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

EVIDENCE:
- an assignment of a cotangent vector to each point p, by definition such that for each vector field X.
- They provide a basis for the tangent space at p.
- This operator applied to a function f gives the directional derivative of f at p in the direction of increasing x μ with x ν , ν ≠ μ fixed.
- In coordinates X can be expanded at each point p in
- The exterior derivative df of a function f is a covector field, i.e.

an assignment of a cotangent vector to each point p, by definition such that for each vector field X.

They provide a basis for the tangent space at p.

This operator applied to a function f gives the directional derivative of f at p in the direction of increasing x μ with x ν , ν ≠ μ fixed.

In coordinates X can be expanded at each point p in

The exterior derivative df of a function f is a covector field, i.e.

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:
- TheAuthors AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,authors,editors,and Prof.AkiraFurusawa publisherdonotwarranttheinformation TheUniversityofTokyo containedinthesebooks,includingthisbook,to DepartmentofAppliedPhysics befreeoferrors.Readersareadvisedtokeepin Tokyo,Japan mindthatstatements,data,illustrations, akiraf@ap.t.u-tokyo.ac.jp proceduraldetailsorotheritemsmay inadvertentlybeinaccurate.
- Dr.PetervanLoock PhysikInstitutLSfürOptik LibraryofCongressCardNo.:appliedfor InstitutTheorieI UniversitätErlangen-Nürnberg BritishLibraryCataloguing-in-PublicationData: Max-Planck-Institut(MPL) Acataloguerecordforthisbookisavailable Erlangen,Germany fromtheBritishLibrary.
- peter.vanloock@mpl.mpg.de Bibliographicinformationpublishedbythe DeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhis publicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableonthe Internetathttp://dnb.d-nb.de.
- ©2011WILEY-VCHVerlagGmbH&Co.KGaA, Boschstr.12,69469Weinheim,Germany Allrightsreserved(includingthoseoftranslation intootherlanguages).Nopartofthisbookmay bereproducedinanyform–byphotoprinting, microfilm,oranyothermeans–nortransmitted ortranslatedintoamachinelanguagewithout writtenpermissionfromthepublishers.Registerednames,trademarks,etc.usedinthisbook, evenwhennotspecificallymarkedassuch,are nottobeconsideredunprotectedbylaw.
- Typesetting le-texpublishingservicesGmbH, Leipzig PrintingandBinding FabulousPrintersPte Ltd,Singapore CoverDesign AdamDesign,Weinheim PrintedinSingapore Printedonacid-freepaper ISBN 978-3-527-40930-3

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

Chosen based on domain + required checks.

Produce bounded conclusion + next actions

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

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

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

Generate falsification tests and identify unknowns or missing evidence.

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

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

TheAuthors AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,authors,editors,and Prof.AkiraFurusawa publisherdonotwarranttheinformation TheUniversityofTokyo containedinthesebooks,includingthisbook,to DepartmentofAppliedPhysics befreeoferrors.Readersareadvisedtokeepin Tokyo,Japan mindthatstatements,data,illustrations, akiraf@ap.t.u-tokyo.ac.jp proceduraldetailsorotheritemsmay inadvertentlybeinaccurate.

Dr.PetervanLoock PhysikInstitutLSfürOptik LibraryofCongressCardNo.:appliedfor InstitutTheorieI UniversitätErlangen-Nürnberg BritishLibraryCataloguing-in-PublicationData: Max-Planck-Institut(MPL) Acataloguerecordforthisbookisavailable Erlangen,Germany fromtheBritishLibrary.

Typesetting le-texpublishingservicesGmbH, Leipzig PrintingandBinding FabulousPrintersPte Ltd,Singapore CoverDesign AdamDesign,Weinheim PrintedinSingapore Printedonacid-freepaper ISBN 978-3-527-40930-3

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Excitedly,youvarytheactionin(7)toseewhatyouget.Asalways,weparametrizewith thepropertime: (cid:7) (cid:5) (cid:7) dxμdxν dxμ S=−m dτ −η + dτA (x(τ)) (9) μν μ dτ dτ dτ Notethatinthesecondterm,A isevaluatedatthespacetimepositionxμ(τ)oftheparticle.
- μ Inotherwords,thefieldA (x)pervadesspacetime,buttheparticleonlysamplesthefield μ atitsparticularlocation.
- The variation of the first term in (9) is easy and was done in chapter III.5, which we repeathereforconvenience: (cid:15) (cid:7) (cid:5) (cid:16) (cid:7) (cid:7) dxμdxν dxμdδxν d2xμ δ −m dτ −η =m dτ η =−m dτ η δxρ (10) μν dτ dτ μν dτ dτ μρ dτ2 Noticethatinthelaststep,forlaterconvenience,wehaverenamedadummy.
- Thevariationofthesecondtermin(9)isabitmoreinvolved: (cid:7) (cid:7) !
- dxμ dδxμ dxμ δ dτA (x) = dτ A (x) +[∂ A (x)δxν] (11) μ μ ν μ dτ dτ dτ WehavetorememberthatA (x)dependsonx inordernottomissthe∂ A (x)termin μ ν μ (11).Integratethefirsttermin(11)byparts: (cid:7) (cid:7) (cid:7) dτA (x) dδxμ =− dτ dA μ (x) δxμ=− dτ∂ A (x) dxν δxμ (12) μ ν μ dτ dτ dτ Puttingthetwotermstogetherandrenamingindices,wefind (cid:7) (cid:7) dxμ dxν δ dτA (x) = dτ(∂ A −∂ A ) δxμ (13) μ μ ν ν μ dτ dτ Theantisymmetrictensorfield F (x)≡∂ A (x)−∂ A (x) (14) μν μ ν ν μ justpoppedout!Somereadersmayrecognizethisastheelectromagneticfield;ifyoudon’t, onceagainreadon.

Excitedly,youvarytheactionin(7)toseewhatyouget.Asalways,weparametrizewith thepropertime: (cid:7) (cid:5) (cid:7) dxμdxν dxμ S=−m dτ −η + dτA (x(τ)) (9) μν μ dτ dτ dτ Notethatinthesecondterm,A isevaluatedatthespacetimepositionxμ(τ)oftheparticle.

μ Inotherwords,thefieldA (x)pervadesspacetime,buttheparticleonlysamplesthefield μ atitsparticularlocation.

The variation of the first term in (9) is easy and was done in chapter III.5, which we repeathereforconvenience: (cid:15) (cid:7) (cid:5) (cid:16) (cid:7) (cid:7) dxμdxν dxμdδxν d2xμ δ −m dτ −η =m dτ η =−m dτ η δxρ (10) μν dτ dτ μν dτ dτ μρ dτ2 Noticethatinthelaststep,forlaterconvenience,wehaverenamedadummy.

Thevariationofthesecondtermin(9)isabitmoreinvolved: (cid:7) (cid:7) !

dxμ dδxμ dxμ δ dτA (x) = dτ A (x) +[∂ A (x)δxν] (11) μ μ ν μ dτ dτ dτ WehavetorememberthatA (x)dependsonx inordernottomissthe∂ A (x)termin μ ν μ (11).Integratethefirsttermin(11)byparts: (cid:7) (cid:7) (cid:7) dτA (x) dδxμ =− dτ dA μ (x) δxμ=− dτ∂ A (x) dxν δxμ (12) μ ν μ dτ dτ dτ Puttingthetwotermstogetherandrenamingindices,wefind (cid:7) (cid:7) dxμ dxν δ dτA (x) = dτ(∂ A −∂ A ) δxμ (13) μ μ ν ν μ dτ dτ Theantisymmetrictensorfield F (x)≡∂ A (x)−∂ A (x) (14) μν μ ν ν μ justpoppedout!Somereadersmayrecognizethisastheelectromagneticfield;ifyoudon’t, onceagainreadon.

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:
- Incorporation of such subjective information might be important to get an accurate estimate of the probability.
- Subjective information Sometimes it is useful to incorporate subjective information into a mathematical model.
- An example of when such approach would be necessary is a situation in which an experimenter bends a coin slightly and tosses it once, recording whether it comes up heads, and is then given the task of predicting the probability that the next flip comes up heads.
- that can be written down and related to the underlying process, whereas neural networks produce an approximation that is opaque.
- Bayesian statistics provides a theoretical framework for incorporating such subjectivity into a rigorous analysis: we specify a prior probability distribution (which can be subjective), and then update this distribution based on empirical data.

Incorporation of such subjective information might be important to get an accurate estimate of the probability.

Subjective information Sometimes it is useful to incorporate subjective information into a mathematical model.

An example of when such approach would be necessary is a situation in which an experimenter bends a coin slightly and tosses it once, recording whether it comes up heads, and is then given the task of predicting the probability that the next flip comes up heads.

that can be written down and related to the underlying process, whereas neural networks produce an approximation that is opaque.

Bayesian statistics provides a theoretical framework for incorporating such subjectivity into a rigorous analysis: we specify a prior probability distribution (which can be subjective), and then update this distribution based on empirical data.

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:
- weaken also the primitive hypotheses from which they were derived.[21]: 36 Hempel provides a useful metaphor that describes the relationship between a conceptual framework and the framework as it is observed and perhaps tested (interpreted framework).
- "The whole system floats, as it were, above the plane of observation and is anchored to it by rules of interpretation.
- These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation.
- By virtue of those interpretative connections, the network

weaken also the primitive hypotheses from which they were derived.[21]: 36 Hempel provides a useful metaphor that describes the relationship between a conceptual framework and the framework as it is observed and perhaps tested (interpreted framework).

"The whole system floats, as it were, above the plane of observation and is anchored to it by rules of interpretation.

These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation.

