Skip to main content

Temporally Symmetric Causal Relations in Minkowski Space-Time

  • Chapter
Space, Time and Geometry

Part of the book series: Synthese Library ((SYLI,volume 56))

  • 156 Accesses

Abstract

This paper is a contribution to the causal theory of special-relativistic (Minkowski) space-time.1 My aim is to give an axiomatic characterization of temporally symmetric causal relations in Minkowski space-time, to show precisely the relation of causal to metrical structure, and to explicate the thesis that space-time ‘has’ a causal and topological structure which ‘underlies’ its metrical structure.2 The paper is largely mathematical in content, but many comments concerning the system appear as notes. Acquaintance with basic topological notions and with the Minkowski formalism of special relativity is presupposed.3 I shall first state the main result to be established and will then provide the philosophical motivation for the construction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Anderson, J. L., Principles of Relativity Physics, Academic Press, New York, 1967.

    Google Scholar 

  • Birkhoff, G. and MacLane, S., A Survey of Modem Algebra ( 3rd ed. ), Macmillan, New York, 1965.

    Google Scholar 

  • Carnap, R., Introduction to Symbolic Logic and Its Applications, Dover, New York, 1958.

    Google Scholar 

  • Davidson, D., ‘Causal Relations’, Journal of Philosophy 64 (1967), pp. 691–703.

    Article  Google Scholar 

  • Gödel, K., ‘An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation’, Reviews of Modern Physics 21 (1949), 447–450 (a).

    Google Scholar 

  • Gödel, K.,‘A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy’, ‘in P. A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist, The Library of Living Philosophers, Inc., Evanston, III., 1949, pp. 557–562 (b).

    Google Scholar 

  • Grünbaum, A., Philosophical Problems of Space and Time, A. Knopf, New York, 1963.

    Google Scholar 

  • Grünbaum, A., Modern Science and Zeno’s Paradoxes, Wesleyan University Press, Middletown, Conn., 1967.

    Google Scholar 

  • Grünbaum, A., ‘Space, Time and Falsifiability’, Philosophy of Science 37 (1970), 469–588.

    Article  Google Scholar 

  • Hurewicz, W. and Wallman, H., Dimension Theory, Princeton University Press, Princeton, N.J., 1941.

    Google Scholar 

  • Lewin, K., ‘Die Zeitliche Geneseordnung’, Zeitschrift für Physik 13 (1923), 62–81.

    Article  Google Scholar 

  • Mehlberg, H., ‘Physical Laws and Time’s Arrow’, in H. Feigl and G. Maxwell (eds.), Current Issues in the Philosophy of Science, Holt, Rinehart, and Winston, New York, 1961, pp. 105–138.

    Google Scholar 

  • Mehlberg, H., ‘Relativity and the Atom’, in P. K. Feyerabend and G. Maxwell (eds.), Mind, Matter and Method, University of Minnesota Press, Minneapolis, 1966, pp. 449–491.

    Google Scholar 

  • Menger, K., ‘What is Dimension?, American Mathematical Monthly 50 (1943), pp. 2–7.

    Article  Google Scholar 

  • Moller, C., The Theory of Relativity, Oxford University Press, Oxford, 1952.

    Google Scholar 

  • Reichenbach, H., The Philosophy of Space and Time, Dover, New York, 1958.

    Google Scholar 

  • Reichenbach, H., Axiomatization of the Theory of Relativity, University of California Press, Berkeley, 1969.

    Google Scholar 

  • Robb,-A. A., A Theory of Time and Space, Cambridge University Press, Cambridge, 1914.

    Google Scholar 

  • Roman, P., Theory of Elementary Particles, North Holland, Amsterdam, 1960.

    Google Scholar 

  • Roy den, H. L., Real Analysis, Macmillan, New York, 1963.

    Google Scholar 

  • Suppes, P., Introduction to Logic, Van Nostrand, Princeton, N. J., 1957.

    Google Scholar 

  • Suppes,P., ‘Axioms for Relativistic Kinematics With or Without Parity’, in L. Henkin, P. Suppes, and A. Tarski (eds.), The Axiomatic Method with Special Reference to Geometry and Physics, North-Holland Publ. Co., Amsterdam, 1959, pp. 291–307.

    Google Scholar 

  • Suppes, P., ‘The Desirability of Formalization in Science’, Journal of Philosophy 65 (1968), 651–664.

    Article  Google Scholar 

  • Trautman, A., ‘Foundations and Current Problems of General Relativity’, Lectures on General Relativity (Brandeis Summer Institute in Theoretical Physics, 1964), Prentice-Hall, Englewood Cliffs, N. J., 1965, pp. 1–248.

    Google Scholar 

  • van Fraassen, Bas C., An Introduction to the Philosophy of Time and Space, Random House, New York, 1970.

    Google Scholar 

  • Weyl, H., Space-Time-Matter, Dover, New York, 1952.

    Google Scholar 

  • Zeeman, E. C., ‘The Topology of Minkowski Space’, Topology 6 (1967), 161–170.

    Article  Google Scholar 

  • Zeeman, E. C., ‘Causality Implies the Lorentz Group’, Journal of Mathematical Physics 5 (1964), 490–493.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1973 D. Reidel Publishing Company, Dordrecht-Holland

About this chapter

Cite this chapter

Berger, G. (1973). Temporally Symmetric Causal Relations in Minkowski Space-Time. In: Suppes, P. (eds) Space, Time and Geometry. Synthese Library, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2650-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-2650-5_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2652-9

  • Online ISBN: 978-94-010-2650-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics