Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- "Observation of Gravitational Waves from a Binary Black Hole Merger" (https://www.ligo.caltec h.edu/system/media_files/binaries/301/original/detection-science-summary.pdf) (PDF).
- S2CID 124959784 (https://api.semanticscholar.org/CorpusID:124959784).
- OCLC 33863376 (https://search.
- Archived (https://web.archive.org/web/20130405083 228/http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives) from the original on 5 April 2013.

"Observation of Gravitational Waves from a Binary Black Hole Merger" (https://www.ligo.caltec h.edu/system/media_files/binaries/301/original/detection-science-summary.pdf) (PDF).

Archived (https://web.archive.org/web/20130405083 228/http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives) from the original on 5 April 2013.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.[12][10] Sometimes c is used for the speed of waves in any material medium, and c for the speed of light in vacuum.[13] This subscripted notation, which is endorsed in official SI literature,[14] has the same form as related electromagnetic constants: namely, μ for the vacuum permeability or magnetic constant, ε for the vacuum permittivity or electric constant, and Z for the impedance of free space.
- In 1903, Max Abraham used c with its modern meaning in a widely read textbook on electromagnetism.
- Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √2 times the speed of light in vacuum.
- Historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865.

Locate highest-signal evidence sentences from chunks for the question.

Check consistency, units, conservation constraints, and whether evidence supports claims.

Compose bounded answer and (if applicable) a proposal/hypothesis clearly labeled.

Generate falsification tests and identify unknowns or missing evidence.

Merge outputs, remove speculation, keep only evidence-backed facts.

Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.[12][10] Sometimes c is used for the speed of waves in any material medium, and c for the speed of light in vacuum.[13] This subscripted notation, which is endorsed in official SI literature,[14] has the same form as related electromagnetic constants: namely, μ for the vacuum permeability or magnetic constant, ε for the vacuum permittivity or electric constant, and Z for the impedance of free space.

In 1903, Max Abraham used c with its modern meaning in a widely read textbook on electromagnetism.

Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √2 times the speed of light in vacuum.

Historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Einstein 1907 and the description in Pais 1982, pp.
- 236–237 and Ohanian & Ruffini 1994, pp.
- Greenstein, Oke & Shipman 1971; the most recent and most accurate Sirius B measurements are published in Barstow, Bond et al.
- Pound–Rebka experiment, see Pound & Rebka 1959, Pound & Rebka 1960; Pound & Snider 1964; a list of further experiments is given in Ohanian & Ruffini 1994, table 4.1 on p.

Einstein 1907 and the description in Pais 1982, pp.

Greenstein, Oke & Shipman 1971; the most recent and most accurate Sirius B measurements are published in Barstow, Bond et al.

Pound–Rebka experiment, see Pound & Rebka 1959, Pound & Rebka 1960; Pound & Snider 1964; a list of further experiments is given in Ohanian & Ruffini 1994, table 4.1 on p.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests (and thus to decide between the candidates where their predictions vary), although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available.[209] Current status Observation of gravitational waves from binary black hole merger GW150914 General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far unambiguously fitted observational and experimental data.
- However, there are strong theoretical reasons to consider the theory to be incomplete.[210] The problem of quantum gravity and the question of the reality of spacetime singularities remain open.[211] Observational data that is taken as evidence for dark energy and dark matter could also indicate the need to consider alternatives or modifications of general relativity.
- evolution equations above), the result is the Wheeler– deWitt equation (an analogue of the Schrödinger equation) which turns out to be ill-defined without a proper ultraviolet (lattice) cutoff.[201] However, with the introduction of what are now known as Ashtekar variables,[202] this leads to a model known as loop quantum Simple spin network of the type gravity.
- Space is represented by a web-like structure called a spin used in loop quantum gravity network, evolving over time in discrete steps.[203] Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced,[204] there are numerous other attempts to arrive at a viable theory of quantum gravity, some examples being the lattice theory of gravity based on the Feynman Path Integral approach and Regge calculus,[191] dynamical triangulations,[205] causal sets,[206] twistor models[207] or the path integral based models of quantum cosmology.[208] All candidate theories still have major formal and conceptual problems to overcome.

They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests (and thus to decide between the candidates where their predictions vary), although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available.[209] Current status Observation of gravitational waves from binary black hole merger GW150914 General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far unambiguously fitted observational and experimental data.

However, there are strong theoretical reasons to consider the theory to be incomplete.[210] The problem of quantum gravity and the question of the reality of spacetime singularities remain open.[211] Observational data that is taken as evidence for dark energy and dark matter could also indicate the need to consider alternatives or modifications of general relativity.

evolution equations above), the result is the Wheeler– deWitt equation (an analogue of the Schrödinger equation) which turns out to be ill-defined without a proper ultraviolet (lattice) cutoff.[201] However, with the introduction of what are now known as Ashtekar variables,[202] this leads to a model known as loop quantum Simple spin network of the type gravity.

Space is represented by a web-like structure called a spin used in loop quantum gravity network, evolving over time in discrete steps.[203] Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced,[204] there are numerous other attempts to arrive at a viable theory of quantum gravity, some examples being the lattice theory of gravity based on the Feynman Path Integral approach and Regge calculus,[191] dynamical triangulations,[205] causal sets,[206] twistor models[207] or the path integral based models of quantum cosmology.[208] All candidate theories still have major formal and conceptual problems to overcome.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- After some time, the water 24-hour clock face in Florence
- The T was oriented eastward in the mornings.
- 3500 BC.[29] An Egyptian device that dates to c.
- At noon, the device was turned around so that it could cast its shadow in the evening direction.[30] Alarm clocks reportedly first appeared in ancient Greece c.

After some time, the water 24-hour clock face in Florence

The T was oriented eastward in the mornings.

3500 BC.[29] An Egyptian device that dates to c.

At noon, the device was turned around so that it could cast its shadow in the evening direction.[30] Alarm clocks reportedly first appeared in ancient Greece c.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- I glance in the rearview mirror, but it’s too dark to see anything except a sliver of the ghost-white mask.
- Taking my left hand off the steering wheel, I place it in my lap and count to ten.
- My phone is buried deep, and I just barely touch it with my index and pointer fingers, somehow managing to pinch it between them.
- Again, I take my left hand slowly off the wheel.

I glance in the rearview mirror, but it’s too dark to see anything except a sliver of the ghost-white mask.

Taking my left hand off the steering wheel, I place it in my lap and count to ten.

My phone is buried deep, and I just barely touch it with my index and pointer fingers, somehow managing to pinch it between them.

Again, I take my left hand slowly off the wheel.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- René Descartes argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse.
- Assuming the distance was not too much shorter than a mile, and that "about a thirtieth of a second is the minimum time interval distinguishable by the unaided eye", Boyer notes that Galileo's experiment could at best be said to have established a lower limit of about 60 miles per second for the velocity of light.[124] In 1667, the Accademia del Cimento of Florence reported that it had performed Galileo's experiment, with the lanterns separated by about one mile, but no delay was observed.[148] The actual delay in this experiment would have been about 11 microseconds.
- In 1638, Galileo Galilei proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away.
- The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer.[101][102] From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it

René Descartes argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse.

Assuming the distance was not too much shorter than a mile, and that "about a thirtieth of a second is the minimum time interval distinguishable by the unaided eye", Boyer notes that Galileo's experiment could at best be said to have established a lower limit of about 60 miles per second for the velocity of light.[124] In 1667, the Accademia del Cimento of Florence reported that it had performed Galileo's experiment, with the lanterns separated by about one mile, but no delay was observed.[148] The actual delay in this experiment would have been about 11 microseconds.

In 1638, Galileo Galilei proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away.

