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

EVIDENCE:
- (cid:8) Atfirstglance,thingsdonotlookgood,sincetheaction(11)S=−m dζ −η dXμdXν μν dζ dζ doesnotmakesenseforamasslessparticle.Toremedythis,consideranotheraction: (cid:7) (cid:15) (cid:3) (cid:4) (cid:16) S ̃=− 1 dζ σ(ζ) dX 2 + m2 (15) 2 dζ σ(ζ) where(asalways)(dX)2=−η dXμdXν .
- Thus, the Euler-Lagrange equation for dζ(cid:12) (cid:14) ̃ ̃ ̃ σ(ζ),namely d δS − δS =0,collapsesto δS =0: dζ δdσ δσ δσ dζ (cid:3) (cid:4) m2 dX 2 = (16) σ(ζ)2 dζ This is an algebraic equation, not a differential equation, for σ(ζ).
- In other words, the dynamicalvariableσ(ζ)doesnothavedynamicsofitsownbutratheristotallyyoked5to Xμ(ζ).
- (Compare this dζ δdXλ dζ μλ dζ dζ with(13).)Usingtheequationofmotionforσ toeliminateitfromthisequationofmotion forX,weobtain ⎛ ⎞ d ⎜ m dXμ⎟ ⎝(cid:6) η ⎠=0 μλ dζ (dX)2 dζ dζ

(cid:8) Atfirstglance,thingsdonotlookgood,sincetheaction(11)S=−m dζ −η dXμdXν μν dζ dζ doesnotmakesenseforamasslessparticle.Toremedythis,consideranotheraction: (cid:7) (cid:15) (cid:3) (cid:4) (cid:16) S ̃=− 1 dζ σ(ζ) dX 2 + m2 (15) 2 dζ σ(ζ) where(asalways)(dX)2=−η dXμdXν .

Thus, the Euler-Lagrange equation for dζ(cid:12) (cid:14) ̃ ̃ ̃ σ(ζ),namely d δS − δS =0,collapsesto δS =0: dζ δdσ δσ δσ dζ (cid:3) (cid:4) m2 dX 2 = (16) σ(ζ)2 dζ This is an algebraic equation, not a differential equation, for σ(ζ).

In other words, the dynamicalvariableσ(ζ)doesnothavedynamicsofitsownbutratheristotallyyoked5to Xμ(ζ).

(Compare this dζ δdXλ dζ μλ dζ dζ with(13).)Usingtheequationofmotionforσ toeliminateitfromthisequationofmotion forX,weobtain ⎛ ⎞ d ⎜ m dXμ⎟ ⎝(cid:6) η ⎠=0 μλ dζ (dX)2 dζ dζ

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 cosmology In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, t , or approximately 10−43 seconds.[28] There is no P currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time.
- Immeasurably hot and dense, the state of the Planck epoch was succeeded by the grand unification epoch, where gravitation is separated from the unified force of the Standard Model, in turn followed by the inflationary epoch, which ended after about 10−32 seconds (or about 1011 t ).[29] P Table 3 lists properties of the observable universe today expressed in Planck units.[30][31] Table 3: Today's universe in Planck units Property of Approximate present-day observable number Equivalents universe of Planck units Age 8.08 × 1060 t 4.35 × 1017 s or 1.38 × 1010 years P Diameter 5.4 × 1061 l 8.7 × 1026 m or 9.2 × 1010 light-years P 3 × 1052 kg or 1.5 × 1022 solar masses (only counting stars) Mass approx.
- Barrow and Shaw proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ T−2 throughout the history of the universe.[32] Analysis of the units Planck length The Planck length is about 10−20 times the diameter of a proton.[33] It can be motivated in various ways, such as considering a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius,[33][34][35] though whether those concepts are in fact simultaneously applicable is open to debate.[36] (The same heuristic argument simultaneously motivates the Planck mass.[34])
- At this scale, the unified force of the Standard Model is assumed to be unified with gravitation.

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.

In cosmology In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, t , or approximately 10−43 seconds.[28] There is no P currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time.

Immeasurably hot and dense, the state of the Planck epoch was succeeded by the grand unification epoch, where gravitation is separated from the unified force of the Standard Model, in turn followed by the inflationary epoch, which ended after about 10−32 seconds (or about 1011 t ).[29] P Table 3 lists properties of the observable universe today expressed in Planck units.[30][31] Table 3: Today's universe in Planck units Property of Approximate present-day observable number Equivalents universe of Planck units Age 8.08 × 1060 t 4.35 × 1017 s or 1.38 × 1010 years P Diameter 5.4 × 1061 l 8.7 × 1026 m or 9.2 × 1010 light-years P 3 × 1052 kg or 1.5 × 1022 solar masses (only counting stars) Mass approx.

Barrow and Shaw proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ T−2 throughout the history of the universe.[32] Analysis of the units Planck length The Planck length is about 10−20 times the diameter of a proton.[33] It can be motivated in various ways, such as considering a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius,[33][34][35] though whether those concepts are in fact simultaneously applicable is open to debate.[36] (The same heuristic argument simultaneously motivates the Planck mass.[34])

At this scale, the unified force of the Standard Model is assumed to be unified with gravitation.

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:
- QFTs can also be built on non-Abelian groups, giving rise to non-Abelian gauge theories (also known as Yang–Mills theories).[1]: 489 Quantum chromodynamics, which describes the strong interaction, is a non-Abelian gauge theory with an SU(3) gauge symmetry.
- For any α(x), is an element of the U(1) group, thus QED is said to have U(1) gauge symmetry.[1]: 496 The photon field A may be referred to as the μ U(1) gauge boson.
- U(1) is an Abelian group, meaning that the result is the same regardless of the order in which its elements are applied.
- Arrows pointing forward in time represent the propagation of electrons, while those pointing backward in time represent the propagation of positrons.

QFTs can also be built on non-Abelian groups, giving rise to non-Abelian gauge theories (also known as Yang–Mills theories).[1]: 489 Quantum chromodynamics, which describes the strong interaction, is a non-Abelian gauge theory with an SU(3) gauge symmetry.

For any α(x), is an element of the U(1) group, thus QED is said to have U(1) gauge symmetry.[1]: 496 The photon field A may be referred to as the μ U(1) gauge boson.

U(1) is an Abelian group, meaning that the result is the same regardless of the order in which its elements are applied.

Arrows pointing forward in time represent the propagation of electrons, while those pointing backward in time represent the propagation of positrons.

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:
- Bibcode:1978PhRvD..17.2552G (https://ui.adsabs.harvard.edu/abs/1978PhRvD..17.2552G).
- Classical and Quantum Gravity.
- Bibcode:2021NatSR..1114247S (https://ui.adsabs.harvard.edu/abs/2021NatSR..1114247S).
- arXiv:gr-qc/0208075 (https://arxi v.org/abs/gr-qc/0208075).

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:
- p+, and n0 capture their own atomic electrons instead of emitting positrons, emissions, EC denotes electron and subsequently, these nuclides emit only a neutrino and a capture).
- gamma ray from the excited nucleus (and often also Auger electrons and characteristic X-rays, as a result of the re-ordering of electrons to fill the place of the missing captured electron).
- These types of decay involve the nuclear capture of electrons or emission of electrons or positrons, and thus acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleons.
- This consequently produces a more stable (lower energy) nucleus.

p+, and n0 capture their own atomic electrons instead of emitting positrons, emissions, EC denotes electron and subsequently, these nuclides emit only a neutrino and a capture).

gamma ray from the excited nucleus (and often also Auger electrons and characteristic X-rays, as a result of the re-ordering of electrons to fill the place of the missing captured electron).

These types of decay involve the nuclear capture of electrons or emission of electrons or positrons, and thus acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleons.

This consequently produces a more stable (lower energy) nucleus.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The Physics of Quantum Mechanics.
- The Conceptual Development of Quantum Mechanics.
- Eisberg, Robert; Resnick, Robert (1985).
- ISBN 0-08-203204-1 George Mackey (2004).

The Conceptual Development of Quantum Mechanics.

Eisberg, Robert; Resnick, Robert (1985).

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 squared mass difference between m and m implies that at least one of them must have a mass √ m or m ≥ 7.6×10−5eV2 ≈0.01eV .
- (10.108) ν1 ν2 The squared mass difference between m and m implies that at least one of them must have a mass 1 3 √ m or m ≥ 2.4×10−3eV2 ≈0.05eV .
- The extra factor of two for g in the final column of Table 10.4 s arises because every particle species has an antiparticle (the two spin states of a photon can be construed as each other’s antiparticle).
- When a neutrino is created (or annihilated) by a weak interaction, it is created in a weak eigenstate.Observationsofsolarandatmosphericneutrinosindicatethatneutrinospeciesoscillateintoeach other,implyingthattheweakeigenstatesarenotmasseigenstates.Theweakeigenstatesaredenotedν ,ν , e μ andν ,whilethemasseigenstatesaredenotedν ,ν ,andν .Oscillationdatayieldmasssquareddifferences τ 1 2 3 between the three mass eigenstates (Forero, Tortola, and Valle, 2012) |Δm |2 =(7.6±0.2)×10−5eV2 solar neutrinos , (10.107a) |Δm |2 =(2.4±0.1)×10−3eV2 atmospheric neutrinos .

The squared mass difference between m and m implies that at least one of them must have a mass √ m or m ≥ 7.6×10−5eV2 ≈0.01eV .

(10.108) ν1 ν2 The squared mass difference between m and m implies that at least one of them must have a mass 1 3 √ m or m ≥ 2.4×10−3eV2 ≈0.05eV .

The extra factor of two for g in the final column of Table 10.4 s arises because every particle species has an antiparticle (the two spin states of a photon can be construed as each other’s antiparticle).

When a neutrino is created (or annihilated) by a weak interaction, it is created in a weak eigenstate.Observationsofsolarandatmosphericneutrinosindicatethatneutrinospeciesoscillateintoeach other,implyingthattheweakeigenstatesarenotmasseigenstates.Theweakeigenstatesaredenotedν ,ν , e μ andν ,whilethemasseigenstatesaredenotedν ,ν ,andν .Oscillationdatayieldmasssquareddifferences τ 1 2 3 between the three mass eigenstates (Forero, Tortola, and Valle, 2012) |Δm |2 =(7.6±0.2)×10−5eV2 solar neutrinos , (10.107a) |Δm |2 =(2.4±0.1)×10−3eV2 atmospheric neutrinos .

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:
- I look back down the corridor as Leighton and his men start toward us.
- When Leighton’s men step out, Amanda’s face pales with fear, and a sharp, metallic taste coats the roof of my mouth.
- “Goddammit.” A door at the opposite end of the corridor opens.
- Leighton will know in a matter of seconds.” “Give it another shot.” She scans her card again.

I look back down the corridor as Leighton and his men start toward us.

When Leighton’s men step out, Amanda’s face pales with fear, and a sharp, metallic taste coats the roof of my mouth.

“Goddammit.” A door at the opposite end of the corridor opens.

Leighton will know in a matter of seconds.” “Give it another shot.” She scans her card again.

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:
- to create a measurable effect.
- •Key Point: As disappointing as the Casimir Effect vacuum (and other modified vacua) results are, it should be strongly pointed out that special relativity theory says that if in one inertial reference frame an object travels only one part in 1016 (or even one part in 1032) times faster than c , then one can find another reference frame where departure and arrival times of the object are simultaneous, and thus the velocity is infinite.
- We further note that the coefficient of 11 is the same for the gravitational vacuum as for the other modified vacua examples based on QED.
- Approved for public release; distribution unlimited.

•Key Point: As disappointing as the Casimir Effect vacuum (and other modified vacua) results are, it should be strongly pointed out that special relativity theory says that if in one inertial reference frame an object travels only one part in 1016 (or even one part in 1032) times faster than c , then one can find another reference frame where departure and arrival times of the object are simultaneous, and thus the velocity is infinite.

We further note that the coefficient of 11 is the same for the gravitational vacuum as for the other modified vacua examples based on QED.

Approved for public release; distribution unlimited.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- ⊥,a a In practice, collisions in the early post-inflation Universe tend to isotropize particle distributions, driving not only the pressure but also the bulk velocity to zero, as discussed in more detail in §35.11.
- (29.51) a vector ThesameconclusionfollowsfromtheothervectorEinsteinequation(29.50a).Ifthevectorpressurevanishes, then the vector momentum conservation equation (29.47) ensures that the vector energy flux T0a = f ⊥,a vector redshifts as f ∝a−4, which when plugged into the Einstein equation (29.50a) implies W ∝a−2.
- 780 Cosmological perturbations in a flat FLRW background 29.8.3 Conformal Newtonian gauge: vector Einstein equations The vector (spin-1) Einstein equations in conformal Newtonian gauge are, from the expressions (29.30) for the Einstein tensor, ∇2W =−16πGa2 T0a , (29.50a) a vector ( ∂ a ̇) +2 (∇ W +∇ W )=16πGa2 Tab .
- a a The tendency of vector perturbations to redshift away has the consequence that vector perturbations are usually negligible in standard cosmological models.

⊥,a a In practice, collisions in the early post-inflation Universe tend to isotropize particle distributions, driving not only the pressure but also the bulk velocity to zero, as discussed in more detail in §35.11.

(29.51) a vector ThesameconclusionfollowsfromtheothervectorEinsteinequation(29.50a).Ifthevectorpressurevanishes, then the vector momentum conservation equation (29.47) ensures that the vector energy flux T0a = f ⊥,a vector redshifts as f ∝a−4, which when plugged into the Einstein equation (29.50a) implies W ∝a−2.

780 Cosmological perturbations in a flat FLRW background 29.8.3 Conformal Newtonian gauge: vector Einstein equations The vector (spin-1) Einstein equations in conformal Newtonian gauge are, from the expressions (29.30) for the Einstein tensor, ∇2W =−16πGa2 T0a , (29.50a) a vector ( ∂ a ̇) +2 (∇ W +∇ W )=16πGa2 Tab .

a a The tendency of vector perturbations to redshift away has the consequence that vector perturbations are usually negligible in standard cosmological models.

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:
- If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime.
- In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.[40] Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime.
- This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent.[39] At around the same time, as many physicists were studying the properties of strings, a small group of physicists were examining the possible applications of higher dimensional objects.
- In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an A schematic illustration of the relationship between M-theory, the arbitrary Lagrangian.

If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime.

In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.[40] Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime.

This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent.[39] At around the same time, as many physicists were studying the properties of strings, a small group of physicists were examining the possible applications of higher dimensional objects.

In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an A schematic illustration of the relationship between M-theory, the arbitrary Lagrangian.

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:
- AspectsofGravity II II V U V U r = ∞ oriz o n h r 1 r 1 = 1 r = oriz o n = 1 r = h IV I IV increasing t increasing t I r = 0 r = 0 1 r r = h o rizo = 1 U < 0 r = 1 r = U > 0 n V > 0 h V < 0 r = ∞ o rizo n V = 0 III U = 0 III (a) (b) r = ∞ t = –∞ UV = +1 t = +∞ V U h o r = 1 r = o n UV = +1 rizo oriz UV = –1 n h north pole south pole r = 0 r = 0 0 U V = = t = +∞ UV = –1 t = –∞ r = ∞ (c) Figure2 Kruskal-Szekeres–likecoordinatesfordeSitterspacetime.(a)ThedeSitterhorizonatr=1corresponds toUV =0,namelytheU andV axes,drawnat45◦fromthevertical.Spatialinfinityr=∞correspondsto UV =1.(b)Thelinesofconstanttareshown.InregionI,timepointsupward,thatis,theKillingvectorisfuture directed,butinregionIV,theKillingvectorispastdirected.(c)ThePenrosediagramfordeSitterspacetime.
- hyperbolasUV =−1locatedinregionIVandregionI,respectively.ThedeSitterhorizon atr=1correspondstoUV =0,namelytheU-andV-axes.Finally,spatialinfinityr=∞ correspondstoUV =1.
- Noticethatthemetricinthese(U,V)coordinatesdependsonlyontheproductUV and notonU andV separately.Referringbackto(35)and(39),weseethatthisisofcoursewhy the(t,r)coordinatesarecalledstaticcoordinatesinthefirstplace:themetricin(35)does notdependont.Speakinginafanciertongue,wewouldsaythatthespacetimeadmitsa Killingvector

AspectsofGravity II II V U V U r = ∞ oriz o n h r 1 r 1 = 1 r = oriz o n = 1 r = h IV I IV increasing t increasing t I r = 0 r = 0 1 r r = h o rizo = 1 U < 0 r = 1 r = U > 0 n V > 0 h V < 0 r = ∞ o rizo n V = 0 III U = 0 III (a) (b) r = ∞ t = –∞ UV = +1 t = +∞ V U h o r = 1 r = o n UV = +1 rizo oriz UV = –1 n h north pole south pole r = 0 r = 0 0 U V = = t = +∞ UV = –1 t = –∞ r = ∞ (c) Figure2 Kruskal-Szekeres–likecoordinatesfordeSitterspacetime.(a)ThedeSitterhorizonatr=1corresponds toUV =0,namelytheU andV axes,drawnat45◦fromthevertical.Spatialinfinityr=∞correspondsto UV =1.(b)Thelinesofconstanttareshown.InregionI,timepointsupward,thatis,theKillingvectorisfuture directed,butinregionIV,theKillingvectorispastdirected.(c)ThePenrosediagramfordeSitterspacetime.

hyperbolasUV =−1locatedinregionIVandregionI,respectively.ThedeSitterhorizon atr=1correspondstoUV =0,namelytheU-andV-axes.Finally,spatialinfinityr=∞ correspondstoUV =1.

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:
- deSitter,W.(1916).“OnEinstein’stheoryofgravitationanditsastronomicalconsequences.Secondpaper”.
- “Broken Symmetry and the Mass of Gauge Vector Mesons”.
- Jahrbuch der Radioaktivitaet und Elektronik 4 (cit.
- doi: 10.1142/s0218301313300191.

“Broken Symmetry and the Mass of Gauge Vector Mesons”.

Jahrbuch der Radioaktivitaet und Elektronik 4 (cit.

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:
- τρμν τλ ρμν Whatmakesusthinkthatthereareadditionalsymmetries?Ourfingers.Wecount.Way backwheninchapterI.6,wecountedthat20numberswererequiredtospecifycurvature in4-dimensionalspacetime.Herewecount4×4× 1(4×3)=96componentsinR 2 τρμν thusfar,whichhavetobereducedto20bysymmetries.
- (Recall from chapter I.6 that the comma on the quantity B is purelyfortypographicalconvenience:ithelpsusseparatementallytwosetsofindicesτμ andλσ thatappearfordifferentreasons.) Good!Plugthisinto(cid:25)λ ≡ 1gλτ(∂ g +∂ g −∂ g )tofind ρν 2 ρ τν ν τρ τ ρν (cid:25)λ =ηλτ(B +B −B )xκ+...
- ρμν Since(cid:10)vanishesinalocallyflatsystemandsinceitisatensorbyassumption,itvanishes inallframes.”Thisuniquenessisofcrucialimportancewhenwecometoconstructthe actionforgravity.
- Professor Flat ambles by again, just in time to save us a lot of work.

τρμν τλ ρμν Whatmakesusthinkthatthereareadditionalsymmetries?Ourfingers.Wecount.Way backwheninchapterI.6,wecountedthat20numberswererequiredtospecifycurvature in4-dimensionalspacetime.Herewecount4×4× 1(4×3)=96componentsinR 2 τρμν thusfar,whichhavetobereducedto20bysymmetries.

(Recall from chapter I.6 that the comma on the quantity B is purelyfortypographicalconvenience:ithelpsusseparatementallytwosetsofindicesτμ andλσ thatappearfordifferentreasons.) Good!Plugthisinto(cid:25)λ ≡ 1gλτ(∂ g +∂ g −∂ g )tofind ρν 2 ρ τν ν τρ τ ρν (cid:25)λ =ηλτ(B +B −B )xκ+...

Professor Flat ambles by again, just in time to save us a lot of work.

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 The Open Society and Its Enemies, he argued: Unlimited tolerance must lead to the disappearance of tolerance.
- This view cannot be right, Popper argued, because "nothing ever comes off exactly as intended."[71] According to philosopher David Coady, "Popper has often been cited by critics of conspiracy theories, and his views on the topic continue to constitute an orthodoxy in some circles."[72] However, philosopher Charles Pigden has pointed out that Popper's argument only applies to a very extreme kind of conspiracy theory, not to conspiracy theories generally.[73] Metaphysics Truth As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery."[74] Still, he describes in Objective Knowledge (1972) early concerns about the muchcriticised notion of truth as correspondence.
- If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them.
- We should claim that any movement preaching intolerance places itself outside the law, and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal.[67][68][69][70] The "conspiracy theory of society" Popper criticized what he termed the "conspiracy theory of society", the view that powerful people or groups, godlike in their efficacy, are responsible for purposely bringing about all the ills of society.

In The Open Society and Its Enemies, he argued: Unlimited tolerance must lead to the disappearance of tolerance.

This view cannot be right, Popper argued, because "nothing ever comes off exactly as intended."[71] According to philosopher David Coady, "Popper has often been cited by critics of conspiracy theories, and his views on the topic continue to constitute an orthodoxy in some circles."[72] However, philosopher Charles Pigden has pointed out that Popper's argument only applies to a very extreme kind of conspiracy theory, not to conspiracy theories generally.[73] Metaphysics Truth As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery."[74] Still, he describes in Objective Knowledge (1972) early concerns about the muchcriticised notion of truth as correspondence.

If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them.

We should claim that any movement preaching intolerance places itself outside the law, and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal.[67][68][69][70] The "conspiracy theory of society" Popper criticized what he termed the "conspiracy theory of society", the view that powerful people or groups, godlike in their efficacy, are responsible for purposely bringing about all the ills of society.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The author meticulously examines the evidence both supporting and refuting the claims of the experiment.
- One compelling piece of evidence discussed in the book is the ship's log of the USS Eldridge.
- Berlitz begins by sifting through military documents purportedly related to the USS Eldridge and its enigmatic journey.
- However, Berlitz underscores that the absence of evidence is not necessarily evidence of absence.

The author meticulously examines the evidence both supporting and refuting the claims of the experiment.

One compelling piece of evidence discussed in the book is the ship's log of the USS Eldridge.

Berlitz begins by sifting through military documents purportedly related to the USS Eldridge and its enigmatic journey.

However, Berlitz underscores that the absence of evidence is not necessarily evidence of absence.

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:
- As we move on through this chapter, we shall watch him become dominant.
- concentrating on getting to bed.
- 2.Hawking’s new definition of the horizon, by contrast, was absolute (the same in all reference frames), not relative, so he called it the absolute horizon.
- 3.He had made several important discoveries already, but he was not yet a dominant figure.

As we move on through this chapter, we shall watch him become dominant.

2.Hawking’s new definition of the horizon, by contrast, was absolute (the same in all reference frames), not relative, so he called it the absolute horizon.

3.He had made several important discoveries already, but he was not yet a dominant figure.

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:
- S2CID 84148912 (https://api.semanticscholar.org/CorpusID:84148912).
- ISSN 0003-9519 (https://sear ch.worldcat.org/issn/0003-9519).
- Foschi, Renato; Leone, Matteo (August 2009).
- MacTutor History of Mathematics archive.

ISSN 0003-9519 (https://sear ch.worldcat.org/issn/0003-9519).

Foschi, Renato; Leone, Matteo (August 2009).

MacTutor History of Mathematics archive.

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:
- Thus if Δ≥0, then there exist null geodesics suchthataphotoncanbeinstantaneouslyatrestinr andθ,whereasifΔ<0,thennosuchgeodesicsexist.
- The thicker contours are the outer and inner horizons, which are confocal spheroids with the ringsingularityattheirfocus.Theringsingularityisatρ=0,thesnake’seyes.
- (9.15) ± Between the horizons Δ is negative, and photons cannot be at rest.
- With Δ given by equation (9.3), equation (9.14) gives outer and inner horizons at √ r =M ± M2−Q2−a2 .

Thus if Δ≥0, then there exist null geodesics suchthataphotoncanbeinstantaneouslyatrestinr andθ,whereasifΔ<0,thennosuchgeodesicsexist.

The thicker contours are the outer and inner horizons, which are confocal spheroids with the ringsingularityattheirfocus.Theringsingularityisatρ=0,thesnake’seyes.

(9.15) ± Between the horizons Δ is negative, and photons cannot be at rest.

With Δ given by equation (9.3), equation (9.14) gives outer and inner horizons at √ r =M ± M2−Q2−a2 .

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:
- Examples of these formations can be seen
- The creation of a supermassive black hole appears to play a key role in actively regulating the growth of galaxies by limiting the total amount of additional matter added.[196] During this early epoch, galaxies undergo a major burst of star formation.[197] During the following two billion years, the accumulated matter settles into a galactic disc.[198] A galaxy will continue to absorb infalling material from high-velocity clouds and dwarf galaxies throughout its life.[199] This matter is mostly hydrogen and helium.
- Even seemingly confirmed spectroscopic evidence may turn out to have other origins.
- For example, a high redshift (z ~ 16) photometric observation by James Webb Space Telescope (JWST) was later corrected to be closer to z ~ 5.[189] Nevertheless, confirmed observations from the JWST and other observatories are accumulating, allowing systematic comparison of early galaxies to predictions of theory.[190] Evidence for individual Population III stars in early galaxies is even more challenging.

Examples of these formations can be seen

The creation of a supermassive black hole appears to play a key role in actively regulating the growth of galaxies by limiting the total amount of additional matter added.[196] During this early epoch, galaxies undergo a major burst of star formation.[197] During the following two billion years, the accumulated matter settles into a galactic disc.[198] A galaxy will continue to absorb infalling material from high-velocity clouds and dwarf galaxies throughout its life.[199] This matter is mostly hydrogen and helium.

Even seemingly confirmed spectroscopic evidence may turn out to have other origins.

For example, a high redshift (z ~ 16) photometric observation by James Webb Space Telescope (JWST) was later corrected to be closer to z ~ 5.[189] Nevertheless, confirmed observations from the JWST and other observatories are accumulating, allowing systematic comparison of early galaxies to predictions of theory.[190] Evidence for individual Population III stars in early galaxies is even more challenging.

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:
- "Strings in the Einstein's paradigm of matter".
- arXiv:gr-qc/0009072 (https://arxiv.org/abs/gr-qc/000907 2).
- Bibcode:1935PhRv...48...73E (https://ui.adsabs.harvard.edu/abs/1935PhRv...48...73E).
- doi:10.1088/0264-9381/19/19/302 (https://doi.org/10.1088%2F0264-9381%2F19%2F19%2F302).

"Strings in the Einstein's paradigm of matter".

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:
- shortlyafterflewupverticallyoutofsight.
- ● https://avalonlibrary.net/?dir=ebooks/Valdemar%20Valerian%20-%20Matrix%20I-IV Note:ThisconceptisrepeatedbytheremoteviewinggrouptheFarsightInstitute,whocallsita “DeathTrap.” FormerSRIcontractor(whoitselfwasacontractorfortheArmy)RobertMonroe statessomethingsimilar,thatinterdimensionalbeingsharvesthumanityfortheirenergyand forcethemtorepeattheirlivesonEarth.
- Buddhismteachesreincarnationisanendlesscycleof sufferingonlybrokenbyenlightenment,whileancientGreekGnosticismteacheshumansare divinesoulstrappedinthephysicalworldwhereescapecanonlybeachievedbynotworshiping thefalsegod(Demiurge),butrather,gainingsecretesotericknowledgeaboutwhohumansreally are,wheretheyarefrom,howparasiticalentitiesworkandhowhowtobefreeofasoultrapran byentitiestheyrefertoas“Archons.” ● https://www.worldhistory.org/Gnosticism/ ● https://www.reddit.com/r/EscapingPrisonPlanet/comments/te0fgs/robert monroes resea rch_do_entities_feed_off_of/ ● https://youtu.be/w6dxXAAAIp4 ● https://farsight.org/FarsightPress/Death Traps Farsight Project main page.html (PUBLICDOMAIN) -6March1991—JesseA.Marcelstateswhenhewas11andlivedinRoswell NM,inJuly1947,hisfatherMaj.JesseMarcelwasawakenedinthemiddleofthenightbyhisfather, whowasexcitedandsaw“debris”hisfatherbroughthomeinhiscarfromthedesert;athickmetallicfoil, abrittlebrownish-blackplasticlikemateriallikeBakelite;andfragmentsofI-beamswithhieroglyphicsin apurple-violethue.
- Thomassayshewasinterviewedbypeopleincivilianclothes whyhewasoutsideandwhathesaw;Thomassaidhedidn’ttellthemhesawthetrianglebecausehewas concernedhewouldbedisciplined.

Buddhismteachesreincarnationisanendlesscycleof sufferingonlybrokenbyenlightenment,whileancientGreekGnosticismteacheshumansare divinesoulstrappedinthephysicalworldwhereescapecanonlybeachievedbynotworshiping thefalsegod(Demiurge),butrather,gainingsecretesotericknowledgeaboutwhohumansreally are,wheretheyarefrom,howparasiticalentitiesworkandhowhowtobefreeofasoultrapran byentitiestheyrefertoas“Archons.” ● https://www.worldhistory.org/Gnosticism/ ● https://www.reddit.com/r/EscapingPrisonPlanet/comments/te0fgs/robert monroes resea rch_do_entities_feed_off_of/ ● https://youtu.be/w6dxXAAAIp4 ● https://farsight.org/FarsightPress/Death Traps Farsight Project main page.html (PUBLICDOMAIN) -6March1991—JesseA.Marcelstateswhenhewas11andlivedinRoswell NM,inJuly1947,hisfatherMaj.JesseMarcelwasawakenedinthemiddleofthenightbyhisfather, whowasexcitedandsaw“debris”hisfatherbroughthomeinhiscarfromthedesert;athickmetallicfoil, abrittlebrownish-blackplasticlikemateriallikeBakelite;andfragmentsofI-beamswithhieroglyphicsin apurple-violethue.

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:
- His approach mixed some limited observation with logical deductive arguments, but did not rely on
- evidence, these early observations laid the foundation for later astronomy, as the stars were found to traverse great circles across the sky,[5] which could not explain the positions of the planets.
- While the explanations for the observed positions of the stars were often Ancient Egyptian astronomy is evident in monuments like the ceiling of unscientific and lacking in Senemut's tomb from the Eighteenth Dynasty of Egypt.
- Ancient astronomy Astronomy is one of the oldest natural sciences.

His approach mixed some limited observation with logical deductive arguments, but did not rely on

evidence, these early observations laid the foundation for later astronomy, as the stars were found to traverse great circles across the sky,[5] which could not explain the positions of the planets.

While the explanations for the observed positions of the stars were often Ancient Egyptian astronomy is evident in monuments like the ceiling of unscientific and lacking in Senemut's tomb from the Eighteenth Dynasty of Egypt.

Ancient astronomy Astronomy is one of the oldest natural sciences.

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:
- ∞ Type II : [0,x] for some positive x (usually normalized to be 1).
- The type of a factor can be read off from the possible values of this trace over the projections of the factor, as follows: Type I : 0, x, 2x, ....,nx for some positive x (usually normalized to be 1/n or 1).
- For factors that are separable or finite, two projections are equivalent if and only if they have the same trace.
- Such a trace is unique up to rescaling.

∞ Type II : [0,x] for some positive x (usually normalized to be 1).

The type of a factor can be read off from the possible values of this trace over the projections of the factor, as follows: Type I : 0, x, 2x, ....,nx for some positive x (usually normalized to be 1/n or 1).

For factors that are separable or finite, two projections are equivalent if and only if they have the same trace.

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:
- Although the electron and proton are equal in size of electric charge, they do not have the same mass.* The proton is 1836.11 times as massive as I When we say that an object possesses mass, we mean that it takes force to make it move if It is standing still, or to change its speed or direction of movement if it is already moving.
- The more mass it has, the more force it takes.
- Still, mass and weight are not identical, and while the meaning is clear if we say that the proton is much heavier than the electron, it is safer to say "more massive."
- 8 THE COLLAPSING UNIVERSE ATOMS Since electrons are not subject to the nuclear force, they cannot form part of the nucleus.

Although the electron and proton are equal in size of electric charge, they do not have the same mass.* The proton is 1836.11 times as massive as I When we say that an object possesses mass, we mean that it takes force to make it move if It is standing still, or to change its speed or direction of movement if it is already moving.

The more mass it has, the more force it takes.

Still, mass and weight are not identical, and while the meaning is clear if we say that the proton is much heavier than the electron, it is safer to say "more massive."

8 THE COLLAPSING UNIVERSE ATOMS Since electrons are not subject to the nuclear force, they cannot form part of the nucleus.

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:
- Bibcode:2020PrPNP.11203770T (https://ui.adsabs.harvard.edu/abs/2020PrPNP.11203770T).
- doi:10.1016/j.ppnp.2020.103770 (https://doi.org/10.1016%2Fj.ppnp.2020.103770).
- S2CID 211252559 (https://api.semanticscholar.org/CorpusID:211252559).
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Hypernucleus&oldid=1323112687#Antihypernuclei"

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:
- Any pair of transverse spin states can be chosen as a basis.
- Cosmological perturbations including polarization Well before recombination, frequent collisions drive photons into thermodynamic equilibrium.
- PolarizationproducesdistinctE-mode(electricparity)andB-mode(magneticparity)fluctuations,§35.6.2.
- The general spin eigenstate of a photon is described by a complex polarization vector a, a complex linear combination of right- and

Any pair of transverse spin states can be chosen as a basis.

Cosmological perturbations including polarization Well before recombination, frequent collisions drive photons into thermodynamic equilibrium.

The general spin eigenstate of a photon is described by a complex polarization vector a, a complex linear combination of right- and

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:
- Another important concept is maximally entangled states.
- This strategy can be used to define network topology.[1][11][12] Network structure While models for quantum complex networks are not of identical structure, usually a node represents a set of qubits in the same station (where operations like Bell measurements and entanglement swapping can be applied) and an edge between node and means that a qubit in node is entangled to a qubit in node , although those two qubits are in different places and so cannot physically interact.[1][11] Quantum networks where the links are interaction terms instead of entanglement are also of interest.[13] Notation Each node in the network contains a set of qubits in different states.
- The four states (the Bell states) that maximize the entropy of entanglement between two qubits can be written as follows:[3][10]
- Performing a Bell measurement for qubits A and B, entangles qubits A and B.

Another important concept is maximally entangled states.

This strategy can be used to define network topology.[1][11][12] Network structure While models for quantum complex networks are not of identical structure, usually a node represents a set of qubits in the same station (where operations like Bell measurements and entanglement swapping can be applied) and an edge between node and means that a qubit in node is entangled to a qubit in node , although those two qubits are in different places and so cannot physically interact.[1][11] Quantum networks where the links are interaction terms instead of entanglement are also of interest.[13] Notation Each node in the network contains a set of qubits in different states.

The four states (the Bell states) that maximize the entropy of entanglement between two qubits can be written as follows:[3][10]

Performing a Bell measurement for qubits A and B, entangles qubits A and B.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- The classical energy-momentum is merely the most probable of a range of possibilities.
- Aplanewaveofamasseigenstateiwithenergy-momentum{E ,p⃗ }thatpropatesoverspacetimedistance i i {t,⃗x}changesbyaquantummechanicalphasefactoreiφi withphaseφ i =−E i t+p⃗ i ·⃗x.Thephasedifference φ ≡φ −φ between two mass eigenstates 1 and 2 is 21 2 1 φ =−E t+p⃗ ·⃗x , (42.89) 21 21 21 with E ≡ E −E and p⃗ ≡ p⃗ −p⃗ .
- Akhmedov and Smirnov (2009) give a careful exposition of the 21 2 1 21 2 1

The classical energy-momentum is merely the most probable of a range of possibilities.

Aplanewaveofamasseigenstateiwithenergy-momentum{E ,p⃗ }thatpropatesoverspacetimedistance i i {t,⃗x}changesbyaquantummechanicalphasefactoreiφi withphaseφ i =−E i t+p⃗ i ·⃗x.Thephasedifference φ ≡φ −φ between two mass eigenstates 1 and 2 is 21 2 1 φ =−E t+p⃗ ·⃗x , (42.89) 21 21 21 with E ≡ E −E and p⃗ ≡ p⃗ −p⃗ .

Akhmedov and Smirnov (2009) give a careful exposition of the 21 2 1 21 2 1

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:
- This is known as the Schwarzschild–deSitterspacetime.WewillcomebacktothisinchapterIX.10.
- 2 CalculatetheRiemanntensorintermsofAandB.
- 3 ShowthattheSchwarzschildmetriccanbewrittenintheisotropicform ds2= (cid:15) 1−G 2 M ρ (cid:16) 2 dt2− (cid:3) 1+ GM (cid:4) 4 (cid:12) dρ2+ρ2(dθ2+sin2θdφ2) (cid:14) (25) 1+GM 2ρ 2ρ Whereisthehorizon?
- 2 Einstein 3 Einstein 6 Showthat (cid:3) (cid:4) (cid:15) (cid:16) 2M dr2 ds2= 1− −r2 dt2− +r2d(cid:24)2 r 1−2M −r2 2 r satisfies the Einstein field equation R μν =−3(cid:27)g μν with a cosmological constant.

This is known as the Schwarzschild–deSitterspacetime.WewillcomebacktothisinchapterIX.10.

3 ShowthattheSchwarzschildmetriccanbewrittenintheisotropicform ds2= (cid:15) 1−G 2 M ρ (cid:16) 2 dt2− (cid:3) 1+ GM (cid:4) 4 (cid:12) dρ2+ρ2(dθ2+sin2θdφ2) (cid:14) (25) 1+GM 2ρ 2ρ Whereisthehorizon?

2 Einstein 3 Einstein 6 Showthat (cid:3) (cid:4) (cid:15) (cid:16) 2M dr2 ds2= 1− −r2 dt2− +r2d(cid:24)2 r 1−2M −r2 2 r satisfies the Einstein field equation R μν =−3(cid:27)g μν with a cosmological constant.

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:
- • Orbital and magnetic dipole energies precisely cancel.
- (Here we view F as non-dynamical).
- Motion of charged fermions • Magnetic field on the sphere.
- • Explained by an anomaly argument Ambjorn, Olesen Massless fermions à U(1) chiral symmetry B 4d anomaly à 2d anomaly à there should be massless fermions in 2d.

• Orbital and magnetic dipole energies precisely cancel.

Motion of charged fermions • Magnetic field on the sphere.

• Explained by an anomaly argument Ambjorn, Olesen Massless fermions à U(1) chiral symmetry B 4d anomaly à 2d anomaly à there should be massless fermions in 2d.

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:
- From the position of that center of gravity relative to the two stars it turns out that Sirius A must have 2.5 times the mass of Sirius B.
- (If this weren't so, Bessel wouldn't have noticed a distinct waviness in Sirius's motion across the sky.) From the orbits of Sirius A and Sirius B the location of the center of gravity of the two stars can be determined.
- The same is true when we speak of any other planet-satellite system among the Sun's family of worlds.
- That Sirius A should be 2.4 times the mass of our Sun is not surprising at all.

From the position of that center of gravity relative to the two stars it turns out that Sirius A must have 2.5 times the mass of Sirius B.

(If this weren't so, Bessel wouldn't have noticed a distinct waviness in Sirius's motion across the sky.) From the orbits of Sirius A and Sirius B the location of the center of gravity of the two stars can be determined.

The same is true when we speak of any other planet-satellite system among the Sun's family of worlds.

That Sirius A should be 2.4 times the mass of our Sun is not surprising at all.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The Boltzmann equation (33.42) then reduces to dΘ ∂Θ = +va∇ Θ−G=C[Θ] .
- FouriertransformingtheBoltzmannequation(33.43)overspatialpositionxyieldstheBoltzmannequation for the Fourier components Θ(η,k,p) of the temperature fluctuation, dΘ ∂Θ = −ivkμΘ−G=C[Θ] , (33.44) dη ∂η where μ is the cosine of the angle between the wavevector k and the photon momentum p, μ≡k^·p^.
- 886 Cosmological perturbations: Boltzmann treatment Two of the terms on the left hand side of the perturbed Boltzmann equation (33.21) rearrange to 1 1 0 [( ) 0 ] ∂f dlnp ∂f ∂f dlnT ∂ a ̇ ∂ ∂f + = Θ ̇ + − Θ ∂η dη ∂lnp ∂lnT dη ∂lnT a∂lnp ∂lnT 0 [ 0 ] ∂f dln(aT)∂ln(∂f/∂lnT) = Θ ̇ + Θ .
- (33.43) dη ∂η a As long as the particles are relativistic, the particle velocity is one, v =1; but equation (33.43) allows for a general non-unit velocity v to accommodate neutrinos, which have small masses.

The Boltzmann equation (33.42) then reduces to dΘ ∂Θ = +va∇ Θ−G=C[Θ] .

FouriertransformingtheBoltzmannequation(33.43)overspatialpositionxyieldstheBoltzmannequation for the Fourier components Θ(η,k,p) of the temperature fluctuation, dΘ ∂Θ = −ivkμΘ−G=C[Θ] , (33.44) dη ∂η where μ is the cosine of the angle between the wavevector k and the photon momentum p, μ≡k^·p^.

886 Cosmological perturbations: Boltzmann treatment Two of the terms on the left hand side of the perturbed Boltzmann equation (33.21) rearrange to 1 1 0 [( ) 0 ] ∂f dlnp ∂f ∂f dlnT ∂ a ̇ ∂ ∂f + = Θ ̇ + − Θ ∂η dη ∂lnp ∂lnT dη ∂lnT a∂lnp ∂lnT 0 [ 0 ] ∂f dln(aT)∂ln(∂f/∂lnT) = Θ ̇ + Θ .

(33.43) dη ∂η a As long as the particles are relativistic, the particle velocity is one, v =1; but equation (33.43) allows for a general non-unit velocity v to accommodate neutrinos, which have small masses.

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:
- A byproduct of the recent quantum computing and information research is that a modern theory of entanglement has emerged.
- of human teleportation discussed in Section 3.1.
- And molecules with more than seven spins that can be used as qubits are not feasible at present.
- The prototype’s operation requires that all of the qubits must be in the same molecule.

A byproduct of the recent quantum computing and information research is that a modern theory of entanglement has emerged.

of human teleportation discussed in Section 3.1.

And molecules with more than seven spins that can be used as qubits are not feasible at present.

The prototype’s operation requires that all of the qubits must be in the same molecule.

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:
- If you used the traditional Feynman diagram method, the resultcontainssomethingontheorderof7,000terms.†Whentheresultisexpressedin terms of helicity spinors, the scattering amplitude, for a particular choice of helicities, simplifiesdramaticallyto (cid:15) (cid:16) M(1 − ,2 − ,3 + ,4 + ,5 + )= (cid:21)12(cid:22)4 δ(4) (cid:10)5 λ λ ̃ (9) (cid:21)12(cid:22)(cid:21)23(cid:22)(cid:21)34(cid:22)(cid:21)45(cid:22)(cid:21)51(cid:22) a a a=1 ∗Thissoundsmoremysteriousthanitactuallyis.Thereasonforthatisbecause,forfearofconfusingsome readers,Ihavenotdigressedintoadiscussionofhowtowritepolarizationvectorsintermsofhelicityspinors.
- Suppose you want to 1 2 3 4 5 calculatethistolowestorderinperturbation,inthesimplestpossiblecase(forexample, without any quarks around).
- We refer to this as 5-gluon scattering.
- ̃ Let’s focus on a specific particle and omit the subscript a, writing simply M(λ,λ,h).

If you used the traditional Feynman diagram method, the resultcontainssomethingontheorderof7,000terms.†Whentheresultisexpressedin terms of helicity spinors, the scattering amplitude, for a particular choice of helicities, simplifiesdramaticallyto (cid:15) (cid:16) M(1 − ,2 − ,3 + ,4 + ,5 + )= (cid:21)12(cid:22)4 δ(4) (cid:10)5 λ λ ̃ (9) (cid:21)12(cid:22)(cid:21)23(cid:22)(cid:21)34(cid:22)(cid:21)45(cid:22)(cid:21)51(cid:22) a a a=1 ∗Thissoundsmoremysteriousthanitactuallyis.Thereasonforthatisbecause,forfearofconfusingsome readers,Ihavenotdigressedintoadiscussionofhowtowritepolarizationvectorsintermsofhelicityspinors.

Suppose you want to 1 2 3 4 5 calculatethistolowestorderinperturbation,inthesimplestpossiblecase(forexample, without any quarks around).

̃ Let’s focus on a specific particle and omit the subscript a, writing simply M(λ,λ,h).

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:
- Cybernetics and Human Knowing.
- doi:10.1109/OJEMB.2025.3590598 (https://doi.org/10.1109%2FOJEMB.2025.35905 98).
- Cognitive Science: Integrative Synchronization Mechanisms in Cognitive Neuroarchitectures of the Modern Connectionism.
- Scagliarini, Tomas; Sparacino, Laura; Faes, Luca; Marinazzo, Daniele; Stramaglia, Sebastiano (2024-01-09).

Cognitive Science: Integrative Synchronization Mechanisms in Cognitive Neuroarchitectures of the Modern Connectionism.

Scagliarini, Tomas; Sparacino, Laura; Faes, Luca; Marinazzo, Daniele; Stramaglia, Sebastiano (2024-01-09).

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:
- observations are collected or inspected.
- If these criteria are determined later, when the data to be tested are already known, the test is invalid.[23] The above procedure is actually dependent on the number of the participants (units or sample size) that are included in the study.
- For instance, to avoid having the sample size be too small to reject a null hypothesis, it is recommended that one specify a sufficient sample size from the beginning.
- It is advisable to define a small, medium and large effect size for each of a number of important statistical tests which are used to test the hypotheses.[24] Honours Mount Hypothesis in Antarctica is named in appreciation of the role of hypotheses in scientific research.

observations are collected or inspected.

If these criteria are determined later, when the data to be tested are already known, the test is invalid.[23] The above procedure is actually dependent on the number of the participants (units or sample size) that are included in the study.

For instance, to avoid having the sample size be too small to reject a null hypothesis, it is recommended that one specify a sufficient sample size from the beginning.

It is advisable to define a small, medium and large effect size for each of a number of important statistical tests which are used to test the hypotheses.[24] Honours Mount Hypothesis in Antarctica is named in appreciation of the role of hypotheses in scientific research.

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:
- Card Shuffles and Tricks of Lightning Calculators to Roller Coaster Rides into the Fourth Dimension (1st ed.).
- Physikalische Zeitschrift (in German).
- Bulletin of the American Mathematical Society.
- Bath Spa University: Abstract.

Card Shuffles and Tricks of Lightning Calculators to Roller Coaster Rides into the Fourth Dimension (1st ed.).

Bulletin of the American Mathematical Society.

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:
- ProloguetoBookTwo | 269 gravitationalmass,andsothemotionofanobjectinagravitationalfielddoesnotdepend onitsmass:inavacuum,afeatherandacannonballfallatthesamerate.9 PhysicsstudentsgenerallyidentifyEinsteinasthepersonwhobroughtfametovarious gedankenexperiments.ButinfactthoughtexperimentsgowaybacktoGalileo, atleast.
- Salviati:Butifthisistrue,andifalargestonemoveswithaspeedof,say,eightwhileasmaller moveswithaspeedoffour,thenwhentheyareunited,thesystemwillmovewithaspeedless thaneight;butthetwostoneswhentiedtogethermakeastonelargerthanthatwhichbefore movedwithaspeedofeight.Hencetheheavierbodymoveswithlessspeedthanthelighter; aneffectwhichiscontrarytoyoursupposition.Thusyouseehow,fromyourassumptionthat theheavierbodymovesmorerapidlythanthelighterone,Iinferthattheheavierbodymoves moreslowly.10 Universalityofgravityandaballofwhiskey Let’strytoimaginethepatentclerk’strainofthought.Afallingpersondoesnotknowheis falling,becauseeverythingaroundhimisfallingatthesamerate,inotherwords,because oftheuniversalityofgravity.CanIturnthisaround?Gravitymustbeuniversalbecausea fallingpersondoesnotknowheisfalling.Inaway,fallingcancelsoutgravity.Hmmm, supposeIsomehowreversefallingbythrustingupward.CanIthenproducegravity?Aha!
- Butwhatistohimamysteriousuniversalityislaughablyobvioustotheobserverfloating aboutoutside:thefloorismovinguptomeetthefloatingappleandstoneandsoobviously arrivesatthetwoobjectsatthesametime.
- Byacceleratingtherocket—ineffect,reversingfreefall—wecanproducegravity.Clearly, ifourfriendhaddroppedastoneaswellastheapplefromthesameheightfromthefloor, thestoneandtheapplewill“fall”andhittheflooratexactlythesameinstant.

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:
- However, the accounts become even more extraordinary with the details of the second test.
- The narrative suggests that SSccaann ttoo DDoowwnnllooaadd
- At the heart of these accounts is the USS Eldridge, a destroyer escort that supposedly became invisible—or even teleported—during a secretive military experiment conducted by the U.S.
- Detailed descriptions of the events center on two main occurrences.

However, the accounts become even more extraordinary with the details of the second test.

The narrative suggests that SSccaann ttoo DDoowwnnllooaadd

At the heart of these accounts is the USS Eldridge, a destroyer escort that supposedly became invisible—or even teleported—during a secretive military experiment conducted by the U.S.

Detailed descriptions of the events center on two main occurrences.

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:
- A typical self-luminous watch that uses radium paint contains around 1 microgram of radium.[45] In the mid-1920s, a lawsuit was filed against the United States Radium Corporation by five dying "Radium Girls" – dial painters who had painted radium-based luminous
- The Curies announced their discovery to the French Academy of Sciences on 26 December 1898.[34] The naming of radium dates to about 1899, from the French word radium, formed in Modern Latin from radius (ray): this was in recognition of radium's emission of energy in the form of rays.[35] The gaseous emissions of radium, radon, were recognized and studied extensively by Friedrich Ernst Dorn in the early 1900s, though at the time they were characterized as "radium Marie and Pierre Curie experimenting emanations".[36] with radium, a drawing by André Castaigne In September 1910, Marie Curie and André-Louis Debierne announced that they had isolated radium as a pure metal through the electrolysis of pure radium chloride (RaCl ) solution using a mercury cathode, producing radium–mercury amalgam.[37] This amalgam was then heated in an atmosphere of hydrogen gas to remove the mercury, leaving pure radium metal.[38] Later that same year, E.
- Ebler isolated radium metal by thermal decomposition of its azide, Ra(N ) .[39][40] Radium metal was first industrially produced Glass tube of radium chloride kept by the 3 2 US Bureau of Standards that served as at the beginning of the 20th century by Biraco, a subsidiary the primary standard of radioactivity for company of Union Minière du Haut Katanga (UMHK) in its the United States in 1927.
- This discovery made it possible for the Curies to isolate the radioactive compounds and discover a new element in them.

