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

EVIDENCE:
- Theviewofquantumfieldtheoryasalowenergyeffectivetheorysketchedhererepresentsaremarkable shiftinattitudetowardquantumfieldtheoryoverthepast30years.Traditionally, atermintheactionfora quantumfieldtheoryisclassifiedaccordingtowhetheritsmassdimensionis<4,=4,or>4,knownrespectively assuperrenormalizable, renormalizable, andnonrenormalizable.Textbookstaughtthatsuperrenormalizable interactionswerenice,renormalizableinteractionswerewhatwewant,whilenonrenormalizableinteractions shouldfilluswithfearandloathing.
- (5) C where,again,byhighschooldimensionalanalysiswewereforcedtointroducealengthscalel whichapriori C mayormaynotbethesameasl.Comparewith(4).
- Since(cid:27)isanenergydensitywithdimensionsM/L3∼M4∼1/L4,wecandefinealengthscalel (cid:27)associated withthecosmologicalenergydensityby(cid:27)≡l −4.Apossiblyilluminatingwayofwriting(6)is (cid:27) (cid:2) l (cid:27) ∼ l P l U (7) wherewerenamedl asl ,thelengthscaleorsizeoftheuniverse.Einsteintellsusthatthelengthscaleassociated C U withthedarkenergyorthecosmologicalconstantisthegeometricmean8ofthesmallestandthelargestlengths knowninphysics.Rathermysterious!
- Thecosmologicalconstantparadoxunmaskstheoreticalphysicistsasdouble-talkingsnakeoilsalesmen:†in theeffectiveactionforgravity,theywantltobetinyontheonehandandl tobeenormousontheother.
- Recall from chapter VI.2 that the “1” term is, once again, the dreaded cosmological constant, with the identificationoftheenergydensity(cid:27)as M2 (cid:27)∼ P (6) l2 C Withoutbotheringtopluginnumbers,wecanseethatl isenormous.FromchaptersVI.2andVIII.1,we C knowthattoafirstapproximation,ouruniverseisdominatedbythecosmologicalconstant,akadarkenergy,with thescalefactordeterminedbyEinstein’sfieldequation(a ̇/a)2∼Gρ,sothat∗H2∼G(cid:27)∼(cid:27)/M2.Comparingthis P with(6),weseethatl istheHubblesizeoftheuniverse,andsoisalmostinconceivablylargerthanl,evenif,in C adeparturefromconventionalwisdom,wetakeltobemuchlargerthanthePlancklengthl .Thishumongous P discrepancyamountstoanotherstatementofthecosmologicalconstantparadox.7Natureflagrantlyviolatesthe theorist’scherishednaturalnessdoctrine.

(5) C where,again,byhighschooldimensionalanalysiswewereforcedtointroducealengthscalel whichapriori C mayormaynotbethesameasl.Comparewith(4).

Since(cid:27)isanenergydensitywithdimensionsM/L3∼M4∼1/L4,wecandefinealengthscalel (cid:27)associated withthecosmologicalenergydensityby(cid:27)≡l −4.Apossiblyilluminatingwayofwriting(6)is (cid:27) (cid:2) l (cid:27) ∼ l P l U (7) wherewerenamedl asl ,thelengthscaleorsizeoftheuniverse.Einsteintellsusthatthelengthscaleassociated C U withthedarkenergyorthecosmologicalconstantisthegeometricmean8ofthesmallestandthelargestlengths knowninphysics.Rathermysterious!

Recall from chapter VI.2 that the “1” term is, once again, the dreaded cosmological constant, with the identificationoftheenergydensity(cid:27)as M2 (cid:27)∼ P (6) l2 C Withoutbotheringtopluginnumbers,wecanseethatl isenormous.FromchaptersVI.2andVIII.1,we C knowthattoafirstapproximation,ouruniverseisdominatedbythecosmologicalconstant,akadarkenergy,with thescalefactordeterminedbyEinstein’sfieldequation(a ̇/a)2∼Gρ,sothat∗H2∼G(cid:27)∼(cid:27)/M2.Comparingthis P with(6),weseethatl istheHubblesizeoftheuniverse,andsoisalmostinconceivablylargerthanl,evenif,in C adeparturefromconventionalwisdom,wetakeltobemuchlargerthanthePlancklengthl .Thishumongous P discrepancyamountstoanotherstatementofthecosmologicalconstantparadox.7Natureflagrantlyviolatesthe theorist’scherishednaturalnessdoctrine.

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:
- would a classical particle), and not through both slits (as would a wave).
- Such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through.[72]: 73–76 According to Bohr's complementarity principle, light is neither a wave nor a stream of particles.
- A particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time.[73] The same experiment has been performed for light, electrons, atoms, and molecules.[74][75] The extremely small de Broglie wavelength of objects with larger mass makes experiments increasingly difficult,[76] but in general quantum mechanics considers all matter as possessing both particle and wave behaviors.

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.

would a classical particle), and not through both slits (as would a wave).

Such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through.[72]: 73–76 According to Bohr's complementarity principle, light is neither a wave nor a stream of particles.

A particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time.[73] The same experiment has been performed for light, electrons, atoms, and molecules.[74][75] The extremely small de Broglie wavelength of objects with larger mass makes experiments increasingly difficult,[76] but in general quantum mechanics considers all matter as possessing both particle and wave behaviors.

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.

Copenhagen interpretation - Wikipedia.pdf


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

EVIDENCE:
- The ad’s creator claimed that the fact that the last four letters of the intended word “BUREACRATS” just happened to become detached from this longer word was entirely accidental (see Figure 1.2).
- Nevertheless, advertising production experts said that given the advanced technology used to prepare the ad, an unintentional insertion of this kind was unlikely.

The ad’s creator claimed that the fact that the last four letters of the intended word “BUREACRATS” just happened to become detached from this longer word was entirely accidental (see Figure 1.2).

Nevertheless, advertising production experts said that given the advanced technology used to prepare the ad, an unintentional insertion of this kind was unlikely.

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:
- Some authors have argued that we shouldn’t be comparing clinical and mechanical prediction methods, because practitioners should use both of them in conjunction.
- One concern is that a preference for mechanical prediction will lead to clinicians being replaced by computers.
- First, the clinician might think there’s something so unusual about a given patient that he or she is an exception to the rule.
- There are two variations of this objection, but both are mistaken.
- Some object to mechanical prediction because “probability is irrelevant to the unique individual.” In particular, they claim that knowing the outcomes for other people is of no use when making a decision for a new patient, because “every person is different.” For example, research shows that the probabili ty of successfully treating an individual’s phobia is maximized through exposure-based treatment—treatment that exposes people systematically to their fears (Barlow, 2002).

Some authors have argued that we shouldn’t be comparing clinical and mechanical prediction methods, because practitioners should use both of them in conjunction.

One concern is that a preference for mechanical prediction will lead to clinicians being replaced by computers.

First, the clinician might think there’s something so unusual about a given patient that he or she is an exception to the rule.

There are two variations of this objection, but both are mistaken.

Some object to mechanical prediction because “probability is irrelevant to the unique individual.” In particular, they claim that knowing the outcomes for other people is of no use when making a decision for a new patient, because “every person is different.” For example, research shows that the probabili ty of successfully treating an individual’s phobia is maximized through exposure-based treatment—treatment that exposes people systematically to their fears (Barlow, 2002).

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:
- TheworkshopoccurredatatimewhenSalvatorePais,laterinventoroftheNavy’strianglecraft patent(see2November2017),wasworkingonhisPhDdissertationatCaseWesternReserveUniversity whileservingasaNASAGraduateStudentResearchFellowattheGlennResearchCenter.
- JamesMcAndrew,whichstatesalienbodiesfoundatRoswell,NMandHollomanAFBwereactuallytest dummiesaspartofballoonlaunch-and-recoveryoperations.
- ● https://youtu.be/nd ZXgObNNg (PUBLICDOMAIN) -June1997—FormerUSArmyCol.PhilipJ.Corsoclaimshecameincontact withrecoveredUAPmaterialsandhelpedseedthemintoUSindustry.
- Itiscertainlypossible,givenhisNavytrianglecraftpatentutilizedvacuumfluctuation energyconcepts.
- ● https://archive.org/details/AFD-101027-030/mode/2up ● https://ufologie.patrickgross.org/rw/witnesses.htm (PUBLICDOMAIN) -August1997—NASAsponsorsabreakthroughpropulsionphysicsworkshopat theNASAGlennResearchCenteratLewisFieldinCleveland,OH.

● https://youtu.be/nd ZXgObNNg (PUBLICDOMAIN) -June1997—FormerUSArmyCol.PhilipJ.Corsoclaimshecameincontact withrecoveredUAPmaterialsandhelpedseedthemintoUSindustry.

● https://archive.org/details/AFD-101027-030/mode/2up ● https://ufologie.patrickgross.org/rw/witnesses.htm (PUBLICDOMAIN) -August1997—NASAsponsorsabreakthroughpropulsionphysicsworkshopat theNASAGlennResearchCenteratLewisFieldinCleveland,OH.

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:
- Undoubtedly the Earth had its share of craters, too.
- Energy cannot be lost; it can only be changed into other forms.
- 56 THE COLLAPSING UNIVERSE satellites if we could get pictures of them in sufficient detail.
- In this case the kinetic energy is turned into heat and is concentrated at the center of the world that is formed.
- There are also indications of internal heat in the form of hot springs and volcanoes (which probably gave ancient man the idea of a fiery hell underground).

Undoubtedly the Earth had its share of craters, too.

Energy cannot be lost; it can only be changed into other forms.

56 THE COLLAPSING UNIVERSE satellites if we could get pictures of them in sufficient detail.

In this case the kinetic energy is turned into heat and is concentrated at the center of the world that is formed.

There are also indications of internal heat in the form of hot springs and volcanoes (which probably gave ancient man the idea of a fiery hell underground).

