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

EVIDENCE:
- (27.60) 0 0 0 Φ The Newtonian line-element is, in a form that keeps the Newtonian tetrad manifest, ds2 =− [ (1+Ψ)dt ]2 +δ [ (1−Φ)dxa−hadxc−Wadt ][ (1−Φ)dxb−hbdxd−Wbdt ] , (27.61) ab c d
- 27.8 Newtonian (Copernican) gauge If the unperturbed background is Minkowski space, then the most physical gauge is one in which the 6 perturbationsretainedcoincidewiththe6coordinateandtetradgauge-invariantperturbations(27.13).This gaugeiscalledNewtonian gauge.BecauseinNewtoniangaugetheperturbationsarepreciselythephysical perturbations, if the perturbations are physically weak (small), then the perturbations in Newtonian gauge will necessarily be small.
- I think Newtonian gauge should be called Copernican gauge.
- (27.59d) ab tensor In matrix form, the vierbein perturbation in Newtonian gauge, in a frame where the wavevector k is along the z-direction, are, from equation (27.7), ⎛ Ψ W W 0 ⎞ x y φ mn = ⎜ ⎜ ⎝ 0 0 Φ+ h x h y xx Φ− h x h y xx 0 0 ⎟ ⎟ ⎠ .

(27.60) 0 0 0 Φ The Newtonian line-element is, in a form that keeps the Newtonian tetrad manifest, ds2 =− [ (1+Ψ)dt ]2 +δ [ (1−Φ)dxa−hadxc−Wadt ][ (1−Φ)dxb−hbdxd−Wbdt ] , (27.61) ab c d

27.8 Newtonian (Copernican) gauge If the unperturbed background is Minkowski space, then the most physical gauge is one in which the 6 perturbationsretainedcoincidewiththe6coordinateandtetradgauge-invariantperturbations(27.13).This gaugeiscalledNewtonian gauge.BecauseinNewtoniangaugetheperturbationsarepreciselythephysical perturbations, if the perturbations are physically weak (small), then the perturbations in Newtonian gauge will necessarily be small.

I think Newtonian gauge should be called Copernican gauge.

(27.59d) ab tensor In matrix form, the vierbein perturbation in Newtonian gauge, in a frame where the wavevector k is along the z-direction, are, from equation (27.7), ⎛ Ψ W W 0 ⎞ x y φ mn = ⎜ ⎜ ⎝ 0 0 Φ+ h x h y xx Φ− h x h y xx 0 0 ⎟ ⎟ ⎠ .

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 several large modern telescopes that use a Gregorian configuration such as the Vatican Advanced Technology Telescope, the Magellan telescopes, the Large Binocular Telescope, and the Giant Magellan Telescope.
- Some small spotting scopes are still built this way.
- It usually has a paraboloid primary mirror but at focal ratios of about f/10 or longer a spherical primary mirror can be sufficient for high visual resolution.
- Reflecting telescope designs Gregorian The Gregorian telescope, described by Scottish astronomer and mathematician James Gregory in his 1663 book Optica Promota, employs a concave secondary mirror that reflects the Light path in a Gregorian telescope.

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.

There are several large modern telescopes that use a Gregorian configuration such as the Vatican Advanced Technology Telescope, the Magellan telescopes, the Large Binocular Telescope, and the Giant Magellan Telescope.

Some small spotting scopes are still built this way.

It usually has a paraboloid primary mirror but at focal ratios of about f/10 or longer a spherical primary mirror can be sufficient for high visual resolution.

Reflecting telescope designs Gregorian The Gregorian telescope, described by Scottish astronomer and mathematician James Gregory in his 1663 book Optica Promota, employs a concave secondary mirror that reflects the Light path in a Gregorian telescope.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- In both cases, there will be no interference between the paths anymore, and the probabilities are given by , independently of the phase .
- Relation to other scientific theories Classical mechanics The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space – although they do not tell us which Hilbert space or which operators.
- This approach is known as quantization.[42]: 299 [43] When quantum mechanics was originally formulated, it
- An important guide for making these choices is the correspondence principle, a heuristic which states that the predictions of quantum mechanics reduce to those of classical mechanics in the regime of large quantum numbers.[41] One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.

In both cases, there will be no interference between the paths anymore, and the probabilities are given by , independently of the phase .

Relation to other scientific theories Classical mechanics The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space – although they do not tell us which Hilbert space or which operators.

This approach is known as quantization.[42]: 299 [43] When quantum mechanics was originally formulated, it

An important guide for making these choices is the correspondence principle, a heuristic which states that the predictions of quantum mechanics reduce to those of classical mechanics in the regime of large quantum numbers.[41] One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.

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:
- In most respects Seyfert galaxies seem normal and are not unusually distant from us.
- ENDINGS AND BEGINNINGS 223 100,000 light-years across and in which even the dense central core may be 15,000 light-years across.
- They may make up 1 percent of all known galaxies (meaning as many as a billion altogether), though actually only a dozen examples have been discovered.
- The cores of the Seyfert galaxies, however, are very compact, very bright, and seem unusually hot and active-rather quasarlike in fact.

In most respects Seyfert galaxies seem normal and are not unusually distant from us.

ENDINGS AND BEGINNINGS 223 100,000 light-years across and in which even the dense central core may be 15,000 light-years across.

They may make up 1 percent of all known galaxies (meaning as many as a billion altogether), though actually only a dozen examples have been discovered.

The cores of the Seyfert galaxies, however, are very compact, very bright, and seem unusually hot and active-rather quasarlike in fact.

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:
- Index | 835 generalcurvedspacetime,spatialdistancein, globalcharacterofspace,versuslocal,76–77 290–292 globalpositioningsystem(GPS),287,291 generalinvariance:ofEinstein-Hilbertaction, globe,curvesofconstantlatitudeon,92 comparedtoMaxwellaction,394;ofmatteraction, gluonscattering:amplitudesfor,785;Feynman andconservationofenergymomentum,383–384 diagramsfor,735–736;intermsofabitwistors, generalrelativity:abstractof,20;aseffectivefield 738;intermsofhelicityspinors,735–736 theory,773n;andHamilton’sprinciple,Lorentz’s gluons:inbranemodels,696;inearlyuniverse,526 paperon,397;modificationswithrespectto GMT(GreenwichMeanTime),133n horizons,784;solarsystemtests,309;tensorsin, God:existenceof,520;“WhatisgreaterthanGod?” 312–319.Seealsogravity puzzle,789n generalizeduncertaintyprinciple,769 Goldberger,Murph,onhisaunt,321n generators:breakupintosubgroups,663; of goldenageofcosmology,491 conformalalgebra,615,617;ofLiealgebra,49,51; “golden”guidingprinciple,intheoreticalphysics, ofrotation,192;ofrotationgroup,40;ofSL(4,R) 338 group,737,739;ofSO(3)group,44 Gordon,Walter,Klein-Gordonequation,694 genus,inEulercharacteristics,726 Grace,Louis,constructorofoldman’stoyandofwar GEO600,gravitationalwavedetector,577n chariot,267 geodesicdeviation,552–561,554;andLiederivative, gracefulexitproblem,534 555 gradient:definitionof, 61; notationof, 54; geodesicequation,128;alternativederivationof,130; transformationof,320 Christoffelsymbolsof,129;comovingcoordinates, grandunification,mysteryof,527n 298;curvedspacetime,277–278;invarianceon grandunifiedtheory,527;andcharge,786;inearly rescaling,559;motionincurvedspacetime, universe,518;energyscale,767;andhigher 289;andparalleltransport,545;presenceof dimensionaltheories,681;andKałuza-Klein externalforces,301;rotatingblackholes,459; theory,672;inMversusRplot,14f;magnetic transformationofChristoffelsymbol,330–331 (anti)monopoles,532 geodesicproblem:freeparameters,124f;variational Grassmannvariables,606n;andsupertwistors,739n calculus,123 gravitatingsystem,farfieldof,576 geodesics:atblackholes,426–427;collectionsof, gravitation,fieldequationfor,Einstein’ssearchfor, 554;congruenceof,554;covariantderivative, 341–342 553;determinationonPoincar ́ehalfplane,133; gravitationlaw,Einstein’sbeliefofinconsistency distanceoftwonearby,552,553f;inembedding withprincipleofcausation,404 space,645,665; familyof,134; geometric gravitationalcollapse,ofsphericallysymmetricdust constructionof,133n;intersectionof,134; cloud,373 lightlike,292,646;onPoincar ́ehalfplane,134f; gravitationalconstant,11;timedependentinbrane separationof,552;onspheres,127;timelike,645 models,707 geodeticprecession,549 gravitationalcoupling,768 geometricalentities,intopology,725–727 gravitationalenergy,580–581;binding,455–456;of geometricalview:ofKałuza-Kleintheory,691–693;of hangingstring,114 specialrelativity,582 gravitationalfield:classical,quantumparticles geometrodynamics,inhigherdimensionaltheories, in,771;completionandpromotionof,218; 693 conservationofenergymomentumin,386; geometry:analytic, roleofcoordinates, 48; determinationof,338;dynamicsof,146;and conversionfactorbetweenphysicsand,211; equivalenceprinciple,271;finitesizedobjectsin, covariantderivativefrom,323;dynamicsof, 716–715;inFourierspace,758n;ingreatdistance inhigherdimensionaltheories,693,693f;and ofblackhole,574;momentumof,580–581;nature invariance,42–43,48;ofMinkowskispacetime, of,218–237,231;quantizationof,582;strong 174–193,238;non-existenceofroyalroadto, stationarysource,574;astensorfield,231 Euclid’sremarks,42;ofpoints,isometry,585;of gravitationalfieldlimit,Newtoniangravityas,391 relativisticpointparticleaction,210;ofrotation gravitationalinteraction, 581; comparedto groups,191;andsignificanceofcoordinates, electromagneticinteraction,768 68;ofaworld,6.Seealsodifferentialgeometry; gravitationalLagrangian,339 Riemanniangeometry gravitationallensing,370–371 Ghostwriter,The(Roth),254 gravitationalmass,equalitytoinertialmass,28,257, Gibbons,Gary,discoveryofHawkingradiation,449n 268–269 Gibbons-Hawkingradiation,638;mysteryof,637 gravitationalpotential:actionprinciple,145;around Gibbons-Hawking-Yorkboundaryterm,399n blackholes,410–411,411f;connectiontomass

