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

EVIDENCE:
- Dimensional analysis then requires that the conductivity must scale as σ ∝ R−1.
- The conductivity can depend only on the intrinsic properties of the conducting fluid, and the only intrinsic propertyavailableisitsdensity,whichscalesasρ∝R−2.Itfollowsthattheconductivitymustbeproportional to the square root of the density ρ of the conducting fluid, σ =κρ1/2 , (20.166) where κ is a dimensionless conductivity constant.
- A dimensionless measureoftheconductivity(whichhasunits1/time)istheconductivityσ timesthecharacteristictimescale t ≡GM/c3 of the black hole, which is of order BH T σt ∼ (20.168) BH T BH where kT ≡ (cid:126)/t is the characteristic temperature of the black hole (for a Schwarzschild black hole, BH BH
- 606 General spherically symmetric spacetimes Thebigquestion,exploredusingsphericalchargedblackholesinthenextChapter21,iswhathappensnear their inner horizons?

Dimensional analysis then requires that the conductivity must scale as σ ∝ R−1.

The conductivity can depend only on the intrinsic properties of the conducting fluid, and the only intrinsic propertyavailableisitsdensity,whichscalesasρ∝R−2.Itfollowsthattheconductivitymustbeproportional to the square root of the density ρ of the conducting fluid, σ =κρ1/2 , (20.166) where κ is a dimensionless conductivity constant.

A dimensionless measureoftheconductivity(whichhasunits1/time)istheconductivityσ timesthecharacteristictimescale t ≡GM/c3 of the black hole, which is of order BH T σt ∼ (20.168) BH T BH where kT ≡ (cid:126)/t is the characteristic temperature of the black hole (for a Schwarzschild black hole, BH BH

606 General spherically symmetric spacetimes Thebigquestion,exploredusingsphericalchargedblackholesinthenextChapter21,iswhathappensnear their inner horizons?

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:
- central conclusion remains unchanged and unchallenged: Mechanical predictions are equally or more accurate than clinical predictions.
- This verdict holds true not only for mental health experts making psychiatric diagnoses, forecasting psychotherapy outcome, or predicting suicide attempts, but also for experts predicting performance in college, graduate school, military training, the workplace, or horse races; detecting lies; predicting criminal behavior; and making medical diagnoses or predicting the length of hospitalization or | 228 Chapter 11 Skills & Pills

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.

central conclusion remains unchanged and unchallenged: Mechanical predictions are equally or more accurate than clinical predictions.

This verdict holds true not only for mental health experts making psychiatric diagnoses, forecasting psychotherapy outcome, or predicting suicide attempts, but also for experts predicting performance in college, graduate school, military training, the workplace, or horse races; detecting lies; predicting criminal behavior; and making medical diagnoses or predicting the length of hospitalization or | 228 Chapter 11 Skills & Pills

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 (m = 0, 1, 2, 3) appear in the theory only through the variables , which occur as arbitrary coefficients in the equations of motion.
- In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the
- The fourth is a 3-dimensional scalar density in the surface H ≈ L 0; H ≈ 0 (r = 1, 2, 3).[150] r In the late 1950s, Dirac applied the Hamiltonian methods he had developed to cast Einstein's general relativity in Hamiltonian form[151][152] and to bring to a technical completion the quantisation problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt.
- There are four constraints or weak equations for each point of the surface = constant.

The (m = 0, 1, 2, 3) appear in the theory only through the variables , which occur as arbitrary coefficients in the equations of motion.

In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the

The fourth is a 3-dimensional scalar density in the surface H ≈ L 0; H ≈ 0 (r = 1, 2, 3).[150] r In the late 1950s, Dirac applied the Hamiltonian methods he had developed to cast Einstein's general relativity in Hamiltonian form[151][152] and to bring to a technical completion the quantisation problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt.

There are four constraints or weak equations for each point of the surface = constant.

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:
- Wigner in his analysis of earlier work by W.M.
- Elsasser devoted to a discussion of the origin of life and the multiplication of organisms.
- • Today’s standard references are: W.
- Milonni and M.L.Hardies, Phys.

Wigner in his analysis of earlier work by W.M.

Elsasser devoted to a discussion of the origin of life and the multiplication of organisms.

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

EVIDENCE:
- Let A and B be the rear and front spaceships.
- In the frame of the spaceships, each spaceship sees the other spaceship doing the same thing that it is doing.
- A says that B has the same acceleration that he has, and B sees that A matches her every move.
- So the spaceships stay the same distance apart, and the string does not break.

Let A and B be the rear and front spaceships.

In the frame of the spaceships, each spaceship sees the other spaceship doing the same thing that it is doing.

A says that B has the same acceleration that he has, and B sees that A matches her every move.

So the spaceships stay the same distance apart, and the string does not break.

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:
- (4.93) Recall that the super-Hamiltonian H is a scalar, associated with rest mass, to be distinguished from the conventional Hamiltonian, which is the time component of a vector, associated with energy.
- The effective test-particle Lagrangian (4.25), coupled to electromagnetism, is 1 dxμdxν dxμ L=L +L = g +qA , (4.88) m q 2 μν dλ dλ μ dλ wherethemetricg andelectromagneticpotentialA areconsideredtobegivenfunctionsofthecoordinates μν μ xμ.
- 4.13 Effective (super-)Hamiltonian for a test particle with electromagnetism In the effective approach, the condition (4.29) on the parameter λ is applied after equations of motion are derived.
- The value of the Hamiltonian (4.90) after the equations of motion and condition (4.29) are imposed is constant, m2 H =− .

(4.93) Recall that the super-Hamiltonian H is a scalar, associated with rest mass, to be distinguished from the conventional Hamiltonian, which is the time component of a vector, associated with energy.

The effective test-particle Lagrangian (4.25), coupled to electromagnetism, is 1 dxμdxν dxμ L=L +L = g +qA , (4.88) m q 2 μν dλ dλ μ dλ wherethemetricg andelectromagneticpotentialA areconsideredtobegivenfunctionsofthecoordinates μν μ xμ.

4.13 Effective (super-)Hamiltonian for a test particle with electromagnetism In the effective approach, the condition (4.29) on the parameter λ is applied after equations of motion are derived.

The value of the Hamiltonian (4.90) after the equations of motion and condition (4.29) are imposed is constant, m2 H =− .

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 classic worm hole is that in the movie 2001: A Space Odyssey.
- Inside the worm hole, however, light is trapped by the severe curvature of the space.
- In the first Star Trek movie, the Enterprise is captured in a worm hole when it jumps into warp drive too soon after leaving Earth.
- Light from stars could come in the end of the worm hole the Enterprise entered, or it could come in through the opposite end toward which the ship is headed.

The classic worm hole is that in the movie 2001: A Space Odyssey.

Inside the worm hole, however, light is trapped by the severe curvature of the space.

In the first Star Trek movie, the Enterprise is captured in a worm hole when it jumps into warp drive too soon after leaving Earth.

Light from stars could come in the end of the worm hole the Enterprise entered, or it could come in through the opposite end toward which the ship is headed.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- This leads to the system of equations The first of these is solved for λ and one obtains for stereographic projection −1 Next, the inverse σ (u) = (τ, x) must be calculated.
- Use the same considerations as before, but now with one gets but now with λ depending on u.
- The condition for P lying in the hyperboloid is or leading to With this λ, one obtains Pulling back the metric One has and the map The pulled back metric can be obtained by straightforward methods of calculus;

This leads to the system of equations The first of these is solved for λ and one obtains for stereographic projection −1 Next, the inverse σ (u) = (τ, x) must be calculated.

Use the same considerations as before, but now with one gets but now with λ depending on u.

The condition for P lying in the hyperboloid is or leading to With this λ, one obtains Pulling back the metric One has and the map The pulled back metric can be obtained by straightforward methods of calculus;

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:
- Conversely, if E and F are Euclidean spaces, O ∈ E, O′ ∈ F, and is an isometry, then the map defined by is an isometry of Euclidean spaces.
- The inverse isometry is This means that, up to an isomorphism, there is exactly one Euclidean space of a given dimension.
- An isometry of Euclidean spaces defines an isometry of the associated Euclidean vector spaces.
- The inverse isometry is the map A Euclidean frame allows defining the map which is an isometry of Euclidean spaces.

Conversely, if E and F are Euclidean spaces, O ∈ E, O′ ∈ F, and is an isometry, then the map defined by is an isometry of Euclidean spaces.

The inverse isometry is This means that, up to an isomorphism, there is exactly one Euclidean space of a given dimension.

An isometry of Euclidean spaces defines an isometry of the associated Euclidean vector spaces.

The inverse isometry is the map A Euclidean frame allows defining the map which is an isometry of Euclidean spaces.

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:
- Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy.[28][43] In 1965, Erast Gliner showed that the simplest energy-momentum tensor usable in Einstein's theory of general relativity describes a vacuum-like state of matter.
- False vacuum In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory.
- Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.
- Based on the conservation of energy, this vacuum energy density would create negative pressure.[44]: 1 This vacuum-energy idea led to two concepts, dark energy and a model for inflation.

Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy.[28][43] In 1965, Erast Gliner showed that the simplest energy-momentum tensor usable in Einstein's theory of general relativity describes a vacuum-like state of matter.

False vacuum In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory.

Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.

Based on the conservation of energy, this vacuum energy density would create negative pressure.[44]: 1 This vacuum-energy idea led to two concepts, dark energy and a model for inflation.

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:
- What's more, all the Cepheid variables, even the smallest, are considerably more massive than the Sun.
- How can they undergo an explosive expansion?
- There are, indeed, stars that have been observed to be recurrent novas, which have exploded twice or even three times in the short period of a little over a century in which astronomers have watched such stars closely.
- A suggestion, first proposed in 1955 by the Russian American astronomer Otto Struve (18971963), that seems to be gaining favor is that every nova is a member of a close binary, one of two stars that circle each other at a relatively small distance.