The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer.[101][102] From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- 852 | Index Schwarzschildmetric(continued) spherical,paperbyKruskal,376n;withtrapped of,364;Kruskal-Szekeresdiagramfor,425– surfaces,484 427;near-horizon,445–446;Painlev ́e-Gullstrand sink,incosmicdiagram,511 coordinates,417;perihelionshiftin,371–372; sky,reasonforbeingblue,715 planetaryorbitsin,371–372 SL(2,C)group,730 Schwarzschildradius,409;inKerrsolutions,461, SL(4,R)group:explanationof,739;andtwistors, 465;relationtoactualradius,366;roleinmetric, 737 364–365;ofuniverse,514;anduniverse’sobesity slowrollscenario,535–536 index,443 slowrotationlimit,Kerrblackhole,571 Schwarzschildsingularity:coordinate,365–366; smoothfunctions,anddeltafunction,33e impossibilityof,intoymodelofsphericalcluster Snell’slaw,9e ofnoninteractingparticles,376n SO(3,1)group,730 Schwarzschildsolution:aslimitofKerrsolution, SO(3)group,generatorsof,44 466;withchargedcentralmass(seechargedblack SO(3)transformations,57f holes);Kruskalcoordinatesasextensionto,433; SO(6)group,619 time-dependentmassdistribution,374;Weyl’s SO(D)group:indexnotationof,49;Liealgebrafor, wayto,374 51;Minkowskispacetime,191 Schwarzschildspacetime,292;precessionin,549; softphotontheorems,217n sphericalshellofphotonsin,430f solareclipseexpeditions,367; praisebyJ.J.
- “second,”meaningoftermusedinmeasuring Thomson,369 angles,368n solarsystem, testsofEinsteingravity, and secondderivativeintime,rolefordynamics, Schwarzschild-Drostemetric,309,362–371 Newton’sinsight,401 Soldner,Johann,calculationofdeflectionoflightby secondlawofblackholethermodynamics,472 astrophysicalobjects,366–367 secondordercorrections,tolocallyflatEuclidean solidstatestructures:gaugepotentialof,721.Seealso metric,88 condensedmatterphysics segments,infinitesimal,spaceandtimeexperience solitons,includedinquantumfieldtheory,781 of,180 SO(m,n)groups,andcomplexification,732 self-interactingscalarfield,387e Sommerfeld,Arnold:introductionoffinestructure self-tuning,706 constant,767;lettersfromEinstein,344,366,580 semi-circles,asgeodesics,133 soundhorizon,524 Shapiro,IrwinI.,radarechodelayexperiments, soundspeed:inmetals,ratiotolightspeed,749;in 372–373 staticrelativisticfluid,234 sheets,sweptoutbystrings,216f south-pointingcarriage:functionof,109;modern “shift,”691,693 versionof,104f shortest path: in curved spacetime, 276; southpole,anditslongitude,76 determinationof,155; onearth’ssurface, space:closedcurved,681;conformallyflat,80–81e; 275;andparalleltransport,545;inspacetime, creationof,498,787;curledup,673–674,674f; 176f.Seealsogeodesics;path determinationofcurvature,65–66;dimensionality “shutupandcalculate,”445 andinversesquarelaw,697;homogeneous,289, sign:mostsignificantinphysics,176;rolein 292,491,588,704;hyperbolic,296,491,590,627, electromagnetism,382 633;internal,688,689;isotropic,289,292,305, signerror,inactionvariation,380 491,588,704;localversusglobalcharacterof,76– signfunction,inGreen’sfunction,573 77;maximallysymmetric,585–593,588;metric signature,ofspacetime,changingof,732–733 ingeodesicequation,128;negativelycurved, Silberstein,Ludwik,understandingofEinstein’s maximallysymmetric,610;replacingtime,137; theory,369–370 andspacetime,classificationof,666;ofspheres, similaritytransformations,definitionof,56 anddeSitterspacetime,646;spherical,ofclosed simultaneity:dependenceonobserver,8;Einstein’s universe,633;andtime,lyricalconfoundingof, gedankenexperiments,7–9;failingof,166;fallof, 174n 200 spacecoordinates:asdynamicalvariable,andenergy singleparticles,ignoringgravitationalwaves,566 momentumtensor,381;notation,25 singularities:atBigBang,498; clothed,479; spacemeasurements,metrictensorfor,63–64 coordinate,91–92,365–366,467,467f;physical, spacereflections,inodd-dimensionalspace,721n 418,425,467,479;atpolesofMercatormap, spacelike3-dimensionalhypersurface,693f 365;Schwarzschild,impossibilityof,376n;at spacelikecurves,175 Schwarzschildradius,409;ofSchwarzschild spacelikedistance,175 solution,365;spacetime,atBigBang,498; spacelikeevents,temporalorderingof,204

852 | Index Schwarzschildmetric(continued) spherical,paperbyKruskal,376n;withtrapped of,364;Kruskal-Szekeresdiagramfor,425– surfaces,484 427;near-horizon,445–446;Painlev ́e-Gullstrand sink,incosmicdiagram,511 coordinates,417;perihelionshiftin,371–372; sky,reasonforbeingblue,715 planetaryorbitsin,371–372 SL(2,C)group,730 Schwarzschildradius,409;inKerrsolutions,461, SL(4,R)group:explanationof,739;andtwistors, 465;relationtoactualradius,366;roleinmetric, 737 364–365;ofuniverse,514;anduniverse’sobesity slowrollscenario,535–536 index,443 slowrotationlimit,Kerrblackhole,571 Schwarzschildsingularity:coordinate,365–366; smoothfunctions,anddeltafunction,33e impossibilityof,intoymodelofsphericalcluster Snell’slaw,9e ofnoninteractingparticles,376n SO(3,1)group,730 Schwarzschildsolution:aslimitofKerrsolution, SO(3)group,generatorsof,44 466;withchargedcentralmass(seechargedblack SO(3)transformations,57f holes);Kruskalcoordinatesasextensionto,433; SO(6)group,619 time-dependentmassdistribution,374;Weyl’s SO(D)group:indexnotationof,49;Liealgebrafor, wayto,374 51;Minkowskispacetime,191 Schwarzschildspacetime,292;precessionin,549; softphotontheorems,217n sphericalshellofphotonsin,430f solareclipseexpeditions,367; praisebyJ.J.

“second,”meaningoftermusedinmeasuring Thomson,369 angles,368n solarsystem, testsofEinsteingravity, and secondderivativeintime,rolefordynamics, Schwarzschild-Drostemetric,309,362–371 Newton’sinsight,401 Soldner,Johann,calculationofdeflectionoflightby secondlawofblackholethermodynamics,472 astrophysicalobjects,366–367 secondordercorrections,tolocallyflatEuclidean solidstatestructures:gaugepotentialof,721.Seealso metric,88 condensedmatterphysics segments,infinitesimal,spaceandtimeexperience solitons,includedinquantumfieldtheory,781 of,180 SO(m,n)groups,andcomplexification,732 self-interactingscalarfield,387e Sommerfeld,Arnold:introductionoffinestructure self-tuning,706 constant,767;lettersfromEinstein,344,366,580 semi-circles,asgeodesics,133 soundhorizon,524 Shapiro,IrwinI.,radarechodelayexperiments, soundspeed:inmetals,ratiotolightspeed,749;in 372–373 staticrelativisticfluid,234 sheets,sweptoutbystrings,216f south-pointingcarriage:functionof,109;modern “shift,”691,693 versionof,104f shortest path: in curved spacetime, 276; southpole,anditslongitude,76 determinationof,155; onearth’ssurface, space:closedcurved,681;conformallyflat,80–81e; 275;andparalleltransport,545;inspacetime, creationof,498,787;curledup,673–674,674f; 176f.Seealsogeodesics;path determinationofcurvature,65–66;dimensionality “shutupandcalculate,”445 andinversesquarelaw,697;homogeneous,289, sign:mostsignificantinphysics,176;rolein 292,491,588,704;hyperbolic,296,491,590,627, electromagnetism,382 633;internal,688,689;isotropic,289,292,305, signerror,inactionvariation,380 491,588,704;localversusglobalcharacterof,76– signfunction,inGreen’sfunction,573 77;maximallysymmetric,585–593,588;metric signature,ofspacetime,changingof,732–733 ingeodesicequation,128;negativelycurved, Silberstein,Ludwik,understandingofEinstein’s maximallysymmetric,610;replacingtime,137; theory,369–370 andspacetime,classificationof,666;ofspheres, similaritytransformations,definitionof,56 anddeSitterspacetime,646;spherical,ofclosed simultaneity:dependenceonobserver,8;Einstein’s universe,633;andtime,lyricalconfoundingof, gedankenexperiments,7–9;failingof,166;fallof, 174n 200 spacecoordinates:asdynamicalvariable,andenergy singleparticles,ignoringgravitationalwaves,566 momentumtensor,381;notation,25 singularities:atBigBang,498; clothed,479; spacemeasurements,metrictensorfor,63–64 coordinate,91–92,365–366,467,467f;physical, spacereflections,inodd-dimensionalspace,721n 418,425,467,479;atpolesofMercatormap, spacelike3-dimensionalhypersurface,693f 365;Schwarzschild,impossibilityof,376n;at spacelikecurves,175 Schwarzschildradius,409;ofSchwarzschild spacelikedistance,175 solution,365;spacetime,atBigBang,498; spacelikeevents,temporalorderingof,204

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- All quarks carry an additive, conserved quantum number called a baryon number (B), 1 1 which is + e for quarks and − e for antiquarks.
- Note that the mass of a hadron has very little to do with the mass of its valence quarks; rather, due to mass–energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.
- quarks are not stable wave packets (quanta), but an irregular and transient phenomenon, it is not meaningful to ask which quark is real and which virtual; only the small excess is apparent from the outside in the form of a hadron.
- Therefore, when a hadron or anti-hadron is stated to consist of (typically) two or three quarks, this technically refers to the constant excess of quarks versus antiquarks.

All quarks carry an additive, conserved quantum number called a baryon number (B), 1 1 which is + e for quarks and − e for antiquarks.

Note that the mass of a hadron has very little to do with the mass of its valence quarks; rather, due to mass–energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.

quarks are not stable wave packets (quanta), but an irregular and transient phenomenon, it is not meaningful to ask which quark is real and which virtual; only the small excess is apparent from the outside in the form of a hadron.

Therefore, when a hadron or anti-hadron is stated to consist of (typically) two or three quarks, this technically refers to the constant excess of quarks versus antiquarks.

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Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- We’re running out of chances.” My head is pounding.
- Married to multiple versions of you.
- Remember that first world we stepped into, with the buildings crashing down all around us?” “I’ve lost count of how many Chicagos we’ve been to.” “We’re getting closer to my—” “We’re not getting closer, Jason.
- That’s what you were doing sitting on a bench all day?

We’re running out of chances.” My head is pounding.