Index | 835 generalcurvedspacetime,spatialdistancein, globalcharacterofspace,versuslocal,76–77 290–292 globalpositioningsystem(GPS),287,291 generalinvariance:ofEinstein-Hilbertaction, globe,curvesofconstantlatitudeon,92 comparedtoMaxwellaction,394;ofmatteraction, gluonscattering:amplitudesfor,785;Feynman andconservationofenergymomentum,383–384 diagramsfor,735–736;intermsofabitwistors, generalrelativity:abstractof,20;aseffectivefield 738;intermsofhelicityspinors,735–736 theory,773n;andHamilton’sprinciple,Lorentz’s gluons:inbranemodels,696;inearlyuniverse,526 paperon,397;modificationswithrespectto GMT(GreenwichMeanTime),133n horizons,784;solarsystemtests,309;tensorsin, God:existenceof,520;“WhatisgreaterthanGod?” 312–319.Seealsogravity puzzle,789n generalizeduncertaintyprinciple,769 Goldberger,Murph,onhisaunt,321n generators:breakupintosubgroups,663; of goldenageofcosmology,491 conformalalgebra,615,617;ofLiealgebra,49,51; “golden”guidingprinciple,intheoreticalphysics, ofrotation,192;ofrotationgroup,40;ofSL(4,R) 338 group,737,739;ofSO(3)group,44 Gordon,Walter,Klein-Gordonequation,694 genus,inEulercharacteristics,726 Grace,Louis,constructorofoldman’stoyandofwar GEO600,gravitationalwavedetector,577n chariot,267 geodesicdeviation,552–561,554;andLiederivative, gracefulexitproblem,534 555 gradient:definitionof, 61; notationof, 54; geodesicequation,128;alternativederivationof,130; transformationof,320 Christoffelsymbolsof,129;comovingcoordinates, grandunification,mysteryof,527n 298;curvedspacetime,277–278;invarianceon grandunifiedtheory,527;andcharge,786;inearly rescaling,559;motionincurvedspacetime, universe,518;energyscale,767;andhigher 289;andparalleltransport,545;presenceof dimensionaltheories,681;andKałuza-Klein externalforces,301;rotatingblackholes,459; theory,672;inMversusRplot,14f;magnetic transformationofChristoffelsymbol,330–331 (anti)monopoles,532 geodesicproblem:freeparameters,124f;variational Grassmannvariables,606n;andsupertwistors,739n calculus,123 gravitatingsystem,farfieldof,576 geodesics:atblackholes,426–427;collectionsof, gravitation,fieldequationfor,Einstein’ssearchfor, 554;congruenceof,554;covariantderivative, 341–342 553;determinationonPoincar ́ehalfplane,133; gravitationlaw,Einstein’sbeliefofinconsistency distanceoftwonearby,552,553f;inembedding withprincipleofcausation,404 space,645,665; familyof,134; geometric gravitationalcollapse,ofsphericallysymmetricdust constructionof,133n;intersectionof,134; cloud,373 lightlike,292,646;onPoincar ́ehalfplane,134f; gravitationalconstant,11;timedependentinbrane separationof,552;onspheres,127;timelike,645 models,707 geodeticprecession,549 gravitationalcoupling,768 geometricalentities,intopology,725–727 gravitationalenergy,580–581;binding,455–456;of geometricalview:ofKałuza-Kleintheory,691–693;of hangingstring,114 specialrelativity,582 gravitationalfield:classical,quantumparticles geometrodynamics,inhigherdimensionaltheories, in,771;completionandpromotionof,218; 693 conservationofenergymomentumin,386; geometry:analytic, roleofcoordinates, 48; determinationof,338;dynamicsof,146;and conversionfactorbetweenphysicsand,211; equivalenceprinciple,271;finitesizedobjectsin, covariantderivativefrom,323;dynamicsof, 716–715;inFourierspace,758n;ingreatdistance inhigherdimensionaltheories,693,693f;and ofblackhole,574;momentumof,580–581;nature invariance,42–43,48;ofMinkowskispacetime, of,218–237,231;quantizationof,582;strong 174–193,238;non-existenceofroyalroadto, stationarysource,574;astensorfield,231 Euclid’sremarks,42;ofpoints,isometry,585;of gravitationalfieldlimit,Newtoniangravityas,391 relativisticpointparticleaction,210;ofrotation gravitationalinteraction, 581; comparedto groups,191;andsignificanceofcoordinates, electromagneticinteraction,768 68;ofaworld,6.Seealsodifferentialgeometry; gravitationalLagrangian,339 Riemanniangeometry gravitationallensing,370–371 Ghostwriter,The(Roth),254 gravitationalmass,equalitytoinertialmass,28,257, Gibbons,Gary,discoveryofHawkingradiation,449n 268–269 Gibbons-Hawkingradiation,638;mysteryof,637 gravitationalpotential:actionprinciple,145;around Gibbons-Hawking-Yorkboundaryterm,399n blackholes,410–411,411f;connectiontomass

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:
- Breaking these would have significant ramifications for electronic privacy and security.
- Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible on a classical computer for large integers if they are the product of a few prime numbers (e.g., the product of two 300-digit primes).[69] By contrast, a quantum computer could solve this problem exponentially faster using Shor's algorithm to factor the integer.[70] This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem.
- In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken.
- These are used to protect secure Web pages, encrypted email, and many other types of data.

Breaking these would have significant ramifications for electronic privacy and security.

Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible on a classical computer for large integers if they are the product of a few prime numbers (e.g., the product of two 300-digit primes).[69] By contrast, a quantum computer could solve this problem exponentially faster using Shor's algorithm to factor the integer.[70] This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem.

In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken.

These are used to protect secure Web pages, encrypted email, and many other types of data.

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:
- Archived from the original (http://www.damtp.cam.ac.uk/research/gr/public/gal_lss.html) on April 26, 2012.
- Bibcode:2012ApJ...745..156R (https://ui.adsabs.harvard.edu/abs/2012ApJ...745..156R).
- S2CID 13284968 (https://api.semanticscholar.org/CorpusID:13284968).
- Hoover, Aaron (June 16, 2003).

Archived from the original (http://www.damtp.cam.ac.uk/research/gr/public/gal_lss.html) on April 26, 2012.

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:
- These include, for example, tests of number–phase uncertainty relations in superconducting[118] or quantum optics[119] systems.
- This presumes quantum particles have position and momentum.
- Kemble pointed out[115] in 1937 that such properties cannot be experimentally verified and assuming they exist gives rise to many contradictions; similarly Rudolf Haag notes that position in quantum mechanics is an attribute of an interaction, say between an electron and a detector, not an intrinsic property.[116][117] From this point of view the uncertainty principle is not a fundamental quantum property but a concept "carried over from the language of our ancestors", as Kemble says.
- Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program.

These include, for example, tests of number–phase uncertainty relations in superconducting[118] or quantum optics[119] systems.

This presumes quantum particles have position and momentum.

Kemble pointed out[115] in 1937 that such properties cannot be experimentally verified and assuming they exist gives rise to many contradictions; similarly Rudolf Haag notes that position in quantum mechanics is an attribute of an interaction, say between an electron and a detector, not an intrinsic property.[116][117] From this point of view the uncertainty principle is not a fundamental quantum property but a concept "carried over from the language of our ancestors", as Kemble says.

Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program.

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:
- Walters, Edward and Bruce Maccabee.
- 89thCong., 2d sess., 5 April 1966.
- Reporton UnidentifiedFlying Obiects.
- UnidentifiedFlying Objects: A SelectedBibliography, Washington: Library ofCongress, OCLC 1976.

UnidentifiedFlying Objects: A SelectedBibliography, Washington: Library ofCongress, OCLC 1976.

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:
- From the point of view of each copy of Alice, there are multiple copies of Bob experiencing different results, so Bob cannot have a definite result, and the same is true from the point of view of each copy of Bob.
- It can generate correlations that violate a Bell inequality because it violates an implicit assumption by Bell that measurements have a single outcome.
- Therefore, the violation of a Bell inequality cannot be interpreted as a proof of non-locality.[79]: 28 Non-local hidden variables Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables.[note 5] They are ready to give up locality, explaining the violation of Bell's inequality by means of a non-local hidden variable theory, in which the particles exchange information about their states.
- Therefore, a violation of a Bell inequality can be interpreted as a demonstration that measurements have multiple outcomes.[80] The explanation it provides for the Bell correlations is that when Alice and Bob make their measurements, they split into local branches.

From the point of view of each copy of Alice, there are multiple copies of Bob experiencing different results, so Bob cannot have a definite result, and the same is true from the point of view of each copy of Bob.

It can generate correlations that violate a Bell inequality because it violates an implicit assumption by Bell that measurements have a single outcome.

Therefore, the violation of a Bell inequality cannot be interpreted as a proof of non-locality.[79]: 28 Non-local hidden variables Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables.[note 5] They are ready to give up locality, explaining the violation of Bell's inequality by means of a non-local hidden variable theory, in which the particles exchange information about their states.

Therefore, a violation of a Bell inequality can be interpreted as a demonstration that measurements have multiple outcomes.[80] The explanation it provides for the Bell correlations is that when Alice and Bob make their measurements, they split into local branches.

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:
- It is demonstrative to let and correspond to position and momentum that meets the well known commutator relation, .
- That is the origin of our quantum noise.
- We can show the following, where the are the averages over the wavefunction and other statistical properties.
- When the position is precisely known enough backaction begins to affect the measurement in two ways.

It is demonstrative to let and correspond to position and momentum that meets the well known commutator relation, .

That is the origin of our quantum noise.

We can show the following, where the are the averages over the wavefunction and other statistical properties.