What's more, all the Cepheid variables, even the smallest, are considerably more massive than the Sun.

How can they undergo an explosive expansion?

There are, indeed, stars that have been observed to be recurrent novas, which have exploded twice or even three times in the short period of a little over a century in which astronomers have watched such stars closely.

A suggestion, first proposed in 1955 by the Russian American astronomer Otto Struve (18971963), that seems to be gaining favor is that every nova is a member of a close binary, one of two stars that circle each other at a relatively small distance.

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:
- those goals aren't aligned with ours, we're in trouble".[221] He also considered that the enormous wealth generated by machines needs to be redistributed to prevent exacerbated economic inequality.[221] Hawking was concerned about the future emergence of a race of "superhumans" that would be able to design their own evolution [208] and, as well, argued that computer viruses in today's world should be considered a new form of life, stating that "maybe it says something about human nature, that the only form of life we have created so far is purely destructive.
- Talk about creating life in our own image."[222] Religion and atheism Hawking did not rule out the existence of God, writing in A Brief History of Time: "Is the unified theory so compelling that it brings about its own existence?",[223] also stating "If we discover a complete theory, it would be the ultimate triumph of human reason – for then we should know the mind of God";[224] in his early work, Hawking spoke of God in a metaphorical sense.

those goals aren't aligned with ours, we're in trouble".[221] He also considered that the enormous wealth generated by machines needs to be redistributed to prevent exacerbated economic inequality.[221] Hawking was concerned about the future emergence of a race of "superhumans" that would be able to design their own evolution [208] and, as well, argued that computer viruses in today's world should be considered a new form of life, stating that "maybe it says something about human nature, that the only form of life we have created so far is purely destructive.

Talk about creating life in our own image."[222] Religion and atheism Hawking did not rule out the existence of God, writing in A Brief History of Time: "Is the unified theory so compelling that it brings about its own existence?",[223] also stating "If we discover a complete theory, it would be the ultimate triumph of human reason – for then we should know the mind of God";[224] in his early work, Hawking spoke of God in a metaphorical sense.

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 blinds are open and she’s seated with her back to me, facing a giant monitor.
- I see her lift a cordless handset and stare at the display.
- It all points to the fact that my identity isn’t binary.
- My voice: “You’ve reached the Dessens.

The blinds are open and she’s seated with her back to me, facing a giant monitor.

I see her lift a cordless handset and stare at the display.

It all points to the fact that my identity isn’t binary.

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:
- EquivalencePrincipleandCurvedSpacetime Bynow,youshouldbefamiliarwithhowthisworks;forexample,inthesecondequality, Sρ and(S −1) μ knockeachotheroff.
- The proof is straightforward: when we go from unprimed η ωηκ to primed coordinates, for each pair of contracted indices, S and S −1 knock each other off,andthevariousSsandS −1sleftdanglingarepreciselywhatareneededtomakethe
- We can of course also contractanupperindexfromonetensor(forexampleAμν)withalowerindexfromanother σ tensor(forexampleBτ ).Thisisatrivialstatement,aswecanalwaysdefinethetensor λωρη T μντ ≡AμνBτ and then contract any upper index with any lower index on T (for σλωρη σ λωρη μντ μτ example,T producingthetensorT ).
- Suppose you set μ and ν equal in (12) and sum.

EquivalencePrincipleandCurvedSpacetime Bynow,youshouldbefamiliarwithhowthisworks;forexample,inthesecondequality, Sρ and(S −1) μ knockeachotheroff.

The proof is straightforward: when we go from unprimed η ωηκ to primed coordinates, for each pair of contracted indices, S and S −1 knock each other off,andthevariousSsandS −1sleftdanglingarepreciselywhatareneededtomakethe

We can of course also contractanupperindexfromonetensor(forexampleAμν)withalowerindexfromanother σ tensor(forexampleBτ ).Thisisatrivialstatement,aswecanalwaysdefinethetensor λωρη T μντ ≡AμνBτ and then contract any upper index with any lower index on T (for σλωρη σ λωρη μντ μτ example,T producingthetensorT ).

Suppose you set μ and ν equal in (12) and sum.

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:
- (They aren't in the case of our own Earth, for instance.) Each magnetic pole might sweep around the rotational pole in seconds or in a fraction of a second and spray out electrons as it does so (just as a rotating water sprinkler jets out water).
- This means that the faster the period of a pulsar, the younger it is likely to be and the more rapidly it may be losing energy and slowing down.
- Losing energy, they may not escape altogether, but the energy they lose is in the form of microwaves.
- If a neutron star happens to move one of those jets across our line of sight as it rotates, Earth will get a very brief pulse of microwaves at each rotation.

(They aren't in the case of our own Earth, for instance.) Each magnetic pole might sweep around the rotational pole in seconds or in a fraction of a second and spray out electrons as it does so (just as a rotating water sprinkler jets out water).

This means that the faster the period of a pulsar, the younger it is likely to be and the more rapidly it may be losing energy and slowing down.

Losing energy, they may not escape altogether, but the energy they lose is in the form of microwaves.

If a neutron star happens to move one of those jets across our line of sight as it rotates, Earth will get a very brief pulse of microwaves at each rotation.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- “They carried you in here a little while ago.” I force my eyes to open.
- A man just broke into her apartment and shot her between the eyes.” “Oh God.” Climbing onto the cot, he sits beside me, both of us leaning back against the concrete wall.
- Up close, he looks even worse.
- That wasn’t me.” He looks over at me, as if trying to process the magnitude of that statement.

“They carried you in here a little while ago.” I force my eyes to open.

A man just broke into her apartment and shot her between the eyes.” “Oh God.” Climbing onto the cot, he sits beside me, both of us leaning back against the concrete wall.

That wasn’t me.” He looks over at me, as if trying to process the magnitude of that statement.

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 symptoms of PTSD were first observed Clear descriptions of PTSD date from at following the Vietnam War.
- They include asthma, irritable bowel syndrome, and some headaches.
- Most phobias are traceable directly to Most people with phobias report no negative experiences with the object of direct traumatic experiences with the the fear.
- But it reminds us of a key principle: Even false beliefs may derive from what was once a kernel of truth (see Introduction, p.

The symptoms of PTSD were first observed Clear descriptions of PTSD date from at following the Vietnam War.

They include asthma, irritable bowel syndrome, and some headaches.

Most phobias are traceable directly to Most people with phobias report no negative experiences with the object of direct traumatic experiences with the the fear.

But it reminds us of a key principle: Even false beliefs may derive from what was once a kernel of truth (see Introduction, p.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Well, as long as the only important way in which astronomers could study the sky was by observing the light given off by objects in it, it was useless to bother.
- Then, why bother about neutron stars?
- How could one possibly tell it was a neutron star that happened to be close enough to be made out, rather than an ordinary star that looked that dim only because it was extremely far away?
- NEUTRON STARS 147 what point the electronic fluid would be smashed, and how the neutronium might form-yet it would all just remain figures on paper.

Well, as long as the only important way in which astronomers could study the sky was by observing the light given off by objects in it, it was useless to bother.

How could one possibly tell it was a neutron star that happened to be close enough to be made out, rather than an ordinary star that looked that dim only because it was extremely far away?

NEUTRON STARS 147 what point the electronic fluid would be smashed, and how the neutronium might form-yet it would all just remain figures on paper.

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:
- 866 | CollectionofFormulasandConventions For your convenience, the signs used in some textbooks are summarized and compared in the table.
- For example, Weinberg has s =+ and s =−, so his R and R 1 2 μν are minus the R and R used in this text.
- Thus, his Einstein-Hilbert action reads S= (cid:8) √ μν (cid:8) √ − 1 d4x −gR.Inthistext,S=+ 1 d4x −gR.
- 16πG 16πG Signconventionsusedinvarioustextbooks s s s s =s s 1 2 3 4 2 3 Thistext + + + + Weinberg + − + − MTW + + + + Hartle + + + + Cheng + + + + Schutz + + + + Carroll + + + + HEL − + − − d’Inverno − + + + Note:MTW=Misner,Thorne,andWheeler,HEL=Hobson, Efstathiou,andLasenby.

866 | CollectionofFormulasandConventions For your convenience, the signs used in some textbooks are summarized and compared in the table.

For example, Weinberg has s =+ and s =−, so his R and R 1 2 μν are minus the R and R used in this text.

Thus, his Einstein-Hilbert action reads S= (cid:8) √ μν (cid:8) √ − 1 d4x −gR.Inthistext,S=+ 1 d4x −gR.

16πG 16πG Signconventionsusedinvarioustextbooks s s s s =s s 1 2 3 4 2 3 Thistext + + + + Weinberg + − + − MTW + + + + Hartle + + + + Cheng + + + + Schutz + + + + Carroll + + + + HEL − + − − d’Inverno − + + + Note:MTW=Misner,Thorne,andWheeler,HEL=Hobson, Efstathiou,andLasenby.

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:
- Indeed, there are many anecdotal reports of people seeming to recover decades-old memories of abuse in psychotherapy (Erdelyi, 1985).
- Richard McNally (2003) offered the following explanation—as an alternative to repression—for how delayed recall of child abuse can occur.
- The delay of recall of events isn’t all
- Please keep thinking about it”), to “help clients remember childhood sexual abuse.” Additionally, 25% of the respondents who conducted therapy with adult female clients believed that memory recovery is a key component of treatment, believed they could identify patients with repressed or otherwise unavailable memories as early as the first session, and used two or more memory recovery techniques to enhance recall of disclosure of past events.

Indeed, there are many anecdotal reports of people seeming to recover decades-old memories of abuse in psychotherapy (Erdelyi, 1985).

