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

EVIDENCE:
- But now we understand why it can’t.
- Youareprobablyfamiliarwiththeanalogousstatementsinelectromagnetism.Apulsating sphericallysymmetricchargedistributionalsocannotradiate.Theclassicalstatementthat onlydipoleandhighermomentscangenerateelectromagneticwavescorrespondstothe quantumstatementthatthephotoncarriesspin1.
- We learned from (16) that, far away from the source, the gravitational wave is generated by the quadrupole moment (cid:8) Qij(t)≡ d3yyiyjT00(t,y(cid:3)),andasphericalsymmetricmassdistributionsimplydoesn’t haveone.Theclassicalstatementthatonlyquadrupoleandhighermomentscangenerate gravitationalwavescorrespondstothequantumstatementthatthegravitoncarriesspin2.
- LinearizedGravityandGravitationalWaves | 571 Indeed,wearenowabletoevaluatetheangularmomentumoftheKerrblackholein thelimitofslowrotation.ExpandtheKerrmetric(VII.5.15)forr (cid:12)r , a: S (cid:3) (cid:4) (cid:12) (cid:14) r 2r asin2θ 1 ds2(cid:16)− 1− S dt2− S dtdφ+ (cid:29) (cid:30)dr2+r2 dθ2+sin2θdφ2 (21) r r 1− rS r Comparing(20)and(21),wededucethatr a=2GJ.Thus,wehaveverified,aspromised, S thatthedefinitionJ =MagiveninchapterVII.5reducesinthesmallalimittoourusual understandingofangularmomentum.

We learned from (16) that, far away from the source, the gravitational wave is generated by the quadrupole moment (cid:8) Qij(t)≡ d3yyiyjT00(t,y(cid:3)),andasphericalsymmetricmassdistributionsimplydoesn’t haveone.Theclassicalstatementthatonlyquadrupoleandhighermomentscangenerate gravitationalwavescorrespondstothequantumstatementthatthegravitoncarriesspin2.

LinearizedGravityandGravitationalWaves | 571 Indeed,wearenowabletoevaluatetheangularmomentumoftheKerrblackholein thelimitofslowrotation.ExpandtheKerrmetric(VII.5.15)forr (cid:12)r , a: S (cid:3) (cid:4) (cid:12) (cid:14) r 2r asin2θ 1 ds2(cid:16)− 1− S dt2− S dtdφ+ (cid:29) (cid:30)dr2+r2 dθ2+sin2θdφ2 (21) r r 1− rS r Comparing(20)and(21),wededucethatr a=2GJ.Thus,wehaveverified,aspromised, S thatthedefinitionJ =MagiveninchapterVII.5reducesinthesmallalimittoourusual understandingofangularmomentum.

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:
- 10.7 FLRW metric The full Friedmann-Lemaître-Robertson-Walker spacetime metric is ( dx2 ) ds2 =−dt2+a(t)2 +x2do2 , (10.28) 1−κx2 where t is cosmic time, which is the proper time experienced by comoving observers, who remain at rest in comoving coordinates dx = dθ = dφ = 0.
- Note the trick of one index up, one down, to remove, modulo signs, the distorting effect of the metric on the
- 238 Homogeneous, Isotropic Cosmology Figure10.6 ThePoincarédiskdepictsthegeometryofanopenFLRWuniverseinisotropiccoordinates.Thelinesare linesoflatitudeandlongituderelativetoa“pole” chosenheretobedisplacedfromthecentreofthedisk.Inisotropic coordinates,geodesicscorrespondtocirclesthatintersecttheboundaryofthediskatrightangles,suchasthelines ofconstantlongitudeinthisdiagram.Thelinesoflatituderemainunchangedunderrotationsaboutthepole.
- Any of the alternative versions of the comoving spatial FLRW metric,equations(10.18),(10.20),(10.22),or(10.26),maybeusedasthespatialpartoftheFLRWspacetime metric (10.28).

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.

10.7 FLRW metric The full Friedmann-Lemaître-Robertson-Walker spacetime metric is ( dx2 ) ds2 =−dt2+a(t)2 +x2do2 , (10.28) 1−κx2 where t is cosmic time, which is the proper time experienced by comoving observers, who remain at rest in comoving coordinates dx = dθ = dφ = 0.

Note the trick of one index up, one down, to remove, modulo signs, the distorting effect of the metric on the

Any of the alternative versions of the comoving spatial FLRW metric,equations(10.18),(10.20),(10.22),or(10.26),maybeusedasthespatialpartoftheFLRWspacetime metric (10.28).

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:
- Your subconscious is trying very hard to TELL you something in your dreams.
- 9781405131117_4_005.qxd 30/6/09 11:47 AM Page 105 Life!
- So-called dream dictionaries in books, on the Internet, and in “dream software” programs, which users can download to their computers, contain databases of thousands of dream symbols that promise to help readers decode their dreams’ hidden meanings (Ackroyd, 1993).
- In one episode of the HBO series, The Sopranos, Tony Soprano’s friend appeared to Tony in a dream as a talking fish, leading Tony to suspect him as an FBI informant (“fish” is a slang term for informant) (Sepinwall, 2006).

Your subconscious is trying very hard to TELL you something in your dreams.

So-called dream dictionaries in books, on the Internet, and in “dream software” programs, which users can download to their computers, contain databases of thousands of dream symbols that promise to help readers decode their dreams’ hidden meanings (Ackroyd, 1993).

In one episode of the HBO series, The Sopranos, Tony Soprano’s friend appeared to Tony in a dream as a talking fish, leading Tony to suspect him as an FBI informant (“fish” is a slang term for informant) (Sepinwall, 2006).

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:
- Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on and has a mass gap Δ > 0.
- Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975) [citations adapted].
- See also Abraham–Lorentz force Mathematics portal AdS/CFT correspondence Axiomatic quantum field theory Physics portal Introduction to quantum mechanics Common integrals in quantum field theory Conformal field theory Constructive quantum field theory Dirac's equation Form factor (quantum field theory) Feynman diagram Green–Kubo relations Green's function (many-body theory) Group field theory Lattice field theory List of quantum field theories Local quantum field theory Maximally helicity violating amplitudes Noncommutative quantum field theory Quantization of a field Quantum electrodynamics Quantum field theory in curved spacetime Quantum chromodynamics Quantum flavordynamics Quantum hadrodynamics Quantum hydrodynamics Quantum triviality Relation between Schrödinger's equation and the path integral formulation of quantum mechanics Relationship between string theory and quantum field theory Schwinger–Dyson equation Static forces and virtual-particle exchange Symmetry in quantum mechanics Topological quantum field theory Ward–Takahashi identity Wheeler–Feynman absorber theory Wigner's classification

Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on and has a mass gap Δ > 0.

Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975) [citations adapted].

See also Abraham–Lorentz force Mathematics portal AdS/CFT correspondence Axiomatic quantum field theory Physics portal Introduction to quantum mechanics Common integrals in quantum field theory Conformal field theory Constructive quantum field theory Dirac's equation Form factor (quantum field theory) Feynman diagram Green–Kubo relations Green's function (many-body theory) Group field theory Lattice field theory List of quantum field theories Local quantum field theory Maximally helicity violating amplitudes Noncommutative quantum field theory Quantization of a field Quantum electrodynamics Quantum field theory in curved spacetime Quantum chromodynamics Quantum flavordynamics Quantum hadrodynamics Quantum hydrodynamics Quantum triviality Relation between Schrödinger's equation and the path integral formulation of quantum mechanics Relationship between string theory and quantum field theory Schwinger–Dyson equation Static forces and virtual-particle exchange Symmetry in quantum mechanics Topological quantum field theory Ward–Takahashi identity Wheeler–Feynman absorber theory Wigner's classification

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

List tests or derivations implied by the evidence.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper


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

EVIDENCE:
- Trying not to panic, but I need to be opening more doors, giving us a shot at finding someplace to rest and reset.
- Amanda is quaking, and I want to tell her everything is fine, but it isn’t.
- Ten feet away, standing in weeds in front of a teetering chain-link fence, a wolf glares at me through large amber eyes.
- My Amanda’s shriek has given us away.

Trying not to panic, but I need to be opening more doors, giving us a shot at finding someplace to rest and reset.

Amanda is quaking, and I want to tell her everything is fine, but it isn’t.

Ten feet away, standing in weeds in front of a teetering chain-link fence, a wolf glares at me through large amber eyes.

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:
- allowing the spatial tetrad axes γγ to be chosen more generally, a subject only to the condition (17.3) that they be orthogonal to the tetrad time axis, and therefore lie in the hypersurface of constant time t.
- For example, the spatial tetrad γγ can be chosen to form 3D orthonormal a axes, γ ≡γγ ·γγ =δ , so that the full 4D tetrad metric γ is Minkowski.
- ab a b ab mn This Chapter follows the full tetrad approach to the ADM formalism, but all the results hold for the traditional case where the spatial tetrad axes are set equal to the coordinate spatial axes, equation (17.14).
- Bianchi spacetimes, discussed in §17.4, provide an illustrative example of the application of the ADM

allowing the spatial tetrad axes γγ to be chosen more generally, a subject only to the condition (17.3) that they be orthogonal to the tetrad time axis, and therefore lie in the hypersurface of constant time t.

For example, the spatial tetrad γγ can be chosen to form 3D orthonormal a axes, γ ≡γγ ·γγ =δ , so that the full 4D tetrad metric γ is Minkowski.

ab a b ab mn This Chapter follows the full tetrad approach to the ADM formalism, but all the results hold for the traditional case where the spatial tetrad axes are set equal to the coordinate spatial axes, equation (17.14).