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:
- (revs) GrondslagenvandeQuantummechanica Lecturenotesforthecourse‘GrondslagenvandeQuantummmechanica’,UtrechtUniversity Utrecht: InstitutefortheHistoryandFoundationsofScience,FacultyofScience Eng.tr.: Weerden,A.van(transl)()FoundationsofQuantumMechanics,pre-revisedversion [32] Maes,J.()‘HiddenvariablesandBell’stheorem’ Unpublished essay for the course ‘Quantum Mechanics for Mathematicians’, supervised byDr.B.R.U.Dherin Utrecht: MathematicalInstituteoftheUtrechtUniversity [33] Shannon,C.E.()‘AMathematicalTheoryofCommunication’ BellSystemTechnicalJournal27pp.
- (), Uffink, J.B.M., Dieks, D.G.B.J., Muller, F.A., Seevinck, M.P.
- [30] Braunstein,S.L.,Mann,A.,Revzen,M.()‘MaximalviolationofBellinequalitiesformixed states’ PhysicalReviewLetters68(22)pp.
- () Generalized Functions, vol.
- 863-867 [29] Sakurai,J.J.(auth),Tuan,S.F.(ed)()ModernQuantumMechanics,RevisedEdition Reading: Addison-WesleyPublishingCompany,Inc.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

(revs) GrondslagenvandeQuantummechanica Lecturenotesforthecourse‘GrondslagenvandeQuantummmechanica’,UtrechtUniversity Utrecht: InstitutefortheHistoryandFoundationsofScience,FacultyofScience Eng.tr.: Weerden,A.van(transl)()FoundationsofQuantumMechanics,pre-revisedversion [32] Maes,J.()‘HiddenvariablesandBell’stheorem’ Unpublished essay for the course ‘Quantum Mechanics for Mathematicians’, supervised byDr.B.R.U.Dherin Utrecht: MathematicalInstituteoftheUtrechtUniversity [33] Shannon,C.E.()‘AMathematicalTheoryofCommunication’ BellSystemTechnicalJournal27pp.

(), Uffink, J.B.M., Dieks, D.G.B.J., Muller, F.A., Seevinck, M.P.

863-867 [29] Sakurai,J.J.(auth),Tuan,S.F.(ed)()ModernQuantumMechanics,RevisedEdition Reading: Addison-WesleyPublishingCompany,Inc.

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 provides a convenient way to add velocities in special relativity: the rapidities simply add (for boosts along the same direction), just as spatial rotation angles add (for rotations about the same axis).
- 28 Special Relativity Now set t = iw and α = ia with t and α both real.
- In other words, take the spatial coordinate w to be imaginary, and the rotation angle a likewise to be imaginary.
- (1.22) 1 2 The equivalent formula for the velocities themselves is v +v v = 1 2 , (1.23) 1+v v 1 2 the special relativistic velocity addition formula.
- Thus a boost by velocity v = tanhα followed by a boost 1 1 by velocity v =tanhα in the same direction gives a net velocity boost of v =tanhα where 2 2 α=α +α .

This provides a convenient way to add velocities in special relativity: the rapidities simply add (for boosts along the same direction), just as spatial rotation angles add (for rotations about the same axis).

28 Special Relativity Now set t = iw and α = ia with t and α both real.

In other words, take the spatial coordinate w to be imaginary, and the rotation angle a likewise to be imaginary.

(1.22) 1 2 The equivalent formula for the velocities themselves is v +v v = 1 2 , (1.23) 1+v v 1 2 the special relativistic velocity addition formula.

Thus a boost by velocity v = tanhα followed by a boost 1 1 by velocity v =tanhα in the same direction gives a net velocity boost of v =tanhα where 2 2 α=α +α .

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:
- Since a lens can only be held in place by its edge, the center of a large lens will sag due to gravity, distorting the image it produces.
- Astigmatism – an azimuthal variation of focus around the aperture causing point source images off-axis to appear elliptical.
- Light of different wavelengths travels through a medium Main mirror of James Webb Space other than vacuum at different speeds.
- In a lens the entire volume of material has to be free of imperfection and inhomogeneities, whereas in a mirror, only one surface has to be perfectly polished.
- usually involves a combination of two or three aperture sized lenses (see achromat and apochromat for more details).

Since a lens can only be held in place by its edge, the center of a large lens will sag due to gravity, distorting the image it produces.

Astigmatism – an azimuthal variation of focus around the aperture causing point source images off-axis to appear elliptical.

Light of different wavelengths travels through a medium Main mirror of James Webb Space other than vacuum at different speeds.

In a lens the entire volume of material has to be free of imperfection and inhomogeneities, whereas in a mirror, only one surface has to be perfectly polished.

usually involves a combination of two or three aperture sized lenses (see achromat and apochromat for more details).

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:
- The Earth is white hot at its center, and Jupiter is far hotter still.
- The trouble with this view of the Sun and its structure is that it can easily be shown to be an impossible one.
- In 1853 the German physicist Hermann Ludwig Ferdinand von Helmholtz (1821-1894) tried to calculate how much kinetic energy would be
- COMPRESSED MATTER 71 massive than any planet we know and that it is also blazing with light?
- The Sun, after all, is pouring out energy at a vast rate, and it has certainly been doing it for all of recorded history.

The Earth is white hot at its center, and Jupiter is far hotter still.

The trouble with this view of the Sun and its structure is that it can easily be shown to be an impossible one.

In 1853 the German physicist Hermann Ludwig Ferdinand von Helmholtz (1821-1894) tried to calculate how much kinetic energy would be

COMPRESSED MATTER 71 massive than any planet we know and that it is also blazing with light?

The Sun, after all, is pouring out energy at a vast rate, and it has certainly been doing it for all of recorded history.

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 one of these equations can be solved for t, the expression obtained can be substituted into the other equation to obtain an equation involving x and y only: Solving to obtain and using this in gives the explicit equation while more complicated cases will give an implicit equation of the form If the parametrization is given by rational functions where p, q, and r are set-wise coprime polynomials, a resultant computation allows one to implicitize.
- To take the example of the circle of radius a, the parametric equations can be implicitized in terms of x and y by way of the Pythagorean trigonometric identity.
- Parametric plane curves Parabola The simplest equation for a parabola,
- In higher dimensions (either more than two coordinates or more than one parameter), the implicitization of rational parametric equations may by done with Gröbner basis computation; see Gröbner basis § Implicitization in higher dimension.
- More precisely, the implicit equation is the resultant with respect to t of xr(t) – p(t) and yr(t) – q(t).

If one of these equations can be solved for t, the expression obtained can be substituted into the other equation to obtain an equation involving x and y only: Solving to obtain and using this in gives the explicit equation while more complicated cases will give an implicit equation of the form If the parametrization is given by rational functions where p, q, and r are set-wise coprime polynomials, a resultant computation allows one to implicitize.

To take the example of the circle of radius a, the parametric equations can be implicitized in terms of x and y by way of the Pythagorean trigonometric identity.

Parametric plane curves Parabola The simplest equation for a parabola,

In higher dimensions (either more than two coordinates or more than one parameter), the implicitization of rational parametric equations may by done with Gröbner basis computation; see Gröbner basis § Implicitization in higher dimension.

More precisely, the implicit equation is the resultant with respect to t of xr(t) – p(t) and yr(t) – q(t).

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:
- A Short Account of the History of Mathematics (https://archive.or g/details/shortaccountofhi0000ball) (4th ed.).
- Berger, Marcel (1987), Geometry I, Berlin: Springer, ISBN 3-540-11658-3 Coxeter, H.S.M.
- x+214, doi:10.1002/9781118164518 (https://doi.org/10.1002%2F9781118164518), ISBN 0-471-60839-4, MR 1009557 (https://mathscinet.ams.org/mathscinet-getitem?mr=1009557) Ball, W.W.
- Berger 1987, Proposition 9.1.3.
- (2001) [1994], "Euclidean space" (https://www.encyclopediaofmath.org/index.p hp?title=Euclidean_space), Encyclopedia of Mathematics, EMS Press Retrieved from "https://en.wikipedia.org/w/index.php?title=Euclidean_space&oldid=1323527610"

A Short Account of the History of Mathematics (https://archive.or g/details/shortaccountofhi0000ball) (4th ed.).

Berger, Marcel (1987), Geometry I, Berlin: Springer, ISBN 3-540-11658-3 Coxeter, H.S.M.

(2001) [1994], "Euclidean space" (https://www.encyclopediaofmath.org/index.p hp?title=Euclidean_space), Encyclopedia of Mathematics, EMS Press Retrieved from "https://en.wikipedia.org/w/index.php?title=Euclidean_space&oldid=1323527610"

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:
- 2006) was a vigorous supporter of the many-worlds Children 3, including Lucy interpretation of quantum mechanics.[23][24] He also introduced the notion of a micro black hole.[25] Awards See list Scientific career
- In 1963, at age 21, Hawking was diagnosed with an early-onset slowprogressing form of motor neurone disease that gradually, over decades, paralysed him.[20][21] After the loss of his speech, he communicated through a speech- Hawking, c.
- In 1962, he began his graduate work at Trinity Hall, Cambridge, where, in 1966, he obtained his PhD in applied mathematics and theoretical physics, specialising in general relativity and cosmology.
- 1995) theory of cosmology explained by a union of the general Elaine Mason theory of relativity and quantum mechanics.
- In 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics.

2006) was a vigorous supporter of the many-worlds Children 3, including Lucy interpretation of quantum mechanics.[23][24] He also introduced the notion of a micro black hole.[25] Awards See list Scientific career

In 1963, at age 21, Hawking was diagnosed with an early-onset slowprogressing form of motor neurone disease that gradually, over decades, paralysed him.[20][21] After the loss of his speech, he communicated through a speech- Hawking, c.

In 1962, he began his graduate work at Trinity Hall, Cambridge, where, in 1966, he obtained his PhD in applied mathematics and theoretical physics, specialising in general relativity and cosmology.

1995) theory of cosmology explained by a union of the general Elaine Mason theory of relativity and quantum mechanics.

In 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics.

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:
- The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped.
- Both rest and relativistic mass can be expressed as an energy by applying the well-known relationship E = mc2 , yielding rest energy and "relativistic energy" (total system energy) respectively: The "relativistic" mass and energy concepts are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum.
- However, it turns out that it is impossible to find an objective general definition for the concept of invariant mass in general relativity.
- General relativity In general relativity, the equivalence principle is the equivalence of gravitational and inertial mass.
- Mass–energy equivalence also holds in macroscopic systems.[35] For example, if one takes exactly one kilogram of ice, and applies heat, the mass of the resulting melt-water will be more than a kilogram: it will include the mass from the thermal energy (latent heat) used to melt the ice; this follows from the conservation of energy.[36] This number is small but not negligible: about 3.7 nanograms.

The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped.

Both rest and relativistic mass can be expressed as an energy by applying the well-known relationship E = mc2 , yielding rest energy and "relativistic energy" (total system energy) respectively: The "relativistic" mass and energy concepts are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum.

However, it turns out that it is impossible to find an objective general definition for the concept of invariant mass in general relativity.

General relativity In general relativity, the equivalence principle is the equivalence of gravitational and inertial mass.

Mass–energy equivalence also holds in macroscopic systems.[35] For example, if one takes exactly one kilogram of ice, and applies heat, the mass of the resulting melt-water will be more than a kilogram: it will include the mass from the thermal energy (latent heat) used to melt the ice; this follows from the conservation of energy.[36] This number is small but not negligible: about 3.7 nanograms.

