Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Wenownotethat(1+1)-dimensionalMinkowskispacetimeisaspecialcase:aswecanseein(16),d(cid:24)2 d−2 degeneratesford=2.Insteadofstartingoutwith(t,r)with0≤r<∞, wehave(t,x)with−∞<x<∞ andthus (cid:12) (cid:14) ds2=−dt2+dx2=−dpdq= −dT2+dX2 4cos2Pcos2Q NowthecoordinateXrangesbetween−πandπ,incontrasttothecoordinateR,whichrangesbetween0andπ inthehigherdimensionalcases.Insteadofatriangle,spacetimenowconsistsofadiamondshapedregion,that is,asquarerotatedby45◦.(AnotherwayofsayingthisisthatspatialboundaryS0isnotconnectedandcontains 2points.Incontrast,Sd−2isconnectedford>2.) ForthestatementthatthemaximalextensionofMinkowskispacetimeMd−1,1hasthetopologyofR×Sd−1 tobeapplicablealsoford=2,wecouldidentifythetwopoints(T =0,X=π)and(T =0,X=−π).ThenM1,1 ismaximallyextendedtoR×S1,familiarlyknownasthecylinder.WewillcomebacktothisinchapterIX.11.
- Kruskalwasadistinguishedplasmaphysicist.Thisepisodeinthehistoryofphysicsremindsusthatthere isahugegulfbetween“nonexperts”andcrackpots.
- Forreadersutterlyunfamiliarwiththestory,Irecommendchapters20–22inR.FreedmanandW.Kauffman, TheUniverse.
- Inhindsight,itmightseemsomewhatsurprisingthattheKruskalcoordinateswerefoundonlyin1960.
- Indeed,wemightwanttorenameRasθ,thefamiliarlatitude.(Notethatwehavegeneralizedslightlyfromthe texttoconsiderMd−1,1withnocosttous;asusual,theangularcoordinatesjustgoalongfortheride.) Butifsomebodyhandedusds ̃2withTandRrestrictedtothetriangularregion,wecouldinviteourselvestoextendthisspacetimeoutsidethetriangle:simplyletT runfrom−∞to+∞.Withoutthefactor(cos2Pcos2Q)−1, we can wander outside the triangle in figure 6 with impunity.

Indeed,wemightwanttorenameRasθ,thefamiliarlatitude.(Notethatwehavegeneralizedslightlyfromthe texttoconsiderMd−1,1withnocosttous;asusual,theangularcoordinatesjustgoalongfortheride.) Butifsomebodyhandedusds ̃2withTandRrestrictedtothetriangularregion,wecouldinviteourselvestoextendthisspacetimeoutsidethetriangle:simplyletT runfrom−∞to+∞.Withoutthefactor(cos2Pcos2Q)−1, we can wander outside the triangle in figure 6 with impunity.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- To be precise, is equal to the sum of (expressions corresponding to) all connected diagrams with n external points.
- For every internal vertex , write down a factor .
- With the symmetry factor , following these rules yields exactly the expression above.
- By Fourier transforming the propagator, the Feynman rules can be reformulated from position space into momentum space.[1]: 91–94 In order to compute the n-point correlation function to the k-th order, list all valid Feynman diagrams with n external points and k or fewer vertices, and then use Feynman rules to obtain the expression for each term.
- Components that are totally disconnected from external lines are sometimes called "vacuum bubbles".) In the φ interaction theory discussed above, every vertex must have four legs.[1]: 98 In realistic applications, the scattering amplitude of a certain interaction or the decay rate of a particle can be computed from the S-matrix, which itself can be found using the Feynman diagram method.[1]: 102–115 Feynman diagrams devoid of "loops" are called tree-level diagrams, which describe the lowest-order interaction processes; those containing n loops are referred to as n-loop diagrams, which describe higher-order contributions, or radiative corrections, to the interaction.[32]: 44 Lines whose end points are vertices can be thought of as the propagation of virtual particles.[1]: 31 Renormalization Feynman rules can be used to directly evaluate tree-level diagrams.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

Chosen based on domain + required checks.

Produce bounded conclusion + next actions

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.

Apply expert-specific checks; do not introduce new facts beyond evidence.

To be precise, is equal to the sum of (expressions corresponding to) all connected diagrams with n external points.

For every internal vertex , write down a factor .

With the symmetry factor , following these rules yields exactly the expression above.

By Fourier transforming the propagator, the Feynman rules can be reformulated from position space into momentum space.[1]: 91–94 In order to compute the n-point correlation function to the k-th order, list all valid Feynman diagrams with n external points and k or fewer vertices, and then use Feynman rules to obtain the expression for each term.

Components that are totally disconnected from external lines are sometimes called "vacuum bubbles".) In the φ interaction theory discussed above, every vertex must have four legs.[1]: 98 In realistic applications, the scattering amplitude of a certain interaction or the decay rate of a particle can be computed from the S-matrix, which itself can be found using the Feynman diagram method.[1]: 102–115 Feynman diagrams devoid of "loops" are called tree-level diagrams, which describe the lowest-order interaction processes; those containing n loops are referred to as n-loop diagrams, which describe higher-order contributions, or radiative corrections, to the interaction.[32]: 44 Lines whose end points are vertices can be thought of as the propagation of virtual particles.[1]: 31 Renormalization Feynman rules can be used to directly evaluate tree-level diagrams.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- 14 Special Relativity L ig g ht h t Li Space emiT Figure 1.2 A spacetime diagram shows events in space and time.
- Each point in 4-dimensional spacetime is called an event.
- In a spacetime diagram, the units of space and time are chosen so that light goes one unit of distanceinoneunitoftime,i.e.theunitsaresuchthatthespeedoflightisone,c=1.Thuslightmovesupwardand outwardat45∘ fromverticalinaspacetimediagram.
- This is a spacetime diagram version of the situationillustratedinFigure1.1.ThelinesalongwhichVermilionandCeruleanmovethroughspacetimearecalled their worldlines.
- In a spacetime diagram, time goes upward, while space dimensions are horizontal.

14 Special Relativity L ig g ht h t Li Space emiT Figure 1.2 A spacetime diagram shows events in space and time.

Each point in 4-dimensional spacetime is called an event.

In a spacetime diagram, the units of space and time are chosen so that light goes one unit of distanceinoneunitoftime,i.e.theunitsaresuchthatthespeedoflightisone,c=1.Thuslightmovesupwardand outwardat45∘ fromverticalinaspacetimediagram.

This is a spacetime diagram version of the situationillustratedinFigure1.1.ThelinesalongwhichVermilionandCeruleanmovethroughspacetimearecalled their worldlines.

In a spacetime diagram, time goes upward, while space dimensions are horizontal.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- The solution set may be generated by
- Harmonic oscillator The Schrödinger equation for this situation is where is the displacement and the angular frequency.
- Furthermore, it can be used to describe approximately a wide variety of other systems, including vibrating atoms, molecules,[22] and atoms or ions in lattices,[23] and approximating other potentials near equilibrium points.
- Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy.
- At , in which cannot be zero as this would conflict with the postulate that has norm 1.

Harmonic oscillator The Schrödinger equation for this situation is where is the displacement and the angular frequency.

Furthermore, it can be used to describe approximately a wide variety of other systems, including vibrating atoms, molecules,[22] and atoms or ions in lattices,[23] and approximating other potentials near equilibrium points.

Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy.

At , in which cannot be zero as this would conflict with the postulate that has norm 1.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- The big question, though, is when the big bang took place.
- Others have called it the cosmic egg.
- Astronomers know (or think they know) just how rapidly the universe is expanding now.
- In the last half century evidence for the big bang has accumulated, and nowadays almost all astronomers accept the thought that that is how the universe started.
- How long the cosmic egg existed, or how it was formed, Lemaitre did not venture to guess, but at some moment it must have exploded.

The big question, though, is when the big bang took place.

Astronomers know (or think they know) just how rapidly the universe is expanding now.

In the last half century evidence for the big bang has accumulated, and nowadays almost all astronomers accept the thought that that is how the universe started.

How long the cosmic egg existed, or how it was formed, Lemaitre did not venture to guess, but at some moment it must have exploded.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- b b Thechemicalpotentialoftherelativisticbaryonicfluidislikelytobeclosetozero,correspondingtoequal numbers of particles and anti-particles.
- 620 The interiors of accreting, spherical black holes 21.1.3 Equation of state The density ρ and temperature T of an ideal relativistic baryonic fluid in thermodynamic equilibrium are b b related by π2g ρ = b T4 , (21.9) b 30 b where g =g + g (21.10) b B 8 F is the effective number of relativistic particle species, with g and g being the number of bosonic and B F fermionic species.
- The entropy S of a proper Lagrangian volume element V of the b fluid is then (ρ +p )V S = b b , (21.13) b T b which agrees with the earlier expression (20.187), but now has the correct normalization.
- b In the models considered here, the baryonic equation of state is taken to be w =0.32 .
- In self-similar solutions, the charge of the black hole is produced self-consistently by the accreted charge of the baryonic fluid, so a neutral fluid produces an uncharged black hole.

b b Thechemicalpotentialoftherelativisticbaryonicfluidislikelytobeclosetozero,correspondingtoequal numbers of particles and anti-particles.