Bianchi spacetimes, discussed in §17.4, provide an illustrative example of the application of the ADM

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- An incorrect result or no result can still be produced if the time travel mechanism or algorithm are not guaranteed to be accurate.
- This means, if taken literally, that if time machines exist, there can be no free will.
- Craig Wheeler concludes that: According to the consistency conjecture, any complex interpersonal interactions must work themselves out self-consistently so that there is no paradox.
- You can coexist, take yourself out for a beer, celebrate your birthday together, but somehow circumstances will dictate that you cannot behave in a way that leads to a paradox in time.

Novikov self-consistency principle - Wikipedia.pdf

An incorrect result or no result can still be produced if the time travel mechanism or algorithm are not guaranteed to be accurate.

This means, if taken literally, that if time machines exist, there can be no free will.

Craig Wheeler concludes that: According to the consistency conjecture, any complex interpersonal interactions must work themselves out self-consistently so that there is no paradox.

You can coexist, take yourself out for a beer, celebrate your birthday together, but somehow circumstances will dictate that you cannot behave in a way that leads to a paradox in time.

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:
- 852 Non-equilibrium processes in the FLRW background Temperature T (K) 20000 10000 5000 2000 1000 10 −1 10 −2 −3 .0001 .0002 .0005 .001 .002 cosmic scale factor a snoitcarf noi X a e rec X X p H0 X X X He++ He+ He0 Figure 31.4 Non-equilibrium hydrogen and helium ion fractions as a function of cosmic scale factor a scaled to a0=1.DottedlinesshowXp andX He+ inthermodynamicequilibrium.Thetotalhydrogenandheliumfractionsare XH=1−fn/f+=0.86andX4He = 1 fn/f+=0.07.
- Even so, helium is almost entirely neutral by the time of recombination, so in practice helium has little effect on recombination.
- The Figure shows that the recombination of singly-ionized helium is, like the recombination of protons, delayed compared to thermodynamic equilibrium.
- He+ e He2 Figure 31.4 shows the recombination of hydrogen and helium in the Seager, Sasselov, and Scott (1999) approximation.

852 Non-equilibrium processes in the FLRW background Temperature T (K) 20000 10000 5000 2000 1000 10 −1 10 −2 −3 .0001 .0002 .0005 .001 .002 cosmic scale factor a snoitcarf noi X a e rec X X p H0 X X X He++ He+ He0 Figure 31.4 Non-equilibrium hydrogen and helium ion fractions as a function of cosmic scale factor a scaled to a0=1.DottedlinesshowXp andX He+ inthermodynamicequilibrium.Thetotalhydrogenandheliumfractionsare XH=1−fn/f+=0.86andX4He = 1 fn/f+=0.07.

Even so, helium is almost entirely neutral by the time of recombination, so in practice helium has little effect on recombination.

The Figure shows that the recombination of singly-ionized helium is, like the recombination of protons, delayed compared to thermodynamic equilibrium.

He+ e He2 Figure 31.4 shows the recombination of hydrogen and helium in the Seager, Sasselov, and Scott (1999) approximation.

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 type of metal gives a barrier, the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured.
- Ten years elapsed before Millikan's definitive experiment[7] verified Einstein's prediction.
- During that time many scientists rejected the revolutionary idea of quanta.[8] But Planck's and Einstein's concept was in the air and soon began to affect other physics and quantum theories.
- increase: one electron is ejected for each quantum: more quanta mean more electrons.[6]: 23 Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal.

Introduction to quantum mechanics - Wikipedia.pdf

The type of metal gives a barrier, the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured.

Ten years elapsed before Millikan's definitive experiment[7] verified Einstein's prediction.

During that time many scientists rejected the revolutionary idea of quanta.[8] But Planck's and Einstein's concept was in the air and soon began to affect other physics and quantum theories.

increase: one electron is ejected for each quantum: more quanta mean more electrons.[6]: 23 Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal.

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:
- 2.Einstein believed that gravity is solely a force acting between masses, ignoring the influence of spacetime.
- 3.Chandrasekhar discovered that a white dwarf can exceed 1.4 solar masses without collapsing into a black hole.
- The Search| Quiz and Test 1.In 1975, black holes were recognized primarily as
- 3.By the 1960s, researchers reached a consensus that all massive stars imploded to form neutron stars, not black holes.

2.Einstein believed that gravity is solely a force acting between masses, ignoring the influence of spacetime.

3.Chandrasekhar discovered that a white dwarf can exceed 1.4 solar masses without collapsing into a black hole.

The Search| Quiz and Test 1.In 1975, black holes were recognized primarily as

3.By the 1960s, researchers reached a consensus that all massive stars imploded to form neutron stars, not black holes.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- If one replaces with according to The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to and , which are joined by a hyperplane or in which vanishes.
- An example of a (traversable) wormhole metric is the following:[65] first presented by Ellis (see Ellis wormhole) as a special case of the Ellis drainhole.
- We call such a connection between the two sheets a "bridge".
- The field equations without denominators in the case when can be written

If one replaces with according to The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to and , which are joined by a hyperplane or in which vanishes.

An example of a (traversable) wormhole metric is the following:[65] first presented by Ellis (see Ellis wormhole) as a special case of the Ellis drainhole.

We call such a connection between the two sheets a "bridge".

The field equations without denominators in the case when can be written

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:
- S2CID 250904081 (https://api.sem anticscholar.org/CorpusID:250904081).
- It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes.
- "Lectures on the Infrared Structure of Gravity and Gauge Theory".
- (1917) "In what way does it become manifest in the fundamental laws of physics that space has three dimensions?" Proceedings of the Amsterdam academy 20:200.

S2CID 250904081 (https://api.sem anticscholar.org/CorpusID:250904081).

It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes.

"Lectures on the Infrared Structure of Gravity and Gauge Theory".

(1917) "In what way does it become manifest in the fundamental laws of physics that space has three dimensions?" Proceedings of the Amsterdam academy 20:200.

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:
- ThescientistreferredtoaspecialgroupofscientiststhatworkedwiththePresidentcalledthe “SpecialCommittee.” Hestateshechangedsomepartsofhisstoryre:thecraftin1991andalludedhe hadtoprotectthatinformationashewasincontactwithanofficeinWashingtonD.C.thathadbeen establishedoverthelast6monthstomakeadecisionon“howtokeepeveryonefromfindingoutwhatis reallygoingon.” ● https://www.earthfiles.com/2004/06/05/part-9-ufo-crashretrievals-the-inner-sanctum-status-report -vi-july-1991-by-leonard-h-stringfield/ (PUBLICDOMAIN) -21February1990—JapanesejournalistNorioHayakawastatestheUSNaval ResearchLaboratoryhasa“ParapsychologyResearchUnit”thatcoordinatesactivitieswithDARPA,and someoftheiractivitiesareconductedundertheOfficeofNavalIntelligenceatlocationssuchasArea51.
- ● https://www.bibliotecapleyades.net/branton/esp dulcebook5.htm (PUBLICDOMAIN) -March1990—NATO’sAdvisoryGroupforAerospaceResearchand Development(AGARD)publishesastudythatstatesa“gyroscopicpropulsivedevice”cancounteract gravity.
- OnesuchdeviceexistedatthetimeandwaspatentedintheUKtoE.J.C.Rickman.
- ● https://archive.org/details/HiddenTruthForbiddenKnowledgeStevenM.Greer/page/n211/mode/1up (p211)

● https://www.bibliotecapleyades.net/branton/esp dulcebook5.htm (PUBLICDOMAIN) -March1990—NATO’sAdvisoryGroupforAerospaceResearchand Development(AGARD)publishesastudythatstatesa“gyroscopicpropulsivedevice”cancounteract gravity.

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:
- had a mythical reverence for Newton, which he expressed with a profound question and statement: "Does Mr.
- Newton eat, or drink, or sleep like other men?
- I represent him to myself as a celestial genius, entirely disengaged from matter."[268] Newton has further been called "the towering figure of the Scientific Revolution" and that "In a period rich with outstanding thinkers, Newton was simply the most outstanding." The polymath Johann Wolfgang von Goethe labelled the year in which Galileo Galilei died and Newton was born, 1642, as the "Christmas of the modern age".[6] In the polymath Vilfredo Pareto's estimation, Newton was the greatest human being who ever lived.[269] On the bicentennial of Newton's death in 1927, the astronomer James Jeans stated that he "was certainly the greatest man of science, and perhaps the greatest intellect, the human race has seen".[266] The physicist Peter Rowlands also notes that Newton was "possibly possessed of the most powerful intellect in the whole of human history".[215] Newton conceived four revolutions—in optics, mathematics, mechanics, and gravity—but also foresaw a fifth in electricity, though he lacked the time and energy in old age to fully accomplish it.[270][271] Newton's work is considered the most influential in bringing forth modern science.[45][272][273][274]

had a mythical reverence for Newton, which he expressed with a profound question and statement: "Does Mr.

Newton eat, or drink, or sleep like other men?

I represent him to myself as a celestial genius, entirely disengaged from matter."[268] Newton has further been called "the towering figure of the Scientific Revolution" and that "In a period rich with outstanding thinkers, Newton was simply the most outstanding." The polymath Johann Wolfgang von Goethe labelled the year in which Galileo Galilei died and Newton was born, 1642, as the "Christmas of the modern age".[6] In the polymath Vilfredo Pareto's estimation, Newton was the greatest human being who ever lived.[269] On the bicentennial of Newton's death in 1927, the astronomer James Jeans stated that he "was certainly the greatest man of science, and perhaps the greatest intellect, the human race has seen".[266] The physicist Peter Rowlands also notes that Newton was "possibly possessed of the most powerful intellect in the whole of human history".[215] Newton conceived four revolutions—in optics, mathematics, mechanics, and gravity—but also foresaw a fifth in electricity, though he lacked the time and energy in old age to fully accomplish it.[270][271] Newton's work is considered the most influential in bringing forth modern science.[45][272][273][274]

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:
- Uniformly accelerated motion If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate.
- The latter states that the magnitude of A bouncing ball photographed at 25 frames per second the gravitational force from the Earth upon the using a stroboscopic flash.
- Moreover, some texts organize the basic ideas of Newtonian mechanics into different postulates, other than the three laws as commonly phrased, with the goal of being more clear about what is empirically observed and what is true by definition.[19]: 9 [27] Examples The study of the behavior of massive bodies using Newton's laws is known as Newtonian mechanics.
- This particular value of acceleration is typically denoted : If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion.[44] When air resistance can be neglected, projectiles follow parabola-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal.