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:
- But one of the consequences of the Cartan-Weyl-Dynkin theory discussed in §42.2 is that finitely generated Lie groups are direct products of irreducible groups (Maschke’s theorem), so the restored group must in fact have commuted with the U(1) Higgs factor.
- Similarly to the electroweak Higgs fields, the U(1) bivector calls attentiontoitselfbecauseithappenstobeageneratoroftheSpin(5)×Spin(6)groupthatcommuteswiththe Poincaré group, and it happens to have precisely the properties needed to break Spin(5)×Spin(6) down to the SM group.
- In the conventional picture where the GUT and Lorentzgroupsaredistinct,thespinofafieldisaconservedchargeassociatedwithLorentzsymmetry,andit isnaturaltoassumethatspinremainsanimmutablepropertyofafieldthroughGUTsymmetrybreaking.But inthepresentconstruction,atleastsomeaspectsofsymmetrybreakingareassociatedwithreconfigurationof spacetimeratherthanwithHiggsfields.Forexample,SU(5)isbrokenbecauseitsgeneratorsfailtocommute with the Lorentz generators −iI and I .
- The posited U(1) Higgs field has the additional merits that: (1) it removes the baryon-lepton symmetry group U (1), notably absent from the SM group, from being a symmetry of the SM; and (2) B−L it generates fermionic mass terms distinct from those generated by the electroweak Higgs fields, mass terms that are needed to fill out the fermionic mass matrix in the presence of the T-bit in a manner consistent with observation, §42.4.14.
- The U(1) Higgs field that breaks Spin(5)×Spin(6) symmetry remains present today, and like the electroweak Higgs field must be a scalar to preserve the observed Lorentz symmetry of spacetime.

But one of the consequences of the Cartan-Weyl-Dynkin theory discussed in §42.2 is that finitely generated Lie groups are direct products of irreducible groups (Maschke’s theorem), so the restored group must in fact have commuted with the U(1) Higgs factor.

Similarly to the electroweak Higgs fields, the U(1) bivector calls attentiontoitselfbecauseithappenstobeageneratoroftheSpin(5)×Spin(6)groupthatcommuteswiththe Poincaré group, and it happens to have precisely the properties needed to break Spin(5)×Spin(6) down to the SM group.

In the conventional picture where the GUT and Lorentzgroupsaredistinct,thespinofafieldisaconservedchargeassociatedwithLorentzsymmetry,andit isnaturaltoassumethatspinremainsanimmutablepropertyofafieldthroughGUTsymmetrybreaking.But inthepresentconstruction,atleastsomeaspectsofsymmetrybreakingareassociatedwithreconfigurationof spacetimeratherthanwithHiggsfields.Forexample,SU(5)isbrokenbecauseitsgeneratorsfailtocommute with the Lorentz generators −iI and I .

The posited U(1) Higgs field has the additional merits that: (1) it removes the baryon-lepton symmetry group U (1), notably absent from the SM group, from being a symmetry of the SM; and (2) B−L it generates fermionic mass terms distinct from those generated by the electroweak Higgs fields, mass terms that are needed to fill out the fermionic mass matrix in the presence of the T-bit in a manner consistent with observation, §42.4.14.

The U(1) Higgs field that breaks Spin(5)×Spin(6) symmetry remains present today, and like the electroweak Higgs field must be a scalar to preserve the observed Lorentz symmetry of spacetime.

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:
- Mechanics and Relativity (https://books.open.tudelft.nl/home/catalog/book/1 98), TU Delft OPEN Publishing.
- arXiv:hep-ph/9703240 (https://arxiv.org/abs/he p-ph/9703240).
- Bibcode:2004AHES...59...45N (https://ui.adsabs.harvard.edu/abs/2004 AHES...59...45N).
- The Meaning of Relativity (https://gutenberg.org/ebooks/36276).
- Øyvind Grøn & Sigbjørn Hervik (2007).

Mechanics and Relativity (https://books.open.tudelft.nl/home/catalog/book/1 98), TU Delft OPEN Publishing.

The Meaning of Relativity (https://gutenberg.org/ebooks/36276).

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 United States Department Of Defense And The Intelligence Community Are Withholding Information About Anomalous Phenomena From Congress Testimony by Michael Shellenberger to the Subcommittee On Cybersecurity, Information Technology, and Government Innovation, and the Subcommittee on National Security, the Border, and Foreign Affairs of the House Oversight and Accountability Committee For a hearing on: "Unidentified Anomalous Phenomena: Exposing the Truth" November 13, 2024 Chairwoman Mace, Chairman Grothman, Ranking Member Connolly, Ranking Member Garcia, and members of the Subcommittees: thank you for inviting my testimony.

The United States Department Of Defense And The Intelligence Community Are Withholding Information About Anomalous Phenomena From Congress Testimony by Michael Shellenberger to the Subcommittee On Cybersecurity, Information Technology, and Government Innovation, and the Subcommittee on National Security, the Border, and Foreign Affairs of the House Oversight and Accountability Committee For a hearing on: "Unidentified Anomalous Phenomena: Exposing the Truth" November 13, 2024 Chairwoman Mace, Chairman Grothman, Ranking Member Connolly, Ranking Member Garcia, and members of the Subcommittees: thank you for inviting my testimony.

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:
- a hyperbolic angle (analogous to ordinary angles in Euclidean geometry).[note 8] Because of this rotation, the projection of a primed meter-stick onto the unprimed x-axis is foreshortened, while the projection of an unprimed meter-stick onto the primed x′-axis is likewise foreshortened.
- Mutual time dilation and the twin paradox Mutual time dilation Mutual time dilation and length contraction tend to strike beginners as inherently self-contradictory concepts.
- If an observer in frame S measures a clock, at rest in frame S', as running slower than his', while S' is moving at speed v in S, then the principle of relativity requires that an observer in frame S' likewise measures a clock in frame S, moving at speed −v in S', as running slower than hers.
- the 1 m length of the moving rod, as measured in the primed frame, is the In regards to mutual length contraction, Fig.
- How two clocks can run both slower than the other, is an important question that "goes to the heart of understanding special relativity."[3]: 198 This apparent contradiction stems from not correctly taking into account the different settings of the necessary, related measurements.

a hyperbolic angle (analogous to ordinary angles in Euclidean geometry).[note 8] Because of this rotation, the projection of a primed meter-stick onto the unprimed x-axis is foreshortened, while the projection of an unprimed meter-stick onto the primed x′-axis is likewise foreshortened.

Mutual time dilation and the twin paradox Mutual time dilation Mutual time dilation and length contraction tend to strike beginners as inherently self-contradictory concepts.

If an observer in frame S measures a clock, at rest in frame S', as running slower than his', while S' is moving at speed v in S, then the principle of relativity requires that an observer in frame S' likewise measures a clock in frame S, moving at speed −v in S', as running slower than hers.

the 1 m length of the moving rod, as measured in the primed frame, is the In regards to mutual length contraction, Fig.

How two clocks can run both slower than the other, is an important question that "goes to the heart of understanding special relativity."[3]: 198 This apparent contradiction stems from not correctly taking into account the different settings of the necessary, related measurements.

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:
- He took me to an abandoned power plant.
- Since I saw a geisha mask and a gun, and fear and confusion became the only stars in my sky.
- And there in the darkness, like the filaments of a lightbulb warming to life, the truth finds me.
- If I ever called her “Dani.” He knew who Ryan Holder was.
- My old friend is likely being tortured as I sit here.

Since I saw a geisha mask and a gun, and fear and confusion became the only stars in my sky.

And there in the darkness, like the filaments of a lightbulb warming to life, the truth finds me.

If I ever called her “Dani.” He knew who Ryan Holder was.

My old friend is likely being tortured as I sit here.

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:
- All the other physical quantities that went into the making of the black hole are subsequently hidden behind the horizon.
- Then T 00 =F 0i F 0 i− 1g F σρ Fσρ=(∂ i f)2/(2f6).Similarly, wehaveT ={(∂ i f)2−2(∂ f)2}/(2f2)andofcoursealsothecorrespondingexpressionsforT 22 andT 33 .Clearly, T 0i =0, butT 12 =−(∂ 1 f)(∂ 2 f)/f2doesnotvanish.Asimple checkonthearithmeticisthatthetraceT =gμνT μνvanishes.
- So,exploitourfreedomtochangecoordinatesandsetr=ρ+M.Afewlinesofarithmeticleadustods2= −f(ρ)−2dt2+f(ρ)2(dρ2+ρ2d(cid:24)2), withf(ρ)=1+ M.WenextintroduceCartesiancoordinatesbysetting ρ dρ2+ρ2d(cid:24)2=dx2+dy2+dz2.
- Wheeler has summarized this stateofaffairsbyquippingthat“Blackholeshavenohair.” Appendix1:Extremalblackholesjustsittingthere Letusnowverifythephysicalargumentthattheremustexistanentirefamilyofstaticsolutionsofthecoupled EinsteinandMaxwellequationsdescribingabunchofextremalblackholes“justsittingthere.”Startwithasingle (cid:12) (cid:14) (cid:3) (cid:4) 2 2 extremal black hole.
- 0 ρ OurinspiredguessistosettheonlynonvanishingcomponentofA μtobe (cid:12) (cid:14) A (t,x,y,z)=√ 1 1−f(x,y,z)−1 (7) 4π withthesameunknownfunctionf(x,y,z)asin(6).

All the other physical quantities that went into the making of the black hole are subsequently hidden behind the horizon.

Then T 00 =F 0i F 0 i− 1g F σρ Fσρ=(∂ i f)2/(2f6).Similarly, wehaveT ={(∂ i f)2−2(∂ f)2}/(2f2)andofcoursealsothecorrespondingexpressionsforT 22 andT 33 .Clearly, T 0i =0, butT 12 =−(∂ 1 f)(∂ 2 f)/f2doesnotvanish.Asimple checkonthearithmeticisthatthetraceT =gμνT μνvanishes.

Wheeler has summarized this stateofaffairsbyquippingthat“Blackholeshavenohair.” Appendix1:Extremalblackholesjustsittingthere Letusnowverifythephysicalargumentthattheremustexistanentirefamilyofstaticsolutionsofthecoupled EinsteinandMaxwellequationsdescribingabunchofextremalblackholes“justsittingthere.”Startwithasingle (cid:12) (cid:14) (cid:3) (cid:4) 2 2 extremal black hole.

0 ρ OurinspiredguessistosettheonlynonvanishingcomponentofA μtobe (cid:12) (cid:14) A (t,x,y,z)=√ 1 1−f(x,y,z)−1 (7) 4π withthesameunknownfunctionf(x,y,z)asin(6).