620 The interiors of accreting, spherical black holes 21.1.3 Equation of state The density ρ and temperature T of an ideal relativistic baryonic fluid in thermodynamic equilibrium are b b related by π2g ρ = b T4 , (21.9) b 30 b where g =g + g (21.10) b B 8 F is the effective number of relativistic particle species, with g and g being the number of bosonic and B F fermionic species.

The entropy S of a proper Lagrangian volume element V of the b fluid is then (ρ +p )V S = b b , (21.13) b T b which agrees with the earlier expression (20.187), but now has the correct normalization.

b In the models considered here, the baryonic equation of state is taken to be w =0.32 .

In self-similar solutions, the charge of the black hole is produced self-consistently by the accreted charge of the baryonic fluid, so a neutral fluid produces an uncharged black hole.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Scalar and gravitational perturbations”.
- “Observationalevidencefromsupernovaeforanacceleratinguniverseandacosmologicalconstant”.
- arXiv: 1103.2976 [astro-ph.CO] (cit.
- doi: 10.1088/0264-9381/23/16/S13.
- doi: 10.1088/0264-9381/22/2/014.

Scalar and gravitational perturbations”.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Really there should be 3 space dimensions, but usually it suffices to show 1 spatial dimension, as here.
- In a spacetime diagram, time goes upward, while space dimensions are horizontal.
- In a spacetime diagram, the units of space and time are chosen so that light goes one unit of distanceinoneunitoftime,i.e.theunitsaresuchthatthespeedoflightisone,c=1.Thuslightmovesupwardand outwardat45∘ fromverticalinaspacetimediagram.
- Each point in 4-dimensional spacetime is called an event.
- 14 Special Relativity L ig g ht h t Li Space emiT Figure 1.2 A spacetime diagram shows events in space and time.

Really there should be 3 space dimensions, but usually it suffices to show 1 spatial dimension, as here.

In a spacetime diagram, time goes upward, while space dimensions are horizontal.

In a spacetime diagram, the units of space and time are chosen so that light goes one unit of distanceinoneunitoftime,i.e.theunitsaresuchthatthespeedoflightisone,c=1.Thuslightmovesupwardand outwardat45∘ fromverticalinaspacetimediagram.

Each point in 4-dimensional spacetime is called an event.

14 Special Relativity L ig g ht h t Li Space emiT Figure 1.2 A spacetime diagram shows events in space and time.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- In addition to these, we also have the vacuum pp-wave spacetimes, which include the gravitational plane waves.
- Milne describing an empty universe which has no curvature) Schwarzschild vacuum (which describes the spacetime geometry around a spherical mass), Kerr vacuum (which describes the geometry around a rotating object), Taub–NUT vacuum (a famous counterexample describing the exterior gravitational field of an isolated object with strange properties), Kerns–Wild vacuum (Robert M.
- Khan and Roger Penrose 1971) (a simple colliding plane wave model), Oszváth–Schücking vacuum (the circularly polarized sinusoidal gravitational wave, another famous counterexample).
- These all belong to one or more general families of solutions: the Weyl vacua (Hermann Weyl) (the family of all static vacuum solutions), the Beck vacua (Guido Beck 1925[2]) (the family of all cylindrically symmetric nonrotating vacuum solutions), the Ernst vacua (Frederick J.
- Gowdy) (cosmological models constructed using gravitational waves), Several of the families mentioned here, members of which are obtained by solving an appropriate linear or nonlinear, real or complex partial differential equation, turn out to be very closely related, in perhaps surprising ways.

In addition to these, we also have the vacuum pp-wave spacetimes, which include the gravitational plane waves.

Milne describing an empty universe which has no curvature) Schwarzschild vacuum (which describes the spacetime geometry around a spherical mass), Kerr vacuum (which describes the geometry around a rotating object), Taub–NUT vacuum (a famous counterexample describing the exterior gravitational field of an isolated object with strange properties), Kerns–Wild vacuum (Robert M.

Khan and Roger Penrose 1971) (a simple colliding plane wave model), Oszváth–Schücking vacuum (the circularly polarized sinusoidal gravitational wave, another famous counterexample).

These all belong to one or more general families of solutions: the Weyl vacua (Hermann Weyl) (the family of all static vacuum solutions), the Beck vacua (Guido Beck 1925[2]) (the family of all cylindrically symmetric nonrotating vacuum solutions), the Ernst vacua (Frederick J.

Gowdy) (cosmological models constructed using gravitational waves), Several of the families mentioned here, members of which are obtained by solving an appropriate linear or nonlinear, real or complex partial differential equation, turn out to be very closely related, in perhaps surprising ways.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- In the prologue, we saw how Einstein, through a thought experiment, showed that simultaneitymustfail.Inanotherelegantthoughtexperiment,Einsteinproposedaclock consisting of a pulse of light bouncing between two mirrors separated by distance L (figure1a).Hewas,afterall,apatentexaminerlivinginatimeoftechnologicalinnovations1 ofallsorts,includingever-betterchronometers.2Ms.Unprimehasoneofthesehigh-tech clockswithher.Foreachtick-tock,threeeventsoccur:A=lightleavesthelowermirror, B=lightbouncesoffthetopmirror,andC=lightarrivesbackatthelowermirror.
- III.2 Einstein’s Clock and Lorentz’s Transformation Alice said, “In our country, there’s only one day at a time.” To whichtheRedQueenresponds,“That’sapoorthinwayofdoing things.Nowhere,wemostlyhavedaysandnightstwoorthree atatime,andsometimesinthewinterwetakeasmanyasfive nightstogether—forwarmth,youknow.” —LewisCarroll Thepatentclerkinventsaclock So,howarewetomodifytheGalileantransformationlawssothatthespeedoflightcdoes notobeytheeverydayunderstandingofhowvelocitiesadd?Somehow,particlesofmatter (myfriendsandI,andthefly,inthestoryfromthepreviouschapter)andparticlesoflight (thecamera’sflash)donottallythepassageoftimeandspaceinthesameway.
- Usethefabulouslyastonishingequationc=c!
- LetuswritedowntheseparationbetweeneventsAandCinspaceandtime.Evidently, (cid:10)x=0,(cid:10)y=0,(cid:10)z=0,sincethepulseoflightgetsbacktowhereitstarted.Byconstruction,(cid:10)t =2L/c.
- (cid:5) (cid:5) Buthowdowedetermine(cid:10)x and(cid:10)t separately?

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

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

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

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- To Popper, who was an anti-justificationist, traditional philosophy is misled by the false principle of sufficient reason.
- Bartley III tried to radicalise this idea and made the controversial claim that not only can criticism go beyond empirical knowledge but that everything can be rationally criticised.
- Instead, theories should be tested and scrutinised.
- According to this view, rational discussion about metaphysical ideas, about moral values and even about purposes is possible.
- If they are not open to falsification they can not be scientific.

To Popper, who was an anti-justificationist, traditional philosophy is misled by the false principle of sufficient reason.

Bartley III tried to radicalise this idea and made the controversial claim that not only can criticism go beyond empirical knowledge but that everything can be rationally criticised.

Instead, theories should be tested and scrutinised.

According to this view, rational discussion about metaphysical ideas, about moral values and even about purposes is possible.

If they are not open to falsification they can not be scientific.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- False Memory Syndrome Foundation.
- theunlimitedyou.com/lessons/7-esp.php Etcoff, N.
- False Memory Syndrome Foundation Newsletter, 17(4), 6.
- Hypnotic investigation of psychodynamic processes.
- Sacramento, CA: Citadel Press.

False Memory Syndrome Foundation Newsletter, 17(4), 6.

Hypnotic investigation of psychodynamic processes.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- I think of the thousands of articles and books I’ve read in my lifetime.
- I think of the months I spent in that cleanroom trying to build something that was a pale imitation of this place.
- “What do you mean by ‘real’?” “Are we standing in a physical location?” “I think it’s a manifestation of the mind as it attempts to visually explain something our brains haven’t evolved to comprehend.” “Which is?” “Superposition.” “So we’re experiencing a quantum state right now?” I glance back down the corridor.
- At least for a moment, fear has left me.
- For students of physics and cosmology, the closest one can ever get to the tangible implications of research are ancient galaxies seen through telescopes.

I think of the thousands of articles and books I’ve read in my lifetime.

I think of the months I spent in that cleanroom trying to build something that was a pale imitation of this place.

“What do you mean by ‘real’?” “Are we standing in a physical location?” “I think it’s a manifestation of the mind as it attempts to visually explain something our brains haven’t evolved to comprehend.” “Which is?” “Superposition.” “So we’re experiencing a quantum state right now?” I glance back down the corridor.