By virtue of those interpretative connections, the network

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:
- One way is to simply send the particle to Bob, the other to let the particle interact unitarily with an ancillainsomeknownstate,andthensendtheancillatohim,togetherwithinformationabouthowthe interactiontookplace,sothatBobcanreverseheractionstoprepareareplicaoftheoriginalstate|φ(cid:105).
- To do so the sender, ‘Alice’, and the receiver, ‘Bob’, must prearrange the sharing of an EPR-correlated pair of particles.
- describe how these EPR correlations can assist in the teleportationofaquantumstatefromoneplacetoanotherbyasenderwhoknowsneitherthequantumstateto beteleportednorthelocationoftheintendedreceiver.
- III.2.1 EPR CORRELATIONS In , Einstein, Podolsky and Rosen, abbreviated EPR, published a paper[49] in which they sought to show that quantum mechanics was an incomplete theory.
- The authors start their article, using the well-known crypto-archetypes Alice and Bob[50], with shortlydescribingtwowaysinwhichAlicecanletBobretrievetheunknownstate|φ(cid:105)ofherparticle, where, although the state remains to be unknown, it is certain that Bob ends up with the same state.

One way is to simply send the particle to Bob, the other to let the particle interact unitarily with an ancillainsomeknownstate,andthensendtheancillatohim,togetherwithinformationabouthowthe interactiontookplace,sothatBobcanreverseheractionstoprepareareplicaoftheoriginalstate|φ(cid:105).

To do so the sender, ‘Alice’, and the receiver, ‘Bob’, must prearrange the sharing of an EPR-correlated pair of particles.

describe how these EPR correlations can assist in the teleportationofaquantumstatefromoneplacetoanotherbyasenderwhoknowsneitherthequantumstateto beteleportednorthelocationoftheintendedreceiver.

III.2.1 EPR CORRELATIONS In , Einstein, Podolsky and Rosen, abbreviated EPR, published a paper[49] in which they sought to show that quantum mechanics was an incomplete theory.

The authors start their article, using the well-known crypto-archetypes Alice and Bob[50], with shortlydescribingtwowaysinwhichAlicecanletBobretrievetheunknownstate|φ(cid:105)ofherparticle, where, although the state remains to be unknown, it is certain that Bob ends up with the same state.

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:
- (17.47) ADM 16π ab The ADM Lagrangian (17.47) is fine as
- The spatial restricted Riemann tensor R^ satisfies the usual ab ↔ cd abcd symmetry.
- For ADM, the ab0 restricted spatial connections coincide with the full spatial connections, Γ^ =Γ , so for ADM the spatial abc abc restricted Riemann curvature equals the Riemann curvature tensor restricted to the 3-dimensional spatial hypersurface of constant time.
- Contracting the Ricci tensor yields the Ricci scalar R, R=R^−2D^ Km+KbaK +K2−2KaK .
- Like the restricted Riemann tensor, the restricted Ricci tensor R^ with one time 0 index is not symmetric.

(17.47) ADM 16π ab The ADM Lagrangian (17.47) is fine as

The spatial restricted Riemann tensor R^ satisfies the usual ab ↔ cd abcd symmetry.

For ADM, the ab0 restricted spatial connections coincide with the full spatial connections, Γ^ =Γ , so for ADM the spatial abc abc restricted Riemann curvature equals the Riemann curvature tensor restricted to the 3-dimensional spatial hypersurface of constant time.

Contracting the Ricci tensor yields the Ricci scalar R, R=R^−2D^ Km+KbaK +K2−2KaK .

Like the restricted Riemann tensor, the restricted Ricci tensor R^ with one time 0 index is not symmetric.

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:
- Current Directions in Psychological Science, 14, 55–58.
- Neuromythologies in education.
- McGuire (Ed.), Offender rehabilitation and treatment: Effective programs and policies to reduce re-offending (pp.
- Journal of Personality and Social Psychology, 26, 309–320.
- An examination of the relation between answer-changing, test-wiseness, and performance.

Current Directions in Psychological Science, 14, 55–58.

McGuire (Ed.), Offender rehabilitation and treatment: Effective programs and policies to reduce re-offending (pp.

Journal of Personality and Social Psychology, 26, 309–320.

An examination of the relation between answer-changing, test-wiseness, and performance.

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:
- Do they know Chapters 12-16 what it looks like?
- They role-play the thousands of little pieces and will destroy people and buildings conversation between Catherine and Daniel.
- Do they believe that people can coffin (n) a box to put a dead person into know someone’s future because of star signs?
- Do they know what their sign is?
- statue (n) this looks like a person but is made of stone or metal weapon (n) people use weapons to fight with and hurt other people 2 Ask students to work in groups.

Do they know Chapters 12-16 what it looks like?

They role-play the thousands of little pieces and will destroy people and buildings conversation between Catherine and Daniel.

Do they believe that people can coffin (n) a box to put a dead person into know someone’s future because of star signs?

statue (n) this looks like a person but is made of stone or metal weapon (n) people use weapons to fight with and hurt other people 2 Ask students to work in groups.

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:
- Black Holes Evaporate Chapter 9 Summary: Black Holes and Time Warps Introduction to Gravitational Waves - Gravitational waves are ripples in spacetime produced by massive celestial events like black hole collisions.
- These waves carry information about the dynamics of their sources to Earth, akin to an encoded symphony.
- Formation and Behavior of Black Holes - Massive gas agglomerates lead to star formation, with smaller stars coalescing over time into larger ones that eventually implode to form black holes.
- These black holes can enter orbits around each other, generating gravitational waves as they spiral inwards.

Black Holes Evaporate Chapter 9 Summary: Black Holes and Time Warps Introduction to Gravitational Waves - Gravitational waves are ripples in spacetime produced by massive celestial events like black hole collisions.

These waves carry information about the dynamics of their sources to Earth, akin to an encoded symphony.

Formation and Behavior of Black Holes - Massive gas agglomerates lead to star formation, with smaller stars coalescing over time into larger ones that eventually implode to form black holes.

These black holes can enter orbits around each other, generating gravitational waves as they spiral inwards.

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 components are called the spatial coordinates.
- Physical and kinematic properties , i.e.
- In this case the reference configuration is the configuration at .
- The results obtained are independent of the choice of initial time and reference configuration, .
- An observer standing in the frame of reference observes the changes in the position and physical properties as the material body moves in space as time progresses.

The components are called the spatial coordinates.

Physical and kinematic properties , i.e.

In this case the reference configuration is the configuration at .

The results obtained are independent of the choice of initial time and reference configuration, .

An observer standing in the frame of reference observes the changes in the position and physical properties as the material body moves in space as time progresses.

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:
- Let M be an observable on the subsystem A, then the corresponding observable on the composite system is .
- The partial trace map as given above induces a dual map between the C*-algebras of bounded operators on and given by
- Consider a quantum mechanical system whose state space is the tensor product of Hilbert spaces.
- the following equality should hold: We see that this is satisfied if is as defined above via the partial trace.
- This proves the positive semi-definiteness of .

Let M be an observable on the subsystem A, then the corresponding observable on the composite system is .

The partial trace map as given above induces a dual map between the C*-algebras of bounded operators on and given by

Consider a quantum mechanical system whose state space is the tensor product of Hilbert spaces.

the following equality should hold: We see that this is satisfied if is as defined above via the partial trace.

This proves the positive semi-definiteness of .

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:
- For example, the equation defines an algebraic hypersurface of dimension n − 1 in the Euclidean space of dimension n.
- Generally the polynomial is supposed to be irreducible.
- Smooth hypersurface A hypersurface that is a smooth manifold is called a smooth hypersurface.
- In a space of dimension three, it is a surface.
- Hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

For example, the equation defines an algebraic hypersurface of dimension n − 1 in the Euclidean space of dimension n.

Generally the polynomial is supposed to be irreducible.

Smooth hypersurface A hypersurface that is a smooth manifold is called a smooth hypersurface.

In a space of dimension three, it is a surface.

Hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

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:
- BASIC DEFINITION Remote Viewingll II e Accessing information without the use of: - The normal-five senses - Information from other people - Logical deductions - Direct, connective implementation of electronic or other devices.
- e A talent which is inherent to every human to some degree.
- - Probably a vestigal form of self-preservation.
- - Largely ignored in todays's societal setting.
- - Through proper training, can be developed to a person's individual potential.

BASIC DEFINITION Remote Viewingll II e Accessing information without the use of: - The normal-five senses - Information from other people - Logical deductions - Direct, connective implementation of electronic or other devices.

e A talent which is inherent to every human to some degree.

- Probably a vestigal form of self-preservation.

- Largely ignored in todays's societal setting.

- Through proper training, can be developed to a person's individual potential.

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:
- Thisfactissometimessomewhatmisleadinglypresentedassomethingamazingaboutblackholes.Actually, itfollowsessentiallyfromthevirialtheorem(seeexercise10inchapterIV.2)andisgenerictogravitating systems,includingstars.Asastarlosesitsenergythroughradiation,itgenericallyheatsup.
- ThissuggestsanotherwayofunderstandingHawkingradiation,intermsofquantumtunneling.Workout thewaveequationofaquantumparticleintheSchwarzschildmetric.Classically,aparticleinsidethehorizon tryingtogetoutisfacedwithapotentialbarrier,butaquantumparticlecouldtunnelthroughthebarrier.
- At the time, a Russian group consisting of Y.
- Page independently discovered that rotating black holes radiate, and Feynman agreed with the conclusion, but then they discovered that Zel’dovich et al.
- To learn how quantum electrodynamics deals with the fluctuating photon, see QFT Nut, or any other reputablequantumfieldtheorytext.

At the time, a Russian group consisting of Y.

Page independently discovered that rotating black holes radiate, and Feynman agreed with the conclusion, but then they discovered that Zel’dovich et al.

To learn how quantum electrodynamics deals with the fluctuating photon, see QFT Nut, or any other reputablequantumfieldtheorytext.