Uniformly accelerated motion If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate.

The latter states that the magnitude of A bouncing ball photographed at 25 frames per second the gravitational force from the Earth upon the using a stroboscopic flash.

Moreover, some texts organize the basic ideas of Newtonian mechanics into different postulates, other than the three laws as commonly phrased, with the goal of being more clear about what is empirically observed and what is true by definition.[19]: 9 [27] Examples The study of the behavior of massive bodies using Newton's laws is known as Newtonian mechanics.

This particular value of acceleration is typically denoted : If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion.[44] When air resistance can be neglected, projectiles follow parabola-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal.

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:
- External links Physics at Quanta Magazine (https://quantamagazine.org/physics) Usenet Physics FAQ (https://math.ucr.edu/home/baez/physics/) – FAQ compiled by sci.physics and other physics newsgroups Website of the Nobel Prize in physics (https://www.nobelprize.org/prizes/physics/) Archived (http s://web.archive.org/web/20211207112242/https://www.nobelprize.org/prizes/physics/) 7 December 2021 at the Wayback Machine – Award for outstanding contributions to the subject World of Physics (https://scienceworld.wolfram.com/physics/) Archived (https://web.archive.org/we b/20250625052824/https://scienceworld.wolfram.com/physics/) 25 June 2025 at the Wayback Machine – Online encyclopedic dictionary of physics Nature Physics (https://www.nature.com/nphys/) – Academic journal Physics (https://physics.aps.org/) Archived (https://web.archive.org/web/20250628143118/https://p hysics.aps.org/) 28 June 2025 at the Wayback Machine – Online magazine by the American Physical Society The Vega Science Trust (http://www.vega.org.uk/) Archived (https://web.archive.org/web/2023060 7090448/http://www.vega.org.uk/) 7 June 2023 at the Wayback Machine – Science videos, including physics HyperPhysics website (http://hyperphysics.phy-astr.gsu.edu/Hbase/hframe.html) Archived (https:// web.archive.org/web/20110408200208/http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html) 8 April 2011 at the Wayback Machine – Physics and astronomy mind-map from Georgia State University Physics at MIT OpenCourseWare (https://ocw.mit.edu/courses/physics/) Archived (https://web.arc hive.org/web/20220315082844/https://ocw.mit.edu/courses/physics/) 15 March 2022 at the Wayback Machine – Online course material from Massachusetts Institute of Technology The Feynman Lectures on Physics (https://feynmanlectures.caltech.edu) Archived (https://web.arc hive.org/web/20220304124051/https://feynmanlectures.caltech.edu/) 4 March 2022 at the Wayback Machine
- "Happy 100th, Superconductivity!" (https://do i.org/10.1126%2Fscience.332.6026.189).
- Sears and Zemansky's University Physics with Modern Physics Technology Update (13th ed.).
- A Quantum Approach to Condensed Matter Physics (https://boo ks.google.com/books?id=hyx6BjEX4U8C).

External links Physics at Quanta Magazine (https://quantamagazine.org/physics) Usenet Physics FAQ (https://math.ucr.edu/home/baez/physics/) – FAQ compiled by sci.physics and other physics newsgroups Website of the Nobel Prize in physics (https://www.nobelprize.org/prizes/physics/) Archived (http s://web.archive.org/web/20211207112242/https://www.nobelprize.org/prizes/physics/) 7 December 2021 at the Wayback Machine – Award for outstanding contributions to the subject World of Physics (https://scienceworld.wolfram.com/physics/) Archived (https://web.archive.org/we b/20250625052824/https://scienceworld.wolfram.com/physics/) 25 June 2025 at the Wayback Machine – Online encyclopedic dictionary of physics Nature Physics (https://www.nature.com/nphys/) – Academic journal Physics (https://physics.aps.org/) Archived (https://web.archive.org/web/20250628143118/https://p hysics.aps.org/) 28 June 2025 at the Wayback Machine – Online magazine by the American Physical Society The Vega Science Trust (http://www.vega.org.uk/) Archived (https://web.archive.org/web/2023060 7090448/http://www.vega.org.uk/) 7 June 2023 at the Wayback Machine – Science videos, including physics HyperPhysics website (http://hyperphysics.phy-astr.gsu.edu/Hbase/hframe.html) Archived (https:// web.archive.org/web/20110408200208/http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html) 8 April 2011 at the Wayback Machine – Physics and astronomy mind-map from Georgia State University Physics at MIT OpenCourseWare (https://ocw.mit.edu/courses/physics/) Archived (https://web.arc hive.org/web/20220315082844/https://ocw.mit.edu/courses/physics/) 15 March 2022 at the Wayback Machine – Online course material from Massachusetts Institute of Technology The Feynman Lectures on Physics (https://feynmanlectures.caltech.edu) Archived (https://web.arc hive.org/web/20220304124051/https://feynmanlectures.caltech.edu/) 4 March 2022 at the Wayback Machine

"Happy 100th, Superconductivity!" (https://do i.org/10.1126%2Fscience.332.6026.189).

Sears and Zemansky's University Physics with Modern Physics Technology Update (13th ed.).

A Quantum Approach to Condensed Matter Physics (https://boo ks.google.com/books?id=hyx6BjEX4U8C).

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:
- PMID 12059412 (https://pubmed.ncbi.nlm.nih.gov/12059412).
- S2CID 16668175 (https://api.semanticschol ar.org/CorpusID:16668175).
- S2CID 27717447 (https://api.sema nticscholar.org/CorpusID:27717447).
- S2CID 18980849 (https://api.semanticscholar.org/CorpusID:1898084 9).

S2CID 16668175 (https://api.semanticschol ar.org/CorpusID:16668175).

S2CID 27717447 (https://api.sema nticscholar.org/CorpusID:27717447).

S2CID 18980849 (https://api.semanticscholar.org/CorpusID:1898084 9).

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:
- Further reading Books Phillips, Lee (2024), Einstein's Tutor: The Story of Emmy Noether and the Invention of Modern Physics, PublicAffairs, ISBN 9781541702974 Hasse, Helmut; Noether, Emmy (2006), Lemmermeyer, Franz; Roquette, Peter (eds.), Helmut Hasse und Emmy Noether – Die Korrespondenz 1925–1935 (http://univerlag.uni-goettingen.de/ha ndle/3/isbn-3-938616-35-0) [Helmut Hasse and Emmy Noether – Their Correspondence 1925– 1935] (PDF), Göttingen University, doi:10.17875/gup2006-49 (https://doi.org/10.17875%2Fgup200 6-49), ISBN 978-3-938616-35-2 Articles Angier, Natalie (26 March 2012), "The Mighty Mathematician You've Never Heard Of" (https://ww w.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-nev er-heard-of.html), The New York Times, retrieved 27 January 2024 Blue, Meredith (2001), Galois Theory and Noether's Problem (https://web.archive.org/web/200805 29020714/http://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf) (PDF), 34th Annual Meeting of the Mathematical Association of America, MAA Florida Section, archived from the original (htt p://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf) (PDF) on 29 May 2008, retrieved 9 June Phillips, Lee (26 May 2015), "The female mathematician who changed the course of physics – but couldn't get a job" (https://arstechnica.com/science/2015/05/the-female-mathematician-who-chang ed-the-course-of-physics-but-couldnt-get-a-job/), Ars Technica, California: Condé Nast, retrieved 27 January 2024 "Special Issue on Women in Mathematics" (https://www.ams.org/journals/notices/199109/199109F ullIssue.pdf) (PDF), Notices of the American Mathematical Society, 38 (7), Providence, RI: American Mathematical Society: 701–773, September 1991, ISSN 0002-9920 (https://search.worl dcat.org/issn/0002-9920) Shen, Qinna (September 2019), "A Refugee Scholar from Nazi Germany: Emmy Noether and Bryn Mawr College" (https://repository.brynmawr.edu/german_pubs/19/), The Mathematical Intelligencer, 41 (3): 52–65, doi:10.1007/s00283-018-9852-0 (https://doi.org/10.1007%2Fs00283018-9852-0), S2CID 128009850 (https://api.semanticscholar.org/CorpusID:128009850) Online biographies Byers, Nina (16 March 2001), "Emmy Noether", Contributions of 20th Century Women to Physics (http://cwp.library.ucla.edu/Phase2/Noether,_Amalie_Emmy@861234567.html), UCLA, archived (https://web.archive.org/web/20080212093356/http://cwp.library.ucla.edu/Phase2/Noether,_Amalie _Emmy@861234567.html) from the original on 12 February 2008.
- Taylor, Mandie (22 February 2023), "Emmy Noether", Biographies of Women Mathematicians (htt p://www.agnesscott.edu/lriddle/women/noether.htm), Agnes Scott College.
- Chown, Marcus (5 March 2025), "Emmy Noether: the genius who taught Einstein" (https://www.pr ospectmagazine.co.uk/culture/69396/emmy-noether-albert-einstein-symmetries), Prospect

