Il Nuovo Cimento B (1971-1996)

, Volume 110, Issue 1, pp 81–93 | Cite as

Analysis of the distinct meanings of the notion of «time», in different physical theories

  • C. Rovelli


Problems concerning the concept of time have recently generated a widespread interest. Among these: the role of time in quantum gravity, the choice of an internal time in general relativity, the origin of the «arrow of time», and the time asymmetry in cosmology. These problems often pertain to distinct aspects of the notion of time; unfortunately, however, the use of identical terms for different issues leads often to a confused discussion, and the complexity of the problem of understanding or altering a notion as the notion of time is perhaps underestimated. Here, we analyze the distinct roles that this notion plays in different theories: We find ten distinct versions of the concept of time, all used in the natural sciences, characterized by different properties, or attributes, ascribed to time. We propose a general terminology to express these differences. In addition, we observe that the different notions of time are hierarchically arranged, in the sense that complex attributes of time become necessary only in dealing with progressively more special natural systems, and we derive from this observation some speculations on the significance of the notion of time at the fundamental level.


04.20 General relativity 


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  1. [1]
    Reichenbach H.,The Direction of Time (University of California Press, Berkeley, Cal.) 1956;Davies P. C. W.,The Physics of Time Asymmetry (Surrey University Press) 1974;Penrose R., inGeneral Relativity: An Einstein Centenary Survey, edited byS. W. Hawking andW. Israel (Cambridge University Press, Cambridge) 1979;Hawking S. W.,Phys. Rev. D,32 (1985) 2489.Zee H. D.,The Physical Basis of the Direction of Time (Springer, Berlin) 1989. See also the different contributions to theProceedings of the International Workshop: Physical Origins of Time Asymmetry, Huelva, Spain, September 1991, edited byJ. Halliwel andJ. A. Perez-Mercader (Cambridge University Press, Cambridge) 1992.Google Scholar
  2. [2]
    Isham C. J.,Canonical Quantum Gravity and the Problem of Time, Lectures presented at the NATO Advanced Institute:Recent Problems in Mathematical Physics, Salamanca June 15, 1992, Imperial College preprint, Imperial/TP/91-92/25, and references therein;Kuchar K.,Time and interpretations of quantum gravity, inProceedings of the IV Canadian Conference on General Relativity and Relativistic Astrophysics, edited byG. Kunstatter, D. Vincent andJ. Williams (World Scientific, Singapore) 1992 and references therein.Google Scholar
  3. [3]
    DeWitt B. S.,Phys. Rev.,160 (1967) 1113;Wheeler J. A., inBattelle Rencontres 1967, edited byC. DeWitt andJ. A. Wheeler (Benjamin, New York, N.Y.) 1968;Peres A.,Am. J. Phys.,48 (1980) 552;Page D. N. andWootters W. K.,Phys. Rev. D,27 (1982) 2885;Banks T.,Nucl. Phys. B,249 (1985) 332;Zeh H. D.,Phys. Lett. A,116 (1986) 9;Singh T. P. andPadmanabham T.,Ann. Phys. (N.Y.),196 (1989) 296;Carlip S.,Phys. Rev. D,42 (1993) 2647; see also the different contributions to:Proceedings of the Osgood Hill Conference on Conceptual Problems in Quantum Gravity, Boston 1988, edited byA Ashtekar andJ. Stachel (Birkhauser, Boston) 1993.CrossRefADSzbMATHGoogle Scholar
  4. [4]
    Rovelli C.,Phys. Rev. D,42 (1991) 2638;43 (1991) 442; inProceedings of the Osgood Hill Conference on Conceptual Problems in Quantum Gravity, Boston 1988, edited by A.Ashtekar andJ. Stachel (Birkhauser, Boston) 1993;Anderson A.,The global problem of time, Mc Gill University preprint 92-15, 1992.CrossRefADSGoogle Scholar
