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

EVIDENCE:
- Using Wick's theorem on the terms of the Dyson series, all the terms of the S-matrix for quantum electrodynamics can be computed through the technique of Feynman diagrams.
- diagrams then look the same, but the lines have different interpretations.
- The electron line represents an electron with a given energy and momentum, with a similar interpretation of the photon line.
- A vertex diagram represents the annihilation of one electron and the creation of another together with the absorption or creation of a photon, each having specified energies and momenta.

Using Wick's theorem on the terms of the Dyson series, all the terms of the S-matrix for quantum electrodynamics can be computed through the technique of Feynman diagrams.

diagrams then look the same, but the lines have different interpretations.

The electron line represents an electron with a given energy and momentum, with a similar interpretation of the photon line.

A vertex diagram represents the annihilation of one electron and the creation of another together with the absorption or creation of a photon, each having specified energies and momenta.

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:
- "AAAS Evolution Resources" (http://www.aaas.org/news/press_room/evolution/qanda.shtml).
- Cambridge Scholars Publishing 13.
- Scientific Theory vs Law (https://medium.com/science-journal/scientific-theory-vsscientific-law-5624633a8f1b).
- Princeton: Princeton University Press.

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.

"AAAS Evolution Resources" (http://www.aaas.org/news/press_room/evolution/qanda.shtml).

Scientific Theory vs Law (https://medium.com/science-journal/scientific-theory-vsscientific-law-5624633a8f1b).

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:
- Introduction to Strings and Branes.
- Retrieved from "https://en.wikipedia.org/w/index.php?title=String_theory&oldid=1334185903"
- External links BBC's Parallel Universes (https://www.bbc.co.uk/science/horizon/2001/paralleluni.shtml), 2002 feature documentary by BBC Horizon, episode "Parallel Universes", focuses on history and emergence of M-theory, and scientists involved.
- 1: An Introduction to the Bosonic String.

External links BBC's Parallel Universes (https://www.bbc.co.uk/science/horizon/2001/paralleluni.shtml), 2002 feature documentary by BBC Horizon, episode "Parallel Universes", focuses on history and emergence of M-theory, and scientists involved.

1: An Introduction to the Bosonic String.

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:
- Beginning with Carl Friedrich Gauss's 1832 proof that prime numbers such as five can be factored in Gaussian integers,[159] Évariste Galois's introduction of permutation groups in 1832 (because of his death, his papers were published only in 1846, by Liouville), William Rowan Hamilton's description of quaternions in 1843, and Arthur Cayley's more modern definition of groups in 1854, research turned to determining the properties of ever-moreabstract systems defined by ever-more-universal rules.
- Historical context In the century from 1832 to Noether's death in 1935, the field of mathematics — specifically algebra — underwent a profound revolution whose reverberations are still being felt.
- It may or may not be commutative; this means that the result of applying the operation to a first and a second element is the same as to the second and first — the order of the elements does not matter.[163] If every non-zero element has a multiplicative inverse (an element x such that ax = xa = 1), the ring is called a division ring.
- The first operation must make the set a commutative group, and the second operation is associative and distributive with respect to the first operation.

Beginning with Carl Friedrich Gauss's 1832 proof that prime numbers such as five can be factored in Gaussian integers,[159] Évariste Galois's introduction of permutation groups in 1832 (because of his death, his papers were published only in 1846, by Liouville), William Rowan Hamilton's description of quaternions in 1843, and Arthur Cayley's more modern definition of groups in 1854, research turned to determining the properties of ever-moreabstract systems defined by ever-more-universal rules.

Historical context In the century from 1832 to Noether's death in 1935, the field of mathematics — specifically algebra — underwent a profound revolution whose reverberations are still being felt.

It may or may not be commutative; this means that the result of applying the operation to a first and a second element is the same as to the second and first — the order of the elements does not matter.[163] If every non-zero element has a multiplicative inverse (an element x such that ax = xa = 1), the ring is called a division ring.

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

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 choice was made to look only at the Bell state for which photon 2 and 3 were projected onto the state Ψ  2 3 (and similarly photon 1 and 4 onto Ψ  1 4 Figure 13: experimental set-up for entanglement swapping.
- In this case not the state of the system, but the entanglements to other particles were teleported.
- The detector D in 1 4 4 Fig.(13) was preceded by a polariser that could be set at arbitrary polarisation angles θ.
- An UV pulse creates a pair 1-2 of entangled photons when passing through a non-linear crystal.

The choice was made to look only at the Bell state for which photon 2 and 3 were projected onto the state Ψ  2 3 (and similarly photon 1 and 4 onto Ψ  1 4 Figure 13: experimental set-up for entanglement swapping.

In this case not the state of the system, but the entanglements to other particles were teleported.

The detector D in 1 4 4 Fig.(13) was preceded by a polariser that could be set at arbitrary polarisation angles θ.

An UV pulse creates a pair 1-2 of entangled photons when passing through a non-linear crystal.

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

EVIDENCE:
- Effects of empty nest transition on self-report of psychological and physical well-being.
- The social context of well-being.
- The happiness myth: Why what we think is right is wrong.
- Journal of Marriage and the Family, 40, 549–556.

Effects of empty nest transition on self-report of psychological and physical well-being.

The happiness myth: Why what we think is right is wrong.

Journal of Marriage and the Family, 40, 549–556.

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:
- In C, the gravitational force exists everywhere, namely F(x) exists as a function,andwhatappearsinNewton’sequationisjustF(x)evaluatedatthepositionof the particle x(t).
- Withsix eyes,wecouldhaveprecisestereoscopicvisioninalldirections at once, including straight up.
- Newton’sLaws | 31 ∗ hereindicateshowtheNewtonianorbit (andalsotheEinsteinianorbit,aswewillseein partVI)couldbedetermined.Seeexercise2.
- Badnotationalert!In(1),theforceontherighthandsideshouldbewrittenasFi(x(t)) (in many cases).

In C, the gravitational force exists everywhere, namely F(x) exists as a function,andwhatappearsinNewton’sequationisjustF(x)evaluatedatthepositionof the particle x(t).

Withsix eyes,wecouldhaveprecisestereoscopicvisioninalldirections at once, including straight up.

Newton’sLaws | 31 ∗ hereindicateshowtheNewtonianorbit (andalsotheEinsteinianorbit,aswewillseein partVI)couldbedetermined.Seeexercise2.

Badnotationalert!In(1),theforceontherighthandsideshouldbewrittenasFi(x(t)) (in many cases).

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:
- (16.134) m 2 λ mn κm An integration by parts brings the variation to ∮ ∫ ( ) δS =− 1Σ mnε d3xλ+ 1D Σλmn+T[mn] ε d4x .
- Therefore the integrand of the rightmost integral in equation (16.135) must vanish, implying the conservation law 1D Σλmn+T[mn] =0 .
- (16.133) mnλ λ mn ThecoefficientsofthevariationδS ofthematteractionwithrespecttoδemκ andδΓ arebydefinition m mnλ theenergy-momentumandspinangular-momentumofthematter,equations(16.121)and(16.117).Inserting thevariations(16.132)and(16.133)withrespecttoLorentztransformationsyieldsthevariationofthematter action under a Lorentz transformation, ∫ δS =− (1ΣλmnD ε +T εmκ) d4x .
- Consequently, although the vierbein is a coordinate and tetrad tensor, its Lie derivative is a coordinate tensorbutnotatetradtensor.Thesolutiontothedifficultyispointedoutatthebeginningof§5.2.1ofHehl et al.

(16.134) m 2 λ mn κm An integration by parts brings the variation to ∮ ∫ ( ) δS =− 1Σ mnε d3xλ+ 1D Σλmn+T[mn] ε d4x .

Therefore the integrand of the rightmost integral in equation (16.135) must vanish, implying the conservation law 1D Σλmn+T[mn] =0 .

(16.133) mnλ λ mn ThecoefficientsofthevariationδS ofthematteractionwithrespecttoδemκ andδΓ arebydefinition m mnλ theenergy-momentumandspinangular-momentumofthematter,equations(16.121)and(16.117).Inserting thevariations(16.132)and(16.133)withrespecttoLorentztransformationsyieldsthevariationofthematter action under a Lorentz transformation, ∫ δS =− (1ΣλmnD ε +T εmκ) d4x .

Consequently, although the vierbein is a coordinate and tetrad tensor, its Lie derivative is a coordinate tensorbutnotatetradtensor.Thesolutiontothedifficultyispointedoutatthebeginningof§5.2.1ofHehl et al.

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:
- Astrophysicists, however, explain this marked phenomenon by assuming the presence of large amounts of dark matter.
- General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.
- This allowed a description of the motions of light and mass that was consistent with all available observations.
- In situations where either dimensionless parameter is large, then general relativity must be used to describe the system.

Newton's law of universal gravitation - Wikipedia.pdf

Astrophysicists, however, explain this marked phenomenon by assuming the presence of large amounts of dark matter.

General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.

This allowed a description of the motions of light and mass that was consistent with all available observations.

In situations where either dimensionless parameter is large, then general relativity must be used to describe the system.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Thus, if we restrict new information to the right hemisphere, the left hemisphere—which is more verbal than the right—will be unable to tell us what the input was, and it may be perplexed to see the left hand acting on the segregated knowledge, for reasons it can’t fathom.
- In this regard, brain researchers have become more cautious in recent years while many pop psychologists have run wild.
- The right hemisphere receives input from and controls the movements of the left side of the body, and the left hemisphere does the same for the right.
- For example, if the researcher shows the right hemisphere of a splitbrain subject a photograph of a naked man, she may giggle.

Thus, if we restrict new information to the right hemisphere, the left hemisphere—which is more verbal than the right—will be unable to tell us what the input was, and it may be perplexed to see the left hand acting on the segregated knowledge, for reasons it can’t fathom.

In this regard, brain researchers have become more cautious in recent years while many pop psychologists have run wild.

The right hemisphere receives input from and controls the movements of the left side of the body, and the left hemisphere does the same for the right.

For example, if the researcher shows the right hemisphere of a splitbrain subject a photograph of a naked man, she may giggle.

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 time at which each hemisphere points farthest or nearest from its star is known as its solstice.
- It day being the longest, the other has its winter solstice when its oscillates between 22.1° and 24.5° on a day is shortest.
- Each planet has two in the course of its orbit; when one hemisphere has its summer solstice with its Earth's axial tilt is about 23.4°.
- Jupiter's axial tilt is very small, so its seasonal variation is minimal; Uranus, on the other hand, has an axial tilt so extreme it is virtually on its side, which means that its hemispheres are either continually in sunlight or continually in darkness around the time of its solstices.[69] In the Solar System, Mercury, Venus, Ceres, and Jupiter have very small tilts; Pallas, Uranus, and Pluto have extreme ones; and Earth, Mars, Vesta, Saturn, and Neptune have moderate ones.[70][71][72][73] Among exoplanets, axial tilts are not known for certain, though most hot Jupiters are believed to have a negligible axial tilt as a result of their proximity to their stars.[74] Similarly, the axial tilts of the

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

It day being the longest, the other has its winter solstice when its oscillates between 22.1° and 24.5° on a day is shortest.

Each planet has two in the course of its orbit; when one hemisphere has its summer solstice with its Earth's axial tilt is about 23.4°.

Jupiter's axial tilt is very small, so its seasonal variation is minimal; Uranus, on the other hand, has an axial tilt so extreme it is virtually on its side, which means that its hemispheres are either continually in sunlight or continually in darkness around the time of its solstices.[69] In the Solar System, Mercury, Venus, Ceres, and Jupiter have very small tilts; Pallas, Uranus, and Pluto have extreme ones; and Earth, Mars, Vesta, Saturn, and Neptune have moderate ones.[70][71][72][73] Among exoplanets, axial tilts are not known for certain, though most hot Jupiters are believed to have a negligible axial tilt as a result of their proximity to their stars.[74] Similarly, the axial tilts of the

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Butwearealreadyacquaintedwithsuchanobject,theChristoffelsymbol(cid:25) fromway ̃ backinchaptersI.7,II.1,II.2,andV.3.Ournotation(cid:25) isintentionallysuggestive!Tosee that(cid:25)mightwork,werecallitsdefinition: (cid:25)μ ≡ 1gμσ(∂ g +∂ g −∂ g ) (4) λν 2 λ νσ ν σλ σ λν It involves ordinary partial derivatives of the metric tensor g and thus, for the same μν reason as in (2), (cid:25) can’t possibly transform like a tensor.
- We can thus hope that the nontensorialpieceinthetransformationlawof(cid:25)willcancelpreciselytheunwantedsecond termin(2).This“smellsright”:thederivativesofg in(4)describetheveryeffectweare μν worriedabout,namelythevariationfrompointtopointofthecoordinateaxesrelativeto whichthecomponentsofourvectorWμaredefined.
- Construct D Wμ by adding something to λ ∂ Wμ to cancel the second term in (2).
- ∗Oneofmyprofessors,thedistinguishedtheoreticalphysicistMurphGoldberger,wasfondofshouting,“If myaunthadballs,shewouldbemyuncle!”Believeme,thismadeadeepimpressiononaChinesekidfresh fromBrazil.

Butwearealreadyacquaintedwithsuchanobject,theChristoffelsymbol(cid:25) fromway ̃ backinchaptersI.7,II.1,II.2,andV.3.Ournotation(cid:25) isintentionallysuggestive!Tosee that(cid:25)mightwork,werecallitsdefinition: (cid:25)μ ≡ 1gμσ(∂ g +∂ g −∂ g ) (4) λν 2 λ νσ ν σλ σ λν It involves ordinary partial derivatives of the metric tensor g and thus, for the same μν reason as in (2), (cid:25) can’t possibly transform like a tensor.

We can thus hope that the nontensorialpieceinthetransformationlawof(cid:25)willcancelpreciselytheunwantedsecond termin(2).This“smellsright”:thederivativesofg in(4)describetheveryeffectweare μν worriedabout,namelythevariationfrompointtopointofthecoordinateaxesrelativeto whichthecomponentsofourvectorWμaredefined.

Construct D Wμ by adding something to λ ∂ Wμ to cancel the second term in (2).

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- [Hint: Work to linear t order in Φ.
- Note that u2 is of linear order in Φ.] 3.
- For a massless particle, the proper time along a geodesic is zero, and the affine parameter λ must be used instead of the proper time.
- The 4-velocity of a massless particle can be defined to be (and really this is just the 4-momentum pμ up to an arbitrary overall factor) vμ ≡dxμ/dλ={vt,vx,vy,vz}.

Note that u2 is of linear order in Φ.] 3.

For a massless particle, the proper time along a geodesic is zero, and the affine parameter λ must be used instead of the proper time.

The 4-velocity of a massless particle can be defined to be (and really this is just the 4-momentum pμ up to an arbitrary overall factor) vμ ≡dxμ/dλ={vt,vx,vy,vz}.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Although the results were fruitful, the theory also apparently implied the existence of negative energy states, which would cause atoms to be unstable, since they could always decay to lower energy states by the emission of radiation.[6]: 71–72 The prevailing view at the time was that the world was composed of two very different ingredients: material particles (such as electrons) and quantum fields (such as photons).
- Material particles were considered to be eternal, with their physical state described by the probabilities of finding each particle in any given region of space or range of velocities.
- it could be used to derive the Klein–Nishina formula for relativistic Compton scattering.
- On the other hand, photons were considered merely the excited states of the underlying quantized electromagnetic field, and could be freely created or destroyed.

Although the results were fruitful, the theory also apparently implied the existence of negative energy states, which would cause atoms to be unstable, since they could always decay to lower energy states by the emission of radiation.[6]: 71–72 The prevailing view at the time was that the world was composed of two very different ingredients: material particles (such as electrons) and quantum fields (such as photons).

Material particles were considered to be eternal, with their physical state described by the probabilities of finding each particle in any given region of space or range of velocities.

it could be used to derive the Klein–Nishina formula for relativistic Compton scattering.

On the other hand, photons were considered merely the excited states of the underlying quantized electromagnetic field, and could be freely created or destroyed.

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:
- (Number, we must note, is used in two senses – both of what is counted or the countable and also of that with which we count.
- Archived (https://web.archive.org/web/20140626030252/htt p://classics.mit.edu/Aristotle/physics.4.iv.html) from the original on 26 June 2014.
- google.com/books?id=7TPIDL9RdsoC&pg=PA7).
- Archived (https://web.archive.org/web/2 0120119043221/http://en.wikisource.org/wiki/Nicene_and_Post-Nicene_Fathers:_Series_I/Volume _I/Confessions/Book_XI/Chapter_14) from the original on 19 January 2012.

(Number, we must note, is used in two senses – both of what is counted or the countable and also of that with which we count.

Archived (https://web.archive.org/web/20140626030252/htt p://classics.mit.edu/Aristotle/physics.4.iv.html) from the original on 26 June 2014.

Archived (https://web.archive.org/web/2 0120119043221/http://en.wikisource.org/wiki/Nicene_and_Post-Nicene_Fathers:_Series_I/Volume _I/Confessions/Book_XI/Chapter_14) from the original on 19 January 2012.

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:
- of this early time remain unsettled.
- The Standard Model of particle physics is only tested up to temperatures of order 1017K (10 TeV) in particle colliders, such as the Large Hadron Collider.
- Moreover, new physical phenomena not yet covered by the Standard Model could have been important before the time of neutrino decoupling, when the temperature of the universe was about 1010K (1 MeV).[24] Electron-positron annihilation Between 1 second and 10 seconds after the Big Bang

Chronology of the universe - Wikipedia.pdf

The Standard Model of particle physics is only tested up to temperatures of order 1017K (10 TeV) in particle colliders, such as the Large Hadron Collider.

Moreover, new physical phenomena not yet covered by the Standard Model could have been important before the time of neutrino decoupling, when the temperature of the universe was about 1010K (1 MeV).[24] Electron-positron annihilation Between 1 second and 10 seconds after the Big Bang

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:
- “Where we can talk in private.
- What’s happening?” “We’ll go someplace safe,” I whisper.
- The driver glances back and asks with a heavy Russian accent, “Where to now?”
- I tell Daniela to wait, and then I step out of the car and walk toward my son.

What’s happening?” “We’ll go someplace safe,” I whisper.

The driver glances back and asks with a heavy Russian accent, “Where to now?”

I tell Daniela to wait, and then I step out of the car and walk toward my son.

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:
- TheaimofthisChapteristogiveacondensedintroductiontothefundamentalsofgeneralrelativity,using the traditional coordinate-based approach to general relativity.
- The approach is neither the most insightful nor the most powerful, but it is the fastest route to connecting the metric to the energy-momentum content of spacetime.
- The Chapter does not attempt to convey a deep conceptual understanding, which I think is difficulttogainfromthemathematicsbyitself.LaterChapters,startingwithChapter7ontheSchwarzschild geometry, present visualizations intended to aid conceptual understanding.
- The other three known forces of Nature, the electromagnetic, weak, and colour (strong) forces, are described by renormalizable quantum field theories, the so-called Standard Model of Physics, that agree extraordinarily well with experiment, and whose predictions have continued to be confirmed by ever more precisemeasurements.Attemptstoquantizegeneralrelativityinasimilarfashionfail.Theattempttounite general relativity and quantum mechanics continues to exercise some of the brightest minds in physics.

TheaimofthisChapteristogiveacondensedintroductiontothefundamentalsofgeneralrelativity,using the traditional coordinate-based approach to general relativity.

The approach is neither the most insightful nor the most powerful, but it is the fastest route to connecting the metric to the energy-momentum content of spacetime.

The Chapter does not attempt to convey a deep conceptual understanding, which I think is difficulttogainfromthemathematicsbyitself.LaterChapters,startingwithChapter7ontheSchwarzschild geometry, present visualizations intended to aid conceptual understanding.

The other three known forces of Nature, the electromagnetic, weak, and colour (strong) forces, are described by renormalizable quantum field theories, the so-called Standard Model of Physics, that agree extraordinarily well with experiment, and whose predictions have continued to be confirmed by ever more precisemeasurements.Attemptstoquantizegeneralrelativityinasimilarfashionfail.Theattempttounite general relativity and quantum mechanics continues to exercise some of the brightest minds in physics.

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:
- Wearefamiliarwiththe well known example of spooky action at a distance (entangled qubits), but adding
- Secondly, while quite a few ways of violating the averaged energy condition were mentioned in this paper, there might exist other, more elegant methods which are yet to be discovered and which would greatly simplify the creation of a traversable wormhole.
- First of all, even with the many existing descriptions of constructions of traversable wormholes, we are nowhere close to actually creating one, or at least to imagining an experiment which would, once put into practice, bring into existence such an object.
- Thirdly, the extent of the implications of traversable wormholes on quantum informationtheoriesandinformationtransportisstillunknown.

Wearefamiliarwiththe well known example of spooky action at a distance (entangled qubits), but adding

Secondly, while quite a few ways of violating the averaged energy condition were mentioned in this paper, there might exist other, more elegant methods which are yet to be discovered and which would greatly simplify the creation of a traversable wormhole.

First of all, even with the many existing descriptions of constructions of traversable wormholes, we are nowhere close to actually creating one, or at least to imagining an experiment which would, once put into practice, bring into existence such an object.

Thirdly, the extent of the implications of traversable wormholes on quantum informationtheoriesandinformationtransportisstillunknown.

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 first, the principle of deferred measurement, states that any measurement can be moved to the end of the circuit.
- Notice that the circuit that decodes allows the information to be converted the Bell state is the adjoint to the circuit that encodes, or creates, from quantum information to a Bell states (described above).
- For example, the Bell state is a pure state, but the reduced density operator of the first qubit is a mixed state.
- Because Bell states are entangled states, information on the entire system may be known, while withholding information on the individual subsystems.

The first, the principle of deferred measurement, states that any measurement can be moved to the end of the circuit.

Notice that the circuit that decodes allows the information to be converted the Bell state is the adjoint to the circuit that encodes, or creates, from quantum information to a Bell states (described above).

For example, the Bell state is a pure state, but the reduced density operator of the first qubit is a mixed state.

Because Bell states are entangled states, information on the entire system may be known, while withholding information on the individual subsystems.

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:
- Taken together these theories became the basis for what would later be called classical physics.[31]: 2 A few experimental results remained inexplicable.
- The character of electron emission of illuminated metals differed from predictions.
- Both of these theories came about due to inaccuracies in classical mechanics in certain situations.
- Classical electromagnetism presumed a medium, an luminiferous aether to support the propagation of waves, but this medium could not be detected.

Taken together these theories became the basis for what would later be called classical physics.[31]: 2 A few experimental results remained inexplicable.

The character of electron emission of illuminated metals differed from predictions.

Both of these theories came about due to inaccuracies in classical mechanics in certain situations.

Classical electromagnetism presumed a medium, an luminiferous aether to support the propagation of waves, but this medium could not be detected.

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:
- S2CID 118187860 (https://api.semanticscholar.org/CorpusID:118187860).
- (https://web.archive.org/we b/20150704043700/http://sci-ed.org/documents/Lauginie-M.pdf) (PDF).
- "The Fire That Comes from the Eye".
- Roger Bacon and the origins of Perspectiva in the Middle Ages: a critical edition and English translation of Bacon's Perspectiva, with introduction and notes (https://books.g oogle.com/books?id=jSPHMKbjYkQC&pg=PA143).

Roger Bacon and the origins of Perspectiva in the Middle Ages: a critical edition and English translation of Bacon's Perspectiva, with introduction and notes (https://books.g oogle.com/books?id=jSPHMKbjYkQC&pg=PA143).

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:
- Converse The relations ≤ and ≥ are each other's converse, meaning that for any real numbers a and b: a ≤ b and b ≥ a are equivalent.
- If either of the premises is a strict inequality, then the conclusion is a strict inequality: If a ≤ b and b < c, then a < c.
- Multiplication and division The properties that deal with multiplication and division state that for any real numbers, a, b and non-zero c:
- Properties on the number line Inequalities are governed by the following properties.

Inequality (mathematics) - Wikipedia.pdf

Converse The relations ≤ and ≥ are each other's converse, meaning that for any real numbers a and b: a ≤ b and b ≥ a are equivalent.

If either of the premises is a strict inequality, then the conclusion is a strict inequality: If a ≤ b and b < c, then a < c.

Multiplication and division The properties that deal with multiplication and division state that for any real numbers, a, b and non-zero c:

Properties on the number line Inequalities are governed by the following properties.

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

EVIDENCE:
- 1060 The Standard Model of Physics and beyond The quadratic Casimir invariants (42.58) differ correspondingly, ⎧ 2 SU(2) ⎨ C (2l)=l(l+1)× 1 Spin(3) .
- The Dynkin metrics of SU(4) and Spin(6) are ⎧ ⎛ ⎞ 3 2 1 ⎪⎪⎪⎪⎪⎪⎪⎨ 1 ⎝ 2 ⎠ SU(4) g ij = ⎛ 4 2 2 ⎞ , (42.77) ⎪⎪⎪⎪⎪⎪⎪⎩ 1 ⎝ 2 ⎠ Spin(6) which are related by permuting the first two rows and columns, 1 ↔ 2.
- The Dynkin metric of SU(2) is the 1×1 matrix 1( ) g = 1 .
- Therefore Spin(4) is isomorphic to SU(2)×SU(2).

1060 The Standard Model of Physics and beyond The quadratic Casimir invariants (42.58) differ correspondingly, ⎧ 2 SU(2) ⎨ C (2l)=l(l+1)× 1 Spin(3) .

The Dynkin metrics of SU(4) and Spin(6) are ⎧ ⎛ ⎞ 3 2 1 ⎪⎪⎪⎪⎪⎪⎪⎨ 1 ⎝ 2 ⎠ SU(4) g ij = ⎛ 4 2 2 ⎞ , (42.77) ⎪⎪⎪⎪⎪⎪⎪⎩ 1 ⎝ 2 ⎠ Spin(6) which are related by permuting the first two rows and columns, 1 ↔ 2.

The Dynkin metric of SU(2) is the 1×1 matrix 1( ) g = 1 .

Therefore Spin(4) is isomorphic to SU(2)×SU(2).

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

EVIDENCE:
- This is the way it came to appear: Atoms are compressed at the center of the Earth, and the expansive force of these compressed atoms is great enough to hold up all the substance of the overlying layers of the planet like so many miniature Atlases.
- It came to be understood that the tiny atom is a loose structure of particles far tinier still.
- Even the little Atlases have their breaking point, however.
- The mass of the Sun, a thousand times as great as that of Jupiter, under the inward pull of an enormous gravitation reach and pass the limits of strength of intact atoms.

This is the way it came to appear: Atoms are compressed at the center of the Earth, and the expansive force of these compressed atoms is great enough to hold up all the substance of the overlying layers of the planet like so many miniature Atlases.

It came to be understood that the tiny atom is a loose structure of particles far tinier still.

Even the little Atlases have their breaking point, however.

The mass of the Sun, a thousand times as great as that of Jupiter, under the inward pull of an enormous gravitation reach and pass the limits of strength of intact atoms.

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

EVIDENCE:
- In Amelino-Camelia, G; Kowalski-Glikman, J (eds.).
- Optical Fiber Communications (https://archive.org/details/opticalfibercomm00ge rd/page/32) (3 ed.).
- "Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London" (https://doi.org/10.1098%2 Frstl.1694.0048).
- (https://ui.adsabs.harvard.edu/abs/1677RSPT...12..893.).

In Amelino-Camelia, G; Kowalski-Glikman, J (eds.).

Optical Fiber Communications (https://archive.org/details/opticalfibercomm00ge rd/page/32) (3 ed.).

"Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London" (https://doi.org/10.1098%2 Frstl.1694.0048).

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

EVIDENCE:
- Nitpickers,please!It’swhatIcouldsayin30seconds!
- The answer to that question will lead us to curved spacetimeandEinsteingravity.4 Truthisnotrelative Laterinlife,Einsteinmoanedthatheshouldhavecalledhiswork“invarianttheory”instead of “relativity theory.” Had he been more judicious in his choice of words, you, I, and Einsteinwouldhavebeensparedthespectacleofeminenthumanitiesscholarsasserting that“Truthisrelative”since“Thereisnoabsolutetruth:Einsteinproveditso.”Ofcourse, youknowthatEinsteinsaidexactlytheopposite.Physicsmustbeinvariantandtrue.
- Therelations(1)and(2)betweenspaceandtime weremodified.
- What could that force possibly be?

The answer to that question will lead us to curved spacetimeandEinsteingravity.4 Truthisnotrelative Laterinlife,Einsteinmoanedthatheshouldhavecalledhiswork“invarianttheory”instead of “relativity theory.” Had he been more judicious in his choice of words, you, I, and Einsteinwouldhavebeensparedthespectacleofeminenthumanitiesscholarsasserting that“Truthisrelative”since“Thereisnoabsolutetruth:Einsteinproveditso.”Ofcourse, youknowthatEinsteinsaidexactlytheopposite.Physicsmustbeinvariantandtrue.

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

EVIDENCE:
- Energy conservation requires that |u| = |v|.
- 6-3 between a moving particle colliding with an equal mass stationary particle.
- Unlike the Newtonian case, the angle between the two particles after collision is less than 90°, is dependent on the angle of scattering, and becomes smaller and smaller as the velocity of the incident particle approaches the speed of light: The relativistic momentum and total relativistic energy of a particle are given by (6-4)
- (c) Reverting to the stationary frame, the rebound velocities are v ± u.

Energy conservation requires that |u| = |v|.

6-3 between a moving particle colliding with an equal mass stationary particle.

Unlike the Newtonian case, the angle between the two particles after collision is less than 90°, is dependent on the angle of scattering, and becomes smaller and smaller as the velocity of the incident particle approaches the speed of light: The relativistic momentum and total relativistic energy of a particle are given by (6-4)

(c) Reverting to the stationary frame, the rebound velocities are v ± u.