Remember that first world we stepped into, with the buildings crashing down all around us?” “I’ve lost count of how many Chicagos we’ve been to.” “We’re getting closer to my—” “We’re not getting closer, Jason.

That’s what you were doing sitting on a bench all day?

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Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- The influence of other planets is ignored.
- For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.[89] Newtonian (red) vs.
- Einsteinian orbit (blue) The effect can also be derived by using either the exact of a lone planet orbiting a star.
- Schwarzschild metric (describing spacetime around a spherical mass)[90] or the much more general postNewtonian formalism.[91] It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations).[92] Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),[93] as well as in binary pulsar systems, where it is larger by five orders of magnitude.[94]

The influence of other planets is ignored.

For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.[89] Newtonian (red) vs.

Einsteinian orbit (blue) The effect can also be derived by using either the exact of a lone planet orbiting a star.

Schwarzschild metric (describing spacetime around a spherical mass)[90] or the much more general postNewtonian formalism.[91] It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations).[92] Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),[93] as well as in binary pulsar systems, where it is larger by five orders of magnitude.[94]

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Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- This is because the body treats radium as calcium and deposits it in the bones, where radioactivity degrades marrow and can mutate bone cells.
- Exposure to radium, internal or external, can cause cancer and other disorders, because radium and radon emit alpha and gamma rays upon their decay, which kill and mutate cells.[15] Radium is generally considered the most toxic of the radioactive elements.[87] Some of the biological effects of radium include the first case of "radium-dermatitis", reported in 1900, two years after the element's discovery.
- When ingested, 80% of the ingested radium leaves the body through the feces, while the other 20% goes into the bloodstream, mostly accumulating in the bones.
- Hazards Radium is highly radioactive, as is its immediate decay product, radon gas.

This is because the body treats radium as calcium and deposits it in the bones, where radioactivity degrades marrow and can mutate bone cells.

Exposure to radium, internal or external, can cause cancer and other disorders, because radium and radon emit alpha and gamma rays upon their decay, which kill and mutate cells.[15] Radium is generally considered the most toxic of the radioactive elements.[87] Some of the biological effects of radium include the first case of "radium-dermatitis", reported in 1900, two years after the element's discovery.

When ingested, 80% of the ingested radium leaves the body through the feces, while the other 20% goes into the bloodstream, mostly accumulating in the bones.

Hazards Radium is highly radioactive, as is its immediate decay product, radon gas.

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- There are 3 integrals of motion p associated with the 3 Killing vectors γγ , plus 1 integral of motion a a associated with conservation of rest mass m, p =constant (a=1,2,3) , pnp =−m2 .
- The components of the energy-momentum tensor T are mn the energy density ρ(t), the energy flux f (t), and the pressure p (t), a ab T =ρ , T =−f , T =p .
- (17.108b) cb a ab c a Equations(17.107)combinetoyieldasecondorderordinarydifferentialequationforthespatialtetradmetric γ (t).
- Equation (17.109) is the Raychaudhuri equation (17.76) in a Bianchi spacetime.

There are 3 integrals of motion p associated with the 3 Killing vectors γγ , plus 1 integral of motion a a associated with conservation of rest mass m, p =constant (a=1,2,3) , pnp =−m2 .

The components of the energy-momentum tensor T are mn the energy density ρ(t), the energy flux f (t), and the pressure p (t), a ab T =ρ , T =−f , T =p .

(17.108b) cb a ab c a Equations(17.107)combinetoyieldasecondorderordinarydifferentialequationforthespatialtetradmetric γ (t).

Equation (17.109) is the Raychaudhuri equation (17.76) in a Bianchi spacetime.

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- The third term in the integrand of equation (16.169) is R ·e−1δ(eeλ∧eκ)=2R ·(eλ∧δeκ)− ( R ·(eλ∧eκ) ) e ·δeμ κλ κλ κλ μ = ( 2R ·eλ−Re ) ·δeκ κλ κ =2G ·δeκ , (16.172) κ where the second line again follows from the multivector triple-product relation (13.39), and G is the κ Einstein vector G ≡R ·eλ− 1Re = ( R − 1Re ) γγm .
- (16.176) ∂xκ 2 κ The left hand side of equation (16.176) is e−1∂(eeλ∧eκ) =∂∧eλ−eλ∧ ( e ·(∂∧eμ) ) .
- 446 Action principle for electromagnetism and gravity The first term in the integrand of equation (16.169) integrates by parts to (eλ∧eκ)· ∂δΓ λ =D ̊ ( (eλ∧eκ)·δΓ ) − e−1∂(eeλ∧eκ) ·δΓ .
- The dλ ≡ elλd in equation (16.178) are the vierbein mn lmn

The third term in the integrand of equation (16.169) is R ·e−1δ(eeλ∧eκ)=2R ·(eλ∧δeκ)− ( R ·(eλ∧eκ) ) e ·δeμ κλ κλ κλ μ = ( 2R ·eλ−Re ) ·δeκ κλ κ =2G ·δeκ , (16.172) κ where the second line again follows from the multivector triple-product relation (13.39), and G is the κ Einstein vector G ≡R ·eλ− 1Re = ( R − 1Re ) γγm .

(16.176) ∂xκ 2 κ The left hand side of equation (16.176) is e−1∂(eeλ∧eκ) =∂∧eλ−eλ∧ ( e ·(∂∧eμ) ) .

446 Action principle for electromagnetism and gravity The first term in the integrand of equation (16.169) integrates by parts to (eλ∧eκ)· ∂δΓ λ =D ̊ ( (eλ∧eκ)·δΓ ) − e−1∂(eeλ∧eκ) ·δΓ .

The dλ ≡ elλd in equation (16.178) are the vierbein mn lmn

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Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- The spinor reverse to the spinor (14.154) is ψ ≡ε⊤ q =ε⊤ (1+In)λU .
- Physically, when a null spinor is Lorentz transformed, it ⇑↑ gets blueshifted (multiplied by a real scalar).
- (14.157) ⇑↑ ⇑↑ The spinor is null, qq =0, because the boost factor is null, (1+In)(1−In)=0.
- A general right- or left-handed Weyl spinor may be written uniquely as the right- or left-handed basis spinor defined by equation (14.158) pre-multiplied by a positive real scalar λ and a purely spatial rotor U, ψ =λU(1±γ )ε .

The spinor reverse to the spinor (14.154) is ψ ≡ε⊤ q =ε⊤ (1+In)λU .

Physically, when a null spinor is Lorentz transformed, it ⇑↑ gets blueshifted (multiplied by a real scalar).

(14.157) ⇑↑ ⇑↑ The spinor is null, qq =0, because the boost factor is null, (1+In)(1−In)=0.

A general right- or left-handed Weyl spinor may be written uniquely as the right- or left-handed basis spinor defined by equation (14.158) pre-multiplied by a positive real scalar λ and a purely spatial rotor U, ψ =λU(1±γ )ε .

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- As an illustration of the striking disconnect between money and happiness, the average life satisfaction of Forbes magazine’s 400 richest Americans was 5.8 on a 7-point scale (Diener, Horowitz, & Emmons, 1985).
- Most of us adapt fairly quickly to our life circumstances, both good and bad.
- 9781405131117_4_006.qxd 30/6/09 11:47 AM Page 125 each born with a distinctive happiness “set point,” a genetically influenced baseline level of happiness from which we bounce up and down in response to short-term life events, but to which we soon return once we’ve adapted to these events (Lykken, 2000).
- More direct evidence for the hedonic treadmill comes from studies of people who’ve experienced either (1) extremely positive or (2) extremely negative, even tragic, life events.

As an illustration of the striking disconnect between money and happiness, the average life satisfaction of Forbes magazine’s 400 richest Americans was 5.8 on a 7-point scale (Diener, Horowitz, & Emmons, 1985).

Most of us adapt fairly quickly to our life circumstances, both good and bad.

9781405131117_4_006.qxd 30/6/09 11:47 AM Page 125 each born with a distinctive happiness “set point,” a genetically influenced baseline level of happiness from which we bounce up and down in response to short-term life events, but to which we soon return once we’ve adapted to these events (Lykken, 2000).

More direct evidence for the hedonic treadmill comes from studies of people who’ve experienced either (1) extremely positive or (2) extremely negative, even tragic, life events.

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List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Indian, Tamil-language, science fiction, political action thriller film Maanaadu.[13][14] Time loops have been used as a recurring theme in Doctor Who, with the episode "Heaven Sent" being described as "Doctor Who's definitive loop-based story".[15] Japanese popular culture The time loop is a popular trope in Japanese pop culture media, especially anime.[16] Its use in Japanese fiction dates back to Yasutaka Tsutsui's science fiction novel The Girl Who Leapt Through Time (1965), one of the earliest works to feature a time loop, about a high school girl who repeatedly relives the same day.
- It was later adapted into a 1972 live-action Japanese television series, a hit 1983 live-action film, a 2006 anime film, and a 2010 live-action film.[17][18][19] The 1983 live-action film adaptation of The Girl Who Leapt Through Time was a major box office success in Japan,[19] where it

Indian, Tamil-language, science fiction, political action thriller film Maanaadu.[13][14] Time loops have been used as a recurring theme in Doctor Who, with the episode "Heaven Sent" being described as "Doctor Who's definitive loop-based story".[15] Japanese popular culture The time loop is a popular trope in Japanese pop culture media, especially anime.[16] Its use in Japanese fiction dates back to Yasutaka Tsutsui's science fiction novel The Girl Who Leapt Through Time (1965), one of the earliest works to feature a time loop, about a high school girl who repeatedly relives the same day.