When the position is precisely known enough backaction begins to affect the measurement in two ways.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- In this case, if Bob subsequently measures spin along the z-axis, there is 100% probability that he will obtain −z.
- In state I, the electron has spin pointing upward along the z-axis (+z) and the positron has spin pointing downward along the z-axis (−z).
- There is nothing special about choosing the zaxis: according to quantum mechanics the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction.[21]: 318 Whatever axis their spins are measured along, they are always found to be opposite.
- The quantum state determines the probable outcomes of any measurement performed on the system.

Einstein–Podolsky–Rosen paradox - Wikipedia.pdf

In this case, if Bob subsequently measures spin along the z-axis, there is 100% probability that he will obtain −z.

In state I, the electron has spin pointing upward along the z-axis (+z) and the positron has spin pointing downward along the z-axis (−z).

There is nothing special about choosing the zaxis: according to quantum mechanics the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction.[21]: 318 Whatever axis their spins are measured along, they are always found to be opposite.

The quantum state determines the probable outcomes of any measurement performed on the system.

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:
- to be satisfied within every model that is local and complete.
- In quantum teleportation (Figure 7) one scans out part of the information from object A (the original), which one wants to teleport, while causing the remaining, unscanned, part of the information in A to pass, via EPR entanglement, into another object C which has never been in contact with A.
- Figure 6 compares conventional facsimile transmission with the quantum teleportation process seen in Figure 7.
- Bell’s inequalities make it possible to test whether local hidden-variable models can account for observed physical phenomena in lab experiments.

to be satisfied within every model that is local and complete.

In quantum teleportation (Figure 7) one scans out part of the information from object A (the original), which one wants to teleport, while causing the remaining, unscanned, part of the information in A to pass, via EPR entanglement, into another object C which has never been in contact with A.

Figure 6 compares conventional facsimile transmission with the quantum teleportation process seen in Figure 7.

Bell’s inequalities make it possible to test whether local hidden-variable models can account for observed physical phenomena in lab experiments.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The strong energy condition is obeyed by all normal/Newtonian matter, but a false vacuum can violate it.
- Extending these results is an open problem.
- effective field theories on Minkowski spacetime, the averaged null energy condition holds for everyday quantum fields.
- Then the strong energy condition requires ; but for the state known as a false vacuum, we have .[7]

The strong energy condition is obeyed by all normal/Newtonian matter, but a false vacuum can violate it.

Extending these results is an open problem.

effective field theories on Minkowski spacetime, the averaged null energy condition holds for everyday quantum fields.

Then the strong energy condition requires ; but for the state known as a false vacuum, we have .[7]

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:
- InEinsteingravity,itiseasytocausetheuniversetoexpandexponentially:allyouhave todo,aswesawinchapterVI.2,istointroduceaconstantenergydensityinthevacuum, effectivelyacosmologicalconstant.Inparticletheory,itiseasytoproduceaconstantenergy density: a scalar field that does not vary in spacetime would do that, as you learned in chapterVI.4.Thus,withthebenefitofhindsight,itisdoublyeasytomaketheuniversego throughaninflationaryepoch.
- For φ(x) constant, Tμν=−gμνV(φ).
- Amusingly,Einstein’sintroductionofthecosmologicalconstant,farfromablunderas theuninformedcalledit,turnsouttobeessentialforcosmology,bothobservationallyand theoretically.
- Numerically,toaccordwithobservation,thescalefactora(t)needstohaveexpandedby a factor of 1030, starting from ∼10 −36 second after the Big Bang to ∼10 −35second after theBigBang.Therequirednumberofe-foldingsisthus30log10∼70.Notethatthese numbersdonotcomeoutofthetheorybutarerequiredtoaccordwithexperiment.

InEinsteingravity,itiseasytocausetheuniversetoexpandexponentially:allyouhave todo,aswesawinchapterVI.2,istointroduceaconstantenergydensityinthevacuum, effectivelyacosmologicalconstant.Inparticletheory,itiseasytoproduceaconstantenergy density: a scalar field that does not vary in spacetime would do that, as you learned in chapterVI.4.Thus,withthebenefitofhindsight,itisdoublyeasytomaketheuniversego throughaninflationaryepoch.

Numerically,toaccordwithobservation,thescalefactora(t)needstohaveexpandedby a factor of 1030, starting from ∼10 −36 second after the Big Bang to ∼10 −35second after theBigBang.Therequirednumberofe-foldingsisthus30log10∼70.Notethatthese numbersdonotcomeoutofthetheorybutarerequiredtoaccordwithexperiment.

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 nice review of the problematic nature of such spacetimes is given by Kagramanova et al.
- The jump in the time coordinate is problematic, because it means that a particle passing through a pole leaps forwards or backwards in time, the choice of forwards or backwards depending on which side of the pole the geodesic is deemed to pass.
- As usual for a well-behaved azimuthally symmetric spacetime, when a geodesic passes infinitesimally close to a pole, the azimuthal angle φ along the geodesic jumps by ±π, the sign depending on which side of the pole the geodesic is deemed to pass; but since the angle φ is periodic in 2π,theambiguityinsigndoesnotleadtoanetambiguityintheangleφ.TheproblemforNUTspacetimes, where ω does not vanish, is that when a geodesic passes infinitesimally close to a pole, the time coordinate y t also jumps by ±ω π.
- Whataccountsforthesingularbehaviouralongpoles?Theansweristhatthereisastringoftorsionalong each pole.

A nice review of the problematic nature of such spacetimes is given by Kagramanova et al.

The jump in the time coordinate is problematic, because it means that a particle passing through a pole leaps forwards or backwards in time, the choice of forwards or backwards depending on which side of the pole the geodesic is deemed to pass.

As usual for a well-behaved azimuthally symmetric spacetime, when a geodesic passes infinitesimally close to a pole, the azimuthal angle φ along the geodesic jumps by ±π, the sign depending on which side of the pole the geodesic is deemed to pass; but since the angle φ is periodic in 2π,theambiguityinsigndoesnotleadtoanetambiguityintheangleφ.TheproblemforNUTspacetimes, where ω does not vanish, is that when a geodesic passes infinitesimally close to a pole, the time coordinate y t also jumps by ±ω π.

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

EVIDENCE:
- Sun Stars are given a single-letter classification according to K 4,000–5,250 K Epsilon Indi their spectra, ranging from type O, which are very hot, to M 2,600–3,850 K Proxima Centauri M, which are so cool that molecules may form in their atmospheres.
- A variety of rare spectral types are given special classifications.
- The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M.
- Each letter has 10 sub-divisions, numbered from 0 to 9, in order of decreasing temperature.

Sun Stars are given a single-letter classification according to K 4,000–5,250 K Epsilon Indi their spectra, ranging from type O, which are very hot, to M 2,600–3,850 K Proxima Centauri M, which are so cool that molecules may form in their atmospheres.

A variety of rare spectral types are given special classifications.

The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M.

Each letter has 10 sub-divisions, numbered from 0 to 9, in order of decreasing temperature.

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

EVIDENCE:
- But you and I are free to choose whatever vielbein we like, as was already mentioned inconnectionwith(4).Supposethatatagivenpoint,myvielbeineαisrelatedtoyoursby eα=(cid:27)α e ̃β.
- The first term becomes d((cid:27)e ̃)=(cid:27)de ̃+(d(cid:27))e ̃=−(cid:27)ω ̃e ̃+(d(cid:27))(cid:27) −1e.
- For the 2-sphere, de1=0 and de2=cosθdθdφ, and so the connectionhasonlyonenonvanishingcomponent:ω12=−ω21=−cosθdφ.
- (Here the minus sign is conventional and is part of the αβ definitionofω.)Sinceeisa1-form,itfollowsthatdeisa2-formandhence ωα =ωα dxμ (10) β βμ isalsoa1-form,knownastheconnection1-form:itconnectsnearbyframes.Givene,(9) enables us to determine ω.

But you and I are free to choose whatever vielbein we like, as was already mentioned inconnectionwith(4).Supposethatatagivenpoint,myvielbeineαisrelatedtoyoursby eα=(cid:27)α e ̃β.

The first term becomes d((cid:27)e ̃)=(cid:27)de ̃+(d(cid:27))e ̃=−(cid:27)ω ̃e ̃+(d(cid:27))(cid:27) −1e.

For the 2-sphere, de1=0 and de2=cosθdθdφ, and so the connectionhasonlyonenonvanishingcomponent:ω12=−ω21=−cosθdφ.

(Here the minus sign is conventional and is part of the αβ definitionofω.)Sinceeisa1-form,itfollowsthatdeisa2-formandhence ωα =ωα dxμ (10) β βμ isalsoa1-form,knownastheconnection1-form:itconnectsnearbyframes.Givene,(9) enables us to determine ω.

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

EVIDENCE:
- ab Choose a point of the spacetime.
- (17.95) 3 2 1 1 1 3 2 2 3 2 1 3 3 2 Under a rescaling of axes ∂ ∝ 1/a , the eigenvalues scale as n ∝ a /(a a ) and cyclically for n and n .
- 17.4 Bianchi spacetimes 509 Table 17.1: Classification of Bianchi spaces Eigenvalues Type n n n k =0 k ̸=0 1 2 3 0 0 0 I V 0 0 + II IV 0 − + VI VI 0 + + VII VII − + + VIII + + + IX 17.4.3 Classification of Bianchi spaces Bianchi spaces are classified according to the invariant properties of their constant structure coefficients cc .
- c c 1 1 2 3 2 3 Thusbyarescalingofaxes,eachofthenon-zeroeigenvaluesn canbescaledtoany othervalueof thesame c sign.

(17.95) 3 2 1 1 1 3 2 2 3 2 1 3 3 2 Under a rescaling of axes ∂ ∝ 1/a , the eigenvalues scale as n ∝ a /(a a ) and cyclically for n and n .

17.4 Bianchi spacetimes 509 Table 17.1: Classification of Bianchi spaces Eigenvalues Type n n n k =0 k ̸=0 1 2 3 0 0 0 I V 0 0 + II IV 0 − + VI VI 0 + + VII VII − + + VIII + + + IX 17.4.3 Classification of Bianchi spaces Bianchi spaces are classified according to the invariant properties of their constant structure coefficients cc .

c c 1 1 2 3 2 3 Thusbyarescalingofaxes,eachofthenon-zeroeigenvaluesn canbescaledtoany othervalueof thesame c sign.