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

EVIDENCE:
- Consequently any continuum or line Lyman photon emitted as a result of a recombination or transition to the ground state would be quickly absorbed.
- (31.61) dt p e + 2 2 2 Equation (31.61) ignores stimulated recombination, which is a e−E2/T ≪1 correction to the rate.
- The second process is that, although most decays 2s outofthe2pstateproducedaLymanα photonthatwasimmediatelyabsorbedbyanearbyhydrogenatom, theexpansionoftheUniverseredshiftedtheemittedphoton,andasmallfractionP oftheemittedLymanα S photonssucceededinredshiftingoutofthelinewithoutbeingreabsorbed.ThefractionP ofemittedphotons S that escape in an expanding medium can be approximated using the Sobolev formalism, §31.10.
- The first process is 2-photon decay out of the 2s state, which occurs at a rate A =8.22458s−1.

Consequently any continuum or line Lyman photon emitted as a result of a recombination or transition to the ground state would be quickly absorbed.

(31.61) dt p e + 2 2 2 Equation (31.61) ignores stimulated recombination, which is a e−E2/T ≪1 correction to the rate.

The second process is that, although most decays 2s outofthe2pstateproducedaLymanα photonthatwasimmediatelyabsorbedbyanearbyhydrogenatom, theexpansionoftheUniverseredshiftedtheemittedphoton,andasmallfractionP oftheemittedLymanα S photonssucceededinredshiftingoutofthelinewithoutbeingreabsorbed.ThefractionP ofemittedphotons S that escape in an expanding medium can be approximated using the Sobolev formalism, §31.10.

The first process is 2-photon decay out of the 2s state, which occurs at a rate A =8.22458s−1.

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

EVIDENCE:
- As discussed previously with regard to the Gullstrand-Painlevé river, §19.2.3, the tidal change δωk , m equation (19.66), in the river field seen by a fishy is not the full change δxν∂ωk /∂xν relative to the m background coordinates, but rather the change relative to the river δωk =(δxν −δxν ) ∂ωk m = [ δxν −βν(δt −asin2θδφ ) ]∂ωk m , (19.68) m river ∂xν ff ff ∂xν with the change in the velocity and twist of the river itself subtracted off.
- Like a static electric field, the velocity vector βa is the gradient of a potential ∂ ∫ r βa =δa βdr , (19.64) α∂xα but unlike a magnetic field the twist vector μa is not pure curl: rather, it is μa + ζa that is pure curl.
- That there exists a tetrad (the Doran-Cartesian tetrad) where the tetrad-frame connections are a coordinate gradient of a bivector, equation (19.57), is a peculiar feature of ideal black holes.
- As a result, the fishy sees a tidal change δωk in the river field m ∂ωk δωk =δξn m .

As discussed previously with regard to the Gullstrand-Painlevé river, §19.2.3, the tidal change δωk , m equation (19.66), in the river field seen by a fishy is not the full change δxν∂ωk /∂xν relative to the m background coordinates, but rather the change relative to the river δωk =(δxν −δxν ) ∂ωk m = [ δxν −βν(δt −asin2θδφ ) ]∂ωk m , (19.68) m river ∂xν ff ff ∂xν with the change in the velocity and twist of the river itself subtracted off.

Like a static electric field, the velocity vector βa is the gradient of a potential ∂ ∫ r βa =δa βdr , (19.64) α∂xα but unlike a magnetic field the twist vector μa is not pure curl: rather, it is μa + ζa that is pure curl.

That there exists a tetrad (the Doran-Cartesian tetrad) where the tetrad-frame connections are a coordinate gradient of a bivector, equation (19.57), is a peculiar feature of ideal black holes.

As a result, the fishy sees a tidal change δωk in the river field m ∂ωk δωk =δξn m .

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

EVIDENCE:
- Timeline of information theory Yockey, H.P.
- History of information theory Shannon, C.E.
- doi:10.1109/memb.2006.1578661 (https://doi.org/10.1109%2Fmemb.2006.1578661).
- PMID 16485389 (https://pubmed.ncbi.nlm.nih.gov/16485389).

Timeline of information theory Yockey, H.P.

History of information theory Shannon, C.E.

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

EVIDENCE:
- During teleportation the radio signals emitted by the
- If you watch it do this often enough, the twinkling sort of motion from one state to the other begins to seem like a continuous motion.
- If this is the case, then the three-dimensional nets of neurons that code thoughts in our brain may form four-dimensional patterns to achieve fourdimensional thought.
- Möbius discovered in 1827 that it is in fact possible to turn a three-dimensional solid object into its mirror image by an appropriate rotation through four-dimensional space (a.k.a.

During teleportation the radio signals emitted by the

If you watch it do this often enough, the twinkling sort of motion from one state to the other begins to seem like a continuous motion.

If this is the case, then the three-dimensional nets of neurons that code thoughts in our brain may form four-dimensional patterns to achieve fourdimensional thought.

Möbius discovered in 1827 that it is in fact possible to turn a three-dimensional solid object into its mirror image by an appropriate rotation through four-dimensional space (a.k.a.

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

EVIDENCE:
- Notwithstanding its restricted validity,[44] Moseley's law not only established the objective meaning of atomic number, but as Bohr noted, it also did more than the Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge.
- Van den Broek had published his model in January 1913 showing the periodic table was arranged according to charge while Bohr's atomic model was not published until July 1913.[45] The K-alpha line of Moseley's time is now known to be a pair of close lines, written as (Kα and Kα ) 1 2 in Siegbahn notation.

Notwithstanding its restricted validity,[44] Moseley's law not only established the objective meaning of atomic number, but as Bohr noted, it also did more than the Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge.

Van den Broek had published his model in January 1913 showing the periodic table was arranged according to charge while Bohr's atomic model was not published until July 1913.[45] The K-alpha line of Moseley's time is now known to be a pair of close lines, written as (Kα and Kα ) 1 2 in Siegbahn notation.

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

EVIDENCE:
- Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler–Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as |ω | −s in the above.[28] n More recent theory Casimir's analysis of idealized metal plates was generalized to arbitrary dielectric and realistic metal plates by Evgeny Lifshitz and his students.[5][29] Using this approach, complications of the bounding surfaces, such as the modifications to the Casimir force due to finite conductivity, can be calculated numerically using the tabulated complex dielectric functions of the bounding materials.
- The zero-point energy on both sides of the plate is considered.
- Lifshitz's theory for two metal plates reduces to Casimir's idealized force law for large separations a much a4
- where ħ is the reduced Planck constant, c is the speed of light, a is the distance between the two plates The force is negative, indicating that the force is attractive: by moving the two plates closer together, F c the energy is lowered.

Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler–Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as |ω | −s in the above.[28] n More recent theory Casimir's analysis of idealized metal plates was generalized to arbitrary dielectric and realistic metal plates by Evgeny Lifshitz and his students.[5][29] Using this approach, complications of the bounding surfaces, such as the modifications to the Casimir force due to finite conductivity, can be calculated numerically using the tabulated complex dielectric functions of the bounding materials.

The zero-point energy on both sides of the plate is considered.

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

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

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

EVIDENCE:
- All make extensive use of Barnum statements in their readings.You’re also likely to observe the Barnum Effect at work during your next visit to a Chinese restaurant.
- Still other Barnum items refer to trivial weaknesses that are so prevalent in the general population as to be virtually meaningless for assessment purposes (for example, “I sometimes have difficulty making decisions”) or to assertions that are impossible to disconfirm (for example, “I have a great deal of unrecognized potential”).
- Who doesn’t sometimes desire approval, and how could we prove that someone who appears fiercely independent doesn’t possess a deeply hidden need for approval?
- About three fourths of individuals with autism are mentally retarded, and most are male.

All make extensive use of Barnum statements in their readings.You’re also likely to observe the Barnum Effect at work during your next visit to a Chinese restaurant.

Still other Barnum items refer to trivial weaknesses that are so prevalent in the general population as to be virtually meaningless for assessment purposes (for example, “I sometimes have difficulty making decisions”) or to assertions that are impossible to disconfirm (for example, “I have a great deal of unrecognized potential”).

Who doesn’t sometimes desire approval, and how could we prove that someone who appears fiercely independent doesn’t possess a deeply hidden need for approval?

About three fourths of individuals with autism are mentally retarded, and most are male.

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

EVIDENCE:
- See also Abraham–Lorentz force Physics portal Acoustic metric Beyond black holes Black hole electron Black hole starship Cosmic censorship hypothesis Dynamical horizon Event Horizon Telescope Hawking radiation Kugelblitz (astrophysics) Micro black hole Rindler coordinates Notes 1.
- A complete description of local event horizons generated by gravity is expected to, at minimum, require a theory of quantum gravity.
- Black hole complementarity is actually suggested by the scaling laws of strings approaching the event horizon, suggesting that in the Schwarzschild chart they stretch to cover the horizon and thermalize into a Planck length-thick membrane.
- For accelerating particles, this manifests as the Unruh effect, which causes space around the particle to appear to be filled with matter and radiation.

See also Abraham–Lorentz force Physics portal Acoustic metric Beyond black holes Black hole electron Black hole starship Cosmic censorship hypothesis Dynamical horizon Event Horizon Telescope Hawking radiation Kugelblitz (astrophysics) Micro black hole Rindler coordinates Notes 1.

A complete description of local event horizons generated by gravity is expected to, at minimum, require a theory of quantum gravity.

Black hole complementarity is actually suggested by the scaling laws of strings approaching the event horizon, suggesting that in the Schwarzschild chart they stretch to cover the horizon and thermalize into a Planck length-thick membrane.

For accelerating particles, this manifests as the Unruh effect, which causes space around the particle to appear to be filled with matter and radiation.