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:
- SarfatticlaimsheisclosetoBechtel,wasclose totheReaganAdministrationandformerSDIproponentandSecDefCasparWeinberger,andstateshe receivedphonecallsfroma“mechanicalvoice”whenhewasyoungthatputhimintoahypnoticstate wherehewasledtotheorizeaboutquantumvacuumenergyandfaster-than-lightpropulsion.
- Davisstatestheclaimsof LockheedreceivingUAPinformationfromtheAECin1977arefalse.
- Jacques Valleestatesitwas“undeniable”hewasachildprodigy.
- “Generallyspeaking,weletthenormalFOIA processworkasitissupposedto...butwehavebeenrequestingthatFOIAofficescoordinatewithuson
- ● https://silvarecord.com/2020/09/20/are-satellites-tracking-ufos/ (PUBLICDOMAIN) -29February2020—RetiredDODseniortechnologyanalystPaulMuradstates thecompany“Orbitech”(possiblyOrbitalTechnologiesCorporation,Orbitec)helpedhimengineeran electromagneticenergydeviceknownasthe“MorningstarEnergyBox.” Theboxproduceda7% reductioninmassofatestobject.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- The Planck length is a distance scale of interest in speculations about quantum gravity.
- One convention for the Planck charge is to choose it so that the electrostatic repulsion of two objects with Planck charge and mass that are held 1 Planck length apart balances the Newtonian attraction between them.[48] Some authors have argued that the Planck force is on the order of the maximum force that can occur between two bodies.[49][50] However, the validity of these conjectures has been disputed.[51][52] Planck temperature At the Planck temperature, the wavelength of light emitted by thermal radiation reaches the Planck length.
- The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 J, equivalent to about 2.5×10−8 E .[44][45] P Proposals for theories of doubly special relativity posit that, in addition to the speed of light, an energy scale is also invariant for all inertial observers.
- Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.[40] The strings of string theory are modeled to be on the order of the Planck length.[41][42] In theories with large extra dimensions, the Planck length calculated from the observed value of can be smaller than the true, fundamental Planck length.[11]: 61 [43] Planck time No current physical theory adequately describes the earliest period of the Big Bang model on the order of the Planck time.[28] Planck energy The Planck energy E is approximately equal to the energy released in the combustion of the fuel in an P automobile fuel tank (57.2 L at 34.2 MJ/L of chemical energy).
- There are no known physical models able to describe temperatures greater than T ; a quantum P theory of gravity would be required

The Planck length is a distance scale of interest in speculations about quantum gravity.

One convention for the Planck charge is to choose it so that the electrostatic repulsion of two objects with Planck charge and mass that are held 1 Planck length apart balances the Newtonian attraction between them.[48] Some authors have argued that the Planck force is on the order of the maximum force that can occur between two bodies.[49][50] However, the validity of these conjectures has been disputed.[51][52] Planck temperature At the Planck temperature, the wavelength of light emitted by thermal radiation reaches the Planck length.

The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 J, equivalent to about 2.5×10−8 E .[44][45] P Proposals for theories of doubly special relativity posit that, in addition to the speed of light, an energy scale is also invariant for all inertial observers.

Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.[40] The strings of string theory are modeled to be on the order of the Planck length.[41][42] In theories with large extra dimensions, the Planck length calculated from the observed value of can be smaller than the true, fundamental Planck length.[11]: 61 [43] Planck time No current physical theory adequately describes the earliest period of the Big Bang model on the order of the Planck time.[28] Planck energy The Planck energy E is approximately equal to the energy released in the combustion of the fuel in an P automobile fuel tank (57.2 L at 34.2 MJ/L of chemical energy).

There are no known physical models able to describe temperatures greater than T ; a quantum P theory of gravity would be required

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:
- Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line.
- Trivial examples of spacetime curves A curve that consists of a horizontal line segment (a line at constant coordinate time), may represent a rod in spacetime and would not be a world line in the proper sense.
- Once the object is not approximated as a mere point but has extended volume, it traces not a world line but rather a world tube.
- World lines as a method of describing events A one-dimensional line or curve can be represented by the coordinates as a function of one parameter.
- A line at constant space coordinate (a vertical line using the convention adopted above) may represent a particle at rest (or a stationary observer).

Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line.

Trivial examples of spacetime curves A curve that consists of a horizontal line segment (a line at constant coordinate time), may represent a rod in spacetime and would not be a world line in the proper sense.

Once the object is not approximated as a mere point but has extended volume, it traces not a world line but rather a world tube.

World lines as a method of describing events A one-dimensional line or curve can be represented by the coordinates as a function of one parameter.

A line at constant space coordinate (a vertical line using the convention adopted above) may represent a particle at rest (or a stationary observer).

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:
- Maybe it’s a reflection of what you were feeling at the moment you opened the door.” She takes the last bite of food and tosses her empty MRE packet into the fire.
- Jason.” “What?” “Before we opened the door to the hangar and saw the other versions of you and me getting caught, you had mentioned that very thing happening.” “Did I?” “You were talking about the idea of the multiverse, and everything that can happen will happen, and you said that somewhere there was a version of you and me that never made it into the box.
- I say, “Think about the first world we saw—that ruined Chicago, with the buildings crumbling all around us.
- Moments later, you opened a door and we watched that exact scenario play out.” I feel the spine-tingling rush of a revelation sweeping over me.
- “The doors in the corridor are the connections to an infinite array of parallel worlds, right?

Maybe it’s a reflection of what you were feeling at the moment you opened the door.” She takes the last bite of food and tosses her empty MRE packet into the fire.

Jason.” “What?” “Before we opened the door to the hangar and saw the other versions of you and me getting caught, you had mentioned that very thing happening.” “Did I?” “You were talking about the idea of the multiverse, and everything that can happen will happen, and you said that somewhere there was a version of you and me that never made it into the box.

I say, “Think about the first world we saw—that ruined Chicago, with the buildings crumbling all around us.

Moments later, you opened a door and we watched that exact scenario play out.” I feel the spine-tingling rush of a revelation sweeping over me.

“The doors in the corridor are the connections to an infinite array of parallel worlds, right?

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:
- Instandardcalculus,integrationisinversetodifferentiation.Inthetheoryofdifferentialforms,integration is inverse to something called exterior differentiation, §15.9.
- The apparatus developed by mathematicians to allow integration over curved hypersurfaces is called differential forms, §15.6.
- Geometric Differentiation and Integration The problem of integrating over a curved hypersurface crops up routinely in general relativity, for example in developing the Lagrangian or Hamiltonian mechanics of a field, Chapter 16.
- The exterior derivative, conventionally written d (distinguished here by latin font), is the (coordinate and tetrad) scalar derivative operator ∂ d≡dxν ∧ , (15.1) ∂xν the wedge ∧ signifying that the derivative is a curl.
- The exterior ν n derivative d is isomorphic to the torsion-free covariant spacetime curl D ̊∧ (see equation (15.67) for a more precise statement of the isomorphism), d↔D ̊∧ .

Instandardcalculus,integrationisinversetodifferentiation.Inthetheoryofdifferentialforms,integration is inverse to something called exterior differentiation, §15.9.

The apparatus developed by mathematicians to allow integration over curved hypersurfaces is called differential forms, §15.6.

Geometric Differentiation and Integration The problem of integrating over a curved hypersurface crops up routinely in general relativity, for example in developing the Lagrangian or Hamiltonian mechanics of a field, Chapter 16.

The exterior derivative, conventionally written d (distinguished here by latin font), is the (coordinate and tetrad) scalar derivative operator ∂ d≡dxν ∧ , (15.1) ∂xν the wedge ∧ signifying that the derivative is a curl.

The exterior ν n derivative d is isomorphic to the torsion-free covariant spacetime curl D ̊∧ (see equation (15.67) for a more precise statement of the isomorphism), d↔D ̊∧ .

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:
- EXPERIMENTALTELEPORTATION Incaseteleportationdoestakeplace,theprobabilityfora d1f1f2,or −45◦,detectionisreduced to0,whiletheprobabilityfora d2f1f2,or +45◦,detectionis25%,sincethatwastheprobabilityof finding a coincidence at the detectors f1 and f2, with a probability of unity at detector d2, the state havingbeenteleported.
- Thevisibilityofteleportationinthree-foldcoincidences, aftercorrectionforthespuriousresults causedbytheemissionofmorethanonepairofEPR photonsduringonedown-conversion,isshown infigureIV.4,table1inthearticle.
- Todemonstratethatteleportationworksforacompletebasis forpolarizationstates, theexperimentisrepeatedforteleportationofaninitial−45◦ polarization, of whichthedatacanbeseenintheright-handsideoffigureIV.3.
- As mentioned above, values for the visibilities of the dip in the three-fold coincidences in figureIV.3areobtainedaftersubtractingtheoffsetcausedbythespuriousthree-foldcoincidences.
- Since equally likely two photon pairs can be created in one down-conversion, this can cause three-fold coincidenceswhichhavenothingtodowithteleportation.

EXPERIMENTALTELEPORTATION Incaseteleportationdoestakeplace,theprobabilityfora d1f1f2,or −45◦,detectionisreduced to0,whiletheprobabilityfora d2f1f2,or +45◦,detectionis25%,sincethatwastheprobabilityof finding a coincidence at the detectors f1 and f2, with a probability of unity at detector d2, the state havingbeenteleported.

As mentioned above, values for the visibilities of the dip in the three-fold coincidences in figureIV.3areobtainedaftersubtractingtheoffsetcausedbythespuriousthree-foldcoincidences.

Since equally likely two photon pairs can be created in one down-conversion, this can cause three-fold coincidenceswhichhavenothingtodowithteleportation.