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

EVIDENCE:
- For a moment, Daniela looks like she’s about to break down, but she holds it together.
- I cross the threshold, put my hand on the door, and catch one last glimpse of my world.
- I keep waiting for something to happen as my heart hammers in my chest.
- Light from the high windows streaming down onto the old generators as fifty versions of me all stare toward the box in a stunned and eerie and devastated silence.

For a moment, Daniela looks like she’s about to break down, but she holds it together.

I cross the threshold, put my hand on the door, and catch one last glimpse of my world.

I keep waiting for something to happen as my heart hammers in my chest.

Light from the high windows streaming down onto the old generators as fifty versions of me all stare toward the box in a stunned and eerie and devastated silence.

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:
- under a U (1)electromagneticgaugetransformation(41.25).Thechargeofanelectronorpositronisunambiguous, em and the complex conjugate of an electron is unambiguously a positron, per equations (42.99).
- But a chiral spinor such as e can be obtained as either an electron or a positron in the limit of diverging boost and V↑ vanishing mass, so e could have either charge.
- By itself, a massless, chiral spinor does not contain enough V↑ informationtodeterminethesignofitscharge.Todisambiguatetheircharge,thechiralspinorsintheDirac chart (42.98) are written without or with a conjugation * symbol: unconjugated spinors (no *) have the charge of an electron, while conjugated spinors (with *) have the charge of a positron.
- So disambiguated, the charges of the chiral spinors in the Dirac chart (42.98) can be read off from their bits: spinors with spin

under a U (1)electromagneticgaugetransformation(41.25).Thechargeofanelectronorpositronisunambiguous, em and the complex conjugate of an electron is unambiguously a positron, per equations (42.99).

But a chiral spinor such as e can be obtained as either an electron or a positron in the limit of diverging boost and V↑ vanishing mass, so e could have either charge.

By itself, a massless, chiral spinor does not contain enough V↑ informationtodeterminethesignofitscharge.Todisambiguatetheircharge,thechiralspinorsintheDirac chart (42.98) are written without or with a conjugation * symbol: unconjugated spinors (no *) have the charge of an electron, while conjugated spinors (with *) have the charge of a positron.

So disambiguated, the charges of the chiral spinors in the Dirac chart (42.98) can be read off from their bits: spinors with spin

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

EVIDENCE:
- Geons and Spacetime foam • After the pioneering work by Einstein and Rosen, in 1935, the field lay dormant for a good 20 years.
- • Interest in systems of this nature was rekindled in 1955 by John Wheeler, who was beginning to be interested in topological issues in General Relativity: (Resulted in the paper “Geons”, Phys.Rev.
- 1955) • The “geon” concept was coined by Wheeler to denote a “gravitational-electromagnetic entity”.

Geons and Spacetime foam • After the pioneering work by Einstein and Rosen, in 1935, the field lay dormant for a good 20 years.

• Interest in systems of this nature was rekindled in 1955 by John Wheeler, who was beginning to be interested in topological issues in General Relativity: (Resulted in the paper “Geons”, Phys.Rev.

1955) • The “geon” concept was coined by Wheeler to denote a “gravitational-electromagnetic entity”.

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

EVIDENCE:
- (3.10) λμν 2 μ λν ν λμ 6 λν μ λμ ν The Weyl evolution equations (3.9) can be regarded as the gravitational analogue of Maxwell’s equations of electromagnetism.
- 92 More on the coordinate approach In 4-dimensional spacetime, there are 20 such independent contracted identities, consisting of 4 trace identities obtained by contracting over λν, and 16 trace-free identities.
- (3.12) λν This doubly-contracted Bianchi identity, which is the same as equation (2.130), enforces conservation of energy-momentum.
- (3.8) [κ λμ] [κ λ μ] τ τ [κ λ μ] [υ ρσ] If the Riemann tensor is separated into its trace (Ricci) and traceless (Weyl) parts, equation (3.1), then the contracted Bianchi identities (3.7) become the Weyl evolution equations DκC =J , (3.9) κλμν λμν where J is the Weyl current λμν J ≡ 1(D G −D G )− 1(g D G−g D G) .

(3.10) λμν 2 μ λν ν λμ 6 λν μ λμ ν The Weyl evolution equations (3.9) can be regarded as the gravitational analogue of Maxwell’s equations of electromagnetism.

92 More on the coordinate approach In 4-dimensional spacetime, there are 20 such independent contracted identities, consisting of 4 trace identities obtained by contracting over λν, and 16 trace-free identities.

(3.12) λν This doubly-contracted Bianchi identity, which is the same as equation (2.130), enforces conservation of energy-momentum.

(3.8) [κ λμ] [κ λ μ] τ τ [κ λ μ] [υ ρσ] If the Riemann tensor is separated into its trace (Ricci) and traceless (Weyl) parts, equation (3.1), then the contracted Bianchi identities (3.7) become the Weyl evolution equations DκC =J , (3.9) κλμν λμν where J is the Weyl current λμν J ≡ 1(D G −D G )− 1(g D G−g D G) .

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

EVIDENCE:
- HeuristicThoughtsaboutQuantumGravity | 769 experiment,thentheyhavenophysicalrealityandwemightaswellconsiderthemnon-existent.
- Would quantizing gravity lead to a deeperunderstandingofnature?Wewillhavetosee,evidently.
- I would take issue with the statement “If individual gravitons cannot be observed .
- Tome,thiskindofhandwavingargumentisratherfastandloose,andshould(andcould)berefined.Indeed, Meaddidrefinehisargument,firsttakingintoaccountmomentumconservationandthenreplacingNewtonian gravitybyEinsteiniangravity.

Would quantizing gravity lead to a deeperunderstandingofnature?Wewillhavetosee,evidently.

I would take issue with the statement “If individual gravitons cannot be observed .

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

EVIDENCE:
- cover (a covering space with a finite-to-one covering map) that is a Haken manifold.
- In a posting on the ArXiv on 25 Aug 2009,[14] Daniel Wise implicitly implied (by referring to a then unpublished longer manuscript) that he had proven the Virtually fibered conjecture for the case where the 3-manifold is closed, hyperbolic, and Haken.
- This was followed by a survey article in Electronic Research Announcements in Mathematical Sciences.[15] Several more preprints[16] have followed, including the aforementioned longer manuscript by Wise.[17] In March 2012, during a conference at Institut Henri Poincaré in Paris, Ian Agol announced he could prove the virtually Haken conjecture for closed hyperbolic 3-manifolds.[18] The proof built on results of Kahn and Markovic[19][20] in their proof of the Surface subgroup conjecture and results of Wise in proving the Malnormal Special

cover (a covering space with a finite-to-one covering map) that is a Haken manifold.

In a posting on the ArXiv on 25 Aug 2009,[14] Daniel Wise implicitly implied (by referring to a then unpublished longer manuscript) that he had proven the Virtually fibered conjecture for the case where the 3-manifold is closed, hyperbolic, and Haken.

This was followed by a survey article in Electronic Research Announcements in Mathematical Sciences.[15] Several more preprints[16] have followed, including the aforementioned longer manuscript by Wise.[17] In March 2012, during a conference at Institut Henri Poincaré in Paris, Ian Agol announced he could prove the virtually Haken conjecture for closed hyperbolic 3-manifolds.[18] The proof built on results of Kahn and Markovic[19][20] in their proof of the Surface subgroup conjecture and results of Wise in proving the Malnormal Special

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

EVIDENCE:
- A sound is coming from inside the bathroom.
- I knock on the hollow-core door.
- I pull the sheets and blankets up to Charlie’s shoulders and kiss him on the forehead.
- “Daniela?” I hear her catch her breath.

A sound is coming from inside the bathroom.

I pull the sheets and blankets up to Charlie’s shoulders and kiss him on the forehead.

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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:
- ● https://www.documentcloud.org/documents/6185702-Eric-Davis-meeting-with-Adm-Wilson ● https://isgp-studies.com/afio-members-and-biographies-list ● https://youtu.be/pY1XHQBqIY8 ● https://sgp.fas.org/othergov/sapoc.html Note:ThenotesofthismeetingoriginatedfromtheestateoflateastronautEdgarMitchell,who workedwithDavisattheNationalInstituteforDiscoveryScience(NIDSci)andpresumably receivedthenotesataNIDScimeetingafterwards.
- GansleralsotellsWilsontodropthematter.
- AttheendofDavis’andWilson’smeeting,thecontractorTRWismentionedinrelationtoa HughesAircraftattorneyJeffreyW.GriffithandaclientofhisMaryElizabethElliott.
- WilsonalsostateshetalkstoUSDATJacquesGansleraboutthematter,whotellshim UFOsare“real,”butalienabductionsarenot.

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

EVIDENCE:
- The use of Petrosian magnitudes also have the disadvantage of missing most of the light outside the Petrosian aperture, which is defined relative to the galaxy's overall brightness profile, especially for elliptical galaxies, with higher signal-to-noise ratios on higher distances and redshifts.[158] A correction for this method has been issued by Graham et al.
- Gathering the overall luminous flux of the galaxy has been employed by at least four methods: the first being a circular aperture extending 7 arcseconds from the center, an isophote at 20 mag/arcsec2, a "total" aperture defined by the radial light distribution that covers the supposed extent of the galaxy, and the Kron aperture (defined as 2.5 times the first-moment radius, an integration of the flux of the "total" aperture).[159] Larger-scale structures Deep-sky surveys show that galaxies are often found in groups and clusters.
- The detail of the method used by 2MASS has been described thoroughly in a document by Jarrett et al., with the survey measuring several parameters.[159] The standard aperture ellipse (area of detection) is defined by the infrared isophote at the K band s (roughly 2.2 μm wavelength) of 20 mag/arcsec2.
- in 2005, based on the assumption that galaxies follow Sérsic's law.[156] Near-infrared method This method has been used by 2MASS as an adaptation from the previously used methods of isophotal measurement.

The use of Petrosian magnitudes also have the disadvantage of missing most of the light outside the Petrosian aperture, which is defined relative to the galaxy's overall brightness profile, especially for elliptical galaxies, with higher signal-to-noise ratios on higher distances and redshifts.[158] A correction for this method has been issued by Graham et al.

