Spacetime singularity resolution by M-theory fivebranes calibrated geometry, Anti-de Sitter

关于太阳黑洞的英文作文Title: Exploring the Mysteries of Solar Black Holes。

Introduction:Solar black holes, also known as stellar black holes, are enigmatic celestial objects that continue to fascinate astronomers and physicists alike. These cosmic phenomenaare born from the collapse of massive stars, leading to the formation of incredibly dense regions in space with gravitational fields so strong that not even light can escape from them. In this essay, we delve into theintricacies of solar black holes, exploring their formation, characteristics, and the profound impact they have on the universe.Formation of Solar Black Holes:Solar black holes originate from the explosive deathsof massive stars, known as supernovae. When a star exhaustsits nuclear fuel, it can no longer withstand its own gravitational force, causing it to collapse under its own weight. This collapse results in a supernova explosion, where the outer layers of the star are expelled into space, leaving behind the core.If the core of the star is sufficiently massive –typically several times the mass of the Sun – it undergoes further collapse, forming a black hole. This process compresses the mass of the core into an infinitesimally small point known as a singularity, surrounded by an event horizon beyond which no information or matter can escape.Characteristics of Solar Black Holes:Solar black holes possess several uniquecharacteristics that distinguish them from other celestial objects:1. Gravitational Singularity: At the center of a black hole lies a gravitational singularity, where matter is infinitely dense and spacetime curvature is infinitelysteep. The laws of physics, as we understand them, break down at this point, leading to a theoretical realm where our current understanding fails.2. Event Horizon: Surrounding the singularity is the event horizon, the boundary beyond which escape is impossible. Once an object crosses the event horizon, it is inexorably drawn towards the singularity, never to return.3. No Hair Theorem: According to the no-hair theorem, black holes are characterized by only three properties: mass, electric charge, and angular momentum. All other information about the material that formed the black hole is lost beyond the event horizon.Impact on the Universe:Solar black holes play a significant role in shaping the cosmos, influencing the dynamics of galaxies, stars, and even spacetime itself:1. Galactic Evolution: Black holes, including solarblack holes, are thought to reside at the centers of most galaxies. Their immense gravitational pull can influence the motion of stars and gas within galaxies, affectingtheir evolution over cosmic timescales.2. Stellar Dynamics: In binary star systems, a solar black hole can gravitationally interact with its companion star, leading to phenomena such as accretion disk formation and the emission of X-rays. These interactions can provide valuable insights into the properties of black holes and their surrounding environments.3. Time Dilation: The extreme gravitational fields near black holes cause time to dilate significantly. This phenomenon, predicted by Einstein's theory of general relativity, has practical implications for space exploration and our understanding of the nature of spacetime.Conclusion:Solar black holes stand as some of the most enigmaticand intriguing objects in the universe. From their mysterious formation to their profound impact on the cosmos, these cosmic behemoths continue to captivate theimagination of scientists and laypeople alike. As we probe deeper into the nature of black holes, we unlock newinsights into the fundamental laws that govern the universe and our place within it.。

a r X i v :g r -q c /0209001v 1 31 A u g 2002CIRI/02-swrskg01What is the spacetime of physically realizable spherical collapse?Sanjay M.Wagh 1,Ravindra V.Saraykar 1,2,and Keshlan inder 31Central India Research Institute,Post Box 606,Laxminagar,Nagpur 440022,India E-mail:cirinag@.in 2Also at:Department of Mathematics,Nagpur University Campus,Nagpur 440010,India.E-mail:sarayaka@.in3School of Mathematical &Statistical Sciences,University of Natal,Durban 4041,South Africa.E-mail:govinder@nu.ac.za (Dated:August 31,2002)We argue that a particular spacetime,a spherically symmetric spacetime with hyper-surface orthogonal,radial,homothetic Killing vector,is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in its full “physical”generality.PACS numbers:04.20.-q,04.20.CvKeywords:Gravitational collapse -spherical symmetry -radial homothety -physically realizableI.INTRODUCTIONAny sufficiently sparsely distributed ordinary “neutral”matter is dusty,that is,collision-less and pressureless.Further,emission of radiation and,hence,radiation is not expected in such dust.In Newtonian gravity,as well as in general rel-ativity,we can then study gravitational collapse from this dusty “initial”state of matter.Under the action of its self-gravity,dust mat-ter collapses.Then,self-gravity leads to mass or energy-flux in some preferential direction,the ra-dial direction for a spherical spacetime.But,this is not the flux of radiation.Therefore,there is no mass-flux in the rest frame of collapsing dusty matter,but it is present for other observers in the spacetime.Next stage of collapse is reached when particles of dust begin to collide with each other.Negligi-ble amount of radiation,but existing nonetheless,is expected from whatever atomic excitations or from whatever free electrons get created in atomic collisions in such matter.Therefore,dusty matter evolves into matter with pressure and radiation,both simultaneously non-vanishing.The energy-flux can no longer be removed by going to the rest frame of matter.As far as Newtonian gravity and general relativ-ity,both,are concerned,we may study the grav-itational collapse beginning even as matter with non-vanishing pressure and radiation.At some stage,exothermic,thermonuclear reac-tions begin in matter with non-negligible pressure.With it,a star is born in the spacetime.This is the manner of gravitational collapse of dusty matter leading to the birth of a star.Till theexothermic thermonuclear reactions in the stellar core support the overlying stellar layers,such a stellar object is gravitationally stable.But,the spacetime continues to be dynamic since radiation is present in it.The stellar object may also accrete matter from its surrounding while emitting radiation.Once again,in Newtonian gravity and in general relativity,both,we may study the collapse of this “initial”stellar configuration of matter.Now,as and when “heating”of the overlying stellar layers decreases due to changes in exother-mic thermonuclear processes in the core of the star,the self-gravity of the stellar object leads to its