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

EVIDENCE:
- 9781405131117_1_pre.qxd 30/6/09 11:42 AM Page vii CONTENTS Preface xiii Acknowledgments xix Introduction The Wide World of Psychomythology 1 1 Brain Power Myths about the Brain and Perception 21 #1 Most People Use Only 10% of Their Brain Power 21 #2 Some People Are Left-Brained, Others Are Right-Brained 25 #3 Extrasensory Perception Is a Well-Established Scientific Phenomenon 29 #4 Visual Perceptions Are Accompanied by Tiny Emissions from the Eyes 33 #5 Subliminal Messages Can Persuade People to Purchase Products 36 2 From Womb to Tomb Myths about Development and Aging 45 #6 Playing Mozart’s Music to Infants Boosts Their Intelligence 45 #7 Adolescence Is Inevitably a Time of Psychological Turmoil 49 #8 Most People Experience a Midlife Crisis in Their 40s or Early 50s 52

9781405131117_1_pre.qxd 30/6/09 11:42 AM Page vii CONTENTS Preface xiii Acknowledgments xix Introduction The Wide World of Psychomythology 1 1 Brain Power Myths about the Brain and Perception 21 #1 Most People Use Only 10% of Their Brain Power 21 #2 Some People Are Left-Brained, Others Are Right-Brained 25 #3 Extrasensory Perception Is a Well-Established Scientific Phenomenon 29 #4 Visual Perceptions Are Accompanied by Tiny Emissions from the Eyes 33 #5 Subliminal Messages Can Persuade People to Purchase Products 36 2 From Womb to Tomb Myths about Development and Aging 45 #6 Playing Mozart’s Music to Infants Boosts Their Intelligence 45 #7 Adolescence Is Inevitably a Time of Psychological Turmoil 49 #8 Most People Experience a Midlife Crisis in Their 40s or Early 50s 52

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:
- A more explicit definition of the exterior derivative is given by equation (15.63).
- The exterior ν n derivative d is isomorphic to the torsion-free covariant spacetime curl D ̊∧ (see equation (15.67) for a more precise statement of the isomorphism), d↔D ̊∧ .
- Iftorsionispresent,thenthetorsion-fullcovariantderivativediffersfromthetorsion-freecovariantderivative,equation(2.68).Insections15.1–15.4,thecovariantderivativeD andthecovariantspacetimederivative n D signifyeitherthetorsion-fullorthetorsion-freederivative;alltheresultsholdeitherway.Inthetheoryof differentialforms,however,startingat§15.6,thecovariantspacetimederivativeisthetorsion-freederivative D ̊ even when torsion is present.
- A closely related derivative is the covariant spacetime derivative D defined by D ≡eνD =γγnD , (15.2) ν n where D and D are respectively the coordinate- and tetrad-frame covariant derivatives.

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.

A more explicit definition of the exterior derivative is given by equation (15.63).

The exterior ν n derivative d is isomorphic to the torsion-free covariant spacetime curl D ̊∧ (see equation (15.67) for a more precise statement of the isomorphism), d↔D ̊∧ .

Iftorsionispresent,thenthetorsion-fullcovariantderivativediffersfromthetorsion-freecovariantderivative,equation(2.68).Insections15.1–15.4,thecovariantderivativeD andthecovariantspacetimederivative n D signifyeitherthetorsion-fullorthetorsion-freederivative;alltheresultsholdeitherway.Inthetheoryof differentialforms,however,startingat§15.6,thecovariantspacetimederivativeisthetorsion-freederivative D ̊ even when torsion is present.

A closely related derivative is the covariant spacetime derivative D defined by D ≡eνD =γγnD , (15.2) ν n where D and D are respectively the coordinate- and tetrad-frame covariant derivatives.

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:
- Greenstein, Oke & Shipman 1971; the most recent and most accurate Sirius B measurements are published in Barstow, Bond et al.
- 236–237 and Ohanian & Ruffini 1994, pp.
- Einstein derived these effects using the equivalence principle as early as 1907, cf.
- Starting with the Hafele–Keating experiment, Hafele & Keating 1972a and Hafele & Keating 1972b, and culminating in the Gravity Probe A experiment; an overview of experiments can be found in Ohanian & Ruffini 1994, table 4.1 on p.

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

Einstein derived these effects using the equivalence principle as early as 1907, cf.

Starting with the Hafele–Keating experiment, Hafele & Keating 1972a and Hafele & Keating 1972b, and culminating in the Gravity Probe A experiment; an overview of experiments can be found 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:
- There are two asymptotic regions.
- (b) (a) Figure 3: (a) Another representation of the blue spatial slice of figure 2.
- The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions.
- (b) Here we have two distant entangled black holes in the same space.

(b) (a) Figure 3: (a) Another representation of the blue spatial slice of figure 2.

The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions.

(b) Here we have two distant entangled black holes in the same space.

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

List tests or derivations implied by the evidence.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper


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

EVIDENCE:
- Topology Atlas (http://at.yorku.ca/index.html) Archived (https://web.archive.org/web/20240428164 301/http://at.yorku.ca/index.html) 28 April 2024 at the Wayback Machine Topology Course Lecture Notes (http://at.yorku.ca/i/a/a/b/23.htm) Archived (https://web.archive.or g/web/20110805165214/http://at.yorku.ca/i/a/a/b/23.htm) 5 August 2011 at the Wayback Machine Aisling McCluskey and Brian McMaster, Topology Atlas.
- August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology (https://archive.org/details/mbiu sstripdrau00pick).
- (Provides a well-motivated, geometric account of general topology, and shows the use of groupoids in discussing van Kampen's theorem, covering spaces, and orbit spaces.) Wacław Sierpiński, General Topology, Dover Publications, 2000, ISBN 0-486-41148-6 Pickover, Clifford A.
- Elementary Topology: A First Course (http://www.pdmi.ras.ru/~olegviro/topoman/index.html) Viro, Ivanov, Netsvetaev, Kharlamov.

Topology Atlas (http://at.yorku.ca/index.html) Archived (https://web.archive.org/web/20240428164 301/http://at.yorku.ca/index.html) 28 April 2024 at the Wayback Machine Topology Course Lecture Notes (http://at.yorku.ca/i/a/a/b/23.htm) Archived (https://web.archive.or g/web/20110805165214/http://at.yorku.ca/i/a/a/b/23.htm) 5 August 2011 at the Wayback Machine Aisling McCluskey and Brian McMaster, Topology Atlas.

August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology (https://archive.org/details/mbiu sstripdrau00pick).

(Provides a well-motivated, geometric account of general topology, and shows the use of groupoids in discussing van Kampen's theorem, covering spaces, and orbit spaces.) Wacław Sierpiński, General Topology, Dover Publications, 2000, ISBN 0-486-41148-6 Pickover, Clifford A.

Elementary Topology: A First Course (http://www.pdmi.ras.ru/~olegviro/topoman/index.html) Viro, Ivanov, Netsvetaev, Kharlamov.

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:
- i.org/10.1080%2F00029890.1988.11971963).
- "Hypersurface" (https://www.encyclopediaofmath.org/index.php?title=Hypersurface), Encyclopedia of Mathematics, EMS Press, 2001 [1994] Shoshichi Kobayashi and Katsumi Nomizu (1969), Foundations of Differential Geometry Vol II, Wiley Interscience P.A.
- Beal (2004) Visualization of hypersurfaces and multivariable (objective) functions by partial globalization (https://dx.doi.org/10.1007/s00371-004-0260-4), The Visual Computer 20(10):665–81.
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Hypersurface&oldid=1275236801"

"Hypersurface" (https://www.encyclopediaofmath.org/index.php?title=Hypersurface), Encyclopedia of Mathematics, EMS Press, 2001 [1994] Shoshichi Kobayashi and Katsumi Nomizu (1969), Foundations of Differential Geometry Vol II, Wiley Interscience P.A.

Beal (2004) Visualization of hypersurfaces and multivariable (objective) functions by partial globalization (https://dx.doi.org/10.1007/s00371-004-0260-4), The Visual Computer 20(10):665–81.

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:
- Every sequence of non-negative integers λi = {λ1,...,λn} defines a highest vector that gives rise to a distinct representation, and every representation is characterized by such a sequence of non-negative integers.
- The vectors of a representation can be obtained by starting with the highest (or lowest) vector and successively applying lowering and raising operators in all possible ways until the lowest (or highest) vector is reached.
- The scaling factor 2/(α · α ), which equals 1 for all but at most one i i of the vectors α in the set (42.52), is introduced to simplify the subsequent definition (42.54) of Dynkin i coordinates.
- For any representation, there is always a lowest vector with the smallest possible charge, and a highest vector with the largest possible charge.

Every sequence of non-negative integers λi = {λ1,...,λn} defines a highest vector that gives rise to a distinct representation, and every representation is characterized by such a sequence of non-negative integers.

The vectors of a representation can be obtained by starting with the highest (or lowest) vector and successively applying lowering and raising operators in all possible ways until the lowest (or highest) vector is reached.

The scaling factor 2/(α · α ), which equals 1 for all but at most one i i of the vectors α in the set (42.52), is introduced to simplify the subsequent definition (42.54) of Dynkin i coordinates.

For any representation, there is always a lowest vector with the smallest possible charge, and a highest vector with the largest possible charge.

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:
- PMID 826945 (https://pubmed.ncbi.nlm.nih.gov/826945).
- Archived (htt ps://web.archive.org/web/20220730093159/https://www.psychologytoday.com/us/blog/growing-frie ndships/201403/time-management-kids) from the original on 30 July 2022.
- Núñez, Rafael; Cooperrider, Kensy; Doan, D; Wassmann, Jürg (1 July 2012).
- "Contours of time: Topographic construals of past, present, and future in the Yupno valley of Papua New Guinea".

Archived (htt ps://web.archive.org/web/20220730093159/https://www.psychologytoday.com/us/blog/growing-frie ndships/201403/time-management-kids) from the original on 30 July 2022.

