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

EVIDENCE:
- A lot depends on the distance of the binary.
- It is too massive to be either a white dwarf or a neutron star, and the inference seems to be, then, that the invisible star is a black hole.
- This is still rather indirect evidence, and not all astronomers agree that Cygnus X-1 is a black hole.
- Furthermore, HD-226868 seems to be expanding as though it were entering the red-giant stage.
- A few other binaries have since been observed in which one of the pair may be a black hole.

A lot depends on the distance of the binary.

It is too massive to be either a white dwarf or a neutron star, and the inference seems to be, then, that the invisible star is a black hole.

This is still rather indirect evidence, and not all astronomers agree that Cygnus X-1 is a black hole.

Furthermore, HD-226868 seems to be expanding as though it were entering the red-giant stage.

A few other binaries have since been observed in which one of the pair may be a black hole.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- times greater than the gravitational force of the moon on that baby.
- Furthermore, the moon’s tides are influenced not by its phase—that is, by how much of it is visible to us on earth—but by its distance from earth (Kelly, Laverty, & Saklofske, 1990).
- Indeed, during a “new moon,” the phase at which the moon is invisible to us on earth, the moon exerts just as much gravitational influence as it does during a full moon.
- These flawed explanations aside, we can still ask the question of whether the full moon exerts any meaningful effects on behavior.
- Because well over 100 published studies have examined this issue, scientists now have | 202 Chapter 9 Sad, Mad, and Bad

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.

times greater than the gravitational force of the moon on that baby.

Furthermore, the moon’s tides are influenced not by its phase—that is, by how much of it is visible to us on earth—but by its distance from earth (Kelly, Laverty, & Saklofske, 1990).

Indeed, during a “new moon,” the phase at which the moon is invisible to us on earth, the moon exerts just as much gravitational influence as it does during a full moon.

These flawed explanations aside, we can still ask the question of whether the full moon exerts any meaningful effects on behavior.

Because well over 100 published studies have examined this issue, scientists now have | 202 Chapter 9 Sad, Mad, and Bad

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:
- Consider a normal spatial rotation in which a primed frame is rotated in the wx-plane clockwise by an angle a about the origin, relative to the unprimed frame.
- A rotation between time t and space x is a Lorentz boost in the x-direction.
- As the spacetime wheel boosts, a point on the wheel describes an invariant hyperbola.
- The relation between the coordinates {w′,x′} and {w,x} of a point in the two frames is ( w′ ) ( cosa −sina )( w ) = .
- 1.8 The spacetime wheel 27 t x Figure1.14 Aspacetimewheel.

Consider a normal spatial rotation in which a primed frame is rotated in the wx-plane clockwise by an angle a about the origin, relative to the unprimed frame.

A rotation between time t and space x is a Lorentz boost in the x-direction.

As the spacetime wheel boosts, a point on the wheel describes an invariant hyperbola.

The relation between the coordinates {w′,x′} and {w,x} of a point in the two frames is ( w′ ) ( cosa −sina )( w ) = .

1.8 The spacetime wheel 27 t x Figure1.14 Aspacetimewheel.

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:
- 13 (https://archive.org/details/quantumcomputati00niel_993/page/ n46).
- Yanofsky, Noson S.; Mannucci, Mirco (2013).
- The Pauli Z basis is usually called the computational basis, where the relative phase have no effect on measurement.
- doi:10.1137/S0097539795293172 (https://doi.org/1 0.1137%2FS0097539795293172).
- Because measurement collapses the quantum state, measuring the state in one basis hides some of the values that would have been measurable in the other basis; See the uncertainty principle.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

Yanofsky, Noson S.; Mannucci, Mirco (2013).

The Pauli Z basis is usually called the computational basis, where the relative phase have no effect on measurement.

Because measurement collapses the quantum state, measuring the state in one basis hides some of the values that would have been measurable in the other basis; See the uncertainty principle.

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 Hole Embedding Diagram Schwarzschild solution to General Relativity for t = constant, θ = π /2: 2 2 2 2 ds = dr + r dφ " 2GM % $ 1− ' # rc & z The Schwarzschild Wormhole or Einstein-Rosen Bridge (Flamm 1916, Physikalische Zeitschrift.
- XVII: 448; Einstein & Rosen 1935, Phys.
- 48 73; y Misner & Wheeler 1957, Ann.

Black Hole Embedding Diagram Schwarzschild solution to General Relativity for t = constant, θ = π /2: 2 2 2 2 ds = dr + r dφ " 2GM % $ 1− ' # rc & z The Schwarzschild Wormhole or Einstein-Rosen Bridge (Flamm 1916, Physikalische Zeitschrift.

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 L1MDIS OVERVIEW e Purpose eMission e Definitions e Management e Personnel Participation • I I Benefits e Primary Methodologies e Secondary Methodologies e Categories of Taskings e Types of Targets e Operations Methodology e Summary SECRET NOFORN STAR GATE LIMDIS 11M8983-2 DCH -

SECRET NOFORN STAR GATE L1MDIS OVERVIEW e Purpose eMission e Definitions e Management e Personnel Participation • I I Benefits e Primary Methodologies e Secondary Methodologies e Categories of Taskings e Types of Targets e Operations Methodology e Summary SECRET NOFORN STAR GATE LIMDIS 11M8983-2 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:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- McCandlishalsostatesHalPuthoffexplainedtohimhowzeropointenergy couldbeusedtopropelacraft;itisunknownifPuthoffbelievedacraftwasstoredatNorton.
- Thefilmalsostates“freeenergy”researchersStefanMarinovinAustriafelloutofawindowin 1997,coldfusionexpertEugeneMallovediedofbluntforcetraumain2004beforeapresentation,zero pointenergyphysicistAriedeGeusdiedinaparkedcarin2007beforeatriptosecurefunding,zeropoint energyStardrivepatentMarkTomiondiedunexpectedlyin2009aftercorrespondingwithMcCandlish.
- Thefilmmakerwhocreatedthismovie,JamesAllen,diedofheavymetalpoisoningthreemonths afterthefilmfinishedediting.
- ● https://youtu.be/afLsRsd5roY ● https://gizadeathstar.com/2021/05/the-sad-and-mysterious-death-of-ufologist-mark-mccandlish/ (PUBLICDOMAIN) -30January2015—RetiredUSNavyPettyOfficerFirstClassflightEngineer “Brian”tellsufologistLindaMoultonHowehesawalargeholetoanundergroundfacility5-10miles fromthegeographicSouthPole;hestatestheareawassupposedtobeanoflyzonebutduringan emergencymedevac,theyflewthroughthearea.
- ● https://www.earthfiles.com/2022/04/14/part-1-update-u-s-navy-flight-engineer-saw-silver-discs-a nd-entrance-to-alleged-e-t-and-human-collaboration-base-in-antarctica/ ● https://www.earthfiles.com/2022/04/16/part-2-antarctica-retired-navy-flight-engineer-warned-bynsa-to-stop-talking-about-missing-scientists/ Note:Heprovidesphotos,aservicemedalcertificateandaudiotestimonythatsuggeststhereis mediumconfidenceinhistestimony;howevertheonlylinkstoUAPandthepotentialproject occurringinafacilityundertheicearespeculationbyHoweandunnecessary.

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:
- ,e ,ν ,e ), and L L R R the three quark multiplets (uc,dc,uc,dc) of colours c = r,g,b.
- f However, T-bit doubling doubles the number n of fermion multiplets, as is evident in the chart (42.110), f andaswillbediscussedfurtherin§42.4.14.Eachspinorcomesintwospecies,withweakchiralityrespectively aligned and anti-aligned with its Dirac chirality, equations (42.174).
- The colour group Spin(6) acts on enlarged L L R R fermion multiplets that contain leptons as well as quarks, (ν ,u ), (ν ,u ), (e ,d ), and (e ,d ).
- In both L L R R L L R R Spin(5) and Spin(6), the number of fermion multiplets is still n =4×3=12.
- The observed masses of fermions after electroweak symmetry breaking, Table 42.3, vary from tiny compared to the electroweak scale (neutrinos) to comparable to the electroweak scale (the top quark, at 173GeV).

,e ,ν ,e ), and L L R R the three quark multiplets (uc,dc,uc,dc) of colours c = r,g,b.

f However, T-bit doubling doubles the number n of fermion multiplets, as is evident in the chart (42.110), f andaswillbediscussedfurtherin§42.4.14.Eachspinorcomesintwospecies,withweakchiralityrespectively aligned and anti-aligned with its Dirac chirality, equations (42.174).

The colour group Spin(6) acts on enlarged L L R R fermion multiplets that contain leptons as well as quarks, (ν ,u ), (ν ,u ), (e ,d ), and (e ,d ).

In both L L R R L L R R Spin(5) and Spin(6), the number of fermion multiplets is still n =4×3=12.