gravitational contraction.These are,in general,very slow and involved processes.Gravitational contraction leads to generation of pressure by compression and by the occurrence of exothermic thermonuclear reactions of heavier nu-clei.The star may stabilize once more.This chain,of gravitational contraction of star,followed by pressure increase,followed by subse-quent stellar stabilization,continues as long as thermonuclear processes produce enough heat to support the overlying stellar layers.The theory of the atomic nucleus shows that exothermic nuclear processes do not occur when Iron nucleus forms.With time,the rate of heat generation in iron-dominated-core becomes insuf-ficient to support the overlying stellar layers which may then bounce offthe iron-core resulting into a stellar explosion,a supernova.Then,many,different such,stages of evolution are the results of physical processes that are un-related to the phenomenon of gravitation.These are,for example,collisions of particles of matter,electromagnetic and other forces between atomic or sub-atomic constituents of matter etc.As an example,let some non-gravitational pro-cess,opposing collapse,result into pressure that does not appreciably rise in response to small con-traction of the stellar matter.That is,pressure does not appreciably rise when gravitationalfield is increased by a small amount Then,the collapse of a sufficiently massive object would not be halted by that particular non-gravitational process.There-fore,a mass limit is obtained in this situation.For example,electron degeneracy pressure leads to the Chandrasekhar limit[1].Clearly,some of the non-gravitational processes determine the gravitational stability of physical objects.This is true in Newtonian gravity as well as in general relativity,both.In general relativity,non-gravitational processes are included via the energy-momentum tensor for matter.Non-gravitational processes determine the relation of density and pressure of matter.The temporal evolution of matter is to be determined from such a relation,and from other physical rela-tions,if any.It is therefore that,by physically realizable grav-itational collapse,we mean collapse that leads matter,step by step,through the above different “physical”stages of evolution.Hence,the spacetime of“physically realizable”collapse of matter must be able to begin with any stage in the chain of evolution of matter under the action of its self-gravity.The temporal evolution from any“initial”data,any“physical”stage in question,is to be obtained from applicable non-gravitational properties of matter.But,a supernova remnant,or a star that failed to explode,may be quite massive for its self-gravity to dominate over all conceivable competing reasons opposing it at various stages of further evolution. This may also happen as a result of mass-accretion taking the object in question over some mass-limit in operation.The collapse is,now,unstoppable.A spacetime singularity is expected to form in such unstoppable collapse.Associated with studies of unstoppable collapse is the issue of whether the physically realizable gravitational collapse leads to a black hole or to a naked spacetime singularity.This is the issue of the Cosmic Censorship Hypothesis(CCH)[2]. Clearly,the answer to this very important ques-tion in general relativity can then be obtained only on the basis of the spacetime of the physically re-alizable gravitational collapse.Now,we show below that,for spherical symme-try,a spacetime with hyper-surface orthogonal,ra-dial,homothetic Killing vector provides“all”the above steps of evolution of matter.II.SPACETIME OF PHYSICALLYREALIZABLE COLLAPSEOne radially homothetic spacetime has the fol-lowing metric[3]in co-moving coordinates: ds2=−y2dt2+γ2(y′)2B2dr2+y2Y2dΩ2(1) with y=y(r),an overhead prime indicating a derivative with respect to r,B≡B(t),Y≡Y(t) andγbeing a constant.As can be easily verified,the metric(1)admits a spacelike Homothetic Killing Vector(HKV)of the formX a=(0,yy2Y B+2¨By2γ2B2+2y2Y2+4¨Ysome t =t s .Thus,the singularity of first type is asingular hyper-surface for (1).The singularity of the second type is a singular sphere of coordinate radius r .The singular sphere reduces to a singular point for r =0that is the center of symmetry.Singularities of the second type constitute a part of the initial data,singular data,for the evolution.The metric (1)has evident degeneracies when y (r )=0,y (r )→∞either on a degenerate sphere of coordinate radius r ,for some “thick”shell or globally.Another degeneracy occurs for y (r )=constant for some “thick”shell or globally.In what follows,we shall assume that there is no singular initial-data and that there are no evi-dently degenerate situations for the metric (1).Temporal evolution in (1)The Einstein tensor for (1)is:G tt =1γ2B 2+˙Y2BY (5)G rr =γ2B 2y ′2Y −˙Y2γ2B 2−1B−Y˙Y ˙B γ2B 2(7)G φφ=sin 2θG θθ(8)G tr =2˙By′2σ33=1Y−˙B6σ.Therefore,the spacetime of (1)is,in general,shearing and radiating,both.With our assumptions of no singular and degen-erate initial data,we then have a “cosmological”situation -continued spherical collapse of matter from the assumed “initial”state.Now,for the co-moving observer with four-velocity U =1∂t ,the radial velocity of thefluid is V r =˙Ywhere an overhead dot denotes a time derivative.The co-moving observer is ac-celerating for (1)since ˙Ua =U a ;b U b is,in gen-eral,non-vanishing for y ′=0.The expansion isΘ=1B+2˙Yy 2˙Y2Y 2−1y 2˙Y2Y B+1γ2B 2(14)We also obtain2¨YB =22(ρ+3p )(15)Then,from (15),the relation of pressure anddensity of matter is the required additional “phys-ical”information.Also required is other relevant “physical”information to determine the radiation generation in the spacetime of (1).To provide for the required information of “phys-ical”nature is a non-trivial task in general relativ-ity just as it is for Newtonian gravity.The details of these considerations are,of course,beyond the scope of this letter.However,it is clear that thefield equations de-termine only the temporal functions from the prop-erties of matter in the spacetime of(1). Moreover,it is also clear that matter will con-tinue to pile up on such a star in a“cosmolog-ical setting”and,hence,such a star will always be taken over any mass-limit in operation at any stage of its evolution that will,ultimately,lead to the singular hyper-surface of the spacetime of(1). The radial dependence of matter properties is “specified”as1/y2but thefield equations of gen-eral relativity do not determine the metric function y(r)in(1).Therefore,the radial distribution of matter is ar-bitrary in terms of the co-moving radial coordinate r.This is the“maximal”physical freedom com-patible with the assumption of spherical symme-try,we may note.Note,however,that the phys-ical generality here is not be taken to mean the “geometrical”generality.III.ISSUE