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:
- is a coordinate tensor (a coordinate scalar), but not a tetrad tensor.
- It transforms under a coordinate gauge m transformation (26.9) as e μ(x)→e′ μ(x)−L e μ , (26.17) m m ε m where the Lie derivative of the inverse vierbein is, equation (7.137), ∂εμ ∂e μ L e μ =−e κ +εκ m ε m m ∂xκ ∂xκ =−∂ (enμε )+εk∂ e μ m n k m =−enμ( ∂ ε −εkd +εkd ) m n nkm nmk =−enμ [ ∂ ε +εk( ̊Γ − ̊Γ )] .
- The Lie derivative of a tetrad tensor, as defined in this book, is a coordinate tensor but not a tetrad tensor.
- (26.14) ε ∂xκ The change εκ∂ Am is a coordinate tensor (specifically, a coordinate scalar), but not a tetrad tensor.
- 26.7 Coordinate gauge transformations 727 coordinatescalarwhenitsLiederivativeistaken.Underacoordinategaugetransformation(26.9),atetradframe 4-vector Am transforms as Am(x)→A′m(x)=Am(x)−L Am , (26.13) ε where the Lie derivative is, equation (7.133), ∂Am L Am =εκ not a tetrad tensor .

is a coordinate tensor (a coordinate scalar), but not a tetrad tensor.

It transforms under a coordinate gauge m transformation (26.9) as e μ(x)→e′ μ(x)−L e μ , (26.17) m m ε m where the Lie derivative of the inverse vierbein is, equation (7.137), ∂εμ ∂e μ L e μ =−e κ +εκ m ε m m ∂xκ ∂xκ =−∂ (enμε )+εk∂ e μ m n k m =−enμ( ∂ ε −εkd +εkd ) m n nkm nmk =−enμ [ ∂ ε +εk( ̊Γ − ̊Γ )] .

The Lie derivative of a tetrad tensor, as defined in this book, is a coordinate tensor but not a tetrad tensor.

(26.14) ε ∂xκ The change εκ∂ Am is a coordinate tensor (specifically, a coordinate scalar), but not a tetrad tensor.

26.7 Coordinate gauge transformations 727 coordinatescalarwhenitsLiederivativeistaken.Underacoordinategaugetransformation(26.9),atetradframe 4-vector Am transforms as Am(x)→A′m(x)=Am(x)−L Am , (26.13) ε where the Lie derivative is, equation (7.133), ∂Am L Am =εκ not a tetrad tensor .

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:
- However, equations (17.48) are valid in general, including in the traditional case where the spatial axes are taken equal to the spatial coordinate tangent axes, equation (17.14), in which case Γ and Γ are not antisymmetric in their first two indices.
- (11.53) , (17.48d) abc abc where the relevant vierbein derivatives d are lmn 1 1 d =− ∂ α , d =− e ∂ βα , d =γ e β∂ ec .
- 500 Conventional Hamiltonian (3+1) approach are, from the general formula (11.53) with vanishing torsion (note that d =0 since e0 =0), 0an α Γ =−Γ ≡K =−d , (17.48a) a00 0a0 a 00a Γ =−Γ ≡K = 1(∂ γ +d +d −d −d ) , (17.48b) a0b 0ab ab 2 0 ab ab0 ba0 a0b b0a Γ ≡Γ^ =K −d +d , (17.48c) ab0 ab0 ab ab0 a0b Γ ≡Γ^ =same as eq.
- (17.52) 0 ab ab0 ba0 a0b b0a ab The time derivatives in expression (17.52) are the directed time derivatives ∂ γ of the spatial tetrad 0 ab metric (the tetrad metric γ is not
- If the spatial tetrad metric γ is taken to be constant, which is true if for example the spatial ab tetrad axes γγ are taken to be orthonormal, then the tetrad connections Γ and Γ , equations (17.48c) a ab0 abc and (17.48d), are antisymmetric in their first two indices.

However, equations (17.48) are valid in general, including in the traditional case where the spatial axes are taken equal to the spatial coordinate tangent axes, equation (17.14), in which case Γ and Γ are not antisymmetric in their first two indices.

(11.53) , (17.48d) abc abc where the relevant vierbein derivatives d are lmn 1 1 d =− ∂ α , d =− e ∂ βα , d =γ e β∂ ec .

500 Conventional Hamiltonian (3+1) approach are, from the general formula (11.53) with vanishing torsion (note that d =0 since e0 =0), 0an α Γ =−Γ ≡K =−d , (17.48a) a00 0a0 a 00a Γ =−Γ ≡K = 1(∂ γ +d +d −d −d ) , (17.48b) a0b 0ab ab 2 0 ab ab0 ba0 a0b b0a Γ ≡Γ^ =K −d +d , (17.48c) ab0 ab0 ab ab0 a0b Γ ≡Γ^ =same as eq.

(17.52) 0 ab ab0 ba0 a0b b0a ab The time derivatives in expression (17.52) are the directed time derivatives ∂ γ of the spatial tetrad 0 ab metric (the tetrad metric γ is not

If the spatial tetrad metric γ is taken to be constant, which is true if for example the spatial ab tetrad axes γγ are taken to be orthonormal, then the tetrad connections Γ and Γ , equations (17.48c) a ab0 abc and (17.48d), are antisymmetric in their first two indices.

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:
- For example, in a problem with rotational symmetry, working with the more concrete description of three-dimensional space assumes a choice of basis, corresponding to a set of axes.
- Conversely, can be obtained by starting with and 'forgetting' the Cartesian product structure, or equivalently the standard choice of basis.
- Stated another way, a preferred choice of axes breaks the rotational symmetry of physical space.
- This then allows the definition of the standard basis defined by where is the Kronecker delta.
- As opposed to a general vector space , the space is sometimes referred to as a coordinate space.[49] Physically, it is conceptually desirable to use the abstract formalism in order to assume as little structure as possible if it is not given by the parameters of a particular problem.

For example, in a problem with rotational symmetry, working with the more concrete description of three-dimensional space assumes a choice of basis, corresponding to a set of axes.

Conversely, can be obtained by starting with and 'forgetting' the Cartesian product structure, or equivalently the standard choice of basis.

Stated another way, a preferred choice of axes breaks the rotational symmetry of physical space.

This then allows the definition of the standard basis defined by where is the Kronecker delta.

As opposed to a general vector space , the space is sometimes referred to as a coordinate space.[49] Physically, it is conceptually desirable to use the abstract formalism in order to assume as little structure as possible if it is not given by the parameters of a particular problem.

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 observation of dark energy appears to suggest that there is a hitherto unknown mass scale of ∼10 −3eV in physics.
- TheCosmologicalConstantParadox | 747 electronmassm ?Surely,thebasicprinciplesthatgointoquantumfieldtheoryhavebeen e verifiedexperimentallyuptothatkindofenergyscale.Youthenpredictavacuumenergy densityofm4=m /(1/m )3.
- EvenwithM aslowas∼m ,youarestillwaywayoff.Doyouseethevacuumfilledwith c e onem c2worthofenergyinavolumethesizeoftheComptonwavelengthoftheelectron?
- The evidence seems increasingly to favor this simplest of hypotheses.
- In the late 1990s (strangely, around the same time dark energywasdiscovered),neutrinos,whichupuntilthattimewerethoughttobemassless, were experimentally found to oscillate, which implies, according to standard particle theory, that they are massive.

The observation of dark energy appears to suggest that there is a hitherto unknown mass scale of ∼10 −3eV in physics.

TheCosmologicalConstantParadox | 747 electronmassm ?Surely,thebasicprinciplesthatgointoquantumfieldtheoryhavebeen e verifiedexperimentallyuptothatkindofenergyscale.Youthenpredictavacuumenergy densityofm4=m /(1/m )3.

EvenwithM aslowas∼m ,youarestillwaywayoff.Doyouseethevacuumfilledwith c e onem c2worthofenergyinavolumethesizeoftheComptonwavelengthoftheelectron?

The evidence seems increasingly to favor this simplest of hypotheses.

In the late 1990s (strangely, around the same time dark energywasdiscovered),neutrinos,whichupuntilthattimewerethoughttobemassless, were experimentally found to oscillate, which implies, according to standard particle theory, that they are massive.

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:
- SECRET NOFORN STAR GATE L1MOIS OVERVIEW e Purpose eMission e Definitions e Management e Personnel Participation e Benefits e Primary Methodologies • I Secondary Methodologie~ e Categories of Taskings e Types of Targets e Operations Methodology e Summary SECRET NOFORN STAR GATE LIMOIS 09M8983-2 DCH -

SECRET NOFORN STAR GATE L1MOIS OVERVIEW e Purpose eMission e Definitions e Management e Personnel Participation e Benefits e Primary Methodologies • I Secondary Methodologie~ e Categories of Taskings e Types of Targets e Operations Methodology e Summary SECRET NOFORN STAR GATE LIMOIS 09M8983-2 DCH -

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:
- (It is also possible that the ball that exits the wormhole knocks its past self off course from the worm hole completely.
- D-branes Thesis Vortex Operators in gauge field theories (https://search.library.ber Polchinski's contributions to D-brane physics were a keley.edu/discovery/fulldisplay?d primary trigger of the 2nd superstring revolution and ocid=alma991049444299706532 the physics of holographic gauge-gravity dualities.
- Thorne dubbed this problem "Polchinski's paradox" in 1994.[12] Later students of the whimsical problem came up with solutions which managed to avoid any inconsistencies, by having the ball emerge from the future at a different angle than the one used to generate the paradox, and deliver its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow.
- advisor Doctoral Robert Leigh Polchinski's paradox students Iosif Bena In an unpublished communication to Kip Thorne circa Mariana Graña 1990, commenting on the Novikov self-consistency principle (in relation to sending objects or people through a traversable wormhole into the past, and the time paradoxes that could result), Polchinski raised a potentially paradoxical situation involving a billiard ball sent through a wormhole which sends it back in time.
- Even with the original ball being knocked off course the future ball would still be there and could bounce off the original ball and enter the wormhole again closing the paradox.