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

EVIDENCE:
- Universe is well described by 4D An example of compactification: At large spacetime, there are several reasons why physicists consider distances, a two dimensional surface with one circular dimension looks onetheories in other dimensions.
- In some cases, by modeling dimensional.
- spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily.[a] There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics.[13] Finally, there exist scenarios in which there could actually be more than 4D of spacetime which have nonetheless managed to escape detection.[20]

Universe is well described by 4D An example of compactification: At large spacetime, there are several reasons why physicists consider distances, a two dimensional surface with one circular dimension looks onetheories in other dimensions.

spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily.[a] There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics.[13] Finally, there exist scenarios in which there could actually be more than 4D of spacetime which have nonetheless managed to escape detection.[20]

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

EVIDENCE:
- Gauss, and in the first rank of experimentalists, thereby putting "Newton in a class by himself among empirical scientists, for one has trouble in thinking of any other candidate who was in the first rank of even two of these categories." Also noted is "At least in comparison to subsequent scientists, Newton was also exceptional in his ability to put his scientific effort in much wider perspective".[288] Gauss himself had Archimedes and Newton as his heroes,[289] and used terms such as clarissimus or magnus to describe other intellectuals such as great mathematicians and philosophers, but reserved summus for Newton only, and once realising the immense influence of Newton's work on scientists such as Lagrange and Pierre-Simon Laplace, Gauss then exclaimed that "Newton remains forever the master of all masters!"[278][290] In his book Great Physicists, the chemist William H.
- In 1999, an opinion poll of 100 of the day's leading physicists voted Einstein the "greatest physicist ever," with Newton the runner-up, while a parallel survey of rank-and-file physicists ranked Newton as the greatest.[295][296] In 2005, a dual survey of the public and members of Britain's Royal Society asked two questions: who made the bigger overall contributions to science and who made the bigger positive contributions to humankind, with the candidates being Newton or Einstein.
- Cropper highlighted the unparalleled genius of Newton, stating:[291] On one assessment there should be no doubt: Newton was the greatest creative genius physics has ever seen.
- Albert Einstein kept a picture of Newton on his study wall alongside ones of Michael Faraday and of James Clerk Maxwell.[292] Einstein stated that Newton's creation of calculus in relation to his laws of motion was "perhaps the greatest advance in thought that a single individual was ever privileged to make."[293] He also noted the influence of Newton, stating that:[294] The whole evolution of our ideas about the processes of nature, with which we have been concerned so far, might be regarded as an organic development of Newton's ideas.

Gauss, and in the first rank of experimentalists, thereby putting "Newton in a class by himself among empirical scientists, for one has trouble in thinking of any other candidate who was in the first rank of even two of these categories." Also noted is "At least in comparison to subsequent scientists, Newton was also exceptional in his ability to put his scientific effort in much wider perspective".[288] Gauss himself had Archimedes and Newton as his heroes,[289] and used terms such as clarissimus or magnus to describe other intellectuals such as great mathematicians and philosophers, but reserved summus for Newton only, and once realising the immense influence of Newton's work on scientists such as Lagrange and Pierre-Simon Laplace, Gauss then exclaimed that "Newton remains forever the master of all masters!"[278][290] In his book Great Physicists, the chemist William H.

In 1999, an opinion poll of 100 of the day's leading physicists voted Einstein the "greatest physicist ever," with Newton the runner-up, while a parallel survey of rank-and-file physicists ranked Newton as the greatest.[295][296] In 2005, a dual survey of the public and members of Britain's Royal Society asked two questions: who made the bigger overall contributions to science and who made the bigger positive contributions to humankind, with the candidates being Newton or Einstein.

Cropper highlighted the unparalleled genius of Newton, stating:[291] On one assessment there should be no doubt: Newton was the greatest creative genius physics has ever seen.

Albert Einstein kept a picture of Newton on his study wall alongside ones of Michael Faraday and of James Clerk Maxwell.[292] Einstein stated that Newton's creation of calculus in relation to his laws of motion was "perhaps the greatest advance in thought that a single individual was ever privileged to make."[293] He also noted the influence of Newton, stating that:[294] The whole evolution of our ideas about the processes of nature, with which we have been concerned so far, might be regarded as an organic development of Newton's ideas.

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

EVIDENCE:
- Adiscwith blinkingredlightsapproacheshimandgetswithin350feet,bathinghiscockpitinblue-whitelight.
- EdwardBaloccoisscrambledinanF9F PantherfromNavalAuxiliaryAirStationEdenton,NCtointerceptanunknowntarget.
- ● https://www.cia.gov/readingroom/docs/CIA-RDP81R00560R000100030026-1.pdf(p30-31) ● http://www.cufon.org/cufon/tp corres.htm (PUBLICDOMAIN) -9February1953—USAFPublicInformationOfficerAlbertM.Chopclaims theCIA“killed”apressreleasewrittenuponaUAPfilmedonUtah.
- BaloccoandCapt.ThomasRiggsaredebriefedandtoldnottomentiontheincidenttoanyone.

● https://www.cia.gov/readingroom/docs/CIA-RDP81R00560R000100030026-1.pdf(p30-31) ● http://www.cufon.org/cufon/tp corres.htm (PUBLICDOMAIN) -9February1953—USAFPublicInformationOfficerAlbertM.Chopclaims theCIA“killed”apressreleasewrittenuponaUAPfilmedonUtah.

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

EVIDENCE:
- Wormhole Metric and Geodesic Equations ds2 = −dt2+dr2+(b2+r2)(dθ2+sin2θdφ2).
- d2t = 0 dτ2 (cid:34) (cid:35) d2r (cid:18) dθ (cid:19)2 (cid:18) dφ (cid:19)2 = r +sin2θ dτ2 dτ dτ d (cid:18) dθ (cid:19) (cid:18) dφ (cid:19)2 (b2+r2) = (b2+r2)sinθcosθ dτ dτ dτ (cid:18) (cid:19) d dφ (b2+r2)sin2θ = 0.
- dτ dτ Christoffel Symbols Γr = −r, Γr = −r sin2θ, Γθ = r = Γθ , θθ φφ θr b2+r2 rθ Γθ = −sinθcosθ, Γφ = r = Γφ ,Γφ = cotθ = Γφ .

Wormhole Metric and Geodesic Equations ds2 = −dt2+dr2+(b2+r2)(dθ2+sin2θdφ2).

dτ dτ Christoffel Symbols Γr = −r, Γr = −r sin2θ, Γθ = r = Γθ , θθ φφ θr b2+r2 rθ Γθ = −sinθcosθ, Γφ = r = Γφ ,Γφ = cotθ = Γφ .

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

EVIDENCE:
- 29.1 Unperturbed line-element It is convenient to choose the coordinate system xμ ≡ {x0,x1,x2,x3} ≡ {η,x,y,z} to consist of conformal time η together with comoving Cartesian coordinates x ≡ xα ≡ {x,y,z}.
- The coordinate metric of the unperturbed background flat FLRW geometry is then ds2 =a(η)2( −dη2+dx2+dy2+dz2) , (29.1) where a(η) is the cosmic scale factor.
- The strategy is to start in a completely general gauge, and to discover how the conformal Newtonian (Copernican) gauge, which is used in subsequent Chapters, emerges naturally as that gauge in which the perturbations are precisely the physical perturbations.
- With some modifications arising from cosmological expansion, perturbation theory on a flat FLRW background is quite similar to perturbation theory in flat (Minkowski) space, Chapter 27.

29.1 Unperturbed line-element It is convenient to choose the coordinate system xμ ≡ {x0,x1,x2,x3} ≡ {η,x,y,z} to consist of conformal time η together with comoving Cartesian coordinates x ≡ xα ≡ {x,y,z}.

The coordinate metric of the unperturbed background flat FLRW geometry is then ds2 =a(η)2( −dη2+dx2+dy2+dz2) , (29.1) where a(η) is the cosmic scale factor.

The strategy is to start in a completely general gauge, and to discover how the conformal Newtonian (Copernican) gauge, which is used in subsequent Chapters, emerges naturally as that gauge in which the perturbations are precisely the physical perturbations.

With some modifications arising from cosmological expansion, perturbation theory on a flat FLRW background is quite similar to perturbation theory in flat (Minkowski) space, Chapter 27.

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

EVIDENCE:
- It is difficult to fathom what will be in store for the teleportation of human beings given some possible future technology.
- It is difficult to see how far computer technology will advance towards meeting this requirement.
- QISP was funded for $19 million in 1999.
- This is a major ethical and technical question that will have to be addressed by future research.

It is difficult to fathom what will be in store for the teleportation of human beings given some possible future technology.

It is difficult to see how far computer technology will advance towards meeting this requirement.

QISP was funded for $19 million in 1999.

This is a major ethical and technical question that will have to be addressed by future research.

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

EVIDENCE:
- Interestingly, some early findings on sleep-assisted learning yielded encouraging results.
- In an episode of the popular television program, Friends, Chandler Bing (portrayed by Matthew Perry) attempts to quit smoking by playing a tape containing suggestions to stop smoking during sleep.
- But does the popular conception of sleep-assisted learning stack up to its advocates’ impressive claims?
- Nor do they show that people can later recall these externally presented stimuli in everyday life if they’re not awakened from their dreams.

Interestingly, some early findings on sleep-assisted learning yielded encouraging results.

In an episode of the popular television program, Friends, Chandler Bing (portrayed by Matthew Perry) attempts to quit smoking by playing a tape containing suggestions to stop smoking during sleep.

But does the popular conception of sleep-assisted learning stack up to its advocates’ impressive claims?

Nor do they show that people can later recall these externally presented stimuli in everyday life if they’re not awakened from their dreams.

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:
- Bernstein, Ethan; Vazirani, Umesh (1997).
- "Non-Abelian anyons and topological quantum computation" (https://journals.ap s.org/rmp/abstract/10.1103/RevModPhys.80.1083).
- Tacchino, Francesco; Chiesa, Alessandro; Carretta, Stefano; Gerace, Dario (19 December 2019).
- Nayak, Chetan; Simon, Steven H.; Stern, Ady; Freedman, Michael; Das Sarma, Sankar (12 September 2008).

Bernstein, Ethan; Vazirani, Umesh (1997).

"Non-Abelian anyons and topological quantum computation" (https://journals.ap s.org/rmp/abstract/10.1103/RevModPhys.80.1083).

Tacchino, Francesco; Chiesa, Alessandro; Carretta, Stefano; Gerace, Dario (19 December 2019).