OF REGULARITY OF CENTER A spherical spacetime admits an SO(3)group of rotational symmetry.The orbits of the symmetry group are closed ones.The center of the spheri-cally symmetric spacetime geometry is defined to be the“invariant point”of the SO(3)group of ro-tations,as it must be.Galilean invariance of the Newtonian equations implies that every observer observes the shrinkage of orbits of the rotation group to zero radius at the center of a spherically symmetric object. Consequently,we may demand that the orbits of the rotation group also shrink to zero radius for a spherically symmetric spacetime.Such a space-time is said to possess a regular center.Now,for(1),y(r)is the“area radius”.When y|r=0=0,the orbits of the rotation group SO(3) do not shrink to zero radius at the center of the spacetime although the curvature invariants re-mainfinite at the center.Also,when y|r=0=0,the orbits of the rotation group shrink to zero radius at the center but the curvature invariants blow up at the center,then.It is well-known[5]that the center and the initial data for matter,both,are not simultaneously reg-ular for a spherical spacetime with hyper-surface orthogonal HKV.Therefore,the spacetime of(1)does not possess a regular center and regular matter data,simulta-neously,and we may consider it to be“unphysical”even when its matter follows the expected“physi-cal”evolution.However,this issue requires careful analysis.It is crucial to ask:who,which observer,is observ-ing the orbits of the rotation group shrink to zero radius?This is important in general relativity though not in Newtonian gravity.Consider the Schwarzschild spacetime.The asymptotic observer does not see any sphere,cen-tered on the mass-point,shrink to any radius below r=2M,the“infinite red-shift surface”.Then,for the asymptotic observer,r=2M is the center of the spacetime!Thus,the“area ra-dius”has this minimum value for the asymptotic observer.It is no coincidence that this minimum value of the“area radius”as observed by the asymptotic observer is related to the gravitational mass or the Schwarzschild mass M.Recall the well-know Newtonian theorem:“The gravitational force on a body that lies outside a closed spherical shell of matter is the same as it would be if all the shell’s matter were concentrated into a point at its center.”The general relativistic manifestation of this Newtonian result is that the spacetime of a spheri-cal body must possess non-vanishing central value for mass in that spacetime.For suitable observer, the orbits of the rotation group are not expected to shrink to zero radius at the center of a spherical spacetime with matter.The co-moving observer of(1)is the“equiv-alent”of the asymptotic observer of the Schwarzschild spacetime in that it is also the “cosmological”observer for(1).Then,for this observer,orbits of the rotation group SO(3)are not expected to shrink to zero“area radius”at the center of the spacetime of(1).Therefore,the conflict of the“non-regularity”of the center and the“physical”evolution of matter in(1)can be resolved with this observation. Now,let us call a star for which the orbits of the rotation group do not shrink to zero radius at its center a strange star,in contrast to the“standard”spherical star for which the center is regular.Then, it is clear from the above that all the spherical stars embedded in a cosmological surrounding are expected to be strange stars in the sense described above.IV.CONCLUDING REMARKS Many spacetimes of spherically symmetric na-ture are known[6].For example,the“original”Schwarzschild[7],the“standard”Schwarzschild (or,Hilbert-Droste,[7]),the Vaidya,the Tolman-Bondi class,the Friedmann-Lemaitre-Robertson-Walker spacetimes.Some of these known exam-ples of spherically symmetric spacetime geometries contain no matter,only radiation dust,only mat-ter dust,etc.To construct the spacetime of a“physically re-alizable”spherical collapse of matter,we therefore need to“match”different,appropriate,such space-time geometries.Of course,this is a non-trivial and,mostly,very difficult task.But,these different spacetime geometries are, clearly,different choices of y(r)in(1).For ex-ample,consider collapse from initial dusty matter with vacuum“exterior”.Then,y(r)is infinite in the exterior.The spacetime of(1)then provides the“final”spacetime that may be obtained after matching many different spacetimes with appropriate physi-cal conditions of matter.It is,therefore,the space-time of physically realizable collapse of spherically symmetric matter.We have,therefore,studied the shear-free col-lapse in[8]and the collapse with shear and energy flux in[9].We have also obtained source free elec-tromagneticfields using the Hertz-Debye formal-ism[10]in[9].In these studies,some general con-clusions as well as the explicit forms for temporal metric functions have been presented for a simple equation of state of the barotropic form p=αρwhereαis a constant.We have also studied,in [11],the phenomenon of Hawking radiation in a radially homothetic spacetime of the metric(1).[1]Chandrasekhar S(1931)Ap J7481Chandrasekhar S(1958)An introduction to the study of stellar structure(New York:Dover) [2]Penrose R(1998)in Black Holes and Singlarities:S.Chandrasekhar Symposium(Ed.R.M.Wald, Yale:Yale University Press)[3]Wagh S M,Govender M,Govinder K S,MaharajS D,Muktibodh P S and Moodley M(2001)Class.Quantum Grav.182147-2162[4]Synge J L(1964)in Relativity,Groups and Topol-ogy,Les Houches Lectures(New York:Gordon and Breach)[5]Macintosh,C.B.(1975)Gen.Rel.Grav.7199[6]Kramer, D.,Stephani,H.,MacCallum,M. A.H.and Herlt,E.(1980)Exact Solutions of Ein-stein’s Field Equations(Cambridge UniversityPress,Cambridge)[7]Abrams L S(1979)Phys.Rev.D202474.Alsoavailable as Database:gr-qc/0201044[8]Wagh S M,Saraykar R V,Muktibodh P S andGovinder K S(2002)Title:Radially homoth-etic,Shear-free,Spherical gravitational collapse Preprint:CIRI/07swpmkg[9]Wagh S M(2002)Title:Spherical gravitationalcollapse and electromagneticfields in radially ho-mothetic spacetimes Preprint:CIRI/02-sw01 [10]Cohen J M and Kegeles L S(1974)Phys.Rev.D101070-1084[11]Wagh S M(2002)Title:Hawking radiation inspatially homothetic,spherical collapse Preprint: CIRI/smw06。