A typical self-luminous watch that uses radium paint contains around 1 microgram of radium.[45] In the mid-1920s, a lawsuit was filed against the United States Radium Corporation by five dying "Radium Girls" – dial painters who had painted radium-based luminous

The Curies announced their discovery to the French Academy of Sciences on 26 December 1898.[34] The naming of radium dates to about 1899, from the French word radium, formed in Modern Latin from radius (ray): this was in recognition of radium's emission of energy in the form of rays.[35] The gaseous emissions of radium, radon, were recognized and studied extensively by Friedrich Ernst Dorn in the early 1900s, though at the time they were characterized as "radium Marie and Pierre Curie experimenting emanations".[36] with radium, a drawing by André Castaigne In September 1910, Marie Curie and André-Louis Debierne announced that they had isolated radium as a pure metal through the electrolysis of pure radium chloride (RaCl ) solution using a mercury cathode, producing radium–mercury amalgam.[37] This amalgam was then heated in an atmosphere of hydrogen gas to remove the mercury, leaving pure radium metal.[38] Later that same year, E.

Ebler isolated radium metal by thermal decomposition of its azide, Ra(N ) .[39][40] Radium metal was first industrially produced Glass tube of radium chloride kept by the 3 2 US Bureau of Standards that served as at the beginning of the 20th century by Biraco, a subsidiary the primary standard of radioactivity for company of Union Minière du Haut Katanga (UMHK) in its the United States in 1927.

This discovery made it possible for the Curies to isolate the radioactive compounds and discover a new element in them.

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:
- Where two patches abut, the contributions from the common edge cancel, because consistent circulation about the boundaries causes the integral along the common edge to be in opposite directions, as illustrated in Figure 15.1.
- 400 Geometric Differentiation and Integration The last line of equations (15.93) expresses the fourth in more compact notation, with ∂patch denoting the boundary, the 4 edges, of the patch.
- The 1-form dφ constructed from φ is welldefined, being single-valued and continuous everywhere on the circle, but φ itself is not.
- Equations (15.93) prove Stokes’ theorem for a patch.

Where two patches abut, the contributions from the common edge cancel, because consistent circulation about the boundaries causes the integral along the common edge to be in opposite directions, as illustrated in Figure 15.1.

400 Geometric Differentiation and Integration The last line of equations (15.93) expresses the fourth in more compact notation, with ∂patch denoting the boundary, the 4 edges, of the patch.

The 1-form dφ constructed from φ is welldefined, being single-valued and continuous everywhere on the circle, but φ itself is not.

Equations (15.93) prove Stokes’ theorem for a patch.

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:
- (1994), Introduction to Commutative Algebra, Addison-Wesley and Avalon Publishing, ISBN 978-0201407518 Byers, Nina (December 1996), E.
- (1970), "Invariant theory, old and new" (https://doi.org/10.1 016%2F0001-8708%2870%2990015-0), Advances in Mathematics, 4 (1): 1–80, doi:10.1016/0001-8708(70)90015-0 (https://doi.org/10.1016%2F0001-8708%2870%2990015-0), ISSN 0001-8708 (https://search.worldcat.org/issn/0001-8708), MR 0255525 (https://mathscinet.a ms.org/mathscinet-getitem?mr=0255525) Dörnte, Wilhelm (1929), "Untersuchungen über einen verallgemeinerten Gruppenbegriff" (http://gd z.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002370530) [Investigations on a generalised conception of groups], Mathematische Zeitschrift (in German), 29 (1): 1–19, doi:10.1007/BF01180515 (https://doi.org/10.1007%2FBF01180515) Falckenberg, Hans (1912), Verzweigungen von Lösungen nichtlinearer Differentialgleichungen (htt ps://gdz.sub.uni-goettingen.de/id/PPN314875379) [Ramifications of Solutions of Nonlinear Differential Equations] (PhD thesis) (in German) Fitting, Hans (1933), "Die Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nicht kommutativen Gruppen" (https://gdz.sub.uni-goettingen.de/id/PPN235181684_0107) [The Theory of Automorphism-Rings of Abelian Groups and Their Analogs in Noncommutative Groups], Mathematische Annalen (in German), 107 (1): 514–542, doi:10.1007/BF01448909 (http s://doi.org/10.1007%2FBF01448909)
- uni-goettingen.de/id/PPN235181684_0106) [On the Arithmetic Theory of Algebraic Functions], Mathematische Annalen (in German), 106 (1): 77–102, doi:10.1007/BF01455878 (https://doi.org/1 0.1007%2FBF01455878) Dick, Auguste (1981), Emmy Noether: 1882–1935, translated by Blocher, H.I., Boston: Birkhäuser, doi:10.1007/978-1-4684-0535-4 (https://doi.org/10.1007%2F978-1-4684-0535-4), ISBN 978-37643-3019-4 Ding, Shisun; Kang, Ming-Chang; Tan, Eng-Tjioe (1999), "Chiungtze C.
- 99–111, ISBN 978-0-8247-1550-2, OCLC 7837628 (https://search.worldcat.org/oclc/7837628) Atiyah, Michael; MacDonald, Ian G.

(1994), Introduction to Commutative Algebra, Addison-Wesley and Avalon Publishing, ISBN 978-0201407518 Byers, Nina (December 1996), E.

(1970), "Invariant theory, old and new" (https://doi.org/10.1 016%2F0001-8708%2870%2990015-0), Advances in Mathematics, 4 (1): 1–80, doi:10.1016/0001-8708(70)90015-0 (https://doi.org/10.1016%2F0001-8708%2870%2990015-0), ISSN 0001-8708 (https://search.worldcat.org/issn/0001-8708), MR 0255525 (https://mathscinet.a ms.org/mathscinet-getitem?mr=0255525) Dörnte, Wilhelm (1929), "Untersuchungen über einen verallgemeinerten Gruppenbegriff" (http://gd z.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002370530) [Investigations on a generalised conception of groups], Mathematische Zeitschrift (in German), 29 (1): 1–19, doi:10.1007/BF01180515 (https://doi.org/10.1007%2FBF01180515) Falckenberg, Hans (1912), Verzweigungen von Lösungen nichtlinearer Differentialgleichungen (htt ps://gdz.sub.uni-goettingen.de/id/PPN314875379) [Ramifications of Solutions of Nonlinear Differential Equations] (PhD thesis) (in German) Fitting, Hans (1933), "Die Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nicht kommutativen Gruppen" (https://gdz.sub.uni-goettingen.de/id/PPN235181684_0107) [The Theory of Automorphism-Rings of Abelian Groups and Their Analogs in Noncommutative Groups], Mathematische Annalen (in German), 107 (1): 514–542, doi:10.1007/BF01448909 (http s://doi.org/10.1007%2FBF01448909)

uni-goettingen.de/id/PPN235181684_0106) [On the Arithmetic Theory of Algebraic Functions], Mathematische Annalen (in German), 106 (1): 77–102, doi:10.1007/BF01455878 (https://doi.org/1 0.1007%2FBF01455878) Dick, Auguste (1981), Emmy Noether: 1882–1935, translated by Blocher, H.I., Boston: Birkhäuser, doi:10.1007/978-1-4684-0535-4 (https://doi.org/10.1007%2F978-1-4684-0535-4), ISBN 978-37643-3019-4 Ding, Shisun; Kang, Ming-Chang; Tan, Eng-Tjioe (1999), "Chiungtze C.

99–111, ISBN 978-0-8247-1550-2, OCLC 7837628 (https://search.worldcat.org/oclc/7837628) Atiyah, Michael; MacDonald, Ian G.

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 a condition in which participants listened to audiotaped confessions, police were more likely to believe that the false confessions were actually truthful.
- Gisli Gudjonsson (1992) conducted a comprehensive evaluation of Lucas, and concluded that he said and did things for immediate gain and attention, eager to please and impress people.
- But an even more serious concern about false confessions is that judges and jurors are likely to view them as persuasive evidence of guilt (Conti, 1999; Kassin, 1998; Wrightsman, Nietzel, & Fortune, 1994).
- People may confess voluntarily to crimes they didn’t commit for a myriad of other reasons, including a need for self-punishment to “pay for” real or imagined past transgressions; a desire to protect the real perpetrator, such as a spouse or child; or because they find it difficult to distinguish fantasy from reality (Gudjonsson, 2003; Kassin & Gudjonsson, 2004).

In a condition in which participants listened to audiotaped confessions, police were more likely to believe that the false confessions were actually truthful.

Gisli Gudjonsson (1992) conducted a comprehensive evaluation of Lucas, and concluded that he said and did things for immediate gain and attention, eager to please and impress people.

But an even more serious concern about false confessions is that judges and jurors are likely to view them as persuasive evidence of guilt (Conti, 1999; Kassin, 1998; Wrightsman, Nietzel, & Fortune, 1994).

People may confess voluntarily to crimes they didn’t commit for a myriad of other reasons, including a need for self-punishment to “pay for” real or imagined past transgressions; a desire to protect the real perpetrator, such as a spouse or child; or because they find it difficult to distinguish fantasy from reality (Gudjonsson, 2003; Kassin & Gudjonsson, 2004).

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:
- Recap to Part IV Livinginagalaxyfarfaraway,youadmirethebeautyoftherelativisticfreeparticleaction andcontemplatehowtodeprivetheparticleofitsfreedom.
- Asfaryoucansee,thereareonlytwooptions:putthepotentialeitheroutside,orinside, thesquareroot.Two,and(apparently)onlytwo,options.
- Withthefirstoption,youdiscoverhowchargedparticlesheartheelectromagneticfield, andevenbetter,youalsodiscoverthegaugeprinciple.Understandingthegaugeprinciple, youcanunderstandhowtheelectromagneticfieldrespondstothemovementofcharged particles.
- Intoxicated by your success, you go on to discover “half of gravity” by sneaking the potentialintothesquareroot.Youthencometotheastonishinginsightthatgravityslows downtheflowoftime.Yousureareasmartguy,nodoubtaboutit.