Further reading Books Phillips, Lee (2024), Einstein's Tutor: The Story of Emmy Noether and the Invention of Modern Physics, PublicAffairs, ISBN 9781541702974 Hasse, Helmut; Noether, Emmy (2006), Lemmermeyer, Franz; Roquette, Peter (eds.), Helmut Hasse und Emmy Noether – Die Korrespondenz 1925–1935 (http://univerlag.uni-goettingen.de/ha ndle/3/isbn-3-938616-35-0) [Helmut Hasse and Emmy Noether – Their Correspondence 1925– 1935] (PDF), Göttingen University, doi:10.17875/gup2006-49 (https://doi.org/10.17875%2Fgup200 6-49), ISBN 978-3-938616-35-2 Articles Angier, Natalie (26 March 2012), "The Mighty Mathematician You've Never Heard Of" (https://ww w.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-nev er-heard-of.html), The New York Times, retrieved 27 January 2024 Blue, Meredith (2001), Galois Theory and Noether's Problem (https://web.archive.org/web/200805 29020714/http://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf) (PDF), 34th Annual Meeting of the Mathematical Association of America, MAA Florida Section, archived from the original (htt p://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf) (PDF) on 29 May 2008, retrieved 9 June Phillips, Lee (26 May 2015), "The female mathematician who changed the course of physics – but couldn't get a job" (https://arstechnica.com/science/2015/05/the-female-mathematician-who-chang ed-the-course-of-physics-but-couldnt-get-a-job/), Ars Technica, California: Condé Nast, retrieved 27 January 2024 "Special Issue on Women in Mathematics" (https://www.ams.org/journals/notices/199109/199109F ullIssue.pdf) (PDF), Notices of the American Mathematical Society, 38 (7), Providence, RI: American Mathematical Society: 701–773, September 1991, ISSN 0002-9920 (https://search.worl dcat.org/issn/0002-9920) Shen, Qinna (September 2019), "A Refugee Scholar from Nazi Germany: Emmy Noether and Bryn Mawr College" (https://repository.brynmawr.edu/german_pubs/19/), The Mathematical Intelligencer, 41 (3): 52–65, doi:10.1007/s00283-018-9852-0 (https://doi.org/10.1007%2Fs00283018-9852-0), S2CID 128009850 (https://api.semanticscholar.org/CorpusID:128009850) Online biographies Byers, Nina (16 March 2001), "Emmy Noether", Contributions of 20th Century Women to Physics (http://cwp.library.ucla.edu/Phase2/Noether,_Amalie_Emmy@861234567.html), UCLA, archived (https://web.archive.org/web/20080212093356/http://cwp.library.ucla.edu/Phase2/Noether,_Amalie _Emmy@861234567.html) from the original on 12 February 2008.

Taylor, Mandie (22 February 2023), "Emmy Noether", Biographies of Women Mathematicians (htt p://www.agnesscott.edu/lriddle/women/noether.htm), Agnes Scott College.

Chown, Marcus (5 March 2025), "Emmy Noether: the genius who taught Einstein" (https://www.pr ospectmagazine.co.uk/culture/69396/emmy-noether-albert-einstein-symmetries), Prospect

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:
- From equation (17.144) conclude that T equals an integral over scale factor a, ∫ da lnT =3K .
- (17.150) K 8πa6 The Kasner curvature density ρ behaves like a perfect fluid with positive energy and an ultra-hard K equation of state, w =1.
- (17.153) K [ √ ]2/(1−w) 1+ 1+(a/a )3(1−w) K Conclude that the small and large a limits of T are, for w ≤1, { (a/a )3 a≪a , K K T/T → (17.154) K 1 a≫a .
- For the particular case of a cosmological constant, w =−1, show that K = Λ/3, and that √ √ a/a =sinh1/3( 3Λt) , T/T =tanh( 3Λt/2) .

From equation (17.144) conclude that T equals an integral over scale factor a, ∫ da lnT =3K .

(17.150) K 8πa6 The Kasner curvature density ρ behaves like a perfect fluid with positive energy and an ultra-hard K equation of state, w =1.

(17.153) K [ √ ]2/(1−w) 1+ 1+(a/a )3(1−w) K Conclude that the small and large a limits of T are, for w ≤1, { (a/a )3 a≪a , K K T/T → (17.154) K 1 a≫a .

For the particular case of a cosmological constant, w =−1, show that K = Λ/3, and that √ √ a/a =sinh1/3( 3Λt) , T/T =tanh( 3Λt/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:
- “I’m not crazy.” It becomes very quiet in the loft.
- “MRI says no.” “Then maybe people are messing with him.
- “A man of science, a physics professor, is living here in Chicago.
- On the walk back, something happens.

“I’m not crazy.” It becomes very quiet in the loft.

“MRI says no.” “Then maybe people are messing with him.

“A man of science, a physics professor, is living here in Chicago.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Bibcode:1995PhRvL..74.1064B (https://ui.adsabs.harvard.edu/a bs/1995PhRvL..74.1064B).
- Bibcode:1990PhRvD..41.1796P (https://ui.adsabs.harvard.edu/abs/1990PhRvD..41.1796P).
- Bibcode:2003tsra.symp...77N (https://ui.adsabs.harvard.edu/abs/2003tsra.symp...77N).
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Ring_singularity&oldid=1319761276"

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- I look back at Charlie, and then over at Daniela.
- We have nothing left but one another, and yet, in this moment, I’m happier than I’ve ever been.
- My left eye is purple, badly swollen, and the skin over my left cheekbone has turned black from the blood pooling underneath.
- This is your decision too.” “I don’t want to leave.” “I know.” “But I guess we have to.” The strangest thought passes through my consciousness like a fleeting summer cloud.

I look back at Charlie, and then over at Daniela.

We have nothing left but one another, and yet, in this moment, I’m happier than I’ve ever been.

My left eye is purple, badly swollen, and the skin over my left cheekbone has turned black from the blood pooling underneath.

This is your decision too.” “I don’t want to leave.” “I know.” “But I guess we have to.” The strangest thought passes through my consciousness like a fleeting summer cloud.

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:
- He set the problem to the graduate students in his relativity class, who became coauthors of Newman et al.
- Newman told me (private communication 2009) that, after seeing Kerr’s work, he quickly realised that the extension to a charged black hole was straightforward.
- You can read in that paper that the discovery was not mere chance: Kerr used sophisticated mathematical methods to make it.
- Kerr-Newman Black Hole The geometry of a stationary, rotating, uncharged black hole in asymptotically flat empty space was discovered unexpectedly by Roy Kerr in 1963 (Kerr, 1963).

He set the problem to the graduate students in his relativity class, who became coauthors of Newman et al.

Newman told me (private communication 2009) that, after seeing Kerr’s work, he quickly realised that the extension to a charged black hole was straightforward.

You can read in that paper that the discovery was not mere chance: Kerr used sophisticated mathematical methods to make it.

Kerr-Newman Black Hole The geometry of a stationary, rotating, uncharged black hole in asymptotically flat empty space was discovered unexpectedly by Roy Kerr in 1963 (Kerr, 1963).

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851.[48] He completed his Ph.D.
- in June 1926 with the first thesis on quantum mechanics to be submitted anywhere.[49] He then continued his research in Copenhagen and Göttingen.[48] In the spring of 1929, he was a visiting professor at the University of Wisconsin–Madison.[50][51] Personal life Family In 1937, Dirac married[52] Margit Wigner, the sister of physicist Eugene Wigner[53] and a divorcee.[54] Dirac raised Margit's two children, Judith and Gabriel, as if they were his own.[55] Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.[56]

an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851.[48] He completed his Ph.D.

in June 1926 with the first thesis on quantum mechanics to be submitted anywhere.[49] He then continued his research in Copenhagen and Göttingen.[48] In the spring of 1929, he was a visiting professor at the University of Wisconsin–Madison.[50][51] Personal life Family In 1937, Dirac married[52] Margit Wigner, the sister of physicist Eugene Wigner[53] and a divorcee.[54] Dirac raised Margit's two children, Judith and Gabriel, as if they were his own.[55] Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.[56]

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:
- Theδfunctionissomehowtreatedasanadvancedtopicinmathematicalphysics,butin fact,asyouwillsee,itisanextremelyusefulfunctionthatIwilluseextensivelyinthisbook, forexampleinchaptersII.1andIII.6.Morepropertiesoftheδfunctionwillbeintroduced asneeded.
- Newton’sLaws | 27 – τ δ(t) –τ 0 τ t → Figure1 Thedeltafunction,whichcould bethoughtofasaninfinitelysharpspike, isstrictlyspeakingnotafunction,butthe limitofasequenceoffunctions.
- Thus, take F(t)=wδ(t), where the function δ(t) rises sharply just before t =0, rapidly reaches its maximum at t =0, and then sharply drops to 0.
- The lack of conservationiseasytounderstand:(4)doesnotincludetheagentadministeringthekick.In general,atime-dependentforceindicatesthatthedescriptionisnotdynamicallycomplete.

Newton’sLaws | 27 – τ δ(t) –τ 0 τ t → Figure1 Thedeltafunction,whichcould bethoughtofasaninfinitelysharpspike, isstrictlyspeakingnotafunction,butthe limitofasequenceoffunctions.

Thus, take F(t)=wδ(t), where the function δ(t) rises sharply just before t =0, rapidly reaches its maximum at t =0, and then sharply drops to 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:
- This results in a shift of Bob’s particles of a and b, leaving him with the teleported state of particle1.
- It was strongly related to the original experimental realisation of quantum teleportation described above and it made use of Type-II parametric down-conversion.
- 1   Ψ            (48) 1234 1 2 1 2 3 4 3 4
- The newly formed entangled pair consisted of particles that had no common past (37).

This results in a shift of Bob’s particles of a and b, leaving him with the teleported state of particle1.

It was strongly related to the original experimental realisation of quantum teleportation described above and it made use of Type-II parametric down-conversion.

The newly formed entangled pair consisted of particles that had no common past (37).