It was later adapted into a 1972 live-action Japanese television series, a hit 1983 live-action film, a 2006 anime film, and a 2010 live-action film.[17][18][19] The 1983 live-action film adaptation of The Girl Who Leapt Through Time was a major box office success in Japan,[19] where it

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Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- This energy is converted to other forms of electromagnetic energy of lower frequency, such as visible light, by the time it reaches the star's outer layers.[176] The color of a star, as determined by the most intense frequency of the visible light, depends on the temperature of the star's outer layers, including its photosphere.[177] Besides visible light, stars emit forms of electromagnetic radiation that are invisible to the human eye.
- Smaller stars such as the Sun have surface temperatures of a few thousand K.
- The particle radiation emitted by a star is manifested as the stellar wind,[174] which streams from the outer layers as electrically charged protons and alpha and beta particles.
- In fact, stellar electromagnetic radiation

This energy is converted to other forms of electromagnetic energy of lower frequency, such as visible light, by the time it reaches the star's outer layers.[176] The color of a star, as determined by the most intense frequency of the visible light, depends on the temperature of the star's outer layers, including its photosphere.[177] Besides visible light, stars emit forms of electromagnetic radiation that are invisible to the human eye.

Smaller stars such as the Sun have surface temperatures of a few thousand K.

The particle radiation emitted by a star is manifested as the stellar wind,[174] which streams from the outer layers as electrically charged protons and alpha and beta particles.

In fact, stellar electromagnetic radiation

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Prelude | 19 Figure1 Galileo’svision:butterfliesflynormallyin acabinonasmoothlymovingship.
- and x (cid:5)=x+ut, y (cid:5)=y, and z (cid:5)=z (2) withutheconstantrelativevelocitybetweenthetwoobservers.
- Wesimplydifferentiate: d d x t(cid:5) (cid:5) = d d x t (cid:5) = d d x t +u.Thus,ifMs.Unprimetossesaballforward withspeedv,Mr.Primeseestheballmovingforwardwithspeedv (cid:5)=v+u,inaccordance witheverydayobservation,asknowntoyou,me,andSalviati.WehavederivedtheGalilean ∗ law fortheadditionofvelocities: v (cid:5)=v+u (3) Differentiatingagain,weobtaintheball’saccelerationa (cid:5)= dv(cid:5) = dv =a.SinceNewton’s dt dt law of motion F =ma involves acceleration, we conclude that Newtonian mechanics is invariantundertheGalileantransformation,asSalviatitoldus.
- ∗Whichyoucanverifythesedaysatanymajorairportwithamovingsidewalk.

Prelude | 19 Figure1 Galileo’svision:butterfliesflynormallyin acabinonasmoothlymovingship.

and x (cid:5)=x+ut, y (cid:5)=y, and z (cid:5)=z (2) withutheconstantrelativevelocitybetweenthetwoobservers.

Wesimplydifferentiate: d d x t(cid:5) (cid:5) = d d x t (cid:5) = d d x t +u.Thus,ifMs.Unprimetossesaballforward withspeedv,Mr.Primeseestheballmovingforwardwithspeedv (cid:5)=v+u,inaccordance witheverydayobservation,asknowntoyou,me,andSalviati.WehavederivedtheGalilean ∗ law fortheadditionofvelocities: v (cid:5)=v+u (3) Differentiatingagain,weobtaintheball’saccelerationa (cid:5)= dv(cid:5) = dv =a.SinceNewton’s dt dt law of motion F =ma involves acceleration, we conclude that Newtonian mechanics is invariantundertheGalileantransformation,asSalviatitoldus.

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- The field has the dimension of acceleration; in the SI, its unit is m/s2.
- It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon).
- In that case As per Gauss's law, field in a symmetric body can be found by the mathematical equation: where is a closed surface and is the mass enclosed by the surface.
- This has the consequence that there exists a gravitational potential field V(r) such that If m is a point mass or the mass of a sphere with homogeneous mass distribution, the force field g(r) outside the sphere is isotropic, i.e., depends only on the distance r from the center of the sphere.

Newton's law of universal gravitation - Wikipedia.pdf

The field has the dimension of acceleration; in the SI, its unit is m/s2.

It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon).

In that case As per Gauss's law, field in a symmetric body can be found by the mathematical equation: where is a closed surface and is the mass enclosed by the surface.

This has the consequence that there exists a gravitational potential field V(r) such that If m is a point mass or the mass of a sphere with homogeneous mass distribution, the force field g(r) outside the sphere is isotropic, i.e., depends only on the distance r from the center of the sphere.

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Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Whether general relativity forbids closed time-like curves for all realistic conditions is still being researched.[40] Wormholes Wormholes are a hypothetical warped spacetime permitted by the Einstein field equations of general relativity.[41]: 100 A proposed time-travel machine using a traversable wormhole would hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced propulsion system, and then brought back to the point of origin.
- Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance.
- For both these methods, time dilation causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently through the wormhole than outside

Whether general relativity forbids closed time-like curves for all realistic conditions is still being researched.[40] Wormholes Wormholes are a hypothetical warped spacetime permitted by the Einstein field equations of general relativity.[41]: 100 A proposed time-travel machine using a traversable wormhole would hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced propulsion system, and then brought back to the point of origin.

Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance.

For both these methods, time dilation causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently through the wormhole than outside

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Turning north, I begin to run, my shoes crunching wave-polished rocks.
- A three-foot seawall stands in my path, and I scale the concrete, barking my shins on the way over and staying on all fours as I crawl through the hedgerow, branches grabbing my shirt and face, clawing at my eyes.
- That dog is still barking in the distance, but looking back toward the lake, I see no flashlights, hear no voices.
- From the direction of the office park, I hear an engine revving.

Turning north, I begin to run, my shoes crunching wave-polished rocks.

A three-foot seawall stands in my path, and I scale the concrete, barking my shins on the way over and staying on all fours as I crawl through the hedgerow, branches grabbing my shirt and face, clawing at my eyes.

That dog is still barking in the distance, but looking back toward the lake, I see no flashlights, hear no voices.

From the direction of the office park, I hear an engine revving.

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Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- =ξπD Aκλ...+Aκλ...D ξπ+Aκλ...D ξπ...
- −Aπλ...Sκ −Aκπ...Sλ ) ξρ a coordinate tensor .
- ∂xπ πν...∂xμ μπ...∂xν μν...∂xπ μν...∂xπ (7.151) with an overall ∂A term, and a +∂ξ term for each covariant index and a −∂ξ term for each contravariant index.
- (7.150) ξ μ ∂xκ κ∂xμ As in the Lie derivative of a contravariant vector, equation (7.138), the coordinate derivatives in the Lie derivative (7.150) of a covariant vector can be replaced by torsion-free covariant derivatives.

−Aπλ...Sκ −Aκπ...Sλ ) ξρ a coordinate tensor .

∂xπ πν...∂xμ μπ...∂xν μν...∂xπ μν...∂xπ (7.151) with an overall ∂A term, and a +∂ξ term for each covariant index and a −∂ξ term for each contravariant index.

(7.150) ξ μ ∂xκ κ∂xμ As in the Lie derivative of a contravariant vector, equation (7.138), the coordinate derivatives in the Lie derivative (7.150) of a covariant vector can be replaced by torsion-free covariant derivatives.

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- I should do something, say something, but I feel paralyzed by the suddenness of the man’s presence.
- “What does he want?” She points at me.
- He aims it at both of us, and as he kicks the door closed I smell old and recent cigarette smoke wafting into the loft.
- There’s a strange distance between what’s happening and my processing of it.

I should do something, say something, but I feel paralyzed by the suddenness of the man’s presence.

He aims it at both of us, and as he kicks the door closed I smell old and recent cigarette smoke wafting into the loft.

There’s a strange distance between what’s happening and my processing of it.

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Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Qudits and qutrits The term qudit denotes the unit of quantum information that can be realized in suitable d-level quantum systems.[10] Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits.
- Applications The Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms.
- It is for example possible to have 5-level qudits.
- After applying CNOT, the output is the Bell State: .

Qudits and qutrits The term qudit denotes the unit of quantum information that can be realized in suitable d-level quantum systems.[10] Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits.

Applications The Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms.

It is for example possible to have 5-level qudits.

After applying CNOT, the output is the Bell State: .

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Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Such a choice is only possible if the surface is orientable, and in this case there are exactly two different orientations.
- This means that the transition functions in the atlas of are -functions.
- If the figure can be consistently positioned at all points of the surface without turning into its mirror image, then this will induce an orientation in the above sense on each of the triangles of the triangulation by selecting the direction of each of the triangles based on the order red-green-blue of colors of any of the figures in the interior of the triangle.
- However, some 4-manifolds do not have a triangulation, and in general for some -manifolds have triangulations that are inequivalent.

Such a choice is only possible if the surface is orientable, and in this case there are exactly two different orientations.

This means that the transition functions in the atlas of are -functions.

If the figure can be consistently positioned at all points of the surface without turning into its mirror image, then this will induce an orientation in the above sense on each of the triangles of the triangulation by selecting the direction of each of the triangles based on the order red-green-blue of colors of any of the figures in the interior of the triangle.