SkyrmionIn particle theory,the skyrmion (/ˈskɜrmi.ɒn/)is a hy-pothetical particle related originally [1]to baryons .It was described by Tony Skyrme and consists of a quantum su-perposition of baryons and resonance states.[2]Skyrmions as topological objects are also important in solid state physics ,especially in the emerging technology of spintronics .A two-dimensional magnetic skyrmion ,as a topological object,is formed,e.g.,from a 3D effective-spin “hedgehog”(in the field of micromagnetics :out of a so-called "Bloch point "singularity of homotopy degree +1)by a stereographic projection ,whereby the positive north-pole spin is mapped onto a far-offedge circle of a 2D-disk,while the negative south-pole spin is mapped onto the center of the disk.1Mathematical definitionIn field theory,skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model with a non-trivial target manifold topology –hence,they are topological solitons .An example occurs in chiral models [3]of mesons,where the target manifold is a homogeneous space of the structure group (SU (N )L ×SU (N )RSU (N )diag)where SU (N )L and SU (N )R are the left and right parts of the SU (N )matrix,and SU (N ) ₐ is the diagonal subgroup .If spacetime has the topology S 3×R ,then classical con-figurations can be classified by an integral winding num-ber [4]because the third homotopy groupπ3(SU (N )L ×SU (N )R SU (N )diag ∼=SU (N ))is equivalent to the ring of integers,with the congruence sign referring to homeomorphism .A topological term can be added to the chiral Lagrangian,whose integral depends only upon the homotopy class ;this results in superselection sectors in the quantised model .A skyrmion can be approximated by a soliton of the Sine-Gordon equation ;after quantisation by the Bethe ansatz or otherwise,it turns into a fermion inter-acting according to the massive Thirring model .Skyrmions have been reported,but not conclu-sively proven,to be in Bose-Einstein condensates ,[5]superconductors ,[6]thin magnetic films [7]and also chiral nematic liquid crystals .[8]2Skyrmions in an emerging tech-nologyOne particular form of the skyrmions is found in mag-netic materials that break the inversion symmetry and where the Dzyaloshinskii-Moriya interaction plays an im-portant role.They form “domains”as small as a 1nm (e.g.in Fe on Ir(111)[9]).The small size of mag-netic skyrmions makes them a good candidate for fu-ture data storage solutions.Physicists at the University of Hamburg have managed to read and write skyrmions using scanning tunneling microscopy.[10]The topological charge,representing the existence and non-existence of skyrmions,can represent the bit states “1”and “0”.3References[1]At later stages the model was also related to mesons .[2]Wong,Stephen (2002).“What exactly is a Skyrmion?".arXiv :hep-ph/0202250[hep/ph ].[3]Chiral models stress the difference between “left-handedness”and “right-handedness”.[4]The same classification applies to the mentioned effective-spin “hedgehog”singularity":spin upwards at the north-pole,but downward at the southpole.See also Döring,W.(1968).“Point Singularities in Mi-cromagnetism”.Journal of Applied Physics 39(2):1006.Bibcode :1968JAP....39.1006D .doi :10.1063/1.1656144.[5]Al Khawaja,Usama;Stoof,Henk (2001).“Skyrmionsin a ferromagnetic Bose–Einstein condensate”.Nature 411(6840):918–20.Bibcode :2001Natur.411..918A .doi :10.1038/35082010.PMID 11418849.[6]Baskaran,G.(2011).“Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K$_2$Fe$_4$Se$_5$".arXiv :1108.3562[cond-mat.supr-con ].[7]Kiselev,N.S.;Bogdanov,A.N.;Schäfer,R.;Rößler,U.K.(2011).“Chiral skyrmions in thin magnetic films:New objects for magnetic storage technologies?".Journal of Physics D:Applied Physics 44(39):392001.arXiv :1102.2726.Bibcode :2011JPhD...44M2001K .doi :10.1088/0022-3727/44/39/392001.[8]Fukuda,J.-I.;Žumer,S.(2011).“Quasi-two-dimensional Skyrmion lattices in a chiralnematic liquid crystal”.Nature Communica-tions 2:246.Bibcode :2011NatCo...2E.246F .doi :10.1038/ncomms1250.PMID 21427717.123REFERENCES [9]Heinze,Stefan;Von Bergmann,Kirsten;Menzel,Matthias;Brede,Jens;Kubetzka,André;Wiesen-danger,Roland;Bihlmayer,Gustav;Blügel,Ste-fan(2011).“Spontaneous atomic-scale magneticskyrmion lattice in two dimensions”.Nature Physics7(9):713–718.Bibcode:2011NatPh...7..713H.doi:10.1038/y summary(Jul31,2011).[10]Romming,N.;Hanneken, C.;Menzel,M.;Bickel,J. E.;Wolter, B.;Von Bergmann,K.;Kubet-zka, A.;Wiesendanger,R.(2013).“Writing andDeleting Single Magnetic Skyrmions”.Science341(6146):636–9.Bibcode:2013Sci...341..636R.doi:10.1126/ysummary–(Aug8,2013).3 4Text and image sources,contributors,and licenses4.1Text•Skyrmion Source:/wiki/Skyrmion?oldid=637550141Contributors:Michael Hardy,Charles Matthews,Phys, Icairns,Lumidek,Pjacobi,Jag123,Fwb22,Rjwilmsi,Conscious,Wikid77,Headbomb,Lincoln F.Stern,Tarotcards,KylieTastic,Pix-elBot,Doprendek,Addbot,Luckas-bot,Yobot,Citation bot,Obersachsebot,Omnipaedista,Citation bot1,Merongb10,Meier99,Korepin, EmausBot,JSquish,ZéroBot,StringTheory11,AManWithNoPlan,Isocliff,Parcly Taxel,Bibcode Bot,BattyBot,ChrisGualtieri,Andy-howlett,1andreasse,Nicohoho,NorskMaelstrom,Noah Van Horne and Anonymous:74.2Images•File:Portal-puzzle.svg Source:/wikipedia/en/f/fd/Portal-puzzle.svg License:Public domain Contributors:?Original artist:?4.3Content license•Creative Commons Attribution-Share Alike3.0。

关于空间时间的英语作文Title: Exploring the Mysteries of Spacetime。

Space and time, two fundamental concepts that have intrigued humanity for centuries, are intricately intertwined in the fabric of the universe. From the elegant equations of Einstein's theory of relativity to the mind-bending phenomena of black holes and wormholes, the exploration of spacetime has opened doors to a deeper understanding of our cosmos. In this essay, we delve into the mysteries of spacetime and its profound implicationsfor our understanding of the universe.The Unity of Space and Time:In classical physics, space and time were treated as separate entities. However, with the advent of Einstein's theory of relativity in the early 20th century, it became clear that space and time are intimately connected. According to relativity, space and time form a four-dimensional continuum known as spacetime. In this framework, events are described not just by their spatial coordinates but also by their temporal coordinates, and the fabric of spacetime itself can be warped by the presence of matterand energy.Einstein's Theory of General Relativity:At the heart of our understanding of spacetime lies Einstein's theory of general relativity, whichrevolutionized our conception of gravity. According to general relativity, massive objects like stars and planets warp the fabric of spacetime around them, causing other objects to move along curved paths in response to this curvature. This explains the phenomenon of gravity as the bending of spacetime itself, rather than a force acting ata distance.Black Holes: Portals to the Unknown:One of the most intriguing consequences of general relativity is the existence of black holes. Black holes areregions of spacetime where the gravitational pull is so intense that nothing, not even light, can escape fromwithin a certain boundary called the event horizon. Beyond this point, the laws of physics as we know them break down, leading to a singularity—a point of infinite density where spacetime itself becomes infinitely curved. Black holes challenge our understanding of the universe and raise