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:
- (19) 2a Clever,no?ThatguywouldhavesurelygottentheFieldsMedalhaditexisted.Thattablet blewmeawaywhenIsawit.IwonderedwhetherthatBabyloniancouldhavethought,in hiswildestimagination,thathisdiscoveryalsoheldthesecretofspaceandtime.Ifso,he deservedtheNobelPrizeinadditiontotheFieldsMedal.
- Takethesmallsquareofsidebandreplaceitbyarectangleofequalarea,ofsidesaand b2/a.Cuttherectangleintotwoequalsmallerrectangles,andpastethemontothesides, kitty-corner,ofthelargesquareofsidea.Theauthorofthetabletwastryingtotellyouthat theresultisalmostasquareofsidea+ b2 .
- ∗Whatfigure2showsisofcoursemyattemptatcopyingthetablet,nottheoriginaltablet.
- 2a HereisthealgebraictranslationoftheBabyloniantablet (cid:2) b2 a2+b2(cid:16)a+ +...

2a HereisthealgebraictranslationoftheBabyloniantablet (cid:2) b2 a2+b2(cid:16)a+ +...

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 addition to carrying on with her research, she taught classes in abstract algebra and algebraic geometry.
- Olga Taussky-Todd, a distinguished algebraist taught by Noether, described a luncheon during which Noether, wholly engrossed in a discussion of mathematics, "gesticulated wildly" as she ate and "spilled her food constantly and wiped it off from her dress, completely unperturbed".[114] Appearance-conscious students cringed as she retrieved the handkerchief from her blouse and ignored the increasing disarray of her hair during a lecture.
- Biographers suggest that she was mostly unconcerned about appearance and manners, focusing on her studies.
- She worked with the topologists Lev Pontryagin and Nikolai Chebotaryov, who later praised her contributions to the development of Galois theory.[123][124][125] Noether taught at Moscow State University in 1928–1929.

In addition to carrying on with her research, she taught classes in abstract algebra and algebraic geometry.

Olga Taussky-Todd, a distinguished algebraist taught by Noether, described a luncheon during which Noether, wholly engrossed in a discussion of mathematics, "gesticulated wildly" as she ate and "spilled her food constantly and wiped it off from her dress, completely unperturbed".[114] Appearance-conscious students cringed as she retrieved the handkerchief from her blouse and ignored the increasing disarray of her hair during a lecture.

Biographers suggest that she was mostly unconcerned about appearance and manners, focusing on her studies.

She worked with the topologists Lev Pontryagin and Nikolai Chebotaryov, who later praised her contributions to the development of Galois theory.[123][124][125] Noether taught at Moscow State University in 1928–1929.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- One person recalls a lively discussion about politics as a friendly debate; another recalls the identical discussion as a heated argument.
- In one survey of over 600 undergraduates at a midwestern university, 27% agreed that memory operates like a tape recorder (Lenz, Ek, & Mills, 2009).
- 9781405131117_4_003.qxd 30/6/09 11:48 AM Page 65 A REMEMBRANCE OF THINGS PAST Myths about Memory Myth Human Memory Works like a Tape Recorder or 11 Video Camera, and Accurately Records the # Events We’ve Experienced When people attend reunions or get together with childhood friends to swap “old war stories,” they’re often impressed with a simple fact: Their recollections of many events differ, in many cases dramatically.
- If our memories were perfect, we’d never forget a friend’s birthday, where we misplaced our iPod, or the exact date, time, and place of our first kiss.

One person recalls a lively discussion about politics as a friendly debate; another recalls the identical discussion as a heated argument.

In one survey of over 600 undergraduates at a midwestern university, 27% agreed that memory operates like a tape recorder (Lenz, Ek, & Mills, 2009).

9781405131117_4_003.qxd 30/6/09 11:48 AM Page 65 A REMEMBRANCE OF THINGS PAST Myths about Memory Myth Human Memory Works like a Tape Recorder or 11 Video Camera, and Accurately Records the # Events We’ve Experienced When people attend reunions or get together with childhood friends to swap “old war stories,” they’re often impressed with a simple fact: Their recollections of many events differ, in many cases dramatically.

If our memories were perfect, we’d never forget a friend’s birthday, where we misplaced our iPod, or the exact date, time, and place of our first kiss.

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 degree of freedom of a kinematic chain is
- It is a combination of a revolute joint and a sliding joint.
- This joint has two degrees of freedom.
- Kinematic chains Rigid bodies ("links") connected by kinematic pairs ("joints") are known as kinematic chains.

The degree of freedom of a kinematic chain is

It is a combination of a revolute joint and a sliding joint.

Kinematic chains Rigid bodies ("links") connected by kinematic pairs ("joints") are known as kinematic chains.

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 this case the method goes by the name of Gelfand–Naimark–Segal construction.
- For certain non-σ-finite measure spaces, usually considered pathological, L∞(X) is not a von Neumann algebra; for example, the σ-algebra of measurable sets might be the countable-cocountable algebra on an uncountable set.
- Examples The essentially bounded functions on a σ-finite measure space form a commutative (type I ) von Neumann algebra acting on the L2 functions.
- If we have any unitary representation of a group G on a Hilbert space H then the bounded operators commuting with G form a von Neumann algebra G′, whose projections correspond exactly to the closed subspaces of H invariant under G.

In this case the method goes by the name of Gelfand–Naimark–Segal construction.

For certain non-σ-finite measure spaces, usually considered pathological, L∞(X) is not a von Neumann algebra; for example, the σ-algebra of measurable sets might be the countable-cocountable algebra on an uncountable set.

Examples The essentially bounded functions on a σ-finite measure space form a commutative (type I ) von Neumann algebra acting on the L2 functions.

If we have any unitary representation of a group G on a Hilbert space H then the bounded operators commuting with G form a von Neumann algebra G′, whose projections correspond exactly to the closed subspaces of H invariant under G.

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:
- wrote, that "Isaac Newton was a heretic.
- Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture and Observations upon the Prophecies of Daniel, and the Apocalypse of St.
- he never made a public declaration of his private faith—which the orthodox would have deemed extremely radical.
- He hid his faith so well that scholars are still unraveling his personal beliefs." Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an anti-trinitarian.[228] Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock.

wrote, that "Isaac Newton was a heretic.

Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture and Observations upon the Prophecies of Daniel, and the Apocalypse of St.

he never made a public declaration of his private faith—which the orthodox would have deemed extremely radical.

He hid his faith so well that scholars are still unraveling his personal beliefs." Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an anti-trinitarian.[228] Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock.

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:
- equivalence of inertial and gravitational mass.
- By using the mass–energy equivalence, Einstein showed that the gravitational mass of a body is proportional to its energy content, which was one of the early results in developing general relativity.
- While it would appear that he did not at first think geometrically about spacetime,[3]: 219 in the further development of general relativity, Einstein fully incorporated the spacetime formalism.

equivalence of inertial and gravitational mass.

By using the mass–energy equivalence, Einstein showed that the gravitational mass of a body is proportional to its energy content, which was one of the early results in developing general relativity.

While it would appear that he did not at first think geometrically about spacetime,[3]: 219 in the further development of general relativity, Einstein fully incorporated the spacetime formalism.

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 source of the entangled photons was parametric down-conversion as described below.
- She sends the measurement outcome to Bob classically after which he can transform his particle of the entangled pair by a unitary transformation to the original particle 1(7).
- For a projection of Alice’s particles 1 and 2 onto a Bell state basis it was necessary that both particles could not be distinguished.
- She and Bob share an entangled pair on one of which Alice performs a Bell state measurement.

The source of the entangled photons was parametric down-conversion as described below.

She sends the measurement outcome to Bob classically after which he can transform his particle of the entangled pair by a unitary transformation to the original particle 1(7).

For a projection of Alice’s particles 1 and 2 onto a Bell state basis it was necessary that both particles could not be distinguished.

She and Bob share an entangled pair on one of which Alice performs a Bell state measurement.

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:
- An Exceptionally Simple Theory of Everything (Garret Lisi's E8 model) Experimental tests As was emphasized above, quantum gravitational effects are extremely weak and therefore difficult to test.
- For this reason, the possibility of experimentally testing quantum gravity had not received much attention prior to the late 1990s.
- However, since the 2000s, physicists have realized that evidence for quantum gravitational effects can guide the development of the theory.
- Had the signal in fact been primordial in origin, it could have been an indication of quantum gravitational effects, but it soon transpired that the polarization was due to interstellar dust interference.[72] See also De Sitter relativity Orders of magnitude (length) Dilaton Penrose interpretation Doubly special relativity Planck epoch Gravitational decoherence Planck units Gravitomagnetism Swampland (physics) Hawking radiation Virtual black hole List of quantum gravity researchers Weak Gravity Conjecture Notes 1.

An Exceptionally Simple Theory of Everything (Garret Lisi's E8 model) Experimental tests As was emphasized above, quantum gravitational effects are extremely weak and therefore difficult to test.

For this reason, the possibility of experimentally testing quantum gravity had not received much attention prior to the late 1990s.

However, since the 2000s, physicists have realized that evidence for quantum gravitational effects can guide the development of the theory.

Had the signal in fact been primordial in origin, it could have been an indication of quantum gravitational effects, but it soon transpired that the polarization was due to interstellar dust interference.[72] See also De Sitter relativity Orders of magnitude (length) Dilaton Penrose interpretation Doubly special relativity Planck epoch Gravitational decoherence Planck units Gravitomagnetism Swampland (physics) Hawking radiation Virtual black hole List of quantum gravity researchers Weak Gravity Conjecture Notes 1.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- Spinor tensors inherit their boost and spin weights from those of the basis spinors.
- 1006 Super spacetime algebra Positivechiralityspinorsarecalledright-handed,whilenegativechiralityspinorsarecalledleft-handed.The first two basis spinors are right-handed, while the last two are left-handed, γ ε =ε , γ ε =ε , γ ε =−ε , γ ε =−ε .
- A right-handed spatial rotation R = e−Iσ3θ/2 = cos(θ/2)−Iσ sin(θ/2) by rotation angle θ about the spin axis (3-axis) multiplies the basis spinors ε by 3 a e±iθ/2 according to ε →e−iθ/2ε , ε →eiθ/2ε , ε →e−iθ/2ε , ε →eiθ/2ε .
- (39.26) V↑ V↑ U↓ U↓ U↑ U↑ V↓ V↓ The transformations (39.26) confirm that the basis spinors with a ↑ index have spin weight +1, while the basis spinors with a ↓ index have spin weight −1.

