Abstract
The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta ofevents as its fundamental description. The evolution of the events, as functions of a universal invariant world, or historical, time, traces out the world lines that represent the phenomena (e.g., particles) which are observed in the laboratory. The positions in time of each of the events, i.e., the time of their potential detection, are, in this framework, controlled by this universal parameter τ, the time at which they are generated (and may proceed in the positive or negative sense). We find that the notion of thestate of a system requires generalization; at any given τ, it involves information about the system at timest(τ) ≠ τ. The correlation of what may be measured att(τ) with what is generated at τ is necessarily quite rigid, and is related covariantly to the spacelike correlations found in interference experiments. We find, furthermore, that interaction with Maxwell electromagnetism leads back to a static picture of the world, with no real evolution. As a consequence of this result, and the requirement of gauge invariance for the quantum mechanical evolution equation, we conclude that electromagnetism is described by a pre-Maxwell field, whose τ-integral (or asymptotic behavior as τ → ∞) may be identified with the Maxwell field. We therefore consider the world of events in space time, interacting through τ-dependent pre-Maxwell fields, as far as electrodynamics is concerned, as the objective dynamical reality. Our perception of the world, through laboratory detectors and our eyes, are based onintegration over τ over intervals sufficiently large to obtain an aposteriori description of the phenomena which coincides with the Maxwell theory. Fundamental notions, such as the conservation of charge, rest on this construction. The decomposition of the common notion of time into two essentially different aspects, one associated with an unvarying flow, and the second with direct observation subject to dynamical modification, has profound philosophical consequences, of which we are able to explore here only a few.
Similar content being viewed by others
References
J. R. Fanchi,Phys. Rev. A 34, 4859 (1987).
R. Landauer,Found. Phys. 16, 551 (1987); R. P. Feynman,Found. Phys. 16, 507 (1987).
Quoted in I. Prigogine,From Being to Becoming: Time and Complexity in the Physical Sciences (W. H. Freeman, San Francisco, 1980).
P. C. W. Davies,The Physics of Time-Asymmetry (Surrey University Press, London, 1974).
E. M. Zemach,Phil. Stud. 23, 68 (1972);Analysis 39, 143 (1979).
H. P. Stapp,Found. Phys. 12, 363 (1982). See also, R. Penrose, “Singularities and time asymmetry,” in S. W. Hawking and W. Israel, eds.,General Relativity: An Einstein Centenary Survey (Cambridge University Press, Cambridge, 1979), p. 581; G. J. Whitrow,The Natural Philosophy of Time (Clarendon Press, Oxford, 1980).
J. Géhénniau and I. Prigogine,Found. Phys. 16, 437 (1986).
G. J. Whitrow,The Natural Philosophy of Time (The Clarendon Press, Oxford, 1980).
D. Papineau,Brit. J. Phil. Sci. 36, 273 (1985).
H. P. Stapp, ——loc. cit.
L. P. Horwitz and C. Piron,Helv. Phys. Acta 46, 316 (1973). See also, J. R. Fanchi and R. E. Collins,Found. Phys. 8, 851 (1978), and Ref. 34 for references to more recent work.
I. Newton, as translated by Andrew Motte (1729), quoted in Max Born,Einstein's Theory of Relativity (Dover, New York, 1962), p. 57.
S. Weinberg,Gravitation and Cosmology (Wiley, New York, 1972).
F. Reuse,Found. Phys. 9, 865 (1979);Helv. Phys. Acta 53, 416 (1980).
P. G. Bergmann,Introduction to the Theory of Relativity (Prentice-Hall, New York, 1942).
E. C. G. Stueckelberg,Helv. Phys. Acta 14, 372, 588 (1941).
V. A. Fock,Phys. Z. Sowjetunion 12, 404 (1937).
R. P. Feynman,Phys. Rev. 80, 440 (1950). L. P. Horwitz and C. Piron,loc. cit., formulated the theory for more than one body.