Nayak, Chetan; Simon, Steven H.; Stern, Ady; Freedman, Michael; Das Sarma, Sankar (12 September 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:
- about host galaxies and detections of X-ray lines associated with gamma-ray bursts.
- This formula predicts a gamma ray flux for the planet Jupiter that is some six orders of magnitude larger than it is actually observed to be.
- That is, furthermore, without taking into account the fact that other Solar System material in addition to the solar wind infalls to Jupiter.[6]
- The discovery of a supernova associated with a gamma-ray burst in 2002 provided compelling evidence that massive stars are the origin of gamma-ray bursts.[17] Since 2002, more supernovae have been observed to be associated with gamma-ray bursts, and massive stars as the origin of gamma-ray bursts has been firmly established.

about host galaxies and detections of X-ray lines associated with gamma-ray bursts.

This formula predicts a gamma ray flux for the planet Jupiter that is some six orders of magnitude larger than it is actually observed to be.

That is, furthermore, without taking into account the fact that other Solar System material in addition to the solar wind infalls to Jupiter.[6]

The discovery of a supernova associated with a gamma-ray burst in 2002 provided compelling evidence that massive stars are the origin of gamma-ray bursts.[17] Since 2002, more supernovae have been observed to be associated with gamma-ray bursts, and massive stars as the origin of gamma-ray bursts has been firmly established.

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:
- Energy levels The potential energy of an electron in an atom is negative relative to when the distance from the nucleus goes to infinity; its dependence on the electron's position reaches the minimum inside the nucleus, roughly in inverse proportion to the distance.
- The lowest energy inclusively.
- For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.
- stationary state, while an electron transition to a higher level results in an excited state.[91] The electron's energy increases along with n because the (average) distance to the nucleus increases.

Energy levels The potential energy of an electron in an atom is negative relative to when the distance from the nucleus goes to infinity; its dependence on the electron's position reaches the minimum inside the nucleus, roughly in inverse proportion to the distance.

For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.

stationary state, while an electron transition to a higher level results in an excited state.[91] The electron's energy increases along with n because the (average) distance to the nucleus increases.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- the muon and the muon neutrino; the third generation consists of the top and bottom quarks and the tau and tau neutrino.[28] The most natural explanation for this would be that quarks and leptons of higher generations are excited states of the first generations.
- If this turns out to be the case, it would imply that quarks and leptons are composite particles, rather than elementary particles.[29] This quark–lepton definition of matter also leads to what can be described as "conservation of (net) matter" laws—discussed later below.
- Alternatively, one could return to the mass–volume–space concept of matter, leading to the next definition, in which antimatter becomes included as a subclass of matter.

the muon and the muon neutrino; the third generation consists of the top and bottom quarks and the tau and tau neutrino.[28] The most natural explanation for this would be that quarks and leptons of higher generations are excited states of the first generations.

If this turns out to be the case, it would imply that quarks and leptons are composite particles, rather than elementary particles.[29] This quark–lepton definition of matter also leads to what can be described as "conservation of (net) matter" laws—discussed later below.

Alternatively, one could return to the mass–volume–space concept of matter, leading to the next definition, in which antimatter becomes included as a subclass of matter.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- "Hubble Reaches the "Undiscovered Country" of Primeval Galaxies" (https://www.nasa.gov/missio n_pages/hubble/science/undiscovered-country.html) (Press release).
- PMID 17781305 (https://pubmed.ncbi.nlm.nih.gov/17781305).
- "Roemer and the first determination of the velocity of light (1676)" (https://bab el.hathitrust.org/cgi/imgsrv/download/pdf?id=uc1.b4375710;orient=0;size=100;seq=5;attachment= 0).
- S2CID 145428377 (http s://api.semanticscholar.org/CorpusID:145428377).

"Hubble Reaches the "Undiscovered Country" of Primeval Galaxies" (https://www.nasa.gov/missio n_pages/hubble/science/undiscovered-country.html) (Press release).

"Roemer and the first determination of the velocity of light (1676)" (https://bab el.hathitrust.org/cgi/imgsrv/download/pdf?id=uc1.b4375710;orient=0;size=100;seq=5;attachment= 0).

S2CID 145428377 (http s://api.semanticscholar.org/CorpusID:145428377).

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:
- It is related to the Hermitian conjugate Dirac spinor ψ† by equation (14.130), and
- The problem is that the Dirac 1 2 1 2 representation of a Dirac spinor ψ is a column vector, and two column vectors cannot be multiplied.
- The scalar product must be a complex (with respect to the quantum mechanical imaginary i) number that is invariant under Lorentz transformations.
- This suggests defining a row Dirac spinor ψ reverse to the column Dirac spinor ψ defined by equation (14.112) by ψ ≡ε⊤ q , (14.114) ⇑↑ whereq isthematrixrepresentationofthereverseq ofthecomplexquaternionq,andε⊤ denotesthebasisof a row Dirac spinors obtained by transposing the basis of column Dirac spinors defined by equations (14.108), ε⊤ = ( 1 0 0 0 ) , ε⊤ = ( 0 1 0 0 ) , ε⊤ = ( 0 0 1 0 ) , ε⊤ = ( 0 0 0 1 ) .

It is related to the Hermitian conjugate Dirac spinor ψ† by equation (14.130), and

The problem is that the Dirac 1 2 1 2 representation of a Dirac spinor ψ is a column vector, and two column vectors cannot be multiplied.

The scalar product must be a complex (with respect to the quantum mechanical imaginary i) number that is invariant under Lorentz transformations.

This suggests defining a row Dirac spinor ψ reverse to the column Dirac spinor ψ defined by equation (14.112) by ψ ≡ε⊤ q , (14.114) ⇑↑ whereq isthematrixrepresentationofthereverseq ofthecomplexquaternionq,andε⊤ denotesthebasisof a row Dirac spinors obtained by transposing the basis of column Dirac spinors defined by equations (14.108), ε⊤ = ( 1 0 0 0 ) , ε⊤ = ( 0 1 0 0 ) , ε⊤ = ( 0 0 1 0 ) , ε⊤ = ( 0 0 0 1 ) .

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- restoring causality and locality 4 Macroscopic realism is usually explained with the example of the Schrödinger cat.
- Consider a measurement on a cat to determine whether it is alive or dead (two macroscopically distinct states).
- It would be illogical to consider the cat as being both alive and dead before the measurement took place.
- In a system with two or more macroscopically distinct states, macroscopic realism claims that the system must always be in one of the two states.

restoring causality and locality 4 Macroscopic realism is usually explained with the example of the Schrödinger cat.

Consider a measurement on a cat to determine whether it is alive or dead (two macroscopically distinct states).

It would be illogical to consider the cat as being both alive and dead before the measurement took place.

In a system with two or more macroscopically distinct states, macroscopic realism claims that the system must always be in one of the two states.

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:
- (42.8) L R As discussed in Exercise 38.3, spinors in 2N dimensions are linear combinations of 2N basis spinors ε a
- The map (42.7) is into only if U (1)×SU(3) is modded by Z , because if z is Y 3 anythirdrootofunitythen{z, diagz−1}∈U (1)×SU(3)mapstothesameelement{1,1}ofSU (2)×SU(4).
- hypercharges 0, 4, −2, and −2, again in 3 3 agreement with Table 42.1.
- Consequently the Pati-Salam group on the right hand side of the embedding (42.5) is isomorphic to Spin(4)×Spin(6), SU (2)×SU (2)×SU(4)∼ =Spin(4)×Spin(6) .

(42.8) L R As discussed in Exercise 38.3, spinors in 2N dimensions are linear combinations of 2N basis spinors ε a

The map (42.7) is into only if U (1)×SU(3) is modded by Z , because if z is Y 3 anythirdrootofunitythen{z, diagz−1}∈U (1)×SU(3)mapstothesameelement{1,1}ofSU (2)×SU(4).

hypercharges 0, 4, −2, and −2, again in 3 3 agreement with Table 42.1.

Consequently the Pati-Salam group on the right hand side of the embedding (42.5) is isomorphic to Spin(4)×Spin(6), SU (2)×SU (2)×SU(4)∼ =Spin(4)×Spin(6) .

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:
- 3 Verifyth(cid:6)atinPainlev ́e-Gullstrandcoordinates,anobserverinradialplungestartingatrestatinfinityfollows dr =− rS,asmustbethecase,sinceintransformingfromtheSchwarzschildcoordinates,wedidnot dτ r (cid:6) changer.Showalsothat dr =− rS.
- 2 Determinetheshapeoftheorbitoflightinthepresenceofablackhole.
- ParticlesandLightaroundaBlackHole | 417 Well,well,thatConfusioismoreastutethanwethink.Indeed,theLagrangian (cid:9)(cid:3) r (cid:4)(cid:3) dt (cid:4) 2 (cid:3) r (cid:4) −1 (cid:3) dr (cid:4) 2 (cid:3) dθ (cid:4) 2 (cid:3) dφ (cid:4) 2 (cid:11) 2 1 L= 1− S − 1− S −r2 −r2sin2θ r dτ r dτ dτ dτ governing the motion of a particle in Schwarzschild spacetime is manifestly invariant under t →−t.
- dT r ∗TwicetheprimeministerofFrance.

3 Verifyth(cid:6)atinPainlev ́e-Gullstrandcoordinates,anobserverinradialplungestartingatrestatinfinityfollows dr =− rS,asmustbethecase,sinceintransformingfromtheSchwarzschildcoordinates,wedidnot dτ r (cid:6) changer.Showalsothat dr =− rS.

ParticlesandLightaroundaBlackHole | 417 Well,well,thatConfusioismoreastutethanwethink.Indeed,theLagrangian (cid:9)(cid:3) r (cid:4)(cid:3) dt (cid:4) 2 (cid:3) r (cid:4) −1 (cid:3) dr (cid:4) 2 (cid:3) dθ (cid:4) 2 (cid:3) dφ (cid:4) 2 (cid:11) 2 1 L= 1− S − 1− S −r2 −r2sin2θ r dτ r dτ dτ dτ governing the motion of a particle in Schwarzschild spacetime is manifestly invariant under t →−t.

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 ratios of corresponding sides of the two yellow triangles are constant, so that r/a = b/s = n/m = β′.
- To reduce the complexity of the equations slightly, there are a variety of different shorthand notations for ct: and are common.
- If u′ is set equal to c, then the formula yields u = c regardless of the starting value of v.
- From the platform, the composite speed of the bullet is given by u = c(s + r)/(a + b).

