Special Relativity  

In General > s.a. minkowski spacetime; modified classical mechanics [relationship to Newtonian mechanics].
* Motivation: (E) If Galilean relativity is right, when I move at the speed of light I should see a static pattern, but Maxwell's equations do not admit such a solution!
* Postulates: (i) All inertial observers are equivalent (including laws of electromagnetism); (ii) The speed of light c is constant, independent of the motion of the observer (or the source) – inconsistent with Galilean physics; > s.a. lorentz symmetry.
* Particles / fields: Dynamical equations must be tensorial (Lorentz-covariant), a severe restriction on physical laws; > s.a. relativistic particles.
* Remark: Not all coordinate systems are allowed; Hilbert used 1 timelike and 3 spacelike coordinates; More recently, 4 null ones have also been used [@ Hilbert GN(17)].
blue bullet Particle-related concepts: see energy; force; momentum; particle models; special-relativistic kinematics.

Applications, Effects, Tests > s.a. causality violations; constants [speed of light]; electromagnetism.
* Constancy of c: Michelson-Morley experiment; Ether-drift experiments based on the Mössbauer effect; 2000, Independence of vsource confirmed to 1 × 10−20, with γ-rays from GRBs; 2001, improved Kennedy-Thorndike Tests on independence of vlab; 2002, Experiments by University of Konstanz and Düsseldorf checked isotropy of c to 1.7 parts in 1015 with optical cavities; Precise tests are motivated in part by some versions of string theory.
* Time dilation: High-speed electrons from certain radioactive decays, accelerated particles, cosmic rays and muons; Conceptually better than atomic clocks.
* Properties of materials: Special relativity shifts around the energy levels of electrons in gold atoms, causing the metal to absorb blue light, and thereby making reflected light appear more yellow.
@ General references: Holton AJP(62)jun [RL]; Drell PhyA(79); Sherwin PRA(87); Pool Sci(90)nov [including antirelativity]; Vetharaniam & Stedman PLA(93); Will in(05)gq, Wolf et al LNP(06)phy/05 [rev]; Varcoe CP(06) [with slow light]; in Thorne & Blandford 15 [applications].
@ Astrophysics, particle physics: Coleman & Glashow PLB(97) [cosmic rays and neutrinos]; Fogli et al PRD(99)hp [violations and neutrino oscillations].
@ Experiments: Zhang 97; Bonizzoni & Giuliani phy/00-wd [time dilation, history]; Braxmaier et al PRL(02) [KT experiments]; Dryzek & Singleton AJP(07)aug [constancy of c]; Bertolami & Páramos a1212 [status]; Ahmed et al a1310, Wojtsekhowski EPL(14)-a1409, a1509 [anisotropy of the speed of light]; > s.a. lorentz-group phenomenology.
@ In other fields: Van Bladel 84; Ghisellini ap/99-conf [astrophysics]; Aloisio et al PRD(00)ap, Grillo & Aloisio ap/00-conf [cosmic rays].
@ Paradoxes: Terletskii 68; Matsas PRD(03)gq, Vieira EPL(16)-a1611 [submarine paradox]; García-Islas RMF-a1412 [four-particles paradox].
@ Other effects: Wolf & Petit PRA(97) [GPS test]; Low EJP(07); Werner a1904-MG15 [Struble effect, de Sitter's binary star test].
@ And technology: Mermin AJP(88)jul; Taylor AJP(89)jun [microcomputers]; Ahuja et al PRL(11) + focus(11)jan [lead-acid batteries].
> Related topics: see Kennedy-Thorndike Test; Lorentz-FitzGerald Contraction; mass [E = mc2, etc]; Rigid Body; Sagnac Effect.