Gathering the overall luminous flux of the galaxy has been employed by at least four methods: the first being a circular aperture extending 7 arcseconds from the center, an isophote at 20 mag/arcsec2, a "total" aperture defined by the radial light distribution that covers the supposed extent of the galaxy, and the Kron aperture (defined as 2.5 times the first-moment radius, an integration of the flux of the "total" aperture).[159] Larger-scale structures Deep-sky surveys show that galaxies are often found in groups and clusters.

The detail of the method used by 2MASS has been described thoroughly in a document by Jarrett et al., with the survey measuring several parameters.[159] The standard aperture ellipse (area of detection) is defined by the infrared isophote at the K band s (roughly 2.2 μm wavelength) of 20 mag/arcsec2.

in 2005, based on the assumption that galaxies follow Sérsic's law.[156] Near-infrared method This method has been used by 2MASS as an adaptation from the previously used methods of isophotal measurement.

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

EVIDENCE:
- And if that’s the case, then we have the ability to go wherever we want.
- “The doors in the corridor are the connections to an infinite array of parallel worlds, right?
- Moments later, you opened a door and we watched that exact scenario play out.” I feel the spine-tingling rush of a revelation sweeping over me.
- 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.

And if that’s the case, then we have the ability to go wherever we want.

“The doors in the corridor are the connections to an infinite array of parallel worlds, right?

Moments later, you opened a door and we watched that exact scenario play out.” I feel the spine-tingling rush of a revelation sweeping over me.

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.

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

EVIDENCE:
- The time at which each hemisphere points farthest or nearest from its star is known as its solstice.
- Each planet therefore has seasons, resulting in changes to the climate over the course of its year.
- The argument of periapsis (or perihelion in the Solar System) is the angle between a planet's ascending node and its closest approach to its star.[62] Axial tilt Planets have varying degrees of axial tilt; they spin at an angle to the plane of their stars' equators.
- The eccentricity of an orbit describes the elongation of a planet's elliptical (oval) orbit.

The time at which each hemisphere points farthest or nearest from its star is known as its solstice.

Each planet therefore has seasons, resulting in changes to the climate over the course of its year.

The argument of periapsis (or perihelion in the Solar System) is the angle between a planet's ascending node and its closest approach to its star.[62] Axial tilt Planets have varying degrees of axial tilt; they spin at an angle to the plane of their stars' equators.

The eccentricity of an orbit describes the elongation of a planet's elliptical (oval) orbit.

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

EVIDENCE:
- the AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information.[78] Applications to nuclear physics In addition to its applications to theoretical problems in quantum gravity, the AdS/CFT correspondence has been applied to a variety of problems in quantum field theory.
- One physical system that has been studied using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators.
- This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies.
- Such collisions cause the quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvin, conditions similar to those present at around 10 −11 seconds after the Big Bang.[79] The physics of the quark–gluon plasma is governed by a theory called quantum chromodynamics, but this theory is mathematically intractable in problems involving the quark–gluon plasma.[c] In an article appearing in 2005, Đàm Thanh Sơn and his collaborators showed that the AdS/CFT

the AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information.[78] Applications to nuclear physics In addition to its applications to theoretical problems in quantum gravity, the AdS/CFT correspondence has been applied to a variety of problems in quantum field theory.

One physical system that has been studied using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators.

This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies.

Such collisions cause the quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvin, conditions similar to those present at around 10 −11 seconds after the Big Bang.[79] The physics of the quark–gluon plasma is governed by a theory called quantum chromodynamics, but this theory is mathematically intractable in problems involving the quark–gluon plasma.[c] In an article appearing in 2005, Đàm Thanh Sơn and his collaborators showed that the AdS/CFT

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

EVIDENCE:
- The total hydrogen and helium fractions are XH =1−fn/f+ =0.86 and X4He = 1 fn/f+ =0.07 where fp ≡ 1−fn = 0.875 and fn ≡ nn/n b = 0.125 are the neutron- and proton-to-baryon ratios, Exercise 31.1.
- Inserting this equilibrium condition into equation (31.13), p e H valid for non-relativistic Boltzmann species, implies the relation between the number densities n , n , and p e n of protons, electrons, and hydrogen atoms in level nl, nl n n g g ( m T )3/2 p e = p e e e−En/T .
- 31.3.3 Ionization state in thermodynamic equilibrium In thermodynamic equilibrium, the chemical potentials of protons, electrons, and neutral hydrogen atoms are related by μ +μ = μ , equation (10.127).
- Thedashedverticallineindicateswhererecombinationactuallyoccurs(wheretheThomsonscatteringopticaldepth isunity),somewhatlaterthanpredictedbyequilibrium.

The total hydrogen and helium fractions are XH =1−fn/f+ =0.86 and X4He = 1 fn/f+ =0.07 where fp ≡ 1−fn = 0.875 and fn ≡ nn/n b = 0.125 are the neutron- and proton-to-baryon ratios, Exercise 31.1.

Inserting this equilibrium condition into equation (31.13), p e H valid for non-relativistic Boltzmann species, implies the relation between the number densities n , n , and p e n of protons, electrons, and hydrogen atoms in level nl, nl n n g g ( m T )3/2 p e = p e e e−En/T .

31.3.3 Ionization state in thermodynamic equilibrium In thermodynamic equilibrium, the chemical potentials of protons, electrons, and neutral hydrogen atoms are related by μ +μ = μ , equation (10.127).

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

EVIDENCE:
- The Gaussian and Hamiltonian constraints are constraint equations in the sense commonly used by relativists: if the equations are arranged to be satisfied on the initial spatialhypersurfaceofconstanttime,thentheconservationequationsensurethattheequationswillcontinue to be satisfied thereafter.
- Split into time and spatial components, the gravitational Lagrangian 4-form (16.234) is L g =− I π ( e2 α ̄ ∧ ( d t Γ α ̄ +d α Γ t ̄+ 1[Γ α ̄ ,Γ t ̄] ) +e t ̄∧(e∧R) α ̄ ) .
- The left hand sides of the Gaussian and Hamiltonian constraints satisfy corresponding conservation laws enforced by the contracted Bianchi identities (16.406).
- (16.313) α ̄ t α ̄ 2 α ̄ α ̄ t α ̄ Equation(16.313)effectivelyreplacesthetimederivatived withe ∧d ,consistentwiththetimederivative t α ̄ t intheequationsofmotion(16.311).TheremainingtermsinthegravitationalLagrangian(16.312)rearrange as follows.

The Gaussian and Hamiltonian constraints are constraint equations in the sense commonly used by relativists: if the equations are arranged to be satisfied on the initial spatialhypersurfaceofconstanttime,thentheconservationequationsensurethattheequationswillcontinue to be satisfied thereafter.

Split into time and spatial components, the gravitational Lagrangian 4-form (16.234) is L g =− I π ( e2 α ̄ ∧ ( d t Γ α ̄ +d α Γ t ̄+ 1[Γ α ̄ ,Γ t ̄] ) +e t ̄∧(e∧R) α ̄ ) .

The left hand sides of the Gaussian and Hamiltonian constraints satisfy corresponding conservation laws enforced by the contracted Bianchi identities (16.406).

(16.313) α ̄ t α ̄ 2 α ̄ α ̄ t α ̄ Equation(16.313)effectivelyreplacesthetimederivatived withe ∧d ,consistentwiththetimederivative t α ̄ t intheequationsofmotion(16.311).TheremainingtermsinthegravitationalLagrangian(16.312)rearrange as follows.

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

EVIDENCE:
- (31.68) between B and A , the 2 2 12 21 relation (31.72) may also be written as an expression for the departure coefficient b , b β +A b = p1 2 21 , (31.73) 21 β +A 2 21 in terms of the departure coefficient b , the value of n n /n relative to its value in thermodynamic equip1 p e 1 librium, n n ⧸( n n ) X X n g ( m T )−3/2 b ≡ p e p e = p e + 1 e eE1/T .
- (31.74) p1 n n X g g 2π(cid:126)2 1 1 TE 1 p e

(31.68) between B and A , the 2 2 12 21 relation (31.72) may also be written as an expression for the departure coefficient b , b β +A b = p1 2 21 , (31.73) 21 β +A 2 21 in terms of the departure coefficient b , the value of n n /n relative to its value in thermodynamic equip1 p e 1 librium, n n ⧸( n n ) X X n g ( m T )−3/2 b ≡ p e p e = p e + 1 e eE1/T .

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

EVIDENCE:
- (35.38) s lm s lms 4π The expansion (35.37) differs from the convention of Hu and White (1997) in that (a) the expansion is with respect to Y* as opposed to Y , (b) there is an extra factor of (−i)m−s, (c) the spin harmonics −s lm s lm Y* (p^,χ)includeafactorofe−isχ.Thepointofexpandingwithrespectto Y* isthat Θ isthenthe −s lm −s lm s lm coefficientofthespin-weightsandm(ratherthansand−m)termunderrotationsaboutrespectivelythep^ andk^ directions,consistentwiththeconventioninthisbookthatthespin-weightofanobjectcanbereadoff from its covariant indices.
- s lm The index on the scalar (m = 0) fluctuation is often omitted for brevity, Θ = Θ .
- The factor of (−i)m−s is introduced to cancel the factor of (−)m−s between D lms anditscomplexconjugate,equation(35.129),ensuringrealityconditions(35.46)ontheharmoniccoefficients that match those on the Newman-Penrose components of the gravitational potentials.
- 932 Cosmological perturbations including polarization Θ is, consistent with the expansion (33.47) of the scalar (m = 0) fluctuation Θ, with k^ taken along the s 3-direction (z-direction), ∞ min(l,2) ∑ ∑ √ Θ(η,k,p^,χ)= (−i)l+m−s 4π(2l+1) Θ (η,k) Y* (p^,χ) s s lm −s lm l=|s|m=−min(l,2) ∞ min(l,2) ∑ ∑ = (−i)l+m−s(2l+1) Θ (η,k)D (φ,θ,χ) , (35.37) s lm lms l=|s|m=−min(l,2) where Y (p^,χ)arethespin-weightedsphericalharmonicsdefinedbyequation(35.84),andD (φ,θ,χ)are s lm lms theWignerrotationmatricesdiscussedin§35.12.2.Theanglesθandφarethepolarcoordinatesofthephoton directionp^.Modes Θ with|m|=0,1,2correspondrespectivelytoscalar,vector,andtensorfluctuations.