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 restricted covariant derivative D^ differs from ADM only in that the restricted connections now k excludethepartdependingonderivativesoftheconformalfactor,whichhavebeenabsorbedintothespatial componentsK ofthegeneralizedextrinsiccurvature.Thevierbeinem andthetetradmetricγ continue abc μ lm to commute with the restricted covariant derivative D , equations (17.30) and (17.31).
- (17.84) a a00 a a Unlike in ADM, K is not the same as the acceleration K .
- (17.81) abc ac b bc a TheaccelerationK ≡K ,extrinsiccurvatureK ≡K ,andrestrictedconnectionsΓ^ withfinalindex a a00 ab a0b ab0 the time index 0 are unchanged by the conformal decomposition.
- Thus the generalized extrinsic curvature K nowconsistsoftheaccelerationK ,theextrinsiccurvatureK ,andthederivativesK oftheconlmn a00 a0b abc formal factor defined by equation (17.81).
- 506 Conventional Hamiltonian (3+1) approach where K is the spatial tensor abc K =γ ∂ lna−γ ∂ lna .

The restricted covariant derivative D^ differs from ADM only in that the restricted connections now k excludethepartdependingonderivativesoftheconformalfactor,whichhavebeenabsorbedintothespatial componentsK ofthegeneralizedextrinsiccurvature.Thevierbeinem andthetetradmetricγ continue abc μ lm to commute with the restricted covariant derivative D , equations (17.30) and (17.31).

(17.84) a a00 a a Unlike in ADM, K is not the same as the acceleration K .

(17.81) abc ac b bc a TheaccelerationK ≡K ,extrinsiccurvatureK ≡K ,andrestrictedconnectionsΓ^ withfinalindex a a00 ab a0b ab0 the time index 0 are unchanged by the conformal decomposition.

Thus the generalized extrinsic curvature K nowconsistsoftheaccelerationK ,theextrinsiccurvatureK ,andthederivativesK oftheconlmn a00 a0b abc formal factor defined by equation (17.81).

506 Conventional Hamiltonian (3+1) approach where K is the spatial tensor abc K =γ ∂ lna−γ ∂ lna .

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:
- The Penrose diagram 10.19 depicts both closed and open FLRW geometries, but the open geometry is shiftedby90∘ totheequator,sothatitappearstointerleavewiththeclosedgeometryinsteadofoverlapping it.
- 282 Homogeneous, Isotropic Cosmology Penrose diagram.
- The resulting P Penrose coordinates for de Sitter space are t =atan(sinhψ)=atan(u/r ) , (10.179a) P H r =χ=atan(r/w) .
- Whenmatterispresent,BigCrunchesandBigBangsare,settingasidequantumgravity,genuinesingularities that cannot be removed by a coordinate transformation.
- As long as the spacetime is purevacuum,thereisnowaytotellwhetherspacetimeisexpandingorcollapsing.Onlywhenthespacetime contains matter of some kind, as our Universe does, can a preferred set of comoving coordinates be defined.

The Penrose diagram 10.19 depicts both closed and open FLRW geometries, but the open geometry is shiftedby90∘ totheequator,sothatitappearstointerleavewiththeclosedgeometryinsteadofoverlapping it.

282 Homogeneous, Isotropic Cosmology Penrose diagram.

The resulting P Penrose coordinates for de Sitter space are t =atan(sinhψ)=atan(u/r ) , (10.179a) P H r =χ=atan(r/w) .

Whenmatterispresent,BigCrunchesandBigBangsare,settingasidequantumgravity,genuinesingularities that cannot be removed by a coordinate transformation.

As long as the spacetime is purevacuum,thereisnowaytotellwhetherspacetimeisexpandingorcollapsing.Onlywhenthespacetime contains matter of some kind, as our Universe does, can a preferred set of comoving coordinates be defined.

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:
- ∙ Atrajectoryisatconstantlatitudeifitisatconstantpolarangleθ,orequivalentlyatconstanty ≡−cosθ, y =constant .
- (23.54) Constant latitude orbits occur where the angular potential P2, equation (23.10b), not only vanishes, but is y an extremum, dP2 P2 = y =0 , (23.55) y dy the derivative being taken with the constants of motion E, L, and K of the orbit being held fixed.
- 674 Trajectories in ideal rotating black holes 23.9 Constant latitude trajectories in the Kerr-Newman geometry For simplicity, the next several sections, up to and including §23.20, are restricted to Kerr-Newman black holes with zero magnetic charge, Q =0, and zero cosmological constant, Λ=0.
- (23.59) It is convenient to call such an orbit circular even if the orbit is at finite inclination (not confined to the equatorial plane) about a rotating black hole, and therefore follows the surface of a spheroid (in BoyerLindquist coordinates).
- Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .

∙ Atrajectoryisatconstantlatitudeifitisatconstantpolarangleθ,orequivalentlyatconstanty ≡−cosθ, y =constant .

(23.54) Constant latitude orbits occur where the angular potential P2, equation (23.10b), not only vanishes, but is y an extremum, dP2 P2 = y =0 , (23.55) y dy the derivative being taken with the constants of motion E, L, and K of the orbit being held fixed.

674 Trajectories in ideal rotating black holes 23.9 Constant latitude trajectories in the Kerr-Newman geometry For simplicity, the next several sections, up to and including §23.20, are restricted to Kerr-Newman black holes with zero magnetic charge, Q =0, and zero cosmological constant, Λ=0.

(23.59) It is convenient to call such an orbit circular even if the orbit is at finite inclination (not confined to the equatorial plane) about a rotating black hole, and therefore follows the surface of a spheroid (in BoyerLindquist coordinates).

Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .

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:
- S2CID 199405246 h/datasheetText.aspx?bassnum=PTSAH).
- Retrieved ear.html) from the original on 2017-01-04.
- "Maximizing specific energy by breeding deuterium".
- "American Eastern White Pine Wood" (http://www.matweb.com/searc ps://doi.org/10.1088%2F1741-4326%2Fab394c).
- ringtoolbox.com/weigt-wood-d_821.html).

Retrieved ear.html) from the original on 2017-01-04.

"Maximizing specific energy by breeding deuterium".

"American Eastern White Pine Wood" (http://www.matweb.com/searc ps://doi.org/10.1088%2F1741-4326%2Fab394c).

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:
- Bibcode:2005CQGra..22.3461C (https://ui.adsabs.harvard.edu/abs/2005CQGra..
- "Relating chronology protection and unitarity through holography".
- arXiv:gr-qc/9603012v2 (https://arxiv.org/abs/gr-qc/9603012v2).
- "The quantum physics of chronology protection".
- S2CID 118595727 (https://api.semanticscholar.org/CorpusID:11 8595727).

"Relating chronology protection and unitarity through holography".

"The quantum physics of chronology protection".

S2CID 118595727 (https://api.semanticscholar.org/CorpusID:11 8595727).

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 protection conjecture - Wikipedia.pdf


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

EVIDENCE:
- The cosmological model is the same as in Figure 33.1, §32.3.
- The left hand side of the Boltzmann equation (31.32) is, for either massless or massive particles, df dpa ∂f dp^ ∂f dp∂f =pm∂ f + =E∂ f +pa∂ f + · + .
- 880 Cosmological perturbations: Boltzmann treatment )3cpM3−h( )k(P Ω =0.69 Λ Ω =0.31 m b=1.32 1.2 1.0 .001 .01 .1 1 k (hMpc −1) slaudiseR N S Figure33.5 ModelmatterpowerspectrumcomputedfromaBoltzmanncomputation,comparedtoobservationsfrom the North (N) and South (S) Galactic Caps of the the Sloan Digital Sky Survey IV (Gil-Marín et al., 2020).
- The model power spectrum may be compared to those computedinthesimpleandhydrodynamicapproximations,Figure30.15andFigure32.4.Thethin(pink)lineisthe modelpowerspectruminthehydrodynamicapproximation.
- (33.8) dλ m dλ ∂pa 0 a dλ ∂p^ dλ∂p Hereλisanaffineparameteralongtheworldlineofaparticle,andpm ≡{E,p}isthetetrad-framemomentum oftheparticle.Bothdp^/dλand∂f/∂p^vanishintheunperturbedbackground,sodp^/dλ·∂f/∂p^isofsecond order, and can be neglected to linear order, so that df dp∂f =E∂ f +pa∂ f + .

The cosmological model is the same as in Figure 33.1, §32.3.

The left hand side of the Boltzmann equation (31.32) is, for either massless or massive particles, df dpa ∂f dp^ ∂f dp∂f =pm∂ f + =E∂ f +pa∂ f + · + .

880 Cosmological perturbations: Boltzmann treatment )3cpM3−h( )k(P Ω =0.69 Λ Ω =0.31 m b=1.32 1.2 1.0 .001 .01 .1 1 k (hMpc −1) slaudiseR N S Figure33.5 ModelmatterpowerspectrumcomputedfromaBoltzmanncomputation,comparedtoobservationsfrom the North (N) and South (S) Galactic Caps of the the Sloan Digital Sky Survey IV (Gil-Marín et al., 2020).

The model power spectrum may be compared to those computedinthesimpleandhydrodynamicapproximations,Figure30.15andFigure32.4.Thethin(pink)lineisthe modelpowerspectruminthehydrodynamicapproximation.

(33.8) dλ m dλ ∂pa 0 a dλ ∂p^ dλ∂p Hereλisanaffineparameteralongtheworldlineofaparticle,andpm ≡{E,p}isthetetrad-framemomentum oftheparticle.Bothdp^/dλand∂f/∂p^vanishintheunperturbedbackground,sodp^/dλ·∂f/∂p^isofsecond order, and can be neglected to linear order, so that df dp∂f =E∂ f +pa∂ f + .

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:
- Black hole thermodynamics For an ideal Λ-Kerr-Newman black hole, variations of the black hole’s mass M, electric charge Q, angular momentum J ≡ aM, and of the cosmological constant Λ ≡ 8πGρ are related to variations of the area λ A=4πR2 =4π(r2+a2) of the horizon by κ dM = dA+ΦdQ+ωdJ −V dρ , (25.1) 8π Λ where κ is the acceleration, Φ the electric potential, ω the angular velocity, and V the enclosed volume at the horizon, r−M 2Λr κ= − , (25.2a) R2 3 Qr Φ= , (25.2b) R2 a ω = , (25.2c) R2 V = πrR2 .
- (25.2d) Equations (25.1) and (25.2) hold at any horizon, wherever the horizon function Δ vanishes, including at a x cosmological horizon, which exists if the vacuum energy ρ is positive.
- The acceleration κ satisfies Λ 1dΔ κ=− x .
- (25.3) 2 dx The acceleration κ vanishes when the horizon is extremal, that is, where two horizons merge into one, which happens when the horizon function Δ is not only zero but also an extremum.
- x Equation (25.1) can be recast as d(M +ρ V)= dA+ΦdQ+ωdJ −p dV , (25.4) Λ 8πκ Λ in which the energy within the horizon is taken to be the energy M +ρ V including the contribution from Λ vacuum energy.