At least for a moment, fear has left me.

For students of physics and cosmology, the closest one can ever get to the tangible implications of research are ancient galaxies seen through telescopes.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

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

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

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

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

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

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- In situations where either dimensionless parameter is large, then general relativity must be used to describe the system.
- Calculations using general relativity are in much closer agreement with the astronomical observations.
- General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.
- The predicted angular deflection of light rays by gravity (treated as particles travelling at the expected speed) that is calculated by using Newton's theory is only one-half of the deflection that is observed by astronomers.
- Observations conflicting with Newton's formula Newton's theory does not fully explain the precession of the perihelion of the orbits of the planets, especially that of Mercury, which was detected long after the life of Newton.[19] There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th century.

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

Calculations using general relativity are in much closer agreement with the astronomical observations.

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

The predicted angular deflection of light rays by gravity (treated as particles travelling at the expected speed) that is calculated by using Newton's theory is only one-half of the deflection that is observed by astronomers.

Observations conflicting with Newton's formula Newton's theory does not fully explain the precession of the perihelion of the orbits of the planets, especially that of Mercury, which was detected long after the life of Newton.[19] There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th century.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Newton's law of universal gravitation - Wikipedia.pdf


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

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

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

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

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

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

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Environmentdictatesmotion.Thecurvatureofspacetimetellstheappleandthestoneto followthesamepathfromthetopofthetowertotheground.Thecurvatureoftheearth tellsthepilotstofollowthesamepathfromLosAngelestoTaipei.
- Thisamazingrevelationabouttheroleofspacetimeoffersanelegantlysimpleexplanationoftheuniversalityofgravity.Gravitycurvesspacetime.That’sit.Spacetimeiscurved andgravity’sjobisdone.It’snowuptoeveryparticleintheuniversetofollowthebestpath inthiscurvedenvironment.Thisexplainswhygravityactsindiscriminatelyoneveryparticleinexactlythesameway.Nexttimeyoutakeanastyfall,whetherontheskislopeorinthe bathtub,justthink,everyparticleinyourbodyismerelytryingtogetthebestdealforitself.
- InsteadofthelinearGalileantransformation,wenowhavey=x− 1at2.Differentiating twice,weobtain d2y d2x = −a (1) dt2 dt2 Thus,theobserverintheacceleratedframeinsiststhatthereisaforce,givenbythemass moftheparticletimes d2x =a (2) dt2 Notethattheforceisproportionaltotheinertialmass.Simpleyetprofound!
- WarmupwiththesimplestexampleofafreelymovingNewtonianparticleinonespatial dimension obeying d2y =0.
- Thisisallfamiliarstuff,experiencedoftenindailylife.Ridinginaspeedingcar,weare thrownforwardwhenthedriversuddenlyslamsonthebrake.Beginningphysicsstudents learnthisasthe“effectofinertia.”Awetdogshakingitselfdryknowshowtoexploitthis effect.

InsteadofthelinearGalileantransformation,wenowhavey=x− 1at2.Differentiating twice,weobtain d2y d2x = −a (1) dt2 dt2 Thus,theobserverintheacceleratedframeinsiststhatthereisaforce,givenbythemass moftheparticletimes d2x =a (2) dt2 Notethattheforceisproportionaltotheinertialmass.Simpleyetprofound!

WarmupwiththesimplestexampleofafreelymovingNewtonianparticleinonespatial dimension obeying d2y =0.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- T Tentaclesconsistingofspacelikegeodesics Tocoordinatizethespacetimesurroundingγ,we,sittingatP,nowsendouttentacles4consistingofspacelike geodesicsζ(na,P)withnaaunitvector(thatis,avectorsatisfyingδ ab nanb=1),determiningthedirectionin whichaparticulargeodesicζ(na,P)emanatesfromP.Seefigure2.Inotherwords,thegeodesicζ(na,P)is characterizedbythepointPandthedirectionnainwhichitsalliesforthfromP.
- andthewallsofthelabtosetupthespacecoordinates.RightthereIhavethelocallyflatcoordinatesofmychoice.
- So,tocontinue,wearegiventhecoordinatesxμ,andwewanttofindtheFerminormalcoordinatesyμ= (y0,yi)≡(T,yi).Forconvenience,wegavey0thenicknameT.FocusonapointPonγ andassigntopointP thetimey0≡T =τ,thepropertimeτ elapsedsincepropertimestartedtickingatsomepointinthepast.See figure2.
- OnwardtoFerminormalcoordinates.Supposethat,afteraproperdistanceσ,thisparticulargeodesicζ(na,P) reachessomepointQ.ThenweassigntothepointQthecoordinates y0=T, yi=σnaδi (18) a
- AspectsofGravity γ P Q ζ(nb, P) ζ(na, P) Figure2 ConstructionofFerminormalcoordinatesthatarelocallyflat,notonlyatasinglepoint butalsoalonganentiregeodesic.

OnwardtoFerminormalcoordinates.Supposethat,afteraproperdistanceσ,thisparticulargeodesicζ(na,P) reachessomepointQ.ThenweassigntothepointQthecoordinates y0=T, yi=σnaδi (18) a

AspectsofGravity γ P Q ζ(nb, P) ζ(na, P) Figure2 ConstructionofFerminormalcoordinatesthatarelocallyflat,notonlyatasinglepoint butalsoalonganentiregeodesic.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions as its index set.
- When dealing carefully with classical fields at finite temperature, the mathematical methods of continuous random fields are used, because thermally fluctuating classical fields are nowhere differentiable.
- Continuous random fields Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable functions, but they are in any case almost always twice differentiable.
- One important example is mean field theory.
- If there is a symmetry of the problem, not involving spacetime, under which these components transform into each other, then this set of symmetries is called an internal symmetry.

Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions as its index set.

When dealing carefully with classical fields at finite temperature, the mathematical methods of continuous random fields are used, because thermally fluctuating classical fields are nowhere differentiable.

Continuous random fields Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable functions, but they are in any case almost always twice differentiable.

One important example is mean field theory.

If there is a symmetry of the problem, not involving spacetime, under which these components transform into each other, then this set of symmetries is called an internal symmetry.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- this decay process happening around us.[4] However, under this hypothesis there should be strange matter in the universe: 1.
- Quark stars (often called "strange stars") consist of quark matter from their core to their surface.
- They would be several kilometers across, and may have a very thin crust of nuclear matter.[2] 2.
- Strangelets are small pieces of strange matter, perhaps as small as nuclei.
- They would be produced when strange stars are formed or collide, or when a nucleus decays.[1] See also Exotic matter – Physics term for multiple concepts Quark star – Compact exotic star which forms matter consisting mostly of quarks Strangeness and quark–gluon plasma – subatomic signature Strangelet – Type of hypothetical particle Quark – Elementary particle, fundamental constituent of matter

this decay process happening around us.[4] However, under this hypothesis there should be strange matter in the universe: 1.

Quark stars (often called "strange stars") consist of quark matter from their core to their surface.

They would be several kilometers across, and may have a very thin crust of nuclear matter.[2] 2.

Strangelets are small pieces of strange matter, perhaps as small as nuclei.

They would be produced when strange stars are formed or collide, or when a nucleus decays.[1] See also Exotic matter – Physics term for multiple concepts Quark star – Compact exotic star which forms matter consisting mostly of quarks Strangeness and quark–gluon plasma – subatomic signature Strangelet – Type of hypothetical particle Quark – Elementary particle, fundamental constituent of matter

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- of the sun across the sky, the phases of the moon, and the passage of a free-swinging pendulum.
- More modern systems include the Global Positioning System, other satellite systems, Coordinated Universal Time and mean solar time.
- Although these systems differ from one another, with careful measurements they can be synchronized.
- In physics, time is a fundamental concept to define other quantities, such as velocity.
- To avoid a circular definition,[15] time in physics is operationally defined as "what a clock reads", specifically a count of repeating events such as the SI second.[6][16][17] Although this aids in practical

of the sun across the sky, the phases of the moon, and the passage of a free-swinging pendulum.

More modern systems include the Global Positioning System, other satellite systems, Coordinated Universal Time and mean solar time.

Although these systems differ from one another, with careful measurements they can be synchronized.

In physics, time is a fundamental concept to define other quantities, such as velocity.

To avoid a circular definition,[15] time in physics is operationally defined as "what a clock reads", specifically a count of repeating events such as the SI second.[6][16][17] Although this aids in practical

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- General relativity models gravity as How can the theory of curvature of spacetime: in the slogan of John Archibald Wheeler, quantum mechanics be "Spacetime tells matter how to move; matter tells spacetime how to merged with the theory curve."[16] On the other hand, quantum field theory is typically of general relativity / formulated in the flat spacetime used in special relativity.
- Overview Much of the difficulty in meshing these theories at all energy scales Unsolved problem in comes from the different assumptions that these theories make on physics how the universe works.
- What verifiable another quantum field, the resulting theory is not predictions does any renormalizable.[17] Even in the simpler case where the curvature of theory of quantum gravity make?
- If one attempts to treat gravity as simply scales?
- In the early 21st century, new experiment designs and technologies have arisen which suggest that indirect approaches to testing quantum gravity may be feasible over the next few decades.[12][13][14][15] This field of study is called phenomenological quantum gravity.