Spinor tensors inherit their boost and spin weights from those of the basis spinors.

1006 Super spacetime algebra Positivechiralityspinorsarecalledright-handed,whilenegativechiralityspinorsarecalledleft-handed.The first two basis spinors are right-handed, while the last two are left-handed, γ ε =ε , γ ε =ε , γ ε =−ε , γ ε =−ε .

A right-handed spatial rotation R = e−Iσ3θ/2 = cos(θ/2)−Iσ sin(θ/2) by rotation angle θ about the spin axis (3-axis) multiplies the basis spinors ε by 3 a e±iθ/2 according to ε →e−iθ/2ε , ε →eiθ/2ε , ε →e−iθ/2ε , ε →eiθ/2ε .

(39.26) V↑ V↑ U↓ U↓ U↑ U↑ V↓ V↓ The transformations (39.26) confirm that the basis spinors with a ↑ index have spin weight +1, while the basis spinors with a ↓ index have spin weight −1.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- There is strong evidence that the observable universe is composed almost entirely of ordinary matter, as opposed to an equal mixture of matter and antimatter.[5] This asymmetry of matter and antimatter in the visible universe is one of the great unsolved problems in physics.[6] The process by which this
- The nuclei of antihelium have been artificially produced, albeit with difficulty, and are the most complex anti-nuclei so far observed.[4] Physical principles indicate that complex antimatter atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements.
- For example, a positron (the antiparticle of the electron) and an antiproton (the antiparticle of the proton) can form an antihydrogen atom.
- In theory, a particle and its antiparticle (for example, a proton and an antiproton) have the same mass, but opposite electric charge, and other differences in quantum numbers.

There is strong evidence that the observable universe is composed almost entirely of ordinary matter, as opposed to an equal mixture of matter and antimatter.[5] This asymmetry of matter and antimatter in the visible universe is one of the great unsolved problems in physics.[6] The process by which this

The nuclei of antihelium have been artificially produced, albeit with difficulty, and are the most complex anti-nuclei so far observed.[4] Physical principles indicate that complex antimatter atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements.

For example, a positron (the antiparticle of the electron) and an antiproton (the antiparticle of the proton) can form an antihydrogen atom.

In theory, a particle and its antiparticle (for example, a proton and an antiproton) have the same mass, but opposite electric charge, and other differences in quantum numbers.

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:
- New Haven London: Yale University Press.
- Newton to Richard Bentley 10 December 1692, in Turnbull et al.
- "Isaac Newton on Science and Religion".
- The Leibniz-Clarke Correspondence (https://archive.org/details/leibnizcla rkecor00clar/page/11).

New Haven London: Yale University Press.

Newton to Richard Bentley 10 December 1692, in Turnbull et al.

The Leibniz-Clarke Correspondence (https://archive.org/details/leibnizcla rkecor00clar/page/11).

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:
- that inconsistencies and paradoxes associated with time travel do not occur.
- Answer:Discovering the laws of quantum gravity could revolutionize our understanding of the universe, revealing how spacetime structured itself during the Big Bang, explaining black hole singularities, and potentially clarifying whether time travel is feasible.
- 8.Question What does the matricide paradox illustrate about time travel?
- 9.Question What are some potential future implications of discovering the laws of quantum gravity?

that inconsistencies and paradoxes associated with time travel do not occur.

Answer:Discovering the laws of quantum gravity could revolutionize our understanding of the universe, revealing how spacetime structured itself during the Big Bang, explaining black hole singularities, and potentially clarifying whether time travel is feasible.

8.Question What does the matricide paradox illustrate about time travel?

9.Question What are some potential future implications of discovering the laws of quantum gravity?

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:
- background, there are A map of the cosmic microwave background produced by several questions that remain unanswered.
- For the Wilkinson Microwave Anisotropy Probe example, the standard Big Bang model does not explain why the universe appears to be the same in all directions, why it appears flat on very large distance scales, or why certain hypothesized particles such as magnetic monopoles are not observed in experiments.[85]

background, there are A map of the cosmic microwave background produced by several questions that remain unanswered.

For the Wilkinson Microwave Anisotropy Probe example, the standard Big Bang model does not explain why the universe appears to be the same in all directions, why it appears flat on very large distance scales, or why certain hypothesized particles such as magnetic monopoles are not observed in experiments.[85]

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:
- WHITE DWARFS RED GIANTS AND DARK COMPANIONS THERE IS A DIFFERENCE between planets and stars that in the long run is more crucial than the mere fact that planets are less massive than stars, or that planets are cold and opaque and that stars are hot and glowing.
- Stars, however, are in a state of dynamic stability, for a star maintains its structure at the cost of something within that is constantly chang81
- Planets are in a state of essentially static stability.
- Were it alone in the universe, Earth might be frozen and lifeless but its physical structure would persist, perhaps forever.

WHITE DWARFS RED GIANTS AND DARK COMPANIONS THERE IS A DIFFERENCE between planets and stars that in the long run is more crucial than the mere fact that planets are less massive than stars, or that planets are cold and opaque and that stars are hot and glowing.

Stars, however, are in a state of dynamic stability, for a star maintains its structure at the cost of something within that is constantly chang81

Planets are in a state of essentially static stability.

Were it alone in the universe, Earth might be frozen and lifeless but its physical structure would persist, perhaps forever.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- This is because the body treats radium as calcium and deposits it in the bones, where radioactivity degrades marrow and can mutate bone cells.
- The French physicist Antoine Becquerel carried a small ampoule of radium in his waistcoat pocket for six hours and reported that his skin became ulcerated.
- Pierre Curie attached a tube filled with radium to his arm for ten hours, which resulted in the appearance of a skin lesion, suggesting the use of radium to attack cancerous tissue as it had attacked healthy tissue.[88] Handling of radium has been blamed for Marie Curie's death, due to aplastic anemia,[89] though analysis of her levels of radium exposure done after her death find them within accepted safe levels and attribute her illness and death to her use of radiography.[90] A significant amount of radium's danger comes from its daughter radon, which as a gas can enter the body far more readily than can its parent radium.[15] Regulation The first published recommendations for protection against radium and radiation in general were made by the British X-ray and Radium Protection Committee and were adopted internationally in 1928 at the first meeting of the International Commission on Radiological Protection (ICRP), following preliminary guidance written by the Röntgen Society.[91] This meeting led to further developments of radiation protection programs[92] coordinated across all countries represented by the commission.[93] Exposure to radium is still regulated internationally by the ICRP, alongside the World Health Organization.[94] The International Atomic Energy Agency (IAEA) publishes safety standards and provides recommendations for the handling of and exposure to radium in its works on naturally occurring radioactive materials and the broader International Basic Safety Standards,[95] which are not enforced by the IAEA but are available for adoption by members of the organization.[96] In addition, in efforts to reduce the quantity of old radiotherapy devices that contain radium, the IAEA has worked since 2022[97] to manage and recycle disused 226Ra sources.[98][99]
- When ingested, 80% of the ingested radium leaves the body through the feces, while the other 20% goes into the bloodstream, mostly accumulating in the bones.

This is because the body treats radium as calcium and deposits it in the bones, where radioactivity degrades marrow and can mutate bone cells.

The French physicist Antoine Becquerel carried a small ampoule of radium in his waistcoat pocket for six hours and reported that his skin became ulcerated.

Pierre Curie attached a tube filled with radium to his arm for ten hours, which resulted in the appearance of a skin lesion, suggesting the use of radium to attack cancerous tissue as it had attacked healthy tissue.[88] Handling of radium has been blamed for Marie Curie's death, due to aplastic anemia,[89] though analysis of her levels of radium exposure done after her death find them within accepted safe levels and attribute her illness and death to her use of radiography.[90] A significant amount of radium's danger comes from its daughter radon, which as a gas can enter the body far more readily than can its parent radium.[15] Regulation The first published recommendations for protection against radium and radiation in general were made by the British X-ray and Radium Protection Committee and were adopted internationally in 1928 at the first meeting of the International Commission on Radiological Protection (ICRP), following preliminary guidance written by the Röntgen Society.[91] This meeting led to further developments of radiation protection programs[92] coordinated across all countries represented by the commission.[93] Exposure to radium is still regulated internationally by the ICRP, alongside the World Health Organization.[94] The International Atomic Energy Agency (IAEA) publishes safety standards and provides recommendations for the handling of and exposure to radium in its works on naturally occurring radioactive materials and the broader International Basic Safety Standards,[95] which are not enforced by the IAEA but are available for adoption by members of the organization.[96] In addition, in efforts to reduce the quantity of old radiotherapy devices that contain radium, the IAEA has worked since 2022[97] to manage and recycle disused 226Ra sources.[98][99]

When ingested, 80% of the ingested radium leaves the body through the feces, while the other 20% goes into the bloodstream, mostly accumulating in the bones.

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:
- New approaches to thinking about time, came from new thinking about the connectedness of space, and all that came from the desire to make a film that could, among other things, explore issues of science and faith.
- The novel was a great success, and the film finally moved out of the perdition of production hell.
- Worm Holes This particular attack on time travel arose from a work of science fiction.
- The film, too, was a great success, but Sagan succumbed to a leukemia-related disease before it was released.

New approaches to thinking about time, came from new thinking about the connectedness of space, and all that came from the desire to make a film that could, among other things, explore issues of science and faith.

The novel was a great success, and the film finally moved out of the perdition of production hell.

Worm Holes This particular attack on time travel arose from a work of science fiction.

The film, too, was a great success, but Sagan succumbed to a leukemia-related disease before it was released.