Núñez, Rafael; Cooperrider, Kensy; Doan, D; Wassmann, Jürg (1 July 2012).

"Contours of time: Topographic construals of past, present, and future in the Yupno valley of Papua New Guinea".

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:
- matter is anything that is made of the same things that atoms and molecules are made of".
- (However, notice that one also can make from these building blocks matter that is not atoms or molecules.) Then, because electrons are leptons, and protons and neutrons are made of quarks, this definition in turn leads to the definition of matter as being "quarks and leptons", which are two of the four types of elementary fermions (the other two being antiquarks and antileptons, which can be considered antimatter as described later).
- Carithers and Grannis state: "Ordinary matter is composed entirely of firstgeneration particles, namely the [up] and [down] quarks, plus the electron and its neutrino."[19] (Higher generations particles quickly decay into first-generation particles, and thus are not commonly encountered.[21])

matter is anything that is made of the same things that atoms and molecules are made of".

(However, notice that one also can make from these building blocks matter that is not atoms or molecules.) Then, because electrons are leptons, and protons and neutrons are made of quarks, this definition in turn leads to the definition of matter as being "quarks and leptons", which are two of the four types of elementary fermions (the other two being antiquarks and antileptons, which can be considered antimatter as described later).

Carithers and Grannis state: "Ordinary matter is composed entirely of firstgeneration particles, namely the [up] and [down] quarks, plus the electron and its neutrino."[19] (Higher generations particles quickly decay into first-generation particles, and thus are not commonly encountered.[21])

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:
- General Relativity (https://archive.org/details/generalrelativit0000wald).
- 4.3.2: University of Chicago Press.
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Geodesics_in_general_relativity&oldid=1333463963"
- "Proving the principle: Taking geodesic dynamics too seriously in Einstein’s theory (htt p://philsci-archive.pitt.edu/9158/1/Tamir_-_Proving_the_Principle.pdf)", Studies In History and Philosophy of Modern Physics 43(2), 137–154 (2012).

Geodesics in general relativity - Wikipedia.pdf

"Proving the principle: Taking geodesic dynamics too seriously in Einstein’s theory (htt p://philsci-archive.pitt.edu/9158/1/Tamir_-_Proving_the_Principle.pdf)", Studies In History and Philosophy of Modern Physics 43(2), 137–154 (2012).

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 of these studies offer no support for an autism epidemic: They suggest that diagnoses of autism are skyrocketing in the absence of any genuine increase in autism’s prevalence.
- In one investigation, researchers tracked the prevalence of autism diagnoses between 1992 and 1998 in an area of England using the same diagnostic criteria at both time points (Chakrabarti & Fombonne, 2005).
- Nor is there any evidence that vaccines containing stronger doses of thimerosal are
- For example, several large American, European, and Japanese studies revealed that even as the rates of vaccinations stayed the same or went down, the rates of diagnosed autism increased (Herbert, Sharp, & Gaudiano, 2002; Honda, Shimizu, & Rutter, 2005).

All of these studies offer no support for an autism epidemic: They suggest that diagnoses of autism are skyrocketing in the absence of any genuine increase in autism’s prevalence.

In one investigation, researchers tracked the prevalence of autism diagnoses between 1992 and 1998 in an area of England using the same diagnostic criteria at both time points (Chakrabarti & Fombonne, 2005).

Nor is there any evidence that vaccines containing stronger doses of thimerosal are

For example, several large American, European, and Japanese studies revealed that even as the rates of vaccinations stayed the same or went down, the rates of diagnosed autism increased (Herbert, Sharp, & Gaudiano, 2002; Honda, Shimizu, & Rutter, 2005).

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:
- American Psychologist, 53, 320–321.
- American Psychologist, 8, 1089–1098.
- The “general acceptance” of psychological research on eyewitness testimony.
- Joiner, T., Pettit, J., & Rudd, M.

The “general acceptance” of psychological research on eyewitness testimony.

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:
- CollectionofFormulasandConventions | 861 Locallyflatcoordinatesystem g (x)=η +B xλxσ +..., B = ∂ ∂ g (27) τμ τμ τμ,λσ τμ,λσ λ σ τμ R =B −B −B +B (28) τρμν τν,μρ ρν,μτ τμ,νρ ρμ,ντ Riemanncurvaturetensor Rσ =(∂ (cid:25)σ +(cid:25)σ (cid:25)κ )−(∂ (cid:25)σ +(cid:25)σ (cid:25)κ ) (29) ρμν μ νρ μκ νρ ν μρ νκ μρ Riccitensor R =Rσ =(∂ (cid:25)σ +(cid:25)σ (cid:25)κ )−(∂ (cid:25)σ +(cid:25)σ (cid:25)κ ) (30) μν μσν σ μν κσ μν ν μσ κν μσ Bianchiidentity D R +D R +D R =0 (31) ν ρμσλ σ ρμλν λ ρμνσ Dμ(R − 1g R)=DμE =0 (32) μν 2 μν μν Einstein’sfieldequationandaction (cid:7) √ S =+ d4x −gR (33) EH 16πG δgσρ=−gσμδg gνρ (34) μν √ √ δ −g= 1 −ggμνδg (35) 2 μν Rμν− 1gμνR=+8πGTμν (36) Rμν=+8πG(Tμν− 1gμνT) (37) (cid:7) √ δS =+1 d4x −gTμνδg (38) matter 2 μν Newton’sfieldequation ∇2(cid:26)=4πGρ (39) GM g =−(1+2(cid:26)), (cid:26)=− (40) 00 r Staticsymmetricspacetime ds2=−A(r)dt2+B(r)dr2+r2dθ2+r2sin2θdφ2 (41) A(cid:5) A(cid:5) B(cid:5) r rsin2θ (cid:25)t = , (cid:25)r = , (cid:25)r = , (cid:25)r =− , (cid:25)r =− , tr 2A tt 2B rr 2B θθ B φφ B 1 1 (cid:25)θ = , (cid:25)φ = , rθ r rφ r (cid:25)θ =−sinθcosθ, (cid:25)φ =cotθ (42) φφ θφ

CollectionofFormulasandConventions | 861 Locallyflatcoordinatesystem g (x)=η +B xλxσ +..., B = ∂ ∂ g (27) τμ τμ τμ,λσ τμ,λσ λ σ τμ R =B −B −B +B (28) τρμν τν,μρ ρν,μτ τμ,νρ ρμ,ντ Riemanncurvaturetensor Rσ =(∂ (cid:25)σ +(cid:25)σ (cid:25)κ )−(∂ (cid:25)σ +(cid:25)σ (cid:25)κ ) (29) ρμν μ νρ μκ νρ ν μρ νκ μρ Riccitensor R =Rσ =(∂ (cid:25)σ +(cid:25)σ (cid:25)κ )−(∂ (cid:25)σ +(cid:25)σ (cid:25)κ ) (30) μν μσν σ μν κσ μν ν μσ κν μσ Bianchiidentity D R +D R +D R =0 (31) ν ρμσλ σ ρμλν λ ρμνσ Dμ(R − 1g R)=DμE =0 (32) μν 2 μν μν Einstein’sfieldequationandaction (cid:7) √ S =+ d4x −gR (33) EH 16πG δgσρ=−gσμδg gνρ (34) μν √ √ δ −g= 1 −ggμνδg (35) 2 μν Rμν− 1gμνR=+8πGTμν (36) Rμν=+8πG(Tμν− 1gμνT) (37) (cid:7) √ δS =+1 d4x −gTμνδg (38) matter 2 μν Newton’sfieldequation ∇2(cid:26)=4πGρ (39) GM g =−(1+2(cid:26)), (cid:26)=− (40) 00 r Staticsymmetricspacetime ds2=−A(r)dt2+B(r)dr2+r2dθ2+r2sin2θdφ2 (41) A(cid:5) A(cid:5) B(cid:5) r rsin2θ (cid:25)t = , (cid:25)r = , (cid:25)r = , (cid:25)r =− , (cid:25)r =− , tr 2A tt 2B rr 2B θθ B φφ B 1 1 (cid:25)θ = , (cid:25)φ = , rθ r rφ r (cid:25)θ =−sinθcosθ, (cid:25)φ =cotθ (42) φφ θφ

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:
- reformulation was made in 1788 by Joseph Louis Lagrange.
- Lagrangian mechanics was in turn refactored in 1833 by William Rowan Hamilton.[39] Some difficulties in classical mechanics were discovered in the late 19th century that could only be resolved by revisions to physics.
- One of the issues related to compatibility with electromagnetic theory, and the famous Michelson–Morley experiment.
- The resolution of these problems led to the

reformulation was made in 1788 by Joseph Louis Lagrange.

Lagrangian mechanics was in turn refactored in 1833 by William Rowan Hamilton.[39] Some difficulties in classical mechanics were discovered in the late 19th century that could only be resolved by revisions to physics.

One of the issues related to compatibility with electromagnetic theory, and the famous Michelson–Morley experiment.

The resolution of these problems led to the

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 two constants a and b are determined by the initial position and initial m velocity,oralternatively ∗ bytheinitialpositionatt =0andbythefinalpositionatsome timet =T.Energy,butnotmomentum,isconserved.
- TheforceF isafunctionofspace.Newton’sequation d2x m =−kx (2) dt2 is ea(cid:6)sily solved in terms of two integration constants: x(t)=acosωt +bsinωt, with ω= k.
- FromNewtontoRiemann:CoordinatestoCurvature Some readers may feel that I am overly pedantic here, but in fact this fundamental inequalityofstatusbetweenxandt willcometoaheadwhenwegettothespecialtheory ofrelativity.(Inowdropthearrowonx(cid:3).)PerhapsEinsteinasastudentwasbotheredby thisbadnotation.Onewaytoremedythesituationistouseq(orq )todenotetheposition a ofparticles,asinmoreadvancedtreatments.ButhereIbowtotraditionandcontinueto usex.
- TheforceF isafunctionoftime.Thisexampleallowsmetointroducethehighlyuseful Dirac1 delta function, or simply delta function.2 By the word “kick” we mean that the time scale τ during which the force acts is much less than the other time scales we are ∗SeepartII.