(35.38) s lm s lms 4π The expansion (35.37) differs from the convention of Hu and White (1997) in that (a) the expansion is with respect to Y* as opposed to Y , (b) there is an extra factor of (−i)m−s, (c) the spin harmonics −s lm s lm Y* (p^,χ)includeafactorofe−isχ.Thepointofexpandingwithrespectto Y* isthat Θ isthenthe −s lm −s lm s lm coefficientofthespin-weightsandm(ratherthansand−m)termunderrotationsaboutrespectivelythep^ andk^ directions,consistentwiththeconventioninthisbookthatthespin-weightofanobjectcanbereadoff from its covariant indices.

s lm The index on the scalar (m = 0) fluctuation is often omitted for brevity, Θ = Θ .

The factor of (−i)m−s is introduced to cancel the factor of (−)m−s between D lms anditscomplexconjugate,equation(35.129),ensuringrealityconditions(35.46)ontheharmoniccoefficients that match those on the Newman-Penrose components of the gravitational potentials.

932 Cosmological perturbations including polarization Θ is, consistent with the expansion (33.47) of the scalar (m = 0) fluctuation Θ, with k^ taken along the s 3-direction (z-direction), ∞ min(l,2) ∑ ∑ √ Θ(η,k,p^,χ)= (−i)l+m−s 4π(2l+1) Θ (η,k) Y* (p^,χ) s s lm −s lm l=|s|m=−min(l,2) ∞ min(l,2) ∑ ∑ = (−i)l+m−s(2l+1) Θ (η,k)D (φ,θ,χ) , (35.37) s lm lms l=|s|m=−min(l,2) where Y (p^,χ)arethespin-weightedsphericalharmonicsdefinedbyequation(35.84),andD (φ,θ,χ)are s lm lms theWignerrotationmatricesdiscussedin§35.12.2.Theanglesθandφarethepolarcoordinatesofthephoton directionp^.Modes Θ with|m|=0,1,2correspondrespectivelytoscalar,vector,andtensorfluctuations.

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

EVIDENCE:
- Analysis of this game shows that no classical local hidden-variable theory can explain the correlations that can result from entanglement.
- It is also required that Alice and Bob's responses can only depend on the bits they see: so Alice's response depends only on , and similarly for Bob.
- These agents will be abbreviated respectively.
- In the following sections, it is shown that if Alice and Bob use only classical strategies involving their local information (and potentially some random coin tosses), it is impossible for them to win with a probability higher than 75%.

Analysis of this game shows that no classical local hidden-variable theory can explain the correlations that can result from entanglement.

It is also required that Alice and Bob's responses can only depend on the bits they see: so Alice's response depends only on , and similarly for Bob.

These agents will be abbreviated respectively.

In the following sections, it is shown that if Alice and Bob use only classical strategies involving their local information (and potentially some random coin tosses), it is impossible for them to win with a probability higher than 75%.

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

EVIDENCE:
- 413–414 (https://arc hive.org/details/observationanaly0000gray/page/413).
- "Stellar Collisions and the Interior Structure of Blue Stragglers".
- S2CID 119262962 (https://api.semanticscholar.org/CorpusID:119262962).
- S2CID 16502974 (https://api.semanticscholar.org/ CorpusID:16502974).

"Stellar Collisions and the Interior Structure of Blue Stragglers".

S2CID 16502974 (https://api.semanticscholar.org/ CorpusID:16502974).

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

EVIDENCE:
- not explicitly defined by the IAU due to the large relative uncertainty (10−4 ) of ☉ the Newtonian constant of gravitation G.
- Since the product of the Newtonian constant of gravitation and solar mass together (GM ) has been determined to much greater precision, the IAU defined the ☉ nominal solar mass parameter to be: nominal solar mass parameter: GM = 1.327 1244 ×1020 m3 /s2[56] ☉ The nominal solar mass parameter can be combined with the most recent (2014) CODATA estimate of the Newtonian constant of gravitation G to derive the solar mass to be approximately 1.9885 ×1030 kg.
- Although the exact values for the luminosity, radius, mass parameter, and mass may

not explicitly defined by the IAU due to the large relative uncertainty (10−4 ) of ☉ the Newtonian constant of gravitation G.

Since the product of the Newtonian constant of gravitation and solar mass together (GM ) has been determined to much greater precision, the IAU defined the ☉ nominal solar mass parameter to be: nominal solar mass parameter: GM = 1.327 1244 ×1020 m3 /s2[56] ☉ The nominal solar mass parameter can be combined with the most recent (2014) CODATA estimate of the Newtonian constant of gravitation G to derive the solar mass to be approximately 1.9885 ×1030 kg.

Although the exact values for the luminosity, radius, mass parameter, and mass may

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

EVIDENCE:
- The U (1) Dynkin index S (U (1),spinor) is therefore an average of 40/8= 5 times that Y 2 Y 3 3 of SU (2), per fermion.
- Spin(N) has a unique spin representation, but SU(N) has spinor representations of spinor grades p≤N/2.
- Y The Dynkin index of U (1) that enters equation (42.171) equals the hypercharge squared summed over Y the particles of the SM, suitably normalized.
- f L TheweakgroupSpin(5),whichunifiesleft-andright-handedfermions,actsonenlargedfermionmultiplets that include both left- and right-handed weak chiral components, the lepton multiplet (ν ,e ,ν ,e ), and L L R R the three quark multiplets (uc,dc,uc,dc) of colours c = r,g,b.

The U (1) Dynkin index S (U (1),spinor) is therefore an average of 40/8= 5 times that Y 2 Y 3 3 of SU (2), per fermion.

Spin(N) has a unique spin representation, but SU(N) has spinor representations of spinor grades p≤N/2.

Y The Dynkin index of U (1) that enters equation (42.171) equals the hypercharge squared summed over Y the particles of the SM, suitably normalized.

f L TheweakgroupSpin(5),whichunifiesleft-andright-handedfermions,actsonenlargedfermionmultiplets that include both left- and right-handed weak chiral components, the lepton multiplet (ν ,e ,ν ,e ), and L L R R the three quark multiplets (uc,dc,uc,dc) of colours c = r,g,b.

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

EVIDENCE:
- He is also credited as the originator of bipolar coordinates in a strict sense.[85][86] A private manuscript of Newton's which dates to 1664–66 contains what is the earliest known problem in the field of geometric probability.
- However, a 1690s manuscript later analysed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons.[48][71][77] In 1717, and probably with Newton's help, James Stirling proved that every cubic was one of these four types.
- In letters with Samuel Pepys in 1693, they corresponded over the Newton–Pepys problem, which was a problem about the probability of throwing sixes from a certain number of dice.
- His 1671 Method of Fluxions work preceded the earliest publication on the subject by Jacob Bernoulli in 1691.

He is also credited as the originator of bipolar coordinates in a strict sense.[85][86] A private manuscript of Newton's which dates to 1664–66 contains what is the earliest known problem in the field of geometric probability.

However, a 1690s manuscript later analysed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons.[48][71][77] In 1717, and probably with Newton's help, James Stirling proved that every cubic was one of these four types.

In letters with Samuel Pepys in 1693, they corresponded over the Newton–Pepys problem, which was a problem about the probability of throwing sixes from a certain number of dice.

His 1671 Method of Fluxions work preceded the earliest publication on the subject by Jacob Bernoulli in 1691.

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

EVIDENCE:
- Suppose the universe began as an endlessly thin volume of gravel, dust, and gas.
- The tendency will be for all objects to bloat into matter held together by the electromagnetic force or not held together at all.
- Even black holes will, little by little, disgorge, and in the end the universe will be a vast, incredibly thin cloud of gravel, dust, and gas growing endlessly vaster and thinner.
- As the universe expands and gravitation grows ever weaker, those objects held together primarily by gravitational force will expand and become less compact and dense.

Suppose the universe began as an endlessly thin volume of gravel, dust, and gas.

The tendency will be for all objects to bloat into matter held together by the electromagnetic force or not held together at all.

Even black holes will, little by little, disgorge, and in the end the universe will be a vast, incredibly thin cloud of gravel, dust, and gas growing endlessly vaster and thinner.

As the universe expands and gravitation grows ever weaker, those objects held together primarily by gravitational force will expand and become less compact and dense.

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

EVIDENCE:
- Moderne Algebra, a central two-volume text in the field; its second volume, published in 1931, borrowed heavily from Noether's work.[71] Noether did not seek recognition, but he included as a note in the seventh edition "based in part on lectures by E.
- Noether".[72][73][74] Beginning in 1927, Noether worked closely with Emil Artin, Richard Brauer, and Helmut Hasse on noncommutative algebras.[40][71]

Moderne Algebra, a central two-volume text in the field; its second volume, published in 1931, borrowed heavily from Noether's work.[71] Noether did not seek recognition, but he included as a note in the seventh edition "based in part on lectures by E.

Noether".[72][73][74] Beginning in 1927, Noether worked closely with Emil Artin, Richard Brauer, and Helmut Hasse on noncommutative algebras.[40][71]

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

EVIDENCE:
- Using the Lambert W function the solution is written as: .
- Moreover one sees immediately that in the region external to the black hole whereas in the region internal to the black hole In these new coordinates the metric of the Schwarzschild black hole manifold is given by written using the (− + + +) metric signature convention and where the angular component of the metric (the Riemannian metric of the 2-sphere) is: .
- Here is the gravitational constant multiplied by the Schwarzschild mass parameter, and this article is using units where = 1.
- It follows that on the union of the exterior region, the event horizon and the interior region the Schwarzschild radial coordinate (not to be confused with the Schwarzschild radius ), is determined in terms of Kruskal–Szekeres coordinates as the (unique) solution of the equation: Kruskal–Szekeres diagram.

Kruskal–Szekeres coordinates - Wikipedia.pdf

Using the Lambert W function the solution is written as: .