However, some 4-manifolds do not have a triangulation, and in general for some -manifolds have triangulations that are inequivalent.

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Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- 34.2 Harmonics of the CMB photon distribution 903 The e−ikμ(η−η0) factor in the integrand on the right hand side of equation (34.9) can be expanded in harmonics through the general formula ∞ ∑ e−iyμ = (−i)l(2l+1)P (μ)j (y) , (34.10) l l l=0 √ where j (y) ≡ π/(2y)J (y) are spherical Bessel functions, and here y ≡ k(η−η ).
- (34.13) ln nl The Legendre functions P (μ) are polynomials in μ, §33.14.
- With the ISW and scattering source terms I and S written out explicitly, equation (34.16) is an integral from the Big Bang (η =0) to the present time n
- The harmonic expansion of equation (34.9) is thus ln ln ∫ η0 { ∑ 2 } Θ (η ,k)+δ Ψ(η ,k)= e−τI(η,k)j [k(η −η)]+g(η) S (η,k)j [k(η−η )] dη , (34.16) l 0 l0 0 l 0 n ln 0 0 n=0 where g(η) is the visibility function defined by equation (34.7).

34.2 Harmonics of the CMB photon distribution 903 The e−ikμ(η−η0) factor in the integrand on the right hand side of equation (34.9) can be expanded in harmonics through the general formula ∞ ∑ e−iyμ = (−i)l(2l+1)P (μ)j (y) , (34.10) l l l=0 √ where j (y) ≡ π/(2y)J (y) are spherical Bessel functions, and here y ≡ k(η−η ).

(34.13) ln nl The Legendre functions P (μ) are polynomials in μ, §33.14.

With the ISW and scattering source terms I and S written out explicitly, equation (34.16) is an integral from the Big Bang (η =0) to the present time n

The harmonic expansion of equation (34.9) is thus ln ln ∫ η0 { ∑ 2 } Θ (η ,k)+δ Ψ(η ,k)= e−τI(η,k)j [k(η −η)]+g(η) S (η,k)j [k(η−η )] dη , (34.16) l 0 l0 0 l 0 n ln 0 0 n=0 where g(η) is the visibility function defined by equation (34.7).

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Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- What we're really interested in is the mass of the Earth, so let's alter the equation by the usual algebraic techniques to put the m' all by itself on the left-hand side of the equation.
- The distance between the falling body and the Earth is a little complicated.
- The equation becomes: Fcl2 m =G m.
- (Equation 9) If we have values for every symbol on the righthand side of the equation, we can multiply the value of F by the value of d, multiply the product again by d, divide this result by G, divide the quotient by m, and that will give the value for n', the mass of the Earth.

What we're really interested in is the mass of the Earth, so let's alter the equation by the usual algebraic techniques to put the m' all by itself on the left-hand side of the equation.

The distance between the falling body and the Earth is a little complicated.

(Equation 9) If we have values for every symbol on the righthand side of the equation, we can multiply the value of F by the value of d, multiply the product again by d, divide this result by G, divide the quotient by m, and that will give the value for n', the mass of the Earth.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Internal conversion decay, like isomeric transition gamma decay and neutron emission, involves the release of energy by an excited nuclide, without the transmutation of one element into another.
- If energy circumstances are favorable, a given radionuclide may undergo many competing types of decay, with some
- In a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms.
- A neutrino is not emitted, and none of the electron(s) and photon(s) emitted originate in the nucleus, even though the energy to emit all of them does originate there.

Internal conversion decay, like isomeric transition gamma decay and neutron emission, involves the release of energy by an excited nuclide, without the transmutation of one element into another.

If energy circumstances are favorable, a given radionuclide may undergo many competing types of decay, with some

In a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms.

A neutrino is not emitted, and none of the electron(s) and photon(s) emitted originate in the nucleus, even though the energy to emit all of them does originate there.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- In 1999, an airline tried to entice potential flyers by informing them that “It’s been said that we use only 10% of our brain capacity.
- That desired promotion, stellar grade point average, or authorship of the next bestselling novel is within your grasp, say the sellers of cerebral miracle remedies.
- 9781405131117_4_001.qxd 30/6/09 11:48 AM Page 22 (1983) wrote that “If you’re like most people, you’re using only ten percent of your brainpower” (p.
- First of all, our brain has been shaped by natural selection.

In 1999, an airline tried to entice potential flyers by informing them that “It’s been said that we use only 10% of our brain capacity.

That desired promotion, stellar grade point average, or authorship of the next bestselling novel is within your grasp, say the sellers of cerebral miracle remedies.

9781405131117_4_001.qxd 30/6/09 11:48 AM Page 22 (1983) wrote that “If you’re like most people, you’re using only ten percent of your brainpower” (p.

First of all, our brain has been shaped by natural selection.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- The torsion tensor Sm is antisymmetric in k ↔ l, as is evident from its kl definition (11.48).
- (11.50) kl For vanishing torsion, equation (11.49) implies d +Γ =d +Γ not a tetrad tensor , (11.51) mkl mkl mlk mlk which is equivalent to the usual symmetry condition Γ = Γ on the coordinate frame connections in λκμ λμκ view of the relation (11.44) between tetrad and coordinate connections.
- (11.53) lnm lmn mln mnl nlm nml
- 11.13 No-torsion condition General relativity assumes vanishing torsion Sm =0 .

The torsion tensor Sm is antisymmetric in k ↔ l, as is evident from its kl definition (11.48).

(11.50) kl For vanishing torsion, equation (11.49) implies d +Γ =d +Γ not a tetrad tensor , (11.51) mkl mkl mlk mlk which is equivalent to the usual symmetry condition Γ = Γ on the coordinate frame connections in λκμ λμκ view of the relation (11.44) between tetrad and coordinate connections.

11.13 No-torsion condition General relativity assumes vanishing torsion Sm =0 .

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.
- "Nonsingular, big-bounce cosmology from spinor-torsion coupling" (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.85.107502).
- arXiv:1607.03480 (https://arxiv.org/abs/1607.03 480).
- Descubren nuevas evidencias de la transición al blanco de los agujeros negros, Universidad Complutense de Madrid.

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.

"Nonsingular, big-bounce cosmology from spinor-torsion coupling" (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.85.107502).

Descubren nuevas evidencias de la transición al blanco de los agujeros negros, Universidad Complutense de Madrid.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- (cid:8) √ 2 GiventhecovariantderivativeD ν Wμin(5),integrate dDx −gT μ νD ν Wμtoobtainthecovariantdivergence ofthetensorTν.Verifythatitagreeswiththeresultof(1).
- The subject of this appendix is somewhat off the subject of this chapter, but I wish to introduce you to an interestingandamusingareaofphysics,namelythatofconstructinganalogcurvedspacetimeinthelab.Before yousay“what?”,notetheword“analog.” (cid:8)Tosetupthediscussion,considerascalarfieldφ(x)inMinkowskispacetimegovernedbytheactionS= − ddx( 1ημν∂ μ φ∂ ν φ+V(φ)),withV(φ)somefunctionofφ.(Youmightrecallthatwefirstencounteredan actionofthisformwaybackinappendix2ofchapterII.3,beforeweevengottospecialrelativity.)Tokeepthe discussionsimple,wewillignoreV(φ)orsimplysetitto0.
- Appendix7:Curvedspacetimeinthelab?
- NowthatwehavefollowedEinsteintothescalarfie(cid:12)ldacti(cid:14)onincurvedspacetime,wefollowEulerandLagrange tothecorrespondingequationofmotion,namely∂ μ δ∂ δ μ L φ =0.Thisworksouttobe 1 √ √ −g ∂ μ ( −ggμν∂ ν φ)=0 (36) Applyingwhatwelearnedinthischapter,werecognizethisasjustD μ Dμφ=0,thecurvedspacetimeversionof theflatspacetimeequationofmotion∂ μ ∂μφ=0.

(cid:8) √ 2 GiventhecovariantderivativeD ν Wμin(5),integrate dDx −gT μ νD ν Wμtoobtainthecovariantdivergence ofthetensorTν.Verifythatitagreeswiththeresultof(1).

The subject of this appendix is somewhat off the subject of this chapter, but I wish to introduce you to an interestingandamusingareaofphysics,namelythatofconstructinganalogcurvedspacetimeinthelab.Before yousay“what?”,notetheword“analog.” (cid:8)Tosetupthediscussion,considerascalarfieldφ(x)inMinkowskispacetimegovernedbytheactionS= − ddx( 1ημν∂ μ φ∂ ν φ+V(φ)),withV(φ)somefunctionofφ.(Youmightrecallthatwefirstencounteredan actionofthisformwaybackinappendix2ofchapterII.3,beforeweevengottospecialrelativity.)Tokeepthe discussionsimple,wewillignoreV(φ)orsimplysetitto0.