Richard McNally (2003) offered the following explanation—as an alternative to repression—for how delayed recall of child abuse can occur.

Please keep thinking about it”), to “help clients remember childhood sexual abuse.” Additionally, 25% of the respondents who conducted therapy with adult female clients believed that memory recovery is a key component of treatment, believed they could identify patients with repressed or otherwise unavailable memories as early as the first session, and used two or more memory recovery techniques to enhance recall of disclosure of past events.

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 researchers then gradually weakened the magnetic fields and detected the antiatoms using two sensors as they escaped and annihilated.
- Most of the anti-atoms came out of the bottom opening, and only one-quarter out of the top.[24] There are compelling theoretical reasons to believe that, aside from the fact that antiparticles have different signs on all charges (such as electric and baryon charges), matter and antimatter have exactly the same properties.[25][26] This means a particle and its corresponding antiparticle must have

The researchers then gradually weakened the magnetic fields and detected the antiatoms using two sensors as they escaped and annihilated.

Most of the anti-atoms came out of the bottom opening, and only one-quarter out of the top.[24] There are compelling theoretical reasons to believe that, aside from the fact that antiparticles have different signs on all charges (such as electric and baryon charges), matter and antimatter have exactly the same properties.[25][26] This means a particle and its corresponding antiparticle must have

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:
- −asinφ 0 cosφ Recallfromearlierinthischapterthate(cid:3) 1 = acosφ ,e(cid:3) 2 = 0 ,andn(cid:3)= sinφ .First, 0 1 0 using (5), we already worked out the metric g =a2, g =g =0, g =1.
- Thus, G=−pq and μν μ,ν 11 22 12 21 S=p−q.
- For a sphere of radius a, p=−q =a, and so G=a2=E.
- ThequantitiesG andS presentuswithtwomeasuresofcurvature.Howdoweknow which one is intrinsic?

−asinφ 0 cosφ Recallfromearlierinthischapterthate(cid:3) 1 = acosφ ,e(cid:3) 2 = 0 ,andn(cid:3)= sinφ .First, 0 1 0 using (5), we already worked out the metric g =a2, g =g =0, g =1.

Thus, G=−pq and μν μ,ν 11 22 12 21 S=p−q.

For a sphere of radius a, p=−q =a, and so G=a2=E.

ThequantitiesG andS presentuswithtwomeasuresofcurvature.Howdoweknow which one is intrinsic?

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:
- among eating disordered patients than patients with other psychiatric disorders.
- Children can’t become seriously depressed.
- The rates of depression in women increase The rates of nonpsychotic depression are dramatically during the postpartum period.
- 9781405131117_4_009.qxd 30/6/09 11:45 AM Page 206 Fiction Fact People with hypochondriasis are typically People with hypochondriasis are typically convinced they’re suffering from many convinced they’re suffering from one different illnesses.

among eating disordered patients than patients with other psychiatric disorders.

Children can’t become seriously depressed.

The rates of depression in women increase The rates of nonpsychotic depression are dramatically during the postpartum period.

9781405131117_4_009.qxd 30/6/09 11:45 AM Page 206 Fiction Fact People with hypochondriasis are typically People with hypochondriasis are typically convinced they’re suffering from many convinced they’re suffering from one different illnesses.

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:
- 7.Question What can we infer about the future of black hole research and its implications for our understanding of the universe?
- Answer:The ongoing research into black holes could potentially unlock fundamental insights about the nature of reality, including the laws of physics that govern the universe.
- Thorne uses a narrative style that blends factual scientific principles with imaginative storytelling.
- 8.Question How does the author convey the complexities and wonders of the universe in the book?

7.Question What can we infer about the future of black hole research and its implications for our understanding of the universe?

Answer:The ongoing research into black holes could potentially unlock fundamental insights about the nature of reality, including the laws of physics that govern the universe.

Thorne uses a narrative style that blends factual scientific principles with imaginative storytelling.

8.Question How does the author convey the complexities and wonders of the universe in 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:
- The requirements of regularity and nondegeneracy of ensure that closed causal curves (such as those consisting of a single point) are not automatically admitted by all spacetimes.
- If the manifold is time-orientable then the non-spacelike curves can further be classified depending on their orientation with respect to time.
- A chronological, null or causal curve in is

The requirements of regularity and nondegeneracy of ensure that closed causal curves (such as those consisting of a single point) are not automatically admitted by all spacetimes.

If the manifold is time-orientable then the non-spacelike curves can further be classified depending on their orientation with respect to time.

A chronological, null or causal curve in is

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:
- For it, outcome A was that six dice are tossed with at least one six appearing, outcome B that twelve dice are tossed with at least two sixes appearing, and outcome C in which eighteen dice are tossed with at least three sixes appearing.
- He is also credited as the originator of bipolar coordinates in a strict sense.[85][86] A private manuscript of Newton's which dates to 1664–66 contains what is the earliest known problem in the field of geometric probability.
- Newton was probably first to develop a system of polar coordinates in a strictly analytic sense, with his work in relation to the topic being superior, in both generality and flexibility, to any other during his lifetime.
- However, a 1690s manuscript later analysed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons.[48][71][77] In 1717, and probably with Newton's help, James Stirling proved that every cubic was one of these four types.

For it, outcome A was that six dice are tossed with at least one six appearing, outcome B that twelve dice are tossed with at least two sixes appearing, and outcome C in which eighteen dice are tossed with at least three sixes appearing.

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

Newton was probably first to develop a system of polar coordinates in a strictly analytic sense, with his work in relation to the topic being superior, in both generality and flexibility, to any other during his lifetime.

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

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- (cid:8) WhatabouttheEinstein-Hilbertaction?Let’stryS= R αβ ∗(eαeβ).Again,theansweriseasytoguess.We needad-formtointegrateover,involving1powerofthecurvature2-formandnopowerofderivative.Toobtain ad-form,wemultiplythecurvature2-formbya(d−2)-form:theonlypossibilityinthiscontextisthestarofthe 2-formeαeβ.Again,betweenusfriends,doyoudoubtthis?Okay,let’scheck(but,tosavewritingandtospare youthestreamofindices,onlyfor4-dimensionalspacetime): (cid:12) (cid:14) (cid:12) (cid:14)(cid:12) √ (cid:14) R ∗ eαeβ = R dxωdxψ (cid:8) μν −geαeβdxρdxσ αβ αβωψ ρσ μ ν √ √ =R (cid:8) μν −gdxωdxψdxρdxσ=R (cid:8) μν −g(cid:8)ωψρσd4x μνωψ ρσ μνωψ ρσ √ √ =R μνωψ gμωgνψ −gd4x= −gd4xR (16) (usingthegeneralizationof(6)andagainignoringoverallnumericalfactors),asexpected.
- IsuspectthatmanyreadersprobablyfirstencounteredtheEulercharacteristic,likeme,inapopularbookof mathematics.Forme,itwasarealeyeopener.First,letuslookattheempiricaldata.Thecubehas8verticesor corners,12edges(4onthetop,4onthebottom,and4ontheside),and6faces.Hence,V =8,E=12,F=6.
- TheEulercharacteristicisevidentlyatopologicalquantity.Wecanlengthenandshortentheedgesofthe tetrahedrawearegluingtogetherwithoutchangingV,E,andF.
- Thus,(cid:10)F=+4−2=2.Similarly,wecanseethat(cid:10)V =+4−3=1and(cid:10)E=+6−3=3.Hence,wehave (cid:10)χ=(cid:10)V −(cid:10)E+(cid:10)F=1−3+2=0.Nowwecangluezillionsofthesetetrahedratogethertoapproximate anyobjectwelike.Ateverygluing,theEulercharacteristicdoesnotchange.Henceχ=2foranysphericallookingblob.ThediscussionmakesclearthatwearecountingtheV,E,andF onthesurface.(Theinteriorof theobject,consistingofthefaceswehavegluedtogetherandtheiredgesandvertices,hasbeen“lostforever,” sotospeak.)Throughout,wewillbestudyingasurfaceora2-manifold,notthe3-dimensionalblobenclosedby thesurface.

(cid:8) WhatabouttheEinstein-Hilbertaction?Let’stryS= R αβ ∗(eαeβ).Again,theansweriseasytoguess.We needad-formtointegrateover,involving1powerofthecurvature2-formandnopowerofderivative.Toobtain ad-form,wemultiplythecurvature2-formbya(d−2)-form:theonlypossibilityinthiscontextisthestarofthe 2-formeαeβ.Again,betweenusfriends,doyoudoubtthis?Okay,let’scheck(but,tosavewritingandtospare youthestreamofindices,onlyfor4-dimensionalspacetime): (cid:12) (cid:14) (cid:12) (cid:14)(cid:12) √ (cid:14) R ∗ eαeβ = R dxωdxψ (cid:8) μν −geαeβdxρdxσ αβ αβωψ ρσ μ ν √ √ =R (cid:8) μν −gdxωdxψdxρdxσ=R (cid:8) μν −g(cid:8)ωψρσd4x μνωψ ρσ μνωψ ρσ √ √ =R μνωψ gμωgνψ −gd4x= −gd4xR (16) (usingthegeneralizationof(6)andagainignoringoverallnumericalfactors),asexpected.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Archived (https://web.archive.org/web/20230807122526/https://pictures.royalsocie ty.org/image-rs-8492) from the original on 7 August 2023.
- Science: A History; 1543–2001 (https://archive.org/details/isbn_9780713997 316/page/164).
- "Isaac Newton and Astrology: Witness for the Defence or for the Prosecution?" (https://webspace.science.uu.nl/~gent0113/astrology/newton.htm).
- "14" (https://archive.org/stream/lettersonenglan00voltgoog#page/n102).