The observed masses of fermions after electroweak symmetry breaking, Table 42.3, vary from tiny compared to the electroweak scale (neutrinos) to comparable to the electroweak scale (the top quark, at 173GeV).

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- The BSSN formalism on the other hand, §16.16.2, retains equation (16.355) as a distinct equation of motion.
- (16.356c) Equation (16.355) is an equation of motion in the sense that it involves a time derivative d Γ ; but Γ t a ̄α ̄ a ̄α ̄ is not one of the momenta Γ ̄0α ̄ conjugate to the area element e2 a ̄α ̄ , so equation (16.355) has a different status from the 9+9 equations of motion (16.354).
- of motion: e a ̄α ̄ ∧ ( d t Γ ̄0α ̄ + 1 2 [Γ a ̄t ̄,Γ ̄0α ̄ ]+d α Γ ̄0t ̄ + 1 2 [Γ a ̄α ̄ ,Γ ̄0t ̄ ] ) +e a ̄t ̄∧R ̄0α ̄ =8πT ** ̄0t ̄ , (16.356b) 3 eqs.
- of motion: −d t e2 a ̄α ̄ + 1 [Γ a ̄t ̄,e2 a ̄α ̄ ]−e a ̄α ̄ ∧ ( d α e a ̄t ̄+ 1 [Γ a ̄α ̄ ,e a ̄t ̄] ) +e a ̄t ̄∧S a ̄α ̄ =8πΣ ** a ̄t ̄, (16.356a) 9 eqs.
- The earlier equations (16.311) had the problem that the time derivative in the equation of motion for Γ was e ∧d as opposed to just d .

The BSSN formalism on the other hand, §16.16.2, retains equation (16.355) as a distinct equation of motion.

(16.356c) Equation (16.355) is an equation of motion in the sense that it involves a time derivative d Γ ; but Γ t a ̄α ̄ a ̄α ̄ is not one of the momenta Γ ̄0α ̄ conjugate to the area element e2 a ̄α ̄ , so equation (16.355) has a different status from the 9+9 equations of motion (16.354).

of motion: e a ̄α ̄ ∧ ( d t Γ ̄0α ̄ + 1 2 [Γ a ̄t ̄,Γ ̄0α ̄ ]+d α Γ ̄0t ̄ + 1 2 [Γ a ̄α ̄ ,Γ ̄0t ̄ ] ) +e a ̄t ̄∧R ̄0α ̄ =8πT ** ̄0t ̄ , (16.356b) 3 eqs.

of motion: −d t e2 a ̄α ̄ + 1 [Γ a ̄t ̄,e2 a ̄α ̄ ]−e a ̄α ̄ ∧ ( d α e a ̄t ̄+ 1 [Γ a ̄α ̄ ,e a ̄t ̄] ) +e a ̄t ̄∧S a ̄α ̄ =8πΣ ** a ̄t ̄, (16.356a) 9 eqs.

The earlier equations (16.311) had the problem that the time derivative in the equation of motion for Γ was e ∧d as opposed to just 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:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- ISBN 978-981-256-380-4 Wheeler, John A.; Feynman, Richard P.
- World Scientific (with title "Feynman's Thesis: a New Approach to Quantum Theory") (published 2005).
- "Interaction with the Absorber as the Mechanism of Radiation" (https://web.archive.org/web/20200417074134/https://authors.library.caltech.edu/110 95/).
- Feynman, Richard P.; Welton, T.
- doi:10.1103/RevModPhys.20.367 (https://doi.org/10.1103%2FRevMod Phys.20.367).

ISBN 978-981-256-380-4 Wheeler, John A.; Feynman, Richard P.

World Scientific (with title "Feynman's Thesis: a New Approach to Quantum Theory") (published 2005).

"Interaction with the Absorber as the Mechanism of Radiation" (https://web.archive.org/web/20200417074134/https://authors.library.caltech.edu/110 95/).

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- To analyze data collected previously by other investigators on this method, they used a statistical technique called meta-analysis, which allows researchers to combine the results of many studies and treat them as though they were one large study.
- Lance Storm and Suitbert Ertel (2001) responded to Milton and Wiseman (1999) with another meta-analysis of 79 Ganzfeld studies, dating from 1974 to 1996, and contended that their analysis supported the claim that the Ganzfeld procedure detected ESP.
- A person in another room then attempts to mentally transmit pictures to subjects, who later rate the extent to which each of four pictures matches the mental imagery they experienced during the session.
- It’s clear that the question of whether
- To establish this uniform sensory field, ESP experimenters cover the eyes of relaxed subjects with ping-pong ball halves, and direct a floodlight containing a red beam toward their eyes.

To analyze data collected previously by other investigators on this method, they used a statistical technique called meta-analysis, which allows researchers to combine the results of many studies and treat them as though they were one large study.

Lance Storm and Suitbert Ertel (2001) responded to Milton and Wiseman (1999) with another meta-analysis of 79 Ganzfeld studies, dating from 1974 to 1996, and contended that their analysis supported the claim that the Ganzfeld procedure detected ESP.

A person in another room then attempts to mentally transmit pictures to subjects, who later rate the extent to which each of four pictures matches the mental imagery they experienced during the session.

To establish this uniform sensory field, ESP experimenters cover the eyes of relaxed subjects with ping-pong ball halves, and direct a floodlight containing a red beam toward their eyes.

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:
- He turns the handle, and I hear the latch bolt slide from its housing.
- A wind through the door carries the scent of wet earth and unknown flowers.
- Charlie steps toward the door and takes hold of the handle.
- When they finally adjust, I see Charlie silhouetted in the open doorway of the box.
- I put my hand on Charlie’s shoulder.

He turns the handle, and I hear the latch bolt slide from its housing.

A wind through the door carries the scent of wet earth and unknown flowers.

Charlie steps toward the door and takes hold of the handle.

When they finally adjust, I see Charlie silhouetted in the open doorway of the box.

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:
- Beliefs in the memory-enhancing powers of hypnosis have a long and at times checkered history.
- 9781405131117_4_003.qxd 30/6/09 11:48 AM Page 71 statement that “memory is permanently stored in the mind” and that “...with hypnosis, or other specialized techniques, these inaccessible details could eventually be recovered.” In a sample of over 850 psychotherapists, Michael Yapko (1994) found that large proportions endorsed the following items with high-to-moderate frequency: (1) 75%: “Hypnosis enables people to accurately remember things they otherwise could not.” (2) 47%: “Therapists can have greater faith in details of a traumatic event when obtained hypnotically than otherwise.” (3) 31%: “When someone has a memory of a trauma while in hypnosis, it objectively must actually have occurred.” (4) 54%: “Hypnosis can be used to recover memories of actual events as far back as birth.” In other surveys (Poole, Lindsay, Memon, & Bull, 1995), between about a third (29% and 34%) and a fifth (20%; Polusny & Follette, 1996) of psychotherapists reported that they used hypnosis to help clients recall memories of suspected sexual abuse.
- In such movies as In Like Flint, Kiss the Girls, Dead on Sight, and The Resurrection Syndrome, witnesses recall the exact details of crimes or long-forgotten childhood events with the aid of
- In a famous case, Janet (1889) used hypnosis to “age regress” (mentally relive an earlier time period) his patient Marie to her childhood, when she was traumatized by seeing a child with a facial deformity.
- Janet was one of the first therapists to use hypnosis to help patients recover memories of traumatic events that he assumed caused their psychological difficulties.

Beliefs in the memory-enhancing powers of hypnosis have a long and at times checkered history.

9781405131117_4_003.qxd 30/6/09 11:48 AM Page 71 statement that “memory is permanently stored in the mind” and that “...with hypnosis, or other specialized techniques, these inaccessible details could eventually be recovered.” In a sample of over 850 psychotherapists, Michael Yapko (1994) found that large proportions endorsed the following items with high-to-moderate frequency: (1) 75%: “Hypnosis enables people to accurately remember things they otherwise could not.” (2) 47%: “Therapists can have greater faith in details of a traumatic event when obtained hypnotically than otherwise.” (3) 31%: “When someone has a memory of a trauma while in hypnosis, it objectively must actually have occurred.” (4) 54%: “Hypnosis can be used to recover memories of actual events as far back as birth.” In other surveys (Poole, Lindsay, Memon, & Bull, 1995), between about a third (29% and 34%) and a fifth (20%; Polusny & Follette, 1996) of psychotherapists reported that they used hypnosis to help clients recall memories of suspected sexual abuse.

In such movies as In Like Flint, Kiss the Girls, Dead on Sight, and The Resurrection Syndrome, witnesses recall the exact details of crimes or long-forgotten childhood events with the aid of

In a famous case, Janet (1889) used hypnosis to “age regress” (mentally relive an earlier time period) his patient Marie to her childhood, when she was traumatized by seeing a child with a facial deformity.

Janet was one of the first therapists to use hypnosis to help patients recover memories of traumatic events that he assumed caused their psychological difficulties.