  5. [5]
    See, for instance,Barbour J., talk at the Center for Philosophy of Science, Pittsburgh, Penn., 1992;Smolin L.,Time structure and evolution in cosmology, Syracuse University preprint, 1992.Google Scholar
  6. [6]
    Hajicek P.,Phys. Rev. D,34 (1986) 1040;Class. Quantum Grav.,7 (1990) 871;Lecture Notes in Quantum Cosmology (University of Bern, Bern) 1990;Wald R. M.,A proposal for solving the problem of time in canonical quantum gravity, University of Chicago preprint (no date);Ashtekar A.,Lectures on Non-perturbative Quantum Gravity (Birkhauser, Boston, Mass.) 1991.MathSciNetCrossRefADSGoogle Scholar
  7. [7]
    Wald R. M.,Phys. Rev. D,21 (1980) 2742;Hawking S. W.,Commun. Math. Phys.,87 (1982) 395;Hartle J. B. andHawking S. W.,Phys. Rev. D,28 (1983) 2960;Page Don. N.,Phys. Rev. D,34 (1986) 2267;Barbour J. B.,Leibnizian time, Machian dynamics and quantum gravity, inQuantum Concepts in Space and Time, edited byC. J. Isham andR. Penrose (Cambridge University Press, Cambridge) 1986;Halliwell J. J.,Phys. Rev. D,36 (1987) 3626;Unruh W. G.,Time and quantum gravity, unpublished notes (1988);Barbour J. B. andSmolin L.,Can quantum mechanics be sensibly applied to the universe as a whole?, Yale preprint, April 1988;Sorkin R.,On the role of time in the sum over histories framework for gravity, Syracuse preprint, 1988;Hartle J. B.Quantum kinematics of spacetime, Santa Barbara University preprint UCSBTH-87-79;Phys. Rev. D,37 (1988) 2818;Sorkin R.,On the role of time in the sum-over-histories framework for quantum gravity, Syracuse University report (1988);Padmanabhan T.,Int. J. Mod. Phys. A,4 (1989) 4735;Singh T. P. andPadmanabhan T.,Ann. Phys. (N.Y.),196 (1989) 296;Gibbons G. W.,Complex numbers, quantum mechanics and the beginning of time, UCSBTH preprint 93-03, 1993. See also the books:Grunbaum A.,Philosophical Problems of Space and time (Knopf, New York, N.Y.) 1963;The Nature of Time, edited byT. Gold andD. L. Shumacher (Cornell University Press, Ithaca, N.Y.) 1967;Kroes P.,Time: its Structure and Role in Physical Theories (D. Reidel) 1985.MathSciNetCrossRefADSGoogle Scholar
  8. [8]
    Fraser J. T.,Of Time, Passion, and Knowledge (Princeton University Press, Princeton, NJ) 1990.Google Scholar
  9. [9]
    Rovelli C.,Class. Quantum Grav.,8 (1991) 297, 317.MathSciNetCrossRefADSGoogle Scholar
  10. [10]
    Rovelli C.,Class. Quantum Grav.,10 (1993) 1549, 1567.MathSciNetCrossRefADSzbMATHGoogle Scholar
  11. [11]
    For a review of the present-status quantum gravity seeIsham C. J.,Conceptual and geometrical problems in quantum gravity, inRecent Aspects of Quantum Fields, edited byH. Mitter andH. Gausterer (Springer-Verlag, Berlin) 1991, p. 123;Rovelli C.,Class. Quantum Grav.,8 (1991) 1613.CrossRefGoogle Scholar
  12. [12]
    Hartle J.,Phys. Scr.,36 (1991) 228.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Wheeler J., seminar at theSaratosa Meeting on Foundational Problems in Theoretical Physics, Saratosa, Fla., 1992.Google Scholar
  14. [14]
    Eddington A. S.,The Nature of the Physical World (MacMillan, New York, N.Y.) 1930, pp. 99–102.Google Scholar
  15. [15]
    Barbour J. andBertotti B.,Proc. R. Soc. London, Ser. A,382 (1982) 295.MathSciNetCrossRefADSzbMATHGoogle Scholar
  16. [16]
    Earman J.,A Primer on Determinism (D. Reidel, Dordrecht) 1986.CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1995

Authors and Affiliations

  • C. Rovelli
    • 1
    • 2
    • 3
  1. 1.Physics DepartmentUniversity of PittsburghPittsburghUSA
  2. 2.Dipartimento di Fisica dell’UniversitàTrentoItaly
  3. 3.Sezione di PadovaINFNPadovaItaly

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