The two constants a and b are determined by the initial position and initial m velocity,oralternatively ∗ bytheinitialpositionatt =0andbythefinalpositionatsome timet =T.Energy,butnotmomentum,isconserved.

TheforceF isafunctionofspace.Newton’sequation d2x m =−kx (2) dt2 is ea(cid:6)sily solved in terms of two integration constants: x(t)=acosωt +bsinωt, with ω= k.

FromNewtontoRiemann:CoordinatestoCurvature Some readers may feel that I am overly pedantic here, but in fact this fundamental inequalityofstatusbetweenxandt willcometoaheadwhenwegettothespecialtheory ofrelativity.(Inowdropthearrowonx(cid:3).)PerhapsEinsteinasastudentwasbotheredby thisbadnotation.Onewaytoremedythesituationistouseq(orq )todenotetheposition a ofparticles,asinmoreadvancedtreatments.ButhereIbowtotraditionandcontinueto usex.

TheforceF isafunctionoftime.Thisexampleallowsmetointroducethehighlyuseful Dirac1 delta function, or simply delta function.2 By the word “kick” we mean that the time scale τ during which the force acts is much less than the other time scales we are ∗SeepartII.

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:
- The radiation temperature, called Hawking temperature, is inversely proportional to the black hole's mass, so micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass.
- Background Modern black holes were first predicted by Einstein's 1915 theory of general relativity.
- Hawking radiation would reduce the mass and rotational energy of black holes and consequently cause black hole evaporation.
- Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish.

The radiation temperature, called Hawking temperature, is inversely proportional to the black hole's mass, so micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass.

Background Modern black holes were first predicted by Einstein's 1915 theory of general relativity.

Hawking radiation would reduce the mass and rotational energy of black holes and consequently cause black hole evaporation.

Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish.

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:
- doi:10.1103/PhysRevX.11.041050 (http s://doi.org/10.1103%2FPhysRevX.11.041050).
- Weisberg & Taylor 2003; for the pulsar discovery, see Hulse & Taylor 1975; for the initial evidence for gravitational radiation, see Taylor 1994 99.
- For example Jaranowski & Królak 2005 86.
- 4.2.1, Ohanian & Ruffini 1994, pp.

Weisberg & Taylor 2003; for the pulsar discovery, see Hulse & Taylor 1975; for the initial evidence for gravitational radiation, see Taylor 1994 99.

For example Jaranowski & Królak 2005 86.

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 line ends at the "chiral critical point", marked by a star in this figure, which is a special temperature and density at which striking physical phenomena, analogous to critical opalescence, are expected.
- However, because such a description requires the proper understanding of QCD in its non-perturbative regime, which is still far from being completely understood, any theoretical advance remains very challenging.
- and density) and phases where it is unbroken (high temperature and density).
- (Reference for this section:[15][16][17]).

The line ends at the "chiral critical point", marked by a star in this figure, which is a special temperature and density at which striking physical phenomena, analogous to critical opalescence, are expected.

However, because such a description requires the proper understanding of QCD in its non-perturbative regime, which is still far from being completely understood, any theoretical advance remains very challenging.

and density) and phases where it is unbroken (high temperature and density).

(Reference for this section:[15][16][17]).

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:
- ● https://www.thedrive.com/content-b/message-editor%2F1571426976078-conquest2.jpg?auto=we bp&optimize=high&quality=70&width=1200 ● https://www.sunrisepage.com/uft/files/media/Conquest_of_Gravity_Aim_of_Top_Scientists_in_ US.docx Note:ThearticlealsomentionsGeorgeS.Trimble’sRIAS(see1955),andstatesitisfinanced byGlennL.MartinCo.butisolatedfromthecompany’saircraftbuildingbusinessandmanaged byWelcomeBender.
- FormerUNCPresidentGordonGrayapprovedfundingforIPP;GraywasformerlySecretaryof theArmy,AssistantSecretaryofDefenseandspecialassistanttothePresidentoftheUnitedStates (Truman,Eisenhower).
- Anti-gravityisreportedlybeingstudiedattheInstituteforAdvancedStudyatPrinceton University,theUniversityofIndiana’sSchoolofAdvancedMathematicalStudies,thePurdueUniversity ResearchFoundation,MIT,theRogerBabsonGravityResearchInstituteofNewBoston,NH,andthe InstituteofPurePhysics(IPP)attheUniversityofNorthCarolina.
- TheBoardincludedrepresentativesfromDOD andDCI.

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

EVIDENCE:
- Misner, Charles W.; Thorne, Kip.
- An Introduction to Mechanics (https://archive.org/deta ils/introductiontome00dani).
- Springer Graduate Texts in Mathematics.
- JSTOR 27757388 (https://www.jstor.org/stable/27757388).

An Introduction to Mechanics (https://archive.org/deta ils/introductiontome00dani).

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

EVIDENCE:
- Any medium supporting oscillations has an analogue of the Casimir effect.
- For example, beads on a string[10][11] as well as plates submerged in turbulent water[12] or gas[13] illustrate the Casimir force.
- In the same year Casimir, together with Dirk Polder, described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface which is called the Casimir–Polder force.[4] Their result is a generalization of the London–van der Waals force and includes retardation due to Casimir forces on parallel plates the finite speed of light.
- In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics it is significant in some aspects of emerging microtechnologies and nanotechnologies.[14] Physical properties The typical example is of two uncharged conductive plates in a vacuum, placed a few nanometers apart.

Any medium supporting oscillations has an analogue of the Casimir effect.

For example, beads on a string[10][11] as well as plates submerged in turbulent water[12] or gas[13] illustrate the Casimir force.

In the same year Casimir, together with Dirk Polder, described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface which is called the Casimir–Polder force.[4] Their result is a generalization of the London–van der Waals force and includes retardation due to Casimir forces on parallel plates the finite speed of light.

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics it is significant in some aspects of emerging microtechnologies and nanotechnologies.[14] Physical properties The typical example is of two uncharged conductive plates in a vacuum, placed a few nanometers apart.

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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:
- Recall that, in chapter I.7 on classical differential geometry, the mite professors came (cid:3) to the concept of covariant derivative by simply dropping from the vector ∂ W(x) the ν component sticking out of the surface.
- λ Oneday, abrightyoungguypointedoutthatthemitesavantsshouldhavecalculated the covariant derivatives D Wμ=∂ Wμ+(cid:25) μ Wν, instead of the ordinary derivatives λ λ λν ∂ Wμ.Thesymbol(cid:25) μ hadalreadybeendetermined(waybackinchapterII.2bystudying λ λν
- CovariantDifferentiation | 323 Adding(8)and(9),weseethatthecharacterdefectineachofthemcanceleachother,so that indeed D (cid:5) W (cid:5)μ(x (cid:5) )=(S −1) ρ SμD Wν transforms like a tensor with one upper and λ λ ν ρ onelowerindex.
- Thecovariantderivativefromgeometry Another motif from an earlier part of this book resonates with the present discussion.

Recall that, in chapter I.7 on classical differential geometry, the mite professors came (cid:3) to the concept of covariant derivative by simply dropping from the vector ∂ W(x) the ν component sticking out of the surface.

λ Oneday, abrightyoungguypointedoutthatthemitesavantsshouldhavecalculated the covariant derivatives D Wμ=∂ Wμ+(cid:25) μ Wν, instead of the ordinary derivatives λ λ λν ∂ Wμ.Thesymbol(cid:25) μ hadalreadybeendetermined(waybackinchapterII.2bystudying λ λν

CovariantDifferentiation | 323 Adding(8)and(9),weseethatthecharacterdefectineachofthemcanceleachother,so that indeed D (cid:5) W (cid:5)μ(x (cid:5) )=(S −1) ρ SμD Wν transforms like a tensor with one upper and λ λ ν ρ onelowerindex.

Thecovariantderivativefromgeometry Another motif from an earlier part of this book resonates with the present discussion.

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

EVIDENCE:
- A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content (e.g., facts and relationships of the actual historical world as it is unfolding).
- Any human movement that involves no conscious choice and thinking could not be an example of praxis or doing.[c] Formality Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter.
- There are theories in many and varied fields of study, including the arts and sciences.
- change or movement themselves for their own ends.

A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content (e.g., facts and relationships of the actual historical world as it is unfolding).

Any human movement that involves no conscious choice and thinking could not be an example of praxis or doing.[c] Formality Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter.

There are theories in many and varied fields of study, including the arts and sciences.

change or movement themselves for their own ends.

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

EVIDENCE:
- A driving wind blasts us straight-on, and as the snow intensifies, the world ahead takes on the appearance of a furiously shaken snow globe.
- I have no idea how far we’ve come from the box.
- My ring of thread is encrusted with ice.
- and I’m already beginning to lose the fine-motor control in my hands.

A driving wind blasts us straight-on, and as the snow intensifies, the world ahead takes on the appearance of a furiously shaken snow globe.

I have no idea how far we’ve come from the box.

My ring of thread is encrusted with ice.

and I’m already beginning to lose the fine-motor control in my hands.

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

EVIDENCE:
- The reason may come from the simplicity of calculation while the phenomenon is still similar to the complicated case.
- This case is known as "extreme Reissner-Nordstrom black hole".
- In other words, t is always timelike coordinate except at r = μ, both t and r becomes null coordinates.
- One may ask that how much energy of the particle to take itself to this point.

The reason may come from the simplicity of calculation while the phenomenon is still similar to the complicated case.

This case is known as "extreme Reissner-Nordstrom black hole".

In other words, t is always timelike coordinate except at r = μ, both t and r becomes null coordinates.

