrecht, 1979); in Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1983). On the question of measurability of electromagnetic field quantities.
[66] L. Rosenfeld, Nucl. Phys. 40, 353 (1963). On quantization of fields.
[67] N. Bohr and L. Rosenfeld, Phys. Rev. D78, 794 (1950). Field and charge measurements in quantum electrodynamics.
[68] L. Rosenfeld, in Niels Bohr and the Development of Physics, ed. W. Pauli (Pergamon, London, 1955). On quantum electrodynamics.
[69] W. Heitler, The Quantum Theory of Radiation (Oxford University Press, New York, 3rd ed., 1954).
[70] A. Peres and N. Rosen, Phys. Rev. 118, 335 (1960). Quantum limitations on the measurements of the gravitational field.
[71] B. S. DeWitt, in Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, New York, 1962). The quantization of gravity.
[72] T. Regge, Nuovo Cim. 7, 215 (1958). Gravitational fields and quantum mechanics.
[73] H.-H. Borzeszkowski and H.-J. Treder, Found. Phys. 12, 1113 (1982). Quantum theory and Einstein’s general relativity.
[74] H.-J. Treder, Found. Phys. 15, 161 (1985). The Planckions as the largest elementary particles and the smallest test bodies.
[75] L. Landau and R. Peierls, Z. Phys. 69, 56 (1931); in Collected Papers of Landau, ed. D. ter Haar (Gordon and Breach, New York, 1965); in Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1983). Extension of the uncertainty principle to the relativistic quantum theory.
[76] M. B. Mensky, Phys. Lett. A155, 229 (1991). The action uncertainty principle in continuous quantum measurements.
[77] M. B. Mensky, Phys. Lett. A162, 219 (1992). The action uncertainty principle and quantum gravity.
[78] J. J. Halliwell, Phys. Rev. D48, 4785 (1993). Quantum mechanical histories and the uncertainty principle II. Fluctuations about classical predictability.
[79] L. Susskind, Phys. Rev. Lett. 71, 2368 (1993). String theory and the principle of black hole complementarity.
[80] L. Susskind, Phys. Rev. D49, 6606 (1994). Strings, black holes and Lorentz contraction.
[81] M. Maggiore, Phys. Rev. D49, 2918 (1994). Black hole complementarity and the physical origin of the stretched horizon.
[82] T. Jacobson, Phys. Rev. D44, 1731 (1991). Black-hole evaporation and ultrashort distances.
[83] L. Susskind, L. Thorlacius and J. Uglum, Phys. Rev. D48, 3743 (1993). The stretched horizon and black hole complementarity.
[84] L. Susskind and L. Thorlacius, Phys. Rev. D49, 966 (1994). Gedanken experiments involving black holes.
[85] G. ’t Hooft, Nucl. Phys. B256, 727 (1985). On the quantum structure of a black hole.
[86] G. ’t Hooft, Nucl. Phys. B335, 138 (1990). The black hole interpretation of strings.
[87] J. J. Halliwell, in Quantum Cosmology and Baby Universes, eds. S. Coleman et al. (World Scientific, Singapore, 1990). Introductory lectures on quantum cosmology.
[88] J. A. Wheeler, Ann. Phys. 2, 604 (1957). On the nature of quantum geometrodynamics.
[89] J. A. Wheeler, Geometrodynamics (Ac. Press, London, 1962).
[90] S. W. Hawking, Nucl. Phys. B144, 349 (1978). Spacetime foam.
[91] S. W. Hawking, Phys. Rev. D37, 904 (1988). Wormholes in spacetime.
[92] S. W. Hawking, Mod. Phys. Lett. A5, 145 (1990). Baby universes.
[93] S. W. Hawking, Mod. Phys. Lett. A5, 453 (1990). Baby universes II.
[94] A. Strominger, in Particles, Strings and Supernovae, eds. A. Jevicki and C. I. Tan (World Scientific, Singapore, 1989). Baby universes.
[95] S. W. Hawking and D.N. Page, Phys. Rev. D42, 2655 (1990). Spectrum of wormholes.
[96] L. J. Garay, Phys. Rev. D44, 1059 (1991). Quantum state of wormholes and path integral.
[97] L. J. Garay, Phys. Rev. D48, 1710 (1993). Hilbert space of wormholes.
[98] S. W. Hawking, in General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel, (Cambridge University Press, Cambridge, 1979). The path integral approach to quantum gravity.
[99] S. Coleman, Nucl. Phys. B310, 643 (1988). Why there is nothing rather than something: a theory of the cosmological constant.
[100] I. Klebanov, L. Susskind and T. Banks, Nucl. Phys. B317, 665 (1989). Wormholes and the cosmological constant.
[101] J. Preskill, Nucl. Phys. B323, 141 (1989). Wormholes in spacetime and the constants of nature.