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:
- Understand the causes: False confessions.
- R., Carlson, E., Rotert, M., Egeland, B., & Sroufe, L.
- The birth order effect: How to better understand yourself and others.
- Subtyping non-eating disordered overweight and obesity along an affect dimension.
- Canetto (Eds.), Review of suicidology (pp.

Understand the causes: False confessions.

R., Carlson, E., Rotert, M., Egeland, B., & Sroufe, L.

The birth order effect: How to better understand yourself and others.

Subtyping non-eating disordered overweight and obesity along an affect dimension.

Canetto (Eds.), Review of suicidology (pp.

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:
- Tostudythecollapseofasphericalcloudofmatterintoablackholerequiresgeneralizing themetric(4)usedheretothetimedependentmetricmentionedinappendix3tochapter VI.3.
- —ArthurS.Eddington,commentsattheRoyalAstronomical SocietyMeeting,onJanuary11,1935 AsIhavealreadysaid, adetailedanalysisofstellarequilibriumusingvariousequations ofstateP(ρ)isbeyondthescopeofthistext,eventhough,asthereaderprobablyknows, the results from such an analysis constitute some of the most spectacular highlights of stellarastrophysics.Forexample,ifthepressureissuppliedbythequantummotionofthe electronsinthestar,namelytheFermipressureofdegenerateelectrons(seeanytexton statisticalmechanics), thestellarmassM cannotexceedanupperlimitofabout1.4M(cid:23), knownastheChandrasekharlimit.
- shows that a star of mass greater than a certain limit M .
- RelativisticStellarInteriors | 455 Stellarcollapseintoblackholes Chandrasekhar .
- I am content to point out a key physical feature of the relativistic equation for stellar equilibrium.Weseethattheexpressioninthefirstparenthesesin(13)effectivelychanges themassdensityρinNewtoniangravity(15)toρ+P.Thisimportantpieceofphysicscan betracedallthewaybacktospecialrelativity:pressure, beinganenergydensity, counts alsoasamassdensity.Thus,asinfallingmatterpilesontoasuperdensestarandsqueezes itgravitationally,thestarresistsbyincreasingitsinternalpressureP,whichonlyaddsto themassdensitybearingin.Inessence,thisviciouscycleisattherootofthephysicsof blackholeformation.

—ArthurS.Eddington,commentsattheRoyalAstronomical SocietyMeeting,onJanuary11,1935 AsIhavealreadysaid, adetailedanalysisofstellarequilibriumusingvariousequations ofstateP(ρ)isbeyondthescopeofthistext,eventhough,asthereaderprobablyknows, the results from such an analysis constitute some of the most spectacular highlights of stellarastrophysics.Forexample,ifthepressureissuppliedbythequantummotionofthe electronsinthestar,namelytheFermipressureofdegenerateelectrons(seeanytexton statisticalmechanics), thestellarmassM cannotexceedanupperlimitofabout1.4M(cid:23), knownastheChandrasekharlimit.

shows that a star of mass greater than a certain limit M .

RelativisticStellarInteriors | 455 Stellarcollapseintoblackholes Chandrasekhar .

I am content to point out a key physical feature of the relativistic equation for stellar equilibrium.Weseethattheexpressioninthefirstparenthesesin(13)effectivelychanges themassdensityρinNewtoniangravity(15)toρ+P.Thisimportantpieceofphysicscan betracedallthewaybacktospecialrelativity:pressure, beinganenergydensity, counts alsoasamassdensity.Thus,asinfallingmatterpilesontoasuperdensestarandsqueezes itgravitationally,thestarresistsbyincreasingitsinternalpressureP,whichonlyaddsto themassdensitybearingin.Inessence,thisviciouscycleisattherootofthephysicsof blackholeformation.

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:
- According to AA, to prevail over the all-consuming mental obsession to drink, members must commit to believing that a Higher Power greater than themselves (who’s often, although not necessarily, God) can restore their “sanity” (Step 2), and turn their will and their lives over to the care of their Higher Power as they understand Him (Step 3).
- Until quite recently, the idea that abstinence is the only treatment goal for alcoholics—people with a physical and psychological dependence on alcohol, and life problems stemming from drinking—was embraced not only by the general public, but by the alcohol treatment community, as exemplified by the popular AA program.
- More recent Academy Award-winning films, including The Days of Wine and Roses (1962) and Leaving Las Vegas (1995), have brought out the darker side of alcoholism by depicting alcohol’s devastating effects on relationships and mental health, even the prospect of suicide.
- A survey of 43,093 adults conducted by the National Institute of Alcohol Abuse and Alcoholism
- Studies show that drinkers who join AA are more likely to get back on the wagon than those who receive no treatment (Kownacki & Shadish, 1999; Timko, Moos, Finney, & Lesar, 2000).

According to AA, to prevail over the all-consuming mental obsession to drink, members must commit to believing that a Higher Power greater than themselves (who’s often, although not necessarily, God) can restore their “sanity” (Step 2), and turn their will and their lives over to the care of their Higher Power as they understand Him (Step 3).

Until quite recently, the idea that abstinence is the only treatment goal for alcoholics—people with a physical and psychological dependence on alcohol, and life problems stemming from drinking—was embraced not only by the general public, but by the alcohol treatment community, as exemplified by the popular AA program.

More recent Academy Award-winning films, including The Days of Wine and Roses (1962) and Leaving Las Vegas (1995), have brought out the darker side of alcoholism by depicting alcohol’s devastating effects on relationships and mental health, even the prospect of suicide.

A survey of 43,093 adults conducted by the National Institute of Alcohol Abuse and Alcoholism

Studies show that drinkers who join AA are more likely to get back on the wagon than those who receive no treatment (Kownacki & Shadish, 1999; Timko, Moos, Finney, & Lesar, 2000).

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:
- Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

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:
- Suppose V, W are Hilbert spaces, and let be an orthonormal basis for W.
- Since the vectors form a basis for , the maps form a basis for .
- Another case of this abstract notion of partial trace takes place in the category of finite sets and bijections between them, in which the monoidal product is disjoint union.
- One can show that for any finite sets, X,Y,U and bijection there exists a corresponding "partially traced" bijection .
- Partial trace for operators on Hilbert spaces The partial trace generalizes to operators on infinite dimensional Hilbert spaces.

Suppose V, W are Hilbert spaces, and let be an orthonormal basis for W.

Since the vectors form a basis for , the maps form a basis for .

Another case of this abstract notion of partial trace takes place in the category of finite sets and bijections between them, in which the monoidal product is disjoint union.

One can show that for any finite sets, X,Y,U and bijection there exists a corresponding "partially traced" bijection .

Partial trace for operators on Hilbert spaces The partial trace generalizes to operators on infinite dimensional Hilbert spaces.

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:
- As long as I stay inside, he can’t really hurt me.
- “Out of the car, Jason.” I realize that I see the interior of the Navigator as a kind of lifeboat.
- The wind inflicts a raw, serrated bite on my exposed skin, which is covered in gooseflesh.
- You don’t want my blood in here.” — When I come to, he’s dragging me out of the front seat by my arms.
- “Jason.” My chest is heaving, I’m starting to hyperventilate, black spots detonating across my field of vision.

As long as I stay inside, he can’t really hurt me.

“Out of the car, Jason.” I realize that I see the interior of the Navigator as a kind of lifeboat.

The wind inflicts a raw, serrated bite on my exposed skin, which is covered in gooseflesh.

You don’t want my blood in here.” — When I come to, he’s dragging me out of the front seat by my arms.

“Jason.” My chest is heaving, I’m starting to hyperventilate, black spots detonating across my field of vision.

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:
- BigBang:Fromnospacetospace Wehaveavoideddealingwiththetime-timecomponent(16)ofEinstein’sfieldequation ̈ −3R =4πG(ρ+3P),seeingthatitinvolvesasecondderivative.However,itdoesconvey R an important message: as long as ρ+3P >0, the acceleration R ̈ <0, so that R ̇ always decreases, regardless of whether the universe is closed, flat, or open.
- At present, R>0, since we see redshifts.
- Hence the curve ̇ R(t) is convex downward.
- This argument also indicates thatauniversecontainingonlythecosmologicalconstantcouldevadethisargumentand avoidhavingaBigBanginitspast(aswehaveseeninchapterVI.2,andaswewillseein chapterIX.10).
- 3R (cid:5) In contrast, a matter filled open universe, obeying R ̇ = 8πGρ 0 R 0 3 +1, will expand 3R forever,eventuallyreachingR ̇ (cid:16)1,withacurvaturedrivenexpansion,evenasthematter densitydilutestopracticallynothing.

BigBang:Fromnospacetospace Wehaveavoideddealingwiththetime-timecomponent(16)ofEinstein’sfieldequation ̈ −3R =4πG(ρ+3P),seeingthatitinvolvesasecondderivative.However,itdoesconvey R an important message: as long as ρ+3P >0, the acceleration R ̈ <0, so that R ̇ always decreases, regardless of whether the universe is closed, flat, or open.