NowthatwehavefollowedEinsteintothescalarfie(cid:12)ldacti(cid:14)onincurvedspacetime,wefollowEulerandLagrange tothecorrespondingequationofmotion,namely∂ μ δ∂ δ μ L φ =0.Thisworksouttobe 1 √ √ −g ∂ μ ( −ggμν∂ ν φ)=0 (36) Applyingwhatwelearnedinthischapter,werecognizethisasjustD μ Dμφ=0,thecurvedspacetimeversionof theflatspacetimeequationofmotion∂ μ ∂μφ=0.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- But one solution was so strange that Einstein himself was very skeptical about.
- Or what is known as a Wormhole.
- Later, in 1935 Einstein and Rosen [4] studied the extension of Schwarzchild solution to predict an even stranger object, knows as Einstein-Rosen Bridge.
- This solution is called the Schwazchild solution It predicted the existence of Black holes a very dense object having an enormous gravity even spacetime will not make sense because of it!

But one solution was so strange that Einstein himself was very skeptical about.

Later, in 1935 Einstein and Rosen [4] studied the extension of Schwarzchild solution to predict an even stranger object, knows as Einstein-Rosen Bridge.

This solution is called the Schwazchild solution It predicted the existence of Black holes a very dense object having an enormous gravity even spacetime will not make sense because of it!

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- a radiation source in some industrial radiography devices to check for flawed metallic parts, similarly to X-ray imaging.[15] When mixed with beryllium, radium acts as a neutron source.[55][85] Up until at least 2004, radium-beryllium neutron sources were still sometimes used,[15][86] but other materials such as polonium and americium have become more common for use in neutron sources.
- RaBeF -based (α, n) neutron sources have been deprecated despite the high number of neutrons they emit (1.84×106 neutrons per second) in favour of 241Am–Be sources.[87] As of 2011, the isotope 226Ra is mainly used to form 227Ac by neutron irradiation in a nuclear reactor.[29]

a radiation source in some industrial radiography devices to check for flawed metallic parts, similarly to X-ray imaging.[15] When mixed with beryllium, radium acts as a neutron source.[55][85] Up until at least 2004, radium-beryllium neutron sources were still sometimes used,[15][86] but other materials such as polonium and americium have become more common for use in neutron sources.

RaBeF -based (α, n) neutron sources have been deprecated despite the high number of neutrons they emit (1.84×106 neutrons per second) in favour of 241Am–Be sources.[87] As of 2011, the isotope 226Ra is mainly used to form 227Ac by neutron irradiation in a nuclear reactor.[29]

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- THE PLANETS 45 TABLE 8-Escape Velocities from the Planets Escape Velocity (km/sec) Mercury 4.2 Venus 10.3 Earth 11.23 Moon 2.40 Mars 5.0 Jupiter 60.5 Saturn 35.2 Uranus 21.7 Neptune 24 Pluto 5 Earth's surface is 6,371 kilometers from the center, its gravitation weakens to 1/4 its surface value at a height of 6,371 kilometers above the surface.
- Therefore one must rise to a height of 71,450 kilometers above Jupiter's surface before its gravitation drops to 1/4 its surface value, and to a height of 214,350 kilometers above its surface before its gravitation drops to 1/16 of its surface value.
- Jupitei, however, has a surface that is 71,450 kilometers from its center.
- At a height of 19,113 kilometers above the surface, the distance from the center of the Earth is 4 times what it was at the surface, and Earth's gravitation is only 1/16 its surface value.

THE PLANETS 45 TABLE 8-Escape Velocities from the Planets Escape Velocity (km/sec) Mercury 4.2 Venus 10.3 Earth 11.23 Moon 2.40 Mars 5.0 Jupiter 60.5 Saturn 35.2 Uranus 21.7 Neptune 24 Pluto 5 Earth's surface is 6,371 kilometers from the center, its gravitation weakens to 1/4 its surface value at a height of 6,371 kilometers above the surface.

Therefore one must rise to a height of 71,450 kilometers above Jupiter's surface before its gravitation drops to 1/4 its surface value, and to a height of 214,350 kilometers above its surface before its gravitation drops to 1/16 of its surface value.

Jupitei, however, has a surface that is 71,450 kilometers from its center.

At a height of 19,113 kilometers above the surface, the distance from the center of the Earth is 4 times what it was at the surface, and Earth's gravitation is only 1/16 its surface value.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.[35] Main concepts The following
- 853) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.[26] Thābit ibn Qurra (known as Thebit in Latin) (836–901) dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry.[27] Omar Woman teaching geometry.
- 1314), Gersonides (1288–1344), Alfonso, John Wallis, and Giovanni Girolamo Saccheri, that by the 19th century led to the discovery of hyperbolic geometry.[29] In the early 17th century, there were two important developments in geometry.
- Khayyam (1048–1131) found geometric solutions to cubic Illustration at the beginning of a equations.[28] The theorems of Ibn al-Haytham (Alhazen), Omar medieval translation of Euclid's Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Elements, c.

As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.[35] Main concepts The following

853) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.[26] Thābit ibn Qurra (known as Thebit in Latin) (836–901) dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry.[27] Omar Woman teaching geometry.

1314), Gersonides (1288–1344), Alfonso, John Wallis, and Giovanni Girolamo Saccheri, that by the 19th century led to the discovery of hyperbolic geometry.[29] In the early 17th century, there were two important developments in geometry.

Khayyam (1048–1131) found geometric solutions to cubic Illustration at the beginning of a equations.[28] The theorems of Ibn al-Haytham (Alhazen), Omar medieval translation of Euclid's Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Elements, c.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- One Seyfert galaxy, NGC 4151, may have as many as 10 billion stars in a nucleus only 12 light-years across.
- We would then consider it a quasar, and the very distant quasars may simply be the intensely luminous nuclei of very large, very active Seyfert galaxies.
- The rate of matter flow may vary for reasons we do not as yet un-
- Perhaps the mere fact that a certain volume of space is subject to black-hole formation may also make it subject to the blossoming out of a white-hole.

One Seyfert galaxy, NGC 4151, may have as many as 10 billion stars in a nucleus only 12 light-years across.

We would then consider it a quasar, and the very distant quasars may simply be the intensely luminous nuclei of very large, very active Seyfert galaxies.

The rate of matter flow may vary for reasons we do not as yet un-

Perhaps the mere fact that a certain volume of space is subject to black-hole formation may also make it subject to the blossoming out of a white-hole.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Obviously, we would rather not deal with ̈ secondderivativesifwecanhelpit.Using(16)toeliminateR in(18), wefinallyendup witharemarkablysimplefirstorderdifferentialequation R ̇2+k= 8πG ρR2 (19) NotethatP doesnotappearin(19).
- IdonottakethisNewtonianpseudo-derivationseriouslybutvalueitasahighlyuseful mnemonic that could also serve to motivate pedagogically the subtle physics contained in(19).
- Theuniverseexpandsaccordingtowhatitisfullof To me, it is amazing that cosmic expansion is governed by two simple equations (19) and(20).(Ofcourse,thisislargelyduetotheperfectcosmologicalprinciple.)Inthenext
- Theunitmasshaskineticenergy 1R ̇2and,byNewton’ssuperbtheorems,potentialenergy −G(4πR3/3)ρ/R.Byenergyconservation,itstotalenergy 1R ̇2−G(4πR3/3)ρ/Rshould beconserved.Callingthisconstant−1k, weobtain(19)andevenunderstandwherethe 8π/3comesfrom!

Obviously, we would rather not deal with ̈ secondderivativesifwecanhelpit.Using(16)toeliminateR in(18), wefinallyendup witharemarkablysimplefirstorderdifferentialequation R ̇2+k= 8πG ρR2 (19) NotethatP doesnotappearin(19).

IdonottakethisNewtonianpseudo-derivationseriouslybutvalueitasahighlyuseful mnemonic that could also serve to motivate pedagogically the subtle physics contained in(19).

Theuniverseexpandsaccordingtowhatitisfullof To me, it is amazing that cosmic expansion is governed by two simple equations (19) and(20).(Ofcourse,thisislargelyduetotheperfectcosmologicalprinciple.)Inthenext

Theunitmasshaskineticenergy 1R ̇2and,byNewton’ssuperbtheorems,potentialenergy −G(4πR3/3)ρ/R.Byenergyconservation,itstotalenergy 1R ̇2−G(4πR3/3)ρ/Rshould beconserved.Callingthisconstant−1k, weobtain(19)andevenunderstandwherethe 8π/3comesfrom!

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Write the null quaternion q as q =p+Ir (14.26) wherepandr arerealquaternions,bothofwhichmustbenon-zeroifq isnon-trivial.Thenequation(14.23) is true with pr n=ı n = .
- Equivalently, 1 2 3 a a q =(1+In′)p=(1+Iı n′)p , (14.24) a a where n′ is the real unimodular vector quaternion pnp n′ = , (14.25) |p|2 with real components {n′,n′,n′} satisfying n′n′ =1.
- Show that any non-trivial null complex quaternion q can be written uniquely in the form q =p(1+In)=p(1+Iı n ) , (14.23) a a where p is a real quaternion, and n = ı n is a real unimodular vector quaternion, with real components a a {n ,n ,n } satisfying n n =1.
- Nilpotent complex quaternions.Anobjectwhosesquareiszeroissaidtobenilpotent.

Write the null quaternion q as q =p+Ir (14.26) wherepandr arerealquaternions,bothofwhichmustbenon-zeroifq isnon-trivial.Thenequation(14.23) is true with pr n=ı n = .

Equivalently, 1 2 3 a a q =(1+In′)p=(1+Iı n′)p , (14.24) a a where n′ is the real unimodular vector quaternion pnp n′ = , (14.25) |p|2 with real components {n′,n′,n′} satisfying n′n′ =1.