Archived (https://web.archive.org/web/20230807122526/https://pictures.royalsocie ty.org/image-rs-8492) from the original on 7 August 2023.

Science: A History; 1543–2001 (https://archive.org/details/isbn_9780713997 316/page/164).

"Isaac Newton and Astrology: Witness for the Defence or for the Prosecution?" (https://webspace.science.uu.nl/~gent0113/astrology/newton.htm).

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- doi:10.1103/PhysRevLett.82.896 (https://doi.org/10.1103%2FPhysRevLett.82.896).
- Princeton, NJ: Princeton University Press.
- "Michelson-Morley Experiment".
- Physical Review Letters (Submitted manuscript).

Aether (classical element) - Wikipedia.pdf

Princeton, NJ: Princeton University Press.

Physical Review Letters (Submitted manuscript).

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:
- If one measures with respect to and the other , they never see the outcomes However, sometimes they see the outcome when measuring with respect to , since This leads to the paradox: having the outcome we conclude that if one of the experimenters had measured with respect to the basis instead, the outcome must have been or , since and
- (For brevity, here and henceforth "local theory" means "local hidden variables theory".) However, quantum mechanics permits an even stronger violation of local theories: a possibilistic one, in which local theories cannot even agree with quantum mechanics on which events are possible or impossible in an entangled scenario.
- Experimentalists such as Alain Aspect have verified the quantum violation of the CHSH inequality [1] as well as other formulations of Bell's inequality, to invalidate the local hidden variables hypothesis and confirm that reality is indeed nonlocal in the EPR sense.
- Possibilistic nonlocality Bell's demonstration is probabilistic in the sense that it shows that the precise probabilities predicted by quantum mechanics for some entangled scenarios cannot be met by a local hidden variable theory.

If one measures with respect to and the other , they never see the outcomes However, sometimes they see the outcome when measuring with respect to , since This leads to the paradox: having the outcome we conclude that if one of the experimenters had measured with respect to the basis instead, the outcome must have been or , since and

(For brevity, here and henceforth "local theory" means "local hidden variables theory".) However, quantum mechanics permits an even stronger violation of local theories: a possibilistic one, in which local theories cannot even agree with quantum mechanics on which events are possible or impossible in an entangled scenario.

Experimentalists such as Alain Aspect have verified the quantum violation of the CHSH inequality [1] as well as other formulations of Bell's inequality, to invalidate the local hidden variables hypothesis and confirm that reality is indeed nonlocal in the EPR sense.

Possibilistic nonlocality Bell's demonstration is probabilistic in the sense that it shows that the precise probabilities predicted by quantum mechanics for some entangled scenarios cannot be met by a local hidden variable theory.

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 equations for neutrinos are equations (35.47), generalizing the scalar neutrino equations (33.91).
- 2 lm lm lm Collisions (before neutrino decoupling in
- These generalize the lm lm lm scalar Boltzmann equations (33.81) for unpolarized photons.
- TheBoltzmannequationsforpolarizedphotonsaregivenbyequations(35.45),withgravitationalredshift source terms G (not to be confused with the Einstein tensor) given by equations (35.41), and Thomsonlm scattering collision terms C[Θ ], C[E ], and C[B ] given by equations (35.68).

The Boltzmann equations for neutrinos are equations (35.47), generalizing the scalar neutrino equations (33.91).

2 lm lm lm Collisions (before neutrino decoupling in

These generalize the lm lm lm scalar Boltzmann equations (33.81) for unpolarized photons.

TheBoltzmannequationsforpolarizedphotonsaregivenbyequations(35.45),withgravitationalredshift source terms G (not to be confused with the Einstein tensor) given by equations (35.41), and Thomsonlm scattering collision terms C[Θ ], C[E ], and C[B ] given by equations (35.68).

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:
- Further reading The following titles, all by working physicists, attempt to communicate quantum theory to laypeople, using a minimum of technical apparatus.
- Brian Cox and Jeff Forshaw (2011) The Quantum Universe.
- arXiv:quant-ph/9801014 (https://arxiv.org/abs/quant-ph/9801014).
- Tokyo: Japan Physical Society.

Introduction to quantum mechanics - Wikipedia.pdf

Further reading The following titles, all by working physicists, attempt to communicate quantum theory to laypeople, using a minimum of technical apparatus.

Brian Cox and Jeff Forshaw (2011) The Quantum Universe.

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:
- An affine basis define barycentric coordinates for every point.
- Many other coordinates systems can be defined on a Euclidean space E of dimension n, in the following way.
- It preserves also the inner product since An isometry of Euclidean vector spaces is a linear isomorphism.[c][8]
- Isometries An isometry between two metric spaces is a bijection preserving the distance,[b] that is In the case of a Euclidean vector space, an isometry that maps the origin to the origin preserves the norm since the norm of a vector is its distance from the zero vector.

An affine basis define barycentric coordinates for every point.

Many other coordinates systems can be defined on a Euclidean space E of dimension n, in the following way.

It preserves also the inner product since An isometry of Euclidean vector spaces is a linear isomorphism.[c][8]

Isometries An isometry between two metric spaces is a bijection preserving the distance,[b] that is In the case of a Euclidean vector space, an isometry that maps the origin to the origin preserves the norm since the norm of a vector is its distance from the zero vector.

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:
- When they brought a metallized sphere close up to the plate, the attractive Casimir force between the two objects made the plate rotate.
- They also studied the dynamical behaviour of the MEMS device by making the plate oscillate.
- The Casimir force reduced the rate of oscillation and led to nonlinear phenomena, such as hysteresis and bistability in the frequency response of the oscillator.
- According to the team, the system's behaviour agreed well with theoretical calculations.[64] The Casimir effect shows that quantum field theory allows the energy density in very small regions of space to be negative relative to the ordinary vacuum energy, and the energy densities cannot be arbitrarily negative as the theory breaks down at atomic distances.[65]: 175 [66][67] Such prominent

When they brought a metallized sphere close up to the plate, the attractive Casimir force between the two objects made the plate rotate.

They also studied the dynamical behaviour of the MEMS device by making the plate oscillate.

The Casimir force reduced the rate of oscillation and led to nonlinear phenomena, such as hysteresis and bistability in the frequency response of the oscillator.

According to the team, the system's behaviour agreed well with theoretical calculations.[64] The Casimir effect shows that quantum field theory allows the energy density in very small regions of space to be negative relative to the ordinary vacuum energy, and the energy densities cannot be arbitrarily negative as the theory breaks down at atomic distances.[65]: 175 [66][67] Such prominent

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:
- However, this was considered merely a mathematical trick.[3]: 18 Fields began to take on an existence of their own with the development of electromagnetism in the 19th century.
- He introduced fields as properties of space (even when it is devoid of matter) having physical effects.
- This description of fields remains to this day.[2][4]: 301 [5]: 2 The theory of classical electromagnetism was completed in 1864 with Maxwell's equations, which described the relationship between the electric field, the magnetic field, electric current, and electric charge.
- Michael Faraday coined the English term "field" in 1845.

However, this was considered merely a mathematical trick.[3]: 18 Fields began to take on an existence of their own with the development of electromagnetism in the 19th century.

He introduced fields as properties of space (even when it is devoid of matter) having physical effects.

This description of fields remains to this day.[2][4]: 301 [5]: 2 The theory of classical electromagnetism was completed in 1864 with Maxwell's equations, which described the relationship between the electric field, the magnetic field, electric current, and electric charge.

Michael Faraday coined the English term "field" in 1845.

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:
- indicates that the right partner of each product is a row spinor, [ε ,ε ]· = ε ε⊤ ·−ε ε⊤ ·.
- Similarly the antisymmetric outer products of left-handed spinors form a U↓ V↑ U↓ V↑ V↑ U↓ left-handed scalar singlet, [ε ,ε ]·= 1(1−γ ) .
- (39.63) U↑ U↑ u+ U↑ V↓ 2 vu +− V↓ V↓ v− In the chiral representation (39.13), the 8 outer products of basis spinors of opposite chirality map to odd multivectorsofthespacetimealgebraasfollows.Again,theboostandspinweightsoftheleftandrighthand
- (39.62) V↑ V↑ v+ V↑ U↓ 2 vu +− U↓ U↓ u− The symmetric outer products of left-handed spinors form a triplet of left-handed bivectors, {ε ,ε }·=−γγ , {ε ,ε }·=−1(γγ +γγ ) , {ε ,ε }·=γγ .

indicates that the right partner of each product is a row spinor, [ε ,ε ]· = ε ε⊤ ·−ε ε⊤ ·.

Similarly the antisymmetric outer products of left-handed spinors form a U↓ V↑ U↓ V↑ V↑ U↓ left-handed scalar singlet, [ε ,ε ]·= 1(1−γ ) .

(39.63) U↑ U↑ u+ U↑ V↓ 2 vu +− V↓ V↓ v− In the chiral representation (39.13), the 8 outer products of basis spinors of opposite chirality map to odd multivectorsofthespacetimealgebraasfollows.Again,theboostandspinweightsoftheleftandrighthand

(39.62) V↑ V↑ v+ V↑ U↓ 2 vu +− U↓ U↓ u− The symmetric outer products of left-handed spinors form a triplet of left-handed bivectors, {ε ,ε }·=−γγ , {ε ,ε }·=−1(γγ +γγ ) , {ε ,ε }·=γγ .

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:
- Magnificent Principia: Exploring Isaac Newton's Masterpiece (https://books.go ogle.com/books?id=lRhnAAAAQBAJ&pg=PA11).
- The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism.
- A Biographical Sketch of Sir Isaac Newton (https://books.google.
- Archived (htt ps://web.archive.org/web/20170812011359/http://news.bbc.co.uk/1/hi/sci/tech/541840.stm) from the original on 12 August 2017.