Recap to Part IV Livinginagalaxyfarfaraway,youadmirethebeautyoftherelativisticfreeparticleaction andcontemplatehowtodeprivetheparticleofitsfreedom.

Intoxicated by your success, you go on to discover “half of gravity” by sneaking the potentialintothesquareroot.Youthencometotheastonishinginsightthatgravityslows downtheflowoftime.Yousureareasmartguy,nodoubtaboutit.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The relentless barrage of misinformation about aging persists through adulthood.
- John Hess (1991) chronicled how the media blame the elderly unfairly for many social and political ills, including high taxes, bankrupting the national budget due to the high costs of medical care and social security, and cutbacks on programs for children and the disabled.
- Sharply contradicting these perceptions, research demolishes the myth that old age (beginning at age 60–65)
- Moreover, people rate memory problems in the elderly as signs of mental incompetence, but consider memory problems in younger individuals as due to inattention or a lack of effort (Cuddy & Fiske, 2002).

The relentless barrage of misinformation about aging persists through adulthood.

John Hess (1991) chronicled how the media blame the elderly unfairly for many social and political ills, including high taxes, bankrupting the national budget due to the high costs of medical care and social security, and cutbacks on programs for children and the disabled.

Sharply contradicting these perceptions, research demolishes the myth that old age (beginning at age 60–65)

Moreover, people rate memory problems in the elderly as signs of mental incompetence, but consider memory problems in younger individuals as due to inattention or a lack of effort (Cuddy & Fiske, 2002).

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:
- Article subsection Cosmic time[2]: 72 Redshift Temperature[2]: 72 Description Cosmic inflation expands space by a factor of the order of Inflation unknown not applicable 1026 over a time of the order of 10−36 to 10−32 seconds.[10] Converts the energy in the inflation field into a thermal bath of Standard Model Reheating unknown unknown particles, initiating the Hot Big Bang.
- The quark–gluon plasma of matter Quantum 1015 K – 1012 K particles coalesce into chromodynamics phase 20×10−6 s 1012 (150 GeV/k – 150 MeV/k ) hadrons: mostly transition B B protons, neutrons, and pions.[8]: 6 Neutrinos cease interacting with baryonic matter, and form cosmic neutrino 1010 K background.[8]: 6 The Neutrino decoupling 1 s 6×109 sphere of space that (1 MeV/k ) B will become the observable universe is approximately 10 light-years in radius at this time.
- Many mechanisms have been proposed.[11] Matter and antimatter are created with one extra particle of matter for every 1010 pairs.
- Many mechanisms have been proposed but no observations select one.[8]: 7 The strong interaction becomes distinct from the electroweak interaction.

Chronology of the universe - Wikipedia.pdf

Article subsection Cosmic time[2]: 72 Redshift Temperature[2]: 72 Description Cosmic inflation expands space by a factor of the order of Inflation unknown not applicable 1026 over a time of the order of 10−36 to 10−32 seconds.[10] Converts the energy in the inflation field into a thermal bath of Standard Model Reheating unknown unknown particles, initiating the Hot Big Bang.

The quark–gluon plasma of matter Quantum 1015 K – 1012 K particles coalesce into chromodynamics phase 20×10−6 s 1012 (150 GeV/k – 150 MeV/k ) hadrons: mostly transition B B protons, neutrons, and pions.[8]: 6 Neutrinos cease interacting with baryonic matter, and form cosmic neutrino 1010 K background.[8]: 6 The Neutrino decoupling 1 s 6×109 sphere of space that (1 MeV/k ) B will become the observable universe is approximately 10 light-years in radius at this time.

Many mechanisms have been proposed.[11] Matter and antimatter are created with one extra particle of matter for every 1010 pairs.

Many mechanisms have been proposed but no observations select one.[8]: 7 The strong interaction becomes distinct from the electroweak interaction.

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:
- Thus U(N) and SU(N) are subgroups of Spin(2N) as claimed.
- The Lie algebra of commutators of the generators (38.180) coincides with the Lie algebra of commutators in which 1γγ ∧γγ is represented by the N ×N matrix 1 with 1 in the 2 +i −j ij ij’th entry and 0 elsewhere, 1γγ ∧γγ →1 .
- Such a ±i +i −j bivector flips the i’th bit of a spinor from down to up, and the j’th bit from up to down, preserving the total number of up bits of the spinor.
- These generators must be real linear combinations of orthonormal Spin(2N) bivectors that, when expressed in terms of spin vectors γγ , are (complex) linear combinations of bivectors of the form γγ ∧γγ .

Thus U(N) and SU(N) are subgroups of Spin(2N) as claimed.

The Lie algebra of commutators of the generators (38.180) coincides with the Lie algebra of commutators in which 1γγ ∧γγ is represented by the N ×N matrix 1 with 1 in the 2 +i −j ij ij’th entry and 0 elsewhere, 1γγ ∧γγ →1 .

Such a ±i +i −j bivector flips the i’th bit of a spinor from down to up, and the j’th bit from up to down, preserving the total number of up bits of the spinor.

These generators must be real linear combinations of orthonormal Spin(2N) bivectors that, when expressed in terms of spin vectors γγ , are (complex) linear combinations of bivectors of the form γγ ∧γγ .

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:
- arXiv:0707.1889 (https:// arxiv.org/abs/0707.1889).
- Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.
- Bibcode:2008RvMP...80.1083N (https://ui.adsabs.harvard.edu/abs/2008 RvMP...80.1083N).
- Bibcode:2002CMaPh.227..605F (https://ui.adsabs.harvard.edu/abs/2002CMaPh.227..605F).

Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

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:
- 1 & 2 (New ed.), Wiley-Interscience, ISBN 0-471-15733-3.
- Weyl, Hermann (1918), Raum, Zeit, Materie (5 editions to 1922, with notes by Jürgen Ehlers (1980), translated 4th edition Space, Time, Matter by Henry Brose, 1922 (Methuen, reprinted 1952 by Dover) ed.), Springer, Berlin, ISBN 0-486-60267-2 Secondary references Kobayashi, Shoshichi; Nomizu, Katsumi (1996), Foundations of Differential Geometry, Vols.
- Volume 1, chapter III gives a detailed account of affine connections from the perspective of principal bundles on a manifold, parallel transport, development, geodesics, and associated differential operators.
- Lumiste, Ülo (2001a) [1994], "Affine connection" (https://www.encyclopediaofmath.org/index.php?t itle=Affine_connection), in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, EMS Press, ISBN 978-1-55608-010-4.

1 & 2 (New ed.), Wiley-Interscience, ISBN 0-471-15733-3.

Weyl, Hermann (1918), Raum, Zeit, Materie (5 editions to 1922, with notes by Jürgen Ehlers (1980), translated 4th edition Space, Time, Matter by Henry Brose, 1922 (Methuen, reprinted 1952 by Dover) ed.), Springer, Berlin, ISBN 0-486-60267-2 Secondary references Kobayashi, Shoshichi; Nomizu, Katsumi (1996), Foundations of Differential Geometry, Vols.

Volume 1, chapter III gives a detailed account of affine connections from the perspective of principal bundles on a manifold, parallel transport, development, geodesics, and associated differential operators.

Lumiste, Ülo (2001a) [1994], "Affine connection" (https://www.encyclopediaofmath.org/index.php?t itle=Affine_connection), in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, EMS Press, ISBN 978-1-55608-010-4.

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:
- It was predicted that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately perfect fluid is analogous to gravity (see Analog models of gravity).[45] Observations of Hawking radiation were reported in sonic black holes employing Bose–Einstein condensates.[46][47][48] In September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation.[49] However, the results remain unverified and debatable,[50][51] and its status as a genuine confirmation remains in doubt.[52] See also Black hole information paradox Black hole thermodynamics Black hole starship Blandford–Znajek process and Penrose process, other extractions of black-hole energy Gibbons–Hawking effect Thorne–Hawking–Preskill bet Unruh effect References 1.
- American Museum of Natural History.
- doi:10.1038/248030a0 (https://doi.org/10.1038%2F248030a0).
- S2CID 4290107 (https://api.semanticscholar.org/CorpusID:4290107).

It was predicted that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately perfect fluid is analogous to gravity (see Analog models of gravity).[45] Observations of Hawking radiation were reported in sonic black holes employing Bose–Einstein condensates.[46][47][48] In September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation.[49] However, the results remain unverified and debatable,[50][51] and its status as a genuine confirmation remains in doubt.[52] See also Black hole information paradox Black hole thermodynamics Black hole starship Blandford–Znajek process and Penrose process, other extractions of black-hole energy Gibbons–Hawking effect Thorne–Hawking–Preskill bet Unruh effect References 1.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Metrics in ADM form are adapted to a certain family of inertial observers, but these observers are not really physically distinguished from other such families.
- Farnes' theory relies on negative masses that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable Hubble parameter.[17] As Farnes' theory allows a positive mass (i.e.
- This might explain the widespread misconception that this spacetime is a solution of the field equation of general relativity.
- Enormous tidal forces, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.[5] The original warp-drive metric and simple variants of it happen to have the ADM form, which is often used in discussing the initial-value formulation of general relativity.

Metrics in ADM form are adapted to a certain family of inertial observers, but these observers are not really physically distinguished from other such families.

Farnes' theory relies on negative masses that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable Hubble parameter.[17] As Farnes' theory allows a positive mass (i.e.

This might explain the widespread misconception that this spacetime is a solution of the field equation of general relativity.

Enormous tidal forces, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.[5] The original warp-drive metric and simple variants of it happen to have the ADM form, which is often used in discussing the initial-value formulation of general relativity.

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:
- Psychological Science and Common Sense One reason we’re easily seduced by psychomythology is that it jibes with our common sense: our gut hunches, intuitions, and first impressions.
- 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.
- Most of these books acknowledge the limitations of common sense in evaluating the truth of scientific claims, but contend that psychologists have traditionally underestimated the accuracy of our hunches.