General relativity models gravity as How can the theory of curvature of spacetime: in the slogan of John Archibald Wheeler, quantum mechanics be "Spacetime tells matter how to move; matter tells spacetime how to merged with the theory curve."[16] On the other hand, quantum field theory is typically of general relativity / formulated in the flat spacetime used in special relativity.

Overview Much of the difficulty in meshing these theories at all energy scales Unsolved problem in comes from the different assumptions that these theories make on physics how the universe works.

What verifiable another quantum field, the resulting theory is not predictions does any renormalizable.[17] Even in the simpler case where the curvature of theory of quantum gravity make?

If one attempts to treat gravity as simply scales?

In the early 21st century, new experiment designs and technologies have arisen which suggest that indirect approaches to testing quantum gravity may be feasible over the next few decades.[12][13][14][15] This field of study is called phenomenological quantum gravity.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- and one up quark, and the proton is composed of two up quarks and one down quark.[29] A baryon is composed of three quarks, and a meson is composed of two quarks (one normal, one anti).
- Baryons and mesons are collectively called hadrons.
- Quarks inside hadrons are governed by the strong interaction, thus are subjected to quantum chromodynamics (color charges).
- The bounded quarks must have their color charge to be neutral, or "white" for analogy with mixing the primary colors.[30] More exotic hadrons can have other types, arrangement or number of quarks (tetraquark, pentaquark).[31] An atom is made from protons, neutrons and electrons.[32] By modifying the particles inside a normal atom, exotic atoms can be formed.[33] A simple example would be the hydrogen-4.1, which has one of its electrons replaced with a muon.[34]

and one up quark, and the proton is composed of two up quarks and one down quark.[29] A baryon is composed of three quarks, and a meson is composed of two quarks (one normal, one anti).

Baryons and mesons are collectively called hadrons.

Quarks inside hadrons are governed by the strong interaction, thus are subjected to quantum chromodynamics (color charges).

The bounded quarks must have their color charge to be neutral, or "white" for analogy with mixing the primary colors.[30] More exotic hadrons can have other types, arrangement or number of quarks (tetraquark, pentaquark).[31] An atom is made from protons, neutrons and electrons.[32] By modifying the particles inside a normal atom, exotic atoms can be formed.[33] A simple example would be the hydrogen-4.1, which has one of its electrons replaced with a muon.[34]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- (34.4c) 2 2 2 TherelativelysimplestructureoftheThomsonscatteringsourcefunctions(34.4),containingonlymonopole, dipole, and quadrupole contributions, stems from the simple structure (33.55) of the quantum mechanical amplitude squared ⟨|M|2⟩ for non-relativistic electron-photon scattering, which contains only monopole and quadrupole contributions.
- The dipole source S is a Doppler term from the motion of the photon-baryon fluid at velocity v .
- Theradiativetransfer equation(34.1)canbewritten (note that τ ̇ is negative) eikμη+τ d [ e−ikμη−τ(Θ+Ψ) ] =I−τ ̇S .
- 34.1.1 Visibility function Introduce the visibility function g(η) defined by g(η)≡−τ ̇e−τ .
- 34.1 Radiative transfer of CMB photons 901 source terms arising from Thomson scattering, Figure 35.1, a sum of monopole, dipole, and quadrupole harmonics, S(η,k,μ)≡Θ (η,k)+Ψ(η,k)−iμv (η,k)− 1Θ (η,k)P (μ) 0 b 2 2 2 ∑ = (−i)nS (η,k)P (μ) , (34.3) n n n=0 with harmonic coefficients S (η,k), n S ≡Θ +Ψ , (34.4a) 0 0 S ≡v , (34.4b) 1 b S ≡ 1Θ .

(34.4c) 2 2 2 TherelativelysimplestructureoftheThomsonscatteringsourcefunctions(34.4),containingonlymonopole, dipole, and quadrupole contributions, stems from the simple structure (33.55) of the quantum mechanical amplitude squared ⟨|M|2⟩ for non-relativistic electron-photon scattering, which contains only monopole and quadrupole contributions.

The dipole source S is a Doppler term from the motion of the photon-baryon fluid at velocity v .

Theradiativetransfer equation(34.1)canbewritten (note that τ ̇ is negative) eikμη+τ d [ e−ikμη−τ(Θ+Ψ) ] =I−τ ̇S .

34.1.1 Visibility function Introduce the visibility function g(η) defined by g(η)≡−τ ̇e−τ .

34.1 Radiative transfer of CMB photons 901 source terms arising from Thomson scattering, Figure 35.1, a sum of monopole, dipole, and quadrupole harmonics, S(η,k,μ)≡Θ (η,k)+Ψ(η,k)−iμv (η,k)− 1Θ (η,k)P (μ) 0 b 2 2 2 ∑ = (−i)nS (η,k)P (μ) , (34.3) n n n=0 with harmonic coefficients S (η,k), n S ≡Θ +Ψ , (34.4a) 0 0 S ≡v , (34.4b) 1 b S ≡ 1Θ .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- The scare with the cab has flattened my buzz, and I browse the freezer cases in something of a fog, lethargic and sleepy.
- Without thinking, I step into the street against a crosswalk signal and instantly register the sound of tires locking up, of rubber squealing across pavement.
- The occupants of three separate cars are kind enough to slow down so they can flip me off.
- Pull your head out of your ass!” Horns begin to blare behind the cab.
- And then my hands are flat against the warm, yellow metal of the hood and the cabbie is leaning out his window, screaming at me, “You dipshit, you almost died!

The scare with the cab has flattened my buzz, and I browse the freezer cases in something of a fog, lethargic and sleepy.

Without thinking, I step into the street against a crosswalk signal and instantly register the sound of tires locking up, of rubber squealing across pavement.

The occupants of three separate cars are kind enough to slow down so they can flip me off.

Pull your head out of your ass!” Horns begin to blare behind the cab.

And then my hands are flat against the warm, yellow metal of the hood and the cabbie is leaning out his window, screaming at me, “You dipshit, you almost died!

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- For writers on kinematics before Galileo, since small time intervals could not be measured, the affinity between time and motion was obscure.
- At Oxford, Merton College sheltered a group of scholars devoted to natural science, mainly physics, astronomy and mathematics, who were of similar stature to the intellectuals at the University of Paris.
- The initial conditions are given by the constant values at t = 0, The solution r(t) to the equation of motion, with specified initial values, describes the system for all times t after t = 0.
- Other dynamical variables like the momentum p of the object, or quantities derived from r and p like angular momentum, can be used in place of r as the quantity to solve for from some equation of motion, although the position of the object at time t is by far the most sought-after quantity.
- But they had nothing other than a set of algorithms to guide them.

For writers on kinematics before Galileo, since small time intervals could not be measured, the affinity between time and motion was obscure.

At Oxford, Merton College sheltered a group of scholars devoted to natural science, mainly physics, astronomy and mathematics, who were of similar stature to the intellectuals at the University of Paris.

The initial conditions are given by the constant values at t = 0, The solution r(t) to the equation of motion, with specified initial values, describes the system for all times t after t = 0.

Other dynamical variables like the momentum p of the object, or quantities derived from r and p like angular momentum, can be used in place of r as the quantity to solve for from some equation of motion, although the position of the object at time t is by far the most sought-after quantity.

But they had nothing other than a set of algorithms to guide them.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- The basic rules of probability amplitudes that will be used are:[2]: 93 a.
- What (a) says is that once the physical means for observing which alternative occurred is removed, one cannot still say that the event is occurring through "exactly one of the alternatives" in the sense of adding probabilities; one must add the amplitudes instead.[2]: 82 Similarly, the independence criterion in (b) is very important: it only applies to processes which are not "entangled".
- probability amplitudes mentioned above (P(A to B), E(C to D) and j) acts just like our everyday probability (a simplification made in Feynman's book).
- A typical question from a physical standpoint is: "What is the probability of finding an electron at C (another place and a later time) and a photon at D (yet another place and time)?".
- by introducing a new apparatus into the system).

The basic rules of probability amplitudes that will be used are:[2]: 93 a.

What (a) says is that once the physical means for observing which alternative occurred is removed, one cannot still say that the event is occurring through "exactly one of the alternatives" in the sense of adding probabilities; one must add the amplitudes instead.[2]: 82 Similarly, the independence criterion in (b) is very important: it only applies to processes which are not "entangled".

probability amplitudes mentioned above (P(A to B), E(C to D) and j) acts just like our everyday probability (a simplification made in Feynman's book).