At present, R>0, since we see redshifts.

Hence the curve ̇ R(t) is convex downward.

This argument also indicates thatauniversecontainingonlythecosmologicalconstantcouldevadethisargumentand avoidhavingaBigBanginitspast(aswehaveseeninchapterVI.2,andaswewillseein chapterIX.10).

3R (cid:5) In contrast, a matter filled open universe, obeying R ̇ = 8πGρ 0 R 0 3 +1, will expand 3R forever,eventuallyreachingR ̇ (cid:16)1,withacurvaturedrivenexpansion,evenasthematter densitydilutestopracticallynothing.

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:
- Surveys show that even most psychotherapists agree that memories are fixed more or less permanently in the mind (Loftus & Loftus, 1980; Yapko, 1994).
- If our memories were perfect, we’d never forget a friend’s birthday, where we misplaced our iPod, or the exact date, time, and place of our first kiss.
- This kind of observation should be sufficient to challenge the widespread belief that our memories work like video cameras or DVDs.
- One person recalls a lively discussion about politics as a friendly debate; another recalls the identical discussion as a heated argument.
- In one survey of over 600 undergraduates at a midwestern university, 27% agreed that memory operates like a tape recorder (Lenz, Ek, & Mills, 2009).

Surveys show that even most psychotherapists agree that memories are fixed more or less permanently in the mind (Loftus & Loftus, 1980; Yapko, 1994).

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

This kind of observation should be sufficient to challenge the widespread belief that our memories work like video cameras or DVDs.

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

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

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:
- JSTOR 4027945 (https://www.jstor.org/stable/ 4027945).
- Archived from the original (http://www.haydenplanetarium.or g/tyson/read/2005/11/01/the-perimeter-of-ignorance) on 6 September 2018.
- New Haven London: Yale University Press.
- "Isaac Newton, heretic: the strategies of a Nicodemite".
- Brewster states that Newton was never known as an Arian during his lifetime, it was William Whiston, an Arian, who first argued that "Sir Isaac Newton was so hearty for the Baptists, as well as for the Eusebians or Arians, that he sometimes suspected these two were the two witnesses in the Revelations," while others like Hopton Haynes (a Mint

JSTOR 4027945 (https://www.jstor.org/stable/ 4027945).

Archived from the original (http://www.haydenplanetarium.or g/tyson/read/2005/11/01/the-perimeter-of-ignorance) on 6 September 2018.

New Haven London: Yale University Press.

"Isaac Newton, heretic: the strategies of a Nicodemite".

Brewster states that Newton was never known as an Arian during his lifetime, it was William Whiston, an Arian, who first argued that "Sir Isaac Newton was so hearty for the Baptists, as well as for the Eusebians or Arians, that he sometimes suspected these two were the two witnesses in the Revelations," while others like Hopton Haynes (a Mint

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:
- An additional effort concentrated on screening and selection of personnel.
- Moreover, a five-year psychoenergetics program (FYs* 1986-1990) using Army Medical research and development funds authorized by the then U.S.
- — Objectives included formulating a long-range comprehensive plan, developing an integrated foreign data base, publishing foreign assessments, developing proper documentation, obtaining external assistance.
- — Project STAR GATE established on 31 January 1991.
- — Published Foreign Assessments, Long-Range Comprehensive Plan by 30 May 1991.

An additional effort concentrated on screening and selection of personnel.

Moreover, a five-year psychoenergetics program (FYs* 1986-1990) using Army Medical research and development funds authorized by the then U.S.

— Objectives included formulating a long-range comprehensive plan, developing an integrated foreign data base, publishing foreign assessments, developing proper documentation, obtaining external assistance.

— Project STAR GATE established on 31 January 1991.

— Published Foreign Assessments, Long-Range Comprehensive Plan by 30 May 1991.

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:
- O'Connor, John J.; Robertson, Edmund F.
- Algebras are geometric facts which are proved."".
- MacTutor History of Mathematics Archive.
- "Al-Sabi Thabit ibn Qurra al-Harrani" (https://mathshisto ry.st-andrews.ac.uk/Biographies/Thabit.html).
- O'Connor, John J.; Robertson, Edmund F.

Algebras are geometric facts which are proved."".

MacTutor History of Mathematics Archive.

"Al-Sabi Thabit ibn Qurra al-Harrani" (https://mathshisto ry.st-andrews.ac.uk/Biographies/Thabit.html).

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Fittsbelievessomeofthe unauthorizedfundingwasfordomestic“clandestinemilitaryR&D,”someofwhichwasUAPrelatedand divertedfromDOD/HUDtoillegalprograms.
- Thesewouldbeexpensiveprogramssincethe costofsecrecycanbeseveraltimesbiggerthantheresearch...theblackprogramscollectivelyhave budgetsinthe$10Brangeannually.
- “Ifthereisanythingnearaworkingantigravity craft,they’vekeptitveryquiet,”Kobitzstates.
- ● https://www.amazon.com/Plain-Sight-investigation-impossible-science-ebook/dp/B08V YR4DZ6(p309) (PUBLICDOMAIN) -11December2017—FormerAssistantSecretaryofHousingandUrban DevelopmentCatherineAustinFittspublishesapaperwithaMichiganStateUniversityeconomistthat finds$21trillioninunauthorizedspendinginthedepartmentsofDefenseandHousingandUrban Developmentbetween1998and2015.
- Note:FormerU.S.NavyDir.ofScienceandTechnologyDevelopmentNatKobitztold journalistRossCoulthartin2021thathemadeafew“discreteinquiries”relatedtothetriangle craftpatentandNAVAIR.

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:
- This effect makes visual descriptions of the effects of special relativity especially prone to mistakes.[9] Special relativity also has profound technical consequences.
- When comparing two sets of coordinates in relative motion the Lorentz transformation replaces the Galilean transformation of Newtonian mechanics.[10]: 98 Other effects include the relativistic corrections to the Doppler effect and the Thomas precession.[1][2] It also explains how electricity and
- In Lorentzian geometry, 'distances' become 'intervals' and include a time coordinate with a minus sign.
- A defining feature of special relativity is the replacement of Euclidean geometry with Lorentzian geometry.[10]: 8 Distances in Euclidean geometry are calculated with the Pythagorean theorem and only involved spatial coordinates.
- In special relativity, covering ten times more distance on the ground in the same amount of time according to a moving watch does not result in a speed up as seen from the ground by a factor of ten.[3]: 28 Consequences Special relativity has a wide range of consequences that have been experimentally verified.[4][5] The conceptual effects include: The relativity of simultaneity – events that appear simultaneous to one observer may not be simultaneous to an observer in motion[3]: 49 § Time dilation – time measured between two events by observers in motion differ § Length contraction – distances between two events by observers in motion differ The § Lorentz transformation of velocities – velocities no longer simply add Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula , where is the speed of light in vacuum.[6][7] Special relativity replaced the conventional notion of an absolute, universal time with the notion of a time that is local to each observer.[8]: 33 Information about distant objects can arrive no faster than the speed of light so visual observations always report events that have happened in the past.

This effect makes visual descriptions of the effects of special relativity especially prone to mistakes.[9] Special relativity also has profound technical consequences.

When comparing two sets of coordinates in relative motion the Lorentz transformation replaces the Galilean transformation of Newtonian mechanics.[10]: 98 Other effects include the relativistic corrections to the Doppler effect and the Thomas precession.[1][2] It also explains how electricity and

In Lorentzian geometry, 'distances' become 'intervals' and include a time coordinate with a minus sign.

A defining feature of special relativity is the replacement of Euclidean geometry with Lorentzian geometry.[10]: 8 Distances in Euclidean geometry are calculated with the Pythagorean theorem and only involved spatial coordinates.

In special relativity, covering ten times more distance on the ground in the same amount of time according to a moving watch does not result in a speed up as seen from the ground by a factor of ten.[3]: 28 Consequences Special relativity has a wide range of consequences that have been experimentally verified.[4][5] The conceptual effects include: The relativity of simultaneity – events that appear simultaneous to one observer may not be simultaneous to an observer in motion[3]: 49 § Time dilation – time measured between two events by observers in motion differ § Length contraction – distances between two events by observers in motion differ The § Lorentz transformation of velocities – velocities no longer simply add Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula , where is the speed of light in vacuum.[6][7] Special relativity replaced the conventional notion of an absolute, universal time with the notion of a time that is local to each observer.[8]: 33 Information about distant objects can arrive no faster than the speed of light so visual observations always report events that have happened in the past.