The ratios of corresponding sides of the two yellow triangles are constant, so that r/a = b/s = n/m = β′.

To reduce the complexity of the equations slightly, there are a variety of different shorthand notations for ct: and are common.

If u′ is set equal to c, then the formula yields u = c regardless of the starting value of v.

From the platform, the composite speed of the bullet is given by u = c(s + r)/(a + b).

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:
- Let the start of the second arrow be at the end of the first.
- can reach the detector at P by bouncing off the mirror (in blue) at various points.
- The direction of the product is found by arrows, which start at emission and end at detection of adding the angles that each of the two have been a particle.
- The rules as regards adding or multiplying, however, are the same as above.

Let the start of the second arrow be at the end of the first.

can reach the detector at P by bouncing off the mirror (in blue) at various points.

The direction of the product is found by arrows, which start at emission and end at detection of adding the angles that each of the two have been a particle.

The rules as regards adding or multiplying, however, are the same as above.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- ● https://www.amazon.com/Plain-Sight-investigation-impossible-science-ebook/dp/B08V YR4DZ6(p216) (PUBLICDOMAIN) -16August2018—ATTSAstatementofworksoughtHalPuthoff’sEarthtech Internationaltostudythepropertiesof“potentiallyexoticmaterials.” ● https://ufos-scientificresearch.blogspot.com/2018/09/details-of-contracts-between-to-stars.html (PUBLICDOMAIN) -28October2018—EricDavisstatesonaradiobroadcastthetheDel,RioTX UAPcrashwasarealeventandwasasuccessfulcrashretrieval.
- ● https://silvarecord.com/2018/10/28/dr-eric-davis-confirms-del-rio-texas-ufo-event-was-a-successf ul-crash-retrieval-2/ (PUBLICDOMAIN) -29November2018—MitreCorp’sJASONGroupinaSecretestimatewrites thatitcannotfindasingleplausiblesourceofenergythatcanproduceallthesymptomsUSGpersonnel reportrelatedtoHavanaSyndrome.Thisincludesbothaudio/videosignalsandthereportedmedical
- TTSApurchasedallegedUAPmetamaterialsoverthefollowingtwoyearsandreacheda collaborativeR&DagreementwiththeUSArmy’sCombatCapabilitiesDevelopmentCommand (USACCDC)toadvancedevelopmentsinmaterialscience,spacetimemetricengineering,quantum physics,beamedenergypropulsionandactivecamouflage.
- “We’regoingtobebringingouthardware,”DeLongeclaimed.

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:
- (17.56) β αβ ∂xγ αγ∂xβ βγ∂xα AsisusualwithaLiederivative,equation(7.152),thecoordinatederivatives∂/∂xαinequation(17.56)canbe replaced,ifdesired,bytherestrictedcovariantderivativesD^ .Sincetherestrictedcovariantderivativeofthe α spatial coordinate metric g vanishes, the Lie derivative L^ g can be written (compare equation (7.154)), αβ β αβ L^ g =D^ β +D^ β .
- Of the remaining connections (17.48), the acceleration K , equation (17.48a), αβ a and the purely spatial connections Γ , equation (17.48d), involve only spatial derivatives of the vierbein, abc nottimederivatives.TheseconnectionsareneededintheADMequations,butaretreatedasidentitiesrather thanequationsofmotion.Thatis,theequationofmotion(17.55)determinesthetimeevolutionofthespatial vierbein e , or rather of the spatial coordinate metric g , which is the quadratic combination (17.9) of aβ αβ
- (17.59) 0 α ∂xα In the coordinate frame, the trace equation is (see equation (7.23) for the Lie derivative of a metric determinant) ( ∂lng ∂lng ∂βα) L lng = +βα +2 =2K , (17.60) u α ∂t ∂xα ∂xα where g =|g |=γe2 is the determinant of the coordinate-frame spatial metric.
- aβ αβ Recast in the coordinate frame, the equation of motion (17.51) is ∂g ∂g ∂βγ ∂βγ αβ +βγ αβ +g +g =2αK .

(17.56) β αβ ∂xγ αγ∂xβ βγ∂xα AsisusualwithaLiederivative,equation(7.152),thecoordinatederivatives∂/∂xαinequation(17.56)canbe replaced,ifdesired,bytherestrictedcovariantderivativesD^ .Sincetherestrictedcovariantderivativeofthe α spatial coordinate metric g vanishes, the Lie derivative L^ g can be written (compare equation (7.154)), αβ β αβ L^ g =D^ β +D^ β .

Of the remaining connections (17.48), the acceleration K , equation (17.48a), αβ a and the purely spatial connections Γ , equation (17.48d), involve only spatial derivatives of the vierbein, abc nottimederivatives.TheseconnectionsareneededintheADMequations,butaretreatedasidentitiesrather thanequationsofmotion.Thatis,theequationofmotion(17.55)determinesthetimeevolutionofthespatial vierbein e , or rather of the spatial coordinate metric g , which is the quadratic combination (17.9) of aβ αβ

(17.59) 0 α ∂xα In the coordinate frame, the trace equation is (see equation (7.23) for the Lie derivative of a metric determinant) ( ∂lng ∂lng ∂βα) L lng = +βα +2 =2K , (17.60) u α ∂t ∂xα ∂xα where g =|g |=γe2 is the determinant of the coordinate-frame spatial metric.

aβ αβ Recast in the coordinate frame, the equation of motion (17.51) is ∂g ∂g ∂βγ ∂βγ αβ +βγ αβ +g +g =2αK .

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 calculation of the speeds of the cosmological event and particle horizons was given in a paper on the FLRW cosmological model, approximating the Universe as composed of non-interacting constituents, each one being a perfect fluid.[7][8] Apparent horizon of an accelerated particle If a particle is moving at a constant velocity in a non-expanding universe free of gravitational fields, any event that occurs in that Universe will eventually be observable by the particle, because the forward light cones from these events intersect the particle's world line.
- If d → ∞ 0 p (i.e., points arbitrarily as far away as can be observed), then no event horizon exists.
- On the other hand, if the particle is accelerating, in some situations light cones from some events never intersect the particle's world line.
- This differs from the concept of the particle horizon, which represents the largest comoving distance from which light emitted in the past could reach the observer at a given time.

A calculation of the speeds of the cosmological event and particle horizons was given in a paper on the FLRW cosmological model, approximating the Universe as composed of non-interacting constituents, each one being a perfect fluid.[7][8] Apparent horizon of an accelerated particle If a particle is moving at a constant velocity in a non-expanding universe free of gravitational fields, any event that occurs in that Universe will eventually be observable by the particle, because the forward light cones from these events intersect the particle's world line.

If d → ∞ 0 p (i.e., points arbitrarily as far away as can be observed), then no event horizon exists.

On the other hand, if the particle is accelerating, in some situations light cones from some events never intersect the particle's world line.

This differs from the concept of the particle horizon, which represents the largest comoving distance from which light emitted in the past could reach the observer at a given time.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- The covariant second derivative of (cid:8) along the dτ geodesic, D2(cid:8)μ , isdefinedbythecovariantderivativeof D(cid:8)μ alongthegeodesic, treating Dτ2 Dτ D(cid:8)μ asavector(ofcourse).Inotherwords, Dτ (cid:3) (cid:4) (cid:3) (cid:4) D2(cid:8)μ d d(cid:8)μ dxν dxν d(cid:8)λ dxω = +(cid:25)μ (cid:8)λ +(cid:25)μ +(cid:25)λ (cid:8)κ Dτ2 dτ dτ νλ dτ νλ dτ dτ ωκ dτ d2(cid:8)μ (cid:29) (cid:30) dxρ dxν = + ∂ (cid:25)μ (cid:8)λ dτ2 ρ νλ dτ dτ dxν dxλ dxρ dxν =−∂ (cid:25)μ (cid:8)ρ+∂ (cid:25)μ (cid:8)λ ρ νλ dτ dτ ρ νλ dτ dτ (cid:12) (cid:14) dxσ dxρ = ∂ (cid:25)μ −∂ (cid:25)μ (cid:8)λ (5) ρ σλ λ σρ dτ dτ where we have exploited local flatness in the second equality and used (3) in the third equality.Inthelastequality,wemerelyrearrangedthedummies.
- As mentioned in chapter V.6, the covariant derivative of (cid:8) along the geodesic is dτ2 definedby D(cid:8)μ d(cid:8)μ dxν = +(cid:25)μ (cid:8)λ (4) Dτ dτ νλ dτ which, unlike d(cid:8)μ , is assuredly a vector.
- yμ(τ) єμ(τ) Figure1 Twonearbygeodesicscandeviate fromorapproacheachother.
- Nowwerecognizetheexpression(∂ (cid:25) μ −∂ (cid:25)μ )in(5)asjustwhattheRiemanncurvaρ σλ λ σρ turetensorR μ =(∂ (cid:25) μ +(cid:25)μ (cid:25)κ )−(∂ (cid:25)μ +(cid:25) μ (cid:25)κ )reducestowhenevaluated σρλ ρ λσ ρκ λσ λ ρσ λκ ρσ inlocallyflatcoordinates.Thus,wehavederived,quickandfast,theequation1ofgeodesic deviation: D2(cid:8)μ dxσ dxρ =Rμ (cid:8)λ (6) Dτ2 σρλ dτ dτ

The covariant second derivative of (cid:8) along the dτ geodesic, D2(cid:8)μ , isdefinedbythecovariantderivativeof D(cid:8)μ alongthegeodesic, treating Dτ2 Dτ D(cid:8)μ asavector(ofcourse).Inotherwords, Dτ (cid:3) (cid:4) (cid:3) (cid:4) D2(cid:8)μ d d(cid:8)μ dxν dxν d(cid:8)λ dxω = +(cid:25)μ (cid:8)λ +(cid:25)μ +(cid:25)λ (cid:8)κ Dτ2 dτ dτ νλ dτ νλ dτ dτ ωκ dτ d2(cid:8)μ (cid:29) (cid:30) dxρ dxν = + ∂ (cid:25)μ (cid:8)λ dτ2 ρ νλ dτ dτ dxν dxλ dxρ dxν =−∂ (cid:25)μ (cid:8)ρ+∂ (cid:25)μ (cid:8)λ ρ νλ dτ dτ ρ νλ dτ dτ (cid:12) (cid:14) dxσ dxρ = ∂ (cid:25)μ −∂ (cid:25)μ (cid:8)λ (5) ρ σλ λ σρ dτ dτ where we have exploited local flatness in the second equality and used (3) in the third equality.Inthelastequality,wemerelyrearrangedthedummies.

