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

EVIDENCE:
- Certifying quantum teleportation When implementing the quantum teleportation protocol, different experimental noises may arise affecting the state transference.[39] The usual way to benchmark a particular teleportation procedure is by using the average fidelity: Given an arbitrary teleportation protocol producing output states with probability for an initial state , the average fidelity is defined as:[40] where the integration is performed over the Haar measure defined by assuming maximal uncertainty over the initial quantum states , and is the Uhlmann-Jozsa fidelity.
- After this operation, Bob's qubit will take on the state , and Alice's qubit becomes an (undefined) part of an entangled state.
- This points out a particular issue when
- For every qubit teleported, Alice needs to send Bob two classical bits of information.

Certifying quantum teleportation When implementing the quantum teleportation protocol, different experimental noises may arise affecting the state transference.[39] The usual way to benchmark a particular teleportation procedure is by using the average fidelity: Given an arbitrary teleportation protocol producing output states with probability for an initial state , the average fidelity is defined as:[40] where the integration is performed over the Haar measure defined by assuming maximal uncertainty over the initial quantum states , and is the Uhlmann-Jozsa fidelity.

After this operation, Bob's qubit will take on the state , and Alice's qubit becomes an (undefined) part of an entangled state.

For every qubit teleported, Alice needs to send Bob two classical bits of information.

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 units where the speed of light is one, c=1, Vermilion’s mirror in Figure 1.8 is one tick away from her, and from her point of view the vertical distance between Cerulean and his mirror is the same, one tick.
- They both agree that their clocksareidentical.Inthemiddlepanel,CeruleanismovingtotherightatspeedvrelativetoVermilion.Thevertical distance to the mirror is unchanged by Cerulean’s motion in a direction orthogonal to the direction to the mirror.
- 1.6 Lorentz transformation A Lorentz transformation is a rotation of space and time.
- Since the speed of light is constant, VermilionthinksCerulean’sclocktakeslongertotick,byafactorγ,thanherown.Thesidesofthetriangleformed by the distance 1 to the mirror, the length γ of the lightpath to Cerulean’s clock, and the distance γv travelled by Cerulean,formaright-angledtriangle,illustratedintherightpanel.

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

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

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

Generate falsification tests and identify unknowns or missing evidence.

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

In units where the speed of light is one, c=1, Vermilion’s mirror in Figure 1.8 is one tick away from her, and from her point of view the vertical distance between Cerulean and his mirror is the same, one tick.

They both agree that their clocksareidentical.Inthemiddlepanel,CeruleanismovingtotherightatspeedvrelativetoVermilion.Thevertical distance to the mirror is unchanged by Cerulean’s motion in a direction orthogonal to the direction to the mirror.

1.6 Lorentz transformation A Lorentz transformation is a rotation of space and time.

Since the speed of light is constant, VermilionthinksCerulean’sclocktakeslongertotick,byafactorγ,thanherown.Thesidesofthetriangleformed by the distance 1 to the mirror, the length γ of the lightpath to Cerulean’s clock, and the distance γv travelled by Cerulean,formaright-angledtriangle,illustratedintherightpanel.

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 Lagrangian of the charged field φ involves the torsion-free derivative D ̊ φ of the field.
- 16.5 Electromagnetic action Electromagnetism is a gauge field based on the simplest of all continuous groups, the 1-dimensional unitary group U(1) of rotations about a circle.
- To ensure that the Lagrangianremainsinvariantalsounderanelectromagneticgaugetransformation(16.19),thederivativeD ̊ μ must be augmented by an electromagnetic connection A , which equals the thing historically known as the μ electromagnetic potential.
- 16.5.1 Electromagnetic gauge transformations Under an electromagnetic gauge transformation, a field φ of charge e transforms as φ→e−ieθφ , (16.19) wherethephaseθ(x)issomearbitraryfunctionofspacetime.Thechargeeisdimensionless(inunitsc=(cid:126)= 1).

The Lagrangian of the charged field φ involves the torsion-free derivative D ̊ φ of the field.

16.5 Electromagnetic action Electromagnetism is a gauge field based on the simplest of all continuous groups, the 1-dimensional unitary group U(1) of rotations about a circle.

To ensure that the Lagrangianremainsinvariantalsounderanelectromagneticgaugetransformation(16.19),thederivativeD ̊ μ must be augmented by an electromagnetic connection A , which equals the thing historically known as the μ electromagnetic potential.

16.5.1 Electromagnetic gauge transformations Under an electromagnetic gauge transformation, a field φ of charge e transforms as φ→e−ieθφ , (16.19) wherethephaseθ(x)issomearbitraryfunctionofspacetime.Thechargeeisdimensionless(inunitsc=(cid:126)= 1).

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:
- To date, no other accurate method for measuring gravitational mass has been discovered.[20] Newton's cannonball Newton's cannonball was a thought experiment used to bridge the gap between Galileo's gravitational acceleration and Kepler's elliptical orbits.
- The mass of the Earth can be determined using Kepler's method (from the orbit of Earth's Moon), or it can be determined by measuring the gravitational acceleration on the Earth's surface, and multiplying that by the square of the Earth's radius.
- If the the Earth."[19]: 513 Newton further reasons that if an object speed is low, the cannonball quickly falls back to Earth (A, B).
- By finding the exact relationship between a body's gravitational mass and its gravitational field, Newton provided a second method for measuring gravitational mass.

To date, no other accurate method for measuring gravitational mass has been discovered.[20] Newton's cannonball Newton's cannonball was a thought experiment used to bridge the gap between Galileo's gravitational acceleration and Kepler's elliptical orbits.

The mass of the Earth can be determined using Kepler's method (from the orbit of Earth's Moon), or it can be determined by measuring the gravitational acceleration on the Earth's surface, and multiplying that by the square of the Earth's radius.

If the the Earth."[19]: 513 Newton further reasons that if an object speed is low, the cannonball quickly falls back to Earth (A, B).

By finding the exact relationship between a body's gravitational mass and its gravitational field, Newton provided a second method for measuring gravitational mass.

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:
- Solid lines indicate unstable orbits; dashed lines indicatestableorbits;longdashedlinesmarkthetransitionbetweenunstableandstableorbits.Theradiir− andr+ oftheinnerandouterhorizonsareshownforreference.
- Lines are labelled with values of the inclination parameter α, varying from equatorial orbits (α = 0) to polar orbits (α = 1).
- with + for prograde (aL > 0) orbits, − for retrograde (aL < 0) orbits.
- The azimuthal angular momentum p p J ≡L/E per unit energy on the photon sphere is, from equation (23.70a) in the limit P →±∞, p t R2−3Mr +2Q2+a2M/r J = p p p .

Solid lines indicate unstable orbits; dashed lines indicatestableorbits;longdashedlinesmarkthetransitionbetweenunstableandstableorbits.Theradiir− andr+ oftheinnerandouterhorizonsareshownforreference.

Lines are labelled with values of the inclination parameter α, varying from equatorial orbits (α = 0) to polar orbits (α = 1).

with + for prograde (aL > 0) orbits, − for retrograde (aL < 0) orbits.

The azimuthal angular momentum p p J ≡L/E per unit energy on the photon sphere is, from equation (23.70a) in the limit P →±∞, p t R2−3Mr +2Q2+a2M/r J = p p p .

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

EVIDENCE:
- For instance, the configuration of a screw can be described by five coordinates.[71] In general topology, the concept of dimension has been extended from natural numbers, to infinite dimension (Hilbert spaces, for example) and positive real numbers (in fractal geometry).[72] In algebraic geometry, the dimension of The Koch snowflake, with fractal dimension=log4/log3 and topological an algebraic variety has received a number of apparently dimension=1 different definitions, which are all equivalent in the most common cases.[73]
- Classically, the only instruments used in most geometric constructions are the compass and straightedge.[d] Also, every construction had to be complete in a finite number of steps.
- Dimension Traditional geometry allowed dimensions 1 (a line or curve), 2 (a plane or surface), and 3 (our ambient world conceived of as three-dimensional space).
- Congruence and similarity Congruence and similarity are concepts that describe when two shapes have similar characteristics.[67] In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape.[68] Hilbert, in his work on creating a more rigorous foundation for geometry, treated Visual checking of the Pythagorean congruence as an undefined term whose properties are theorem for the (3, 4, 5) triangle as in the defined by axioms.

For instance, the configuration of a screw can be described by five coordinates.[71] In general topology, the concept of dimension has been extended from natural numbers, to infinite dimension (Hilbert spaces, for example) and positive real numbers (in fractal geometry).[72] In algebraic geometry, the dimension of The Koch snowflake, with fractal dimension=log4/log3 and topological an algebraic variety has received a number of apparently dimension=1 different definitions, which are all equivalent in the most common cases.[73]

Classically, the only instruments used in most geometric constructions are the compass and straightedge.[d] Also, every construction had to be complete in a finite number of steps.

Dimension Traditional geometry allowed dimensions 1 (a line or curve), 2 (a plane or surface), and 3 (our ambient world conceived of as three-dimensional space).

Congruence and similarity Congruence and similarity are concepts that describe when two shapes have similar characteristics.[67] In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape.[68] Hilbert, in his work on creating a more rigorous foundation for geometry, treated Visual checking of the Pythagorean congruence as an undefined term whose properties are theorem for the (3, 4, 5) triangle as in the defined by axioms.

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:
- Observe that Alice does not need to communicate to Bob which gate to apply in order to obtain the correct classical bits from his projective measurement.
- In common usage the tensor product symbol may be omitted: .
- Alice and Bob may be in different locations, an unlimited distance from each other.
- The protocol starts with the preparation of an entangled state, which is later shared between Alice and Bob.

Observe that Alice does not need to communicate to Bob which gate to apply in order to obtain the correct classical bits from his projective measurement.

In common usage the tensor product symbol may be omitted: .

Alice and Bob may be in different locations, an unlimited distance from each other.

The protocol starts with the preparation of an entangled state, which is later shared between Alice and Bob.

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:
- Up on my feet, stunned, dazed, ears ringing, blood running down the side of my face.
- Crash face-first into pavement.
- It isn’t much of a hold, but it’s just enough to keep me from falling.
- Leighton appears in the open window frame above me.

Up on my feet, stunned, dazed, ears ringing, blood running down the side of my face.

It isn’t much of a hold, but it’s just enough to keep me from falling.

Leighton appears in the open window frame above me.