profound questions about the nature of reality.Wormholes: Gateways to Other Realms:In the realm of theoretical physics, wormholes are hypothetical tunnels through spacetime that could potentially connect distant regions of the universe or even different universes altogether. Wormholes are predicted by the equations of general relativity, but whether they actually exist and whether they could be traversable remains an open question. If traversable wormholes were to exist, they could provide a means of interstellar travel or even allow for journeys through time, leading tofascinating possibilities for exploration and discovery.Spacetime and the Fate of the Universe:The study of spacetime also has profound implicationsfor cosmology—the study of the origin, evolution, and eventual fate of the universe. By modeling the dynamics of spacetime on cosmic scales, scientists have developed various theories about the ultimate destiny of our universe. Will it continue expanding indefinitely, eventually becoming a cold, dark void? Or will it reach a point of maximum expansion and begin to contract, culminating in a fiery cataclysm known as the Big Crunch? The answers to these questions depend on the properties of spacetime andthe distribution of matter and energy within it.Conclusion:In conclusion, the exploration of spacetime has opened up new vistas of understanding and discovery, challenging our preconceived notions of space, time, and reality. From the elegant equations of general relativity to the mysterious realms of black holes and wormholes, the studyof spacetime continues to captivate the imagination ofscientists and laypeople alike. As we peer ever deeper into the fabric of the cosmos, we may yet uncover even more profound truths about the nature of existence itself.。

a rXiv:q uant-ph/981189v13N ov1998Cosmic quantum measurementbyI.C.PercivalDepartment of Physics Queen Mary and Westfield College,University of London Mile End Road,London E14NS,England Abstract Hardy’s theorem states that the hidden variables of any realistic theory of quan-tum measurement,whose predictions agree with ordinary quantum theory,must have a preferred Lorentz frame.This presents the conflict between special rel-ativity and any realistic dynamics of quantum measurement in a severe form.The conflict is resolved using a ‘measurement field’,which provides a timelike function of spacetime points and a definition of simultaneity in the context of a curved spacetime.Locally this theory is consistent with special relativity,but globally,special relativity is not enough;the time dilation of general relativity and the standard cosmic time of the Robertson-Walker cosmologies are both essential.A simple but crude example is a relativistic quantum measurement dynamics based on the nonrelativistic measurement dynamics of L¨u ders.98Nov 30,QMW-PH-98-??Submitted to ??11Introduction2Hardy’s theorem3Simultaneity4Not proper time5Cosmology6Measurementfield7A simple relativistic measurement dynamics8Discussion and conclusions1IntroductionThe theoretical ideas of Hardy[24],Bell[7],Wheeler[41]and Hawking and Seifert[21,36],combined with the long-range entanglement experiments of Tit-tel,Gisin and collaborators[37,38],lead to an elementary cosmological dynam-ics of quantum measurement that satisfies the principles of special and general relativity.According to Bohr[11,42],the result of a quantum measurement is influenced by the condition of the measuring apparatus.Dynamical theories of quantum measurement ascribe this influence to a dynamical process.Here the influence is due to interaction with a cosmic backgroundfield,the measurementfield which plays the role of hidden variables in some other dynamical theories.By an ex-tension of the Einstein,Podolsky and Rosen thought experiment[16],John Bell showed[8],[9]that quantum theories which represent quantum measurement as a dynamical process are nonlocal.Hardy[24]showed the need for a preferred Lorentz frame.The measurementfield provides the frame.Generalized quantum measurement is a physical process by which the state of a quantum system influences the value of a classical variable.It includes any such process,for example laboratory measurements,but also other,very different, processes[28].These include the cosmic rays that produced small but detectable dislocations in mineral crystals during the Jurassic era,and the quantumfluc-tuations in the early universe that may have caused today’s anisotropies in the universe.It includes those quantumfluctuations that are amplified by chaotic dynamics to produce significant changes in classical dynamical variables.For such measurements,these are the dynamical variables of the measurer,although there is no measuring apparatus in the usual sense.Assume,therefore,that quantum measurement is universal,that the measure-ment process is taking place throughout spacetime,with the possible exception of the neighbourhood of some spacetime singularities.Here I also assume that2quantum measurement dynamics includes a specific representation for the evo-lution of an individual quantum system:the evolution of an ensemble is not enough.And assume that there are no causal loops in spacetime.This picture and the results that follow are based on the followingfive principles PR1-5and two theorems PR6,7:PR1.Kepler-Galileo-Humans are not at the centre of the universe,in any sense.PR2.Newton-Laplace-Every physical process has a dynamical expla-nation.PR3.Einstein-Special relativity.PR4.Einstein-General relativity.PR5.Cosmological-On sufficiently large scales the universe is spatially isotropic and therefore uniform.PR6.Hardy[24]-Measurement dynamics inflat spacetime and consis-tent with ordinary quantum theory needs a special Lorentz frame.PR7.Hardy simultaneity-Measurement dynamics in curved spacetime needs a definition of simultaneity for events with spacelike separation.I also assume that The principles PR1and PR2together are incompatible with ordinary quantum mechanics,in which quantum measurement is the preserve of humans,and does not require a dynamical explanation.Despite this,it is our most successful theory.A good reason for the recent revival of alternative realis-tic theories which are compatible with these principles is the greater control we have over quantum systems,which raises the possibility of distinguishing differ-ent quantum theories of measurement experimentally.Notice that the(weak) version of the Newton-Laplace principle PR2does not require the dynamics to be deterministic.Aharanov and Albert[1,2,3]pointed to the particular difficulties of reconciling special relativity and realistic quantum theories.According to Shimony[33], special relativity and quantum mechanics might live in‘peaceful coexistence’, but Hardy’s theorem suggests a fundamental conflict between the expected re-sults