Spacetime  

Historical / Philosophical Aspects > s.a. Event; geometry; philosophy of science; physics; quantum cosmology.
* History: 1754, D'Alembert, in the article on dimensions in the Encyclopédie, v4 p1010, proposes to use time as a fourth dimension [@ Lang 87, p5]; 1921, Weyl identifies the mathematical structures in relativistic spacetime; 1924, Reichenbach proposes a conceptual axiomatization; 1972, Ehlers-Pirani-Schild propose a physical axiomatization of the conformal structure.
* Substantialism: (Spatialism, Absolutism) Spacetime is a fundamental entity whose existence is intrinsic, it contains events but nothing changes; Dynamics is a derived property (Newton, Grünbaum, ...); Quite an old point of view, but subject to criticism based on radical local indeterminism.
* Relationism: (Process philosophy) There are just spatial and temporal relations between bodies-events; Time-becoming is the fundamental ontological feature, everything else is emergent; Substance is just a cross-section of a basic process (Aristotle, Leibniz, ...).
* Debate: Some claim that the relationalist position has been rejected by the developments in physics, and in relativity one usually assumes implicitly that spacetime is a physical object like others; But recently there have been ideas (especially from quantum gravity) to replace it with other more fundamental notions; Besides, in quantum theory, the (initial) position of Heisenberg that only observable quantities should enter the theory, and Chew's S-matrix approach to quantum field theory, discard the notion of spacetime; Most positions are intermediate; For example, Earman has advocated a third option based on Leibniz algebras.
* Conventionalism: The philosophical theory according to which the real world does not imply any particular geometrical model, and all models which give equal experimental predictions should be considered equivalent; Proposed by Carnap; > s.a. formulations of general relativity [flat spacetime], spatial geometry of the universe.

Spacetime Measurements > s.a. atomic physics [interferometry]; riemann tensor.
@ Measurement theory: Møller 72, ch8; Desloge FP(89) [device]; Mashhoon PLA(90) [limitations], in(98)gq/00; Coleman & Korté in(92); Boniolo & de Felice FP(00) [philosophical foundations]; Sen CMP(08) [and notion of a geometrical point]; Amelino-Camelia & Stachel GRG(09) [spacetime intervals].
@ Spatial distances, lengths: Schmidt GRG(96)gq/95; Mashhoon & Muench AdP(02)gq [accelerated frames].
@ Related topics: Itzhaki PRD(96)ht/95 [and black-hole information]; Liu & Mashhoon PLA(00)gq [in Kaluza-Klein theories]; Bahder AJP(01)mar-gq [spacetime "navigation"]; Crawford & Tereno GRG(02)gq/01 [and observers]; Mensky G&C(02)gq [in terms of paths].

Specific Topics > see classical types; foundations of quantum mechanics; models of spacetime; quantum spacetime.
> Related topics: see Hole Argument; Spacetime Algebra; special subsets; topology; Tropes.

References > s.a. models [evolving space vs spacetime]; time [block universe vs evolution].
@ General: Mach 06; Reichenbach 57; Sklar 74; Earman et al ed-77; Bloodwell QJRAS(85); M Friedman 86; Hinckfuss BJPS(88); Earman 89; Mundy PhSc(89)dec; Jammer 93 [overview]; Nerlich 94; Majer & Schmidt ed-95; Bertolami gq/06-in.
@ Historical: Capek ed-76; Clark 92; Bertolami a0804-in [Minkowski's contribution]; Edelheit SHPSA(09) [Patrizi's 1500s theory of space].
@ Books, I: Ridley 95; Morris 99; Pickover 99.
@ General / mathematical: Torretti 83; Matolcsi 84; Gray 89; Ray 91; Pollini & Tarozzi ed-92; Yau IJMPA(02) [mostly strings].
@ Philosophical: Grünbaum 73; Stein in(77); Sklar 85; Nerlich 94; Schommers 94; Hellman BJPS(98) [constructive math]; Slowik PhSc(99)mar [Descartes and relational motion]; Zimmermann gq/00, gq/00-in [pregeometry, spin networks]; Bitsakis FP(05) [re a priorism]; Petkov 05; DiSalle 06; Friedman SHPMP(07); Hilbert & Huggett PhSc(06)dec [how space is internalized]; Petkov FP(07) [reality of spacetime]; Caruso et al a0907 [Kant and space dimensionality].
@ Space / spacetime points: Arntzenius PhSc(03)dec; Butterfield BJPS(06) [against "pointillisme" in mechanics].
@ Relationism: Capek 61; Harris 65; Barbour BJPS(82); Mundy PhSc(83)jun; Butterfield BJPS(84); Catton & Solomon PhSc(88)jun; Weinstein BJPS(01) [and quantum mechanics]; Anderson SHPMP(07)gq/05-in [geometrodynamics]; Skow BJPS(07) [re Sklar's 1974 relationalist interpretation of Newtonian mechanics].
@ Substantialism: Rynasiewicz PhSc(92)dec [criticism, including Earman's Leibniz or Einstein algebras]; & Earman, & Rynasiewicz, Levrini S&E(02) [educational implications]; Bain PhSc(03)dec [Einstein algebras and hole argument against]; Baker PhSc(05)dec [and the cosmological constant].
@ Substantialism vs Relationism: Maudlin PhSc(93)jun; Lorente in(94)gq/03 [relational theories]; Hoefer BJPS(98); in Baez gq/99 [and quantum gravity]; Dorato FP(00) ["structural spacetime realism"]; Auyang SHPMP(01); Dieks SHPMP(01).
@ Conventionalism: Gimbel SHPMP(04) [on Reichenbach]; Sklar PhSc(04)dec; Mormann PhSc(05)dec [indefensibility]; Slowik PhSc(05)dec [and the substantival-relationist debate]; > s.a. lorentz invariance.
@ Related topics: Meschini & Lehto FP(06)gq/05 [physical status of empty spacetime]; Verozub gq/96-in [spacetime geometry not absolute]; Mondragon & López a0711; Lorente a0712-in [ontology and causal spin foam]; Manchak GRG(09) [is spacetime hole-free?]; Kleman a0905 [and matter as condensed-matter-type defects]; Tartaglia & Radicella CQG-a0903, a0911-in [spacetime as a strained elastic continuum, and cosmology].
> Online resources: see Internet Encyclopedia of Science pages.


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