A typical question from a physical standpoint is: "What is the probability of finding an electron at C (another place and a later time) and a photon at D (yet another place and time)?".

by introducing a new apparatus into the system).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- TensorsinGeneralRelativity | 317 lefthandsideatensor.ThequotienttheoremstatesthatgiventwotensorsP andW and Pσ =QωκWσ , we can conclude that Q is a tensor.
- We simply mentally replace η by the unitmatrixand(cid:27)byR.TherestrictiononRdefinestherotationgroup.
- Lorentztransformation,changeofcoordinates,curvedspace, andcurvedspacetime:Notquitethesamedeal Ikeepemphasizingthatoneunifiedformalismcanbeusedtodiscussrotation,Lorentz transformation,changeofcoordinates,curvedspace,andcurvedspacetime.Butitisalso important to understand the crucial differences among them.
- Pythagoras, is left unchanged by a group of linear transformations, Lorentz transformationsinonecase,androtationsintheother.
- Let us summarize and contrast.

TensorsinGeneralRelativity | 317 lefthandsideatensor.ThequotienttheoremstatesthatgiventwotensorsP andW and Pσ =QωκWσ , we can conclude that Q is a tensor.

We simply mentally replace η by the unitmatrixand(cid:27)byR.TherestrictiononRdefinestherotationgroup.

Lorentztransformation,changeofcoordinates,curvedspace, andcurvedspacetime:Notquitethesamedeal Ikeepemphasizingthatoneunifiedformalismcanbeusedtodiscussrotation,Lorentz transformation,changeofcoordinates,curvedspace,andcurvedspacetime.Butitisalso important to understand the crucial differences among them.

Pythagoras, is left unchanged by a group of linear transformations, Lorentz transformationsinonecase,androtationsintheother.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- If they find thin wisps of gas in the skies that seem to form part of a shell, they suspect that at one time, in the center of that shell, a supernova had exploded.
- There we have a large patch of glowing gas.
- (That rate of outward movement, so much greater than in the case of a planetary nebula, is itself evidence of the incomparable power of the supernova explosion.) Calculating backwards, it seems that all the gas was back at the center just about the time of the 1054 supernova.
- 136 THE COLLAPSING UNIVERSE What's more, shells of gas are blown off by a supernova, shells that dwarf those produced by planetary nebula in terms of both mass and energy.
- In 1844 the Irish astronomer William Parsons, Lord Rosse (1800-1867), examined it closely with a large telescope he had built and observed that the cloud is filled with irregular filaments that reminded him of the legs of a crab.

If they find thin wisps of gas in the skies that seem to form part of a shell, they suspect that at one time, in the center of that shell, a supernova had exploded.

There we have a large patch of glowing gas.

(That rate of outward movement, so much greater than in the case of a planetary nebula, is itself evidence of the incomparable power of the supernova explosion.) Calculating backwards, it seems that all the gas was back at the center just about the time of the 1054 supernova.

136 THE COLLAPSING UNIVERSE What's more, shells of gas are blown off by a supernova, shells that dwarf those produced by planetary nebula in terms of both mass and energy.

In 1844 the Irish astronomer William Parsons, Lord Rosse (1800-1867), examined it closely with a large telescope he had built and observed that the cloud is filled with irregular filaments that reminded him of the legs of a crab.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- "Fundamental limitations on 'warp drive' spacetimes".
- de/xmlui/bitstream/handle/10900/48159/pdf/09warp.html) Marcelo B.
- S2CID 119010055 (https://api.semanticscholar.org/CorpusID:119010055).
- González-Díaz, Pedro (14 July 2000).
- org/10.1016%2FS0370-2693%2897%2901226-4).

"Fundamental limitations on 'warp drive' spacetimes".

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Triangles A geodesic triangle is formed by the geodesics joining each A geodesic on a triaxial ellipsoid.
- way than on a sphere; in particular, they are not closed in general (see figure).
- On the sphere, the geodesics are great circle arcs, forming a spherical triangle.
- Metric geometry In metric geometry, a geodesic is a curve which is everywhere locally a distance minimizer.
- More precisely, a curve γ : I → M from an interval I of the reals to the metric space M is a geodesic if there is a constant v ≥ 0 such that for any t ∈ I there is a neighborhood J of t in I such that for any t , t ∈ J 1 2

Triangles A geodesic triangle is formed by the geodesics joining each A geodesic on a triaxial ellipsoid.

way than on a sphere; in particular, they are not closed in general (see figure).

On the sphere, the geodesics are great circle arcs, forming a spherical triangle.

Metric geometry In metric geometry, a geodesic is a curve which is everywhere locally a distance minimizer.

More precisely, a curve γ : I → M from an interval I of the reals to the metric space M is a geodesic if there is a constant v ≥ 0 such that for any t ∈ I there is a neighborhood J of t in I such that for any t , t ∈ J 1 2

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Noting the form of X0 and X4, we realize that it would be wise to go to light cone coordinatesX ±=X0±X4.Inparticular,X +=X0+X4=Let,anequationthatdescribes
- DeSitterSpacetime | 631 / (cid:12) (cid:14)0 / (cid:12) (cid:14)0 ds2=L2 −dt2+e2t dr2+r2d(cid:24)2 =L2 −dt2+e2t dx2+dy2+dz2 (23) Remarkably, this is precisely the expanding universe that we discussed in chapters VI.2 and VIII.1, and in which we may be living.
- When we descend to a specific description tied to a particular coordinate choice,theseisometriesarestillthere,thoughhardertosee.Themetricin(23)provides a good example.
- It depends explicitly on time and so is definitely not invariant under timetranslation;however,itisinvariantundert →t +εaccompaniedbyxi→xi−εxi: e2tdx(cid:3)2→e2ε(1−ε)2e2tdx(cid:3)2(cid:16)e2tdx(cid:3)2+O(ε2).Inotherwords,wehaveaKillingvectorξμ= (1,−xi).Thisamountstoafancymathematicalwayofsayingthattheuniverseexpands exponentially!TheKillingvectortellsusthatthepassageoftimecanbecompensatedfor byshrinkingthespatialcoordinates.
- Isometriesandlightconecoordinates We started out in the embedding space Md,1 with a manifold endowed with plenty of isometries.

Noting the form of X0 and X4, we realize that it would be wise to go to light cone coordinatesX ±=X0±X4.Inparticular,X +=X0+X4=Let,anequationthatdescribes

DeSitterSpacetime | 631 / (cid:12) (cid:14)0 / (cid:12) (cid:14)0 ds2=L2 −dt2+e2t dr2+r2d(cid:24)2 =L2 −dt2+e2t dx2+dy2+dz2 (23) Remarkably, this is precisely the expanding universe that we discussed in chapters VI.2 and VIII.1, and in which we may be living.

When we descend to a specific description tied to a particular coordinate choice,theseisometriesarestillthere,thoughhardertosee.Themetricin(23)provides a good example.

It depends explicitly on time and so is definitely not invariant under timetranslation;however,itisinvariantundert →t +εaccompaniedbyxi→xi−εxi: e2tdx(cid:3)2→e2ε(1−ε)2e2tdx(cid:3)2(cid:16)e2tdx(cid:3)2+O(ε2).Inotherwords,wehaveaKillingvectorξμ= (1,−xi).Thisamountstoafancymathematicalwayofsayingthattheuniverseexpands exponentially!TheKillingvectortellsusthatthepassageoftimecanbecompensatedfor byshrinkingthespatialcoordinates.

Isometriesandlightconecoordinates We started out in the embedding space Md,1 with a manifold endowed with plenty of isometries.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- states that “It’s been my experience that only opposites attract because that’s the nature of reality” (the italics are Hendrix’s, not ours, by the way).
- “The great myth in our culture,” he later says, “is that compatibility is the grounds for a relationship—actually, compatibility is grounds for boredom.” Another Internet site, called “Dating Tipster,” informs visitors that “The saying ‘opposites attract’ is definitely true in some instances.
- Perhaps it’s the | 136 Chapter 7 The Social Animal

states that “It’s been my experience that only opposites attract because that’s the nature of reality” (the italics are Hendrix’s, not ours, by the way).

“The great myth in our culture,” he later says, “is that compatibility is the grounds for a relationship—actually, compatibility is grounds for boredom.” Another Internet site, called “Dating Tipster,” informs visitors that “The saying ‘opposites attract’ is definitely true in some instances.

Perhaps it’s the | 136 Chapter 7 The Social Animal

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- the Planck relation: , where is the Planck constant.
- The stationary orbits are obtained by the condition that the ratio of the total energy emitted in forming the state and the frequency of the electron rotation about the positive nucleus is an integer multiple of .
- In atomic state corresponding to the maximum emitted energy, the stationary orbits are attained at distances for which the angular momentum of the revolving electron is equal to the reduced Planck constant, .
- The first two postulates formulate the experimental observations that absorption and emission of radiation for hydrogen do not obey the rules known at the time.
- The third postulate restates Planck's quantum theory of radiation which was already widely accepted by 1913.

the Planck relation: , where is the Planck constant.