Magnificent Principia: Exploring Isaac Newton's Masterpiece (https://books.go ogle.com/books?id=lRhnAAAAQBAJ&pg=PA11).

The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism.

A Biographical Sketch of Sir Isaac Newton (https://books.google.

Archived (htt ps://web.archive.org/web/20170812011359/http://news.bbc.co.uk/1/hi/sci/tech/541840.stm) from the original on 12 August 2017.

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:
- Journal of Mathematical Physics.
- Bibcode:1973JMP....14.1017P (https://ui.adsabs.harvard.edu/abs/1973JMP....14.1017P).
- ISSN 0022-2488 (https://search.
- doi:10.1063/1.1666431 (https://doi.org/10.1063%2F1.1666431).

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 beautiful stone ring shone like silver in the middle of lines of computers and machines.
- The scientist started a strange-looking machine on wheels.
- The scientist was watching another computer.
- It's harder than anythingonEarth.' 'Okay, let's see ifjackson's right,' West said to a scientist at a computer.A machine moved the seven signsround the ring.'Stop!' said the scientist,watching the computer.When the last sign came to its place, there was a sudden noise, like a strange music.

The beautiful stone ring shone like silver in the middle of lines of computers and machines.

The scientist started a strange-looking machine on wheels.

The scientist was watching another computer.

It's harder than anythingonEarth.' 'Okay, let's see ifjackson's right,' West said to a scientist at a computer.A machine moved the seven signsround the ring.'Stop!' said the scientist,watching the computer.When the last sign came to its place, there was a sudden noise, like a strange music.

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:
- You’re not who you say you are.
- “What’s happening?” “We’re going to finish what we started the night you returned.
- “I want to leave.” “And I want you to start telling the truth.” “I told you the truth.” “No, you told Daniela Vargas the truth.” On the other side of the glass, a door opens and a man staggers into the theater, led by one of the guards clutching the back of his neck.
- “Sit!” Leighton’s voice is as loud as a gunshot.

“What’s happening?” “We’re going to finish what we started the night you returned.

“I want to leave.” “And I want you to start telling the truth.” “I told you the truth.” “No, you told Daniela Vargas the truth.” On the other side of the glass, a door opens and a man staggers into the theater, led by one of the guards clutching the back of his neck.

“Sit!” Leighton’s voice is as loud as a gunshot.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- It remains for a complete theory of quantum gravity to solve this puzzle.
- Often linked to the arrow of time and our modern view of it
- Nevertheless, some semi-classical calculations had shown that some CTC’s do not do that [11].
- WormholePhysics QuantumWormholePhysics Summary When quantum correction to GR are taken into an account, closed timelike cures will not be stable.

It remains for a complete theory of quantum gravity to solve this puzzle.

Often linked to the arrow of time and our modern view of it

Nevertheless, some semi-classical calculations had shown that some CTC’s do not do that [11].

WormholePhysics QuantumWormholePhysics Summary When quantum correction to GR are taken into an account, closed timelike cures will not be stable.

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 exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by 10−21 or less.
- Einsteinian orbit (blue) The effect can also be derived by using either the exact of a lone planet orbiting a star.
- Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed.[85] Some exact solutions describe gravitational waves without any approximation, e.g., a wave train traveling through empty space[86] or Gowdy universes, varieties of an expanding cosmos filled with gravitational waves.[87] But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are the only way to construct appropriate models.[88] Ring of test particles deformed by a passing (linearized, amplified for better Orbital effects and the relativity of direction visibility) gravitational wave General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies.
- The influence of other planets is ignored.

the exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by 10−21 or less.

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

Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed.[85] Some exact solutions describe gravitational waves without any approximation, e.g., a wave train traveling through empty space[86] or Gowdy universes, varieties of an expanding cosmos filled with gravitational waves.[87] But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are the only way to construct appropriate models.[88] Ring of test particles deformed by a passing (linearized, amplified for better Orbital effects and the relativity of direction visibility) gravitational wave General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies.

The influence of other planets is ignored.

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:
- Action Comment 1 Light at 397 nm Doppler preparation 2 Light at 729 nm Sideband cooling 3 Light at 397 nm Optical pumping 4 R+(π/2,3π/2) Entangle ion #3 with motional qubit 5 RC(π,3π/2) Prepare ion #2 for entanglement elgnatnE 6 R+(π,π/2) Entangle ion #2 with ion #3 7 Wait for 1μs – 10000 μs Stand-by for teleportation 8 RH(π,0) Hide target ion 9 RC(θ ,φ ) Prepare source ion #1 in state χ 1 χ χ 10 R+(π,3π/2) Get motional qubit from ion #2 2 √ 11 R+(π/ 2,π/2) Composite pulse for phasegate 12 R+(π,0) Composite pulse for phasegate 1 √ 13 R+(π/ 2,π/2) Composite pulse for phasegate 14 R+(π,0) Composite pulse for phasegate 15 RC(π,π/2) Spin echo on ion #1 16 RH(π,π) Unhide ion #3 for spin echo 17 RC(π,π/2) Spin echo on ion #3 18 RH(π,0) Hide ion #3 again 19 R+(π,π/2) Write motional qubit back to ion #2 20 RC(π/2,3π/2) Part of rotation into Bell-basis sisab-lleB otni etatoR 21 RC(π/2,π/2) Finalize rotation into Bell basis 22 RH(π,0) Hide ion #2 23 PMDetection for 250 μs Read out ion #1 with photomultiplier 24 RH(π,0) Hide ion #1 25 RH(π,π) Unhide ion #2 26 PMDetection for 250 μs Read out ion #2 with photomultiplier tuo-daeR 27 RH(π,0) Hide ion #2 28 Wait 300 μs Let system rephase; part of spin echo 29 RH(π,π) Unhide ion #3 30 RC(π/2,3π/2+φ) Change basis 3 (cid:190) 31 RC(π,φ) iσ conditioned on 3 x =−iσ 32 RC(π,π/2+φ) -iσ z PMDetection #1 3 y -noceR noitcurts 33 RC(π,φ) iσ conditioned on PMDetection #2 3 x 34 RC(θ ,φ +π+φ) Inverse of preparation of χ with offset φ 3 χ χ 35 Light at 397 nm Read out of ion #3 with camera Table1: Toimplementtheteleportation,weusepulsesoncarriertransitionsRC(θ,φ) i and RH(θ,φ) (no change of the motional state of the ion crystal) and, additionally, i on the blue sideband R+(θ,φ) (change of the motional state) on ion i.
- The index i C denotes carrier transitions between the two logical eigenstates, while the index H labels transitions from the S (m =−1/2) to the D (m =−5/2)-level.
- For the 1/2 J 5/2 J definitions of RC,H,+(θ,φ) see the refs.

Action Comment 1 Light at 397 nm Doppler preparation 2 Light at 729 nm Sideband cooling 3 Light at 397 nm Optical pumping 4 R+(π/2,3π/2) Entangle ion #3 with motional qubit 5 RC(π,3π/2) Prepare ion #2 for entanglement elgnatnE 6 R+(π,π/2) Entangle ion #2 with ion #3 7 Wait for 1μs – 10000 μs Stand-by for teleportation 8 RH(π,0) Hide target ion 9 RC(θ ,φ ) Prepare source ion #1 in state χ 1 χ χ 10 R+(π,3π/2) Get motional qubit from ion #2 2 √ 11 R+(π/ 2,π/2) Composite pulse for phasegate 12 R+(π,0) Composite pulse for phasegate 1 √ 13 R+(π/ 2,π/2) Composite pulse for phasegate 14 R+(π,0) Composite pulse for phasegate 15 RC(π,π/2) Spin echo on ion #1 16 RH(π,π) Unhide ion #3 for spin echo 17 RC(π,π/2) Spin echo on ion #3 18 RH(π,0) Hide ion #3 again 19 R+(π,π/2) Write motional qubit back to ion #2 20 RC(π/2,3π/2) Part of rotation into Bell-basis sisab-lleB otni etatoR 21 RC(π/2,π/2) Finalize rotation into Bell basis 22 RH(π,0) Hide ion #2 23 PMDetection for 250 μs Read out ion #1 with photomultiplier 24 RH(π,0) Hide ion #1 25 RH(π,π) Unhide ion #2 26 PMDetection for 250 μs Read out ion #2 with photomultiplier tuo-daeR 27 RH(π,0) Hide ion #2 28 Wait 300 μs Let system rephase; part of spin echo 29 RH(π,π) Unhide ion #3 30 RC(π/2,3π/2+φ) Change basis 3 (cid:190) 31 RC(π,φ) iσ conditioned on 3 x =−iσ 32 RC(π,π/2+φ) -iσ z PMDetection #1 3 y -noceR noitcurts 33 RC(π,φ) iσ conditioned on PMDetection #2 3 x 34 RC(θ ,φ +π+φ) Inverse of preparation of χ with offset φ 3 χ χ 35 Light at 397 nm Read out of ion #3 with camera Table1: Toimplementtheteleportation,weusepulsesoncarriertransitionsRC(θ,φ) i and RH(θ,φ) (no change of the motional state of the ion crystal) and, additionally, i on the blue sideband R+(θ,φ) (change of the motional state) on ion i.

The index i C denotes carrier transitions between the two logical eigenstates, while the index H labels transitions from the S (m =−1/2) to the D (m =−5/2)-level.

For the 1/2 J 5/2 J definitions of RC,H,+(θ,φ) see the refs.

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:
- AsinExercise30.11,youmayfindthatyourintegrationroutinegetsstucktryingtointegratetheoscillating radiation monopole and dipole once the mode is well inside the horizon, kη ≫ 1.
- (30.145) m The proportionality (30.145) explains the origin of the scalar index n.
- Deduce the m matter power spectrum P (η ,k), equation (30.140), at the present time, η = η .
- The first factor δ /Φ is proportional to ak2; the second is a m function g(a) only of cosmic scale factor a; and the third is a function T (k) only of wavenumber k.