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:
- μ HereiswhereIthinkbeginnerscangetabitconfused.Ifyouhaveanymathsenseatall, youwouldexpectthatweusetheinverseofη,andyouwouldbeabsolutelyright.Surely, if you use η to move indices downstairs, you would use the inverse of η to move them upstairs.Buttheinverseofthematrix ⎛ ⎞ −1 0 0 0 ⎜ ⎟ ⎜ ⎜ 0 +1 0 0 ⎟ ⎟ ⎜ ⎟ ⎜ ⎝ 0 0 +1 0 ⎟ ⎠ 0 0 0 +1 isitself.Sotraditionally,theinverseofηisdenotedbythesamesymbol,butwithtwoupper indices, like this: ημν.
- 3 0 Thenextquestionmightbe:givenp ,howdowegetbacktopμ?
- We define ημν by η00=−1, η11=η22=η33=+1, and ημν=0 if μ(cid:7)=ν.
- MinkowskiandtheGeometryofSpacetime | 183 contravariant vectors (pμ for example) and covariant vectors (p for example), but let μ ∗ me assure the beginners that there is nothing terribly profound going on here.

μ HereiswhereIthinkbeginnerscangetabitconfused.Ifyouhaveanymathsenseatall, youwouldexpectthatweusetheinverseofη,andyouwouldbeabsolutelyright.Surely, if you use η to move indices downstairs, you would use the inverse of η to move them upstairs.Buttheinverseofthematrix ⎛ ⎞ −1 0 0 0 ⎜ ⎟ ⎜ ⎜ 0 +1 0 0 ⎟ ⎟ ⎜ ⎟ ⎜ ⎝ 0 0 +1 0 ⎟ ⎠ 0 0 0 +1 isitself.Sotraditionally,theinverseofηisdenotedbythesamesymbol,butwithtwoupper indices, like this: ημν.

3 0 Thenextquestionmightbe:givenp ,howdowegetbacktopμ?

We define ημν by η00=−1, η11=η22=η33=+1, and ημν=0 if μ(cid:7)=ν.

MinkowskiandtheGeometryofSpacetime | 183 contravariant vectors (pμ for example) and covariant vectors (p for example), but let μ ∗ me assure the beginners that there is nothing terribly profound going on here.

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:
- "Finding the Real Feynman" (http://tech.mit.edu/V119/N10/col10 lipman.10c.html).
- "Calisphere: Richard Feynman playing the conga drum" (https://calisphere.org/item/ca3d38126be 7f368422ee9a6e0870667/).
- "Saving the Feynman van" (https://www.symmetrymagazine.or g/article/may-2014/saving-the-feynman-van).
- Jepsen, Kathryn (August 5, 2014).

"Finding the Real Feynman" (http://tech.mit.edu/V119/N10/col10 lipman.10c.html).

"Calisphere: Richard Feynman playing the conga drum" (https://calisphere.org/item/ca3d38126be 7f368422ee9a6e0870667/).

"Saving the Feynman van" (https://www.symmetrymagazine.or g/article/may-2014/saving-the-feynman-van).

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:
- Because of the changing density in Earth's interior this is not quite so.
- The average density of the core is 10.7 g/cm3.
- This density rises further as one penetrates deeper into the core, and at the very center of the Earth it is something like 12 g/cm8.
- (Earlier in the book I said that if the Earth had an even density throughout, the gravitational pull would decline steadily as we penetrated beneath the surface and would reach zero at the center.

Because of the changing density in Earth's interior this is not quite so.

The average density of the core is 10.7 g/cm3.

This density rises further as one penetrates deeper into the core, and at the very center of the Earth it is something like 12 g/cm8.

(Earlier in the book I said that if the Earth had an even density throughout, the gravitational pull would decline steadily as we penetrated beneath the surface and would reach zero at the center.

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 coordinates of the event are different in a different reference frame.[18]: 67 inertial reference frame: a region of a reference frame where objects at rest with respect to the frame stay as rest, or if in uniform motion, stay in motion; also called a free-float frame.[10]: 31 prime system, frame, or coordinate.
- To emphasize the relationship between two systems of coordinates, both use the same x,y,z axes but one will be marked with a prime (') symbol.
- Events have coordinates x, y, z for space and t for time.
- The more technical background ideas include: spacetime: geometrical space and time considered together.[10]: 18 spacetime interval between two events: a measure of separation between events that incorporates both the spatial distance between them and the duration of time separating them:[10]: 9 coordinate system or reference frame: a way to locate events in spacetime.

The coordinates of the event are different in a different reference frame.[18]: 67 inertial reference frame: a region of a reference frame where objects at rest with respect to the frame stay as rest, or if in uniform motion, stay in motion; also called a free-float frame.[10]: 31 prime system, frame, or coordinate.

To emphasize the relationship between two systems of coordinates, both use the same x,y,z axes but one will be marked with a prime (') symbol.

Events have coordinates x, y, z for space and t for time.

The more technical background ideas include: spacetime: geometrical space and time considered together.[10]: 18 spacetime interval between two events: a measure of separation between events that incorporates both the spatial distance between them and the duration of time separating them:[10]: 9 coordinate system or reference frame: a way to locate events in spacetime.

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:
- produce closed timelike curves if the rotation rate were fast enough,[5] he did not prove this.
- But Hawking comments: "it can't be done with positive energy density everywhere!
- I can prove that to build a finite time machine, you need negative energy."[6] Hawking's argument appears in his 1992 paper on the chronology protection conjecture (though the argument is distinct from the conjecture itself, since the argument asserts that classical general relativity predicts a finite region containing closed timelike curves can only be created if there is a violation of the weak energy condition in that region, whereas the conjecture predicts that closed timelike curves will prove to be impossible in a future theory of quantum gravity which replaces general relativity).
- In the paper, he examines "the case that the causality violations appear in a finite

produce closed timelike curves if the rotation rate were fast enough,[5] he did not prove this.

But Hawking comments: "it can't be done with positive energy density everywhere!

I can prove that to build a finite time machine, you need negative energy."[6] Hawking's argument appears in his 1992 paper on the chronology protection conjecture (though the argument is distinct from the conjecture itself, since the argument asserts that classical general relativity predicts a finite region containing closed timelike curves can only be created if there is a violation of the weak energy condition in that region, whereas the conjecture predicts that closed timelike curves will prove to be impossible in a future theory of quantum gravity which replaces general relativity).

In the paper, he examines "the case that the causality violations appear in a finite

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 relevance of this quantity is discussed in §21.10.
- The Weyl curvature scalar hits the Planck scale, |C|=1, while the baryonic proper density ρ is still well below the Planck density, so this singularity is curvature-dominated.
- The mass is M∙ =4×106M⊙, the accretion rate is M ̇ ∙ =10−16, and the equation of stateisw b =0.32.TherightpanelshowsaPenrosediagramofthemodel.
- The b mass and accretion rate have been taken to be M =4×106M , M ̇ =10−16 , (21.14) ∙ ⊙ ∙ whicharemotivatedbythefactthatthemassofthesupermassiveblackholeatthecentreoftheMilkyWay is 4×106M , and its accretion rate is of order (Planck units are c=G=(cid:126)=1) ⊙ Mass of MW black hole 4×106M 6×1060 Planck units ≈ ⊙ ≈ ≈10−16 .

The relevance of this quantity is discussed in §21.10.

The Weyl curvature scalar hits the Planck scale, |C|=1, while the baryonic proper density ρ is still well below the Planck density, so this singularity is curvature-dominated.

The mass is M∙ =4×106M⊙, the accretion rate is M ̇ ∙ =10−16, and the equation of stateisw b =0.32.TherightpanelshowsaPenrosediagramofthemodel.

The b mass and accretion rate have been taken to be M =4×106M , M ̇ =10−16 , (21.14) ∙ ⊙ ∙ whicharemotivatedbythefactthatthemassofthesupermassiveblackholeatthecentreoftheMilkyWay is 4×106M , and its accretion rate is of order (Planck units are c=G=(cid:126)=1) ⊙ Mass of MW black hole 4×106M 6×1060 Planck units ≈ ⊙ ≈ ≈10−16 .

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:
- diagrams provided a way to make predictions with QED by finding a probability amplitude for each possible way that an interaction could occur.
- The diagrams showed in particular that the electromagnetic force is the exchange of photons between interacting particles.[52] The Lamb shift is an example of a quantum electrodynamics prediction that has been experimentally verified.
- It is an effect whereby the quantum nature of the electromagnetic field makes the energy levels in an atom or ion deviate slightly from what they would otherwise be.
- As a result, spectral lines may shift or split.

Introduction to quantum mechanics - Wikipedia.pdf

diagrams provided a way to make predictions with QED by finding a probability amplitude for each possible way that an interaction could occur.

The diagrams showed in particular that the electromagnetic force is the exchange of photons between interacting particles.[52] The Lamb shift is an example of a quantum electrodynamics prediction that has been experimentally verified.

It is an effect whereby the quantum nature of the electromagnetic field makes the energy levels in an atom or ion deviate slightly from what they would otherwise be.

As a result, spectral lines may shift or split.

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:
- WKB solution of equations such T as (32.76) was discussed in §32.5.
- (32.84) Thus the effect of dissipation is to damp temperature fluctuations exponentially at scales smaller than the diffusion scale k .
- (32.77) 9 15 The terms proportional to the linear derivative d/dη in equation (32.76) are damping terms, which may s be collected into an overall damping coefficient κ, ( d2 +2κ d +k2 ) (Θ −Φ)=−k2[ (1+R)Ψ+Φ ] .
- (32.78) dη2 dη 0 s s The damping coefficient κ is a sum of adiabatic κ and dissipative κ parts, a d 1dlnc k2c ( 16 R2 ) κ≡κ +κ , κ =− s , κ = s + .

WKB solution of equations such T as (32.76) was discussed in §32.5.

(32.84) Thus the effect of dissipation is to damp temperature fluctuations exponentially at scales smaller than the diffusion scale k .

(32.77) 9 15 The terms proportional to the linear derivative d/dη in equation (32.76) are damping terms, which may s be collected into an overall damping coefficient κ, ( d2 +2κ d +k2 ) (Θ −Φ)=−k2[ (1+R)Ψ+Φ ] .

(32.78) dη2 dη 0 s s The damping coefficient κ is a sum of adiabatic κ and dissipative κ parts, a d 1dlnc k2c ( 16 R2 ) κ≡κ +κ , κ =− s , κ = s + .