Show that any non-trivial null complex quaternion q can be written uniquely in the form q =p(1+In)=p(1+Iı n ) , (14.23) a a where p is a real quaternion, and n = ı n is a real unimodular vector quaternion, with real components a a {n ,n ,n } satisfying n n =1.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- A working hypothesis is a provisionallyaccepted hypothesis used for the purpose of pursuing further progress in research.
- A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought.
- The English word hypothesis comes from the ancient Greek word ὑπόθεσις (hypothesis), whose literal or etymological sense is "putting or placing under" and hence in extended use has many other meanings including "supposition".[1][3][4][5] In Plato's Meno (86e–87b), Socrates dissects virtue with a method which he says is used by mathematicians,[6] that of "investigating from a hypothesis".[7] In this sense, 'hypothesis' refers to a clever idea or a short cut, or a convenient mathematical approach that simplifies cumbersome
- Hypothesis A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon.

A working hypothesis is a provisionallyaccepted hypothesis used for the purpose of pursuing further progress in research.

A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought.

The English word hypothesis comes from the ancient Greek word ὑπόθεσις (hypothesis), whose literal or etymological sense is "putting or placing under" and hence in extended use has many other meanings including "supposition".[1][3][4][5] In Plato's Meno (86e–87b), Socrates dissects virtue with a method which he says is used by mathematicians,[6] that of "investigating from a hypothesis".[7] In this sense, 'hypothesis' refers to a clever idea or a short cut, or a convenient mathematical approach that simplifies cumbersome

Hypothesis A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Includesbibliographicalreferencesandindex.
- Generalrelativity(Physics)—Textbooks.
- ISBN978-0-691-14558-7(hardback) 1.
- pages cm— (Inanutshell) Summary:“ThisuniquetextbookprovidesanaccessibleintroductiontoEinstein’sgeneraltheoryof relativity,asubjectofbreathtakingbeautyandsupremeimportanceinphysics.Withhistrademarkblend ofwitandincisiveness,A.ZeeguidesreadersfromthefundamentalsofNewtonianmechanicstothemost excitingfrontiersofresearchtoday,includingdeSitterandanti–deSitterspacetimes,Kałuza-Kleintheory, andbraneworlds.UnlikeotherbooksonEinsteingravity, thisbookemphasizestheactionprincipleand grouptheoryasguidesinconstructingphysicaltheories.Zeetreatsvarioustopicsinaspiralstylethatiseasy onbeginners,andincludesanecdotesfromthehistoryofphysicsthatwillappealtostudentsandexperts alike.Hetakesafriendlyapproachtotherequiredmathematics,yetdoesnotshyawayfrommoreadvanced mathematicaltopicssuchasdifferentialforms.Theextensivediscussionofblackholesincludesrotatingand extremalblackholesandHawkingradiation.Theidealtextbookforundergraduateandgraduatestudents, EinsteinGravityinaNutshellalsoprovidesanessentialresourceforprofessionalphysicistsandisaccessible toanyonefamiliarwithclassicalmechanicsandelectromagnetism.Itfeaturesnumerousexercisesaswell asdetailedappendicescoveringamultitudeoftopicsnotreadilyfoundelsewhere.

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List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- This apparently paradoxical situation is again a consequence of the relativity of simultaneity as demonstrated by the analysis via Minkowski diagram.
- It says that any observer in an inertial reference frame measuring the vacuum speed of light relative to themself obtains the same value regardless of his own motion and that of the light source.
- second observer moving together with the object, so that for him the object is at rest, it has the proper length OB at t′ = 0.
- Fig 4-4 Relativistic length contraction, as depicted in a single Loedel spacetime diagram.

This apparently paradoxical situation is again a consequence of the relativity of simultaneity as demonstrated by the analysis via Minkowski diagram.

It says that any observer in an inertial reference frame measuring the vacuum speed of light relative to themself obtains the same value regardless of his own motion and that of the light source.

second observer moving together with the object, so that for him the object is at rest, it has the proper length OB at t′ = 0.

Fig 4-4 Relativistic length contraction, as depicted in a single Loedel spacetime diagram.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- 38.15 The super geometric algebra in arbitrarily many spatial dimensions 991 In the case N =3, this gives ( ) 1 0 γγ =γγ ∧γγ = , (38.128) 3 + − 0 −1 in agreement with the Pauli matrix equation (38.8).
- The algebra is a complex (with N respecttoi)vectorspaceofdimension22[N/2],representedinthechiralconstruction(38.109)by2[N/2]× 2[N/2] matrices.
- For example, the N = 2 geometric algebra is the complex vector space generated by 1,γγ ,γγ ,γγ ∧γγ , while the N = 3 geometric algebra (the Pauli algebra) is the complex vector space + − + − generated by 1,γγ ,γγ ,γγ , the pseudoscalar I being identified with the imaginary i.
- N Insummary,thealgebraofspinorouterproductsin2[N/2]dimensionsisisomorphictothegeometric algebra for both even and odd N, modulo κ in the case of odd N.

38.15 The super geometric algebra in arbitrarily many spatial dimensions 991 In the case N =3, this gives ( ) 1 0 γγ =γγ ∧γγ = , (38.128) 3 + − 0 −1 in agreement with the Pauli matrix equation (38.8).

The algebra is a complex (with N respecttoi)vectorspaceofdimension22[N/2],representedinthechiralconstruction(38.109)by2[N/2]× 2[N/2] matrices.

For example, the N = 2 geometric algebra is the complex vector space generated by 1,γγ ,γγ ,γγ ∧γγ , while the N = 3 geometric algebra (the Pauli algebra) is the complex vector space + − + − generated by 1,γγ ,γγ ,γγ , the pseudoscalar I being identified with the imaginary i.

N Insummary,thealgebraofspinorouterproductsin2[N/2]dimensionsisisomorphictothegeometric algebra for both even and odd N, modulo κ in the case of odd N.

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List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- The3vectorsWμ= dxμ (forthe3possiblechoicesofσ;again,whendifferentiatingwithrespecttooneof dσ theσs,weholdtheothertwoσsandτ fixed)orthogonaltoVμ spana3-dimensionalsubspace.Thematrix Pμν=gμν+VμVνclearlyprojectsintothissubspace:PμνV ν =0,PμνP ν λ=Pμλ,andPμνP νμ =3.Then DWμ Dτ =VνD ν Wμ=WνD ν Vμ≡Bμ ν Wν (10) ∗Inthisconnection,IquotefromareviewofQFTNutfortheAmericanMathematicalSociety:“Itisoften deepertoknowwhysomethingistrueratherthantohaveaproofthatitistrue.”Seehttp://www.kitp.ucsb.edu/ members/PM/zee/revMath.html.
- The reader encountering Einstein gravity for the first time could certainly skip over this, or perhaps read only the first section, in which I explain intuitively why ∗ whatissaidtobetrue isinfacttrue.
- Appendix2:TheRaychaudhuriequation Mathematically,abundleoftimelikegeodesicsxμ(τ,σ1,σ2,σ3),labeledbythreerealvariablesσ,isknownasa congruenceinacertainregionif,inthatregion,eachpointliesononeandonlyonegeodesic.Thisimpliesthat thegeodesicsinourbundledonotintersect.Assoonastheyintersect,the“congruence”isover.Asmentioned inthetext,acongruenceoftimelikegeodesicscouldservetocoordinatizethatregion.
- PickapointPononespecificgeodesicanddenotethetangentvectorbyVμ=d d x τ μ .WehaveVμV μ =−1,the definitionofτ,andVμD μ Vν=0,thegeodesicequation.Notationalert!InthedefinitionofVμ,thedifferentiation withrespecttoτ isclearlytobedoneholdingthelabelsσ fixed; wewanttofollowaspecificgeodesic.But throughoutthisbook,thetangentvectortoageodesichasalwaysbeendenotedby dxμ (sincewehavealways dτ consideredonesinglegeodesicatatime,oratmosttwogeodesics,asinthischapter),anditwouldbeoddto suddenlystartwriting∂xμ forthetangentvector.Ithinkthatitwouldbebest,inthisappendixandinappendix4, ∂τ toaskyoutokeepinmindwhatyouareholdingfixedbyfollowingthephysics,ratherthantohaveverticalbars allovertheplaceindicatingwhatisbeingheldfixed,particularlyinappendix4withitsabundanceofvertical bars(asyouwillsee).

The3vectorsWμ= dxμ (forthe3possiblechoicesofσ;again,whendifferentiatingwithrespecttooneof dσ theσs,weholdtheothertwoσsandτ fixed)orthogonaltoVμ spana3-dimensionalsubspace.Thematrix Pμν=gμν+VμVνclearlyprojectsintothissubspace:PμνV ν =0,PμνP ν λ=Pμλ,andPμνP νμ =3.Then DWμ Dτ =VνD ν Wμ=WνD ν Vμ≡Bμ ν Wν (10) ∗Inthisconnection,IquotefromareviewofQFTNutfortheAmericanMathematicalSociety:“Itisoften deepertoknowwhysomethingistrueratherthantohaveaproofthatitistrue.”Seehttp://www.kitp.ucsb.edu/ members/PM/zee/revMath.html.