AsinExercise30.11,youmayfindthatyourintegrationroutinegetsstucktryingtointegratetheoscillating radiation monopole and dipole once the mode is well inside the horizon, kη ≫ 1.

(30.145) m The proportionality (30.145) explains the origin of the scalar index n.

Deduce the m matter power spectrum P (η ,k), equation (30.140), at the present time, η = η .

The first factor δ /Φ is proportional to ak2; the second is a m function g(a) only of cosmic scale factor a; and the third is a function T (k) only of wavenumber k.

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:
- (35.8) χ,ε The elliptic angle ε varies from ε=0 for pure right-circular polarization, to ε=π/4 for linear polarization, toε=π/2forpureleft-circularpolarization.Thepolarizationangleχistheanglebywhichthepolarization ellipse is rotated right-handedly from the 1-axis.
- In classical √ electromagnetism, a real wave is the real part of a complex wave (35.10), multiplied by 2 to get the mean-squared amplitude right.
- The mean-squared potential is ⟨A ̄ ·A⟩=⟨A ̄ ·A ⟩=A2 .
- Relation of the polarization vector to the electromagnetic potential.

(35.8) χ,ε The elliptic angle ε varies from ε=0 for pure right-circular polarization, to ε=π/4 for linear polarization, toε=π/2forpureleft-circularpolarization.Thepolarizationangleχistheanglebywhichthepolarization ellipse is rotated right-handedly from the 1-axis.

In classical √ electromagnetism, a real wave is the real part of a complex wave (35.10), multiplied by 2 to get the mean-squared amplitude right.

The mean-squared potential is ⟨A ̄ ·A⟩=⟨A ̄ ·A ⟩=A2 .

Relation of the polarization vector to the electromagnetic potential.

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 outermost electron in lithium orbits at roughly the Bohr radius, since the two inner
- This means that the innermost electrons orbit at approximately 1/2 the Bohr radius.
- For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at Z = 2.
- The electrons in outer orbits do not only orbit the nucleus, but they also move around the inner electrons, so the effective charge Z that they feel is reduced by the number of the electrons in the inner orbit.

The outermost electron in lithium orbits at roughly the Bohr radius, since the two inner

This means that the innermost electrons orbit at approximately 1/2 the Bohr radius.

For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at Z = 2.

The electrons in outer orbits do not only orbit the nucleus, but they also move around the inner electrons, so the effective charge Z that they feel is reduced by the number of the electrons in the inner orbit.

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:
- Should DOD find anything that revises these findings, we will appropriately share the information promptly with Congress, subject to classification and access limitations, so as to protect sensitive sources and methods.
- Senate and House Select Committees on Intelligence, describes the testimony that members of Congress and staffers have heard from individuals claiming first-hand knowledge of legacy, potentially illegal, UAP programs.36 The US government appears to know significantly more about UAPs than it is revealing.
- “They are stating that anything AARO is doing is involved in a law enforcement investigation,” he explained, which allows AARO to not release it.
- I refer you to the findings of AARO’s Historical Record Report Volume I, available on www.aaro.mil.

Should DOD find anything that revises these findings, we will appropriately share the information promptly with Congress, subject to classification and access limitations, so as to protect sensitive sources and methods.

Senate and House Select Committees on Intelligence, describes the testimony that members of Congress and staffers have heard from individuals claiming first-hand knowledge of legacy, potentially illegal, UAP programs.36 The US government appears to know significantly more about UAPs than it is revealing.

“They are stating that anything AARO is doing is involved in a law enforcement investigation,” he explained, which allows AARO to not release it.

I refer you to the findings of AARO’s Historical Record Report Volume I, available on www.aaro.mil.

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:
- Noether's most important contributions to mathematics were to the development of this new field, abstract algebra.[160] Background on abstract algebra and begriffliche Mathematik (conceptual mathematics) Two of the most basic objects in abstract algebra are groups and rings: A group consists of a set of elements and a single operation which combines a first and a second element and returns a third.
- The first operation must make the set a commutative group, and the second operation is associative and distributive with respect to the first operation.
- A field is defined as a commutative[f] division ring.
- For instance, the integers form a commutative ring whose elements are the integers, and the combining operations are addition and multiplication.

Noether's most important contributions to mathematics were to the development of this new field, abstract algebra.[160] Background on abstract algebra and begriffliche Mathematik (conceptual mathematics) Two of the most basic objects in abstract algebra are groups and rings: A group consists of a set of elements and a single operation which combines a first and a second element and returns a third.

The first operation must make the set a commutative group, and the second operation is associative and distributive with respect to the first operation.

A field is defined as a commutative[f] division ring.

For instance, the integers form a commutative ring whose elements are the integers, and the combining operations are addition and multiplication.

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 prologue, we saw how Einstein, through a thought experiment, showed that simultaneitymustfail.Inanotherelegantthoughtexperiment,Einsteinproposedaclock consisting of a pulse of light bouncing between two mirrors separated by distance L (figure1a).Hewas,afterall,apatentexaminerlivinginatimeoftechnologicalinnovations1 ofallsorts,includingever-betterchronometers.2Ms.Unprimehasoneofthesehigh-tech clockswithher.Foreachtick-tock,threeeventsoccur:A=lightleavesthelowermirror, B=lightbouncesoffthetopmirror,andC=lightarrivesbackatthelowermirror.
- (cid:5) (cid:5) Buthowdowedetermine(cid:10)x and(cid:10)t separately?
- Usethefabulouslyastonishingequationc=c!
- III.2 Einstein’s Clock and Lorentz’s Transformation Alice said, “In our country, there’s only one day at a time.” To whichtheRedQueenresponds,“That’sapoorthinwayofdoing things.Nowhere,wemostlyhavedaysandnightstwoorthree atatime,andsometimesinthewinterwetakeasmanyasfive nightstogether—forwarmth,youknow.” —LewisCarroll Thepatentclerkinventsaclock So,howarewetomodifytheGalileantransformationlawssothatthespeedoflightcdoes notobeytheeverydayunderstandingofhowvelocitiesadd?Somehow,particlesofmatter (myfriendsandI,andthefly,inthestoryfromthepreviouschapter)andparticlesoflight (thecamera’sflash)donottallythepassageoftimeandspaceinthesameway.

In the prologue, we saw how Einstein, through a thought experiment, showed that simultaneitymustfail.Inanotherelegantthoughtexperiment,Einsteinproposedaclock consisting of a pulse of light bouncing between two mirrors separated by distance L (figure1a).Hewas,afterall,apatentexaminerlivinginatimeoftechnologicalinnovations1 ofallsorts,includingever-betterchronometers.2Ms.Unprimehasoneofthesehigh-tech clockswithher.Foreachtick-tock,threeeventsoccur:A=lightleavesthelowermirror, B=lightbouncesoffthetopmirror,andC=lightarrivesbackatthelowermirror.

(cid:5) (cid:5) Buthowdowedetermine(cid:10)x and(cid:10)t separately?

III.2 Einstein’s Clock and Lorentz’s Transformation Alice said, “In our country, there’s only one day at a time.” To whichtheRedQueenresponds,“That’sapoorthinwayofdoing things.Nowhere,wemostlyhavedaysandnightstwoorthree atatime,andsometimesinthewinterwetakeasmanyasfive nightstogether—forwarmth,youknow.” —LewisCarroll Thepatentclerkinventsaclock So,howarewetomodifytheGalileantransformationlawssothatthespeedoflightcdoes notobeytheeverydayunderstandingofhowvelocitiesadd?Somehow,particlesofmatter (myfriendsandI,andthefly,inthestoryfromthepreviouschapter)andparticlesoflight (thecamera’sflash)donottallythepassageoftimeandspaceinthesameway.

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:
- My words are beginning to sound slurred.
- And there was a time when it could have been.” “You killed your ambition, didn’t you?” “It died of natural causes.
- I know you don’t understand, but there’s so much I want to ask.” “About what?” “What it’s like to be you.” “What do you mean?” He hesitates, then: “How do you feel about your place in the world, Jason?” I say slowly, deliberately, “That’s an interesting question considering the night you’ve put me through.” “Are you happy in your life?” In the shadow of this moment, my life is achingly beautiful.
- Of neglect.” “And do you know exactly how that happened?

My words are beginning to sound slurred.

And there was a time when it could have been.” “You killed your ambition, didn’t you?” “It died of natural causes.

I know you don’t understand, but there’s so much I want to ask.” “About what?” “What it’s like to be you.” “What do you mean?” He hesitates, then: “How do you feel about your place in the world, Jason?” I say slowly, deliberately, “That’s an interesting question considering the night you’ve put me through.” “Are you happy in your life?” In the shadow of this moment, my life is achingly beautiful.

Of neglect.” “And do you know exactly how that happened?

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:
- It is the nuclei that make up the really massive portion of matter, and it is they that are the true contributors to the mass of any object.
- Within the electronic fluid, nuclei can move freely and can approach each other more closely, as closely as chance dictates.
- Degenerate matter can be much denser than ordinary matter.
- Matter in which the electron shells are broken and in which the nuclei move about in an electronic fluid is called degenerate matter.

It is the nuclei that make up the really massive portion of matter, and it is they that are the true contributors to the mass of any object.

Within the electronic fluid, nuclei can move freely and can approach each other more closely, as closely as chance dictates.

Degenerate matter can be much denser than ordinary matter.