One may ask that how much energy of the particle to take itself to this point.

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

EVIDENCE:
- Archived (https://web.archive.org/web/201 60709121743/http://hubblesite.org/newscenter/archive/releases/2007/07/full/) from the original on 9 July 2016.
- The Astrophysical Journal Letters.
- Demory, Brice-Olivier; de Wit, Julien; Lewis, Nikole; Fortney, Jonathan; et al.
- arXiv:0705.0993 (https://arxiv.org/abs/0705.0993).

Archived (https://web.archive.org/web/201 60709121743/http://hubblesite.org/newscenter/archive/releases/2007/07/full/) from the original on 9 July 2016.

Demory, Brice-Olivier; de Wit, Julien; Lewis, Nikole; Fortney, Jonathan; et al.

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

EVIDENCE:
- Yet investigators have found that their reports are almost always inaccurate, as gauged by judges’ comparisons of these reports with the actual physical characteristics of the target locations.
- Consistent with this possibility, research suggests that OBEs arise from the failure of different brain areas to integrate information from different senses (Blanke & Thut, 2007).
- Tempting as it is to speculate that our consciousness can break free of the shackles of our physical bodies, research doesn’t support this hypothesis.
- A straightforward way to test the notion that consciousness actually exits the body is to find out whether people can report accurately on what they “see” at a remote location during an OBE.

Yet investigators have found that their reports are almost always inaccurate, as gauged by judges’ comparisons of these reports with the actual physical characteristics of the target locations.

Consistent with this possibility, research suggests that OBEs arise from the failure of different brain areas to integrate information from different senses (Blanke & Thut, 2007).

Tempting as it is to speculate that our consciousness can break free of the shackles of our physical bodies, research doesn’t support this hypothesis.

A straightforward way to test the notion that consciousness actually exits the body is to find out whether people can report accurately on what they “see” at a remote location during an OBE.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- There’s no oxygen in the room.
- I see a man get up from where he’s been sitting on the floor.
- They came early for the lottery.
- I look back up the stairs, the blood rushing in my ears so loud it temporarily blocks out everything in a waterfall of panic-driven white noise.

I see a man get up from where he’s been sitting on the floor.

I look back up the stairs, the blood rushing in my ears so loud it temporarily blocks out everything in a waterfall of panic-driven white noise.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- PARTICLES AND FORCES 21 we end up with a final product of 1 x 108 dynes, or 0.000000000000000000000000000000000000000000000000000000001 dynes (Here is an example of why exponential figures are used by scientists in preference to ordinary decimals.) We can therefore say that for a proton and an electron separated by 1 centimeter the gravitational attraction between them can be represented as: F(g) 1 x dynes.
- Once again, distance is measured in centimeters, and if we measure the electric charge in what are called electrostatic units, it is not necessary to insert a term analogous to the gravitational constant provided the objects are separated by a vacuum.
- (Of course, since I am assuming the objects are alone in the universe, there is necessarily
- Exactly one hundred years after Newton worked out the equation for gravitational force the French physicist Charles Augustin de Coulomb (1736-1806) was able to show that a very similar equation could be used to determine the intensity of the electromagnetic force.

PARTICLES AND FORCES 21 we end up with a final product of 1 x 108 dynes, or 0.000000000000000000000000000000000000000000000000000000001 dynes (Here is an example of why exponential figures are used by scientists in preference to ordinary decimals.) We can therefore say that for a proton and an electron separated by 1 centimeter the gravitational attraction between them can be represented as: F(g) 1 x dynes.

Once again, distance is measured in centimeters, and if we measure the electric charge in what are called electrostatic units, it is not necessary to insert a term analogous to the gravitational constant provided the objects are separated by a vacuum.

(Of course, since I am assuming the objects are alone in the universe, there is necessarily

Exactly one hundred years after Newton worked out the equation for gravitational force the French physicist Charles Augustin de Coulomb (1736-1806) was able to show that a very similar equation could be used to determine the intensity of the electromagnetic force.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure.
- Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's horizon, is not a physical barrier.[157] Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole) and the axisymmetric Kerr solution (used to describe a rotating, stationary black hole, and introducing interesting features such as the ergosphere).
- Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the form of energy conditions) are used to derive general results.[155] Event horizons Using global geometry, some spacetimes can be shown to contain boundaries called horizons, which demarcate one region from the rest of spacetime.
- With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass–energy, linear momentum, angular momentum, and location at a specified time.

In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure.

Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's horizon, is not a physical barrier.[157] Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole) and the axisymmetric Kerr solution (used to describe a rotating, stationary black hole, and introducing interesting features such as the ergosphere).

Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the form of energy conditions) are used to derive general results.[155] Event horizons Using global geometry, some spacetimes can be shown to contain boundaries called horizons, which demarcate one region from the rest of spacetime.

With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass–energy, linear momentum, angular momentum, and location at a specified time.

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

EVIDENCE:
- In modern times, the Global Positioning System in coordination with the Network Time Protocol can be used to Chip-scale atomic clocks, such as this synchronize timekeeping systems across the globe.
- UTC differs from TAI by an integral number of seconds.
- A day is usually 24 hours or 86,400 seconds in length; however, the duration of a calendar day can vary due to daylight saving time and leap seconds.
- International Atomic Time (TAI) is the primary international time standard from which other time standards are calculated.

In modern times, the Global Positioning System in coordination with the Network Time Protocol can be used to Chip-scale atomic clocks, such as this synchronize timekeeping systems across the globe.

UTC differs from TAI by an integral number of seconds.

A day is usually 24 hours or 86,400 seconds in length; however, the duration of a calendar day can vary due to daylight saving time and leap seconds.

International Atomic Time (TAI) is the primary international time standard from which other time standards are calculated.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- The energy and momentum moments of the distribution c define the dark matter overdensity δ and bulk velocity vvv , while the pressure is of order v2, and can be c c c neglected to linear order (note the different fonts for particle velocity v and bulk velocity v), ∫ g d3p T00 ≡ f m c c ≡ρ ̄ (1+δ ) , (33.28a) c c c (2π(cid:126))3 c c ∫ g d3p T0a ≡ f m va c c ≡ρ ̄ va , (33.28b) c c c c (2π(cid:126))3 c c ∫ g d3p Tab ≡ f m vavb c c =0 .
- Show that in a general gauge, and including not just scalar but also vector and tensor fluctuations, equation (33.15) is dλ a [ pa ] = 1+ψ+ (∇ w ̃+w ̃ ) , (33.25) dη E E a a while equation (33.16) yields the gravitational redshift term dln(ap) Ep^a [ ( ∂ a ̇ m2) ] G≡ =φ ̇+ −∇ ψ+ + (∇ w ̃+w ̃ ) dη p a ∂η aE2 a a [ ] + p^ap^b −∇ ∇ (w−h ̇)− 1(∇ W +∇ W )+∇ w ̃ +h ̇ .
- The unperturbed mean density is ρ ̄ , which evolves with cosmic scale factor a as c ρ ̄ ∝a−3 .
- 33.3 Non-baryonic cold dark matter 883 Exercise 33.3.

The energy and momentum moments of the distribution c define the dark matter overdensity δ and bulk velocity vvv , while the pressure is of order v2, and can be c c c neglected to linear order (note the different fonts for particle velocity v and bulk velocity v), ∫ g d3p T00 ≡ f m c c ≡ρ ̄ (1+δ ) , (33.28a) c c c (2π(cid:126))3 c c ∫ g d3p T0a ≡ f m va c c ≡ρ ̄ va , (33.28b) c c c c (2π(cid:126))3 c c ∫ g d3p Tab ≡ f m vavb c c =0 .

Show that in a general gauge, and including not just scalar but also vector and tensor fluctuations, equation (33.15) is dλ a [ pa ] = 1+ψ+ (∇ w ̃+w ̃ ) , (33.25) dη E E a a while equation (33.16) yields the gravitational redshift term dln(ap) Ep^a [ ( ∂ a ̇ m2) ] G≡ =φ ̇+ −∇ ψ+ + (∇ w ̃+w ̃ ) dη p a ∂η aE2 a a [ ] + p^ap^b −∇ ∇ (w−h ̇)− 1(∇ W +∇ W )+∇ w ̃ +h ̇ .

The unperturbed mean density is ρ ̄ , which evolves with cosmic scale factor a as c ρ ̄ ∝a−3 .

33.3 Non-baryonic cold dark matter 883 Exercise 33.3.

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

EVIDENCE:
- For the resulting vector field to be a spray (on the deleted tangent bundle TM \ {0}) it is enough that the connection be equivariant under positive rescalings, that is, it is enough that, if is transported by to , then must be transported to for any .
- Intuitively, discards the change to velocity and preserves change to base point.
- More generally, the same construction allows one to construct a vector field for any Ehresmann connection on the tangent bundle.
- It is not necessary that, if is also transported to , then must be transported .

For the resulting vector field to be a spray (on the deleted tangent bundle TM \ {0}) it is enough that the connection be equivariant under positive rescalings, that is, it is enough that, if is transported by to , then must be transported to for any .

Intuitively, discards the change to velocity and preserves change to base point.

More generally, the same construction allows one to construct a vector field for any Ehresmann connection on the tangent bundle.

It is not necessary that, if is also transported to , then must be transported .

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

EVIDENCE:
- As the particle is more localized in position space, Δx is smaller than for Δp .
- As the particle is more localized in momentum space, Δp is smaller than for Δx.
- Top: If wavelength λ is unknown, so are momentum p, wave-vector k and energy E (de Broglie relations).
- Position x and momentum p wavefunctions corresponding to quantum particles.

As the particle is more localized in position space, Δx is smaller than for Δp .

As the particle is more localized in momentum space, Δp is smaller than for Δx.

Top: If wavelength λ is unknown, so are momentum p, wave-vector k and energy E (de Broglie relations).

Position x and momentum p wavefunctions corresponding to quantum particles.