Psychological Science and Common Sense One reason we’re easily seduced by psychomythology is that it jibes with our common sense: our gut hunches, intuitions, and first impressions.

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.

Most of these books acknowledge the limitations of common sense in evaluating the truth of scientific claims, but contend that psychologists have traditionally underestimated the accuracy of our hunches.

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:
- Tensor: N 2,±2 − √2 h ±± oscillates about − √2 h ±± .
- Vector: N oscillates about −1W ; 1,±1 √ 3 ± √ 3.
- 944 Cosmological perturbations including polarization Exercise 35.8.
- (35.77c) ∂η2 η∂η 2,±2 5 3 ±± 5 3 ±± Equations (35.77) are forced, damped wave equations with effective sound speed equal to the speed of light.

Tensor: N 2,±2 − √2 h ±± oscillates about − √2 h ±± .

Vector: N oscillates about −1W ; 1,±1 √ 3 ± √ 3.

944 Cosmological perturbations including polarization Exercise 35.8.

(35.77c) ∂η2 η∂η 2,±2 5 3 ±± 5 3 ±± Equations (35.77) are forced, damped wave equations with effective sound speed equal to the speed of light.

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:
- Inparticular,theearthdragsthespacetimeframearoundit.
- TheKerrsolutionturnsouttobearithmeticallycomplex,andsoitwouldbeadvisable todoaback-of-the-envelopeestimateofthiseffectatthispoint.Letthebodyrotatewith angularvelocity(cid:24)∼v/R,whereRdenotestheobject’scharacteristicsize.Throughgravity theobjectcurvesthespacetimearoundit, whichcausestheparticle, inseekingthebest deal(namelythegeodesic),tobe1“draggedalong.”Thestrengthofgravityischaracterized bythedimensionlessratioGM/Rc2,aswehaveseenmanytimes.Thus,wemightexpect (cid:3) (cid:4)(cid:3) (cid:4) GM GM v ω∼ (cid:24)∼ (7) Rc2 Rc2 R Let us also anticipate how the Kerr solution would be parametrized.
- S S Stationarylimitsurface Consideralightrayemitted,initiallywithdr =0anddθ =0,fromsomepoint.Wehave initially 0=ds2=g dt2+2g dtdφ+g dφ2.
- Indeed, it is convenient to continue using the length r ≡2GM =2M, even though we are not S dealingwiththeSchwarzschildsolutionhere.Wethenhavethedimensionlessmeasure ofrotation2a/r =J/M2,whichisoforder∼v/cifwesetR∼r ∼M.

TheKerrsolutionturnsouttobearithmeticallycomplex,andsoitwouldbeadvisable todoaback-of-the-envelopeestimateofthiseffectatthispoint.Letthebodyrotatewith angularvelocity(cid:24)∼v/R,whereRdenotestheobject’scharacteristicsize.Throughgravity theobjectcurvesthespacetimearoundit, whichcausestheparticle, inseekingthebest deal(namelythegeodesic),tobe1“draggedalong.”Thestrengthofgravityischaracterized bythedimensionlessratioGM/Rc2,aswehaveseenmanytimes.Thus,wemightexpect (cid:3) (cid:4)(cid:3) (cid:4) GM GM v ω∼ (cid:24)∼ (7) Rc2 Rc2 R Let us also anticipate how the Kerr solution would be parametrized.

S S Stationarylimitsurface Consideralightrayemitted,initiallywithdr =0anddθ =0,fromsomepoint.Wehave initially 0=ds2=g dt2+2g dtdφ+g dφ2.

Indeed, it is convenient to continue using the length r ≡2GM =2M, even though we are not S dealingwiththeSchwarzschildsolutionhere.Wethenhavethedimensionlessmeasure ofrotation2a/r =J/M2,whichisoforder∼v/cifwesetR∼r ∼M.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The thunderstorms blue areas indicate where potential Antiparticles are created lightning can occur for terrestrial everywhere in the universe gamma ray flashes.
- While the mechanism is not fully understood, it is likely to involve the production of electron–positron pairs, as ordinary matter gains kinetic energy while falling into a stellar remnant.[31][32] Antimatter may exist in relatively large amounts in far-away galaxies due to cosmic inflation in the primordial time of the universe.
- Observations by the European Space Agency's INTEGRAL satellite may explain the origin of a giant antimatter cloud surrounding the Galactic Center.
- Highenergy cosmic rays striking Earth's atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter.

The thunderstorms blue areas indicate where potential Antiparticles are created lightning can occur for terrestrial everywhere in the universe gamma ray flashes.

While the mechanism is not fully understood, it is likely to involve the production of electron–positron pairs, as ordinary matter gains kinetic energy while falling into a stellar remnant.[31][32] Antimatter may exist in relatively large amounts in far-away galaxies due to cosmic inflation in the primordial time of the universe.

Observations by the European Space Agency's INTEGRAL satellite may explain the origin of a giant antimatter cloud surrounding the Galactic Center.

Highenergy cosmic rays striking Earth's atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter.

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:
- Bibcode:1997RvMP...69..995W (https://ui.adsabs.harvard.edu/abs/1997RvMP...69..995W).
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Star&oldid=1329902859"
- "The evolution and explosion of massive stars".
- External links "How To Decipher Classification Codes" (http://www.assa.org.au/sig/variables/classifications.asp).

"The evolution and explosion of massive stars".

External links "How To Decipher Classification Codes" (http://www.assa.org.au/sig/variables/classifications.asp).

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:
- Third law Actioni contrariam semper & æqualem esse To every action, there is always opposed an reactionem: sive corporum duorum actiones equal reaction; or, the mutual actions of two in se mutuo semper esse æquales & in partes bodies upon each other are always equal, and contrarias dirigi.
- By Newton's third law, these forces have equal magnitude but opposite direction, so they cancel when added, and is constant.
- For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.
- The Earth's gravity pulls down upon the book.

Third law Actioni contrariam semper & æqualem esse To every action, there is always opposed an reactionem: sive corporum duorum actiones equal reaction; or, the mutual actions of two in se mutuo semper esse æquales & in partes bodies upon each other are always equal, and contrarias dirigi.

By Newton's third law, these forces have equal magnitude but opposite direction, so they cancel when added, and is constant.

For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.

The Earth's gravity pulls down upon the book.

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:
- "Scientists observe liquid with 'negative mass', which turns physics completely backwards" (https://www.independent.co.uk/news/science/negative-mass-object-washi
- The plasma oscillations [30][31] are represented with the elastic spring , where is the plasma frequency.
- Free electrons gas is mass (density) embedded into the ionic lattice ; is Figure 1.
- A core with mass is becomes also possible the plasma frequency (the left sketch).

"Scientists observe liquid with 'negative mass', which turns physics completely backwards" (https://www.independent.co.uk/news/science/negative-mass-object-washi

The plasma oscillations [30][31] are represented with the elastic spring , where is the plasma frequency.

Free electrons gas is mass (density) embedded into the ionic lattice ; is Figure 1.

A core with mass is becomes also possible the plasma frequency (the left sketch).

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:
- No doubt there is some critical mass below which atom compression is sufficient, and the body is a planet; and above which the central atoms shatter, a nuclear reaction is ignited, and the body is a star.
- Four protons combine to form a helium nucleus, made up of four nucleons-two protons and two neutrons.
- Undoubted stars are known which are much smaller in mass than the Sun.
- Somewhere in the range of mass between that of Jupiter and the Sun there must be that critical mass.

No doubt there is some critical mass below which atom compression is sufficient, and the body is a planet; and above which the central atoms shatter, a nuclear reaction is ignited, and the body is a star.

Four protons combine to form a helium nucleus, made up of four nucleons-two protons and two neutrons.

Undoubted stars are known which are much smaller in mass than the Sun.

Somewhere in the range of mass between that of Jupiter and the Sun there must be that critical mass.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- However, the photon has disappeared in the process of being captured (measured), and its quantum wave function has disappeared with it.
- to create the narrower curve, and vice versa.
- In its place, some macroscopic physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD.
- This is what the Stern–Gerlach experiment shows.

Introduction to quantum mechanics - Wikipedia.pdf

However, the photon has disappeared in the process of being captured (measured), and its quantum wave function has disappeared with it.

to create the narrower curve, and vice versa.

In its place, some macroscopic physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD.

This is what the Stern–Gerlach experiment shows.

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 measurement projected the combined state of particle 1 and 2 on a Bell state basis leaving particle 1and 2 entangled and particle 3 in a pure state.
- These long-range correlations formed the basis of quantum teleportation, which concerned the second part of the paper.
- The non-locality made it possible to teleport the massles information of objects with a speed larger than that of light.
- For teleportation Alice needed to create an entanglement between the initial particle 1 and her particle of the EPR pair (say particle 2).

This measurement projected the combined state of particle 1 and 2 on a Bell state basis leaving particle 1and 2 entangled and particle 3 in a pure state.

These long-range correlations formed the basis of quantum teleportation, which concerned the second part of the paper.

The non-locality made it possible to teleport the massles information of objects with a speed larger than that of light.

For teleportation Alice needed to create an entanglement between the initial particle 1 and her particle of the EPR pair (say particle 2).

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The radium is sealed within a glass envelope with two electrodes, one of which is coated with the radioactive material to create an ion path between the electrodes.[58]
- This ionization ensures reliable and consistent operation by providing a steady current when a high voltage is applied, enhancing the device's performance and stability.
- These devices contain a small amount of radium (in the form of radium bromide)[57] to ionize the fill gas, typically a noble gas like neon or argon.
- by the radiation from the radium.[55] Originally appearing as white, most radium paint from before the 1960s has tarnished to yellow over time.

The radium is sealed within a glass envelope with two electrodes, one of which is coated with the radioactive material to create an ion path between the electrodes.[58]

This ionization ensures reliable and consistent operation by providing a steady current when a high voltage is applied, enhancing the device's performance and stability.

These devices contain a small amount of radium (in the form of radium bromide)[57] to ionize the fill gas, typically a noble gas like neon or argon.

by the radiation from the radium.[55] Originally appearing as white, most radium paint from before the 1960s has tarnished to yellow over time.

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

List tests or derivations implied by the evidence.