Matter in which the electron shells are broken and in which the nuclei move about in an electronic fluid is called degenerate 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:
- "One step closer: UW-Madison scientists help explain scarcity of antimatter" (https://web.archive.org/web/20121228043843/http://www.news.wisc.edu/2 1376).
- S2CID 119233888 (https://api.semanticscholar.o rg/CorpusID:119233888).
- Cosmology: The Science of the Universe (https://books.google.c om/books?id=wzpKc3bZqDoC) (2nd ed.).
- "Negative Numbers And Antimatter Particles".

"One step closer: UW-Madison scientists help explain scarcity of antimatter" (https://web.archive.org/web/20121228043843/http://www.news.wisc.edu/2 1376).

S2CID 119233888 (https://api.semanticscholar.o rg/CorpusID:119233888).

Cosmology: The Science of the Universe (https://books.google.c om/books?id=wzpKc3bZqDoC) (2nd ed.).

"Negative Numbers And Antimatter Particles".

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:
- Astronomical Society of South Australia.
- "Synthesis of the elements in stars: forty years of progress" (http://au thors.library.caltech.edu/10255/1/WALrmp97.pdf) (PDF).
- External links "How To Decipher Classification Codes" (http://www.assa.org.au/sig/variables/classifications.asp).
- doi:10.1103/RevModPhys.69.995 (https://doi.org/10.1103%2FRevModPhys.69.995).

Astronomical Society of South Australia.

"Synthesis of the elements in stars: forty years of progress" (http://au thors.library.caltech.edu/10255/1/WALrmp97.pdf) (PDF).

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

EVIDENCE:
- If supersymmetry were a true symmetry of nature, then it must be a broken symmetry, and the energy of symmetry breaking must be higher than those achievable by present-day experiments.[1]: 797 [32]: 443 Other spacetimes The φ theory, QED, QCD, as well as the whole Standard Model all assume a (3+1)-dimensional Minkowski space (3 spatial and 1 time dimensions) as the background on which the quantum fields are defined.
- Supersymmetry All experimentally known symmetries in nature relate bosons to bosons and fermions to fermions.
- Supersymmetry also offers answers to the grand unification of all gauge coupling constants in the Standard Model as well as the nature of dark matter.[1]: 796–797 [44] Nevertheless, experiments have yet to provide evidence for the existence of supersymmetric particles.
- In a supersymmetric theory, every fermion has a bosonic superpartner and vice versa.[32]: 444 If supersymmetry is promoted to a local symmetry, then the resultant gauge theory is an extension of general relativity called supergravity.[43] Supersymmetry is a potential solution to many current problems in physics.

If supersymmetry were a true symmetry of nature, then it must be a broken symmetry, and the energy of symmetry breaking must be higher than those achievable by present-day experiments.[1]: 797 [32]: 443 Other spacetimes The φ theory, QED, QCD, as well as the whole Standard Model all assume a (3+1)-dimensional Minkowski space (3 spatial and 1 time dimensions) as the background on which the quantum fields are defined.

Supersymmetry All experimentally known symmetries in nature relate bosons to bosons and fermions to fermions.

Supersymmetry also offers answers to the grand unification of all gauge coupling constants in the Standard Model as well as the nature of dark matter.[1]: 796–797 [44] Nevertheless, experiments have yet to provide evidence for the existence of supersymmetric particles.

In a supersymmetric theory, every fermion has a bosonic superpartner and vice versa.[32]: 444 If supersymmetry is promoted to a local symmetry, then the resultant gauge theory is an extension of general relativity called supergravity.[43] Supersymmetry is a potential solution to many current problems in physics.

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:
- Psychologists refer to this phenomenon as differential item functioning, or DIF (Hunter & Schmidt, 2000).
- Today, most experts agree that the question of IQ test bias has been settled about as conclusively as any scientific controversy can be (Gottfredson, 1997, 2009; Jensen, 1980; Sackett et al., 2001; Sackett, Borneman, & Connelly, 2008).
- Fortunately, many researchers have studied the possibility that IQ test scores are biased against women or minorities.
- Two panels assembled by the National Academy of Science (Hartigan & Wigdor, 1989; Wigdor & Garner, 1982) and a Task Force of the American Psychological Association (Neisser et al., 1996), each of which contained individuals representing a diverse range of expertise and opinions, reached the same conclusion: There’s no evidence that IQ tests or other standardized tests, like the SAT, underpredict the performance of women or minorities.

Psychologists refer to this phenomenon as differential item functioning, or DIF (Hunter & Schmidt, 2000).

Today, most experts agree that the question of IQ test bias has been settled about as conclusively as any scientific controversy can be (Gottfredson, 1997, 2009; Jensen, 1980; Sackett et al., 2001; Sackett, Borneman, & Connelly, 2008).

Fortunately, many researchers have studied the possibility that IQ test scores are biased against women or minorities.

Two panels assembled by the National Academy of Science (Hartigan & Wigdor, 1989; Wigdor & Garner, 1982) and a Task Force of the American Psychological Association (Neisser et al., 1996), each of which contained individuals representing a diverse range of expertise and opinions, reached the same conclusion: There’s no evidence that IQ tests or other standardized tests, like the SAT, underpredict the performance of women or minorities.

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:
- Doppler-shift factor as its frequency, which he had previously shown to be true based on Maxwell's equations.[p 1] The first of Einstein's papers on this subject was "Does the Inertia of a Body Depend upon its Energy Content?" in 1905.[p 15] Although Einstein's argument in this paper is nearly universally accepted by physicists as correct, even self-evident, many authors over the years have suggested that it is wrong.[73] Other authors suggest that the argument was merely inconclusive because it relied on some implicit assumptions.[74] Einstein acknowledged the controversy over his derivation in his 1907 survey paper on special relativity.
- There he notes that it is problematic to rely on Maxwell's equations for the heuristic mass– energy argument.
- The argument in his 1905 paper can be carried out with the emission of any massless particles, but the Maxwell equations are implicitly used to make it obvious that the emission of light in particular can be achieved only by doing work.
- To emit electromagnetic waves, all you have to do is shake a charged particle, and this is clearly doing work, so that the emission is of energy.[p 16]

Doppler-shift factor as its frequency, which he had previously shown to be true based on Maxwell's equations.[p 1] The first of Einstein's papers on this subject was "Does the Inertia of a Body Depend upon its Energy Content?" in 1905.[p 15] Although Einstein's argument in this paper is nearly universally accepted by physicists as correct, even self-evident, many authors over the years have suggested that it is wrong.[73] Other authors suggest that the argument was merely inconclusive because it relied on some implicit assumptions.[74] Einstein acknowledged the controversy over his derivation in his 1907 survey paper on special relativity.

There he notes that it is problematic to rely on Maxwell's equations for the heuristic mass– energy argument.

The argument in his 1905 paper can be carried out with the emission of any massless particles, but the Maxwell equations are implicitly used to make it obvious that the emission of light in particular can be achieved only by doing work.

To emit electromagnetic waves, all you have to do is shake a charged particle, and this is clearly doing work, so that the emission is of energy.[p 16]

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:
- IX.8 Differential Forms Applied Calculatingcurvaturewithdifferentialforms In this chapter, I show you that differential forms provide a more efficient method to calculatecurvaturethanthemoretraditionalmethodoffirstworkingouttheChristoffel symbols.Thehumanmindappearstobeillevolvedtohandle3-indexedobjectslikethe ∗ Christoffelsymbols.Whiletheconnection1-formωalsonominallycarries3indices, the indices are actually of two types, and so in reality, you only have to handle either a 1indexedobjectora2-indexedobject,dependingonhowyoulookatit.Besides,the1-form ωαβ=ωαβdxμisantisymmetricinαβ,whileaChristoffelsymbolissymmetricinitstwo μ lowerindices.Ingeneral,anantisymmetricobject(lotsofvanishingcomponents!)ismuch easiertodealwiththanasymmetricone.
- It is easy to write a simple program to calculate the Riemann curvature tensor by brute force using the traditional method.Still,Cartan’smethodinvolvingdifferentialformsiswellworthlearning.
- First, let’s recall from the preceding chapter Cartan’s first and second structural equations: de+ωe=0 (1) and R=dω+ω2 (2) As the emphasis in this chapter is learning to compute with differential forms, I will writeitwithaminimumofproseconnectingtheequations.Youmightcallthischapter engineeringwithdifferentialforms.
- Peopleusedtoargueabouttherelativemeritsofthetwomethods,butwiththeadvent of symbolic manipulation software, the issue is now moot.

IX.8 Differential Forms Applied Calculatingcurvaturewithdifferentialforms In this chapter, I show you that differential forms provide a more efficient method to calculatecurvaturethanthemoretraditionalmethodoffirstworkingouttheChristoffel symbols.Thehumanmindappearstobeillevolvedtohandle3-indexedobjectslikethe ∗ Christoffelsymbols.Whiletheconnection1-formωalsonominallycarries3indices, the indices are actually of two types, and so in reality, you only have to handle either a 1indexedobjectora2-indexedobject,dependingonhowyoulookatit.Besides,the1-form ωαβ=ωαβdxμisantisymmetricinαβ,whileaChristoffelsymbolissymmetricinitstwo μ lowerindices.Ingeneral,anantisymmetricobject(lotsofvanishingcomponents!)ismuch easiertodealwiththanasymmetricone.

It is easy to write a simple program to calculate the Riemann curvature tensor by brute force using the traditional method.Still,Cartan’smethodinvolvingdifferentialformsiswellworthlearning.

First, let’s recall from the preceding chapter Cartan’s first and second structural equations: de+ωe=0 (1) and R=dω+ω2 (2) As the emphasis in this chapter is learning to compute with differential forms, I will writeitwithaminimumofproseconnectingtheequations.Youmightcallthischapter engineeringwithdifferentialforms.

Peopleusedtoargueabouttherelativemeritsofthetwomethods,butwiththeadvent of symbolic manipulation software, the issue is now moot.