(It is also possible that the ball that exits the wormhole knocks its past self off course from the worm hole completely.

D-branes Thesis Vortex Operators in gauge field theories (https://search.library.ber Polchinski's contributions to D-brane physics were a keley.edu/discovery/fulldisplay?d primary trigger of the 2nd superstring revolution and ocid=alma991049444299706532 the physics of holographic gauge-gravity dualities.

Thorne dubbed this problem "Polchinski's paradox" in 1994.[12] Later students of the whimsical problem came up with solutions which managed to avoid any inconsistencies, by having the ball emerge from the future at a different angle than the one used to generate the paradox, and deliver its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow.

advisor Doctoral Robert Leigh Polchinski's paradox students Iosif Bena In an unpublished communication to Kip Thorne circa Mariana Graña 1990, commenting on the Novikov self-consistency principle (in relation to sending objects or people through a traversable wormhole into the past, and the time paradoxes that could result), Polchinski raised a potentially paradoxical situation involving a billiard ball sent through a wormhole which sends it back in time.

Even with the original ball being knocked off course the future ball would still be there and could bounce off the original ball and enter the wormhole again closing the paradox.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Differentiating with respect to time gives the velocity r θ dr with radial component and an additional component rω due to the rotation.
- Differentiating with dt respect to time again obtains the acceleration d2r which breaks into the radial acceleration dt2 , centripetal acceleration –rω , Coriolis acceleration dr 2ω , and angular acceleration rα.
- where ê and ê are the polar unit vectors.
- State of motion Constant r r linear in t r quadratic in t r non-linear in t Uniform translation Uniform translational Non-uniform Constant θ Stationary (constant acceleration translation translational velocity) Uniform angular Uniform angular Angular motion in a Angular motion in a motion in a circle motion in a spiral, θ linear in t spiral, constant radial spiral, varying radial (constant angular constant radial acceleration acceleration velocity) velocity Uniform angular Uniform angular Uniform angular Uniform angular acceleration in a acceleration in a acceleration in a θ quadratic in t acceleration in a spiral, constant radial spiral, constant radial spiral, varying radial circle velocity acceleration acceleration Non-uniform angular Non-uniform angular Non-uniform angular Non-uniform angular acceleration in a acceleration in a acceleration in a θ non-linear in t acceleration in a spiral, constant radial spiral, constant radial spiral, varying radial circle velocity acceleration acceleration General 3D motions In 3D space, the equations in spherical coordinates (r, θ, φ) with corresponding unit vectors ê , ê r θ and ê , the position, velocity, and acceleration generalize respectively to φ
- dt Special cases of motion described by these equations are summarized qualitatively in the table below.

Differentiating with respect to time gives the velocity r θ dr with radial component and an additional component rω due to the rotation.

Differentiating with dt respect to time again obtains the acceleration d2r which breaks into the radial acceleration dt2 , centripetal acceleration –rω , Coriolis acceleration dr 2ω , and angular acceleration rα.

where ê and ê are the polar unit vectors.

State of motion Constant r r linear in t r quadratic in t r non-linear in t Uniform translation Uniform translational Non-uniform Constant θ Stationary (constant acceleration translation translational velocity) Uniform angular Uniform angular Angular motion in a Angular motion in a motion in a circle motion in a spiral, θ linear in t spiral, constant radial spiral, varying radial (constant angular constant radial acceleration acceleration velocity) velocity Uniform angular Uniform angular Uniform angular Uniform angular acceleration in a acceleration in a acceleration in a θ quadratic in t acceleration in a spiral, constant radial spiral, constant radial spiral, varying radial circle velocity acceleration acceleration Non-uniform angular Non-uniform angular Non-uniform angular Non-uniform angular acceleration in a acceleration in a acceleration in a θ non-linear in t acceleration in a spiral, constant radial spiral, constant radial spiral, varying radial circle velocity acceleration acceleration General 3D motions In 3D space, the equations in spherical coordinates (r, θ, φ) with corresponding unit vectors ê , ê r θ and ê , the position, velocity, and acceleration generalize respectively to φ

dt Special cases of motion described by these equations are summarized qualitatively in the table below.

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:
- ytisrevinU aveneG euqitpO PAG Quantum teleportation Nicolas Gisin H.
- Zbinden Groupe de Physique Appliquée-unité d’Optique Université de Genène • The science and the science-fiction of quantum teleportation • Intuitive and mathematical introduction • What is teleported ?
- The no-cloning theorem • The “teleportation channel”: Entanglement • The Geneva experiment • Telecom wavelengths • Time-bin qubits • partial Bell measurement and tests of Bell inequality • Applications: Quantum Key Distribution • Simplifications, limitations • Q relays and Q repeaters

ytisrevinU aveneG euqitpO PAG Quantum teleportation Nicolas Gisin H.

Zbinden Groupe de Physique Appliquée-unité d’Optique Université de Genène • The science and the science-fiction of quantum teleportation • Intuitive and mathematical introduction • What is teleported ?

The no-cloning theorem • The “teleportation channel”: Entanglement • The Geneva experiment • Telecom wavelengths • Time-bin qubits • partial Bell measurement and tests of Bell inequality • Applications: Quantum Key Distribution • Simplifications, limitations • Q relays and Q repeaters

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:
- “What are you doing?” Amanda asks.
- There won’t be enough time, and when the next storm comes, and the next, the box is going to be buried so deep we’ll never have a chance of reaching it.
- — Early the next morning, we stand in the midst of this silent neighborhood, waist-deep in snow and shivering, even though we’re wearing layer upon layer of that poor family’s winter clothes, which we raided from the coat closet.
- The chances of us stumbling upon it through blind luck are minuscule.
- I draw a deep breath into my lungs, and the air is so cold it makes me cough.

There won’t be enough time, and when the next storm comes, and the next, the box is going to be buried so deep we’ll never have a chance of reaching it.

— Early the next morning, we stand in the midst of this silent neighborhood, waist-deep in snow and shivering, even though we’re wearing layer upon layer of that poor family’s winter clothes, which we raided from the coat closet.

The chances of us stumbling upon it through blind luck are minuscule.

I draw a deep breath into my lungs, and the air is so cold it makes me cough.

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:
- Sturrocksayshe’ssentBernardHaischatLockheedMartinsixquestionslikethatbutHaischnever responded.
- ● https://www.bibliotecapleyades.net/sociopolitica/elite/aerospace_commission.htm (PUBLICDOMAIN) -22March2003—StanfordprofessorPeterSturrockconfidestoJacquesVallee thathebelievesHalPuthoff’sworkonzeropointenergyisfullof“circulararguments.” Sturrock mentionsPuthoffpointstothesignificanceoftheratioe/mbutfailedtoseethathe’salsoredefiningmass.
- Greensaysthesamplesarrived inCIApossessionin1982andre-analyzedatLosAlamos,towhichitwasconcludeditwasan aluminum-titaniumalloynotfromEarth.
- Green’sworkatGMcorroboratedthe materialwastitaniumandaluminum.
- “ ● https://web.archive.org/web/20160306030249/https://www.wired.com/2006/06/ufo-hacker-tells-w hat-he-found/ ● https://web.archive.org/web/20061024221521/http://bbcworld.com/content/clickonline_archive_1 8 2006.asp?pageid=665&co pageid=4 (PUBLICDOMAIN) -27November2002—TheCommissionontheFutureoftheU.S.Aerospace IndustrydeliversitsfinalreporttoCongress;itrecommendsaseriesofpublicpolicyreformstoenable theaerospaceindustrytocreatesuperiortechnology.

“ ● https://web.archive.org/web/20160306030249/https://www.wired.com/2006/06/ufo-hacker-tells-w hat-he-found/ ● https://web.archive.org/web/20061024221521/http://bbcworld.com/content/clickonline_archive_1 8 2006.asp?pageid=665&co pageid=4 (PUBLICDOMAIN) -27November2002—TheCommissionontheFutureoftheU.S.Aerospace IndustrydeliversitsfinalreporttoCongress;itrecommendsaseriesofpublicpolicyreformstoenable theaerospaceindustrytocreatesuperiortechnology.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- How does the group Spin(5)×Spin(6) break down to the observed SM group U (1)×SU (2)×SU(3)?
- 1086 The Standard Model of Physics and beyond 42.4.12 The Higgs field that breaks Spin(5)×Spin(6) symmetry As remarked in §42.4.10, the largest subgroup of Spin(11,1) that commutes with the Poincaré group is the group (42.123), Spin(5)×Spin(6).
- (42.155) 3 10 10 10 The expression for S in terms of the baryon-lepton difference B −L is from equation (42.17).
- R-charge and R S-charge are related to Spin(10) durgb charges by R=d+u , S = 2(r +g +b )=−(B−L) .
- Y L With two exceptions, every generator of Spin(5)×Spin(6) that preserves the number of durgb up bits is a generator of the SM, and every generator of Spin(5)×Spin(6) that does not preserve the number of up bits is not a generator of the SM.

How does the group Spin(5)×Spin(6) break down to the observed SM group U (1)×SU (2)×SU(3)?

1086 The Standard Model of Physics and beyond 42.4.12 The Higgs field that breaks Spin(5)×Spin(6) symmetry As remarked in §42.4.10, the largest subgroup of Spin(11,1) that commutes with the Poincaré group is the group (42.123), Spin(5)×Spin(6).

(42.155) 3 10 10 10 The expression for S in terms of the baryon-lepton difference B −L is from equation (42.17).

R-charge and R S-charge are related to Spin(10) durgb charges by R=d+u , S = 2(r +g +b )=−(B−L) .

Y L With two exceptions, every generator of Spin(5)×Spin(6) that preserves the number of durgb up bits is a generator of the SM, and every generator of Spin(5)×Spin(6) that does not preserve the number of up bits is not a generator of the SM.