of quantum measurement and invariance under Lorentz transformations. The principal purpose of this paper is to resolve this apparent conflict between special relativity and the dynamics of quantum measurement.There are now many alternative quantum theories that provide a nonrelativis-tic dynamics of quantum measurement.To my knowledge,there has been no alternative theory that resolves the major problem of reconciling special relativ-ity and the dynamics of quantum measurement in general,or Hardy’s theorem PR6in particular.Nor have I been able to formulate a consistent relativistic dynamical theory of quantum measurement that applies to our universe without including both general relativity and cosmology.3In order to make the paper more accessible,sections2to4include short reviews of the relevant quantum theory for general relativists and cosmologists,and some relevant general relativity and cosmology for quantum theorists.Section2describes Bell’s theorem and Hardy’s theorem.Section3presents an alternative proof of Hardy’s theorem based on a combination of two classically connected Bell experiments.Their spacetime configuration is similar to that of the no-simultaneity thought experiment of Einstein’s original work on spe-cial relativity.It goes on to sketch a proof the Hardy simultaneity theorem, which is an extension of his original theorem,but for curved spacetime,and to state the Hawking-Seifert theorem on timelike functions in some general curved spacetimes.Section4uses general relativistic time dilation to demonstrate that for two clocks at different heights on the Earth or at different locations in the universe, local proper times do not provide a global definition of simultaneity.Two reasons for a cosmological theory of quantum measurement are given in section5,and section6introduces the measurementfield,which provides the simultaneity needed for such a theory,and for the resolution of the conflict between quantum measurement and relativity.Section7sketches a simple example of relativistic measurement dynamics based on the measurementfield,which leaves much room for improvement,and the final section8includes a brief discussion of the relation between this dynamics and some other alternative quantum theories.2Hardy’s theoremHardy’s theorem PR6[24]goes further than Bell’s theorem on nonlocality of quantum measurement.From this theorem it follows that any dynamical theory of measurement,in which the results of the measurements agree with those of ordinary quantum theory,must have a preferred Lorentz frame.The theorem does not determine this frame.Bell’s theorem shows that measurement dynamics is nonlocal if the results of measurements follow the rules of ordinary quantum theory[6,7].Bell demon-strated his theorem by a thought experiment illustrated infigure1,in which two entangled particles,each with spin nonzero,and with total spin zero,are produced from a source S.A component of spin perpendicular to the direction of motion of each particle is measured,one at A,and the other at B,where typically ASB is a straight line,with S at its centre.The alignment of the spin measuring apparatus at A or B is the preparation event,or input,A1or B1, and the measurement and recording of the spin component is the measurement event,or output,A2or B2.Both the events A1,A2at A have spacelike separa-tion from both the events B1,B2at B.In the illustrated example the particles are photons,and a line at45deg represents a photon at the velocity of light.4Figure1:Spacetime diagram of Bell’s experiment.Thin diagonal lines at45o represent the velocity of light.At both A1and B1,the angle is the setting of the angle of spin or polarization measurement,which is an input event,and at A2and B2,+/−represents the recording of the spin or polarization,an output event.Bell’s theorem then states that for any realistic dynamics of quantum measure-ment,if the results agree with ordinary quantum theory,either the input at A1 affects the output at B2or the input at B1affects the output at A2,or both. There must be nonlocal space-like causality.Such an experiment was carried out by Aspect and his collaborators[4,5,30], although there remains at least one loophole to be closed because,despite the considerable care that was taken,it is not clear that the events fully satisfied the spacelike separation condition.[18,39].Hardy demonstrates his theorem through a thought experiment involving two matter interferometers,one for electrons and one for positrons,with an intersec-tion between them that allows annihilation of the particles to produce gamma rays.In its original form,this experiment is likely to remain a thought exper-iment.Improved versions which depend on similar principles and are experi-mentally feasible are given in[13,25].A different derivation based on classical5links between two Bell experiments is given in[29]and section3.3SimultaneityIn classical special relativity withflat spacetimes there is no unique simultaneity for events with spacelike separation.This was demonstrated by Einstein in the famous classical thought experiment,which we describe for later convenience. In Einstein’s experiment,illustrated infigure2,Figure2:Spacetime diagram of Einstein’s simultaneity experiment.The straight lines ASB and A′S′B′represent a source and two receivers at rest in their respective frames.one part consists of a source S which emits aflash of light,and two receivers A and B,equidistant from S in the same straight line,where A,S and B are at6rest in a frame L.It is received simultaneously at A and B with respect to this frame.The other part of the experiment consists of an identical trio A′S′B′,in the same straight line as ASB,which are at rest in a different frame L′,moving with respect to L in the direction AOB,where S and S′are nearly coincident at the time t0when both of themflash.The light from S′is received simultaneously at A′and B′with respect to L′,and this is clearly not simultaneous with respect to L.Hence relativity.There is an alternative proof[29]of Hardy’s theorem,which depends on two Bell experiments in a similar spacetime configuration to Einstein’s simultaneity experiment,and labelled similarly infigure3.This is the double Bell exper-iment.The two Bell experiments are independent at the quantum level,butFigure3:Spacetime diagram of the double Bell experiment,with photons in opticalfibres.The meaning of the symbols corresponds to their meaning in the first twofigures.On the scale of thisfigure,the photons remain at rest while in the delay coils.CL are classical links,by which an output from each experiment determines an input to the other.they are linked classically so that the output A2controls the input A1′,which is in its future lightcone,and the output B2′controls the input B1.According to Bell’s theorem,there are nonlocal