As mentioned in chapter V.6, the covariant derivative of (cid:8) along the geodesic is dτ2 definedby D(cid:8)μ d(cid:8)μ dxν = +(cid:25)μ (cid:8)λ (4) Dτ dτ νλ dτ which, unlike d(cid:8)μ , is assuredly a vector.

yμ(τ) єμ(τ) Figure1 Twonearbygeodesicscandeviate fromorapproacheachother.

Nowwerecognizetheexpression(∂ (cid:25) μ −∂ (cid:25)μ )in(5)asjustwhattheRiemanncurvaρ σλ λ σρ turetensorR μ =(∂ (cid:25) μ +(cid:25)μ (cid:25)κ )−(∂ (cid:25)μ +(cid:25) μ (cid:25)κ )reducestowhenevaluated σρλ ρ λσ ρκ λσ λ ρσ λκ ρσ inlocallyflatcoordinates.Thus,wehavederived,quickandfast,theequation1ofgeodesic deviation: D2(cid:8)μ dxσ dxρ =Rμ (cid:8)λ (6) Dτ2 σρλ dτ dτ

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:
- Moregenerally,anothero (cid:13) bservercoulduseaswavefunctionsg βandg β ∗,insteadoff αandf α ∗,anddecompose thequantumfieldasφ∼ β (b β g β +b β †g β ∗).Shewoulduseb βandb β †asherannihilationandcreationoperators, anddefinehervacuumstate |0B (cid:22)asthestateannihilatedbyb β:b β |0B (cid:22)=0.
- ObserverBwouldsaythatthestate |0A (cid:22)containsparticlesasdefinedbyher.Thismayappearasalongwinded wayofsayingthat |0A (cid:22)isnotequalto |0B (cid:22),butitgoesbeyondthatbyindicatingthatthenumberofb-type particlescontainedin |0A (cid:22)canbecalculatedintermsofthecoefficientsintheBogoliubovtransformation.
- Wearegettingclosetothepunchline!SupposeobserverAsays,“Weareinthestate |0A (cid:22),andtherearen’t anyparticlesaround (cid:13) .”ObserverBwoulddisagree.Toher,sincea αisgivenasalinearcombina (cid:13) tionofb βandb β †, (cid:13) schematically,a α ∼ β (U αβ b β +V αβ b β †),theconditiona α |0A (cid:22)=0amountsto,schematically, β U αβ b β |0A (cid:22)∼ β V αβ b β †|0A (cid:22).Inotherwords,b β ||0A (cid:22),farfrombeing0,isactuallyrelatedtoalinearcombinationofb β †|0A (cid:22).
- BlackHoles labelstheproperties(suchasmomentum)theparticlesmaycarry.Thecorrespondingwavefunctionsarewritten asf αandf α ∗,andtheintegraloverk (cid:3) isreplacedbyasumoverα.Thevacuumstate |0A (cid:22)isdefinedasthestate annihilatedbya α:a α |0A (cid:22)=0.

Moregenerally,anothero (cid:13) bservercoulduseaswavefunctionsg βandg β ∗,insteadoff αandf α ∗,anddecompose thequantumfieldasφ∼ β (b β g β +b β †g β ∗).Shewoulduseb βandb β †asherannihilationandcreationoperators, anddefinehervacuumstate |0B (cid:22)asthestateannihilatedbyb β:b β |0B (cid:22)=0.

ObserverBwouldsaythatthestate |0A (cid:22)containsparticlesasdefinedbyher.Thismayappearasalongwinded wayofsayingthat |0A (cid:22)isnotequalto |0B (cid:22),butitgoesbeyondthatbyindicatingthatthenumberofb-type particlescontainedin |0A (cid:22)canbecalculatedintermsofthecoefficientsintheBogoliubovtransformation.

Wearegettingclosetothepunchline!SupposeobserverAsays,“Weareinthestate |0A (cid:22),andtherearen’t anyparticlesaround (cid:13) .”ObserverBwoulddisagree.Toher,sincea αisgivenasalinearcombina (cid:13) tionofb βandb β †, (cid:13) schematically,a α ∼ β (U αβ b β +V αβ b β †),theconditiona α |0A (cid:22)=0amountsto,schematically, β U αβ b β |0A (cid:22)∼ β V αβ b β †|0A (cid:22).Inotherwords,b β ||0A (cid:22),farfrombeing0,isactuallyrelatedtoalinearcombinationofb β †|0A (cid:22).

BlackHoles labelstheproperties(suchasmomentum)theparticlesmaycarry.Thecorrespondingwavefunctionsarewritten asf αandf α ∗,andtheintegraloverk (cid:3) isreplacedbyasumoverα.Thevacuumstate |0A (cid:22)isdefinedasthestate annihilatedbya α:a α |0A (cid:22)=0.

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:
- For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.
- Frank Wilczek has suggested calling attention to this assumption by designating it "Newton's Zeroth Law".[37] Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant.[38] Likewise, the idea that forces add like vectors (or in other words obey the superposition principle), and the idea that forces change the energy of a body, have both been described as a "fourth law".[note 8]

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

Frank Wilczek has suggested calling attention to this assumption by designating it "Newton's Zeroth Law".[37] Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant.[38] Likewise, the idea that forces add like vectors (or in other words obey the superposition principle), and the idea that forces change the energy of a body, have both been described as a "fourth law".[note 8]

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:
- ExampleA Aparticlein1-dimensionalspacetiedtoaspringoscillatesbackandforth.
- TheforceF isafunctionofspace.Newton’sequation d2x m =−kx (2) dt2 is ea(cid:6)sily solved in terms of two integration constants: x(t)=acosωt +bsinωt, with ω= k.
- The two constants a and b are determined by the initial position and initial m velocity,oralternatively ∗ bytheinitialpositionatt =0andbythefinalpositionatsome timet =T.Energy,butnotmomentum,isconserved.
- ExampleB Wekickaparticlein1-dimensionalspaceatt =0.

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

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

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Archived (https://web.archive.org/web/20160510184735/http://www.usatoday.com/story/news/201 6/05/10/kepler-finds-new-planets/84187098/) from the original on 10 May 2016.
- "A revised estimate of the occurrence rate of terrestrial planets in the habitable zones around kepler m-dwarfs".
- PMC 3845182 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3845182).
- arXiv:1303.2649 (https://arxiv.org/abs/1303.2649).

Archived (https://web.archive.org/web/20160510184735/http://www.usatoday.com/story/news/201 6/05/10/kepler-finds-new-planets/84187098/) from the original on 10 May 2016.

"A revised estimate of the occurrence rate of terrestrial planets in the habitable zones around kepler m-dwarfs".

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- If the dog-leg proposition (§18.9.1) held, then
- i The hypersurfaces of constant action, or phase, shown in Figure 23.12 are lines of constant Z at fixed t.
- 23.24.1 Application of the null singularity theorem to a Λ-Kerr-Newman black hole Penrose’s(1965)originalsingularitytheoremconsideredhypersurface-orthogonalnullcongruences.ThePretorius and Israel (1998) double-null congruence provides an example of such a congruence in the Λ-KerrNewman geometry.
- the action on the initial hypersurface is S =−t.

If the dog-leg proposition (§18.9.1) held, then

i The hypersurfaces of constant action, or phase, shown in Figure 23.12 are lines of constant Z at fixed t.

23.24.1 Application of the null singularity theorem to a Λ-Kerr-Newman black hole Penrose’s(1965)originalsingularitytheoremconsideredhypersurface-orthogonalnullcongruences.ThePretorius and Israel (1998) double-null congruence provides an example of such a congruence in the Λ-KerrNewman geometry.

the action on the initial hypersurface is S =−t.

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:
- Retrieved onservatives-endorsement-general-election-a 19 March 2018.
- Campbell, Denis (18 August 2017).
- "Trump's es-war-of-words-with-stephen-hawking-over-n popularity inexplicable and Brexit spells hs).
- com/politics/2017/aug/27/jeremy-hunt-continu 240.

Retrieved onservatives-endorsement-general-election-a 19 March 2018.

"Trump's es-war-of-words-with-stephen-hawking-over-n popularity inexplicable and Brexit spells hs).

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:
- "CMS Physics Analysis Summary" (https://cds.cern.ch/record/2205245/files/E XO-16-027-pas.pdf).
- Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions (https://archive.org/details/warpedpassagesun00rand_1).
- doi:10.1103/PhysRevLett.83.4690 (https://doi.org/10.1103%2FPhysRevLett.83.4690).
- Gogberashvili, "Our world as an expanding shell", arXiv:hep-ph/9812365 (https://arxiv.org/abs/ hep-ph/9812365).

"CMS Physics Analysis Summary" (https://cds.cern.ch/record/2205245/files/E XO-16-027-pas.pdf).

Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions (https://archive.org/details/warpedpassagesun00rand_1).

Gogberashvili, "Our world as an expanding shell", arXiv:hep-ph/9812365 (https://arxiv.org/abs/ hep-ph/9812365).

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:
- Wolchover, Natalie (22 December 2017).
- "Welcome to" (http://info.cern.ch/).
- "SLAC National Accelerator Laboratory Home Page" (http://www6.slac.stanford.edu/).
- "Fermilab | Science at Fermilab | Benefits to Society" (http://www.fnal.gov/pub/science/benefits/).

"SLAC National Accelerator Laboratory Home Page" (http://www6.slac.stanford.edu/).

"Fermilab | Science at Fermilab | Benefits to Society" (http://www.fnal.gov/pub/science/benefits/).

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

List tests or derivations implied by the evidence.