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- But in the late 19th century the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance they called "aether", which, they postulated, would act as the medium through which these waves, or vibrations, propagated (in many respects similar to the way sound propagates through air).
- Therefore, S and S′ are not comoving.
- frames that move at the same speed in the same direction are said to be comoving.
- The results of various experiments, including the Michelson–Morley experiment in 1887

But in the late 19th century the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance they called "aether", which, they postulated, would act as the medium through which these waves, or vibrations, propagated (in many respects similar to the way sound propagates through air).

frames that move at the same speed in the same direction are said to be comoving.

The results of various experiments, including the Michelson–Morley experiment in 1887

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:
- Equation (23.38) comes from R4{ −P2+ [ Q+(L−aE)2+m2ρ2] Δ } =−R4P2 ≤ 0 , (23.42) t x x x and taking the limit r →0.
- Kerr-Newman case: show that if Q2 > 0 and a2 > 0, then a particle can reach the singularity only if ∙ L=aE and it is moving in the equatorial plane, and if the particle’s charge-to-mass is large enough, √ Q2+a2 |q| ≥ |m| ∙ , (23.40) Q2 ∙ which generalizes the Reissner-Nordström condition (23.39).
- 23.7 Carter integral Q 671 In particular, a neutral particle reaches the singularity only if it has zero angular momentum and is massless.
- Equation (23.37) comes from P2+P2 P2 K= y φ +m2ρ2 ≥ φ , (23.41) Δ y Δ y y and taking the limit y →0.

Equation (23.38) comes from R4{ −P2+ [ Q+(L−aE)2+m2ρ2] Δ } =−R4P2 ≤ 0 , (23.42) t x x x and taking the limit r →0.

Kerr-Newman case: show that if Q2 > 0 and a2 > 0, then a particle can reach the singularity only if ∙ L=aE and it is moving in the equatorial plane, and if the particle’s charge-to-mass is large enough, √ Q2+a2 |q| ≥ |m| ∙ , (23.40) Q2 ∙ which generalizes the Reissner-Nordström condition (23.39).

23.7 Carter integral Q 671 In particular, a neutral particle reaches the singularity only if it has zero angular momentum and is massless.

Equation (23.37) comes from P2+P2 P2 K= y φ +m2ρ2 ≥ φ , (23.41) Δ y Δ y y and taking the limit y →0.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Equations (10.91) and (10.92) imply that the luminosity distance d is related to the circumferential L distance x and the redshift z by d =(1+z)x .
- A magnitude is a logarithmic measure of brightness, defined such that an interval of 5 magnitudes m corresponds to a factor of 100 in linear flux F.
- 10.19.2 Magnitudes The Hubble diagram of Type Ia supernova shown in Figure 10.1 has for its vertical axis the astronomers’ system of magnitudes, a system that dates back to the 2nd century BC Greek astronomer Hipparchus.
- 10.19 Hubble diagram 253 by 4πd2, L L F = .

Equations (10.91) and (10.92) imply that the luminosity distance d is related to the circumferential L distance x and the redshift z by d =(1+z)x .

A magnitude is a logarithmic measure of brightness, defined such that an interval of 5 magnitudes m corresponds to a factor of 100 in linear flux F.

10.19.2 Magnitudes The Hubble diagram of Type Ia supernova shown in Figure 10.1 has for its vertical axis the astronomers’ system of magnitudes, a system that dates back to the 2nd century BC Greek astronomer Hipparchus.

10.19 Hubble diagram 253 by 4πd2, L L F = .

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:
- Greek indices may take the values: 0, 1, 2, 3 and the summation convention is used for repeated indices and .
- The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this
- or falling particle always moves along a geodesic.
- the proper time), and are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) which is symmetric in the two lower indices.

Greek indices may take the values: 0, 1, 2, 3 and the summation convention is used for repeated indices and .

The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this

or falling particle always moves along a geodesic.

the proper time), and are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) which is symmetric in the two lower indices.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Any quantity that vanishes in the unperturbed ε background has, to linear order, vanishing Lie derivative, therefore is coordinate gauge-invariant.
- 27.2 Metric, tetrad connections, and Einstein and Weyl tensors 735 gauge-invariance of the tetrad connections follows more fundamentally from the fact that any quantity that vanishes in the unperturbed background is coordinate gauge-invariant.
- The unperturbed Einstein tensor G vanishes identically.
- (27.17) m ∂t2 All the perturbations G of the Einstein tensor are both coordinate and tetrad gauge-invariant, as follows mn fromthefactthattheexpressions(27.16)dependonlyonthecoordinateandtetradgauge-invariantpotentials Ψ, Φ, W , and h .

Any quantity that vanishes in the unperturbed ε background has, to linear order, vanishing Lie derivative, therefore is coordinate gauge-invariant.

27.2 Metric, tetrad connections, and Einstein and Weyl tensors 735 gauge-invariance of the tetrad connections follows more fundamentally from the fact that any quantity that vanishes in the unperturbed background is coordinate gauge-invariant.

The unperturbed Einstein tensor G vanishes identically.

(27.17) m ∂t2 All the perturbations G of the Einstein tensor are both coordinate and tetrad gauge-invariant, as follows mn fromthefactthattheexpressions(27.16)dependonlyonthecoordinateandtetradgauge-invariantpotentials Ψ, Φ, W , and h .

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:
- 682 Trajectories in ideal rotating black holes m a r g i n a l l y s t n a u b l l l e m a r g i n a l l y s t n a u b l l l e Figure23.4 Locationofstable(shadedgreen)andunstable(shadedamber)circularorbitsinaKerrblackholewith spin(top)slightlysub-extremal(a=0.999M),and(bottom)extremal(a=M).Theplottedlatitudeofeachcircular orbit is its inclination, the maximum latitude reached by the orbit.
- Null (violet), marginally stable (green), and constant-latitude(grey;insidetheAntiverse,atr<0)circularorbitsaremarked.Regionswherecircularorbitsexist are bounded by the two conditions (23.80) (brown and violet).
- Prograde orbits are drawn to the left of the vertical axis, retrograde orbits to the right.
- Outer and inner ergospheres (dashed, purple), outer and inner horizons (red), sisytubes(cyan),andsingularities(black)areshownasinFigures9.1and9.3.

682 Trajectories in ideal rotating black holes m a r g i n a l l y s t n a u b l l l e m a r g i n a l l y s t n a u b l l l e Figure23.4 Locationofstable(shadedgreen)andunstable(shadedamber)circularorbitsinaKerrblackholewith spin(top)slightlysub-extremal(a=0.999M),and(bottom)extremal(a=M).Theplottedlatitudeofeachcircular orbit is its inclination, the maximum latitude reached by the orbit.

Null (violet), marginally stable (green), and constant-latitude(grey;insidetheAntiverse,atr<0)circularorbitsaremarked.Regionswherecircularorbitsexist are bounded by the two conditions (23.80) (brown and violet).

Prograde orbits are drawn to the left of the vertical axis, retrograde orbits to the right.

Outer and inner ergospheres (dashed, purple), outer and inner horizons (red), sisytubes(cyan),andsingularities(black)areshownasinFigures9.1and9.3.

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:
- X rays might come from the suspected neutron star if one were there, or from the gases, or from both.
- 152 THE COLLAPSING UNIVERSE tinct smear.
- If the X rays were coming from the gas, they would decline smoothly in intensity.
- If the X rays were coming from both, they would decline smoothly at first, then experience a sudden drop, then decline further as smoothly as at the start.

X rays might come from the suspected neutron star if one were there, or from the gases, or from both.

152 THE COLLAPSING UNIVERSE tinct smear.

If the X rays were coming from the gas, they would decline smoothly in intensity.

If the X rays were coming from both, they would decline smoothly at first, then experience a sudden drop, then decline further as smoothly as at the start.

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:
- Eventually the helium content becomes predominant, and energy production ceases at the core.
- Instead, for stars of more than 0.4 M , fusion occurs in a slowly expanding shell around the ☉ degenerate helium core.[202] In addition to hydrostatic equilibrium, the interior of a stable star will maintain an energy balance of thermal equilibrium.
- Where this is not the case, then the plasma becomes unstable and convection will occur, forming a convection zone.
- The temperature at the core of a main-sequence or Internal structures of main-sequence stars with masses giant star is at least on the order of 107 K.

Eventually the helium content becomes predominant, and energy production ceases at the core.

Instead, for stars of more than 0.4 M , fusion occurs in a slowly expanding shell around the ☉ degenerate helium core.[202] In addition to hydrostatic equilibrium, the interior of a stable star will maintain an energy balance of thermal equilibrium.

Where this is not the case, then the plasma becomes unstable and convection will occur, forming a convection zone.

The temperature at the core of a main-sequence or Internal structures of main-sequence stars with masses giant star is at least on the order of 107 K.

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:
- Even a particle just sitting there has energy, in fact an enormous amount of energy comparedwiththekineticenergy 1mv2itcou (cid:8) ld (cid:2) acquireineverydaylif (cid:8) e,wi(cid:6)thv(cid:18)c.Let’s restorecandrepeatthederivation:S=−mc (cdt)2−dx(cid:3)2=−mc dt c2−(dx(cid:3) )2= (cid:8) (cid:8) dt −m dt{c2− 1(dx(cid:3) )2+...}= dt{1mv2−mc2+...}.Therefereesnarledthatthisau2 dt 2 thordidn’tevenknowthatanadditiveconstantinV(x)matterednotawhit.Paperrejected.
- Recall from chapter II.3 that for the Lagrangian L(q ̇,q), the Hamiltonian is given by
- Ofcourse,whatactuallyhappenedwasthatyourpaperwasrejectedbyasuccessionof referees.Oneofthemtoldyouthatyoushouldbrushuponyourcalculus.Didn’tyouknow (cid:8) thatintegralsaresupposedtohavetheform dt ofsomefunctionoft?Thisguyiseasy totakecareof:youwrite " (cid:7) (cid:3) (cid:4) dx(cid:3) 2 S=−m dt 1− (6) dt ToshowanotherrefereethatyoucanreproduceNewtonianmechanics,youexpand(6) andrearrangeslightlytoobtain (cid:7) # (cid:3) (cid:4) $ m dx(cid:3) 2 S= dt −m+...
- Hamilton was clever enough to resolve this apparent problem.