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:
- (14.44c) a a a The boost is illustrated in Figure 14.1.
- The rotor corresponding to a pure spatial rotation by angle θ right-handedly about unit real axis R n ≡Iσ n =ı n is the real quaternion R a a,R a a,R θ θ R=e−nRθR/2 =cos R −n sin R .
- The rotor corresponding to a boost by rapidity θ , or equivalently by I velocity v =tanhθ , in unit real direction n ≡Iσ n =ı n is the complex quaternion I R a a,R a a,R θ θ R=e−InRθI/2 =cosh I −In sinh I .
- A Lorentz boost by rapidity θ =atanhv along the γγ -axis (x-axis) (that is, a rotation in the γγ –γγ plane) is given by the Lorentz rotor 0 1 θ θ R=e−In1θ/2 =cosh +γγ ∧γγ sinh .
- For example, a Lorentz boost along the γγ -axis (the x-axis) is a rotation of spacetime in the γγ –γγ plane (the t–x plane).

(14.44c) a a a The boost is illustrated in Figure 14.1.

The rotor corresponding to a pure spatial rotation by angle θ right-handedly about unit real axis R n ≡Iσ n =ı n is the real quaternion R a a,R a a,R θ θ R=e−nRθR/2 =cos R −n sin R .

The rotor corresponding to a boost by rapidity θ , or equivalently by I velocity v =tanhθ , in unit real direction n ≡Iσ n =ı n is the complex quaternion I R a a,R a a,R θ θ R=e−InRθI/2 =cosh I −In sinh I .

A Lorentz boost by rapidity θ =atanhv along the γγ -axis (x-axis) (that is, a rotation in the γγ –γγ plane) is given by the Lorentz rotor 0 1 θ θ R=e−In1θ/2 =cosh +γγ ∧γγ sinh .

For example, a Lorentz boost along the γγ -axis (the x-axis) is a rotation of spacetime in the γγ –γγ plane (the t–x plane).

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:
- As discussed previously with regard to the Gullstrand-Painlevé river, §19.2.3, the tidal change δωk , m equation (19.66), in the river field seen by a fishy is not the full change δxν∂ωk /∂xν relative to the m background coordinates, but rather the change relative to the river δωk =(δxν −δxν ) ∂ωk m = [ δxν −βν(δt −asin2θδφ ) ]∂ωk m , (19.68) m river ∂xν ff ff ∂xν with the change in the velocity and twist of the river itself subtracted off.
- It is an intriguing thought that perhaps the 6 physical degrees of freedom of a general spacetime might always be encoded in the 6 degrees of freedom of a bivector, but that is not true.
- (19.66) m ∂xn Consequently the 4-vector pk is changed by pk →pk+δωk pm .
- With the tetrad connection coefficients given by equation (19.57), the equation of motion (19.27) for a 4-vector pk attached to a fishy following a geodesic in the Doran river translates to dpk ∂ωk =δν munpm .
- (19.67) m Butequation(19.67)correspondstoaninfinitesimalLorentztransformationbyδωk ,equivalenttoaLorentz m boost by δβa and a rotation by δμa.

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

It is an intriguing thought that perhaps the 6 physical degrees of freedom of a general spacetime might always be encoded in the 6 degrees of freedom of a bivector, but that is not true.

(19.66) m ∂xn Consequently the 4-vector pk is changed by pk →pk+δωk pm .

With the tetrad connection coefficients given by equation (19.57), the equation of motion (19.27) for a 4-vector pk attached to a fishy following a geodesic in the Doran river translates to dpk ∂ωk =δν munpm .

(19.67) m Butequation(19.67)correspondstoaninfinitesimalLorentztransformationbyδωk ,equivalenttoaLorentz m boost by δβa and a rotation by δμa.

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:
- Connected sets are sets that cannot be divided into two pieces that are far apart.
- In a metric space, an open set is a union of open disks, where an open disk of radius r centered at x is the set of all points whose distance to x is less than r.
- Intuitively, continuous functions take nearby points to nearby points.
- a doughnut (torus) and of a cow plushie into a sphere Lines and circles, but not figure eights, are one-dimensional manifolds.
- Changing a topology consists of changing the collection of open sets.

Connected sets are sets that cannot be divided into two pieces that are far apart.

In a metric space, an open set is a union of open disks, where an open disk of radius r centered at x is the set of all points whose distance to x is less than r.

Intuitively, continuous functions take nearby points to nearby points.

a doughnut (torus) and of a cow plushie into a sphere Lines and circles, but not figure eights, are one-dimensional manifolds.

Changing a topology consists of changing the collection of open sets.

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:
- basic unit of weight, with each element having a unit of unique weight.
- Dalton decided to call these units "atoms".[8] For example, there are two types of tin oxide: one is a grey Various atoms and molecules from A New System of Chemical Philosophy powder that is 88.1% tin and 11.9% oxygen, and the other is a (John Dalton, 1808) white powder that is 78.7% tin and 21.3% oxygen.
- Adjusting these figures, in the grey powder there is about 13.5 g of

basic unit of weight, with each element having a unit of unique weight.

Dalton decided to call these units "atoms".[8] For example, there are two types of tin oxide: one is a grey Various atoms and molecules from A New System of Chemical Philosophy powder that is 88.1% tin and 11.9% oxygen, and the other is a (John Dalton, 1808) white powder that is 78.7% tin and 21.3% oxygen.

Adjusting these figures, in the grey powder there is about 13.5 g 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:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- The corresponding growing and decaying solutions for the matter overdensity δ are, again in units a =1, m 0 2k2a 2k2a (δ −3Φ) =− Φ −5 , (δ −3Φ) =− Φ .
- 818 Cosmological perturbations: a simplest set of assumptions The growing and decaying solutions to equation (30.119) are, in units a =1, 5Ω H2H(a)∫ a da′ Φ = m 0 , (30.120a) grow 2 a a′3H(a′)3 H Φ = .
- For modes much smaller than the horizon distance today, the time derivative of the potential can be neglected compared to its spatial gradient, |Φ ̇| ≪ |kΦ|.
- But it is possible that there may be some small curvature.
- However, a flat background FLRW metric remains a good approximation for modes whose scales are small compared to the curvature.

The corresponding growing and decaying solutions for the matter overdensity δ are, again in units a =1, m 0 2k2a 2k2a (δ −3Φ) =− Φ −5 , (δ −3Φ) =− Φ .

818 Cosmological perturbations: a simplest set of assumptions The growing and decaying solutions to equation (30.119) are, in units a =1, 5Ω H2H(a)∫ a da′ Φ = m 0 , (30.120a) grow 2 a a′3H(a′)3 H Φ = .

For modes much smaller than the horizon distance today, the time derivative of the potential can be neglected compared to its spatial gradient, |Φ ̇| ≪ |kΦ|.

But it is possible that there may be some small curvature.

However, a flat background FLRW metric remains a good approximation for modes whose scales are small compared to the curvature.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- “I have to ask —you didn’t take these drugs yourself?” “Of course not.” “Last night, you gave Dr.
- Inside of my mouth like cotton.
- Really weird cocktail.” She sips her coffee.
- Randolph your wife’s name and a couple of phone numbers.” “Her cell and our landline.” “I’ve been trying to track her down all morning, but her mobile number belongs to a guy named Ralph, and your landline just keeps going to voicemail.” “Can you read her number back to me?” Springer reads off Daniela’s cell-phone number.
- Your tox screen results are far more illuminating.

“I have to ask —you didn’t take these drugs yourself?” “Of course not.” “Last night, you gave Dr.

Really weird cocktail.” She sips her coffee.

Randolph your wife’s name and a couple of phone numbers.” “Her cell and our landline.” “I’ve been trying to track her down all morning, but her mobile number belongs to a guy named Ralph, and your landline just keeps going to voicemail.” “Can you read her number back to me?” Springer reads off Daniela’s cell-phone number.

Your tox screen results are far more illuminating.

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 defines (as a matter of notation), and may in this notation write
- If A is any fourvector, then in tensor index notation Alternatively, one writes in which the primed indices denote the indices of A in the primed frame.
- The transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates.
- Covariant vectors There are also vector quantities with covariant indices.
- In the corresponding tensor index notation, the above matrix expression is where lower and upper indices label covariant and contravariant components respectively,[27] and the summation convention is applied.

One defines (as a matter of notation), and may in this notation write

If A is any fourvector, then in tensor index notation Alternatively, one writes in which the primed indices denote the indices of A in the primed frame.

The transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates.

Covariant vectors There are also vector quantities with covariant indices.

In the corresponding tensor index notation, the above matrix expression is where lower and upper indices label covariant and contravariant components respectively,[27] and the summation convention is applied.

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:
- InthepreviousChapter22,theformoftheKerr-Newmanline-elementanditscousinswasderivedfromthe condition that geodesics are Hamilton-Jacobi separable.
- Trajectories in ideal rotating black holes a = 0 a = 0.8 a = 0.96 a = 1 Figure 23.1 Silhouettes (black curves) of Kerr black holes with various spin parameters a, from left to right a=0, 0.8, 0.96, and 1 (units M =1), as observed in the equatorial plane from a far distance.
- The (red) ellipses show the horizonsoftheblackholesasanindicationofwhattheblackholeswouldlooklikewithoutanygravitationallensing.
- Thesilhouetteiscompressedontheapproachingsideandexpandedontherecedingside.See§23.14.
- In this Chapter, the Hamilton-Jacobi equations are separated, and the trajectories of neutral and charged particles in the Kerr-Newman geometry are explored.

