An algebraic generalization of a theorem of E. C. Zeeman

Vroegindewey, P.G.

doi:10.1016/1385-7258(74)90016-x

Cited by 10 publications

(5 citation statements)

References 14 publications

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“…15-22], Nevanlinna [24, pp. 159-177], SύBmann [29], Loewner [21], Weyl [35], Ratz [26], Knichal [39], Pimenov [40], Vogt [33], Hawking [15], Michel [22], Gόbel [13], Benz [4], Barucchi [3], Alfonso and Yndurain [2], Borchers and Hegerfeldt [5,17], Gheorghe and Mihul [12], Guts [14], Teppati [30], Zeeman [37], Alexandrow [1,41], Rothaus [27], Vroegindewey [34], Vilms [31] and Zeeman [38] see also Domiaty [8].…”

Section: § 1 Introduction and Discussionmentioning

confidence: 99%

Zeeman topologies on space-times of general relativity theory

Göbel

1976

Commun.Math. Phys.

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In 1964 Zeeman published a paper showing [independently of Alexandrov (1953)] that the causal structure of the light cones on Minkowski space M determines the linear structure of M. This initiated the question whether a topology (more physically than the ordinary one) on M, related to the light cones also implies the linear structure of M. In 1967 Zeeman defined such a new topology -here called Zeeman-topology 3o ~ o n Minkowski space and solved this question for M. In that paper he asked whether it is possible to generalize this program to general relativity. Two of his main questions were: (a) What is the structure of the group G(S) of all homeomorphisms of a spacetime S with respect to the general relativistic analogue of 3o (defined in § 3)? (b) What are the world lines (defined in § 1) with respect to 3o? Without any restrictions on the space-time S we will give the answers: (a) G(S) is the group of all homothetic transformations on S (for an explicite discussion of this result we refer to § 5). (b) World lines are broken geodesies. Including external fields (like Maxwell fields and deviations of3 0 )the answer (b) can be generalized in different physical directions; cf. § 3. Ein Fernrohr wird gezeigt, womit man seinen eίgenen Rϋcken sieht. Es fύhrt durchs Weltall deinen Blick im Kreis zurύck auf dein Genick. Zwar braucht es so geraume Frist, daβ du schon lάngsί verstorben bist, dock wird ein Standbild dir geweiht, empfάngt es ihn zu seiner Zeit. Christian Morgenstern, 9i Bόhmischer Jahrmarkt" Contents § 1. Introduction and Discussion 290 § 2. Definition and Notations 292 § 3. Zeeman Topology on a General Relativistic Space-Time 293 § 4. Further Properties of the Zeeman Topologies on Space-Times 297 §5. The Group of All Homeomorphisms of a Space-Time 298 §6. References 306Note Added in Proof. These topologies will be considered in two forthcoming papers by Hawking, King, McCarthy [42] and Gobel [43]. In [43] the results of [23] will be corrected.

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Section: § 1 Introduction and Discussionmentioning

confidence: 99%

Zeeman topologies on space-times of general relativity theory

Göbel

1976

Commun.Math. Phys.

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“…For the proof of Theorem 5, see [32], [33]. From this theorem we derive that the worldview transformations between observers are Poincaré ones in the models of SpecRel d if d ≥ 3, cf.…”

Section: Consequences For Special Relativity Theorymentioning

confidence: 95%

A Geometrical Characterization of the Twin Paradox and its Variants

Székely

2010

Stud Logica

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The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.Comment: 22 pages, 3 figure

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“…By AxPh 0 and AxEv, w k m is a bijection from Q d to Q d that preserves lines of slope 1, see (4) in Proposition 4.4. Hence Item (1) is a consequence of the Alexandrov-Zeeman theorem generalized for fields, see, e.g., [29], [30]. Now let us see why Item (2) is true.…”

Section: Proofs Of the Theoremsmentioning

confidence: 96%

A Logical Analysis of the Time-Warp Effect of General Relativity

Madarasz,

Nemeti,

Szekely

2007

Preprint

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An algebraic generalization of a theorem of E. C. Zeeman

Cited by 10 publications

References 14 publications

Zeeman topologies on space-times of general relativity theory

Zeeman topologies on space-times of general relativity theory

A Geometrical Characterization of the Twin Paradox and its Variants

A Logical Analysis of the Time-Warp Effect of General Relativity

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