Even a particle just sitting there has energy, in fact an enormous amount of energy comparedwiththekineticenergy 1mv2itcou (cid:8) ld (cid:2) acquireineverydaylif (cid:8) e,wi(cid:6)thv(cid:18)c.Let’s restorecandrepeatthederivation:S=−mc (cdt)2−dx(cid:3)2=−mc dt c2−(dx(cid:3) )2= (cid:8) (cid:8) dt −m dt{c2− 1(dx(cid:3) )2+...}= dt{1mv2−mc2+...}.Therefereesnarledthatthisau2 dt 2 thordidn’tevenknowthatanadditiveconstantinV(x)matterednotawhit.Paperrejected.

Recall from chapter II.3 that for the Lagrangian L(q ̇,q), the Hamiltonian is given by

Ofcourse,whatactuallyhappenedwasthatyourpaperwasrejectedbyasuccessionof referees.Oneofthemtoldyouthatyoushouldbrushuponyourcalculus.Didn’tyouknow (cid:8) thatintegralsaresupposedtohavetheform dt ofsomefunctionoft?Thisguyiseasy totakecareof:youwrite " (cid:7) (cid:3) (cid:4) dx(cid:3) 2 S=−m dt 1− (6) dt ToshowanotherrefereethatyoucanreproduceNewtonianmechanics,youexpand(6) andrearrangeslightlytoobtain (cid:7) # (cid:3) (cid:4) $ m dx(cid:3) 2 S= dt −m+...

Hamilton was clever enough to resolve this apparent problem.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- “I think I don’t want to be in this box for another fucking second.” Amanda steps down into the snow and sinks to her knees in the soft powder.
- I blink and we’re confined to a single box again.
- I feel the drug wink out for me, and this time the sensation is like an ice pick through my left eye.
- A shot of bitter cold hits my face.

“I think I don’t want to be in this box for another fucking second.” Amanda steps down into the snow and sinks to her knees in the soft powder.

I blink and we’re confined to a single box again.

I feel the drug wink out for me, and this time the sensation is like an ice pick through my left eye.

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:
- Like I’m simultaneously watching a movie and acting in it.
- Instrumentation panels covered with cracked gauges and controls.
- “Did you bring me here to kill me?” I ask.
- “I did not.” I feel so comfortable leaning against the old machine, like I’m sinking into it.

Like I’m simultaneously watching a movie and acting in it.

Instrumentation panels covered with cracked gauges and controls.

“Did you bring me here to kill me?” I ask.

“I did not.” I feel so comfortable leaning against the old machine, like I’m sinking into it.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The planets nearest the tunnels might be a safe distance away, but nearer still would be enormous space stations built as bases for the ships moving through the tunnels and as power stations for the home planets.
- Even though the universe is expanding, is it possible that the expansion is balanced by matter being shifted into the past through the wormholes?
- Furthermore, they are heavily weighted toward the greater distances and more remote past.
- 226 THE COLLAPSING UNIVERSE ing point of this sort as it is for an Earth city to be built at some harbor or some river ford.

The planets nearest the tunnels might be a safe distance away, but nearer still would be enormous space stations built as bases for the ships moving through the tunnels and as power stations for the home planets.

Even though the universe is expanding, is it possible that the expansion is balanced by matter being shifted into the past through the wormholes?

Furthermore, they are heavily weighted toward the greater distances and more remote past.

226 THE COLLAPSING UNIVERSE ing point of this sort as it is for an Earth city to be built at some harbor or some river ford.

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 entanglement-assisted teleportation scheme allows one to transmit quantum information using a classical channel.
- This is equivalent to the no-teleportation theorem: it is impossible to transmit quantum information via a classical channel.
- Channel fidelity Another measure of how well a quantum channel preserves information is called channel fidelity, and it arises from fidelity of quantum states.
- When n = m, the best one can achieve is one bit per qubit.

The entanglement-assisted teleportation scheme allows one to transmit quantum information using a classical channel.

This is equivalent to the no-teleportation theorem: it is impossible to transmit quantum information via a classical channel.

Channel fidelity Another measure of how well a quantum channel preserves information is called channel fidelity, and it arises from fidelity of quantum states.

When n = m, the best one can achieve is one bit per qubit.

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 its most sophisticated form, this is the brain of humans, but controls also exist in much less sophisticated ways for species of lower complexity, such as the amoeba.
- The goals bring the purpose into the
- This control organ plays a special role in evolution—it is the "spearhead of evolution".
- own sophisticated views on evolution[86] that go much beyond what the frequentlyquoted passages say.[87] In effect, Popper agreed with some points of both creationists and naturalists, but disagreed with both on crucial aspects.

In its most sophisticated form, this is the brain of humans, but controls also exist in much less sophisticated ways for species of lower complexity, such as the amoeba.

This control organ plays a special role in evolution—it is the "spearhead of evolution".

own sophisticated views on evolution[86] that go much beyond what the frequentlyquoted passages say.[87] In effect, Popper agreed with some points of both creationists and naturalists, but disagreed with both on crucial aspects.

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:
- Furthermore, the moon’s tides are influenced not by its phase—that is, by how much of it is visible to us on earth—but by its distance from earth (Kelly, Laverty, & Saklofske, 1990).
- Indeed, during a “new moon,” the phase at which the moon is invisible to us on earth, the moon exerts just as much gravitational influence as it does during a full moon.
- times greater than the gravitational force of the moon on that baby.
- These flawed explanations aside, we can still ask the question of whether the full moon exerts any meaningful effects on behavior.

Furthermore, the moon’s tides are influenced not by its phase—that is, by how much of it is visible to us on earth—but by its distance from earth (Kelly, Laverty, & Saklofske, 1990).

Indeed, during a “new moon,” the phase at which the moon is invisible to us on earth, the moon exerts just as much gravitational influence as it does during a full moon.

times greater than the gravitational force of the moon on that baby.

These flawed explanations aside, we can still ask the question of whether the full moon exerts any meaningful effects on behavior.

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 Milky Way and the Andromeda Galaxy are the two brightest galaxies within the group; many of the other member galaxies are dwarf companions of these two.[178] The Local Group itself is a part of a cloud-like structure within the Virgo Supercluster, a large, extended structure of groups and clusters of galaxies centered on the Virgo Cluster.[179] In turn, the Virgo Supercluster is a portion of the Laniakea Supercluster.[180] Magnetic fields Galaxies have magnetic fields of their own.
- If there is insufficient kinetic energy, however, the group may evolve into a smaller number of galaxies through mergers.[169] Clusters of galaxies consist of hundreds to thousands of galaxies bound together by gravity.[170] Clusters of galaxies are often dominated by a single giant elliptical galaxy, known as the brightest cluster galaxy, which, over time, tidally destroys its satellite galaxies and adds their mass to its own.[171] Superclusters contain tens of thousands of galaxies, which are found in clusters, groups and sometimes individually.
- At the supercluster scale, galaxies are arranged into sheets and filaments surrounding vast empty voids.[173] Above this scale, the Southern plane of the Milky Way from submillimeter wavelengths[172] universe appears to be the same in all directions (isotropic and homogeneous),[174] though this notion has been challenged in recent years by numerous findings of large-scale structures that appear to be exceeding this scale.
- A group of galaxies is the most common type of galactic cluster; these formations contain the majority of galaxies (as well as most of the baryonic mass) in the universe.[167][168] To remain gravitationally bound to such a group, each member galaxy must have a sufficiently low velocity to prevent it from escaping (see Virial theorem).

The Milky Way and the Andromeda Galaxy are the two brightest galaxies within the group; many of the other member galaxies are dwarf companions of these two.[178] The Local Group itself is a part of a cloud-like structure within the Virgo Supercluster, a large, extended structure of groups and clusters of galaxies centered on the Virgo Cluster.[179] In turn, the Virgo Supercluster is a portion of the Laniakea Supercluster.[180] Magnetic fields Galaxies have magnetic fields of their own.

If there is insufficient kinetic energy, however, the group may evolve into a smaller number of galaxies through mergers.[169] Clusters of galaxies consist of hundreds to thousands of galaxies bound together by gravity.[170] Clusters of galaxies are often dominated by a single giant elliptical galaxy, known as the brightest cluster galaxy, which, over time, tidally destroys its satellite galaxies and adds their mass to its own.[171] Superclusters contain tens of thousands of galaxies, which are found in clusters, groups and sometimes individually.

At the supercluster scale, galaxies are arranged into sheets and filaments surrounding vast empty voids.[173] Above this scale, the Southern plane of the Milky Way from submillimeter wavelengths[172] universe appears to be the same in all directions (isotropic and homogeneous),[174] though this notion has been challenged in recent years by numerous findings of large-scale structures that appear to be exceeding this scale.

A group of galaxies is the most common type of galactic cluster; these formations contain the majority of galaxies (as well as most of the baryonic mass) in the universe.[167][168] To remain gravitationally bound to such a group, each member galaxy must have a sufficiently low velocity to prevent it from escaping (see Virial theorem).

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:
- x | Contents IX.8 DifferentialFormsApplied 607 IX.9 ConformalAlgebra 614 IX.10 DeSitterSpacetime 624 IX.11 AntideSitterSpacetime 649 RecaptoPartIX 668 X Part X: Gravity Past, Present, and Future X.1 Kałuza,Klein,andtheFloweringofHigherDimensions 671 X.2 BraneWorldsandLargeExtraDimensions 696 X.3 EffectiveFieldTheoryApproachtoEinsteinGravity 708 X.4 FiniteSizedObjectsandTidalForcesinEinsteinGravity 714 X.5 TopologicalFieldTheory 719 X.6 ABriefIntroductiontoTwistors 729 X.7 TheCosmologicalConstantParadox 745 X.8 HeuristicThoughtsaboutQuantumGravity 760 RecaptoPartX 775 ClosingWords 777 TimelineofSomeofthePeopleMentioned 791 SolutionstoSelectedExercises 793 Bibliography 819 Index 821 CollectionofFormulasandConventions 859

x | Contents IX.8 DifferentialFormsApplied 607 IX.9 ConformalAlgebra 614 IX.10 DeSitterSpacetime 624 IX.11 AntideSitterSpacetime 649 RecaptoPartIX 668 X Part X: Gravity Past, Present, and Future X.1 Kałuza,Klein,andtheFloweringofHigherDimensions 671 X.2 BraneWorldsandLargeExtraDimensions 696 X.3 EffectiveFieldTheoryApproachtoEinsteinGravity 708 X.4 FiniteSizedObjectsandTidalForcesinEinsteinGravity 714 X.5 TopologicalFieldTheory 719 X.6 ABriefIntroductiontoTwistors 729 X.7 TheCosmologicalConstantParadox 745 X.8 HeuristicThoughtsaboutQuantumGravity 760 RecaptoPartX 775 ClosingWords 777 TimelineofSomeofthePeopleMentioned 791 SolutionstoSelectedExercises 793 Bibliography 819 Index 821 CollectionofFormulasandConventions 859

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:2005PhRvA..71b4101L (https://ui.adsabs.harvard.edu/ abs/2005PhRvA..71b4101L).
- Bibcode:2008GReGr..40..607B (h ttps://ui.adsabs.harvard.edu/abs/2008GReGr..40..607B).
- The road to reality: a complete guide to the laws of the universe (https://ar chive.org/details/roadtoreality00penr_319).
- Archived from the original (http://nautil.us/issue/45/power/w hat-quantum-gravity-needs-is-more-experiments) on 28 January 2018.

