Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T18:05:24.940Z Has data issue: false hasContentIssue false

On the structure of causal spaces

Published online by Cambridge University Press:  24 October 2008

E. H. Kronheimer
Affiliation:
Birkbeck College, London
R. Penrose
Affiliation:
Birkbeck College, London

Abstract

The paper examines the structure obtained by abstracting from the conventional (manifold) representation of relativistic space-time the concept of an event-set equipped with two partial orderings, whose counterparts are the notions ‘causally precedes’ and ‘chronologically precedes in the history of some observer’.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Ahmavaara, Y.The structure of space and the formalism of relativistic quantum theory. I. J. Math. Phys. 6 (1965), 8793.CrossRefGoogle Scholar
(2)Bohm, D. A proposed topological formulation of the quantum theory. The scientist speculates [editor Good, I. J.], pp. 302314. (Heinemann; London, 1962).Google Scholar
(3)Coxeter, H. S. M. and Whitrow, G. J.World-structure and non-Euclidean honeycombs. Proc. Roy. Soc. London Ser. A 201 (1950), 417437.Google Scholar
(4)Finkelstein, D. and Misner, C. W.Some new conservation laws. Ann. Physics 6 (1959), 230243.CrossRefGoogle Scholar
(5)Hawking, S. W.The occurrence of singularities in cosmology. Proc. Roy. Soc. London Ser. A 294 (1966), 511521.Google Scholar
(6)Hill, E. L.Relativistic theory of discrete momentum space and discrete space-time. Phys. Rev. 100 (1955), 17801783.CrossRefGoogle Scholar
(7)Misner, C. W.The flatter regions of Newman, Unti, and Tamburino's generalized Schwarzschild space. J. Math. Phys. 4 (1963), 924937.CrossRefGoogle Scholar
(8)Penrose, R.Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14 (1965), 5759.CrossRefGoogle Scholar
(9)Penrose, R.Zero rest-mass fields including gravitation: asymptotic behaviour. Proc. Roy. Soc. London Ser. A 284 (1965), 159203.Google Scholar
(10)Penrose, R.A remarkably property of plane waves in general relativity. Rev. Mod. Phys. 37 (1965), 215220.CrossRefGoogle Scholar
(11)Schild, A.Discrete space-time and integral Lorentz transformations. Canad. J. Math. 1 (1949), 2947.CrossRefGoogle Scholar
(12)Snyder, H. S.Quantized space-time. Phys. Rev. 71 (1947), 3841.CrossRefGoogle Scholar
(13)Zeeman, E. C.Causality implies the Lorentz group. J. Math. Phys. 5 (1964), 490493.CrossRefGoogle Scholar
(14)Bass, R. W. and Witten, L.Remark on cosmological models. Rev. Mod. Phys. 29 (1957), 452453.CrossRefGoogle Scholar