InthepreviousChapter22,theformoftheKerr-Newmanline-elementanditscousinswasderivedfromthe condition that geodesics are Hamilton-Jacobi separable.

Trajectories in ideal rotating black holes a = 0 a = 0.8 a = 0.96 a = 1 Figure 23.1 Silhouettes (black curves) of Kerr black holes with various spin parameters a, from left to right a=0, 0.8, 0.96, and 1 (units M =1), as observed in the equatorial plane from a far distance.

The (red) ellipses show the horizonsoftheblackholesasanindicationofwhattheblackholeswouldlooklikewithoutanygravitationallensing.

In this Chapter, the Hamilton-Jacobi equations are separated, and the trajectories of neutral and charged particles in the Kerr-Newman geometry are explored.

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:
- Catherine put her'gold udjat eye round Daniel's neck.
- O'Neil seemed to be the only one who wasn't frightened.
- He seemed to fly for thousands of years, until ...
- Daniel shut his eyes, walked into the wall of light, and suddenly saw himself flying among stars, millions of them.
- Daniel, O'Neil, Kawalsky and three other soldiers, Feretti, Brown and Porro, stood waiting with boxes full of things they needed.

Catherine put her'gold udjat eye round Daniel's neck.

O'Neil seemed to be the only one who wasn't frightened.

He seemed to fly for thousands of years, until ...

Daniel shut his eyes, walked into the wall of light, and suddenly saw himself flying among stars, millions of them.

Daniel, O'Neil, Kawalsky and three other soldiers, Feretti, Brown and Porro, stood waiting with boxes full of things they needed.

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:
- Just maybe, a holographic cosmos" (https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologr am.html).
- Bibcode:1995PhRvD..51.3117C (https://ui.adsabs.harvard.edu/abs/1995PhRvD..51.3117C).
- doi:10.1103/PhysRevD.51.3117 (http s://doi.org/10.1103%2FPhysRevD.51.3117).
- Bibcode:1921AnP...370..541W (https://ui.adsabs.harvard.edu/abs/1921AnP...370..
- Archived from the original (http://www.geoffre ylandis.com/wormholes.htp) on 2012-04-15.

Just maybe, a holographic cosmos" (https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologr am.html).

Archived from the original (http://www.geoffre ylandis.com/wormholes.htp) on 2012-04-15.

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:
- "New boson claim faces scrutiny" (https://www.quantamagazine.org/new-boson-claim-faces-scruti ny-20160607/).
- doi:10.1103/PhysRevLett.117.071803 (https://doi.org/10.1103%2F PhysRevLett.117.071803).
- Retrieved from "https://en.wikipedia.org/w/index.php?title=Fifth_force&oldid=1329310338"
- "Scientists may have discovered fifth force of nature, laboratory announces" (https://www.indepen dent.co.uk/news/science/dark-matter-particle-hungary-atomki-nuclear-research-force-nature-a921 0741.html).
- S2CID 206279817 (https://api.semanticscholar.org/CorpusID:206279817).

"New boson claim faces scrutiny" (https://www.quantamagazine.org/new-boson-claim-faces-scruti ny-20160607/).

"Scientists may have discovered fifth force of nature, laboratory announces" (https://www.indepen dent.co.uk/news/science/dark-matter-particle-hungary-atomki-nuclear-research-force-nature-a921 0741.html).

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Amanda drops like someone flipped a power switch, and next to me, my Amanda lets slip a stifled shriek.
- There’s no time travel in the box.
- Leighton’s men have their guns drawn, and they’re moving deliberately into the hangar toward Jason and Amanda.
- My first thought is that we’ve gone back in time, but of course that’s impossible.
- As this other Jason rushes Leighton, the second guard executes a lightning-fast Taser draw and brings him down screaming and twitching on the floor of the hangar.

Amanda drops like someone flipped a power switch, and next to me, my Amanda lets slip a stifled shriek.

Leighton’s men have their guns drawn, and they’re moving deliberately into the hangar toward Jason and Amanda.

My first thought is that we’ve gone back in time, but of course that’s impossible.

As this other Jason rushes Leighton, the second guard executes a lightning-fast Taser draw and brings him down screaming and twitching on the floor of the hangar.

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:
- We consider ourselves remarkably fortunate to have worked with someone as competent, kind, and patient as Chris.
- Chris has provided invaluable guidance throughout this project, and we are deeply indebted to her for her support and encouragement.
- 9781405131117_1_pre.qxd 30/6/09 11:42 AM Page xvi students enter these courses with misconceptions concerning a host of psychological topics, so confronting these misconceptions is often an essential step toward imparting accurate knowledge.
- Practicing psychologists and other mental health professionals (such as psychiatrists, psychiatric nurses, counselors, and social workers), psychology educators, psychological researchers, psychology majors, and psychology graduate students should also find the book to be an enjoyable read, not to mention a valuable reference source.
- Because we have organized the book around 11 domains traditionally covered in introductory psychology courses, such as brain functioning and perception, memory, learning and intelligence, emotion and motivation, social psychology, personality, psychopathology, and psychotherapy, this book can serve as either a freestanding textbook or a textbook supplement for these courses.

We consider ourselves remarkably fortunate to have worked with someone as competent, kind, and patient as Chris.

Chris has provided invaluable guidance throughout this project, and we are deeply indebted to her for her support and encouragement.

9781405131117_1_pre.qxd 30/6/09 11:42 AM Page xvi students enter these courses with misconceptions concerning a host of psychological topics, so confronting these misconceptions is often an essential step toward imparting accurate knowledge.

Practicing psychologists and other mental health professionals (such as psychiatrists, psychiatric nurses, counselors, and social workers), psychology educators, psychological researchers, psychology majors, and psychology graduate students should also find the book to be an enjoyable read, not to mention a valuable reference source.

Because we have organized the book around 11 domains traditionally covered in introductory psychology courses, such as brain functioning and perception, memory, learning and intelligence, emotion and motivation, social psychology, personality, psychopathology, and psychotherapy, this book can serve as either a freestanding textbook or a textbook supplement for these courses.

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:
- K.S.Thorne.BlackHolesandTimeWarps:Einstein’sOutrageousLegacy.W.W.NortonandCompany, 1995.
- J.H.SchwartzandP.M.Schwartz.SpecialRelativity:FromEinsteintoStrings.CambridgeUniversity Press,2004.
- J.AWheeler.AJourneyintoGravityandSpacetime.ScientificAmericanLibrary.W.H.Freeman,1990.
- Princeton University Press, 2010.
- ———.FearfulSymmetry.PrincetonUniversityPress,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:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- (1971), "Oscillatory approach to the singular point in relativistic cosmology", Advances in Physics, 19 (80): 525–573, Bibcode:1970AdPhy..19..525B (https://ui.adsabs.harvard.edu/abs/1970AdPhy..19..525B), doi:10.1080/00018737000101171 (https://doi.org/10.1080%2F00018737000101171); original paper in Russian: Belinsky, V.
- Proceedings of the 17th International Conference, World Scientific, pp.
- (2003), "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results", Astrophys.
- (1973), "Black Holes and Entropy", Phys.
- (2005), "Hubble Space Telescope Spectroscopy of the Balmer lines in Sirius B", Mon.

(1971), "Oscillatory approach to the singular point in relativistic cosmology", Advances in Physics, 19 (80): 525–573, Bibcode:1970AdPhy..19..525B (https://ui.adsabs.harvard.edu/abs/1970AdPhy..19..525B), doi:10.1080/00018737000101171 (https://doi.org/10.1080%2F00018737000101171); original paper in Russian: Belinsky, V.

Proceedings of the 17th International Conference, World Scientific, pp.

(2003), "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results", Astrophys.

(1973), "Black Holes and Entropy", Phys.

(2005), "Hubble Space Telescope Spectroscopy of the Balmer lines in Sirius B", Mon.

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, his friend is convinced that the cat is alive, i.e.
- In a Heisenbergian view, the answer depends on the positioning of Heisenberg cut, which can be placed arbitrarily (at least according to Heisenberg, though not to Bohr[3]).
- How can Wigner and his friend see different wave functions?
- The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles.
- If Wigner's friend is positioned on the same side of the cut as the external observer, his measurements collapse the wave function for both observers.

However, his friend is convinced that the cat is alive, i.e.

In a Heisenbergian view, the answer depends on the positioning of Heisenberg cut, which can be placed arbitrarily (at least according to Heisenberg, though not to Bohr[3]).

How can Wigner and his friend see different wave functions?

The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles.