The road to reality: a complete guide to the laws of the universe (https://ar chive.org/details/roadtoreality00penr_319).

Archived from the original (http://nautil.us/issue/45/power/w hat-quantum-gravity-needs-is-more-experiments) on 28 January 2018.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- A shadow rushes toward me, the distance between us closing faster than I can process what’s happening.
- The second thing I see is the barrel of a gun, four inches from the end of my nose.
- High, arching eyebrows that look drawn.
- This is my favorite section of the walk home, because it’s the darkest and quietest.

A shadow rushes toward me, the distance between us closing faster than I can process what’s happening.

The second thing I see is the barrel of a gun, four inches from the end of my nose.

This is my favorite section of the walk home, because it’s the darkest and quietest.

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:
- Turning out onto the sidewalk of the next street, I look back down the alley, see two shadows moving toward me.
- He crashes into the stairs as the door busts open above us, and two seconds before I run for my life, I commit the most impossible image to memory: one version of myself stepping out of the stairwell with a gun, the other version picking himself up off the stairs, his hands frantically searching for his knife, which has disappeared in the snow.
- The blade in his hand throws a glint of light from the nearby streetlamp, and he advances on me, a knife spearing toward my abdomen—the knife that came standard-issue with the Velocity Laboratories backpack.
- Just as I right myself, a figure emerges out of the shadows of the alley between two Dumpsters.

Turning out onto the sidewalk of the next street, I look back down the alley, see two shadows moving toward me.

He crashes into the stairs as the door busts open above us, and two seconds before I run for my life, I commit the most impossible image to memory: one version of myself stepping out of the stairwell with a gun, the other version picking himself up off the stairs, his hands frantically searching for his knife, which has disappeared in the snow.

The blade in his hand throws a glint of light from the nearby streetlamp, and he advances on me, a knife spearing toward my abdomen—the knife that came standard-issue with the Velocity Laboratories backpack.

Just as I right myself, a figure emerges out of the shadows of the alley between two Dumpsters.

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:
- "Limb darkening coefficients for late-type giant model atmospheres".
- Bibcode:2020MNRAS.499.1918B (https://ui.adsabs.harvard.edu/ab s/2020MNRAS.499.1918B).
- arXiv:astro-ph/0702209 (https://arxiv.org/abs/astro-ph/0702209).
- Archived from the original (http:// www.nso.edu/PR/answerbook/magnitude.html) on 6 February 2008.

"Limb darkening coefficients for late-type giant model atmospheres".

Archived from the original (http:// www.nso.edu/PR/answerbook/magnitude.html) on 6 February 2008.

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 light beam would be set to strike each mirror surface at a very shallow angle while the rotation would ensure that the negative energy pulses would be reflected at a slightly different angle from the positive energy pulses.
- A chamber of sodium gas is placed within the squeezing cavity and a laser beam is directed through the gas.
- The squeezed light beam emerging from the resonator will contain pulses of negative energy interspersed with pulses of positive energy.
- Conceptual Squeezed Light Negative Energy Generator The rotating mirror system can actually be implemented via non-mechanical means.

The light beam would be set to strike each mirror surface at a very shallow angle while the rotation would ensure that the negative energy pulses would be reflected at a slightly different angle from the positive energy pulses.

A chamber of sodium gas is placed within the squeezing cavity and a laser beam is directed through the gas.

The squeezed light beam emerging from the resonator will contain pulses of negative energy interspersed with pulses of positive energy.

Conceptual Squeezed Light Negative Energy Generator The rotating mirror system can actually be implemented via non-mechanical means.

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:
- μ Themetricswecommonlyencounteraresosimplethatwecanevenwritedowneα(x)by μ inspection.Ihastentogiveanexample:thefamiliar2-spherewithds2=dθ2+sin2θdφ2 (thatis,withg =1,g =sin2θ),fromwhichwereadoffe1=1ande2=sinθ (allother θθ φφ θ φ componentsarezero).3In(1),theindicesαandβ,calledLorentzindices,takeondvalues ∗Indeed,wehavealreadyencounteredorthonormalframeswhenwediscussedFerminormalcoordinatesin chapterIX.3.
- Indeed, both the vielbein and differential forms have their origins in humble physical considerations.
- At this point, Professor Flat ambles by again, mumbling, “Even though the world is ∗ round,locallywecanstillerectorthonormalframes ofreference,Descartes’sgoodoldx-, y-,andz-axes,nowcalledlegs.” You and I respond, “Yes, professor, we have learned that Riemannian manifolds are locallyflat.Everydaylifeisflat.” Theideaistowritethemetricas g (x)=η eα(x)eβ(x) (1) μν αβ μ ν AsProfessorFlatexplainedinchapterI.6(inourdemonstrationthatwecanalwayschoose locally flat coordinates at a given point x), in the first step we turn g (x) into η by μν αβ a similarity transformation.
- In (1), we have merely denoted the matrix that appears in thesimilaritytransformationbyeα(x).

μ Themetricswecommonlyencounteraresosimplethatwecanevenwritedowneα(x)by μ inspection.Ihastentogiveanexample:thefamiliar2-spherewithds2=dθ2+sin2θdφ2 (thatis,withg =1,g =sin2θ),fromwhichwereadoffe1=1ande2=sinθ (allother θθ φφ θ φ componentsarezero).3In(1),theindicesαandβ,calledLorentzindices,takeondvalues ∗Indeed,wehavealreadyencounteredorthonormalframeswhenwediscussedFerminormalcoordinatesin chapterIX.3.

Indeed, both the vielbein and differential forms have their origins in humble physical considerations.

At this point, Professor Flat ambles by again, mumbling, “Even though the world is ∗ round,locallywecanstillerectorthonormalframes ofreference,Descartes’sgoodoldx-, y-,andz-axes,nowcalledlegs.” You and I respond, “Yes, professor, we have learned that Riemannian manifolds are locallyflat.Everydaylifeisflat.” Theideaistowritethemetricas g (x)=η eα(x)eβ(x) (1) μν αβ μ ν AsProfessorFlatexplainedinchapterI.6(inourdemonstrationthatwecanalwayschoose locally flat coordinates at a given point x), in the first step we turn g (x) into η by μν αβ a similarity transformation.

In (1), we have merely denoted the matrix that appears in thesimilaritytransformationbyeα(x).

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:
- (3.40) 4π(cid:15) c2r2 r2 4π(cid:15)
- (3.37) ρ μν μ νρ ν ρμ Considering equation (3.36), we have ∇ Fμν = ∂ Fμν +Γμ Fρν +Γν Fμρ, μ μ μρ μρ 1 √ 1 = ∂ Fμν +Fρν√ ∂ −g+ Γν (Fμρ−Fρμ), μ −g ρ 2 μρ = √ 1 ∂ (cid:0) √ −gFρν(cid:1) + 1 (cid:0) Γν Fμρ−Γν Fρμ(cid:1) , −g ρ 2 μρ ρμ = √ ∂ (cid:0) √ −gFρν(cid:1) .
- For large r, the metric becomes to be Minkowski and the function must reduce to the electric (cid:28)eld of a point charge as follow Q C Q E = = , ⇒ C = .
- (3.34) ij ijk ijk θφ θφr r r Therefore, general form of the (cid:28)eld strength tensor satisfying spherical symmetry can be written as   0 −E(r)/c 0 0  E(r)/c 0 0 0  F μν =   0 0 0 −r2sinθB(r)   , (3.35) 0 0 r2sinθB(r) 0 whereE(r)andB(r)arenowarbitrarywell-de(cid:28)nedfunction.

(3.37) ρ μν μ νρ ν ρμ Considering equation (3.36), we have ∇ Fμν = ∂ Fμν +Γμ Fρν +Γν Fμρ, μ μ μρ μρ 1 √ 1 = ∂ Fμν +Fρν√ ∂ −g+ Γν (Fμρ−Fρμ), μ −g ρ 2 μρ = √ 1 ∂ (cid:0) √ −gFρν(cid:1) + 1 (cid:0) Γν Fμρ−Γν Fρμ(cid:1) , −g ρ 2 μρ ρμ = √ ∂ (cid:0) √ −gFρν(cid:1) .

For large r, the metric becomes to be Minkowski and the function must reduce to the electric (cid:28)eld of a point charge as follow Q C Q E = = , ⇒ C = .

(3.34) ij ijk ijk θφ θφr r r Therefore, general form of the (cid:28)eld strength tensor satisfying spherical symmetry can be written as   0 −E(r)/c 0 0  E(r)/c 0 0 0  F μν =   0 0 0 −r2sinθB(r)   , (3.35) 0 0 r2sinθB(r) 0 whereE(r)andB(r)arenowarbitrarywell-de(cid:28)nedfunction.