The stationary orbits are obtained by the condition that the ratio of the total energy emitted in forming the state and the frequency of the electron rotation about the positive nucleus is an integer multiple of .

In atomic state corresponding to the maximum emitted energy, the stationary orbits are attained at distances for which the angular momentum of the revolving electron is equal to the reduced Planck constant, .

The first two postulates formulate the experimental observations that absorption and emission of radiation for hydrogen do not obey the rules known at the time.

The third postulate restates Planck's quantum theory of radiation which was already widely accepted by 1913.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- "Paul Adrien Maurice Dirac" (https://pages.hep.wisc.edu/~ldurand/715html/courseinfo/biographies/ dirac.html).
- University of Wisconsin-Madison.
- Representations (72): 145–166.
- ISSN 0734-6018 (https://search.worldcat.org/issn/0734-6018).
- 1851 Royal Commission Archives 49.

"Paul Adrien Maurice Dirac" (https://pages.hep.wisc.edu/~ldurand/715html/courseinfo/biographies/ dirac.html).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- "Aberración y Relatividad" (https://archive.org/details/Loedel1948Aberraci onYRelatividad) [Aberration and Relativity].
- The Original Usenet Physics FAQ.
- Taylor, Edwin F.; Wheeler, John Archibald (2003).
- Special relativity, a geometric approach: course with exercises and answers followed by the conference "Interstellar travel and antimatter" (http://www.voyagepourpro xima.fr/SR.pdf) (PDF).
- "Can Special Relativity Handle Acceleration?" (https://math.ucr.edu/home/baez/phys ics/Relativity/SR/acceleration.html).

"Aberración y Relatividad" (https://archive.org/details/Loedel1948Aberraci onYRelatividad) [Aberration and Relativity].

Taylor, Edwin F.; Wheeler, John Archibald (2003).

Special relativity, a geometric approach: course with exercises and answers followed by the conference "Interstellar travel and antimatter" (http://www.voyagepourpro xima.fr/SR.pdf) (PDF).

"Can Special Relativity Handle Acceleration?" (https://math.ucr.edu/home/baez/phys ics/Relativity/SR/acceleration.html).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Both sets of three frames were purposely aligned to make direct comparison easier.
- The field would be turned on and the craft would zip off to its stellar destination, never locally breaking the speed of light, but covering the distance in an arbitrarily short time period of time just the same.
- This approach would allow a journey to say Alpha Centauri as measured by an earth bound observer (and spacecraft clocks) measured in weeks or months, rather than decades or centuries.
- earth) using some conventional propulsion system and travel a distance d, then bring the craft to a stop relative to the departure point.
- Comparing Figure 1 to Figure 2 visually displays the asymmetry of the York Time and the symmetry of the energy density.

Both sets of three frames were purposely aligned to make direct comparison easier.

The field would be turned on and the craft would zip off to its stellar destination, never locally breaking the speed of light, but covering the distance in an arbitrarily short time period of time just the same.

This approach would allow a journey to say Alpha Centauri as measured by an earth bound observer (and spacecraft clocks) measured in weeks or months, rather than decades or centuries.

earth) using some conventional propulsion system and travel a distance d, then bring the craft to a stop relative to the departure point.

Comparing Figure 1 to Figure 2 visually displays the asymmetry of the York Time and the symmetry of the energy density.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Thus, we assume that there is an entropy flux, an entropy source, an internal mass density and an internal specific entropy (i.e.
- This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved.
- Let move with a flow velocity and let particles inside have velocities .
- Then the second law of thermodynamics states that the rate of increase of in this region is greater than or equal to the sum of that supplied to (as a flux or from internal sources) and the change of the internal entropy density due to material flowing in and out of the region.
- entropy per unit mass) in the region of interest.

Thus, we assume that there is an entropy flux, an entropy source, an internal mass density and an internal specific entropy (i.e.

This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved.

Let move with a flow velocity and let particles inside have velocities .

Then the second law of thermodynamics states that the rate of increase of in this region is greater than or equal to the sum of that supplied to (as a flux or from internal sources) and the change of the internal entropy density due to material flowing in and out of the region.

entropy per unit mass) in the region of interest.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Onedifficultyconfrontinginflationarytheoriesisknownasthegracefulexitproblem: howdoyouendinflationonceyouhavehadyourfillofthe70e-foldings?Anotherpuzzleis whytheeffectivecosmologicalconstantwasoncelarge(soastodominatethecontribution oftherelativisticmatter,namelyradiationinthegeneralizedsense,totheenergydensity) ∗ butisnowsoincrediblysmall.
- Notsurprisingly,thishasgeneratedinthetheoryliteratureamultitudeofscenariosthat goundersuchnamesasoldinflation,newinflation,chaoticinflation,eternalinflation,and stochasticinflation.Inventyourown!Inchaoticinflation,onedoesnotneedtofine-tune thepotentialV(φ);insteadtheuniverseisvastandinhomogeneous,withV(φ)takingon ∗WewillreturntothecosmologicalconstantinchapterX.7.
- Amusingly,Einstein’sintroductionofthecosmologicalconstant,farfromablunderas theuninformedcalledit,turnsouttobeessentialforcosmology,bothobservationallyand theoretically.
- Sinceweknowalmostnothingabouttheoriginofthisscalarfield,calledratherunimaginativelytheinflaton,andthephysicsthatgoeswithit,peoplefeelfreetodrawwhatever V(φ)wouldproduceadesiredoutcome, forexample, the“slowroll”potentialshownin figure2.Inthispictorialanalogy,theinflatonφ issupposedtostartoutonthenearlyflat plateauandslowlyrolldownhill(seetheappendix),endingupinaminimumthatismany ordersofmagnitudesmaller.
- IntroductiontoOurUniverse Aninflationaryuniverse Thattheuniversewentthroughsomesortofinflationaryepochduringwhichitexpanded exponentiallyseemsquitecompelling,butthespecificsofanyoftheproposedmechanisms shouldprobablybetakenwithagrainofsaltandasmile.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- dx dx For pedagogical clarity, we consider t(cid:6)he ca (cid:29) se w (cid:30) here d d φ x (cid:18) (cid:29) 1, (cid:30) that is, when the string is stretched only by a little bit, so that 1+ dφ 2(cid:16)1+ 1 dφ 2 .
- Buthowdowedifferentiatewithrespecttoafunction?
- (It turns out that this dx 2 dx simplificationisnotnecessary,andyoucanworkthingsoutwithoutit.Seeexercise1.) (cid:8) The gravitational energy is given by dx(−σgφ(x)), where σ denotes the mass per unitlengthofourstring.Notetheminussign:wehavechosenφ(x)topointdownward, asindicatedinthefigure.Again,wehaveassumedthatthestretchissmall.
- Forpedagogicalclarity,letusgobacktothemarbleinthebowlandwriteδv= ∂vδx+ ∂x ∂vδy tofirstorderinδx andδy,somearbitraryandsmallvariationsinthepositionofthe ∂y marble.Wenoticethatδv vanishesifandonlyif ∂v =0and ∂v =0.Tofirstorderinδx ∂x ∂y andδy,thevariationofv vanishesifwehappentobesittingatanextremum.Tosecond
- Ourtaskistofindthespecificfunctionφ(x)thatminimizestheenergyEofthestring.

dx dx For pedagogical clarity, we consider t(cid:6)he ca (cid:29) se w (cid:30) here d d φ x (cid:18) (cid:29) 1, (cid:30) that is, when the string is stretched only by a little bit, so that 1+ dφ 2(cid:16)1+ 1 dφ 2 .

(It turns out that this dx 2 dx simplificationisnotnecessary,andyoucanworkthingsoutwithoutit.Seeexercise1.) (cid:8) The gravitational energy is given by dx(−σgφ(x)), where σ denotes the mass per unitlengthofourstring.Notetheminussign:wehavechosenφ(x)topointdownward, asindicatedinthefigure.Again,wehaveassumedthatthestretchissmall.