interactions NI,such as the setting of the7angle at A1affecting the measurement at B2,or the setting of the angle at B1’affecting the measurement at A2’.If both of these are present,then there is a causal loop A2′−→CL A1−→NI B2−→CL B1′−→NI A2′(1)The assumption that there are no causal loops in spacetime or the equivalent assumption that there is no backward causality,then leads to the exclusion of one of the nonlocal interactions,which makes the dynamics dependent on the Lorentz frame,and so leads to Hardy’s theorem.Details are in the letter [28].As it stands,Hardy’s theorem makes no statement about simultaneity,but this also can be derived using the double Bell experiment.Thus a configuration similary to that used by Einstein to show that classical special relativity has no universal simultaneity,can be used to show that quantum measurement requires universal simultaneity,which is the Hardy simultaneity theorem PR7of the introduction.In flat spacetimes,a preferred Lorentz frame or a standard of rest defines a universal time and simultaneity between distant events.For curved spacetimes,only a local Lorentz frame or standard of rest has meaning,and even if there is a standard of rest for every point,this does not necessarily provide a definition of simultaneity.The examples of the next section show that in the presence of gravitational fields,the local times defined by local preferred Lorentz frames are not necessarily consistent with a universal simultaneity defined throughout a region.For curved spacetimes,simultaneity is a stronger condition.For flat spacetimes they are equivalent.It is therefore important to extend Hardy’s theorem by showing that universal quantum measurement dynamics requires universal simultaneity.It is not feasible to set up the double Bell experiment so that the curvature of spacetime has a significant and relevant effect,but the thought experiment is needed to study the effect of the curvature on the dynamics of quantum measurement.Just as for flat spacetime,the condition that there is no backward causality or equivalently that there is no causal loop [29]requires that there is a time ordering for an event at A with respect to an event at B,which is spatially separated from the event at A.Unfortunately this time ordering depends on the hidden variables or background field,which are not accessible to current experiments.Universal quantum measurement therefore requires a universal time ordering for events with spacelike separation,which is equivalent to a universal simultaneity.This is the Hardy simultaneity theorem,which applies to curved spacetime.It is an extension of the original Hardy theorem and is based on the assumption that the events occur at spacetime points.Some latitude is allowed when they take a finite time or occupy a finite region of space.Hawking [21]and Seifert[32]proved that in all universes in the neighbourhood8of which there is no backward causality,there are timelike functions,spacelike foliations of spacetime and corresponding definitions of simultaneity[36].It is interesting to note that‘no backward causality’is the same condition as that used in[29]to prove that measurement dynamics needs a local Lorentz frame,and is used here to show that it needs simultaneity.Hardy showed that special frames are needed.However,the example of section4illustrates that the existence of a special frame at every point of a curved spacetime does not imply that there is a consistent definition of simultaneity.4Not proper timeThe most obvious choice of a time to define simultaneity is the proper time of local matter,but this is inconsistent,because,as in Einstein’s experiment,the local matter can have different frames.In the neighbourhood of the Earth,we could use the Earth as a standard of rest,but this also is inconsistent,because in gravitationalfields it leads to‘simultaneity’between events that have timelike separation.As an example take two small clocks at rest with respect to the surface of the Earth,one vertically at a height h above the other,where h is small compared with the radius of the Earth.They could be at the top and bottom of a tall building,or one on a table in a laboratory,and one on thefloor beneath it. Suppose they are synchronized at time t=0in the rest frame at this time. At later times,the general relativistic time dilation due to their gravitational potential difference is much greater that the special relativistic time dilation due to their different velocities around the Earth’s centre.The clocks will show a time difference∆t after time t,where∆tc2(2) and g is the acceleration due to the Earth’sfield near its surface.The separation between‘simultaneous’events as given by the two clocks be-comes timelike after a time t for which a signal from one to the other takes a time∆t,where∆t=hg≈1year,(3)which is independent of h.The greater height leads to greater time shifts because of the greater gravitational potential difference,but the time taken for light to travel between the bodies increases in proportion.The fact that t=c/g is so close to the time taken for the Earth to orbit the Sun is a well-known coincidence. One could try to define simultaneity by using some kind of average over local times,but it is not at all clear over what scale the average should be taken:the9scale of the apparatus?of the Earth?of the Solar System?the galaxy?or the universe?An answer to this question is suggested in section6.There is the same problem if we try to use the rest frame of afield to define simultaneity.Suppose that we follow Hardy’s example(see also[34,14])of the universal background radiation.This provides a local standard of rest.We could use any kind of clock in this standard of rest to define the local‘time’. But then there is a gravitational time shift between the clocks in a gravitational potential well,and outside it.So again,using these measures of local time,‘simultaneous’events can have a timelike separation,which is not allowed.The same applies applies to the universal background neutrinofields,or any other backgroundfield,of zero or any other rest mass.Also,as pointed out by Hardy,there is no clear dynamical process whereby the quantum measurement of individual systems can be made to depend on the background radiation.Section6shows that the Hawking-Seifert theorem leads to a possible resolution of this problem of simultaneity.5CosmologyWheeler[41]considered the possibility that entanglement and localization might occur on cosmological scales.We have no observational evidence that entan-glement survives over such distances,but the Hardy simultaneity theorem and the experiments of Tittel,Gisin et al[37]provide two strong arguments for the importance of cosmology to quantum measurement.According to the Hardy simultaneity theorem,quantum measurement needs simultaneity between