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

EVIDENCE:
- Asisevidentfromtheelectromagneticexample,thisdefinitionisusefulevenifweare notinterestedincurvedspacetimeperse.Givenanactioninflatspacetime,wecanalways √ temporarilypromoteη tog , multiplyd4x by −g, use(1)tofindTμν(x), andthen μν μν setg backtotheMinkowskimetricη .Weareguaranteed,aswewillshowshortly,to μν μν obtain an energy momentum tensor satisfying D Tμν(x)=0, and hence ∂ Tμν(x)=0 μ μ in flat spacetime.
- Moreimportantly,thisfundamentaldefinitionoftheenergymomentumtensorleadsus toadeepunderstandingofwhyenergyandmomentumareconserved.Asthederivationis abitlong,Iplaceitinappendix1,whereIwillshowthattheconservationlawD Tμν=0 μ followselegantlyfromtheprincipleofgeneralinvariance.WewouldexpectTμν tohave “nice”properties;itisthevariationnotofanyoldpieceofjunk,butofanexquisiteobject thatcontrolshowthingsmoveandthatdoesnotchangeundercoordinatetransformations.
- EnergyMomentumDistributionTellsSpacetimeHowtoCurve | 383 Indeed,foronceConfusioisright:perhapssurprisingly,S doesnotcontributeto interaction Tμν accordingto(1).Thus,forchargedparticlesinteractingwithoneanother,theenergy momentum tensor that the gravitational field responds to is just the sum of the energy momentumtensorsin(4)and(8): Tμν=Tμν +Tμν particles Maxwell (cid:7) ≡ √ 1 (cid:10) m dτ dX a μdX a ν δ4(x−X )−FμFνλ+ 1 gμνF Fσρ (14) −g a a dτ dτ a λ 4 σρ a a a However,aswewouldexpectphysically,sincethechargedparticlesandtheelectromagμν μν neticfieldcanexchangeenergyandmomentum,thetensorsT andT areno particles Maxwell longerseparatelyconserved.OnlyTμνisconserved.1Wewillreachadeeperunderstanding ofthispointinappendix1.
- Whatexactlyareenergyandmomentum,anyway?

Asisevidentfromtheelectromagneticexample,thisdefinitionisusefulevenifweare notinterestedincurvedspacetimeperse.Givenanactioninflatspacetime,wecanalways √ temporarilypromoteη tog , multiplyd4x by −g, use(1)tofindTμν(x), andthen μν μν setg backtotheMinkowskimetricη .Weareguaranteed,aswewillshowshortly,to μν μν obtain an energy momentum tensor satisfying D Tμν(x)=0, and hence ∂ Tμν(x)=0 μ μ in flat spacetime.

EnergyMomentumDistributionTellsSpacetimeHowtoCurve | 383 Indeed,foronceConfusioisright:perhapssurprisingly,S doesnotcontributeto interaction Tμν accordingto(1).Thus,forchargedparticlesinteractingwithoneanother,theenergy momentum tensor that the gravitational field responds to is just the sum of the energy momentumtensorsin(4)and(8): Tμν=Tμν +Tμν particles Maxwell (cid:7) ≡ √ 1 (cid:10) m dτ dX a μdX a ν δ4(x−X )−FμFνλ+ 1 gμνF Fσρ (14) −g a a dτ dτ a λ 4 σρ a a a However,aswewouldexpectphysically,sincethechargedparticlesandtheelectromagμν μν neticfieldcanexchangeenergyandmomentum,thetensorsT andT areno particles Maxwell longerseparatelyconserved.OnlyTμνisconserved.1Wewillreachadeeperunderstanding ofthispointinappendix1.

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

EVIDENCE:
- Ergo, if light is always in a hurry to get from one point to another, it ∗Ifyoucan’texplainthat,seefigure7.1inFearful.Seealsothecommonmirageshowninfigure7.2:ona hotday,thehighwaybeneathadistantcarappearstobewet,butisinfactdry.Thismirageshowsthatlightonly caresaboutthelocal,nottheglobal,minimumintimeoftransit.
- †BabieshavenoneedforEuclid;assoonastheycancrawl,theymovetowardtheobscureobjectsoftheir desirealongastraightline.
- Butyoudon’thavetocalculatetoseethatthereisanoptimalpath.Onlyacretinwould followthethirdpath(thedashedline)showninthefigure!
- 4 | Prologue x F θ s sand water M C θ w G L Figure1 ThebestpossiblepathforFeynmantofollow togettothedrowninggirlisalongthesolidlines fromFtoG.

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

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

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

EVIDENCE:
- We can obtain the equations of particle motion in a variable dielectric vacuum by performing the standard variations of the Lagrangian density δ(∫ L dx dy dz d dt) with respect to the particle variables.
- delta function that locates μ i 0 the point particle at position r = r ); the second term is the Lagrangian density for the electromagnetic fields themselves, and the last term is the Lagrangian density for K (treated here as a scalar variable).
- This last term emulates the Lagrangian density for the gravitational field.
- Equation (2.32) does not include any quantum gauge field interaction terms because it is beyond the scope of the present incarnation of the PV-GR approach to include them.

We can obtain the equations of particle motion in a variable dielectric vacuum by performing the standard variations of the Lagrangian density δ(∫ L dx dy dz d dt) with respect to the particle variables.

delta function that locates μ i 0 the point particle at position r = r ); the second term is the Lagrangian density for the electromagnetic fields themselves, and the last term is the Lagrangian density for K (treated here as a scalar variable).

This last term emulates the Lagrangian density for the gravitational field.

Equation (2.32) does not include any quantum gauge field interaction terms because it is beyond the scope of the present incarnation of the PV-GR approach to include them.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- Clark wasnotbeingtruthfulwhenherepliedtoRep.SamuelS.Stratton.
- (PUBLICDOMAIN) -15December1978—BradSparksandToddZechelalsoclaimthefollowing: CIAofficialsinchargeoftheparanomal/extrasensorydepartmentsprovidecovertfundingfromCIA/DIA “black”slushfundstoselectUAPresearchersthroughmoneylaunderingandcut-outs,andKitGreen issuedan“order”totakeUAP“offtherecord”withintheIAtopreventAgencyinterestinthesubject frombeingdisclosed.
- MinotAFBandMalmstrom AFBmaintainedpermanentUAPfilesofSACbaseoverflightsdated30August1966and17 March1967.
- ● http://files.abovetopsecret.com/images/member/17f7ee96ee7e.gif ● http://files.abovetopsecret.com/images/member/97c8c30ee9f4.gif ● http://files.abovetopsecret.com/images/member/484a10c214d8.gif ● http://files.abovetopsecret.com/images/member/0c1216a7ed6d.gif ● https://www.ufohastings.com/storage/files/image/2010-10-11/af foia response 1977-10 -04 01.jpg

● http://files.abovetopsecret.com/images/member/17f7ee96ee7e.gif ● http://files.abovetopsecret.com/images/member/97c8c30ee9f4.gif ● http://files.abovetopsecret.com/images/member/484a10c214d8.gif ● http://files.abovetopsecret.com/images/member/0c1216a7ed6d.gif ● https://www.ufohastings.com/storage/files/image/2010-10-11/af foia response 1977-10 -04 01.jpg

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- A different approach, called renormalized perturbation theory, is to use physically meaningful quantities from the very beginning.
- The first three terms are the φ Lagrangian density written in terms of the renormalized quantities, while the latter three terms are referred to as "counterterms".
- In the case of φ theory, the field strength is first redefined: where φ is the bare field, φ is the r renormalized field, and Z is a constant to be determined.
- Then, define δ , δ , and δ such that Z m λ Feynman diagrams for the counterterms will exactly cancel the divergent terms in the normal Feynman diagrams when the limit Λ → ∞ is taken.

A different approach, called renormalized perturbation theory, is to use physically meaningful quantities from the very beginning.

The first three terms are the φ Lagrangian density written in terms of the renormalized quantities, while the latter three terms are referred to as "counterterms".

In the case of φ theory, the field strength is first redefined: where φ is the bare field, φ is the r renormalized field, and Z is a constant to be determined.

Then, define δ , δ , and δ such that Z m λ Feynman diagrams for the counterterms will exactly cancel the divergent terms in the normal Feynman diagrams when the limit Λ → ∞ is taken.

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:
- Plans for a trip to space In late 2006, Hawking revealed in a BBC interview that one of his greatest unfulfilled desires was to travel to space.[337] On hearing this, Richard Branson offered a free flight into space with Virgin Galactic, which Hawking immediately accepted.
- The email implies it was written in response to a "new version" of the claim regarding Hawking.
- Randall describes both her correspondence and Epstein's appearance at the conference as resulting from Epstein's public financing of scientific efforts.[344] Death Hawking died at his home in Cambridge on 14 March 2018, at the age of 76.[345][228][26] His family stated that he "died peacefully".[346][347] He was eulogised by figures in science, entertainment, politics and other areas.[a] The Gonville and Caius College flag flew at half-mast and a book of condolences was signed by students and visitors.[352][353][354] A tribute was made to Hawking in the closing speech by IPC President Andrew Parsons at the closing ceremony of the 2018 Paralympic Winter Games in Pyeongchang, South Korea.[355] His
- Besides personal ambition, he was motivated by the desire to increase public interest in spaceflight and to show the potential of people with disabilities.[214] On 26 April 2007, Hawking flew aboard a specially-modified Boeing 727200 jet operated by Zero-G Corp off the coast of Florida to experience weightlessness.[338] Fears that Hawking taking a zero-gravity flight in a reducedgravity aircraft, April 2007 the manoeuvres would cause him undue discomfort proved incorrect, and the flight was extended to eight parabolic arcs.[337] It was described as a successful test to see if he could withstand the g-forces involved in spaceflight.[339] At the time, the date of Hawking's trip to space was projected to be as early as 2009, but commercial flights to space did not commence before his death.[340] Mention in Jeffrey Epstein email Hawking was mentioned in court documents released in 2024 during the trial of Ghislaine Maxwell, a British child sex trafficker who conspired with American financier Jeffrey Epstein.

Plans for a trip to space In late 2006, Hawking revealed in a BBC interview that one of his greatest unfulfilled desires was to travel to space.[337] On hearing this, Richard Branson offered a free flight into space with Virgin Galactic, which Hawking immediately accepted.

The email implies it was written in response to a "new version" of the claim regarding Hawking.

Randall describes both her correspondence and Epstein's appearance at the conference as resulting from Epstein's public financing of scientific efforts.[344] Death Hawking died at his home in Cambridge on 14 March 2018, at the age of 76.[345][228][26] His family stated that he "died peacefully".[346][347] He was eulogised by figures in science, entertainment, politics and other areas.[a] The Gonville and Caius College flag flew at half-mast and a book of condolences was signed by students and visitors.[352][353][354] A tribute was made to Hawking in the closing speech by IPC President Andrew Parsons at the closing ceremony of the 2018 Paralympic Winter Games in Pyeongchang, South Korea.[355] His

Besides personal ambition, he was motivated by the desire to increase public interest in spaceflight and to show the potential of people with disabilities.[214] On 26 April 2007, Hawking flew aboard a specially-modified Boeing 727200 jet operated by Zero-G Corp off the coast of Florida to experience weightlessness.[338] Fears that Hawking taking a zero-gravity flight in a reducedgravity aircraft, April 2007 the manoeuvres would cause him undue discomfort proved incorrect, and the flight was extended to eight parabolic arcs.[337] It was described as a successful test to see if he could withstand the g-forces involved in spaceflight.[339] At the time, the date of Hawking's trip to space was projected to be as early as 2009, but commercial flights to space did not commence before his death.[340] Mention in Jeffrey Epstein email Hawking was mentioned in court documents released in 2024 during the trial of Ghislaine Maxwell, a British child sex trafficker who conspired with American financier Jeffrey Epstein.