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:
- "Reflections on relativity" (https://web.archive.org/web/20151218205507/http://math pages.com/rr/rrtoc.htm).
- edu/II_42.html) Retrieved from "https://en.wikipedia.org/w/index.php?title=General_relativity&oldid=1336567084"
- "Understanding General Relativity" (http://www.rafimoor.com/english/GRE.htm).
- arXiv:gr-qc/9712019 (https://arxiv.
- Archived from the original (http://www.mathpages.com/r r/rrtoc.htm) on 18 December 2015.

"Reflections on relativity" (https://web.archive.org/web/20151218205507/http://math pages.com/rr/rrtoc.htm).

edu/II_42.html) Retrieved from "https://en.wikipedia.org/w/index.php?title=General_relativity&oldid=1336567084"

"Understanding General Relativity" (http://www.rafimoor.com/english/GRE.htm).

Archived from the original (http://www.mathpages.com/r r/rrtoc.htm) on 18 December 2015.

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:
- (1970), Physics Today, 23, 30 55.
- (1957), “Gravitation without a principle of equivalence,” Rev.
- (1983), Unified Field Theories of More Than 4 Dimensions, Proc.
- (1992), “Nonlinear Magneto-Optical Effect in Vacuum: Inhomogeneity-Originated Second-Harmonic Generation in DC Magnetic Field,” J.
- (1996), Mass Modification Experiment Definition Study, PL-TR-96-3004, Phillips Laboratory-Propulsion Directorate, Air Force Materiel Command, Edwards AFB, CA 70.

(1957), “Gravitation without a principle of equivalence,” Rev.

(1983), Unified Field Theories of More Than 4 Dimensions, Proc.

(1992), “Nonlinear Magneto-Optical Effect in Vacuum: Inhomogeneity-Originated Second-Harmonic Generation in DC Magnetic Field,” J.

(1996), Mass Modification Experiment Definition Study, PL-TR-96-3004, Phillips Laboratory-Propulsion Directorate, Air Force Materiel Command, Edwards AFB, CA 70.

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:
- Recalling the definition (cid:24) = 8πGρ , j j 3H2 j wehave (cid:15) (cid:16) (cid:15) (cid:16) (cid:24) ̇ =(cid:24) ρ ̇ j −2 H ̇ =−(cid:24) 3 (cid:29) 1+w (cid:30) H +2 H ̇ (28) j j j j ρ H H j
- Flowinthecosmicdiagram It is perhaps worth emphasizing that all relevant physics within the present context is containedinthecosmologicalequation R ̇2+k= 8πG ρR2 (24) andenergyconservation d da3 ρa3=−P (25) dt dt The discussion here is merely expressing the same physics in a notation particularly convenientforobservationalcosmology.
- Einstein’s static uni- (cid:27),0 m,0 versecorrespondstosittingatthemaximumofthepotentialinfigure2b.
- For example, we might ask how (cid:24) varies with time.
- ThankstotheBianchiidentity,wecanrecovertherestofEinstein’sfieldequationfrom (24)and(25).Itisinstructivetoverifythis.First,rewrite(25)as ̇ R ρ ̇+3(ρ+P) =0 (26) R Nextdifferentiate(24)toobtainanequationforR ̈ ,eliminatingR ̇ byusing(24)andρ ̇ by using(26).Notsurprisingly,wegetthetime-timecomponentofEinstein’sfieldequation: ̈ R 4πG =− (ρ+3P) (27) R 3 You are of course free to keep on massaging these equations every which way.

Recalling the definition (cid:24) = 8πGρ , j j 3H2 j wehave (cid:15) (cid:16) (cid:15) (cid:16) (cid:24) ̇ =(cid:24) ρ ̇ j −2 H ̇ =−(cid:24) 3 (cid:29) 1+w (cid:30) H +2 H ̇ (28) j j j j ρ H H j

Flowinthecosmicdiagram It is perhaps worth emphasizing that all relevant physics within the present context is containedinthecosmologicalequation R ̇2+k= 8πG ρR2 (24) andenergyconservation d da3 ρa3=−P (25) dt dt The discussion here is merely expressing the same physics in a notation particularly convenientforobservationalcosmology.

Einstein’s static uni- (cid:27),0 m,0 versecorrespondstosittingatthemaximumofthepotentialinfigure2b.

For example, we might ask how (cid:24) varies with time.

ThankstotheBianchiidentity,wecanrecovertherestofEinstein’sfieldequationfrom (24)and(25).Itisinstructivetoverifythis.First,rewrite(25)as ̇ R ρ ̇+3(ρ+P) =0 (26) R Nextdifferentiate(24)toobtainanequationforR ̈ ,eliminatingR ̇ byusing(24)andρ ̇ by using(26).Notsurprisingly,wegetthetime-timecomponentofEinstein’sfieldequation: ̈ R 4πG =− (ρ+3P) (27) R 3 You are of course free to keep on massaging these equations every which way.

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:
- As for a cubic centimeter, it is equal to about 1/16 cubic inch.
- The energy of a bonfire, of burning coal or oil, as well as the energy produced within living tissue, is the result of changes under the control of the electromagnetic force.
- The reverse is true if the atoms or molecules come closer together.
- DENSITY As the atoms or molecules of a given piece of matter move farther apart because of rising temperature or for any other reason, there comes to be less mass in a particular fixed volume of that matter.
- Some of the electron shifts liberate considerable energy.

As for a cubic centimeter, it is equal to about 1/16 cubic inch.

The energy of a bonfire, of burning coal or oil, as well as the energy produced within living tissue, is the result of changes under the control of the electromagnetic force.

The reverse is true if the atoms or molecules come closer together.

DENSITY As the atoms or molecules of a given piece of matter move farther apart because of rising temperature or for any other reason, there comes to be less mass in a particular fixed volume of that matter.

Some of the electron shifts liberate considerable 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:
- FromNewtontoRiemann:CoordinatestoCurvature Itiscommonlysaidinacademiathatthebestwaytomasterasubjectistoteachit.In thisconnection,thecomputerisamore-than-willingstudent.Writeaprogramsuchthat, givenametric,theprogramisabletofindthelocallyflatcoordinatesatanarbitrarypoint.
- Knowing the distance between two infinitesimallyseparatedpoints,wecanfindthedistancebetweentwopointsfarapartby integratingds alonganypathconnectingthetwopoints.Wecanthendefinea“straight line” between two points as that path that minimizes the distance between them.
- †Thisisalsoconfirmedbytheintuitiveexamplein(1)and(2).
- ∼∂∂g..;sincethenumberofcomponentsgrowsquartically withD,wecanevenguessthatitwillcarry4indices.Verynice:thisisallconsistentwith thecurvaturebeingrelatedtoB .
- GuessingwhattheRiemanncurvaturemustlooklike Onesignificantby-productofthiscountingandsubsequentunderstandingoflocalflatness isthatweseewhatthegeneralexpressionforcurvaturemustinvolve.Sincethecurvatureat thepointPisdescribedbythosecomponentsinB thatwecannottransformaway,we μν,λσ conclude ∗ thatthedefinitionofcurvaturemustinvolvetwopowers†ofderivativesacting onthemetricg .Aswehavealreadyseen,ittakeslotsofnumberstodescribecurvature μν completely.Butwealsoknowthatwecouldchangecoordinates(from(x,y)to(u,v),for thesimplecurvedsurfacethatstartedthischapter).Thus,wedon’twantthesenumbersto gallopwildlyoutofourcontrolwhenwechangecoordinates.Nowyouseethattheconcept ofatensor,asdiscussedinchapterI.4,isgoingtoplayabigrole.Infact,the 1D2(D2−1) numbers are the components of a tensor, quite naturally called the Riemann curvature tensor.Withourintuitivediscussionhere,wecananticipatethatthecurvaturetensorwill havetheschematicformR....

Knowing the distance between two infinitesimallyseparatedpoints,wecanfindthedistancebetweentwopointsfarapartby integratingds alonganypathconnectingthetwopoints.Wecanthendefinea“straight line” between two points as that path that minimizes the distance between them.

GuessingwhattheRiemanncurvaturemustlooklike Onesignificantby-productofthiscountingandsubsequentunderstandingoflocalflatness isthatweseewhatthegeneralexpressionforcurvaturemustinvolve.Sincethecurvatureat thepointPisdescribedbythosecomponentsinB thatwecannottransformaway,we μν,λσ conclude ∗ thatthedefinitionofcurvaturemustinvolvetwopowers†ofderivativesacting onthemetricg .Aswehavealreadyseen,ittakeslotsofnumberstodescribecurvature μν completely.Butwealsoknowthatwecouldchangecoordinates(from(x,y)to(u,v),for thesimplecurvedsurfacethatstartedthischapter).Thus,wedon’twantthesenumbersto gallopwildlyoutofourcontrolwhenwechangecoordinates.Nowyouseethattheconcept ofatensor,asdiscussedinchapterI.4,isgoingtoplayabigrole.Infact,the 1D2(D2−1) numbers are the components of a tensor, quite naturally called the Riemann curvature tensor.Withourintuitivediscussionhere,wecananticipatethatthecurvaturetensorwill havetheschematicformR....

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:
- Additionally, for several years the companies had attempted Watch hands coated with radium paint to cover up the effects and avoid liability by insisting that the under ultraviolet light Radium Girls were instead suffering from syphilis.[48] As a result of the lawsuit, and an extensive study by the U.S.
- The radiation dose from an intact device is usually only a hazard when many devices are grouped together or if the device is disassembled or tampered with.[56] Use in electron tubes Radium has been used in electron
- [46] From the 1960s the use of radium paint was discontinued.
- paint on the components of watches and clocks.[46] The dial painters were instructed to lick their brushes to give them a fine point, thereby ingesting radium.[47] Their exposure to radium caused serious health effects which included sores, anemia, and bone cancer.[15] During the litigation, it was determined that the company's scientists and management had taken considerable precautions to protect themselves from the effects of radiation, but it did not seem to protect their employees.
- They are usually no longer luminous; this is not due to radioactive decay of the radium (which has a half-life of 1600 years) but to the fluorescence of the zinc sulfide fluorescent medium being worn out by the radiation from the radium.[55] Originally appearing as white, most radium paint from before the 1960s has tarnished to yellow over time.