Black hole thermodynamics For an ideal Λ-Kerr-Newman black hole, variations of the black hole’s mass M, electric charge Q, angular momentum J ≡ aM, and of the cosmological constant Λ ≡ 8πGρ are related to variations of the area λ A=4πR2 =4π(r2+a2) of the horizon by κ dM = dA+ΦdQ+ωdJ −V dρ , (25.1) 8π Λ where κ is the acceleration, Φ the electric potential, ω the angular velocity, and V the enclosed volume at the horizon, r−M 2Λr κ= − , (25.2a) R2 3 Qr Φ= , (25.2b) R2 a ω = , (25.2c) R2 V = πrR2 .

(25.2d) Equations (25.1) and (25.2) hold at any horizon, wherever the horizon function Δ vanishes, including at a x cosmological horizon, which exists if the vacuum energy ρ is positive.

The acceleration κ satisfies Λ 1dΔ κ=− x .

(25.3) 2 dx The acceleration κ vanishes when the horizon is extremal, that is, where two horizons merge into one, which happens when the horizon function Δ is not only zero but also an extremum.

x Equation (25.1) can be recast as d(M +ρ V)= dA+ΦdQ+ωdJ −p dV , (25.4) Λ 8πκ Λ in which the energy within the horizon is taken to be the energy M +ρ V including the contribution from Λ vacuum energy.

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:
- 11 December1998 M 2of2 3/11/9910:04
- The Office ofNaval Research (ONR) has statedthattheuse offorce fields to makeaship and her crew invisibledoes not conform to knownphysical laws.
- Andrew Furuseth left Norfolk withConvoy UGS-22 on25 Octoberand arrived at Oran on 12 November.
- Albert Einstein's Unified FieldTheory was nevercompleted.
- RAINBOW V, the plan ineffect on 7 December 1941 whenJapan attackedPearl Harbor, was the planthe U.S.

The Office ofNaval Research (ONR) has statedthattheuse offorce fields to makeaship and her crew invisibledoes not conform to knownphysical laws.

Andrew Furuseth left Norfolk withConvoy UGS-22 on25 Octoberand arrived at Oran on 12 November.

Albert Einstein's Unified FieldTheory was nevercompleted.

RAINBOW V, the plan ineffect on 7 December 1941 whenJapan attackedPearl Harbor, was the planthe U.S.

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:
- total energy requirement that would likely outweigh reduced real-estate.
- Sloppy warp fields would appear to be “easier” to engineer than precise warp fields.
- Some additional appealing characteristics of the metric is that the proper acceleration α is zero, meaning there is no acceleration felt in the flat space-time volume inside the warp bubble when the field is turned on, and the coordinate

total energy requirement that would likely outweigh reduced real-estate.

Sloppy warp fields would appear to be “easier” to engineer than precise warp fields.

Some additional appealing characteristics of the metric is that the proper acceleration α is zero, meaning there is no acceleration felt in the flat space-time volume inside the warp bubble when the field is turned on, and the coordinate

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:
- Correct combination of the wave functions in the rotating basis again gave an antisymmetrized, entangled function Eq.(29).
- ψ ψ   C  s x 'c i n o  s α   α c  o  s  C α y1  's ψ i n '3  α    s  i n C α x 's  c i n o s  α  α    ψ C '4 y2 'c  o s c  o α s    2 ψ α  ψ '1  s i n 2  α  ψ '2 (27) However Eq.(27) no longer represented an orthogonal function which is needed to form entangled states.
- C y2 x2 ψ ψ ψ ψ   C C y1 y1 C C x2 y2 ψ ψ (26) The first two wave functions represent photons excited in orthogonal directions, while the latter two represent photons excited in the same direction.
- A qubit is a two quantum state system, where the two states need to have the properties for coherence and superposition leading to Qα0β1.
- 1   1  x y y x φ 1  ψ 1  ψ 2  C 1 C 2 C 1 C 2 ψ 0 (28) 2 2 5 A qubit is the quantum analog of a classical bit.

Correct combination of the wave functions in the rotating basis again gave an antisymmetrized, entangled function Eq.(29).

ψ ψ   C  s x 'c i n o  s α   α c  o  s  C α y1  's ψ i n '3  α    s  i n C α x 's  c i n o s  α  α    ψ C '4 y2 'c  o s c  o α s    2 ψ α  ψ '1  s i n 2  α  ψ '2 (27) However Eq.(27) no longer represented an orthogonal function which is needed to form entangled states.

C y2 x2 ψ ψ ψ ψ   C C y1 y1 C C x2 y2 ψ ψ (26) The first two wave functions represent photons excited in orthogonal directions, while the latter two represent photons excited in the same direction.

A qubit is a two quantum state system, where the two states need to have the properties for coherence and superposition leading to Qα0β1.

1   1  x y y x φ 1  ψ 1  ψ 2  C 1 C 2 C 1 C 2 ψ 0 (28) 2 2 5 A qubit is the quantum analog of a classical bit.

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:
- (1.23) ThisstatecanalsoberepresentedintermsoftheBlochvectorrepresentation, (cid:1)ODjψ θ,φihψ θ,φj (cid:1) (cid:2) 1 1 cosθ sinθe(cid:2)iφ D 1C 2 2 sinθeCiφ (cid:1)cosθ (cid:1) (cid:2) 1 1Cs s (cid:1)is 1 D 3 1 2 D (1Cs(cid:3)σ), (1.24) 2 s Cis 1(cid:1)s 2 1 2 3 withσ D(σ ,σ ,σ )T,thePaulimatrices 1 2 3 (cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2) 0 1 0 (cid:1)i 1 0 σ D , σ D , σ D , (1.25) 1 1 0 2 i 0 3 0 (cid:1)1 and sD(s ,s ,s )D(sinθcosφ,sinθsinφ,cosθ).
- 12 1 IntroductiontoQuantumInformationProcessing manifestinthevonNeumannentropyofastate, S((cid:1)O)(cid:2)(cid:1)Tr(cid:1)Olog(cid:1)O " # X X X D(cid:1)Tr (cid:1) jψ ihψ j (log(cid:1))jψ ihψ j D(cid:1) (cid:1) log(cid:1) .
- Throughout,we willinterchangeablyuse fσ ,σ ,σ g, fσ ,σ ,σ g, 1 2 3 x y z andfX,Y,Zg,respectively,toexpressthePaulimatricesandoperators(whereY D iXZ).
- 1.2.1 Qubit Weshallnowconsiderspecificquantumstatesastheyaretypicallyusedinquantum information.In a two-dimensionalHilbert space, a general pure qubit state canbewrittenas jψ θ,φiDcos(θ/2)j0iCsin(θ/2)eiφ j1i.
- The vector’s tip lies on the surface of the Blochsphere,representing apurestatewithjsj D 1.Formixedstates,wewould havejsj < 1.

(1.23) ThisstatecanalsoberepresentedintermsoftheBlochvectorrepresentation, (cid:1)ODjψ θ,φihψ θ,φj (cid:1) (cid:2) 1 1 cosθ sinθe(cid:2)iφ D 1C 2 2 sinθeCiφ (cid:1)cosθ (cid:1) (cid:2) 1 1Cs s (cid:1)is 1 D 3 1 2 D (1Cs(cid:3)σ), (1.24) 2 s Cis 1(cid:1)s 2 1 2 3 withσ D(σ ,σ ,σ )T,thePaulimatrices 1 2 3 (cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2) 0 1 0 (cid:1)i 1 0 σ D , σ D , σ D , (1.25) 1 1 0 2 i 0 3 0 (cid:1)1 and sD(s ,s ,s )D(sinθcosφ,sinθsinφ,cosθ).

12 1 IntroductiontoQuantumInformationProcessing manifestinthevonNeumannentropyofastate, S((cid:1)O)(cid:2)(cid:1)Tr(cid:1)Olog(cid:1)O " # X X X D(cid:1)Tr (cid:1) jψ ihψ j (log(cid:1))jψ ihψ j D(cid:1) (cid:1) log(cid:1) .

Throughout,we willinterchangeablyuse fσ ,σ ,σ g, fσ ,σ ,σ g, 1 2 3 x y z andfX,Y,Zg,respectively,toexpressthePaulimatricesandoperators(whereY D iXZ).

1.2.1 Qubit Weshallnowconsiderspecificquantumstatesastheyaretypicallyusedinquantum information.In a two-dimensionalHilbert space, a general pure qubit state canbewrittenas jψ θ,φiDcos(θ/2)j0iCsin(θ/2)eiφ j1i.

The vector’s tip lies on the surface of the Blochsphere,representing apurestatewithjsj D 1.Formixedstates,wewould havejsj < 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:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- A super-extremal blackholehasnohorizons.
- After tetrads it will emerge that, in the Boyer-Lindquist tetrad, the Einstein tensor is diagonal, and that the proper density ρ, the proper radial pressure p , and the proper transverse pressure p in that frame are (do not confuse the r ⊥ notation ρ for proper density with the radial parameter ρ, equation (9.2), of the Boyer-Lindquist metric) Q2 ρ=−p =p = .
- 9.13 Energy-momentum tensor The coordinate-frame Einstein tensor of the Kerr-Newman geometry in Boyer-Lindquist coordinates is a bit of a mess.
- The energy-momentum is that of an electric field produced by a charge Q seemingly located at the ring singularity.
- A super-extremal black hole has a naked ring singularity, and CTCs in a sisytube unhidden by a horizon.

After tetrads it will emerge that, in the Boyer-Lindquist tetrad, the Einstein tensor is diagonal, and that the proper density ρ, the proper radial pressure p , and the proper transverse pressure p in that frame are (do not confuse the r ⊥ notation ρ for proper density with the radial parameter ρ, equation (9.2), of the Boyer-Lindquist metric) Q2 ρ=−p =p = .

9.13 Energy-momentum tensor The coordinate-frame Einstein tensor of the Kerr-Newman geometry in Boyer-Lindquist coordinates is a bit of a mess.

The energy-momentum is that of an electric field produced by a charge Q seemingly located at the ring singularity.

A super-extremal black hole has a naked ring singularity, and CTCs in a sisytube unhidden by a horizon.

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:
- We move slowly down the stairs toward the generator room, our footfalls echoing through the vast, open space.
- There’s no oxygen in the room.
- “One million percent.” With Charlie and Daniela clinging to me, I slowly descend the last few steps and start across the broken concrete.
- I hear Daniela let out a trembling breath.
- Daniela says, “We’re not running.” She pulls the gun out of my waistband and links her arm through mine.

We move slowly down the stairs toward the generator room, our footfalls echoing through the vast, open space.