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:
- Although neutral 163Dy is a stable isotope, the fully ionized 163Dy66+ undergoes β− decay into the K and L shells to 163Ho66+ with a half-life of 47 days.[44] Rhenium-187 is another spectacular example.
- In 7Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments.[43] This relatively large effect is because beryllium is a small atom whose valence electrons are in 2s atomic orbitals, which are subject to electron capture in 7Be because (like all s atomic orbitals in all atoms) they naturally penetrate into the nucleus.
- 187Re normally undergoes beta decay to 187Os with a half-life of 41.6 billion years,[45] but studies using fully ionised 187Re atoms (bare nuclei) have found that this can decrease to only 32.9 years.[46] This is attributed to "bound-state β− decay" of the fully ionised atom – the electron is emitted into the "K-shell" (1s atomic orbital), which cannot occur for neutral atoms in which all low-lying bound states are occupied.[47] A number of experiments have found that decay rates of other modes of artificial and naturally occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields.[48] Comparison of laboratory experiments over the last century, studies of the Oklo natural nuclear reactor (which exemplified the effects of thermal neutrons on nuclear decay), and astrophysical observations of the luminosity decays of distant supernovae (which occurred far away so the light has taken a great deal of time to reach us), for example, strongly indicate that unperturbed decay rates have been constant (at least to within the limitations of small experimental errors) as a function of time as well.
- of the Darmstadt Heavy-Ion Research group observed an accelerated β− decay of 163Dy66+.

Although neutral 163Dy is a stable isotope, the fully ionized 163Dy66+ undergoes β− decay into the K and L shells to 163Ho66+ with a half-life of 47 days.[44] Rhenium-187 is another spectacular example.

In 7Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments.[43] This relatively large effect is because beryllium is a small atom whose valence electrons are in 2s atomic orbitals, which are subject to electron capture in 7Be because (like all s atomic orbitals in all atoms) they naturally penetrate into the nucleus.

187Re normally undergoes beta decay to 187Os with a half-life of 41.6 billion years,[45] but studies using fully ionised 187Re atoms (bare nuclei) have found that this can decrease to only 32.9 years.[46] This is attributed to "bound-state β− decay" of the fully ionised atom – the electron is emitted into the "K-shell" (1s atomic orbital), which cannot occur for neutral atoms in which all low-lying bound states are occupied.[47] A number of experiments have found that decay rates of other modes of artificial and naturally occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields.[48] Comparison of laboratory experiments over the last century, studies of the Oklo natural nuclear reactor (which exemplified the effects of thermal neutrons on nuclear decay), and astrophysical observations of the luminosity decays of distant supernovae (which occurred far away so the light has taken a great deal of time to reach us), for example, strongly indicate that unperturbed decay rates have been constant (at least to within the limitations of small experimental errors) as a function of time as well.

of the Darmstadt Heavy-Ion Research group observed an accelerated β− decay of 163Dy66+.

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:
- Speculation on processes occurring before inflation involves physics considered outside of standard cosmology.
- From this point onwards the physics of the early universe is much better understood, and the energies involved in the quark epoch are directly accessible in particle
- Via the Higgs mechanism, all elementary particles interacting with the Higgs field became massive, having been massless at higher energy levels.
- A highprecision version of the Big Bang model using conventional physics, known as Lambda-CDM, agrees with a wide array of astrophysical observations.[20] The concept is not extrapolated back to zero time.[21] Within the standard model of cosmology the initial state is set by a process called inflation.

Chronology of the universe - Wikipedia.pdf

Speculation on processes occurring before inflation involves physics considered outside of standard cosmology.

From this point onwards the physics of the early universe is much better understood, and the energies involved in the quark epoch are directly accessible in particle

Via the Higgs mechanism, all elementary particles interacting with the Higgs field became massive, having been massless at higher energy levels.

A highprecision version of the Big Bang model using conventional physics, known as Lambda-CDM, agrees with a wide array of astrophysical observations.[20] The concept is not extrapolated back to zero time.[21] Within the standard model of cosmology the initial state is set by a process called inflation.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- almanac maker, Thomas Digges, delineated the spheres of the new cosmological system in his Perfit Description of the Caelestiall Orbes ...
- Here he arranged the "orbes" in the new Copernican order, expanding one sphere to carry "the globe of mortalitye", the Earth, the four classical elements, and the Moon, and expanding the sphere of stars infinitely to encompass all the stars and also to serve as "the court of the Great God, the habitacle of the elect, and of the coelestiall angelles."[60]

almanac maker, Thomas Digges, delineated the spheres of the new cosmological system in his Perfit Description of the Caelestiall Orbes ...

Here he arranged the "orbes" in the new Copernican order, expanding one sphere to carry "the globe of mortalitye", the Earth, the four classical elements, and the Moon, and expanding the sphere of stars infinitely to encompass all the stars and also to serve as "the court of the Great God, the habitacle of the elect, and of the coelestiall angelles."[60]

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- This is particularly the case when dealing with kinetic effects (and the associated integrals) such as electron and ion Landau resonances.
- These results will all be presented at the upcoming Spring AGU meeting.
- We are now applying this technique to tearing in the magnetotail with realistic field geometries, to the problem of the linear evolution of the (kinetic) Kelvin Helmholtz, and will shortly begin an application to tearing at the dayside magnetopause.
- We have developed a new method for handling such calculations that evaluates the integral portion of the problem uses PIC techniques similar to those employed in standard simulation codes.

This is particularly the case when dealing with kinetic effects (and the associated integrals) such as electron and ion Landau resonances.

These results will all be presented at the upcoming Spring AGU meeting.

We are now applying this technique to tearing in the magnetotail with realistic field geometries, to the problem of the linear evolution of the (kinetic) Kelvin Helmholtz, and will shortly begin an application to tearing at the dayside magnetopause.

We have developed a new method for handling such calculations that evaluates the integral portion of the problem uses PIC techniques similar to those employed in standard simulation codes.

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:
- Contents v 4.5 Effective Lagrangian for a test particle 101 4.6 Nice Lagrangian for a test particle 102 4.7 Action for a charged test particle in an electromagnetic field 103 4.8 Symmetries and constants of motion 105 4.9 Conformal symmetries 106 4.10 (Super-)Hamiltonian 109 4.11 Conventional Hamiltonian 110 4.12 Conventional Hamiltonian for a test particle 110 4.13 Effective (super-)Hamiltonian for a test particle with electromagnetism 112 4.14 Nice (super-)Hamiltonian for a test particle with electromagnetism 113 4.15 Derivatives of the action 114 4.16 Hamilton-Jacobi equation 115 4.17 Canonical transformations 115 4.18 Symplectic structure 118 4.19 Symplectic scalar product and Poisson brackets 119 4.20 (Super-)Hamiltonian as a generator of evolution 120 4.21 Infinitesimal canonical transformations 120 4.22 Constancy of phase-space volume under canonical transformations 121 4.23 Poisson algebra of integrals of motion 122 Concept Questions 124 What’s important?
- 126 5 Observational Evidence for Black Holes 127 6 Ideal Black Holes 130 6.1 Definition of a black hole 130 6.2 Ideal black hole 131 6.3 No-hair theorem 131 7 Schwarzschild Black Hole 133 7.1 Schwarzschild metric 133 7.2 Stationary, static 134 7.3 Spherically symmetric 135 7.4 Energy-momentum tensor 136 7.5 Birkhoff’s theorem 136 7.6 Horizon 137 7.7 Proper time 138 7.8 Redshift 139 7.9 “Schwarzschild singularity” 139 7.10 Weyl tensor 140 7.11 Singularity 140 7.12 Gullstrand-Painlevé metric 142

Contents v 4.5 Effective Lagrangian for a test particle 101 4.6 Nice Lagrangian for a test particle 102 4.7 Action for a charged test particle in an electromagnetic field 103 4.8 Symmetries and constants of motion 105 4.9 Conformal symmetries 106 4.10 (Super-)Hamiltonian 109 4.11 Conventional Hamiltonian 110 4.12 Conventional Hamiltonian for a test particle 110 4.13 Effective (super-)Hamiltonian for a test particle with electromagnetism 112 4.14 Nice (super-)Hamiltonian for a test particle with electromagnetism 113 4.15 Derivatives of the action 114 4.16 Hamilton-Jacobi equation 115 4.17 Canonical transformations 115 4.18 Symplectic structure 118 4.19 Symplectic scalar product and Poisson brackets 119 4.20 (Super-)Hamiltonian as a generator of evolution 120 4.21 Infinitesimal canonical transformations 120 4.22 Constancy of phase-space volume under canonical transformations 121 4.23 Poisson algebra of integrals of motion 122 Concept Questions 124 What’s important?

