Historical / Philosophical Aspects > s.a. Event; 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 (cf. Parmenides); 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, ...); > s.a. Physical Process; Relationalism.
* 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.

Geometry and Phenomenology > s.a. atomic physics [interferometry]; geometry; models of spacetime; quantum spacetime; riemann tensor; singularities.
* Measuring curvature: A spacetime is locally flat iff there is no geodesic deviation for timelike geodesics (or, equivalently, for null geodesics).
@ 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]; de Felice & Bini 10; Bonder AIP(12)-a1204 [with quantum particles]; Aguilar et al MPLA(12)-a1205 [realistic probes of spacetime structure]; Wohlfarth & Pfeifer PRD(13)-a1210 [from effects on gyroscope systems]; Moretti & Di Criscienzo FiP(13) [no curvature]; Kurylev et al a1405 [from light propagation]; Braun & Fischer a1502 [limits to experimental precision]; Brody & Hughston a2011 [manifestly covariant framework]; > s.a. 3D gravitation [from holonomies].
@ Spatial distances, lengths: Schmidt GRG(96)gq/95; Mashhoon & Muench AdP(02)gq [accelerated frames]; MacLaurin a1911-proc.
@ Visualization: Nichols et al PRD(11)-a1108, Zhang et al PRD(12), PRD(12)-a1208 [via frame-drag vortexes and tidal tendexes]; Lake PRD(12)-a1207, Abdelqader & Lake PRD(12)-a1207, PRD(13)-a1308 [curvature visualization via gradient flows]; Chruściel et al PRD(12)-a1211 [2D projection diagrams].
@ 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]; Sorkin a0911-in [Riemannian metric?]; Tartaglia et al AF(11)-a1109 [relativistic navigation system]; Podolský & Švarc PRD(12)-a1201 [interpretation using geodesic deviation]; Kar & Rajeev PRD(12)-a1207 [non-Riemannian metric from a scalar quantum field theory].
> Related topics: see Hole Argument; Spacetime Algebra; special subsets; topology; Tropes; types of spacetimes; interpretations of quantum mechanics.

References > s.a. models [evolving space vs spacetime]; time [block universe vs evolution].
@ General: Mach 06; Sklar 74; Earman et al ed-77; Blodwell QJRAS(85); Friedman 86; Hinckfuss BJPS(88); Mundy PhSc(89)dec; Jammer 93 [overview]; Nerlich 94; Majer & Schmidt ed-95; Brown 05; Bertolami gq/06-ch; Schuller a1111-ln [possible geometries, aside from Lorentzian geometry]; Ashtekar & Petkov ed-14 [handbook]; Lehmkuhl et al ed-17 [theory of spacetime theories]; Wuppuluri & Ghirardi ed-17 [interdisciplinary].
@ Historical: Capek ed-76; Clark 92; Bertolami a0804-in [Minkowski's contribution]; Martínez 09 [space, time, and motion]; Edelheit SHPSA(09) [Patrizi's 1500s theory of space]; Bacelar a1203 [before and after 1905].
@ Books, I: Ridley 95; Morris 99; Pickover 99; Majid ed-08.
@ General / mathematical: Torretti 83; Matolcsi 84; Gray 89; Ray 91; Pollini & Tarozzi ed-92; Yau IJMPA(02) [strings]; Scholz a1206-in [geometries and gravity theories].
@ Conceptual: Boi Syn(04) [overview]; Stefanov & Giovanelli ed-17; De Haro & de Regt Syn-a1807 [theories without spacetime].
@ Spacetime functionalism: Esfeld Syn-a1903; Lam & Wüthrich Syn-a2003 [and realist perspective on quantum gravity]; Butterfield & Gomes a2008; Gomes & Butterfield a2010 [and geometrodynamics].
@ Philosophical: Reichenbach 57; 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-conf [pregeometry, spin networks]; Bitsakis FP(05) [re a priorism]; DiSalle 06; Friedman SHPMP(07); Hilbert & Huggett PhSc(06)dec [how space is internalized]; Petkov FP(07) [reality of spacetime]; Petkov 09, 10; Caruso & Moreira Xavier a0907, CHFC-a1505 [history of space dimensionality]; Knox BJPS(10) [geometricity of general relativity]; Romero a1105-ln; Arntzenius 12; Maudlin 12 [I]; Huggett & Wüthrich SHPMP(13)-a1206 [the possibility of science without spacetime]; Reichenberger a1605 [review of A Garbe book]; Gün a1612 [space and time in Kant and quantum gravity]; Pitts SHPMP(17)-a1710 [constructivism vs modal provincialism]; Hacyan a1803 [Schopenhauer]; Pitts Erk(18)-a1803 [and particle physics]; > s.a. many-worlds quantum theory; Ontology.
@ Space / spacetime points: Arntzenius PhSc(03)dec; Butterfield BJPS(06) [against "pointillisme" in mechanics]; Tong SA(12)dec [the world is analog]; Arminjon a1807 [space vs spacetime]; Lizzi a1905-proc [in non-commutative geometry].
@ Relationism: Capek 61; 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]; Vucetich IJMPD(11)-a1109 [materialistic relational theory]; Amelino-Camelia a1205 [spacetime as a redundant abstraction, and the relativity of locality]; Vassallo et al EJPS(16)-a1609 [and minimalist matter ontology]; Gomes & Gryb a2011 [support addressing rotational effects].
@ Substantialism: Harris 92; Rynasiewicz PhSc(92)dec [criticism, including Earman's Leibniz or Einstein algebras]; & Earman, & Rynasiewicz, Levrini S&E(02) [educational implications]; Pooley PhD(02); Bain PhSc(03)dec [Einstein algebras and hole argument against]; Baker PhSc(05)dec [and the cosmological constant]; Romero FS-a1109 [non-dynamical view of spacetime]; > s.a. diffeomorphisms; quantum spacetime proposals [spacetime as composite].
@ Substantialism vs Relationism: Earman 89; 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); Vongehr a0912; Romero FS-a1205; Curiel BJPS-a1503.
@ Spacetime structuralism: Slowik pr(08); Wüthrich pr(08); Greaves PhPersp(11); Muller PhSc(11) [refutation of Wüthrich's argument]; Romero FS-a1509.
@ Conventionalism: Gimbel SHPMP(04) [on Reichenbach]; Sklar PhSc(04)dec; Mormann PhSc(05)dec [indefensibility]; Slowik PhSc(05)dec [and the substantival-relationist debate]; Weatherall & Manchak PhSc-a1302 [in classical vs relativistic spacetimes]; > s.a. lorentz invariance.
@ Spacetime as an elastic medium: Tartaglia & Radicella CQG(10)-a0903, a0911-proc, IJMPA(15)-a1510-conf [and cosmology]; Battye & Pearson PRD(13)-a1301 [in massive gravity]; > s.a. Elasticity [stiffness].
@ Related topics: Meschini & Lehto FP(06)gq/05 [physical status of empty spacetime]; Verozub gq/96-talk [spacetime geometry not absolute]; Rovelli in(07) [spacetime without space or time]; Mondragon & López a0711-wd; Manchak GRG(09) [is spacetime hole-free?]; Brown a0911 [metric as spacetime property or emergent field]; Saller 10 [spacetime from particle interactions]; Shurtleff a1103 [fundamental transformations]; Mondragon & López a1205; García Sucre a1404 [rev]; Vaccaro a1605-in [space, time and dynamics]; De Haro a1707 [and dualities]; Martens & Lehmkuhl a2009, a2009 [spacetime-matter distinction].
> Online resources: see Internet Encyclopedia of Science pages.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 25 nov 2020