References > s.a. clocks; determinism; history of special relativity; physics teaching; relativistic quantum mechanics; spacetime.
@ General: Einstein AdP(05), AdP(05), JR(08); Lorentz et al 23.
@ I: Durell 60; Mermin 68; Russell 69; in Lightman 86, 58-69; Fang & Chu 87; Mook & Vargish 87; Rohrlich 87; Fritzsch 94; Ellis & Williams 00; Mermin 05; Bais 07; Styer 11; Griffiths 13; Egdall 14.
@ II: French 68; Rindler 80, 91; Burke 80; Rosser 91; Resnick & Halliday 92; Taylor & Wheeler 92; Mould 94; Moore 95; Adams 97; McGlinn 02; Giulini 05; Ferraro 07; Woodhouse 07; Freund 08; Fayngold 08; Helliwell 09; Takeuchi 10 [pictorial]; Hraskó 11; Dray 12 [geometrical]; Faraoni 13; Christodoulides 16 [including tests and applications]; Nolting 17; Susskind & Friedman 17.
@ III: Das 93; Laurent 95 [geometrical]; Robinson 96 [applications]; Rindler 06; Gourgoulhon 13 [in general frames]; Steane 12; Tsamparlis 19 [with problems].
@ Books and reviews: Bolton 21; Synge 64; Bohm 65; Nevanlinna 68; Møller 72 [including fields]; Dixon 78; Aharoni 85; Bowler 86; Stephenson & Kilmister 87; in Naber 88; Qadir 89; Schröder 90; Naber 92; Will in(06)gq/05 [intro, history]; Müller-Kirsten 08 [and classical mechanics]; Dragon 12.
@ Axiomatic, conceptual: Reichenbach 24, 57; Goldblatt 87; Field AJP(01)may [from spacetime exchange invariance]; Lucas & Hodgson 90; Svozil FP(02)qp/01 [conventionalism]; Balashov & Janssen BJPS(03) [and presentism]; Brown & Pooley phy/04-ch ["constructive" formulation]; Madarász et al FP(06)gq/05 [based on first-order logic]; Feigenbaum a0806 [as extension of Galilean thinking]; Andréka et al a1005, HPR-a1105 [and general relativity]; Székely PhD(09)-a1005 [first-order logic, and accelerated observers]; Frisch SHPMP(11) [special relativity as a principle theory]; Van Camp PhSc(11) [kinematic vs dynamic approaches]; Jizba & Scardigli PRD(12)-a1105, JPCS(12), EPJC(13)-a1301 [emergent special relativity from coarse-graining average of small-scale Brownian motion]; Gürel & Gürel a1107; Gomori & Szabó a1109; Sid-Ahmed a1112; Dotson SHPMP(12) [the Dingle-Popper debate and the issue of symmetry]; Hartmann a1205 [based on measurements]; Gillis a1210-FQXi [relativity is not about ontological features of spacetime]; Andréka & Németi a1307-ch [first-order logic axiomatizations]; Kim a1307 [2D, without linearity assumption]; Drory a1408 [function of the second postulate]; Galiautdinov a1701 [without the second postulate]; Hertzberg & Sandora PRD(17)-a1704 [from theories of massless spin-2 and spin-1 particles, and soft gravitons]; Basu a1812 [without the second postulate].
@ Related topics: Feynman TPT(64); Komar AJP(65)dec [and conformal mappings of the 2-sphere]; Moreau AJP(94)may [wave fronts]; Rindler AJP(94)oct [and general relativity]; Brown & Pooley gq/99-ch [Lorentzian pedagogy]; Giulini LNP(06)mp [algebraic and geometric structures]; Baierlein AJP(06)mar [misconceptions]; Kraus EJP(08) [visualizations]; Weinstein a1205; Ungar a1302 [hyperbolic geometry viewpoint]; Hartman et al a1706 [origin, effective light cone from bound on diffusion].
> Online resources: Einstein Light site (animations); Tatsu Takeuchi's lecture notes (Virginia Tech); Ute Kraus' Space-Time Travel site [visualizations]; David Waite's modernrelativity.

Extensions, Variations > s.a. DSR [deformed or double]; finsler geometry; Fock-Lorentz Symmetry; modified lorentz symmetry; spacetime models.
@ Limits of special relativity: Sidharth FP(08) [and the theory of the electron]; Carmona Symm(18)-a1806 [scenarios].
@ Poincaré's version: Arminjon www(02); Pierseaux PS(03).
@ Based on SO(1, 4), de Sitter group: Aldrovandi et al CQG(07)gq/06; Cacciatori et al AdP(08)-a0807 [introduction]; Aldrovandi & Pereira FP(09) [and quantum gravity], G&C(09)-a0812 [and cosmology], IJMPD(08); Gazeau et al Sigma(10)-a1001 [and Krein spaces]; Beltrán Almeida et al G&C(12)-a1103 [and an evolving cosmological constant]; Yan 15; Araujo et al CQG(17)-a1704 [and dark energy].
@ Other formulations: Hsu & Hsu PLA(94) [only relativity postulate]; Sorensen AJP(95)may [length contraction is physical]; Klauber FPL(98)gq/01 [non time-orthogonal frames]; Rizzi et al FP(05)gq/04-fs [different synchronizations]; Sobczyk a0710-in [geometric algebra]; Minguzzi a1412 [as a limit of an Aristotelian universal friction theory]; > s.a. clifford algebra.
@ Different mathematical basis: De Leo JMP(96)ht/95 [quaternionic]; Iovane et al CSF(04)mp [Fantappiè group and Cantorian spacetime].
@ Other variations: Asaro AJP(96)apr [complex speeds]; Svozil FP(00)phy/98 [2 limit speeds]; Manida gq/99 [varying c]; Unnikrishnan gq/04 ["cosmic relativity"]; Friedman & Gofman PS(10) [acceleration effects]; Mashhoon a1204-proc [non-local special relativity]; Carmona et al PRD(12)-a1206 [deformations of kinematics consistent with the relativity principle]; Madarász & Székely IJTP(13)-a1209 [over the field of rational numbers]; Hill & Cox PRS(12) [relative speeds > c]; Hoffman a1306 [with faster-than-light observers]; > s.a. Perplex Numbers; projective structures; Very Special Relativity.

@ References: Marinov 82; Wesley ed-87; Maddox Nat(90)jul; Ipatova et al SPU(90); Raine EJP(05) [re crank science]; Field a0805 [misunderstanding re plot]; van Dongen SHPMP(10)-a1111 [and other crackpots].
> Websites: Carel van der Togt's From Paradox to Paradigm; The General Science Journal website.

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