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:2006PhP.....8..381B (https://ui.adsabs.harvard.edu/abs/2006PhP.....8..381B).
- com/1984/10/22/obituaries/paul-dirac-nobel-laureate-developed-theory-of-atom.html).
- 8 August 1902 – 20 October 1984" (ht tps://doi.org/10.1098%2Frsbm.1986.0006).
- doi:10.1098/rsbm.1986.0006 (https://doi.org/10.1098%2Frsbm.1986.0006).

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 nature of the annihilation products.
- While electron–positron reactions result in gamma ray photons, these are difficult to direct and use for thrust.
- In reactions between protons and antiprotons, their energy is converted largely into relativistic neutral and charged pions.
- The neutral pions decay almost immediately (with a lifetime of 85 attoseconds) into high-energy photons, but the charged pions decay more slowly (with a lifetime of 26 nanoseconds) and can be deflected magnetically to produce thrust.

the nature of the annihilation products.

While electron–positron reactions result in gamma ray photons, these are difficult to direct and use for thrust.

In reactions between protons and antiprotons, their energy is converted largely into relativistic neutral and charged pions.

The neutral pions decay almost immediately (with a lifetime of 85 attoseconds) into high-energy photons, but the charged pions decay more slowly (with a lifetime of 26 nanoseconds) and can be deflected magnetically to produce thrust.

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:
- "Onthological models predictively inequivalent to quantum theory".
- ncbi.nlm.nih.gov/pmc/articles/PMC3265370).
- Bibcode:1982AmJPh..50..807P (https://ui.adsabs.harvard.edu/abs/1982 AmJPh..50..807P).
- Bibcode:2013PhRvL.110q0404G (https://ui.adsabs.harvard.edu/abs/2013PhRvL.11 0q0404G).

"Onthological models predictively inequivalent to quantum theory".

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:
- y or, rationally A north-south opening hyperbola can be represented parametrically as or, rationally
- as the parameter t varies from 0 to 2π.
- Both parameterizations may be made rational by using the tangent half-angle formula and setting Lissajous curve A Lissajous curve is similar to an ellipse, but the x and y sinusoids are not in phase.
- Hyperbola An east-west opening hyperbola can be represented parametrically by A Lissajous curve where k = 3 and x k = 2.

y or, rationally A north-south opening hyperbola can be represented parametrically as or, rationally

Both parameterizations may be made rational by using the tangent half-angle formula and setting Lissajous curve A Lissajous curve is similar to an ellipse, but the x and y sinusoids are not in phase.

Hyperbola An east-west opening hyperbola can be represented parametrically by A Lissajous curve where k = 3 and x k = 2.

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:
- That is, two knots are isotopic when there exists a continuous function starting at t = 0 giving the K embedding, ending at t = 1 giving the K embedding, with all intermediate values corresponding to embeddings.
- identity map and f are isotopic because they can be connected by rotations.
- An ambient isotopy, studied in this context, is an isotopy of the larger space, considered in light of its action on the embedded submanifold.
- One may try to define knot equivalence based on isotopy instead of the more restricted property of ambient isotopy.

That is, two knots are isotopic when there exists a continuous function starting at t = 0 giving the K embedding, ending at t = 1 giving the K embedding, with all intermediate values corresponding to embeddings.

identity map and f are isotopic because they can be connected by rotations.

An ambient isotopy, studied in this context, is an isotopy of the larger space, considered in light of its action on the embedded submanifold.

One may try to define knot equivalence based on isotopy instead of the more restricted property of ambient isotopy.

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:
- PMC 6987450 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC698745 0).
- Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (reissued ed.).
- Andrew Forsyth (1930) Geometry of Four Dimensions (https://archive.org/details/geometryoffourdi032760mbp), link from Internet Archive.
- (2009), "Tesseract" (https://books.google.com/books?id=JrslMKTgSZwC&pg=PA282), The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publishing, p.

PMC 6987450 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC698745 0).

Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (reissued ed.).

Andrew Forsyth (1930) Geometry of Four Dimensions (https://archive.org/details/geometryoffourdi032760mbp), link from Internet Archive.

(2009), "Tesseract" (https://books.google.com/books?id=JrslMKTgSZwC&pg=PA282), The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publishing, p.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- In particular, her research was based almost entirely on potentially biased samples (she didn’t study a broad cross-section of the population), subjective observations, and unstandardized measurements of people’s emotions across time (BelloHass, Bene, & Mitsumoto, 2002; Friedman & James, 2008).
- Yet research evidence suggests that many dying people don’t pass through her stages in the same order (Copp, 1998).
- Kübler-Ross’s stages may be popular not merely because of the extensive media coverage they’ve attracted, but because they offer people a sense of predictability over the previously unpredictable—the process of dying (Copp, 1998; Kastenbaum, 1998).
- In retrospect, this largely negative scientific evidence shouldn’t have been all that surprising, because Kübler-Ross’s (1969) claims regarding her five stages weren’t based on carefully controlled research.

In particular, her research was based almost entirely on potentially biased samples (she didn’t study a broad cross-section of the population), subjective observations, and unstandardized measurements of people’s emotions across time (BelloHass, Bene, & Mitsumoto, 2002; Friedman & James, 2008).

Yet research evidence suggests that many dying people don’t pass through her stages in the same order (Copp, 1998).

Kübler-Ross’s stages may be popular not merely because of the extensive media coverage they’ve attracted, but because they offer people a sense of predictability over the previously unpredictable—the process of dying (Copp, 1998; Kastenbaum, 1998).

In retrospect, this largely negative scientific evidence shouldn’t have been all that surprising, because Kübler-Ross’s (1969) claims regarding her five stages weren’t based on carefully controlled research.

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:
- Diagram for quantum teleportation of a photon It is worth noticing that the above protocol assumes that the qubits are individually addressable, meaning that the qubits are distinguishable and physically labeled.
- Under this condition, the qubits cannot be individually controlled or measured.
- Nevertheless, a teleportation protocol analogous to that described above can still be (conditionally) implemented by exploiting two independently prepared qubits, with no need of an initial Bell state.
- However, there can be situations where two identical qubits are indistinguishable due to the spatial overlap of their wave functions.

Diagram for quantum teleportation of a photon It is worth noticing that the above protocol assumes that the qubits are individually addressable, meaning that the qubits are distinguishable and physically labeled.

Under this condition, the qubits cannot be individually controlled or measured.

Nevertheless, a teleportation protocol analogous to that described above can still be (conditionally) implemented by exploiting two independently prepared qubits, with no need of an initial Bell state.

However, there can be situations where two identical qubits are indistinguishable due to the spatial overlap of their wave functions.

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:
- share the same gauge fields (there are not multiplegenerationsofgaugefields),admitsthealternativehypothesisthatthe3generationsare,somehow, just different excitations of the same intrinsic object, similarly, perhaps, to that way that atoms and nuclei have excited states.
- 42.1.1 Spin(10) charges Spin(10) reorganizes the charges of the Standard Model in an interestingly different and elegant way.
- The usual SM charges are hypercharge Y and isospin I , and colours r, g, and b.
- Spin(10) reorganizes the 5 L charges as a bit code durgb with each bit (charge) taking values either +1 (↑) or −1 (↓) for each of the 2 2

share the same gauge fields (there are not multiplegenerationsofgaugefields),admitsthealternativehypothesisthatthe3generationsare,somehow, just different excitations of the same intrinsic object, similarly, perhaps, to that way that atoms and nuclei have excited states.

42.1.1 Spin(10) charges Spin(10) reorganizes the charges of the Standard Model in an interestingly different and elegant way.

The usual SM charges are hypercharge Y and isospin I , and colours r, g, and b.

Spin(10) reorganizes the 5 L charges as a bit code durgb with each bit (charge) taking values either +1 (↑) or −1 (↓) for each of the 2 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:
- WecanofcourseimmediatelyjumptoAdSd byreplacingintheprecedingdiscussion (cid:13) X2+Y2 by d−1(Xi)2, and so on and so forth, to obtain ds2=−(1+r2)dt2+ dr2 + i=1 1+r2 r2d(cid:24)2 .JustasinthedeSittercase(see(IX.10.35)),themetrichasthesameformds2= d−2 −f(r)dt2+f(r) −1dr2+r2d(cid:24)2 as the Schwarzschild metric.
- I offered a word of caution about figure IX.10.1; so two words of double caution about figure1.ItishardenoughtohavespatialintuitionaboutM3,1,letaloneM2,2.
- d−1 d−2 Theoriginalembeddingcoordinatesaregivenby T =coshρcost, W =coshρsint, X=sinhρcosθ, Y =sinhρsinθ (11)
- But instead of f(r)= d−2 1−r2inthedeSittercase,wenowhavef(r)=1+r2>0,andthusantideSitterspacetime doesnothaveahorizon.

WecanofcourseimmediatelyjumptoAdSd byreplacingintheprecedingdiscussion (cid:13) X2+Y2 by d−1(Xi)2, and so on and so forth, to obtain ds2=−(1+r2)dt2+ dr2 + i=1 1+r2 r2d(cid:24)2 .JustasinthedeSittercase(see(IX.10.35)),themetrichasthesameformds2= d−2 −f(r)dt2+f(r) −1dr2+r2d(cid:24)2 as the Schwarzschild metric.

I offered a word of caution about figure IX.10.1; so two words of double caution about figure1.ItishardenoughtohavespatialintuitionaboutM3,1,letaloneM2,2.

d−1 d−2 Theoriginalembeddingcoordinatesaregivenby T =coshρcost, W =coshρsint, X=sinhρcosθ, Y =sinhρsinθ (11)

But instead of f(r)= d−2 1−r2inthedeSittercase,wenowhavef(r)=1+r2>0,andthusantideSitterspacetime doesnothaveahorizon.

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

List tests or derivations implied by the evidence.