If Wigner's friend is positioned on the same side of the cut as the external observer, his measurements collapse the wave function for both observers.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Copenhagen interpretation - Wikipedia.pdf


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

EVIDENCE:
- Show that the Einstein tensor corresponding to the Kasner line-element (17.141) is diagonal.
- Show that in this case of a perfect fluid the tetrad-frame Einstein equations are ( a ̇2 K2) G =3 − =8πρ , (17.145a) 00 a2 a6 2a ̈ a ̇2 3K2 G =− − − =8πp .
- From the first law of thermodynamics, show that for a perfect fluid with equation of state p/ρ = w = constant, the density ρ is related to scale factor a by, as in FLRW, ρ∝a−3(1+w) .
- Conclude that the evolution of the scale factor a(t) with time t is determined by the same equation (10.70) as for FLRW, ∫ da t= .
- 17.6 BKL oscillatory collapse 519 with scale factors a =aTqα−1/3 , (17.142) α where a(t) and T(t) are functions of time t, and the constants q are Kasner coefficients satisfying equaα tion (17.135).

Show that the Einstein tensor corresponding to the Kasner line-element (17.141) is diagonal.

Show that in this case of a perfect fluid the tetrad-frame Einstein equations are ( a ̇2 K2) G =3 − =8πρ , (17.145a) 00 a2 a6 2a ̈ a ̇2 3K2 G =− − − =8πp .

From the first law of thermodynamics, show that for a perfect fluid with equation of state p/ρ = w = constant, the density ρ is related to scale factor a by, as in FLRW, ρ∝a−3(1+w) .

Conclude that the evolution of the scale factor a(t) with time t is determined by the same equation (10.70) as for FLRW, ∫ da t= .

17.6 BKL oscillatory collapse 519 with scale factors a =aTqα−1/3 , (17.142) α where a(t) and T(t) are functions of time t, and the constants q are Kasner coefficients satisfying equaα tion (17.135).

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:
- How much time has elapsed on the twin’s own wristwatch during this time?
- Express your answers first in terms of l, v, and γ, and then in years.
- How much time passes on your own watch as you watch (through the telescope) the twin journey back from Alpha to Earth?
- How much time passes on your wristwatch, as seen by your twin through the telescope, during the journey back?
- What is the ratio of these two times?

How much time has elapsed on the twin’s own wristwatch during this time?

Express your answers first in terms of l, v, and γ, and then in years.

How much time passes on your own watch as you watch (through the telescope) the twin journey back from Alpha to Earth?

How much time passes on your wristwatch, as seen by your twin through the telescope, during the journey back?

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:
- 7.17 Kruskal-Szekeres spacetime diagram AfterFinkelsteinhadtransformedcoordinatessothatradiallyinfallinglightraysmovedat45∘inaspacetime diagram, it was natural to look for coordinates in which outgoing as well as infalling light rays are at 45∘.
- KruskalandSzekeresindependentlyprovidedsuchatransformationin1960(Kruskal,1960;Szekeres,1960).
- 7.17 Kruskal-Szekeres spacetime diagram 155 2.0 1.5 1.0 .5 .0 −.5 −1.0 −1.5 −2.0 .0 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Circumferential radius r t emit nietslekniF F Figure7.7 Finkelsteinspacetimediagram,inunitsrs=c=1.HerethetimecoordinateistakentobetheFinkelstein timecoordinatetF,equation(7.80).TheFinkelsteintimecoordinatetF isconstructedsothatradiallyinfallinglight raysareat45∘.
- In other words, on a spacetime diagram in Finkelstein coordinates, Figure 7.7, radially infalling light rays move at 45∘, the same as in a special relativistic spacetime diagram.
- In a spacetime diagram in coordinates t and r*, infalling and outgoing light rays are indeed at 45∘.

7.17 Kruskal-Szekeres spacetime diagram AfterFinkelsteinhadtransformedcoordinatessothatradiallyinfallinglightraysmovedat45∘inaspacetime diagram, it was natural to look for coordinates in which outgoing as well as infalling light rays are at 45∘.

7.17 Kruskal-Szekeres spacetime diagram 155 2.0 1.5 1.0 .5 .0 −.5 −1.0 −1.5 −2.0 .0 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Circumferential radius r t emit nietslekniF F Figure7.7 Finkelsteinspacetimediagram,inunitsrs=c=1.HerethetimecoordinateistakentobetheFinkelstein timecoordinatetF,equation(7.80).TheFinkelsteintimecoordinatetF isconstructedsothatradiallyinfallinglight raysareat45∘.

In other words, on a spacetime diagram in Finkelstein coordinates, Figure 7.7, radially infalling light rays move at 45∘, the same as in a special relativistic spacetime diagram.

In a spacetime diagram in coordinates t and r*, infalling and outgoing light rays are indeed at 45∘.

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:
- doi: 10.1103/PhysRevD.73.124036.
- doi: 10.1088/0004-637X/707/2/916.
- “A space-time calculus based on pairs of null directions”.
- Gebhardt,K.etal.(2011).“TheBlack-HoleMassinM87fromGemini/NIFSAdaptiveOpticsObservations”.
- Gell-Mann, M., Ramond, P., and Slansky, R.

“A space-time calculus based on pairs of null directions”.

Gell-Mann, M., Ramond, P., and Slansky, R.

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 blue arrow illustrates that a person standing on the train tracks measures the bullet as traveling at 0.8 c.
- Spacetime curves in the presence of matter, can propagate waves, bends light, and exhibits a host of other phenomena.[3]: 221 A few of these phenomena are described in the later sections of this article.
- 3-1 illustrates that in Newton's theory, time is universal, not the velocity of light.[41]: 36–37 Consider the following thought experiment: The red arrow illustrates a train that is moving at 0.4 c with respect to the platform.
- More generally, assuming that frame S′ is moving at velocity v with respect to frame S, then within frame S′, observer O′ measures an object moving with velocity u′.
- This is in accordance with our naive expectations.

The blue arrow illustrates that a person standing on the train tracks measures the bullet as traveling at 0.8 c.

Spacetime curves in the presence of matter, can propagate waves, bends light, and exhibits a host of other phenomena.[3]: 221 A few of these phenomena are described in the later sections of this article.

3-1 illustrates that in Newton's theory, time is universal, not the velocity of light.[41]: 36–37 Consider the following thought experiment: The red arrow illustrates a train that is moving at 0.4 c with respect to the platform.

More generally, assuming that frame S′ is moving at velocity v with respect to frame S, then within frame S′, observer O′ measures an object moving with velocity u′.

This is in accordance with our naive expectations.

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:
- Proof that every smooth manifold admits a Riemannian metric An alternative proof uses the Whitney embedding theorem to embed into Euclidean space and then pulls back the metric from Euclidean space to .
- Metric space structure An admissible curve is a piecewise smooth curve whose velocity is nonzero everywhere it is defined.
- Positive combinations of metrics Let be Riemannian metrics on If are any positive smooth functions on , then is another Riemannian metric on Every smooth manifold admits a Riemannian metric Theorem: Every smooth manifold admits a (non-canonical) Riemannian metric.[13] This is a fundamental result.
- The reason is that the proof makes use of a partition of unity.
- However, there are many natural smooth Riemannian manifolds, such as the set of rotations of threedimensional space and hyperbolic space, of which any representation as a submanifold of Euclidean space will fail to represent their remarkable symmetries and properties as clearly as their abstract presentations do.

Proof that every smooth manifold admits a Riemannian metric An alternative proof uses the Whitney embedding theorem to embed into Euclidean space and then pulls back the metric from Euclidean space to .

Metric space structure An admissible curve is a piecewise smooth curve whose velocity is nonzero everywhere it is defined.

Positive combinations of metrics Let be Riemannian metrics on If are any positive smooth functions on , then is another Riemannian metric on Every smooth manifold admits a Riemannian metric Theorem: Every smooth manifold admits a (non-canonical) Riemannian metric.[13] This is a fundamental result.

The reason is that the proof makes use of a partition of unity.

However, there are many natural smooth Riemannian manifolds, such as the set of rotations of threedimensional space and hyperbolic space, of which any representation as a submanifold of Euclidean space will fail to represent their remarkable symmetries and properties as clearly as their abstract presentations do.

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:
- It is clear that is a bijective mapping, and the Jacobian of is given by: which is an upper triangular matrix with ones on the main diagonal, therefore its determinant is 1.
- Applying the change of variable theorem from the previous section we obtain that which if marginalized over leads to the desired probability density function.
- Sums of independent random variables The probability density function of the sum of two independent random variables U and V, each of which has a probability density function, is the convolution of their separate density functions: It is possible to generalize the previous relation to a sum of N independent random variables, with densities U , ..., U : 1 N This can be derived from a two-way change of variables involving Y = U + V and Z = V, similarly to the example below for the quotient of independent random variables.
- Products and quotients of independent random variables Given two independent random variables U and V, each of which has a probability density function, the density of the product Y = UV and quotient Y = U/V can be computed by a change of variables.
- Example: Quotient distribution To compute the quotient Y = U/V of two independent random variables U and V, define the following transformation: Then, the joint density p(y,z) can be computed by a change of variables from U,V to Y,Z, and Y can be derived by marginalizing out Z from the joint density.