Moreover one sees immediately that in the region external to the black hole whereas in the region internal to the black hole In these new coordinates the metric of the Schwarzschild black hole manifold is given by written using the (− + + +) metric signature convention and where the angular component of the metric (the Riemannian metric of the 2-sphere) is: .

Here is the gravitational constant multiplied by the Schwarzschild mass parameter, and this article is using units where = 1.

It follows that on the union of the exterior region, the event horizon and the interior region the Schwarzschild radial coordinate (not to be confused with the Schwarzschild radius ), is determined in terms of Kruskal–Szekeres coordinates as the (unique) solution of the equation: Kruskal–Szekeres diagram.

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

EVIDENCE:
- 9781405131117_4_000int.qxd 30/6/09 11:44 AM Page 5 cook up reasonable-sounding, but false, explanations for our behaviors after the fact (Nisbett & Wilson, 1977).
- I do not recall ever coming across a valid study that contravened common sense.
- Indeed, you may have heard that most psychology is “just common sense” (Furnham, 1983; Houston, 1985; Murphy, 1990).
- More recently, in a New York Times editorial, well-known science writer John Horgan (2005) called for a return to common sense in the evaluation of scientific theories, including those in psychology.

9781405131117_4_000int.qxd 30/6/09 11:44 AM Page 5 cook up reasonable-sounding, but false, explanations for our behaviors after the fact (Nisbett & Wilson, 1977).

I do not recall ever coming across a valid study that contravened common sense.

Indeed, you may have heard that most psychology is “just common sense” (Furnham, 1983; Houston, 1985; Murphy, 1990).

More recently, in a New York Times editorial, well-known science writer John Horgan (2005) called for a return to common sense in the evaluation of scientific theories, including those in psychology.

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

EVIDENCE:
- James Wood and his colleagues found that the overwhelming majority of Rorschach scores are essentially unrelated to personality traits.
- The lone possible exception is dependency (Bornstein, 1996), which a few | Chapter 8 Know Thyself 173
- And responses to the white space nestled within the blots rather than to the blots themselves (“That white area over there looks like a hand broom”) ostensibly indicate rebelliousness toward authority.
- dust”) ostensibly indicate obsessiveness.

James Wood and his colleagues found that the overwhelming majority of Rorschach scores are essentially unrelated to personality traits.

The lone possible exception is dependency (Bornstein, 1996), which a few | Chapter 8 Know Thyself 173

And responses to the white space nestled within the blots rather than to the blots themselves (“That white area over there looks like a hand broom”) ostensibly indicate rebelliousness toward authority.

dust”) ostensibly indicate obsessiveness.

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

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

EVIDENCE:
- 30.11 Radiation-dominated, adiabatic initial conditions 805 1.5 1.0 .5 .0 −.5 −1.0 0 1 2 3 4 5 6 7 8 kηs / π Φ2− dna Φ − Θ adiabatic 3.0 2.5 2.0 1.5 1.0 .5 .0 −.5 −1.0 −1.5 0 1 2 3 4 5 6 7 8 kηs / π Φ2− dna Φ − Θ isocurvature Figure 30.7 The potential Φ and radiation monopole Θ0 for modes that enter the sound horizon kηs = 1 during the radiation-dominated regime well before matter-radiation equality, for (top) adiabatic initial conditions, equations(30.77)and(30.78),and(bottom)isocurvatureinitialconditions,equations(30.84)and(30.85).Thequantities shown are(blue) Θ0−Φ and(black)−2Φ,to illustratethat theformeroscillates about the latteras expectedfrom equation(30.48).Thedifference,(Θ0−Φ)−(−2Φ)=Θ0+Φ,whichisthetemperatureΘ0redshiftedbythepotential Φ,is(forΨ=Φ)themonopolecontributiontothetemperaturefluctuationoftheCMB,equation(34.17).Theunits ofΦandΘ0 aresuchthatζr=1foradiabaticfluctuations,andζc=1forisocurvaturefluctuations.
- suppressthegravitationalpotentialΦ.Thesuppressionofthepotentialisresponsiblefortheturnoverinthe observed power spectrum of matter fluctuations today from large to small scales evident in Figure 30.15.
- The radiation monopole Θ can be inferred either from the Einstein equation (30.73b) with the solu0 tions (30.75) for the potential Φ, or from the Green’s function solution (30.52) in the radiation-dominated regime.
- Either way, the difference Θ −Φ between the radiation monopole and the potential corresponding to the growing mode potential (30.77) is (2siny−ycosy) Θ −Φ=ζ .

30.11 Radiation-dominated, adiabatic initial conditions 805 1.5 1.0 .5 .0 −.5 −1.0 0 1 2 3 4 5 6 7 8 kηs / π Φ2− dna Φ − Θ adiabatic 3.0 2.5 2.0 1.5 1.0 .5 .0 −.5 −1.0 −1.5 0 1 2 3 4 5 6 7 8 kηs / π Φ2− dna Φ − Θ isocurvature Figure 30.7 The potential Φ and radiation monopole Θ0 for modes that enter the sound horizon kηs = 1 during the radiation-dominated regime well before matter-radiation equality, for (top) adiabatic initial conditions, equations(30.77)and(30.78),and(bottom)isocurvatureinitialconditions,equations(30.84)and(30.85).Thequantities shown are(blue) Θ0−Φ and(black)−2Φ,to illustratethat theformeroscillates about the latteras expectedfrom equation(30.48).Thedifference,(Θ0−Φ)−(−2Φ)=Θ0+Φ,whichisthetemperatureΘ0redshiftedbythepotential Φ,is(forΨ=Φ)themonopolecontributiontothetemperaturefluctuationoftheCMB,equation(34.17).Theunits ofΦandΘ0 aresuchthatζr=1foradiabaticfluctuations,andζc=1forisocurvaturefluctuations.

suppressthegravitationalpotentialΦ.Thesuppressionofthepotentialisresponsiblefortheturnoverinthe observed power spectrum of matter fluctuations today from large to small scales evident in Figure 30.15.

The radiation monopole Θ can be inferred either from the Einstein equation (30.73b) with the solu0 tions (30.75) for the potential Φ, or from the Green’s function solution (30.52) in the radiation-dominated regime.

Either way, the difference Θ −Φ between the radiation monopole and the potential corresponding to the growing mode potential (30.77) is (2siny−ycosy) Θ −Φ=ζ .

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

EVIDENCE:
- talking about them and releasing them in a controlled manner in and out of treatment.
- The Marvel comic book and movie character, “The Hulk,” is a metaphor for the consequences of the failure to control rage that always lurks at the fringes of consciousness.
- When mild-mannered Bruce Banner lets too much anger build up or is provoked, he morphs into his rampaging alter-ego, the Hulk.
- | Chapter 7 The Social Animal 147

talking about them and releasing them in a controlled manner in and out of treatment.

The Marvel comic book and movie character, “The Hulk,” is a metaphor for the consequences of the failure to control rage that always lurks at the fringes of consciousness.

When mild-mannered Bruce Banner lets too much anger build up or is provoked, he morphs into his rampaging alter-ego, the Hulk.

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:
- Grusch and other UAP whistleblowers say the government retaliated against them and tried to stop them from going public.
- The training and experience of many UAP witnesses and whistleblowers, including in the US IC and military, undermine facile dismissals of all these individuals as cranks and grifters.
- Last year, Senator Gillibrand said, “There's a lot of fear and so I don't know if we'll ever get to the bottom of it.
- In 2021, John Ratcliffe, the Director of National Intelligence under former President Trump, said that UAP demonstrated “technologies that we don’t have and, frankly, that we are not capable of defending against.”21 Ratcliffe said, U.S.

Grusch and other UAP whistleblowers say the government retaliated against them and tried to stop them from going public.

The training and experience of many UAP witnesses and whistleblowers, including in the US IC and military, undermine facile dismissals of all these individuals as cranks and grifters.

Last year, Senator Gillibrand said, “There's a lot of fear and so I don't know if we'll ever get to the bottom of it.

In 2021, John Ratcliffe, the Director of National Intelligence under former President Trump, said that UAP demonstrated “technologies that we don’t have and, frankly, that we are not capable of defending against.”21 Ratcliffe said, U.S.

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

EVIDENCE:
- in view of equation (3.9) and the antisymmetry of C with respect to the indices κλ.
- The Weyl current κλμν conservationlaw(3.13)followsfromtheform(3.10)oftheWeylcurrent,coupledwithcovariantconservation of the Einstein tensor, equation (2.130), so does not impose any additional non-trivial conditions on the Riemann tensor.
- The Weyl current conservation law (3.13) is the gravitational analogue of the conservation law for electric current that follows from Maxwell’s equations.
- WhereastheEinsteinequationsrelatingtheEinsteintensortotheenergy-momentumtensorarepostulated

in view of equation (3.9) and the antisymmetry of C with respect to the indices κλ.

The Weyl current κλμν conservationlaw(3.13)followsfromtheform(3.10)oftheWeylcurrent,coupledwithcovariantconservation of the Einstein tensor, equation (2.130), so does not impose any additional non-trivial conditions on the Riemann tensor.

The Weyl current conservation law (3.13) is the gravitational analogue of the conservation law for electric current that follows from Maxwell’s equations.

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

EVIDENCE:
- Lifshitz's theory for two metal plates reduces to Casimir's idealized force law for large separations a much a4
- The presence of ħ shows that the Casimir force per unit area is very small, A and that furthermore, the force is inherently of quantum-mechanical origin.
- where ħ is the reduced Planck constant, c is the speed of light, a is the distance between the two plates The force is negative, indicating that the force is attractive: by moving the two plates closer together, F c the energy is lowered.
- By integrating the equation above it is possible to calculate the energy required to separate to infinity the two plates as: where ħ is the reduced Planck constant, c is the speed of light, A is the area of one of the plates, a is the distance between the two plates In Casimir's original derivation,[20] a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart).

Lifshitz's theory for two metal plates reduces to Casimir's idealized force law for large separations a much a4

The presence of ħ shows that the Casimir force per unit area is very small, A and that furthermore, the force is inherently of quantum-mechanical origin.

where ħ is the reduced Planck constant, c is the speed of light, a is the distance between the two plates The force is negative, indicating that the force is attractive: by moving the two plates closer together, F c the energy is lowered.