“One million percent.” With Charlie and Daniela clinging to me, I slowly descend the last few steps and start across the broken concrete.

I hear Daniela let out a trembling breath.

Daniela says, “We’re not running.” She pulls the gun out of my waistband and links her arm through mine.

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:
- 16.5 Electromagnetic action 421 of freedom.
- Some of Dirac’s constraint equations, which Dirac calls “first-class constraints,” are of this character, but others, which Dirac calls “second-class constraints,” are identities that effectively define some fields in terms of others.
- Since the equations of motion (16.46b) already determine completely the spatial coordinates A , the α α identities(16.47b)cannotbeindependentequations,butmustbeinterpretedasdefiningthemagneticfieldas anauxiliaryfieldthatdoesnotrepresentadditionalphysicaldegreesoffreedom.Themagneticfieldisneeded as part of the equations of motion, the second term on the left hand side of the equation of motion (16.46a).
- (16.47b) α β β α αβ The first equation (16.47a) has the property that, as long as the equation is satisfied on the initial spatial hypersurface, then conservation of electric charge ensures that the equation continues to be satisfied thereafter.
- The magnetic field could be discarded after having been replaced by the curl of A

16.5 Electromagnetic action 421 of freedom.

Some of Dirac’s constraint equations, which Dirac calls “first-class constraints,” are of this character, but others, which Dirac calls “second-class constraints,” are identities that effectively define some fields in terms of others.

Since the equations of motion (16.46b) already determine completely the spatial coordinates A , the α α identities(16.47b)cannotbeindependentequations,butmustbeinterpretedasdefiningthemagneticfieldas anauxiliaryfieldthatdoesnotrepresentadditionalphysicaldegreesoffreedom.Themagneticfieldisneeded as part of the equations of motion, the second term on the left hand side of the equation of motion (16.46a).

(16.47b) α β β α αβ The first equation (16.47a) has the property that, as long as the equation is satisfied on the initial spatial hypersurface, then conservation of electric charge ensures that the equation continues to be satisfied thereafter.

The magnetic field could be discarded after having been replaced by the curl of A

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:
- The multiverse exists because every choice we make creates a fork in the road, which leads into a parallel world.
- And eventually, we parted ways.
- We talked more, especially at dinner.
- “So there’s a version of our life where we didn’t keep the baby.
- And he traded my life for his.” The look on Daniela’s face is pure shock and disgust.

The multiverse exists because every choice we make creates a fork in the road, which leads into a parallel world.

“So there’s a version of our life where we didn’t keep the baby.

And he traded my life for his.” The look on Daniela’s face is pure shock and disgust.

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:
- “A Measurement of Excess Antenna Temperature at 4080 Mc/s”.
- Battelle Rencontres: 1967 lectures in mathematics and physics.
- doi: 10.1017/S0305004100033776 (cit.
- “Conformal treatment of infinity”.
- “La mécanique classique et la théorie de la relativité”.

“A Measurement of Excess Antenna Temperature at 4080 Mc/s”.

Battelle Rencontres: 1967 lectures in mathematics and physics.

“La mécanique classique et la théorie de la relativité”.

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:
- Rotationsaredefinedaslineartransformationsdx(cid:3)(cid:5)=Rdx(cid:3)thatleavedsunchanged.The preceding discussion allows us to write this condition as RTR=I.
- FromNewtontoRiemann:CoordinatestoCurvature thefactthat,forexample,Maxwellcouldseethroughthemorassoftheelectromagnetic equationswrittenoutcomponentbycomponent.
- As before, we want tofocusonrotationsbyimposingtheadditionalconditiondetR=1.ThesetofD-by-D matricesR thatsatisfythesetwoconditionsformsthesimpleorthogonalgroupSO(D), whichisjustafancywayofsayingtherotationgroupinD-dimensionalspace.
- SoletusfollowLieandwriteR(cid:16)I +A.ThenRTR=IissolvedbyrequiringA=−AT, namely that A must be antisymmetric.
- ThethreematricesJ ,J ,J areknownasthegeneratorsofthe3-dimensionalrotation x y z groupSO(3).Theygeneraterotations,butareofcoursenottobeconfusedwithrotations, whicharebydefinition3-by-3orthogonalmatriceswithdeterminantequalto1.

Rotationsaredefinedaslineartransformationsdx(cid:3)(cid:5)=Rdx(cid:3)thatleavedsunchanged.The preceding discussion allows us to write this condition as RTR=I.

As before, we want tofocusonrotationsbyimposingtheadditionalconditiondetR=1.ThesetofD-by-D matricesR thatsatisfythesetwoconditionsformsthesimpleorthogonalgroupSO(D), whichisjustafancywayofsayingtherotationgroupinD-dimensionalspace.

SoletusfollowLieandwriteR(cid:16)I +A.ThenRTR=IissolvedbyrequiringA=−AT, namely that A must be antisymmetric.

ThethreematricesJ ,J ,J areknownasthegeneratorsofthe3-dimensionalrotation x y z groupSO(3).Theygeneraterotations,butareofcoursenottobeconfusedwithrotations, whicharebydefinition3-by-3orthogonalmatriceswithdeterminantequalto1.

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:
- (33.43) dη ∂η a As long as the particles are relativistic, the particle velocity is one, v =1; but equation (33.43) allows for a general non-unit velocity v to accommodate neutrinos, which have small masses.
- (33.45) In Fourier space, the gravitational redshift term G, in conformal Newtonian gauge and including only scalar fluctuations, is, equation (33.23), ikμ G=Φ ̇ + Ψ .
- 886 Cosmological perturbations: Boltzmann treatment Two of the terms on the left hand side of the perturbed Boltzmann equation (33.21) rearrange to 1 1 0 [( ) 0 ] ∂f dlnp ∂f ∂f dlnT ∂ a ̇ ∂ ∂f + = Θ ̇ + − Θ ∂η dη ∂lnp ∂lnT dη ∂lnT a∂lnp ∂lnT 0 [ 0 ] ∂f dln(aT)∂ln(∂f/∂lnT) = Θ ̇ + Θ .
- FouriertransformingtheBoltzmannequation(33.43)overspatialpositionxyieldstheBoltzmannequation for the Fourier components Θ(η,k,p) of the temperature fluctuation, dΘ ∂Θ = −ivkμΘ−G=C[Θ] , (33.44) dη ∂η where μ is the cosine of the angle between the wavevector k and the photon momentum p, μ≡k^·p^.
- The Boltzmann equation (33.42) then reduces to dΘ ∂Θ = +va∇ Θ−G=C[Θ] .

(33.43) dη ∂η a As long as the particles are relativistic, the particle velocity is one, v =1; but equation (33.43) allows for a general non-unit velocity v to accommodate neutrinos, which have small masses.

(33.45) In Fourier space, the gravitational redshift term G, in conformal Newtonian gauge and including only scalar fluctuations, is, equation (33.23), ikμ G=Φ ̇ + Ψ .

886 Cosmological perturbations: Boltzmann treatment Two of the terms on the left hand side of the perturbed Boltzmann equation (33.21) rearrange to 1 1 0 [( ) 0 ] ∂f dlnp ∂f ∂f dlnT ∂ a ̇ ∂ ∂f + = Θ ̇ + − Θ ∂η dη ∂lnp ∂lnT dη ∂lnT a∂lnp ∂lnT 0 [ 0 ] ∂f dln(aT)∂ln(∂f/∂lnT) = Θ ̇ + Θ .

FouriertransformingtheBoltzmannequation(33.43)overspatialpositionxyieldstheBoltzmannequation for the Fourier components Θ(η,k,p) of the temperature fluctuation, dΘ ∂Θ = −ivkμΘ−G=C[Θ] , (33.44) dη ∂η where μ is the cosine of the angle between the wavevector k and the photon momentum p, μ≡k^·p^.

The Boltzmann equation (33.42) then reduces to dΘ ∂Θ = +va∇ Θ−G=C[Θ] .

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:
- The surface gravity of A is extremely intense, and the matter it gains undergoes a sudden compression.
- As B expands toward the red-giant stage, it returns the gift: Some of its matter spills over toward A, which is now a white dwarf.
- EXPLODING MATTER 131 giant stage, some of its matter may spill over to B, which is as yet unexpanded.
- Since the gained matter will contain some atoms capable of fusion, the compression may eventually produce a very rapid nuclear reaction once enough is gathered and once it is sufficiently compressed.
- Sirius A and Sirius B would be a good example of this scenario if they were closer together.

The surface gravity of A is extremely intense, and the matter it gains undergoes a sudden compression.

As B expands toward the red-giant stage, it returns the gift: Some of its matter spills over toward A, which is now a white dwarf.

EXPLODING MATTER 131 giant stage, some of its matter may spill over to B, which is as yet unexpanded.

Since the gained matter will contain some atoms capable of fusion, the compression may eventually produce a very rapid nuclear reaction once enough is gathered and once it is sufficiently compressed.

Sirius A and Sirius B would be a good example of this scenario if they were closer together.

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:
- 11.18 Expressions with torsion 309 Einstein’s equations: G =8πGT .
- (11.84) km 11.18 Expressions with torsion If torsion does not vanish, then the Riemann tensor, and consequently also the Ricci and Einstein tensors, canbesplitintotorsion-free(distinguishedbya ̊overscript)andtorsionparts(e.g.Hehl,Heyde,andKerlick 1976).AsimilarsplitoccursintheADMformalismwhereacertaingaugechoice(fixingthetimecomponent γγ ofthetetradtobeorthogonaltohypersurfacesofconstanttime)splitsthetetradconnectionintoatensor part, the extrinsic curvature, and a remainder, equation (17.27).
- (11.88) n mpn n The antisymmetric part of the Einstein tensor is, from contracting equation (11.68), ( ) G =R = 3R l = 3 D Sl +Sp Sl , (11.89) [km] [km] 2 [klm] 2 [k lm] [kl m]p
- (11.86) klmn klmn k mnl l mnk ml pnk mk pnl The Ricci tensor is R =R ̊ −D ̊ K −D ̊nK +K Knp −K Kp , (11.87) km km k m mnk mpn k mpk and the Ricci scalar is R=R ̊−2D ̊ Kn+K Knpm−K Kn .
- (11.82) km km 2 km Bianchi identities in the absence of torsion: D R +D R +D R =0 , (11.83) k lmnp l mknp m klnp which most importantly imply covariant conservation of the Einstein tensor, hence conservation of energymomentum DkT =0 .

11.18 Expressions with torsion 309 Einstein’s equations: G =8πGT .

(11.84) km 11.18 Expressions with torsion If torsion does not vanish, then the Riemann tensor, and consequently also the Ricci and Einstein tensors, canbesplitintotorsion-free(distinguishedbya ̊overscript)andtorsionparts(e.g.Hehl,Heyde,andKerlick 1976).AsimilarsplitoccursintheADMformalismwhereacertaingaugechoice(fixingthetimecomponent γγ ofthetetradtobeorthogonaltohypersurfacesofconstanttime)splitsthetetradconnectionintoatensor part, the extrinsic curvature, and a remainder, equation (17.27).