For example, C. Møller,The Theory of Relativity (The Clarendom Press, Oxford, 1952).
I. Prigogine, Ref. 3.
L. P. Horwitz and Y. Rabin,Lett. Nuovo Cimento 17, 501 (1976). See also Ref. 22.
R. Arshansky, L. P. Horwitz, and Y. Lavie,Found. Phys. 13, 1167 (1983).
P. Ehrenfest,Z. Phys. 45, 455 (1927).
L. P. Horwitz, C. Piron, and F. Reuse,Helv. Phys. Acta 48, 546 (1975); R. Arshansky and L. P. Horwitz,J. Phys. A: Math. Gen. 15, L659 (1982).
J. L. Synge,Classical Dynamics (Handbuch der Physik III) (Springer, Berlin, 1960), p. 212.
E. C. G. Stueckelberg,Helv. Phys. Acta 15, 23 (1942).
R. Kubo,Nuovo Cimento 85A, 293 (1985); L. Hostler,J. Math. Phys. 22, 2307 (1981).
D. Saad, R. Arshansky, and L. P. Horwitz, to be published inFound. Phys.
J. Schwinger,Quantum Kinematics and Dynamics (W. A. Benjamin, New York, 1970).
P. Horwich,Asymmetries in Time (MIT Press, Cambridge, Mass., 1987), where McTaggart (1908) is quoted. (We thank J. Rosen for bringing this work to our attention.) J. W. Dunne,The Serial Universe (Faber and Faber, London, 1934). (We thank Y. Mayer for bringing this work to our attention.)
H. Weyl,Space, Time, Matter (Dover, New York, 1952).
C. Piron,Foundations of Quantum Physics (W. A. Benjamin, Reading, Mass., 1976).
G. Ludwig,Foundations of Quantum Mechanics I, II (Springer, New York, 1982, 1985).
R. Arnshansky and L. P. Horwitz,Found. Phys. 15, 701 (1985). See also M. Usher, M.Sc. Thesis, Tel Aviv University, 1985.
Y. Nambu,Prog. Theor. Phys. 5, 82 (1950).
R. Arshansky and L. P. Horwitz, Tel Aviv University preprints, TAUP 1467-86 and 1481-86, to be published inJour. Math. Phys.
L. P. Horwitz, S. Shashoua, and W. C. Schieve, Tel Aviv University preprint, TAUP 1408-85, to be published.
J. A. Wheeler and R. P. Feynman,Rev. Mod. Phys. 21, 415 (1949).
G. C. Hegerfeldt,Phys. Rev. Lett. 54, 2395 (1985). G. C. Hegerfeldt,Phys. Rev. D10, 3320 (1974).
P. Havas,Bull. Am. Phys. Soc. 1, 337 (1956).
A. Einstein, B. Prodolsky, and N. Rosen,Phys. Rev. 48, 696 (1935).
J. A. Wheeler, “Frontiers of Time,” inProblems in the Foundations of Physics, N. Toraldo di Francia and Bas van Fraassen, eds. (North Holland, Amsterdam, 1979).
R. Arshansky and L. P. Horwitz, Tel Aviv University preprints, TAUP 1520-87, to be published inJour. Math. Phys., and R. Arnshansky, TAUP 1479-86, to be published.
D. G. Currie, T. F. Jordan, and E. C. G. Sudarshan,Rev. Mod. Phys. 35, 350 (1963). See also H. Van Dam and E. P. Wigner,Phys. Rev. 142, 838 (1966).
Author information
Authors and Affiliations
Additional information
Work supported in part by the Van Leer Institute, Jerusalem, Israel.
Rights and permissions
About this article
Cite this article
Horwitz, L.P., Arshansky, R.I. & Elitzur, A.C. On the two aspects of time: The distinction and its implications. Found Phys 18, 1159–1193 (1988). https://doi.org/10.1007/BF01889430
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01889430