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:
- Pan Jianwei Pan Jianwei (Chinese: 潘建伟; pinyin: Pān Jiànwěi; Pan Jianwei born 11 March 1970) is a Chinese academic administrator and quantum physicist.
- Pan is known for his work in the field of quantum entanglement, quantum information and quantum computers.
- In 2017, he was named one of Nature's 10, which labelled him "Father of Quantum".[5] He is an academician of the Chinese Academy of Sciences and the World Academy of Sciences and Executive Vice President of the University of Science and Technology of China.[6] He also serves as one of the Vice Chairman of Jiusan Society.[7] Early life and education Pan was born in Dongyang, Jinhua, Zhejiang province in 1970.
- He is a university 潘建伟 administrator and professor of physics at the University of Science and Technology of China.

Pan Jianwei Pan Jianwei (Chinese: 潘建伟; pinyin: Pān Jiànwěi; Pan Jianwei born 11 March 1970) is a Chinese academic administrator and quantum physicist.

Pan is known for his work in the field of quantum entanglement, quantum information and quantum computers.

In 2017, he was named one of Nature's 10, which labelled him "Father of Quantum".[5] He is an academician of the Chinese Academy of Sciences and the World Academy of Sciences and Executive Vice President of the University of Science and Technology of China.[6] He also serves as one of the Vice Chairman of Jiusan Society.[7] Early life and education Pan was born in Dongyang, Jinhua, Zhejiang province in 1970.

He is a university 潘建伟 administrator and professor of physics at the University of Science and Technology of China.

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:
- Online version: (2006–) "Chemical Substance (https://goldbook.iupac.org/terms/view/C01039.html)".
- Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them (https://books.google.com/books?id=L7poAgAAQBAJ&q=chemical+sub stance+is+a+form+of+matter+having+constant+chemical+composition+and+characteristic+proper ties&pg=PA280).
- Archived (https://web.archive.org/web/2018 0113233820/https://books.google.com/books?id=L7poAgAAQBAJ&pg=PA280&dq=chemical+subs tance+is+a+form+of+matter+having+constant+chemical+composition+and+characteristic+properti es&hl=en&sa=X&ved=0ahUKEwi-k_LI_dXUAhUHyWMKHa8vCowQ6AEIMjAC#v=onepage&q=ch emical%20substance%20is%20a%20form%20of%20matter%20having%20constant%20chemica l%20composition%20and%20characteristic%20properties&f=false) from the original on 13 January 2018.
- Perspectives of reality: an introduction to the philosophy of Hinduism (https://books.google.com/books?id=PJbsAAAAIAAJ).

Online version: (2006–) "Chemical Substance (https://goldbook.iupac.org/terms/view/C01039.html)".

Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them (https://books.google.com/books?id=L7poAgAAQBAJ&q=chemical+sub stance+is+a+form+of+matter+having+constant+chemical+composition+and+characteristic+proper ties&pg=PA280).

Archived (https://web.archive.org/web/2018 0113233820/https://books.google.com/books?id=L7poAgAAQBAJ&pg=PA280&dq=chemical+subs tance+is+a+form+of+matter+having+constant+chemical+composition+and+characteristic+properti es&hl=en&sa=X&ved=0ahUKEwi-k_LI_dXUAhUHyWMKHa8vCowQ6AEIMjAC#v=onepage&q=ch emical%20substance%20is%20a%20form%20of%20matter%20having%20constant%20chemica l%20composition%20and%20characteristic%20properties&f=false) from the original on 13 January 2018.

Perspectives of reality: an introduction to the philosophy of Hinduism (https://books.google.com/books?id=PJbsAAAAIAAJ).

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:
- He wrote, Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time.
- Neumann's book off his shelf, pointed to the same assumption critiqued by Hermann and Bell, and asked why one should believe in it.[20][21] Simon Kochen and Ernst Specker rejected von Neumann's key assumption as early as 1961, but did not publish a criticism of it until 1967.[22] EPR paradox Einstein argued that quantum mechanics could not be a complete theory of physical reality.
- Let us now determine the physical state of the partial system A as completely as possible by measurements.
- Then quantum mechanics allows us to determine the ψ function of the partial system B from the measurements made, and from the ψ function of the total system.

He wrote, Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time.

Neumann's book off his shelf, pointed to the same assumption critiqued by Hermann and Bell, and asked why one should believe in it.[20][21] Simon Kochen and Ernst Specker rejected von Neumann's key assumption as early as 1961, but did not publish a criticism of it until 1967.[22] EPR paradox Einstein argued that quantum mechanics could not be a complete theory of physical reality.

Let us now determine the physical state of the partial system A as completely as possible by measurements.

Then quantum mechanics allows us to determine the ψ function of the partial system B from the measurements made, and from the ψ function of the total system.

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:
- Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete."[26] Bohr is here choosing to define a "physical reality" as limited to a phenomenon that is immediately observable by an arbitrarily chosen and explicitly specified technique, using his own special definition of the term 'phenomenon'.
- Bohm unknowingly rediscovered (and extended) the idea that Louis de Broglie's pilot wave theory had proposed in 1927 (and abandoned) – hence this theory is commonly called "de Broglie-Bohm theory".
- Gerard 't Hooft has disputed the validity of Bell's theorem on the basis of the superdeterminism loophole and proposed some ideas to construct local deterministic models.[30][31] The many-worlds interpretation loophole allows the local, realist theory to violate Bell inequalities due to there being more than one experimental outcome in the interpretation.[32] Bohm's non-local hidden-variable theory In 1952, David Bohm proposed a hidden variable theory.
- He wrote in 1948: As a more appropriate way of expression, one may strongly advocate limitation of the use of the word phenomenon to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.[27][28] This was, of course, in conflict with the EPR criterion of reality.

Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete."[26] Bohr is here choosing to define a "physical reality" as limited to a phenomenon that is immediately observable by an arbitrarily chosen and explicitly specified technique, using his own special definition of the term 'phenomenon'.

Bohm unknowingly rediscovered (and extended) the idea that Louis de Broglie's pilot wave theory had proposed in 1927 (and abandoned) – hence this theory is commonly called "de Broglie-Bohm theory".

Gerard 't Hooft has disputed the validity of Bell's theorem on the basis of the superdeterminism loophole and proposed some ideas to construct local deterministic models.[30][31] The many-worlds interpretation loophole allows the local, realist theory to violate Bell inequalities due to there being more than one experimental outcome in the interpretation.[32] Bohm's non-local hidden-variable theory In 1952, David Bohm proposed a hidden variable theory.

He wrote in 1948: As a more appropriate way of expression, one may strongly advocate limitation of the use of the word phenomenon to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.[27][28] This was, of course, in conflict with the EPR criterion of reality.

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:
- Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container.
- Fluid dynamics has a wide range of applications, including calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions.
- It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion.
- Some fluid-dynamical principles are used in traffic engineering and crowd dynamics.

Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container.

Fluid dynamics has a wide range of applications, including calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions.

It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion.

Some fluid-dynamical principles are used in traffic engineering and crowd dynamics.

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 proposed device allows for the direct detection of quantum vacuum fluctuations and provides a spatial mapping of the negative energy contained inside the caVity.
- • Trapping and Storing Negative Energy: Ford and Roman (Reference 10) have only superficially addressed this topic, and there is very little technical literature that addresses it fully.
- Marecki computed the two-point function and the associated spectral density for the ground state of the quantum electric field in Casimir geometries, and predicts a position- and frequency-dependent pattern of BHD responses if a device of this type is placed inside a Casimir cavity.
- A theoretical program to develop the physics and technology of trapping and storing negative energy will need to be supported, and such a program should be guided by the use of laboratory detectors such as the one proposed in the

The proposed device allows for the direct detection of quantum vacuum fluctuations and provides a spatial mapping of the negative energy contained inside the caVity.

• Trapping and Storing Negative Energy: Ford and Roman (Reference 10) have only superficially addressed this topic, and there is very little technical literature that addresses it fully.

Marecki computed the two-point function and the associated spectral density for the ground state of the quantum electric field in Casimir geometries, and predicts a position- and frequency-dependent pattern of BHD responses if a device of this type is placed inside a Casimir cavity.

A theoretical program to develop the physics and technology of trapping and storing negative energy will need to be supported, and such a program should be guided by the use of laboratory detectors such as the one proposed in 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:
- dT Notes (cid:29) √ (cid:30) (cid:12) (cid:14) 1.
- Theonlyknownexceptionsoccurinthedecayofcertainelementaryparticles.
- max (h−3)h(cid:29) −h√ 3 (cid:30) rS 2.
- Fortherecord,V(r )=h(cid:29)h √ − (h−3)h− (cid:30)2 ,withh≡ l 2 .

Fortherecord,V(r )=h(cid:29)h √ − (h−3)h− (cid:30)2 ,withh≡ l 2 .

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:
- This is known as Newton's theory of colour.[103] His 1672 paper on the nature of white light and colours forms the basis for all work that followed on colour and colour vision.[104] From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration).
- Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves.
- He differentiated 1672 (the first one he made in 1668 was between two uneven sets of data and may have considered an loaned to an instrument maker but there optimal solution regarding bias, although not in terms of is no further record of what happened to effectiveness.[102] it).[93] He showed that coloured light does not change its properties by separating out a coloured beam and shining it on various objects, and that regardless of whether reflected, scattered, or transmitted, the light remains the same colour.
- As a proof of the concept, he constructed a telescope using reflective mirrors instead of lenses as the objective to bypass that problem.

This is known as Newton's theory of colour.[103] His 1672 paper on the nature of white light and colours forms the basis for all work that followed on colour and colour vision.[104] From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration).

Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves.