(11.88) n mpn n The antisymmetric part of the Einstein tensor is, from contracting equation (11.68), ( ) G =R = 3R l = 3 D Sl +Sp Sl , (11.89) [km] [km] 2 [klm] 2 [k lm] [kl m]p

(11.86) klmn klmn k mnl l mnk ml pnk mk pnl The Ricci tensor is R =R ̊ −D ̊ K −D ̊nK +K Knp −K Kp , (11.87) km km k m mnk mpn k mpk and the Ricci scalar is R=R ̊−2D ̊ Kn+K Knpm−K Kn .

(11.82) km km 2 km Bianchi identities in the absence of torsion: D R +D R +D R =0 , (11.83) k lmnp l mknp m klnp which most importantly imply covariant conservation of the Einstein tensor, hence conservation of energymomentum DkT =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:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- BlackHoles V V = U r = 0 line of constant t line of constant r U V = –U (a) V observer r = 0 escapes r = M r = 3M light signal no escape after this point U M = r observer falling toward black hole (b) Figure5 Kruskal-SzekeresdiagramoftheSchwarzschildblackhole.(a)Note thelinesofconstanttandr.(b)Asindicatedbythedashedline,anobserver fallingintoablackholecanescapebeforereachingthehorizonV =U.
- Acommonmisconceptionalert!Thelinesofconstantr arenotgeodesics.Tohoverat constantroutsideablackholerequiresconstantandcarefulfiringofarocketpackstrapped toyourback.(Keepinmindalsothattheangularcoordinatesθ,φaresuppressed,andso eachpointinfigure5correspondstoaunitsphere.)

BlackHoles V V = U r = 0 line of constant t line of constant r U V = –U (a) V observer r = 0 escapes r = M r = 3M light signal no escape after this point U M = r observer falling toward black hole (b) Figure5 Kruskal-SzekeresdiagramoftheSchwarzschildblackhole.(a)Note thelinesofconstanttandr.(b)Asindicatedbythedashedline,anobserver fallingintoablackholecanescapebeforereachingthehorizonV =U.

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:
- that behaves similarly to what is expected from the Higgs boson.[9] The Standard Model, as currently formulated, has 61 elementary particles.[10] Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s.
- The Standard Model has been found to agree with almost all the experimental tests conducted to date.
- However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery (See Theory of Everything).
- In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model, since neutrinos do not have mass in the Standard Model.[11]

that behaves similarly to what is expected from the Higgs boson.[9] The Standard Model, as currently formulated, has 61 elementary particles.[10] Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s.

The Standard Model has been found to agree with almost all the experimental tests conducted to date.

However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery (See Theory of Everything).

In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model, since neutrinos do not have mass in the Standard Model.[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:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- (16.84) Dropping the total derivative term d α (*F α ̄ ∧A t ̄) from the Lagrangian (16.84), and inserting the rest into the defining equation (16.83) yields the conventional Hamiltonian H = π [ (d*F −4π *j) α ̄ ∧A t ̄− *F t ̄∧(dA−F) α ̄ + 1 *F α ̄ ∧F t ̄− 1*F t ̄∧F α ̄ −4π *j t ̄∧A α ̄ ] .
- The final term −j·Ad4x is an interaction term.
- Both terms vanish on the equations of motion.
- One should think of A (xα) and *F (xα) β βγ as being infinite collections of fields indexed by the spatial position xα; the spatial derivatives of the fields are then effectively linear combinations of those fields.
- 428 Action principle for electromagnetism and gravity The combined electromagnetic and charged interaction Lagrangian (16.59) can be written L= π [ d α (*F α ̄ ∧A t ̄)+ *F α ̄ ∧d t A − (d*F −4π *j) α ̄ ∧A t ̄+ *F t ̄∧(dA−F) α ̄ − 1 *F α ̄ ∧F t ̄+ 1*F t ̄∧F α ̄ +4π *j t ̄∧A α ̄ ] .

(16.84) Dropping the total derivative term d α (*F α ̄ ∧A t ̄) from the Lagrangian (16.84), and inserting the rest into the defining equation (16.83) yields the conventional Hamiltonian H = π [ (d*F −4π *j) α ̄ ∧A t ̄− *F t ̄∧(dA−F) α ̄ + 1 *F α ̄ ∧F t ̄− 1*F t ̄∧F α ̄ −4π *j t ̄∧A α ̄ ] .

The final term −j·Ad4x is an interaction term.

Both terms vanish on the equations of motion.

One should think of A (xα) and *F (xα) β βγ as being infinite collections of fields indexed by the spatial position xα; the spatial derivatives of the fields are then effectively linear combinations of those fields.

428 Action principle for electromagnetism and gravity The combined electromagnetic and charged interaction Lagrangian (16.59) can be written L= π [ d α (*F α ̄ ∧A t ̄)+ *F α ̄ ∧d t A − (d*F −4π *j) α ̄ ∧A t ̄+ *F t ̄∧(dA−F) α ̄ − 1 *F α ̄ ∧F t ̄+ 1*F t ̄∧F α ̄ +4π *j t ̄∧A α ̄ ] .

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 reports outlined the history of pre-revolutionary (Czarist) Russian, and WWII and post-WWII era Soviet R&D on psychotronics, human mind/behavior control, and the entire spectrum of parapsychology.
- Another DIA report lists the names and affiliations of all the researchers, as well as the names of the various Soviet and Warsaw Pact research centers, that were involved.
- The researchers were amazed by their repeated results, and were barely able to fathom the altered “state of being” that test specimens underwent during teleportation.
- The Chinese were unable to offer any significant physics hypothesis that could explain their results.
- One DIA report noted that there was an East versus West science debate in the Soviet literature over whether paranormal phenomenon and related experimental data was real or even scientifically sound in comparison to western scientific practice and philosophy.

The reports outlined the history of pre-revolutionary (Czarist) Russian, and WWII and post-WWII era Soviet R&D on psychotronics, human mind/behavior control, and the entire spectrum of parapsychology.

Another DIA report lists the names and affiliations of all the researchers, as well as the names of the various Soviet and Warsaw Pact research centers, that were involved.

The researchers were amazed by their repeated results, and were barely able to fathom the altered “state of being” that test specimens underwent during teleportation.

The Chinese were unable to offer any significant physics hypothesis that could explain their results.

One DIA report noted that there was an East versus West science debate in the Soviet literature over whether paranormal phenomenon and related experimental data was real or even scientifically sound in comparison to western scientific practice and philosophy.

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:
- Theories of the World from Antiquity to the Copernican Revolution (http s://books.google.com/books?id=IGlhN0MI87oC).
- Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols., Paris: Hermann, 1959.
- Mineola, NY: Dover Publications, Inc.
- New York: Robert Appleton Company, 1911.
- Heavenly Spheres, in Great Books of the Western World : 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952 Crowe, Michael J.

Theories of the World from Antiquity to the Copernican Revolution (http s://books.google.com/books?id=IGlhN0MI87oC).

Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols., Paris: Hermann, 1959.

New York: Robert Appleton Company, 1911.

Heavenly Spheres, in Great Books of the Western World : 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952 Crowe, Michael J.

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:
- Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .
- (23.56) a2sin4θ Solutions at any polar angle θ and any angular momentum L exist, ranging from E = ±m at L = 0, to E = ±L/(asin2θ) at L → ±∞.
- (23.54) Constant latitude orbits occur where the angular potential P2, equation (23.10b), not only vanishes, but is y an extremum, dP2 P2 = y =0 , (23.55) y dy the derivative being taken with the constants of motion E, L, and K of the orbit being held fixed.
- 674 Trajectories in ideal rotating black holes 23.9 Constant latitude trajectories in the Kerr-Newman geometry For simplicity, the next several sections, up to and including §23.20, are restricted to Kerr-Newman black holes with zero magnetic charge, Q =0, and zero cosmological constant, Λ=0.
- The solutions with L = 0 are those of the freely-falling observers that define the Doran coordinate system, §9.18.

Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .

(23.56) a2sin4θ Solutions at any polar angle θ and any angular momentum L exist, ranging from E = ±m at L = 0, to E = ±L/(asin2θ) at L → ±∞.

(23.54) Constant latitude orbits occur where the angular potential P2, equation (23.10b), not only vanishes, but is y an extremum, dP2 P2 = y =0 , (23.55) y dy the derivative being taken with the constants of motion E, L, and K of the orbit being held fixed.

674 Trajectories in ideal rotating black holes 23.9 Constant latitude trajectories in the Kerr-Newman geometry For simplicity, the next several sections, up to and including §23.20, are restricted to Kerr-Newman black holes with zero magnetic charge, Q =0, and zero cosmological constant, Λ=0.

The solutions with L = 0 are those of the freely-falling observers that define the Doran coordinate system, §9.18.

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:
- 16.17 Bianchi identities in multivector forms notation 487 16.17.8 Interpretation of the contracted Bianchi identities The contracted torsion Bianchi identity (16.406a) is the 1N(N−1)-component conservation law associated with invariance of the gravitational Lagrangian under Lorentz transformations.
- The contracted Riemann identity(16.406b),orequivalently(16.408),istheN-componentconservationlawassociatedwithinvariance of the gravitational Lagrangian under coordinate transformations.
- The contracted torsion Bianchi identity (16.406a) enforces continued satisfaction of the Gaussian constraint (16.310a).
- The contracted Riemann Bianchi identity (16.406b) enforces continued satisfaction of the Hamiltonian constraint (16.310b).

16.17 Bianchi identities in multivector forms notation 487 16.17.8 Interpretation of the contracted Bianchi identities The contracted torsion Bianchi identity (16.406a) is the 1N(N−1)-component conservation law associated with invariance of the gravitational Lagrangian under Lorentz transformations.

The contracted Riemann identity(16.406b),orequivalently(16.408),istheN-componentconservationlawassociatedwithinvariance of the gravitational Lagrangian under coordinate transformations.

The contracted torsion Bianchi identity (16.406a) enforces continued satisfaction of the Gaussian constraint (16.310a).

The contracted Riemann Bianchi identity (16.406b) enforces continued satisfaction of the Hamiltonian constraint (16.310b).