The reader encountering Einstein gravity for the first time could certainly skip over this, or perhaps read only the first section, in which I explain intuitively why ∗ whatissaidtobetrue isinfacttrue.

PickapointPononespecificgeodesicanddenotethetangentvectorbyVμ=d d x τ μ .WehaveVμV μ =−1,the definitionofτ,andVμD μ Vν=0,thegeodesicequation.Notationalert!InthedefinitionofVμ,thedifferentiation withrespecttoτ isclearlytobedoneholdingthelabelsσ fixed; wewanttofollowaspecificgeodesic.But throughoutthisbook,thetangentvectortoageodesichasalwaysbeendenotedby dxμ (sincewehavealways dτ consideredonesinglegeodesicatatime,oratmosttwogeodesics,asinthischapter),anditwouldbeoddto suddenlystartwriting∂xμ forthetangentvector.Ithinkthatitwouldbebest,inthisappendixandinappendix4, ∂τ toaskyoutokeepinmindwhatyouareholdingfixedbyfollowingthephysics,ratherthantohaveverticalbars allovertheplaceindicatingwhatisbeingheldfixed,particularlyinappendix4withitsabundanceofvertical bars(asyouwillsee).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- ● https://archive.org/details/aliencontacttops00good/page/223/mode/1up?q=bdm(p222-p223) Note:BDMhasseverallinkagestoUAPbesidesemployingShapiro(see26September2022).
- ShermanstatesheistakentoafacilityahalfanhourfromFortMeade,MD,butthathistransportationis blackedoutandheisnevertoldexactlywhereitis.
- HeclaimscertainblackSAPsareactuallycoversfor“alien”projectsknownasLevel1; greyprojects;greymatterorslantmissions.
- Hethenclaimsheis“taught”intcomminclassesthat consistedoflisteningtotonesandtryingtorepeatthembymentallyhummingthem(notverbal).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- 68 THE COLLAPSING UNIVERSE ever.
- The planet might slowly cool off till it had no more heat, in the center or on the surface, and its oceans and atmosphere might freeze, but these are what would be called, from an astronomical standpoint, trivial changes.
- When, therefore, the maximum resistance to compression is exerted by one atom, it is exerted by all under the same pressure.
- If the pressure is further increased, each atom and all the atoms together come to the end of the row.

The planet might slowly cool off till it had no more heat, in the center or on the surface, and its oceans and atmosphere might freeze, but these are what would be called, from an astronomical standpoint, trivial changes.

When, therefore, the maximum resistance to compression is exerted by one atom, it is exerted by all under the same pressure.

If the pressure is further increased, each atom and all the atoms together come to the end of the row.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Answer:In 1975, Chandrasekhar immersed himself in developing a comprehensive mathematical description of
- Serendipity| Q&A 1.Question What were the revolutionary changes in the understanding of black holes during the golden age of black hole research?
- 2.Question How did Subrahmanyan Chandrasekhar contribute to black hole research at the University of Chicago in 1975?
- Physicists realized that all properties of a black hole could be predicted with just three parameters: mass, spin, and electric charge, fundamentally altering the theoretical landscape of general relativity.

Answer:In 1975, Chandrasekhar immersed himself in developing a comprehensive mathematical description of

Serendipity| Q&A 1.Question What were the revolutionary changes in the understanding of black holes during the golden age of black hole research?

2.Question How did Subrahmanyan Chandrasekhar contribute to black hole research at the University of Chicago in 1975?

Physicists realized that all properties of a black hole could be predicted with just three parameters: mass, spin, and electric charge, fundamentally altering the theoretical landscape of general relativity.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Archived (https://web.archive.org/web/20191208165101/ http://iopscience.iop.org/1475-7516/2013/02/015) from the original on 8 December 2019.
- Bennett, Jeffrey; Donahue, Megan; Schneider, Nicholas; Voit, G.
- ISSN 00358711 (https://search.worldcat.org/issn/0035-8711).
- arXiv:1401.5761v1 (https://arxiv.org/abs/1401.5761v1) [hep-th (https://arxiv.org/archive/he p-th)].

Archived (https://web.archive.org/web/20191208165101/ http://iopscience.iop.org/1475-7516/2013/02/015) from the original on 8 December 2019.

Bennett, Jeffrey; Donahue, Megan; Schneider, Nicholas; Voit, G.

arXiv:1401.5761v1 (https://arxiv.org/abs/1401.5761v1) [hep-th (https://arxiv.org/archive/he p-th)].

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- In linguistics In linguistics, the range of dialects spoken over a geographical area that differ slightly between neighboring areas is known as a dialect continuum.
- Expert witnesses particularly are trained to help courts in translating the data into the legal (e.g.
- "Continuity and Infinitesimals" (https://plato.stanford.edu/entries/contin uity/).
- doi:10.1126/science.103.2684.677 (https://doi.org/10.1126%2Fscience.103.2684.677).

In linguistics In linguistics, the range of dialects spoken over a geographical area that differ slightly between neighboring areas is known as a dialect continuum.

Expert witnesses particularly are trained to help courts in translating the data into the legal (e.g.

"Continuity and Infinitesimals" (https://plato.stanford.edu/entries/contin uity/).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Actually,whetheryouknewitornot,youareprobablyalreadyfamiliarwiththePoincar ́elemma.Forexample, surelyyoulearnedsomewherethatifthecurlofavectorfieldvanishes,thevectorfieldislocallythegradientof somescalarfield.
- Appendix2:Exactisclosed,butclosedisnotnecessarilygloballyexact HereImentionanimportantconceptsomewhatoutsidethenarrativeofthisbook,involvingdifferentialforms.
- Istheconverseof(8)true?Kindof.ThePoincar ́elemmastatesthataclosedformislocallyexact.6Inother words,ifdH=0withH somep-form,thenlocally(thatis,withinsomecoordinatepatch) H=dK (23) forsome(p−1)-formK.However,itmayormaynotbethecasethatH=dK globally,thatis,everywhere.
- Talkingthetalk,wesaythat(8)tellsusthatexactformsareclosed.

Istheconverseof(8)true?Kindof.ThePoincar ́elemmastatesthataclosedformislocallyexact.6Inother words,ifdH=0withH somep-form,thenlocally(thatis,withinsomecoordinatepatch) H=dK (23) forsome(p−1)-formK.However,itmayormaynotbethecasethatH=dK globally,thatis,everywhere.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Weallknowthatlighttravelsinastraightline,butwealsonoticeeasilythatwhenlight enterswaterfromair,itbends(asshowninfigure1with“sand”replacedby“air”).Indeed, ∗ thatexplainswhypeoplestandinginswimmingpoolsappeartohavecomicallyshortlegs, aphenomenonyoucantestbystickingapencilinaglassofwater.
- 4 | Prologue x F θ s sand water M C θ w G L Figure1 ThebestpossiblepathforFeynmantofollow togettothedrowninggirlisalongthesolidlines fromFtoG.
- Butyoudon’thavetocalculatetoseethatthereisanoptimalpath.Onlyacretinwould followthethirdpath(thedashedline)showninthefigure!
- Ergo, if light is always in a hurry to get from one point to another, it ∗Ifyoucan’texplainthat,seefigure7.1inFearful.Seealsothecommonmirageshowninfigure7.2:ona hotday,thehighwaybeneathadistantcarappearstobewet,butisinfactdry.Thismirageshowsthatlightonly caresaboutthelocal,nottheglobal,minimumintimeoftransit.

4 | Prologue x F θ s sand water M C θ w G L Figure1 ThebestpossiblepathforFeynmantofollow togettothedrowninggirlisalongthesolidlines fromFtoG.

Ergo, if light is always in a hurry to get from one point to another, it ∗Ifyoucan’texplainthat,seefigure7.1inFearful.Seealsothecommonmirageshowninfigure7.2:ona hotday,thehighwaybeneathadistantcarappearstobewet,butisinfactdry.Thismirageshowsthatlightonly caresaboutthelocal,nottheglobal,minimumintimeoftransit.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- His eyes are still open, blinking slowly, watching us go.
- I have to track through the blood of one more Jason to reach the screen door.
- If you hadn’t tried to stop him, I never would’ve had a chance.” “Really?” “Really.
- Also I’m going to stomp your fucking phone into pieces.

His eyes are still open, blinking slowly, watching us go.

I have to track through the blood of one more Jason to reach the screen door.

If you hadn’t tried to stop him, I never would’ve had a chance.” “Really?” “Really.

Also I’m going to stomp your fucking phone into pieces.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Numerically, it is better to characterize an orbit by L/ 1−α rather than by L itself, since the former remains finite as α → 1, whereas L and 1 − α both tend to zero at α → 1.
- Substituting the two (±) expressions (23.66) for L into dP2/dr, and setting the product of the resulting two expressions for dP2/dr x x equal to zero, equation (23.60), yields a quartic equation p +p P +p P2+p P3+p P4 =0 , (23.67) 0 1 2 3 4

Numerically, it is better to characterize an orbit by L/ 1−α rather than by L itself, since the former remains finite as α → 1, whereas L and 1 − α both tend to zero at α → 1.

Substituting the two (±) expressions (23.66) for L into dP2/dr, and setting the product of the resulting two expressions for dP2/dr x x equal to zero, equation (23.60), yields a quartic equation p +p P +p P2+p P3+p P4 =0 , (23.67) 0 1 2 3 4

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.