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

EVIDENCE:
- 'Take the bomb to the StarGate room.
- Soon the miners arrived at the pyramid.
- Daniel pressed a stone on the dead guard's mask.
- Ifthe Earth men get inside,kill them allagain and send their bomb to Earth.' Outside the pyramid, Skaara ordered everyone to go down on their knees.

Daniel pressed a stone on the dead guard's mask.

Ifthe Earth men get inside,kill them allagain and send their bomb to Earth.' Outside the pyramid, Skaara ordered everyone to go down on their knees.

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

EVIDENCE:
- Despite the mismatch, it is useful to pursue α ̄ the approach further, because it leads to a set of constraint equations commonly called the Gaussian and Hamiltonian constraints.
- Afterthespace+time3+1split,thecoordinatesarethespatialcomponentsoftheLorentzconnectionΓ , α ̄ which is a bivector 1-form with 6×3 = 18 components, and the momentum is the spatial line interval e , α ̄ which is a vector 1-form with 4×3=12 components, Γ =Γ dxα =Γ γγk∧γγldxα , (16.307a) α ̄ α klα e =e dxα =e γγkdxα .
- (16.307b) α ̄ α kα The mismatch between the number 18 of components of the spatial connection Γ and the number 12 α ̄ of components of the spatial line interval e is problematic.
- 466 Action principle for electromagnetism and gravity α ̄)thatrepresentstheremainingspatial-coordinatecomponents.Thet ̄andα ̄subscriptsshouldbeinterpreted as labels, not indices.

Despite the mismatch, it is useful to pursue α ̄ the approach further, because it leads to a set of constraint equations commonly called the Gaussian and Hamiltonian constraints.

Afterthespace+time3+1split,thecoordinatesarethespatialcomponentsoftheLorentzconnectionΓ , α ̄ which is a bivector 1-form with 6×3 = 18 components, and the momentum is the spatial line interval e , α ̄ which is a vector 1-form with 4×3=12 components, Γ =Γ dxα =Γ γγk∧γγldxα , (16.307a) α ̄ α klα e =e dxα =e γγkdxα .

(16.307b) α ̄ α kα The mismatch between the number 18 of components of the spatial connection Γ and the number 12 α ̄ of components of the spatial line interval e is problematic.

466 Action principle for electromagnetism and gravity α ̄)thatrepresentstheremainingspatial-coordinatecomponents.Thet ̄andα ̄subscriptsshouldbeinterpreted as labels, not indices.

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

EVIDENCE:
- (2.127) κ λμνπ λ μκνπ μ κλνπ The torsion-free Bianchi identities can be written in shorthand D R =0 .
- There are 4 ways to pick [κλμ], and 6 ways to pick antisymmetric νπ, giving 4×6 = 24 Bianchi identities, but 4 of the identities, D R = 0, are implied by the cyclic symmetry (2.120), which is a consequence of vanishing torsion.
- 2.22 Bianchi identities The Jacobi identity [D ,[D ,D ]]+[D ,[D ,D ]]+[D ,[D ,D ]]=0 (2.126) κ λ μ λ μ κ μ κ λ implies the Bianchi identities which, for vanishing torsion, are D R +D R +D R =0 .
- 80 Fundamentals of General Relativity The Ricci scalar is R≡gκμR a coordinate tensor (a scalar) .

(2.127) κ λμνπ λ μκνπ μ κλνπ The torsion-free Bianchi identities can be written in shorthand D R =0 .

There are 4 ways to pick [κλμ], and 6 ways to pick antisymmetric νπ, giving 4×6 = 24 Bianchi identities, but 4 of the identities, D R = 0, are implied by the cyclic symmetry (2.120), which is a consequence of vanishing torsion.

2.22 Bianchi identities The Jacobi identity [D ,[D ,D ]]+[D ,[D ,D ]]+[D ,[D ,D ]]=0 (2.126) κ λ μ λ μ κ μ κ λ implies the Bianchi identities which, for vanishing torsion, are D R +D R +D R =0 .

80 Fundamentals of General Relativity The Ricci scalar is R≡gκμR a coordinate tensor (a scalar) .

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

EVIDENCE:
- “Something happened while you were out,” she says.
- “I’ll warm up your plate.” She tries to step past him on her way to the fridge, but he blocks her path.
- It’s been a while since he touched her like this.
- Facing him now, she stares up into his eyes, and maybe it’s because they’ve both been drinking, but there’s an intensity in the air between them, as if every molecule has been charged.

“Something happened while you were out,” she says.

“I’ll warm up your plate.” She tries to step past him on her way to the fridge, but he blocks her path.

It’s been a while since he touched her like this.

Facing him now, she stares up into his eyes, and maybe it’s because they’ve both been drinking, but there’s an intensity in the air between them, as if every molecule has been charged.

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:
- variable" theory (a sort of common-sense formulation of how information is conveyed), but certain systems permitted in quantum mechanics can attain values as high as .
- As an example, the Quantum circuit to create Bell state .
- For the four basic two-qubit inputs, , the circuit outputs the four Bell states (listed above).
- They are known as the four maximally entangled two-qubit Bell states and form a maximally entangled basis, known as the Bell basis, of the four-dimensional Hilbert space for two qubits:[1] Creating Bell states via quantum circuits Although there are many possible ways to create entangled Bell states through quantum circuits, the simplest takes a computational basis as the input, and contains a Hadamard gate and a CNOT gate (see picture).

variable" theory (a sort of common-sense formulation of how information is conveyed), but certain systems permitted in quantum mechanics can attain values as high as .

As an example, the Quantum circuit to create Bell state .

For the four basic two-qubit inputs, , the circuit outputs the four Bell states (listed above).

They are known as the four maximally entangled two-qubit Bell states and form a maximally entangled basis, known as the Bell basis, of the four-dimensional Hilbert space for two qubits:[1] Creating Bell states via quantum circuits Although there are many possible ways to create entangled Bell states through quantum circuits, the simplest takes a computational basis as the input, and contains a Hadamard gate and a CNOT gate (see picture).

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

EVIDENCE:
- (1a, 1b, 2), it descends: He further assumes that the orbit is circular, i.e.
- (4) stems from the virial theorem, and from the classical mechanics relationships between the angular momentum, the kinetic energy and the frequency of revolution.
- Then Bohr assumes that is an integer multiple of the energy of a quantum of light with half the frequency of the electron's revolution frequency,[11]: 4 i.e.: From eq.
- , and, denoting the angular momentum of the electron as L, introduces the equation: Eq.

(1a, 1b, 2), it descends: He further assumes that the orbit is circular, i.e.

(4) stems from the virial theorem, and from the classical mechanics relationships between the angular momentum, the kinetic energy and the frequency of revolution.

Then Bohr assumes that is an integer multiple of the energy of a quantum of light with half the frequency of the electron's revolution frequency,[11]: 4 i.e.: From eq.

, and, denoting the angular momentum of the electron as L, introduces the equation: Eq.

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

EVIDENCE:
- Particles between the outer and inner horizons are outgoing or ingoing as the Hamilton-Jacobi time parameter P , equation (23.5a), is positive or negative, §23.5.
- 24.7 The black hole collider 713 .0 .5 1.0 Spinparametera/M )seerged(edutitalmumixaM m=0 m=E Figure 24.1 Massless (solid) or massive (dashed) collisionless particles that fall from infinite radius can reach the innerhorizonandbeeitheroutgoingoringoingonlyuptoacertainmaximumlatitudeontheinnerhorizon,shown here.Athigherlatitudesontheinnerhorizon,particlesthatfreefallfrominfinityarenecessarilyingoingattheinner horizon.Themaximumaccessiblelatitudedependsonthespinoftheblackhole.Themaximumlatitudevariesfrom √ √ 90∘ (all latitudes are accessible) for a Schwarzschild (non-spinning) black hole, to asin −3+2 3=42∘.9 (m=0) orasin √ 1/3=35∘.3(m=E),arrowed,foranextremalKerrblackhole.
- What happens at the poles on the inner horizon?
- Particles that fall through the outer t horizon are necessarily ingoing at the outer horizon, requiring P < 0 at the outer horizon.

Particles between the outer and inner horizons are outgoing or ingoing as the Hamilton-Jacobi time parameter P , equation (23.5a), is positive or negative, §23.5.

24.7 The black hole collider 713 .0 .5 1.0 Spinparametera/M )seerged(edutitalmumixaM m=0 m=E Figure 24.1 Massless (solid) or massive (dashed) collisionless particles that fall from infinite radius can reach the innerhorizonandbeeitheroutgoingoringoingonlyuptoacertainmaximumlatitudeontheinnerhorizon,shown here.Athigherlatitudesontheinnerhorizon,particlesthatfreefallfrominfinityarenecessarilyingoingattheinner horizon.Themaximumaccessiblelatitudedependsonthespinoftheblackhole.Themaximumlatitudevariesfrom √ √ 90∘ (all latitudes are accessible) for a Schwarzschild (non-spinning) black hole, to asin −3+2 3=42∘.9 (m=0) orasin √ 1/3=35∘.3(m=E),arrowed,foranextremalKerrblackhole.

What happens at the poles on the inner horizon?

Particles that fall through the outer t horizon are necessarily ingoing at the outer horizon, requiring P < 0 at the outer horizon.

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:
- In mn particular Γk un is the generator of a Lorentz transformation along the path of a fishy moving with 4mn velocity un.
- Does that mathematical answer lead to further conceptual insight?
- (19.28) mn Equation (19.28) describes an infinitesimal Lorentz transformation −Γk δξn of the 4-vector pk.
- (19.31) ∂xβ But equation (19.30) is nothing more than an infinitesimal Lorentz boost by a velocity change δβa.

In mn particular Γk un is the generator of a Lorentz transformation along the path of a fishy moving with 4mn velocity un.

Does that mathematical answer lead to further conceptual insight?

(19.28) mn Equation (19.28) describes an infinitesimal Lorentz transformation −Γk δξn of the 4-vector pk.