Additionally, for several years the companies had attempted Watch hands coated with radium paint to cover up the effects and avoid liability by insisting that the under ultraviolet light Radium Girls were instead suffering from syphilis.[48] As a result of the lawsuit, and an extensive study by the U.S.

The radiation dose from an intact device is usually only a hazard when many devices are grouped together or if the device is disassembled or tampered with.[56] Use in electron tubes Radium has been used in electron

[46] From the 1960s the use of radium paint was discontinued.

paint on the components of watches and clocks.[46] The dial painters were instructed to lick their brushes to give them a fine point, thereby ingesting radium.[47] Their exposure to radium caused serious health effects which included sores, anemia, and bone cancer.[15] During the litigation, it was determined that the company's scientists and management had taken considerable precautions to protect themselves from the effects of radiation, but it did not seem to protect their employees.

They are usually no longer luminous; this is not due to radioactive decay of the radium (which has a half-life of 1600 years) but to the fluorescence of the zinc sulfide fluorescent medium being worn out by the radiation from the radium.[55] Originally appearing as white, most radium paint from before the 1960s has tarnished to yellow over time.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- arXiv:2008.05177 (https://arxiv.org/abs/2008.05177) [quant-ph (http s://arxiv.org/archive/quant-ph)].
- doi:10.1103/PhysRevLett.132.030601 (https://doi.org/10.1103%2FPhysRevLett.132.030601).
- "The security implications of quantum cryptography and quantum computing" (http://www.magonlinelibrary.com/doi/10.1016/S1 353-4858%2820%2930105-7).
- "The Quantum Computer Puzzle" (https://www.ams.org/journals/notices/201 605/rnoti-p508.pdf) (PDF).
- "Quantum Computers and the Universe" (https://m-cacm.acm.or g/magazines/2022/12/266916-quantum-computers-and-the-universe/fulltext).

arXiv:2008.05177 (https://arxiv.org/abs/2008.05177) [quant-ph (http s://arxiv.org/archive/quant-ph)].

"The security implications of quantum cryptography and quantum computing" (http://www.magonlinelibrary.com/doi/10.1016/S1 353-4858%2820%2930105-7).

"The Quantum Computer Puzzle" (https://www.ams.org/journals/notices/201 605/rnoti-p508.pdf) (PDF).

"Quantum Computers and the Universe" (https://m-cacm.acm.or g/magazines/2022/12/266916-quantum-computers-and-the-universe/fulltext).

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:
- costliest material to make.[87] In 2006, Gerald Smith estimated $250 million could produce 10 milligrams of positrons[88] (equivalent to $25 billion per gram); in 1999, NASA gave a figure of $62.5 trillion per gram of antihydrogen.[87] This is because production is difficult (only very few antiprotons are produced in reactions in particle accelerators) and because there is higher demand for other uses of particle accelerators.
- According to CERN, it has cost a few hundred million Swiss francs to produce about 1 billionth of a gram (the amount used so far for particle/antiparticle collisions).[89] In comparison, to produce the first atomic weapon, the cost of the Manhattan Project was estimated at $23 billion with inflation during 2007.[90]

costliest material to make.[87] In 2006, Gerald Smith estimated $250 million could produce 10 milligrams of positrons[88] (equivalent to $25 billion per gram); in 1999, NASA gave a figure of $62.5 trillion per gram of antihydrogen.[87] This is because production is difficult (only very few antiprotons are produced in reactions in particle accelerators) and because there is higher demand for other uses of particle accelerators.

According to CERN, it has cost a few hundred million Swiss francs to produce about 1 billionth of a gram (the amount used so far for particle/antiparticle collisions).[89] In comparison, to produce the first atomic weapon, the cost of the Manhattan Project was estimated at $23 billion with inflation during 2007.[90]

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:
- n 1 Ψ ( x , x )  n  1 ψ n ( x ) u n ( x ) (1) 1 “Ghostly action at a distance” was also referred to as non-locality.
- However EPR showed that this assumption and their criterion of reality lead to a paradox.
- The formal definition of non-locality was: instantenous action between distant systems, not consistent with the general theory of relativity.
- The Schrödinger equation provided a description of the combined state at all times, however the individual states after interaction could not be calculated.
- This seemed reasonable, because the information from the wave function agrees well with the information acquired experimentally (without influencing the state).

n 1 Ψ ( x , x )  n  1 ψ n ( x ) u n ( x ) (1) 1 “Ghostly action at a distance” was also referred to as non-locality.

However EPR showed that this assumption and their criterion of reality lead to a paradox.

The formal definition of non-locality was: instantenous action between distant systems, not consistent with the general theory of relativity.

The Schrödinger equation provided a description of the combined state at all times, however the individual states after interaction could not be calculated.

This seemed reasonable, because the information from the wave function agrees well with the information acquired experimentally (without influencing the state).

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:
- Stanford Encyclopedia of Philosophy.
- Bibcode:1973FoPh....3..229B (https://ui.adsabs.harvard.edu/abs/1973FoPh....3..229B).
- "Can the statistical postulate of quantum theory be derived?—A critique of the many-universes interpretation".
- Bibcode:2009arXiv0905.0624K (https://ui.adsa bs.harvard.edu/abs/2009arXiv0905.0624K).
- "Bohmian Mechanics" (https://plato.stanford.edu/entries/qm-bohm/).

"Can the statistical postulate of quantum theory be derived?—A critique of the many-universes interpretation".

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:
- transfer where there is a task of translating research knowledge to be application in practice, and ensuring that practitioners are made aware of it.
- Academics have been criticized for not attempting to transfer the knowledge they produce to practitioners.[15]: 804 [16] Another framing supposes that theory and knowledge seek to understand different problems and model the world in different words (using different ontologies and epistemologies).
- Another framing says that research does not produce theory that is relevant to practice.[15]: 803 In the context of management, Van de Van and Johnson propose a form of engaged scholarship where scholars examine problems that occur in practice, in an interdisciplinary fashion, producing results that create both new practical results as well as new theoretical models, but targeting theoretical results shared in an academic fashion.[15]: 815 They use a metaphor of "arbitrage" of ideas between disciplines, distinguishing it from collaboration.[15]: 803

transfer where there is a task of translating research knowledge to be application in practice, and ensuring that practitioners are made aware of it.

Academics have been criticized for not attempting to transfer the knowledge they produce to practitioners.[15]: 804 [16] Another framing supposes that theory and knowledge seek to understand different problems and model the world in different words (using different ontologies and epistemologies).

Another framing says that research does not produce theory that is relevant to practice.[15]: 803 In the context of management, Van de Van and Johnson propose a form of engaged scholarship where scholars examine problems that occur in practice, in an interdisciplinary fashion, producing results that create both new practical results as well as new theoretical models, but targeting theoretical results shared in an academic fashion.[15]: 815 They use a metaphor of "arbitrage" of ideas between disciplines, distinguishing it from collaboration.[15]: 803

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 locality model for action at a distance is called continuous action.[3] The gray area (a circle here) is a mathematical concept called a "screen".
- The spacetime diagram at the right shows the effect of such a restriction when combined with continuous action.
- No future-input dependence Many locality models explicitly or implicitly ignore the possible effect of future events.
- events that could have caused his present circumstance.
- So in the case of continuous action, events at all times and places affect Alice's and Bob's model.

The locality model for action at a distance is called continuous action.[3] The gray area (a circle here) is a mathematical concept called a "screen".

The spacetime diagram at the right shows the effect of such a restriction when combined with continuous action.

No future-input dependence Many locality models explicitly or implicitly ignore the possible effect of future events.

events that could have caused his present circumstance.

So in the case of continuous action, events at all times and places affect Alice's and Bob's model.

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:
- Moreover, the choice of what factors to normalize, among the factors appearing in the fundamental equations of physics, is not evident, and the values of the Planck units are sensitive to this choice.
- From this, it follows that a factor of 4πr 2 will appear in the denominator of Coulomb's law in rationalized form.[30]: 214–15 (Both the numerical factor and the power of the dependence on r would change if space were higher-dimensional; the correct expressions can be deduced from the geometry of higher-dimensional spheres.[11]: 51 ) Likewise for Newton's law of universal gravitation: a factor of 4π naturally appears in Poisson's equation when relating the gravitational potential to the distribution of matter.[11]: 56 Hence a substantial body of physical theory developed since Planck's 1899 paper suggests normalizing 1 1 not G but 4πG (or 8πG) to 1.
- In theoretical physics, however, this scruple may be set aside, by a process called nondimensionalization.
- This, along with the concept of flux, are the basis for the inverse-square law, Gauss's law, and the divergence operator applied to flux density.
- The effective result is that many fundamental equations of physics, which often include some of the constants used to define Planck units, become equations where these constants are replaced by a 1.

Moreover, the choice of what factors to normalize, among the factors appearing in the fundamental equations of physics, is not evident, and the values of the Planck units are sensitive to this choice.

From this, it follows that a factor of 4πr 2 will appear in the denominator of Coulomb's law in rationalized form.[30]: 214–15 (Both the numerical factor and the power of the dependence on r would change if space were higher-dimensional; the correct expressions can be deduced from the geometry of higher-dimensional spheres.[11]: 51 ) Likewise for Newton's law of universal gravitation: a factor of 4π naturally appears in Poisson's equation when relating the gravitational potential to the distribution of matter.[11]: 56 Hence a substantial body of physical theory developed since Planck's 1899 paper suggests normalizing 1 1 not G but 4πG (or 8πG) to 1.