Forpedagogicalclarity,letusgobacktothemarbleinthebowlandwriteδv= ∂vδx+ ∂x ∂vδy tofirstorderinδx andδy,somearbitraryandsmallvariationsinthepositionofthe ∂y marble.Wenoticethatδv vanishesifandonlyif ∂v =0and ∂v =0.Tofirstorderinδx ∂x ∂y andδy,thevariationofv vanishesifwehappentobesittingatanextremum.Tosecond

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Conservation of entropy per comoving volume implies that the photon temperature T at redshift z is related to the present day photon temperature T by (Exercise 10.19) T ( g )1/3 =(1+z) s,0 , (10.104) T g 0 s where g is the entropy-weighted effective number of relativistic particle species.
- Neutrino oscillation data indicate that at least 2 of the 3 neutrino types have masses that would make
- ratio η ≡n /n of baryon to photon number in the Universe today is less than a billionth, b b γ n ε Ω Ω h2 ( T )−3 η ≡ b = γ b =6.1×10−10 b 0 , (10.103) b n m Ω 0.0224 2.725K γ b γ where ε = π4T /(30ζ(3)) = 2.701T is the mean energy per photon (Exercise 10.15), and m = 939MeV γ 0 0 b is the approximate mass per baryon.
- The value is as reported by the Planck team (Aghanim et al., 2018).
- Neutrinos decoupled at a temperature of about T ≈1MeV.

Conservation of entropy per comoving volume implies that the photon temperature T at redshift z is related to the present day photon temperature T by (Exercise 10.19) T ( g )1/3 =(1+z) s,0 , (10.104) T g 0 s where g is the entropy-weighted effective number of relativistic particle species.

Neutrino oscillation data indicate that at least 2 of the 3 neutrino types have masses that would make

ratio η ≡n /n of baryon to photon number in the Universe today is less than a billionth, b b γ n ε Ω Ω h2 ( T )−3 η ≡ b = γ b =6.1×10−10 b 0 , (10.103) b n m Ω 0.0224 2.725K γ b γ where ε = π4T /(30ζ(3)) = 2.701T is the mean energy per photon (Exercise 10.15), and m = 939MeV γ 0 0 b is the approximate mass per baryon.

The value is as reported by the Planck team (Aghanim et al., 2018).

Neutrinos decoupled at a temperature of about T ≈1MeV.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- This is Daniela with an energy like the first time we met fifteen years ago, before years of life—the normalcy, the elation, the depression, the compromise—transformed her into the woman who now shares my bed: amazing mother, amazing wife, but fighting always against the whispers of what might have been.
- “—just the most amazing night, and I’m so grateful to all of you for coming out to support my new project.
- “¡Salud!” The crowd responds in turn, and as everyone drinks, I move toward her.
- It means the world.” Daniela raises her wineglass.
- My Daniela carries a weight and a distance in her eyes that scare me sometimes.

This is Daniela with an energy like the first time we met fifteen years ago, before years of life—the normalcy, the elation, the depression, the compromise—transformed her into the woman who now shares my bed: amazing mother, amazing wife, but fighting always against the whispers of what might have been.

“—just the most amazing night, and I’m so grateful to all of you for coming out to support my new project.

“¡Salud!” The crowd responds in turn, and as everyone drinks, I move toward her.

It means the world.” Daniela raises her wineglass.

My Daniela carries a weight and a distance in her eyes that scare me sometimes.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- frame of an observer moving at v = 0.
- From this reference frame, event C is observed to occur after event O, and event B is observed to occur before event O.[36] From a different reference frame, the orderings of these nonFigure 2–6.
- Animation illustrating relativity causally-related events can be reversed.
- In particular, one of simultaneity notes that if two events are simultaneous in a particular reference frame, they are necessarily separated by a spacelike interval and thus are noncausally related.
- The observation that simultaneity is not absolute, but depends on the observer's reference frame, is termed the relativity of simultaneity.[36]

From this reference frame, event C is observed to occur after event O, and event B is observed to occur before event O.[36] From a different reference frame, the orderings of these nonFigure 2–6.

Animation illustrating relativity causally-related events can be reversed.

In particular, one of simultaneity notes that if two events are simultaneous in a particular reference frame, they are necessarily separated by a spacelike interval and thus are noncausally related.

The observation that simultaneity is not absolute, but depends on the observer's reference frame, is termed the relativity of simultaneity.[36]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- give a variation of the paradox of an electronic circuit that sends a signal through a time machine to shut itself off, and receives the signal before it sends it.[19][20]
- A billiard ball delivers its past did not happen.[5] Another proposed resolution is simply that self a strike that prevents it from entering the time machine that caused it to strike time travel is impossible.[14] its past self, putting into question how its older self could ever emerge from the Variants time machine and divert its course.[2] The grandfather paradox encompasses any change to the past,[15] and it is presented in many variations, including killing one's past self.[16][1] Both the "retrosuicide paradox" and the "grandfather paradox" appeared in letters written into Amazing Stories in the 1920s.[17] Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", in which the protagonist travels back in time to murder Adolf Hitler before he can rise to power in Germany, thus preventing World War II and the Holocaust.
- Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed.[18] Physicist John Garrison et al.
- If the traveler were not born, they could not kill their grandfather; therefore, the grandfather proceeds to beget the traveler's parent who begets the traveler.
- This scenario is self-contradictory.[5] One proposed resolution for this paradox is that a time traveller A consistency paradox or "grandfather can do anything that did happen, but cannot do anything that paradox".

give a variation of the paradox of an electronic circuit that sends a signal through a time machine to shut itself off, and receives the signal before it sends it.[19][20]

A billiard ball delivers its past did not happen.[5] Another proposed resolution is simply that self a strike that prevents it from entering the time machine that caused it to strike time travel is impossible.[14] its past self, putting into question how its older self could ever emerge from the Variants time machine and divert its course.[2] The grandfather paradox encompasses any change to the past,[15] and it is presented in many variations, including killing one's past self.[16][1] Both the "retrosuicide paradox" and the "grandfather paradox" appeared in letters written into Amazing Stories in the 1920s.[17] Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", in which the protagonist travels back in time to murder Adolf Hitler before he can rise to power in Germany, thus preventing World War II and the Holocaust.

Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed.[18] Physicist John Garrison et al.

If the traveler were not born, they could not kill their grandfather; therefore, the grandfather proceeds to beget the traveler's parent who begets the traveler.

This scenario is self-contradictory.[5] One proposed resolution for this paradox is that a time traveller A consistency paradox or "grandfather can do anything that did happen, but cannot do anything that paradox".

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- “If we just kept walking, where would we end up?” As I say the words, the wonder recedes and the horror creeps in: “There is no end.” — We keep walking to see what happens, if anything will change, if we will change.
- Each box repetition is twelve feet, which means we’ve already gone a full mile.” Amanda stops and lets the backpack slide off her shoulders.
- She sits against the wall, and I take a seat beside her, with the lantern between us.
- But it’s just door after door after door after door.
- In some presentations of quantum mechanics, the thing that contains all the information for the system—before it collapses due to an observation—is called a wave function.

“If we just kept walking, where would we end up?” As I say the words, the wonder recedes and the horror creeps in: “There is no end.” — We keep walking to see what happens, if anything will change, if we will change.

Each box repetition is twelve feet, which means we’ve already gone a full mile.” Amanda stops and lets the backpack slide off her shoulders.

She sits against the wall, and I take a seat beside her, with the lantern between us.

But it’s just door after door after door after door.

In some presentations of quantum mechanics, the thing that contains all the information for the system—before it collapses due to an observation—is called a wave function.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- (16.311b) Theexteriortimederivativehereisthe1-formd ≡dt∂/∂t.Theequationsofmotion(16.311)areproblematic t not only because they remain unbalanced despite the 3+1 split, but also because the time derivative is not d but rather e ∧d .
- The energy-momentum T on the right α ̄
- =8πΣ ** t ̄, (16.311a) 12 equations of motion: e α ̄ ∧ ( d t Γ α ̄ +d α Γ t ̄+ 1 [Γ α ̄ ,Γ t ̄] ) +e t ̄∧R α ̄ =8πT ** t ̄.
- The spin angular-momentum Σ on the right hand side of the Gaussian conα ̄ ** straint equation (16.310a) satisfies the conservation law (16.281).
- Thus the Gaussian and Hamiltonian constraint equations (16.310) can be interpreted as representing ** conserved Noether charges.

(16.311b) Theexteriortimederivativehereisthe1-formd ≡dt∂/∂t.Theequationsofmotion(16.311)areproblematic t not only because they remain unbalanced despite the 3+1 split, but also because the time derivative is not d but rather e ∧d .

=8πΣ ** t ̄, (16.311a) 12 equations of motion: e α ̄ ∧ ( d t Γ α ̄ +d α Γ t ̄+ 1 [Γ α ̄ ,Γ t ̄] ) +e t ̄∧R α ̄ =8πT ** t ̄.

The spin angular-momentum Σ on the right hand side of the Gaussian conα ̄ ** straint equation (16.310a) satisfies the conservation law (16.281).

Thus the Gaussian and Hamiltonian constraint equations (16.310) can be interpreted as representing ** conserved Noether charges.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- How, then, could The principle of invariant light speed – "...
- The term reference frame as used here is an observational perspective in space that is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes (so, at rest or constant velocity).
- The constancy of the speed of light was motivated by Maxwell's theory of electromagnetism [20] and the lack of evidence for the luminiferous ether.[21] There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment.[22][23] In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.
- The derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions, including the isotropy and homogeneity of space and the independence of measuring rods and clocks from their past history.[p 3] Principle of relativity Reference frames and relative motion Reference frames play a crucial role in relativity theory.
- physical laws (especially the constancy of the speed of (except in limiting cases) claim exact light) from the choice of inertial system.