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:
- The mass m is the mass of each of the 2 right-handed weak gauge bosons after Spin(5)×Spin(6) symmetry W breaking; the mass is different from the mass of the 2 left-handed charged weak gauge bosons.
- The mass m is the mass of each of the 6 leptoquark gauge bosons after Spin(5)×Spin(6) symmetry breaking.
- field E generates masses for the non-commuting fields, √ √ m =gsin3θ ⟨E⟩ , m = 2gsin3θ ⟨E⟩ , m = 2 2gcos3θ ⟨E⟩ .
- A C prediction of the model is that the masses m , m , and m are related by H W C √ 2m =m = 3m tan3θ .
- This mass m is different from the mass m of the electroweak H H Higgs boson after electroweak symmetry breaking, because the masses are generated in different ways.

The mass m is the mass of each of the 2 right-handed weak gauge bosons after Spin(5)×Spin(6) symmetry W breaking; the mass is different from the mass of the 2 left-handed charged weak gauge bosons.

The mass m is the mass of each of the 6 leptoquark gauge bosons after Spin(5)×Spin(6) symmetry breaking.

field E generates masses for the non-commuting fields, √ √ m =gsin3θ ⟨E⟩ , m = 2gsin3θ ⟨E⟩ , m = 2 2gcos3θ ⟨E⟩ .

A C prediction of the model is that the masses m , m , and m are related by H W C √ 2m =m = 3m tan3θ .

This mass m is different from the mass m of the electroweak H H Higgs boson after electroweak symmetry breaking, because the masses are generated in different 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:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Springer International Publishing.
- "Dark energy: back to Newton?".
- Three Body Dynamics and Its Applications to Exoplanets (https://books.google.com/books?id=D90tDwAAQBAJ&pg=PA3).
- Brackenridge, John Bruce (1996).
- Physical Chemistry: Multidisciplinary Applications in Society (https://b ooks.google.com/books?id=4WGdBgAAQBAJ&pg=PA251).

Three Body Dynamics and Its Applications to Exoplanets (https://books.google.com/books?id=D90tDwAAQBAJ&pg=PA3).

Physical Chemistry: Multidisciplinary Applications in Society (https://b ooks.google.com/books?id=4WGdBgAAQBAJ&pg=PA251).

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:
- Psychological science in the courtroom: Consensus and controversies.
- How warnings about false claims become recommendations.
- Behaviour Research and Therapy, 11, 599–618.
- Teaching of Psychology, 10, 220–222.
- Taking stock of criminal profiling: A narrative review and meta-analysis.

Psychological science in the courtroom: Consensus and controversies.

How warnings about false claims become recommendations.

Behaviour Research and Therapy, 11, 599–618.

Taking stock of criminal profiling: A narrative review and meta-analysis.

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 global gauge freedoms mean that the scalar and vector perturbations Ψ, Φ, and W are gauge-invariant only up to the a addition of spatially uniform functions of time.
- a a The freedoms are global in the sense that they are spatially uniform functions of time η.
- The tensor perturbation h remains fully gauge-invariant.
- (29.14d) a2 0 a a a a a a a ab ab Eliminating the coordinate shift ε from the transformations (29.14) yields 12 coordinate gauge-invariant m combinations of the perturbations, ( ∂ a ̇) a ̇ ψ− + w ̃ , w−h ̇ , w −h ̇ , w ̃ , φ+ w ̃ , h ̃ , h ̃ , h .
- (29.15) ∂η a scalar v a ector a vect a or a scalar vect a or ten a s b or scalar scalar Six combinations of these coordinate gauge-invariant perturbations depend only on the symmetric part φ +φ of the vierbein perturbations, and are therefore tetrad gauge-invariant as well as coordinate mn nm gauge-invariant.

The global gauge freedoms mean that the scalar and vector perturbations Ψ, Φ, and W are gauge-invariant only up to the a addition of spatially uniform functions of time.

a a The freedoms are global in the sense that they are spatially uniform functions of time η.

The tensor perturbation h remains fully gauge-invariant.

(29.14d) a2 0 a a a a a a a ab ab Eliminating the coordinate shift ε from the transformations (29.14) yields 12 coordinate gauge-invariant m combinations of the perturbations, ( ∂ a ̇) a ̇ ψ− + w ̃ , w−h ̇ , w −h ̇ , w ̃ , φ+ w ̃ , h ̃ , h ̃ , h .

(29.15) ∂η a scalar v a ector a vect a or a scalar vect a or ten a s b or scalar scalar Six combinations of these coordinate gauge-invariant perturbations depend only on the symmetric part φ +φ of the vierbein perturbations, and are therefore tetrad gauge-invariant as well as coordinate mn nm gauge-invariant.

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:
- Electron Mass • Frank Wilczek, Nobel laureate: “We have achieved a beautiful and profound understanding of the origin of most of the mass of ordinary matter, but not of all of it.
- The value of the electron mass, in particular, remains deeply mysterious...” • Consider the energy state of the perturbed quantum vacuum field around the proton, and set this equal to the kinetic energy of the orbiting electron at the ground state.
- 4 1 a 3 c2 m v2 0 v_local e 3 2 • We know the speed of the orbiting electron: v c c/137 • We can solve for the electron mass, and using the predicted value for of 3.9x10-5 kg/m3, we get a predicted electron mass of 9.1x10-31kg.
- v_local a 3 c2 0 v_local m e 2 c Dr.

Electron Mass • Frank Wilczek, Nobel laureate: “We have achieved a beautiful and profound understanding of the origin of most of the mass of ordinary matter, but not of all of it.

The value of the electron mass, in particular, remains deeply mysterious...” • Consider the energy state of the perturbed quantum vacuum field around the proton, and set this equal to the kinetic energy of the orbiting electron at the ground state.

4 1 a 3 c2 m v2 0 v_local e 3 2 • We know the speed of the orbiting electron: v c c/137 • We can solve for the electron mass, and using the predicted value for of 3.9x10-5 kg/m3, we get a predicted electron mass of 9.1x10-31kg.

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 Einstein equation(20.62b)inthecentre-of-massframe,f =0,is∂ β −h β =0,whichwiththeEinsteinequations(20.94) 0 1 0 0 of the shell implies ( ) ( 2β ) 0=∂ [β ]+−β [h ]+ =−4π ∂ (rρ“)+β (ρ“+2p“ ) =−4πr ∂ ρ“+ 0(ρ“+p“ ) .
- (20.107) 0 0 The two equations (20.107) may be recast as evolution equations for the total mass M“ ≡[M]+ of the shell − and for the average interior mass M ̄ , ∂ M“ +4πr2[p]+β =0 , (20.108a) 0 − 0 ∂ M ̄ +4πr2p ̄β =0 , (20.108b) 0 0 where [p]+ and p ̄≡ 1(p−+p+) are respectively the difference and average of the external radial pressures − 2 p± on the shell.
- (20.105) 0 1 − 0 0 − 0 0 ⊥ 0 r ⊥ Equation (20.105) implies that the proper mass-energy m“ of the shell evolves as ∂ m“ +8πrp“ β =0 , (20.106) 0 ⊥ 0 whichlookslikethefirstlawofthermodynamicsintheform∂ m“ +p“ ∂ A=0whereA≡4πr2 istheproper 0 ⊥ 0 area of the shell.
- However, evolution equations for β , β±, and β ̄ can be deduced directly, either from the evolution equations for the masses, or 0 1 1 from the Einstein equations (20.62), M± ∂ β =β±h±− −4πrp± (20.109a) 0 0 1 0 r2 M ̄ m“2 2πm“p“ =β ̄ h ̄ − − −4πrp ̄− ⊥ , (20.109b) 1 0 r2 4r3 r ∂ β± =β h± , (20.109c) 0 1 0 0 M“ ∂ β ̄ =∂ =β h ̄ , (20.109d) 0 1 0m“ 0 0 where h± are proper accelerations experienced by observers in the tetrad frame on each side of the shell, and h ̄ is their average,
- 592 General spherically symmetric spacetimes Evolution equations for the various energies per unit mass β and for the velocity β follow from evolu1 0 tion equations for the proper mass m“ of the shell and for the various interior masses.

The Einstein equation(20.62b)inthecentre-of-massframe,f =0,is∂ β −h β =0,whichwiththeEinsteinequations(20.94) 0 1 0 0 of the shell implies ( ) ( 2β ) 0=∂ [β ]+−β [h ]+ =−4π ∂ (rρ“)+β (ρ“+2p“ ) =−4πr ∂ ρ“+ 0(ρ“+p“ ) .

(20.107) 0 0 The two equations (20.107) may be recast as evolution equations for the total mass M“ ≡[M]+ of the shell − and for the average interior mass M ̄ , ∂ M“ +4πr2[p]+β =0 , (20.108a) 0 − 0 ∂ M ̄ +4πr2p ̄β =0 , (20.108b) 0 0 where [p]+ and p ̄≡ 1(p−+p+) are respectively the difference and average of the external radial pressures − 2 p± on the shell.

(20.105) 0 1 − 0 0 − 0 0 ⊥ 0 r ⊥ Equation (20.105) implies that the proper mass-energy m“ of the shell evolves as ∂ m“ +8πrp“ β =0 , (20.106) 0 ⊥ 0 whichlookslikethefirstlawofthermodynamicsintheform∂ m“ +p“ ∂ A=0whereA≡4πr2 istheproper 0 ⊥ 0 area of the shell.

However, evolution equations for β , β±, and β ̄ can be deduced directly, either from the evolution equations for the masses, or 0 1 1 from the Einstein equations (20.62), M± ∂ β =β±h±− −4πrp± (20.109a) 0 0 1 0 r2 M ̄ m“2 2πm“p“ =β ̄ h ̄ − − −4πrp ̄− ⊥ , (20.109b) 1 0 r2 4r3 r ∂ β± =β h± , (20.109c) 0 1 0 0 M“ ∂ β ̄ =∂ =β h ̄ , (20.109d) 0 1 0m“ 0 0 where h± are proper accelerations experienced by observers in the tetrad frame on each side of the shell, and h ̄ is their average,

592 General spherically symmetric spacetimes Evolution equations for the various energies per unit mass β and for the velocity β follow from evolu1 0 tion equations for the proper mass m“ of the shell and for the various interior masses.

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:
- Gallery A wormhole with no Closed timelike curves (CTC) A Roman ring with two wormholes A Roman ring with four wormholes Notes 1.
- "Traversable wormholes: the Roman ring".
- doi:10.1103/PhysRevD.55.5212 (http s://doi.org/10.1103%2FPhysRevD.55.5212).
- Bibcode:1997PhRvD..55.5212V (https://ui.adsabs.harvard.edu/abs/1997PhRvD..55.5212V).
- S2CID 2869291 (https://api.semanticscholar.org/Corp usID:2869291).

Gallery A wormhole with no Closed timelike curves (CTC) A Roman ring with two wormholes A Roman ring with four wormholes Notes 1.

"Traversable wormholes: the Roman ring".

S2CID 2869291 (https://api.semanticscholar.org/Corp usID:2869291).

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.