In theoretical physics, however, this scruple may be set aside, by a process called nondimensionalization.

This, along with the concept of flux, are the basis for the inverse-square law, Gauss's law, and the divergence operator applied to flux density.

The effective result is that many fundamental equations of physics, which often include some of the constants used to define Planck units, become equations where these constants are replaced by a 1.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Some of these decoupled photons are captured by other hydrogen atoms, the remainder remain free.
- By the end of recombination, most of the protons in the universe have formed neutral atoms.
- Directly combining in a low energy state (ground state) is less efficient, so these hydrogen atoms generally form with the electrons still in a high-energy state, and once combined, the electrons quickly release energy in the form of one or more photons as they transition to a low energy state.
- The universe has become transparent to visible light, radio waves and other electromagnetic radiation for the first time in its history.
- This release of photons is known as photon decoupling.

Some of these decoupled photons are captured by other hydrogen atoms, the remainder remain free.

By the end of recombination, most of the protons in the universe have formed neutral atoms.

Directly combining in a low energy state (ground state) is less efficient, so these hydrogen atoms generally form with the electrons still in a high-energy state, and once combined, the electrons quickly release energy in the form of one or more photons as they transition to a low energy state.

The universe has become transparent to visible light, radio waves and other electromagnetic radiation for the first time in its history.

This release of photons is known as photon decoupling.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Chronology of the universe - Wikipedia.pdf


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

EVIDENCE:
- Idid.12Butthatwastheolddays.Nowadays,studentsofgeneralrelativitycanusereadymadesymbolicmanipulationprograms13todoallthetediouswork.Istronglyurgeyou, however,towriteyourownprograms,asIdid,ratherthanopenacan.Italsogoeswithout
- To paraphrase another of my action heroes, students should be required to gasp and laugh11periodically.WhystudyEinsteingravityunlessyouhavefundoingit?
- TheactionprincipleamazedFeynmanwhenhefirstheardaboutit.Inlearningtheoreticalphysics,Iwas,andam,constantlyamazed.Butinteaching,Iamamazedthatstudents areoftennotamazed.Evenworse,theyarenotamused.
- Perhapsitisdifficultforsomestudentstobeamazedandamusedwhentheyhaveto dragthemselvesthroughmilesofformalism.Sothisexhortationtobeamazedisrelated tomyattempttokeeptheformalismtoanabsoluteminimuminmytextbooksandtoget tothephysics.
- Theimportanceoffeelingamazed,andamused Iamamazedthatstudentsarenotamazed.

To paraphrase another of my action heroes, students should be required to gasp and laugh11periodically.WhystudyEinsteingravityunlessyouhavefundoingit?

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:
- PrecessionofGyroscopes | 551 whereIusedtheresultyouobtainedinexerciseVII.5.2.(Plugginginthenumbersforasatellitearoundthe earth,theLense-Thirringprecessionamountsto∼0.05arcsec/year,whilethedeSitterprecessioncomesoutto be∼7arcsec/year.) WecanalsodeterminetheLense-Thirringprecessionusing(1),pluggingintheChristoffelsymbolsappropriateforarotatingbody.NotethatwedonotneedthefullKerrmetric,onlytheasymptoticbehaviorofg tφ forlarger.WewillseeinchapterIX.4thatthisleadingterm,whichdeterminestheLense-Thirringprecession, canbefixedbygeneralconsiderations.Thelogicactuallygoesfullcircle:asweexplainedinchapterVII.5,an astronomercoulddeterminetheangularmomentumofarotatingbody,beitastarorablackhole,bymeasuring theLense-Thirringprecessionofagyroscopeorbitingthatbody.
- Theexperiment,knownasGravityProbeB,wasfirstconceivedin1959.Thetechnologicalmarvelsinvolved inconstructingaworkinggyroscopeoftherequiredprecisionarebreathtaking.Iurgeyoutosearchfor “GravityProbeB”onthewebandreadabouttheexperiment,includingthecontroversyitgenerated.The experimentultimatelytook50yearsandcost$760million.SeePhysicsToday,July2011,p.14.

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:
- Aside from the echoes of our footfalls, the corridor is soundless.
- A vertical line of light appears and widens.
- Stepping out into the corridor, she adjusts her red pencil skirt and looks back at me.
- When the cell door is open all the way, I see that she’s shouldering a backpack.
- For the moment, we have it all to ourselves.

Aside from the echoes of our footfalls, the corridor is soundless.

A vertical line of light appears and widens.

Stepping out into the corridor, she adjusts her red pencil skirt and looks back at me.

When the cell door is open all the way, I see that she’s shouldering a backpack.

For the moment, we have it all to ourselves.

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:
- College students admit to lying in about one in every three social interactions— that’s about twice a day on average—and people in the community about one in every five interactions—that’s about once a day on average (DePaulo, Kashy, Kirkendol, Wyer, & Epstein, 1996).
- If you answered “No,” the odds are high you’re lying.
- For example, even though about 70% of people believe that shifty eyes are good indicators of lying, research shows otherwise (Vrij, 2008).
- Moreover, most people, including those with special training in security professions, like judges and police officers, often do no better than chance at spotting lies (Ekman & O’Sullivan, 1991; Ekman, O’Sullivan, & Frank, 1999).
- History reveals a veritable parade

College students admit to lying in about one in every three social interactions— that’s about twice a day on average—and people in the community about one in every five interactions—that’s about once a day on average (DePaulo, Kashy, Kirkendol, Wyer, & Epstein, 1996).

If you answered “No,” the odds are high you’re lying.

For example, even though about 70% of people believe that shifty eyes are good indicators of lying, research shows otherwise (Vrij, 2008).

Moreover, most people, including those with special training in security professions, like judges and police officers, often do no better than chance at spotting lies (Ekman & O’Sullivan, 1991; Ekman, O’Sullivan, & Frank, 1999).

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 outgoing (v) and ingoing (u) null directions lie along the basis elements γγ and γγ of the corresponding Newman-Penrose tetrad, v u equations (39.1).
- The condition P =0 requires that L=Eω , so L cannot be constant.
- Thus although the principal null congruences are geodesic, they cannot be described by a lineelementthatishypersurface-orthogonalsimultaneouslyonbothoutgoingandingoingcongruences.According tothetheoremprovedin§18.1,thisimpliesthatthereisnovorticity-freetetradthatalignswiththeprincipal null congruences.
- As expected, the actions S equal −m times x ± the proper times along the outgoing and ingoing congruences.
- The line-element (23.141) of the Doran congruences in hypersurface-orthogonal form is ds2 =ρ2 [ Δ x (−C2dT2+dZ2)+ dy2 + Δ y −ω y 2Δ x ( dφ− ω x Δ y −ω y Δ x dT )2 ] , (23.153) m2β2 Δ (1−ω ω )2 Δ −ω2Δ m y x y y y x where the coefficient C is ( β2Δ )1/2 ( ρ2Δ Δ )1/2 ( ρ2Δ )−1/2 C ≡ y = 1− x y = 1+ x .

The outgoing (v) and ingoing (u) null directions lie along the basis elements γγ and γγ of the corresponding Newman-Penrose tetrad, v u equations (39.1).

The condition P =0 requires that L=Eω , so L cannot be constant.

Thus although the principal null congruences are geodesic, they cannot be described by a lineelementthatishypersurface-orthogonalsimultaneouslyonbothoutgoingandingoingcongruences.According tothetheoremprovedin§18.1,thisimpliesthatthereisnovorticity-freetetradthatalignswiththeprincipal null congruences.

As expected, the actions S equal −m times x ± the proper times along the outgoing and ingoing congruences.

The line-element (23.141) of the Doran congruences in hypersurface-orthogonal form is ds2 =ρ2 [ Δ x (−C2dT2+dZ2)+ dy2 + Δ y −ω y 2Δ x ( dφ− ω x Δ y −ω y Δ x dT )2 ] , (23.153) m2β2 Δ (1−ω ω )2 Δ −ω2Δ m y x y y y x where the coefficient C is ( β2Δ )1/2 ( ρ2Δ Δ )1/2 ( ρ2Δ )−1/2 C ≡ y = 1− x y = 1+ x .

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 Friedmann equations imply the first law of thermodynamics, §10.9.2, and thus enforce conservation of entropy per comoving volume (but see Concept Question 30.5).
- The CMB hasapreciseblackbodyspectrum,notbecauseitisinthermodynamicequilibriumtoday,butratherbecause theCMBwasinthermodynamicequilibriumwithelectronsandnucleiatthetimeofrecombination,andthe CMB has streamed more or less freely through the Universe since recombination.
- A system of photons in thermodynamic equilibrium has a blackbody distribution of energies.
- In the real Universe, entropy increases as a result of fluctuations away from the perfect homogeneity and
- A thermal distribution of relativisticparticlesretainsitsthermaldistributioninanexpandingFLRWuniverse(albeitwithachanging temperature), Exercise 10.13.

The Friedmann equations imply the first law of thermodynamics, §10.9.2, and thus enforce conservation of entropy per comoving volume (but see Concept Question 30.5).

The CMB hasapreciseblackbodyspectrum,notbecauseitisinthermodynamicequilibriumtoday,butratherbecause theCMBwasinthermodynamicequilibriumwithelectronsandnucleiatthetimeofrecombination,andthe CMB has streamed more or less freely through the Universe since recombination.

A system of photons in thermodynamic equilibrium has a blackbody distribution of energies.

In the real Universe, entropy increases as a result of fluctuations away from the perfect homogeneity and

A thermal distribution of relativisticparticlesretainsitsthermaldistributioninanexpandingFLRWuniverse(albeitwithachanging temperature), Exercise 10.13.

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.