126 5 Observational Evidence for Black Holes 127 6 Ideal Black Holes 130 6.1 Definition of a black hole 130 6.2 Ideal black hole 131 6.3 No-hair theorem 131 7 Schwarzschild Black Hole 133 7.1 Schwarzschild metric 133 7.2 Stationary, static 134 7.3 Spherically symmetric 135 7.4 Energy-momentum tensor 136 7.5 Birkhoff’s theorem 136 7.6 Horizon 137 7.7 Proper time 138 7.8 Redshift 139 7.9 “Schwarzschild singularity” 139 7.10 Weyl tensor 140 7.11 Singularity 140 7.12 Gullstrand-Painlevé metric 142

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:
- Think of this as a warm-up before we do the heavy lifting oflearningEinsteingravity.Also,later,wecancomparethesolutionherewithEinstein’s solution.
- We will do it by brute force to show, in contrast, the elegance of the formalism wewilldeveloplater.Differentiate x=rcosθ and y=rsinθ (9) twicetoobtainfirst x ̇=r ̇cosθ−rsinθθ ̇ and y ̇=r ̇sinθ+rcosθθ ̇ (10) andthen x ̈=r ̈cosθ−2r ̇sinθθ ̇−rcosθθ ̇2−rsinθθ ̈ and y ̈=r ̈sinθ+2r ̇cosθθ ̇−rsinθθ ̇2+rcosθθ ̈ (11) (Notethatineachpairoftheseequations,thesecondcouldbeobtainedfromthefirstby thesubstitutionθ →θ − π,sothatcosθ →sinθ,andsinθ →−cosθ.) Multiplying the first equation in (7) by cosθ and the second by sinθ and adding, we obtain,using(11), r ̈−rθ ̇2=− κ (12) r2 Ontheotherhand,multiplyingthefirstequationin(7)bysinθ andthesecondbycosθ andsubtracting,wehave 2r ̇θ ̇+rθ ̈=0 (13) Iremindthereaderagainthatwearedoingallthisinaclumsybruteforcewaytoshow thepoweroftheformalismwearegoingtodeveloplater.
- Newton’sLaws | 29 x ̈=−κx/r3 and y ̈=−κy/r3 (7) Ihavealready,withoutwarning,switchedfromLeibniz’snotationtoNewton’sdotnotation dx d2x x ̇≡ and x ̈≡ (8) dt dt2 Sincethisisoneofthemostbeautifulproblems6intheoreticalphysics,Icannotresist solving it here in all its glory.
- Afterstaringat(13)werecognizethatitisequivalentto d (r2θ ̇ )=0 (14) dt whichimpliesthat θ ̇= l (15) r2 forsomeconstantl.Insertingthisinto(12),wehave l2 κ dv(r) r ̈= − =− (16) r3 r2 dr

Think of this as a warm-up before we do the heavy lifting oflearningEinsteingravity.Also,later,wecancomparethesolutionherewithEinstein’s solution.

We will do it by brute force to show, in contrast, the elegance of the formalism wewilldeveloplater.Differentiate x=rcosθ and y=rsinθ (9) twicetoobtainfirst x ̇=r ̇cosθ−rsinθθ ̇ and y ̇=r ̇sinθ+rcosθθ ̇ (10) andthen x ̈=r ̈cosθ−2r ̇sinθθ ̇−rcosθθ ̇2−rsinθθ ̈ and y ̈=r ̈sinθ+2r ̇cosθθ ̇−rsinθθ ̇2+rcosθθ ̈ (11) (Notethatineachpairoftheseequations,thesecondcouldbeobtainedfromthefirstby thesubstitutionθ →θ − π,sothatcosθ →sinθ,andsinθ →−cosθ.) Multiplying the first equation in (7) by cosθ and the second by sinθ and adding, we obtain,using(11), r ̈−rθ ̇2=− κ (12) r2 Ontheotherhand,multiplyingthefirstequationin(7)bysinθ andthesecondbycosθ andsubtracting,wehave 2r ̇θ ̇+rθ ̈=0 (13) Iremindthereaderagainthatwearedoingallthisinaclumsybruteforcewaytoshow thepoweroftheformalismwearegoingtodeveloplater.

Newton’sLaws | 29 x ̈=−κx/r3 and y ̈=−κy/r3 (7) Ihavealready,withoutwarning,switchedfromLeibniz’snotationtoNewton’sdotnotation dx d2x x ̇≡ and x ̈≡ (8) dt dt2 Sincethisisoneofthemostbeautifulproblems6intheoreticalphysics,Icannotresist solving it here in all its glory.

Afterstaringat(13)werecognizethatitisequivalentto d (r2θ ̇ )=0 (14) dt whichimpliesthat θ ̇= l (15) r2 forsomeconstantl.Insertingthisinto(12),wehave l2 κ dv(r) r ̈= − =− (16) r3 r2 dr

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:
- Bibcode:2009RSPSA.465..631A (https://ui.adsabs.harvard.edu/abs/2009RSPSA.465..631A).
- doi:10.1038/scientificamerican0308-62 (https://doi.org/10.1038%2Fscientificamerican0308-62).
- S2CID 745646 (https:// api.semanticscholar.org/CorpusID:745646).
- "Classical Electrodynamics in Terms of Direct Interparticle Action" (https://doi.org/10.1103%2FRevModPhys.21.425).

Novikov self-consistency principle - Wikipedia.pdf

S2CID 745646 (https:// api.semanticscholar.org/CorpusID:745646).

"Classical Electrodynamics in Terms of Direct Interparticle Action" (https://doi.org/10.1103%2FRevModPhys.21.425).

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- Conway showed that, rather than the entire atom vibrating, vibrations of only one of the electrons in the system described by Thomson might be sufficient to account for spectral series.[13]: II:106 Although Bohr's model would also rely on just the electron to explain the spectrum, he did not assume an electrodynamical model for the atom.
- Three years later, Bohr would use similar equations with different interpretation.
- In 1897, Lord Rayleigh showed that vibrations of electrical systems predicted spectral lines that depend on the square of the vibrational frequency, contradicting the empirical formula which depended directly on the frequency.[5]: 18 [12] In 1907 Arthur W.
- This combination relates the radius of the sphere to the Planck constant: Haas solved for the Planck constant using the then-current value for the radius of the hydrogen atom.

Conway showed that, rather than the entire atom vibrating, vibrations of only one of the electrons in the system described by Thomson might be sufficient to account for spectral series.[13]: II:106 Although Bohr's model would also rely on just the electron to explain the spectrum, he did not assume an electrodynamical model for the atom.

Three years later, Bohr would use similar equations with different interpretation.

In 1897, Lord Rayleigh showed that vibrations of electrical systems predicted spectral lines that depend on the square of the vibrational frequency, contradicting the empirical formula which depended directly on the frequency.[5]: 18 [12] In 1907 Arthur W.

This combination relates the radius of the sphere to the Planck constant: Haas solved for the Planck constant using the then-current value for the radius of the hydrogen atom.

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:
- My name spelled out in Pig Latin: asonjayessenday.
- It’s snowing hard enough that the streets are beginning to empty and the pavement is frosting over, showing the tire tracks of passing cars.
- I head up to the fourth floor and lock myself inside the room behind the deadbolt and the chain.
- I move to the curtains and peek outside.

My name spelled out in Pig Latin: asonjayessenday.

It’s snowing hard enough that the streets are beginning to empty and the pavement is frosting over, showing the tire tracks of passing cars.

I head up to the fourth floor and lock myself inside the room behind the deadbolt and the chain.

I move to the curtains and peek outside.

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:
- Similarly, if the wireframe of a tesseract were lit from "above" (in the fourth dimension), its shadow would be that of a threedimensional cube within another three-dimensional cube suspended in midair (a "flat" surface
- Just as the nearest corner of the cube is the one lying at the center of the image, so the nearest vertex of the tesseract lies not on the boundary of the projected volume, but at its center inside, where all four cells meet.
- This is analogous to the edge-first perspective projection of the tesseract, shown on the right.
- If a light is shone on a three-dimensional object, a two-dimensional shadow is cast.

Similarly, if the wireframe of a tesseract were lit from "above" (in the fourth dimension), its shadow would be that of a threedimensional cube within another three-dimensional cube suspended in midair (a "flat" surface

Just as the nearest corner of the cube is the one lying at the center of the image, so the nearest vertex of the tesseract lies not on the boundary of the projected volume, but at its center inside, where all four cells meet.

This is analogous to the edge-first perspective projection of the tesseract, shown on the right.

If a light is shone on a three-dimensional object, a two-dimensional shadow is cast.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- A Molecule is the smallest particle of matter into which a body can be divided without losing its identity.
- In the 19th century, the term "matter" was actively discussed by a host of scientists and philosophers, and a brief outline can be found in Levere.[96] One textbook discussion from 1870 suggests that matter is what is made up of atoms:[97] Three divisions of matter are recognized in science: masses, molecules and atoms.
- In 1909 the famous physicist J.
- constituents of matter; atoms formed molecules and compounds.[94] The common definition in terms of occupying space and having mass is in contrast with most physical and chemical definitions of matter, which rely instead upon its structure and upon attributes not necessarily related to volume and mass.

A Molecule is the smallest particle of matter into which a body can be divided without losing its identity.

In the 19th century, the term "matter" was actively discussed by a host of scientists and philosophers, and a brief outline can be found in Levere.[96] One textbook discussion from 1870 suggests that matter is what is made up of atoms:[97] Three divisions of matter are recognized in science: masses, molecules and atoms.

constituents of matter; atoms formed molecules and compounds.[94] The common definition in terms of occupying space and having mass is in contrast with most physical and chemical definitions of matter, which rely instead upon its structure and upon attributes not necessarily related to volume and mass.

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:
- κ κ D ̊ u α =∂ u α+ ̊Γα u β − ̊Γ uμαuν =0 , (15.121) α κ α κ βα κ μνκ α in which the connection term ̊Γα =∂lne/∂λβ (all worldtube indices), equation (2.79), enforces covariβα ance with respect to the worldtube coordinate index α of the velocity, while the connection term ̊Γ μνκ (all external indices) enforces covariance with respect to the external coordinate index κ of the velocity.
- As a check, for a point particle, p = 1, of mass μ = m, the Lagrangian (15.113) is L = −me with m e = dτ/dλ, equation (4.8), the induced metric (15.136) is h = −e2 with inverse h00 = −e−2, the

κ κ D ̊ u α =∂ u α+ ̊Γα u β − ̊Γ uμαuν =0 , (15.121) α κ α κ βα κ μνκ α in which the connection term ̊Γα =∂lne/∂λβ (all worldtube indices), equation (2.79), enforces covariβα ance with respect to the worldtube coordinate index α of the velocity, while the connection term ̊Γ μνκ (all external indices) enforces covariance with respect to the external coordinate index κ of the velocity.

As a check, for a point particle, p = 1, of mass μ = m, the Lagrangian (15.113) is L = −me with m e = dτ/dλ, equation (4.8), the induced metric (15.136) is h = −e2 with inverse h00 = −e−2, the

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 US minor league baseball Albuquerque Isotopes' logo shows baseballs as electrons orbiting a large letter "A".
- The JavaScript library React uses planetary-like image as its logo.
- The Unicode Miscellaneous Symbols code point U+269B (⚛) for an atom looks like a planetary atom model.
- The television show The Big Bang Theory uses a planetary-like image in its print logo.

The US minor league baseball Albuquerque Isotopes' logo shows baseballs as electrons orbiting a large letter "A".

The JavaScript library React uses planetary-like image as its logo.

The Unicode Miscellaneous Symbols code point U+269B (⚛) for an atom looks like a planetary atom model.

The television show The Big Bang Theory uses a planetary-like image in its print logo.

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

List tests or derivations implied by the evidence.