(19.31) ∂xβ But equation (19.30) is nothing more than an infinitesimal Lorentz boost by a velocity change δβa.

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:
- PARTICLES AND FORCES 19 comparatively unimportant for our purposes here.
- Gravitation affects any particle with mass, hadrons, leptons, and any combination of thesewhich means all the objects we see around us on Earth and in the sky.* We can expand Table 2 now into Table 4 by adding the weak force and gravitation.
- Both of these will crop up later in the book.
- The gravitational force between them can be expressed by an equation first I There are some particles without mass that are not affected in the ordinary sense by gravitation.

PARTICLES AND FORCES 19 comparatively unimportant for our purposes here.

Gravitation affects any particle with mass, hadrons, leptons, and any combination of thesewhich means all the objects we see around us on Earth and in the sky.* We can expand Table 2 now into Table 4 by adding the weak force and gravitation.

Both of these will crop up later in the book.

The gravitational force between them can be expressed by an equation first I There are some particles without mass that are not affected in the ordinary sense by gravitation.

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:
- ε→0 ε The reason for the minus sign in the definition (7.125) of the Lie derivative is that, as will be seen below, equation(7.151),theprincipaltermintheexpansionoftheLiederivativeofatensorA..
- The Lie derivative is also a covariant derivative: the Lie derivative of a coordinate tensor is a coordinate tensor.
- under the coordinate transformation (7.124) is given by ε times minus its Lie derivative, denoted L Aκλ..., ξ μν...
- The conservation law is a consequence of symmetry of the general relativistic action under coordinate transformations.Finally(thenominalmotivationforintroducingLiederivativeshere),ifaspacetimepossessessome

ε→0 ε The reason for the minus sign in the definition (7.125) of the Lie derivative is that, as will be seen below, equation(7.151),theprincipaltermintheexpansionoftheLiederivativeofatensorA..

The Lie derivative is also a covariant derivative: the Lie derivative of a coordinate tensor is a coordinate tensor.

under the coordinate transformation (7.124) is given by ε times minus its Lie derivative, denoted L Aκλ..., ξ μν...

The conservation law is a consequence of symmetry of the general relativistic action under coordinate transformations.Finally(thenominalmotivationforintroducingLiederivativeshere),ifaspacetimepossessessome

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:
- Maybe it’s a reflection of what you were feeling at the moment you opened the door.” She takes the last bite of food and tosses her empty MRE packet into the fire.
- But what if we’re defining these connections?” “How?” “What if it’s like dream-building, where we’re somehow choosing these specific worlds?” “You’re saying that, out of an infinite number of realities, I intentionally picked this shithole?” “Not intentionally.
- What was our emotional state as we walked into that parking garage?” “Fear.
- I say, “Think about the first world we saw—that ruined Chicago, with the buildings crumbling all around us.

Maybe it’s a reflection of what you were feeling at the moment you opened the door.” She takes the last bite of food and tosses her empty MRE packet into the fire.

But what if we’re defining these connections?” “How?” “What if it’s like dream-building, where we’re somehow choosing these specific worlds?” “You’re saying that, out of an infinite number of realities, I intentionally picked this shithole?” “Not intentionally.

What was our emotional state as we walked into that parking garage?” “Fear.

I say, “Think about the first world we saw—that ruined Chicago, with the buildings crumbling all around us.

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:
- In one study, they asked students to listen to an uplifting piece by Mozart, a depressing piece by another classical composer (Albinoni), and silence (Thompson, Schellenberg, & Husain, 2001).
- Later researchers helped to pin down the source of the Mozart Effect.
- | Chapter 2 From Womb to Tomb 47
- Immediately afterwards, the investigators gave participants a paper folding and cutting task.

In one study, they asked students to listen to an uplifting piece by Mozart, a depressing piece by another classical composer (Albinoni), and silence (Thompson, Schellenberg, & Husain, 2001).

Later researchers helped to pin down the source of the Mozart Effect.

Immediately afterwards, the investigators gave participants a paper folding and cutting task.

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:
- — News story about Z(3900) particle discovery.
- "Experimental tests of asymptotic freedom".
- arXiv:hep-ex/0606035 (https://arxiv.org/abs/hep-ex/0606035).
- External links The dictionary definition of hadron at Wiktionary Retrieved from "https://en.wikipedia.org/w/index.php?title=Hadron&oldid=1327720801"

— News story about Z(3900) particle discovery.

"Experimental tests of asymptotic freedom".

External links The dictionary definition of hadron at Wiktionary Retrieved from "https://en.wikipedia.org/w/index.php?title=Hadron&oldid=1327720801"

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- provided the transformations are linear.
- Standard basis A standard or orthonormal basis for Minkowski space is a set of four mutually orthogonal vectors {e , e , e , e } such that and for which 0 1 2 3 when
- This quadratic form can be used to define a bilinear form via the polarization identity.
- Minkowski metric From the second postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary events called 1 and 2 is:[13] This quantity is not consistently named in the literature.

provided the transformations are linear.

Standard basis A standard or orthonormal basis for Minkowski space is a set of four mutually orthogonal vectors {e , e , e , e } such that and for which 0 1 2 3 when

This quadratic form can be used to define a bilinear form via the polarization identity.

Minkowski metric From the second postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary events called 1 and 2 is:[13] This quantity is not consistently named in the literature.

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:
- possible to reconstruct uniquely a corresponding Calabi–Yau manifold.[91] Instead, two different versions of string theory, type IIA and type IIB, can be compactified on completely different Calabi–Yau manifolds giving rise to the same physics.
- In this situation, the manifolds are called mirror manifolds, and the relationship between the two physical theories is called mirror symmetry.[28] Regardless of whether Calabi–Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences.
- The Calabi–Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions.[28][92]

possible to reconstruct uniquely a corresponding Calabi–Yau manifold.[91] Instead, two different versions of string theory, type IIA and type IIB, can be compactified on completely different Calabi–Yau manifolds giving rise to the same physics.

In this situation, the manifolds are called mirror manifolds, and the relationship between the two physical theories is called mirror symmetry.[28] Regardless of whether Calabi–Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences.

The Calabi–Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions.[28][92]

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:
- the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition.
- Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume.
- He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.
- The universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.[46]

the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition.

Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume.

He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.

The universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.[46]

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:
- Army Surgeon General was begun at SRI in FY 1986.
- To accomplish these objectives, SRI began work to identify explanatory neurophysiological mechanisms and specify phenomenological properties.
- Training, evaluation, and search were emphasized.
- Moreover, a five-year psychoenergetics program (FYs* 1986-1990) using Army Medical research and development funds authorized by the then U.S.

Army Surgeon General was begun at SRI in FY 1986.

To accomplish these objectives, SRI began work to identify explanatory neurophysiological mechanisms and specify phenomenological properties.

Training, evaluation, and search were emphasized.

Moreover, a five-year psychoenergetics program (FYs* 1986-1990) using Army Medical research and development funds authorized by the then U.S.

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:
- Behavior of tensors under inclusion, pullback of covariant tensors under general maps and pushforward of vectors under general maps
- Geometry The meaning of the term geometry for the Minkowski space depends heavily on the context.
- Thus, the structure of Minkowski space is still essential in the description of general relativity.
- It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space.

Behavior of tensors under inclusion, pullback of covariant tensors under general maps and pushforward of vectors under general maps

Geometry The meaning of the term geometry for the Minkowski space depends heavily on the context.

Thus, the structure of Minkowski space is still essential in the description of general relativity.

It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space.