It is clear that is a bijective mapping, and the Jacobian of is given by: which is an upper triangular matrix with ones on the main diagonal, therefore its determinant is 1.

Applying the change of variable theorem from the previous section we obtain that which if marginalized over leads to the desired probability density function.

Sums of independent random variables The probability density function of the sum of two independent random variables U and V, each of which has a probability density function, is the convolution of their separate density functions: It is possible to generalize the previous relation to a sum of N independent random variables, with densities U , ..., U : 1 N This can be derived from a two-way change of variables involving Y = U + V and Z = V, similarly to the example below for the quotient of independent random variables.

Products and quotients of independent random variables Given two independent random variables U and V, each of which has a probability density function, the density of the product Y = UV and quotient Y = U/V can be computed by a change of variables.

Example: Quotient distribution To compute the quotient Y = U/V of two independent random variables U and V, define the following transformation: Then, the joint density p(y,z) can be computed by a change of variables from U,V to Y,Z, and Y can be derived by marginalizing out Z from the joint density.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Probability density function - Wikipedia.pdf


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

EVIDENCE:
- (Particle Data Group, 227 authors) (2018).
- D 48,pp.3743–3761.doi:10.1103/PhysRevD.48.3743.arXiv:hep-th/9306069(cit.onpp.168, 171).
- arXiv: 0801.4415 [gr-qc] (cit.
- (1994).Black holes and time warps: Einstein’s outrageous legacy.W.W.Norton(cit.onpp.10,133).
- “On the singularities of a Riemann manifold”.

(Particle Data Group, 227 authors) (2018).

(1994).Black holes and time warps: Einstein’s outrageous legacy.W.W.Norton(cit.onpp.10,133).

“On the singularities of a Riemann manifold”.

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:
- Bohr Radius • The vacuum perturbation equation just derived can be used to evaluate the state of the quantum vacuum in close proximity of the proton at the center of the Hydrogen atom.
- • The first step is to calculate a quasi-classical density for the hydrogen nucleus.
- The radius of the hydrogen atom nucleus is given as R =1.2x10-15m (R=R ·A1/3 where R = 1.2x10-15m and A is 0 0 0 the atomic number - these are experimentally determined by electron scattering).
- • The radius can be used with the mass of a proton to calculate a quasi-classical density of the hydrogen nucleus: m kg p 2.31x1017 m 4 R 3 m3 3 0 • Using ρ =2/ * 9.9x10-27 kg/m3, along with this quasi-classical density , the perturbed negative v 3 m pressure state of the quantum vacuum around the hydrogen nucleus is calculated to be: kg 3.90x10 5 v_local m v m3 • The question can be asked how much volume of this perturbed state of the quantum vacuum is needed to have the equivalent energy value as the ground state of Hydrogen (13.6eV or 2.18x10-18 Nm) E 3 r a c2 v_local 3 • The calculated radius is r = 5.29x10-11 m, which is an exact match to the given value for the Bohr Radius, a = 5.29x10-11 m.

Bohr Radius • The vacuum perturbation equation just derived can be used to evaluate the state of the quantum vacuum in close proximity of the proton at the center of the Hydrogen atom.

• The first step is to calculate a quasi-classical density for the hydrogen nucleus.

The radius of the hydrogen atom nucleus is given as R =1.2x10-15m (R=R ·A1/3 where R = 1.2x10-15m and A is 0 0 0 the atomic number - these are experimentally determined by electron scattering).

• The radius can be used with the mass of a proton to calculate a quasi-classical density of the hydrogen nucleus: m kg p 2.31x1017 m 4 R 3 m3 3 0 • Using ρ =2/ * 9.9x10-27 kg/m3, along with this quasi-classical density , the perturbed negative v 3 m pressure state of the quantum vacuum around the hydrogen nucleus is calculated to be: kg 3.90x10 5 v_local m v m3 • The question can be asked how much volume of this perturbed state of the quantum vacuum is needed to have the equivalent energy value as the ground state of Hydrogen (13.6eV or 2.18x10-18 Nm) E 3 r a c2 v_local 3 • The calculated radius is r = 5.29x10-11 m, which is an exact match to the given value for the Bohr Radius, a = 5.29x10-11 m.

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:
- (2.159) r Approximate the unperturbed path of light past the mass as a straight line.
- Consider an observer who happens to be at rest in the Newtonian metric, so that ux = uy = uz = 0.
- (2.160) dλ dx ∂y Integrate this equation to show that Δvy 4GM =− .
- Calculate the predicted deflection angle Δφ in arcseconds for light that just grazes the limb of the Sun.
- From the geodesic equation dvκ +Γκ vμvν =0 (2.156) dλ μν show that the spatial components v ≡{vx,vy,vz} satisfy dv =2v×(v×∇Φ) , (2.157) dλ where boldface symbols represent 3D vectors, and in particular ∇Φ is the spatial 3D gradient ∇Φ ≡ ∂Φ/∂xα ={∂Φ/∂x,∂Φ/∂y,∂Φ/∂z}.

(2.159) r Approximate the unperturbed path of light past the mass as a straight line.

Consider an observer who happens to be at rest in the Newtonian metric, so that ux = uy = uz = 0.

(2.160) dλ dx ∂y Integrate this equation to show that Δvy 4GM =− .

Calculate the predicted deflection angle Δφ in arcseconds for light that just grazes the limb of the Sun.

From the geodesic equation dvκ +Γκ vμvν =0 (2.156) dλ μν show that the spatial components v ≡{vx,vy,vz} satisfy dv =2v×(v×∇Φ) , (2.157) dλ where boldface symbols represent 3D vectors, and in particular ∇Φ is the spatial 3D gradient ∇Φ ≡ ∂Φ/∂xα ={∂Φ/∂x,∂Φ/∂y,∂Φ/∂z}.

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:
- of his life, Hawking could now simply press a switch to select phrases, words or letters from a bank of about 2,500–3,000 that were scanned.[312][313] The program was originally run on a desktop computer.
- Elaine Mason's husband, David, a computer engineer, adapted a small computer and attached it to his wheelchair.[314] Released from the need to use somebody to interpret his speech, Hawking commented that "I can communicate better now than before I lost my voice."[315] The voice he used had an American accent and is no longer produced.[316][317] Despite the later availability of other voices, Hawking retained this original voice, saying that he preferred it and identified with it.[318] Originally, Hawking activated a switch using his hand and could produce up to 15 words per minute.[152] Lectures were prepared in advance and were sent to the speech synthesiser in short sections to be delivered.[316]

of his life, Hawking could now simply press a switch to select phrases, words or letters from a bank of about 2,500–3,000 that were scanned.[312][313] The program was originally run on a desktop computer.

Elaine Mason's husband, David, a computer engineer, adapted a small computer and attached it to his wheelchair.[314] Released from the need to use somebody to interpret his speech, Hawking commented that "I can communicate better now than before I lost my voice."[315] The voice he used had an American accent and is no longer produced.[316][317] Despite the later availability of other voices, Hawking retained this original voice, saying that he preferred it and identified with it.[318] Originally, Hawking activated a switch using his hand and could produce up to 15 words per minute.[152] Lectures were prepared in advance and were sent to the speech synthesiser in short sections to be delivered.[316]

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:
- WHITE DWARFS 103 eons until its energy content is only the average for the entire universe-a few degrees above absolute zero.
- There are planetary objects, which are small enough in mass never to have started a nuclear fire, and where gravitational compression is forever balanced by the outward push of compressed intact atoms at the center.
- There are also (or will be someday) black dwarfs, which have sufficient mass to have started a nuclear fire but which, in time, have burned out, and where gravitational compression is forever balanced by the outward push of compressed electrons.
- All the white dwarfs that have ever formed are still shining today, but given enough time, they will fade.
- We can also see clouds of dust and gas in interstellar space, but under the pull of their own gravitational field much of those clouds will eventually condense to form stars and work their way down to the black-dwarf status, also.

WHITE DWARFS 103 eons until its energy content is only the average for the entire universe-a few degrees above absolute zero.

There are planetary objects, which are small enough in mass never to have started a nuclear fire, and where gravitational compression is forever balanced by the outward push of compressed intact atoms at the center.

There are also (or will be someday) black dwarfs, which have sufficient mass to have started a nuclear fire but which, in time, have burned out, and where gravitational compression is forever balanced by the outward push of compressed electrons.

All the white dwarfs that have ever formed are still shining today, but given enough time, they will fade.

We can also see clouds of dust and gas in interstellar space, but under the pull of their own gravitational field much of those clouds will eventually condense to form stars and work their way down to the black-dwarf status, also.

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.