How, then, could The principle of invariant light speed – "...

The term reference frame as used here is an observational perspective in space that is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes (so, at rest or constant velocity).

The constancy of the speed of light was motivated by Maxwell's theory of electromagnetism [20] and the lack of evidence for the luminiferous ether.[21] There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment.[22][23] In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.

The derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions, including the isotropy and homogeneity of space and the independence of measuring rods and clocks from their past history.[p 3] Principle of relativity Reference frames and relative motion Reference frames play a crucial role in relativity theory.

physical laws (especially the constancy of the speed of (except in limiting cases) claim exact light) from the choice of inertial system.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- 42nd Joint Propulsion Conference and Exhibit.
- Mills, Marc G.; Thomas, Nicholas E.
- The Alcubierre drive is a hypothetical method of apparent faster-than-light propulsion for interstellar travel postulated from the theory of general relativity.
- "Detesters, Phasers and Dean Drives".
- 384 (https://archive.org/details/secretsofantigra00lavi/page/384).

42nd Joint Propulsion Conference and Exhibit.

The Alcubierre drive is a hypothetical method of apparent faster-than-light propulsion for interstellar travel postulated from the theory of general relativity.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- In an 1865 paper, one light-year 1.0 year James Clerk Maxwell proposed that light was an one parsec 3.26 years electromagnetic wave and, therefore, travelled at speed c.[7] Albert Einstein postulated that the from the nearest star to Sun (1.3 pc) 4.2 years speed of light c with respect to any inertial frame from the nearest galaxy to Earth 70000 years of reference is a constant and is independent of across the Milky Way 87400
- The speed of light can be used in time of flight one metre 3.3 ns measurements to measure large distances to from geostationary orbit to Earth 119 ms extremely high precision.
- It is the upper limit for the speed Due to its finite speed, sunlight takes 8 minutes and at which information, matter, or energy can 10 to 27 seconds to reach Earth, depending on the travel through space.[4][5][6] time of year.[1] Exact value All forms of electromagnetic radiation, including metres per second 299792458[2] visible light, travel in vacuum at the speed c.
- It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄ 299792458 second.
- In computing, the speed of light fixes one foot 1.0 ns the ultimate minimum communication delay.

In an 1865 paper, one light-year 1.0 year James Clerk Maxwell proposed that light was an one parsec 3.26 years electromagnetic wave and, therefore, travelled at speed c.[7] Albert Einstein postulated that the from the nearest star to Sun (1.3 pc) 4.2 years speed of light c with respect to any inertial frame from the nearest galaxy to Earth 70000 years of reference is a constant and is independent of across the Milky Way 87400

The speed of light can be used in time of flight one metre 3.3 ns measurements to measure large distances to from geostationary orbit to Earth 119 ms extremely high precision.

It is the upper limit for the speed Due to its finite speed, sunlight takes 8 minutes and at which information, matter, or energy can 10 to 27 seconds to reach Earth, depending on the travel through space.[4][5][6] time of year.[1] Exact value All forms of electromagnetic radiation, including metres per second 299792458[2] visible light, travel in vacuum at the speed c.

It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄ 299792458 second.

In computing, the speed of light fixes one foot 1.0 ns the ultimate minimum communication delay.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- sky mixes scalar, vector, and tensor modes with the same l (this is the sum over m in equation (36.31)).
- Vector modes are expected to be overwhelmed by scalar modes in the unpolarized and E-mode polarized CMB, and by tensor modes in the B-mode polarized CMB.
- The reason for the dominance of scalar and tensor over vector modes is that whereas scalar and tensor gravitational potentials remain approximately constant for modes outside the horizon, the vector gravitational potentials W tend to redshift to zero as the Universe expands, equation (29.51).
- Thus vector ± perturbations are usually negligible in standard cosmological models, §35.11.

sky mixes scalar, vector, and tensor modes with the same l (this is the sum over m in equation (36.31)).

Vector modes are expected to be overwhelmed by scalar modes in the unpolarized and E-mode polarized CMB, and by tensor modes in the B-mode polarized CMB.

The reason for the dominance of scalar and tensor over vector modes is that whereas scalar and tensor gravitational potentials remain approximately constant for modes outside the horizon, the vector gravitational potentials W tend to redshift to zero as the Universe expands, equation (29.51).

Thus vector ± perturbations are usually negligible in standard cosmological models, §35.11.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Denote their trajectories by x(cid:3)(t)
- | 57 5 → 2 + 2 + 1 Figure 2 Under SO(3), the 5 objects inside the solid line transform intolinearcombinationsofeachother, butunderthesmallergroupof transformations SO(2), the objects inside each of the 3 dashed lines transform into linear combinations of each other.
- The 5 breaks up as 5→2+2+1.Asinfigure1,thisfigureismeanttobeschematic.
- NowconsiderarestrictiontothesubgroupSO(2).Inotherwords,werestrictourselvesto rotationsaroundthez-axis,thatis,rotationsunderwhichV3→V (cid:5)3=V3,namelyrotations withR33=1andR13,R23,R31,R32allvanishing.SinceSO(2)doesnottouchtheindex 3, weconcludeimmediatelythatthecombinationS11+S22=−S33doesnottransform, or in other words, it transforms as a singlet under SO(2).
- Lookatthe5objects,S11,S22,S12,S13,S23,thatfurnishtherepresentation5ofSO(3).

Denote their trajectories by x(cid:3)(t)

| 57 5 → 2 + 2 + 1 Figure 2 Under SO(3), the 5 objects inside the solid line transform intolinearcombinationsofeachother, butunderthesmallergroupof transformations SO(2), the objects inside each of the 3 dashed lines transform into linear combinations of each other.

The 5 breaks up as 5→2+2+1.Asinfigure1,thisfigureismeanttobeschematic.

NowconsiderarestrictiontothesubgroupSO(2).Inotherwords,werestrictourselvesto rotationsaroundthez-axis,thatis,rotationsunderwhichV3→V (cid:5)3=V3,namelyrotations withR33=1andR13,R23,R31,R32allvanishing.SinceSO(2)doesnottouchtheindex 3, weconcludeimmediatelythatthecombinationS11+S22=−S33doesnottransform, or in other words, it transforms as a singlet under SO(2).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- ever," with Newton the runner-up, while a parallel survey of rank-and-file physicists ranked Newton as the greatest.[295][296] In 2005, a dual survey of the public and members of Britain's Royal Society asked two questions: who made the bigger overall contributions to science and who made the bigger positive contributions to humankind, with the candidates being Newton or Einstein.
- In both groups, and for both questions, the consensus was that Newton had made the greater overall contributions.[297][298] In 1999 Time magazine named Newton the Person of the Century for the 17th century.[270] Newton placed sixth in the 100 Greatest Britons poll conducted by BBC in 2002.
- However, in 2003, he was voted as the greatest Briton in a poll conducted by BBC World, with Winston Churchill second.[299] He was voted as the greatest Cantabrigian by University of Cambridge students in 2009.[300]

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

In both groups, and for both questions, the consensus was that Newton had made the greater overall contributions.[297][298] In 1999 Time magazine named Newton the Person of the Century for the 17th century.[270] Newton placed sixth in the 100 Greatest Britons poll conducted by BBC in 2002.

However, in 2003, he was voted as the greatest Briton in a poll conducted by BBC World, with Winston Churchill second.[299] He was voted as the greatest Cantabrigian by University of Cambridge students in 2009.[300]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- In some extensions of the Standard Model of particle physics, baryogenesis also happened at this stage, creating an imbalance between matter and antimatter (though in extensions to this model, this may have happened earlier).
- The following scenarios have been proposed for the ultimate fate of the universe:
- Little is known about the details of these processes.
- This epoch ended with electroweak symmetry breaking, potentially through a phase transition.
- Before the electroweak symmetry breaking, at a temperature of around 1015 K, approximately 10−15 seconds after the Big Bang, the electromagnetic and weak interaction had not yet separated, and the gauge bosons and fermions had not yet gained mass through the Higgs mechanism.

In some extensions of the Standard Model of particle physics, baryogenesis also happened at this stage, creating an imbalance between matter and antimatter (though in extensions to this model, this may have happened earlier).

The following scenarios have been proposed for the ultimate fate of the universe:

Little is known about the details of these processes.

This epoch ended with electroweak symmetry breaking, potentially through a phase transition.

Before the electroweak symmetry breaking, at a temperature of around 1015 K, approximately 10−15 seconds after the Big Bang, the electromagnetic and weak interaction had not yet separated, and the gauge bosons and fermions had not yet gained mass through the Higgs mechanism.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Chronology of the universe - Wikipedia.pdf