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:
- 822 | Index action(continued) spacetime,664;hyperboliccoordinates,661;of foreverythingelse,347;forfieldsinspacetime stereographicprojection,641 describedbyametric,770;inflatspacetime,379; analyticgeometry,roleofcoordinates,48 formulationbymetricorvielbein,785;offree Anderson,Phil,onparticlephysicists,713n particle,162;gravitationaltimedilation,284;for angles:definedbyphysicists,170;hyperbolic,628; gravity,339,344,346;asinfiniteseriesofterms, importanceof,620 766;Kałuza-Klein,inJordanframe,686;length angularcoordinates:ondeSitterspacetime,627; orenergyscaledependenceof,710;local,246; suppressed,422,426 Lorentz,inKałuza-Kleintheory,678;ofmatter angularcorrelation,cosmicmicrowavebackground (seematteraction);Maxwell,325,332,675–676; fluctuations,523f formotionoffinitesizedobjects,714–715,716; angulardeficits:as“measure”ofcurvature,727;of Newton-Einstein-Hilbert,quantumgravitylimit polyhedra,726–727 of,444;Newton’slawofactionandreaction,470; angularmomentum:aroundblackholes,412–413, nondependenceonmetric,723;nonlocalityin 459;conservationof,30,36–37,48n,126,152, time,754;nonrelativistic,241–242,356;offshell 310;Kerrblackhole,slowrotationlimit,571;loss, informationcarriedby,782;reasonsforemphasis Penroseprocess,471–472;ofparticleonsphere, on,396;relativistic,284–285,308;relativistic 148;ofrotatingblackholes,442,465,576;of string,210n;scalarfield,332;specificationof rotatingbodies,563–577;symmetryof,150 dynamicalvariables,395;termsof,behaviorat angularvelocity:aroundblackholes,414,460; longdistances,722;topological,720–721;total, definedbytimecoordinate,550;forKerrblack Newtonianworld,145;ofuniverse,346,356;as hole,462f;slowlyrotatinggravitationalsources, usuallyformulated,783;ofworld,andenergy 570;insidestationarylimitsurface,471 momentumtensor,378;Yang-Mills,681 annihilatedspacetime,785 actionfunctional,138 annihilationoperator,447–448 actionprinciple,155;basicsofphysics,136–149; annusmirabilis,AlbertEinstein’s,265 differentnotionsof,138;asfundamentalprinciple antandhoneyanalogy,5–6,5f oftheoreticalphysics,783;globalityof,compared antmovement,asexampleofvariationalcalculus, toequationofmotion,141;kinetictermin,140; 128 andleasttimeprinciple,139,144;metaphorfor anthropicprinciple:andcosmologicalconstant life,140;mysteryof,141,155;ofparticlesand paradox,751–752,757;andultimativetheory, fields,145;theoriesbasedon,383;variational 789n calculus,113 antideSitter/conformalfieldtheories(AdS/CFT): actionvariation,holdingdynamicalvariablesfixed, AdS/CFTcorrespondence,649,787;conformal 380 coordinatesof,654,654f;andPoincar ́ehalfplane, activediffeomorphism,397 68 actualbiologicaltime,elapsedbetweeneventAand antideSitterspacetime(AdS),606e,612,649– B,179 666;for2-branemodel,702;AdS2boundaries, additionofvelocities.Seevelocities 664;boundaryof,655;d-dimensional,650,650f; ADM(Arnowitt-Deser-Misner)formulation,of differentformsof,660;inhyperboliccoordinates, gravitationaldynamics,693 661;isometrygroupof,650;motionoflight,659; AdS.SeeantideSitterspacetime motionofmassiveparticles,659–660;Poincar ́e affineparameter,308 coordinates,656;sliceof,658f;stereographic Aharonov-Bohmeffect,789n projectionfor,661;tablefor,662 airresistance,andfreefall,268 anti-gravity,discussionof,392 airlineexample,forprovingcurvatureofearth,66 anticommutation:ofdifferentialforms,597;Jordan’s al-jabr,calculationmethod,208n manuscripton,789n Al-Khwarizmi,calculationofsquareroots,207n antimatter:andchargeconjugationinKałuzaalgebra:conformal, 614–623; deSitter, and Kleintheory,678;creationof,205,206;inearly cosmologicalconstant,755;extensionsof,667; universe,528;Feynmandiagramof,206f;in Lie(seeLiealgebra);Lorentz(seeLorentzalgebra); higherdimensionaltheories,683;inquantum matrix,quickreviewof,742–743;Poincar ́e(see fieldtheory,476 Poincar ́ealgebra) antiparticles,26,437–438 algorithm,etymologyoftheword,207n antipodalcondition,spaceofspheres,646 ambitwistors:powerof,738;representationof,736 antisymmetricmatrices,introductionof,40 Americanfootball,relativityof,171,172f antisymmetricsymbol:incurvedspacetime,723– “analogNewtonian”equation,367 725;asinvarianttensor,60;roleasmetric,734; analyticcontinuation:deSittertoantideSitter usedtocontractindices,719

822 | Index action(continued) spacetime,664;hyperboliccoordinates,661;of foreverythingelse,347;forfieldsinspacetime stereographicprojection,641 describedbyametric,770;inflatspacetime,379; analyticgeometry,roleofcoordinates,48 formulationbymetricorvielbein,785;offree Anderson,Phil,onparticlephysicists,713n particle,162;gravitationaltimedilation,284;for angles:definedbyphysicists,170;hyperbolic,628; gravity,339,344,346;asinfiniteseriesofterms, importanceof,620 766;Kałuza-Klein,inJordanframe,686;length angularcoordinates:ondeSitterspacetime,627; orenergyscaledependenceof,710;local,246; suppressed,422,426 Lorentz,inKałuza-Kleintheory,678;ofmatter angularcorrelation,cosmicmicrowavebackground (seematteraction);Maxwell,325,332,675–676; fluctuations,523f formotionoffinitesizedobjects,714–715,716; angulardeficits:as“measure”ofcurvature,727;of Newton-Einstein-Hilbert,quantumgravitylimit polyhedra,726–727 of,444;Newton’slawofactionandreaction,470; angularmomentum:aroundblackholes,412–413, nondependenceonmetric,723;nonlocalityin 459;conservationof,30,36–37,48n,126,152, time,754;nonrelativistic,241–242,356;offshell 310;Kerrblackhole,slowrotationlimit,571;loss, informationcarriedby,782;reasonsforemphasis Penroseprocess,471–472;ofparticleonsphere, on,396;relativistic,284–285,308;relativistic 148;ofrotatingblackholes,442,465,576;of string,210n;scalarfield,332;specificationof rotatingbodies,563–577;symmetryof,150 dynamicalvariables,395;termsof,behaviorat angularvelocity:aroundblackholes,414,460; longdistances,722;topological,720–721;total, definedbytimecoordinate,550;forKerrblack Newtonianworld,145;ofuniverse,346,356;as hole,462f;slowlyrotatinggravitationalsources, usuallyformulated,783;ofworld,andenergy 570;insidestationarylimitsurface,471 momentumtensor,378;Yang-Mills,681 annihilatedspacetime,785 actionfunctional,138 annihilationoperator,447–448 actionprinciple,155;basicsofphysics,136–149; annusmirabilis,AlbertEinstein’s,265 differentnotionsof,138;asfundamentalprinciple antandhoneyanalogy,5–6,5f oftheoreticalphysics,783;globalityof,compared antmovement,asexampleofvariationalcalculus, toequationofmotion,141;kinetictermin,140; 128 andleasttimeprinciple,139,144;metaphorfor anthropicprinciple:andcosmologicalconstant life,140;mysteryof,141,155;ofparticlesand paradox,751–752,757;andultimativetheory, fields,145;theoriesbasedon,383;variational 789n calculus,113 antideSitter/conformalfieldtheories(AdS/CFT): actionvariation,holdingdynamicalvariablesfixed, AdS/CFTcorrespondence,649,787;conformal 380 coordinatesof,654,654f;andPoincar ́ehalfplane, activediffeomorphism,397 68 actualbiologicaltime,elapsedbetweeneventAand antideSitterspacetime(AdS),606e,612,649– B,179 666;for2-branemodel,702;AdS2boundaries, additionofvelocities.Seevelocities 664;boundaryof,655;d-dimensional,650,650f; ADM(Arnowitt-Deser-Misner)formulation,of differentformsof,660;inhyperboliccoordinates, gravitationaldynamics,693 661;isometrygroupof,650;motionoflight,659; AdS.SeeantideSitterspacetime motionofmassiveparticles,659–660;Poincar ́e affineparameter,308 coordinates,656;sliceof,658f;stereographic Aharonov-Bohmeffect,789n projectionfor,661;tablefor,662 airresistance,andfreefall,268 anti-gravity,discussionof,392 airlineexample,forprovingcurvatureofearth,66 anticommutation:ofdifferentialforms,597;Jordan’s al-jabr,calculationmethod,208n manuscripton,789n Al-Khwarizmi,calculationofsquareroots,207n antimatter:andchargeconjugationinKałuzaalgebra:conformal, 614–623; deSitter, and Kleintheory,678;creationof,205,206;inearly cosmologicalconstant,755;extensionsof,667; universe,528;Feynmandiagramof,206f;in Lie(seeLiealgebra);Lorentz(seeLorentzalgebra); higherdimensionaltheories,683;inquantum matrix,quickreviewof,742–743;Poincar ́e(see fieldtheory,476 Poincar ́ealgebra) antiparticles,26,437–438 algorithm,etymologyoftheword,207n antipodalcondition,spaceofspheres,646 ambitwistors:powerof,738;representationof,736 antisymmetricmatrices,introductionof,40 Americanfootball,relativityof,171,172f antisymmetricsymbol:incurvedspacetime,723– “analogNewtonian”equation,367 725;asinvarianttensor,60;roleasmetric,734; analyticcontinuation:deSittertoantideSitter usedtocontractindices,719

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:
- ISSN 0143-0807 (https://search.worldcat.org/issn/0143-0807).
- S2CID 215832738 (https://api.semanticscholar.org/Cor pusID:215832738).
- How I Killed Pluto and Why It Had It Coming (1st ed.).
- doi:10.1119/1.5109519 (https://doi.org/10.1119%2F1.5109519).

S2CID 215832738 (https://api.semanticscholar.org/Cor pusID:215832738).

How I Killed Pluto and Why It Had It Coming (1st ed.).

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:
- This work became the basis for Fermi–Dirac statistics.[93]: 488 This applies to systems consisting of many identical spin-1/2 particles, or fermions (i.e.
- electrons in solids and liquids, and importantly to the field of conduction in semiconductors.
- For this work,[92] published in 1926, Dirac received a PhD from Cambridge.
- the quantisation rules in a novel and more illuminating manner.

This work became the basis for Fermi–Dirac statistics.[93]: 488 This applies to systems consisting of many identical spin-1/2 particles, or fermions (i.e.

electrons in solids and liquids, and importantly to the field of conduction in semiconductors.

For this work,[92] published in 1926, Dirac received a PhD from Cambridge.

the quantisation rules in a novel and more illuminating manner.

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:
- Scharlau, Winfried, Emmy Noether's Contributions to the Theory of Algebras in Teicher 1999, p.
- "Emmy Noether at the Institute for Advanced Study" (https://storymaps.arcgis.com/stories/e7329d a167ae4fd690da903f2610432d), StoryMaps, ArcGIS, 7 December 2019, archived (https://web.arc hive.org/web/20240416231133/https://storymaps.arcgis.com/stories/e7329da167ae4fd690da903f 2610432d) from the original on 16 April 2024, retrieved 28 August 2020 145.
- (March 2013), "This Month in Physics History: March 23, 1882: Birth of Emmy Noether" (https://www.aps.org/publications/apsnews/201303/physicshistory.cfm), APSNews, 22 (3), American Physical Society, archived (https://web.archive.org/web/20240714164817/https://ww w.aps.org/archives/publications/apsnews/201303/physicshistory.cfm) from the original on 14 July 2024, retrieved 28 August 2020

Scharlau, Winfried, Emmy Noether's Contributions to the Theory of Algebras in Teicher 1999, p.