He differentiated 1672 (the first one he made in 1668 was between two uneven sets of data and may have considered an loaned to an instrument maker but there optimal solution regarding bias, although not in terms of is no further record of what happened to effectiveness.[102] it).[93] He showed that coloured light does not change its properties by separating out a coloured beam and shining it on various objects, and that regardless of whether reflected, scattered, or transmitted, the light remains the same colour.

As a proof of the concept, he constructed a telescope using reflective mirrors instead of lenses as the objective to bypass that problem.

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

List tests or derivations implied by the evidence.


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

EVIDENCE:
- "Negative Mass in General Relativity" (http://ayuba.fr/pdf/bondi1957.pdf) (PDF).
- edu/faculty/ccline/courses/resources/wp/pdf/AJP000216.pdf) (PDF).
- doi:10.1103/RevModPhys.29.423 (https://doi.org/10.1103% 2FRevModPhys.29.423).
- doi:10.1007/BF01940959 (https://doi.org/10.100 7%2FBF01940959).

"Negative Mass in General Relativity" (http://ayuba.fr/pdf/bondi1957.pdf) (PDF).

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:
- Inthediscussionleadingupto(18),weshowedthepoweroftheequivalenceprinciple.Weobtainedtheaction ofanelectromagneticfieldinthepresenceofagravitationalfieldbysimplyreplacingtheMinkowskimetricη μν intheMaxwellactionbyg μν.Wen(cid:8)owrep √ eatthisamazingfeat:weobtaintheactiongoverningascalarfieldin curvedspacetime,namelyS=− 1 ddx −ggμν∂ μ φ∂ ν φ.
- (cid:8) √ 2 GiventhecovariantderivativeD ν Wμin(5),integrate dDx −gT μ νD ν Wμtoobtainthecovariantdivergence ofthetensorTν.Verifythatitagreeswiththeresultof(1).
- Fine—nowwhat?Thepointisthat(36),whenwrittenoutintermsof ∂, ∂ , ∂ ,andsoon(withaslightabuse ∂t ∂x ∂y ofnotationhere),isjustasecondorderpartialdifferentialequation.Butsecondorderpartialdifferentialequations appearinmanyareasofphysics,andsomeofthesecouldbewrittenas(36)forsomeg μν.Forexample,consider the Bose-Einstein condensate as a fluid.5 Its phase angle φ(t,x(cid:3)) satisfies a second order partial differential equation;whenwrittenintheformgivenin(36),theequationcanbeinterpretedasascalarfieldmovingin curvedspacetime.Forinstance,termsthatinvolveboth ∂ and ∂ correspondtotheentrygtxingμνin(36).The ∂t ∂x nameofthegameistosetupsomeflowinthelab(suchasthatofafluidrushingdownadrain)thatcorresponds toaninterestinganalogcurvedspacetime,suchasthatofablackhole!
- NowthatwehavefollowedEinsteintothescalarfie(cid:12)ldacti(cid:14)onincurvedspacetime,wefollowEulerandLagrange tothecorrespondingequationofmotion,namely∂ μ δ∂ δ μ L φ =0.Thisworksouttobe 1 √ √ −g ∂ μ ( −ggμν∂ ν φ)=0 (36) Applyingwhatwelearnedinthischapter,werecognizethisasjustD μ Dμφ=0,thecurvedspacetimeversionof theflatspacetimeequationofmotion∂ μ ∂μφ=0.

Inthediscussionleadingupto(18),weshowedthepoweroftheequivalenceprinciple.Weobtainedtheaction ofanelectromagneticfieldinthepresenceofagravitationalfieldbysimplyreplacingtheMinkowskimetricη μν intheMaxwellactionbyg μν.Wen(cid:8)owrep √ eatthisamazingfeat:weobtaintheactiongoverningascalarfieldin curvedspacetime,namelyS=− 1 ddx −ggμν∂ μ φ∂ ν φ.

(cid:8) √ 2 GiventhecovariantderivativeD ν Wμin(5),integrate dDx −gT μ νD ν Wμtoobtainthecovariantdivergence ofthetensorTν.Verifythatitagreeswiththeresultof(1).

Fine—nowwhat?Thepointisthat(36),whenwrittenoutintermsof ∂, ∂ , ∂ ,andsoon(withaslightabuse ∂t ∂x ∂y ofnotationhere),isjustasecondorderpartialdifferentialequation.Butsecondorderpartialdifferentialequations appearinmanyareasofphysics,andsomeofthesecouldbewrittenas(36)forsomeg μν.Forexample,consider the Bose-Einstein condensate as a fluid.5 Its phase angle φ(t,x(cid:3)) satisfies a second order partial differential equation;whenwrittenintheformgivenin(36),theequationcanbeinterpretedasascalarfieldmovingin curvedspacetime.Forinstance,termsthatinvolveboth ∂ and ∂ correspondtotheentrygtxingμνin(36).The ∂t ∂x nameofthegameistosetupsomeflowinthelab(suchasthatofafluidrushingdownadrain)thatcorresponds toaninterestinganalogcurvedspacetime,suchasthatofablackhole!

NowthatwehavefollowedEinsteintothescalarfie(cid:12)ldacti(cid:14)onincurvedspacetime,wefollowEulerandLagrange tothecorrespondingequationofmotion,namely∂ μ δ∂ δ μ L φ =0.Thisworksouttobe 1 √ √ −g ∂ μ ( −ggμν∂ ν φ)=0 (36) Applyingwhatwelearnedinthischapter,werecognizethisasjustD μ Dμφ=0,thecurvedspacetimeversionof theflatspacetimeequationofmotion∂ μ ∂μφ=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:
- Ten years ago, my first day on the job at Velocity Laboratories, I wrote an intriguing mission statement to the entire team, essentially bringing them up to speed on the concepts of quantum mechanics and the multiverse.
- We have to add a fourth dimension to begin to describe the nature of our existence.
- It adds time, a stream of 3-D cubes, representing space as it moves along time’s arrow.
- Our path through this 4-D spacetime is our worldline (reality), beginning with our birth and ending with our death.

Ten years ago, my first day on the job at Velocity Laboratories, I wrote an intriguing mission statement to the entire team, essentially bringing them up to speed on the concepts of quantum mechanics and the multiverse.

We have to add a fourth dimension to begin to describe the nature of our existence.

It adds time, a stream of 3-D cubes, representing space as it moves along time’s arrow.

Our path through this 4-D spacetime is our worldline (reality), beginning with our birth and ending with our death.

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:
- "Bell inequalities and operator algebras" (https://web.archive.org/web/20191206004134/https://oq p.iqoqi.univie.ac.at/bell-inequalities-and-operator-algebras/).
- Aaronson, Scott (16 January 2020).
- The answer could be incalculable" (https://doi.org/10.1038%2Fd41586-020-00120-6).
- doi:10.1038/d41586-020-00120-6 (https://doi.org/10.1038%2Fd41586-020-00120-6).

"Bell inequalities and operator algebras" (https://web.archive.org/web/20191206004134/https://oq p.iqoqi.univie.ac.at/bell-inequalities-and-operator-algebras/).

The answer could be incalculable" (https://doi.org/10.1038%2Fd41586-020-00120-6).

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:
- Then convert sk back to σa using equation (27.90).] 2.
- (27.96) dt 2 2 Bycomparingyourequation(27.96)totheequationofmotionofa3-vectorrotatingatangularvelocity ω, dσ =ω×σ , (27.97) dt deducetheangularvelocityω withwhichthespinsprecesses.ThetermdependingonΦisthegeodetic, or de Sitter (de Sitter, 1916), precession, while the term depending on W is the frame-dragging, or Lense-Thirring(Thirring,1918;LenseandThirring,1918),precession.[Hint:Recallthe3-vectorformula a×(b×c)=(a·c)b−(a·b)c.
- (27.93) dτ abc ab0 1+u0 0ac 0bc 1+u0 0a0 0b0 [Hint: The first step is to convert σa to sk and uk, using equation (27.91).
- Then apply the geodesic equations (27.92).

Then convert sk back to σa using equation (27.90).] 2.

(27.96) dt 2 2 Bycomparingyourequation(27.96)totheequationofmotionofa3-vectorrotatingatangularvelocity ω, dσ =ω×σ , (27.97) dt deducetheangularvelocityω withwhichthespinsprecesses.ThetermdependingonΦisthegeodetic, or de Sitter (de Sitter, 1916), precession, while the term depending on W is the frame-dragging, or Lense-Thirring(Thirring,1918;LenseandThirring,1918),precession.[Hint:Recallthe3-vectorformula a×(b×c)=(a·c)b−(a·b)c.

(27.93) dτ abc ab0 1+u0 0ac 0bc 1+u0 0a0 0b0 [Hint: The first step is to convert σa to sk and uk, using equation (27.91).

Then apply the geodesic equations (27.92).

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:
- Rather than blaming the causes of the Genovese murder and similar events on apathetic city-goers, Darley and Latane suspected that the causes of bystander nonintervention lay far more in commonplace psychological processes than in the interpersonal nature of the large urban environment.
- Another man on a scooter circled around Torres briefly before departing.
- As Torres lay motionless, numerous bystanders merely watched and did nothing as nine cars swerved around him, not even bothering to stop.
- On May 30, 2008 in Hartford, Connecticut, a 78-year-old man on his way home from buying milk in a grocery store, Angel Arce Torres, was hit by a car in the middle of a busy street during rush hour.

Rather than blaming the causes of the Genovese murder and similar events on apathetic city-goers, Darley and Latane suspected that the causes of bystander nonintervention lay far more in commonplace psychological processes than in the interpersonal nature of the large urban environment.

Another man on a scooter circled around Torres briefly before departing.

As Torres lay motionless, numerous bystanders merely watched and did nothing as nine cars swerved around him, not even bothering to stop.

On May 30, 2008 in Hartford, Connecticut, a 78-year-old man on his way home from buying milk in a grocery store, Angel Arce Torres, was hit by a car in the middle of a busy street during rush hour.

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

List tests or derivations implied by the evidence.