By integrating the equation above it is possible to calculate the energy required to separate to infinity the two plates as: where ħ is the reduced Planck constant, c is the speed of light, A is the area of one of the plates, a is the distance between the two plates In Casimir's original derivation,[20] a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart).

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- eulogised by figures in science, entertainment, politics and other areas.[a] The Gonville and Caius College flag flew at half-mast and a book of condolences was signed by students and visitors.[352][353][354] A tribute was made to Hawking in the closing speech by IPC President Andrew Parsons at the closing ceremony of the 2018 Paralympic Winter Games in Pyeongchang, South Korea.[355] His private funeral took place on 31 March,[356] at Great St Mary's Church, Cambridge.[356][357] Guests at the funeral included The Theory of Everything actors Eddie Redmayne and Felicity Jones, Queen guitarist and astrophysicist Brian May, and model Lily Cole.[358][359] In addition, actor

eulogised by figures in science, entertainment, politics and other areas.[a] The Gonville and Caius College flag flew at half-mast and a book of condolences was signed by students and visitors.[352][353][354] A tribute was made to Hawking in the closing speech by IPC President Andrew Parsons at the closing ceremony of the 2018 Paralympic Winter Games in Pyeongchang, South Korea.[355] His private funeral took place on 31 March,[356] at Great St Mary's Church, Cambridge.[356][357] Guests at the funeral included The Theory of Everything actors Eddie Redmayne and Felicity Jones, Queen guitarist and astrophysicist Brian May, and model Lily Cole.[358][359] In addition, actor

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:
- I slide my slacks and boxer shorts down my legs.
- He drops me in the gravel, where I sit dazed, waiting for my head to clear.
- “I know what you’re thinking,” he says, “and I can hurt you just as easily inside this car.” I’m not getting enough oxygen.
- But I manage to say, breathlessly, “Bullshit.

I slide my slacks and boxer shorts down my legs.

He drops me in the gravel, where I sit dazed, waiting for my head to clear.

“I know what you’re thinking,” he says, “and I can hurt you just as easily inside this car.” I’m not getting enough oxygen.

But I manage to say, breathlessly, “Bullshit.

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:
- amounts of the light gases hydrogen and helium, whereas the smaller planets lose these gases into space.[121] Analysis of exoplanets suggests that the threshold for being able to hold +0.7 on to these light gases occurs at about 2.0 M , so that −0.6 🜨 Earth and Venus are near the maximum size for rocky planets.[54] The composition of Earth's atmosphere is different from the other planets because the various life processes that have Earth's atmosphere transpired on the planet have introduced free molecular oxygen.[122] The atmospheres of Mars and Venus are both dominated by carbon dioxide, but differ drastically in density: the average surface pressure of Mars's atmosphere is less than 1% that of Earth's (too low to allow liquid water to exist),[123] while the average surface pressure of Venus's atmosphere is about 92 times that of Earth's.[124] It is likely that Venus's atmosphere was the result of a runaway greenhouse effect in its history, which today makes it the hottest planet by surface temperature, hotter even than Mercury.[125] Despite hostile surface conditions, temperature, and pressure at about 50–55 km altitude in Venus's atmosphere are close to Earthlike conditions (the only place in the Solar System beyond Earth where this is so), and this region has been suggested as a plausible base for future human exploration.[126] Titan has the only dense nitrogen-rich planetary atmosphere in the Solar System other than Earth's.
- Just as Earth's conditions are close to the triple point of water, allowing it to exist in all three states on the planet's surface, so Titan's are to the triple point of methane.[127] Planetary atmospheres are affected by the varying insolation or internal energy, leading to the formation of dynamic weather systems such as hurricanes (on Earth), planet-wide dust storms (on Mars), a greater-than-Earth-sized anticyclone on Jupiter (called the Great Red Spot), and holes in the atmosphere (on Neptune).[69] Weather patterns detected on exoplanets include a hot region on HD 189733 b twice the size of the Great Red Spot,[128] as well as clouds on the hot Jupiter Kepler-7b,[129] the super-Earth Gliese 1214 b, and others.[130][131] Hot Jupiters, due to their extreme proximities to their host stars, have been shown to be losing their atmospheres into space due to stellar radiation, much like the tails of comets.[132][133] These planets may have vast differences in temperature between their day and night sides that produce supersonic winds,[134] although multiple factors are involved and the details of the atmospheric dynamics that affect the day-night temperature difference are complex.[135][136] Magnetosphere One important

amounts of the light gases hydrogen and helium, whereas the smaller planets lose these gases into space.[121] Analysis of exoplanets suggests that the threshold for being able to hold +0.7 on to these light gases occurs at about 2.0 M , so that −0.6 🜨 Earth and Venus are near the maximum size for rocky planets.[54] The composition of Earth's atmosphere is different from the other planets because the various life processes that have Earth's atmosphere transpired on the planet have introduced free molecular oxygen.[122] The atmospheres of Mars and Venus are both dominated by carbon dioxide, but differ drastically in density: the average surface pressure of Mars's atmosphere is less than 1% that of Earth's (too low to allow liquid water to exist),[123] while the average surface pressure of Venus's atmosphere is about 92 times that of Earth's.[124] It is likely that Venus's atmosphere was the result of a runaway greenhouse effect in its history, which today makes it the hottest planet by surface temperature, hotter even than Mercury.[125] Despite hostile surface conditions, temperature, and pressure at about 50–55 km altitude in Venus's atmosphere are close to Earthlike conditions (the only place in the Solar System beyond Earth where this is so), and this region has been suggested as a plausible base for future human exploration.[126] Titan has the only dense nitrogen-rich planetary atmosphere in the Solar System other than Earth's.

Just as Earth's conditions are close to the triple point of water, allowing it to exist in all three states on the planet's surface, so Titan's are to the triple point of methane.[127] Planetary atmospheres are affected by the varying insolation or internal energy, leading to the formation of dynamic weather systems such as hurricanes (on Earth), planet-wide dust storms (on Mars), a greater-than-Earth-sized anticyclone on Jupiter (called the Great Red Spot), and holes in the atmosphere (on Neptune).[69] Weather patterns detected on exoplanets include a hot region on HD 189733 b twice the size of the Great Red Spot,[128] as well as clouds on the hot Jupiter Kepler-7b,[129] the super-Earth Gliese 1214 b, and others.[130][131] Hot Jupiters, due to their extreme proximities to their host stars, have been shown to be losing their atmospheres into space due to stellar radiation, much like the tails of comets.[132][133] These planets may have vast differences in temperature between their day and night sides that produce supersonic winds,[134] although multiple factors are involved and the details of the atmospheric dynamics that affect the day-night temperature difference are complex.[135][136] Magnetosphere One important

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:
- That depends on the value of the escape velocity, which depends on the value of the overall gravitational force among the galactic units, which depends, it turns out, on the average density of matter in the universe.
- If it is expanding at less than the escape velocity, then the present expansion must eventually come to a halt, and the contraction must then begin.
- Why, in short, might there not be an endlessly oscillating universe?
- There is a certain gravitational force among the galactic units of the universe generally, and there is an escape velocity associated with that force.

That depends on the value of the escape velocity, which depends on the value of the overall gravitational force among the galactic units, which depends, it turns out, on the average density of matter in the universe.

If it is expanding at less than the escape velocity, then the present expansion must eventually come to a halt, and the contraction must then begin.

Why, in short, might there not be an endlessly oscillating universe?

There is a certain gravitational force among the galactic units of the universe generally, and there is an escape velocity associated with that force.

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:
- any other body along the straight line connecting them.
- The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them.
- The eccentricity of the orbit, and thus the type of conic section, is
- Finding the shape of the orbits that an inverse-square force law will produce is known as the Kepler problem.

any other body along the straight line connecting them.

The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them.

The eccentricity of the orbit, and thus the type of conic section, is

Finding the shape of the orbits that an inverse-square force law will produce is known as the Kepler problem.

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:
- This could be an abandoned power plant in South Chicago in any number of worlds.
- The skyline looms to the north, and even though it’s decapitated by the low winter clouds, it’s unmistakably the one I know.
- Even now, flurries blow in off the lake, drifting down like cold confetti.
- Snow from a recent storm has dusted the concrete and coated the generators beneath those glassless upper windows.

This could be an abandoned power plant in South Chicago in any number of worlds.

The skyline looms to the north, and even though it’s decapitated by the low winter clouds, it’s unmistakably the one I know.

Even now, flurries blow in off the lake, drifting down like cold confetti.

Snow from a recent storm has dusted the concrete and coated the generators beneath those glassless upper windows.

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:
- Barnum statements come in several flavors.
- Some are “double-headed” because they apply to people who are either above or below average on a characteristic and by definition apply to essentially everyone (Hines, 2003).
- The third statement in the ACOA profile at the beginning of this piece, which describes taking both too much and too little responsibility for others, is a prime example.
- One website describes ACOAs as both | 194 Chapter 9 Sad, Mad, and Bad

Barnum statements come in several flavors.

Some are “double-headed” because they apply to people who are either above or below average on a characteristic and by definition apply to essentially everyone (Hines, 2003).

The third statement in the ACOA profile at the beginning of this piece, which describes taking both too much and too little responsibility for others, is a prime example.

One website describes ACOAs as both | 194 Chapter 9 Sad, Mad, and Bad

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:
- For the clinical method, this knowledge consists of cases about which the expert has learned or worked with personally.
- 9781405131117_4_011.qxd 30/6/09 11:45 AM Page 229 death.
- Whereas mechanical predictions are perfectly consistent—that is, reliable—clinical predictions aren’t.
- As a consequence, mechanical predictions usually assign more valid weights to new data than do clinical predictions.

For the clinical method, this knowledge consists of cases about which the expert has learned or worked with personally.

Whereas mechanical predictions are perfectly consistent—that is, reliable—clinical predictions aren’t.

As a consequence, mechanical predictions usually assign more valid weights to new data than do clinical predictions.

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

List tests or derivations implied by the evidence.