"Emmy Noether at the Institute for Advanced Study" (https://storymaps.arcgis.com/stories/e7329d a167ae4fd690da903f2610432d), StoryMaps, ArcGIS, 7 December 2019, archived (https://web.arc hive.org/web/20240416231133/https://storymaps.arcgis.com/stories/e7329da167ae4fd690da903f 2610432d) from the original on 16 April 2024, retrieved 28 August 2020 145.

(March 2013), "This Month in Physics History: March 23, 1882: Birth of Emmy Noether" (https://www.aps.org/publications/apsnews/201303/physicshistory.cfm), APSNews, 22 (3), American Physical Society, archived (https://web.archive.org/web/20240714164817/https://ww w.aps.org/archives/publications/apsnews/201303/physicshistory.cfm) from the original on 14 July 2024, retrieved 28 August 2020

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:
- h y e m t o o i r c r y r e o a a w c c c a h o v > u e 1 n t 0 t e s N s f t / o k a r W r t m ic e le a s s u m re a d y Dynam 3 ic 3 T 4 e W st , A 0.
- NAmotpel 2itu-Cdyec Rlei n~gConstant 7~15V2.
- a to te d 196 Seconds (5.1 Points/sec at 2048 Samples/Point) evaluate credibility (so we have ignored it) ~20-110 uNThrust Pulses ~7-10 mN Thruster (2048 Samples/point, 5.1 points/sec) 16-170 mN Thruster Specific Force ~1-20N/kW June 2013 55 Specific Force 0.02-0.4N/kW High fi @ de l 4 it 5 y 0 T W es , t 0 A .4 rt N ic / l k e W 170mN Specific Force ~0.75N/kW Secon (u d n G de e r n d e e ra v t e io lo n p T m e e s n t t A ) rticle 5 6 7 What we suspect: • A variety of industry experiments, for which theory is lacking, may be Q-thrusters including Boeing, Lockheed-Martin, EM Drive, Cannae, etc.
- C6ualN Chin E e M se D u r n iv iv e e t r e si s t t y s c , l b a u im t s n o to w h a a y v e fo d r u U p .

h y e m t o o i r c r y r e o a a w c c c a h o v > u e 1 n t 0 t e s N s f t / o k a r W r t m ic e le a s s u m re a d y Dynam 3 ic 3 T 4 e W st , A 0.

NAmotpel 2itu-Cdyec Rlei n~gConstant 7~15V2.

a to te d 196 Seconds (5.1 Points/sec at 2048 Samples/Point) evaluate credibility (so we have ignored it) ~20-110 uNThrust Pulses ~7-10 mN Thruster (2048 Samples/point, 5.1 points/sec) 16-170 mN Thruster Specific Force ~1-20N/kW June 2013 55 Specific Force 0.02-0.4N/kW High fi @ de l 4 it 5 y 0 T W es , t 0 A .4 rt N ic / l k e W 170mN Specific Force ~0.75N/kW Secon (u d n G de e r n d e e ra v t e io lo n p T m e e s n t t A ) rticle 5 6 7 What we suspect: • A variety of industry experiments, for which theory is lacking, may be Q-thrusters including Boeing, Lockheed-Martin, EM Drive, Cannae, etc.

C6ualN Chin E e M se D u r n iv iv e e t r e si s t t y s c , l b a u im t s n o to w h a a y v e fo d r u U p .

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:
- time the variations in the first observable, say the energy, are reduced below the ZPF such that the energy becomes "negative." "Squeezing" is thus the control of quantum fluctuations and corresponding uncertainties, whereby one can squeeze/reduce the variance of one (physically important) observable quantity provided the variance in the (physically unimportant) conjugate variable is stretched/increased.
- The squeezed quantity possesses an unusually low variance meaning less variance l than would be expected on the basis of the equipartition theorem.
- One can in principle G Electron mass, m~ = 9.11 x 10-31 kg; electron charge, e = 1.602 x lO-11l C.

time the variations in the first observable, say the energy, are reduced below the ZPF such that the energy becomes "negative." "Squeezing" is thus the control of quantum fluctuations and corresponding uncertainties, whereby one can squeeze/reduce the variance of one (physically important) observable quantity provided the variance in the (physically unimportant) conjugate variable is stretched/increased.

The squeezed quantity possesses an unusually low variance meaning less variance l than would be expected on the basis of the equipartition theorem.

One can in principle G Electron mass, m~ = 9.11 x 10-31 kg; electron charge, e = 1.602 x lO-11l 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:
- And in 1997, Gray even transformed his Mars and Venus books into a musical comedy that opened on Broadway.
- (1) Do women talk much more than men?
- 32), she found an overall Cohen’s d of .11, reflecting greater talkativeness among women than men.
- Although Gray and other pop psychologists haven’t conducted any research to back up their claims, many other investigators have examined the evidence bearing on sex differences in communication.

And in 1997, Gray even transformed his Mars and Venus books into a musical comedy that opened on Broadway.

32), she found an overall Cohen’s d of .11, reflecting greater talkativeness among women than men.

Although Gray and other pop psychologists haven’t conducted any research to back up their claims, many other investigators have examined the evidence bearing on sex differences in communication.

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:
- [7] 7 tightly bound than normal nuclei; for example, the lithium hypernucleus Li is 19% smaller than Λ the normal nucleus 6Li.[8][9] However, the hyperons can decay via the weak force; the mean lifetime of a free Λ is 263±2 ps, and that of a Λ hypernucleus is usually slightly shorter.[10] A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s).[11][12] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested.[7] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions.[13] Types Λ hypernuclei The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ.[6] While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion,[a] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons.[15] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon;[16] in hypernuclei, the depth of the Λ potential is approximately 30 MeV.[17] However, onepion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei.[18][19][20] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate.[15] Like all hyperons, Λ hypernuclei can decay through the weak interaction, which changes it to a lighter baryon and emits a meson or a lepton–antilepton pair.
- In free space, the Λ usually decays via the weak force to a proton and a π– meson, or a neutron and a π0, with a total half-life of 263±2 ps.[21] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode.[22] The half-life of the Λ in a hypernucleus

[7] 7 tightly bound than normal nuclei; for example, the lithium hypernucleus Li is 19% smaller than Λ the normal nucleus 6Li.[8][9] However, the hyperons can decay via the weak force; the mean lifetime of a free Λ is 263±2 ps, and that of a Λ hypernucleus is usually slightly shorter.[10] A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s).[11][12] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested.[7] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions.[13] Types Λ hypernuclei The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ.[6] While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion,[a] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons.[15] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon;[16] in hypernuclei, the depth of the Λ potential is approximately 30 MeV.[17] However, onepion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei.[18][19][20] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate.[15] Like all hyperons, Λ hypernuclei can decay through the weak interaction, which changes it to a lighter baryon and emits a meson or a lepton–antilepton pair.

In free space, the Λ usually decays via the weak force to a proton and a π– meson, or a neutron and a π0, with a total half-life of 263±2 ps.[21] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode.[22] The half-life of the Λ in a hypernucleus

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:
- true that for any pure entangled state there exists a choice of measurements that produce Bell nonlocal correlations, but the situation is more complex for mixed states.
- While any Bell nonlocal state must be entangled, there exist (mixed) entangled states which do not produce Bell nonlocal correlations[33] (although, operating on several copies of some of such states,[34] or carrying out local

true that for any pure entangled state there exists a choice of measurements that produce Bell nonlocal correlations, but the situation is more complex for mixed states.

While any Bell nonlocal state must be entangled, there exist (mixed) entangled states which do not produce Bell nonlocal correlations[33] (although, operating on several copies of some of such states,[34] or carrying out local

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:
- The first two postulates formulate the experimental observations that absorption and emission of radiation for hydrogen do not obey the rules known at the time.
- the Planck relation: , where is the Planck constant.
- The stationary orbits are obtained by the condition that the ratio of the total energy emitted in forming the state and the frequency of the electron rotation about the positive nucleus is an integer multiple of .
- In atomic state corresponding to the maximum emitted energy, the stationary orbits are attained at distances for which the angular momentum of the revolving electron is equal to the reduced Planck constant, .

The first two postulates formulate the experimental observations that absorption and emission of radiation for hydrogen do not obey the rules known at the time.

the Planck relation: , where is the Planck constant.

The stationary orbits are obtained by the condition that the ratio of the total energy emitted in forming the state and the frequency of the electron rotation about the positive nucleus is an integer multiple of .

In atomic state corresponding to the maximum emitted energy, the stationary orbits are attained at distances for which the angular momentum of the revolving electron is equal to the reduced Planck constant, .

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:
- As already mentioned in the prologue, we could say, paraphrasing computer scientists,uncommonsensein,uncommonsenseout.Alltheseapparentparadoxescontradict our Newtonian intuition, but they could not possibly contradict logic, as I have emphasizedhere.
- SpaceandTimeUnified ∗ The paradoxes are of course helpful in making students understand the subtle issues behind the Lorentz transformation, and they played an important clarifying role historically.
- Lorentz invariance is actually built into the grammar of the language used in highenergytheory,namelyquantumfieldtheory,fromthestart.
- By continuity, if we can choose a v that makes (cid:10)t (cid:5) vanish,wecanhaveavthatmakes(cid:10)t gonegative.

As already mentioned in the prologue, we could say, paraphrasing computer scientists,uncommonsensein,uncommonsenseout.Alltheseapparentparadoxescontradict our Newtonian intuition, but they could not possibly contradict logic, as I have emphasizedhere.

SpaceandTimeUnified ∗ The paradoxes are of course helpful in making students understand the subtle issues behind the Lorentz transformation, and they played an important clarifying role historically.

Lorentz invariance is actually built into the grammar of the language used in highenergytheory,namelyquantumfieldtheory,fromthestart.

By continuity, if we can choose a v that makes (cid:10)t (cid:5) vanish,wecanhaveavthatmakes(cid:10)t gonegative.

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

List tests or derivations implied by the evidence.