distant events.There is already a cosmological definition of simultaneity for the standard models like the Robertson-Walker metric for isotropic spacetime.Cosmic standard time provides a time function,dividing(or foliating)spacetime into three-dimensional spacelike surfaces of constant cosmic standard time,which are maximally symmetric subspaces of the whole of the spacetime[40].Any timelike function provides a definition of simultaneity,in which events with the same functional value are simultaneous.However,on scales smaller than the cosmological,the spacetime of the universe universe in our epoch is not isotropic,which leads to the problems of defining simultaneity given in the previous section.The second follows from the experiments that demonstrate entanglement over a given distance,which is currently greatest for the Tittel et.al.experiment.A system AB consisting of two parts A and B is in an entangled pure state when AB is in a pure state,but neither A nor B separately is in a pure state. Suppose that the systems A and B are distant from one another.Then spacelike separated measurements of A and of B lead to the nonlocality and simultane-10ity problems of dynamical theories of measurement.The experiment of Tittel and his collaborators[37]shows directly that there can be entanglement over 10km,so simultaneity must be defined over regions of this size.Assuming that generalized measurement is universal,and that the Earth is typical regarding measurement,following the Kepler-Galilean principle PR1,entanglement and its destruction by measurement over distances of10km is present always and everywhere.Nowfill spacetime with overlapping regions of linear dimension 10km in space and10km/c in time.For every overlap region the definitions of simultaneity must be consistent,so by iteration they must be consistent throughout spacetime,or at least where and when generalized measurement takes place.We have no means of checking whether this includes the neighbourhood of singularities in spacetime or very strong gravitationalfields,including the very early universe,the late stages of a closed universe,or in the neighbourhood of a black hole,but the rest of spacetime needs a definition of simultaneity,with a corresponding timelike function and spacelike foliation.6MeasurementfieldExperimenters in anyfield of physics who work in a nearlyflat spacetime,and find that the results of their experiments depend on the Lorentz frame of the apparatus,do not immediately conclude that special relativity is wrong.They look for some previously unsuspected background influence that depends on the environment and which determines a special frame.This influence comes from a background physical system which interacts with the system being studied.No one has found a convincing example for which this procedure fails.Environment is used in a broad sense,and may includefields that penetrate the system. Similarly,the need for a consistent definition of simultaneity for measurement does not contradict special relativity.But it requires a physical system that defines simultaneity and interacts with the measured system.Suppose that this physical system is a measurementfieldµ(x),where x=(x0,x1,x2,x3)are the time and space coordinates of a spacetime point.Make the following further assumptions:11MU1.For the purposes of the present paper,µ(x)is a real classical scalarfiter it will have to be quantized,it may have imaginary components and may not be scalar.MU2.There was an epoch in the early universe with a a cosmic time t. MU3.In this early epochµwas a monotonically increasing function of t.MU4.In local inertial frames and in epochs like ours,µ(x)satisfies the zero-mass Klein-Gordon equation,or wave equation(c=1):∂2The required cosmological principle says that on sufficiently large scales,av-erages over spherical shells are uniform.This is a stronger than the usual cosmological principle,that,usually by implication,refers to averages over solid spheres or similar regions.7A simple relativistic measurement dynamicsA nonrelativistic stochastic measurement dynamics,which is consistent with the Kepler-Galileo and Newton-Laplace principles,was proposed long ago by L¨u ders[26].The mathematics comes from the Copenhagen school,particularly von Neumann and Heisenberg,but the physics is consistent with measurement as a nonrela-tivistic dynamical process,not with the Copenhagen interpretation.Heisenberg gave a descriptive account in[22].Gisin used L¨u ders dynamics as a starting point for the quantum state diffusion approach to measurement[19]. Because the measurements in this nonrelativistic theory are localized in space-time,it can be assumed that they have a definite time order.Consider just one measurement of a dynamical variable of the quantum system with corre-sponding nondegenerate Hermitean operator G with eigenstates|g .Before the measurement,the quantum system is in the initial state|i and afterwards it is in afinal state|f ,which is one of the eigenstates|g .The measurement dynamics is stochastic,and the probability that the system willfinish in state |g isPr |f =|g = i|g 2.(5) In general the classical system also changes its state,from some initial configu-ration to afinal configuration corresponding to the measurement of the value g whose probability(5)depends on|i .This is the influence of the initial quan-tum state of the quantum system on thefinal state of the classical system,that characterizes generalized quantum measurement.The stochastic evolution of classical and quantum systems consists of continuous evolution of each according to their own deterministic dynamics,with sudden stochastic jumps which correspond to the measurements that take place at times determined by the classical system,in which the quantum and classical systems influence each other.In this theory,the classical system can influence the quan-tum system through time-dependent Hamiltonians whose current value depends on the state of a classical system.But the quantum system can only influence a classical system through a measurement.In the corresponding relativistic theory,the jumps do not occur at constant time,but at constant values ofµ.In this way the measurementfield affects the dynamics of quantum measurement,there are no causal loops,and relativistic principles are preserved,at least formally.13This picture of measurement is unsatisfactory in several ways.In particular,the timing of the jumps is not normally determined by the classical system alone. In the modern theory of continuous laboratory measurements,originating with Davies[15],developed by many authors[31,35,12]and now used widely in quantum optics,the timing of the jumps is determined also by the state of the quantum system.Further,the L¨u ders picture assumes that there are distinctly classical and distinctly quantal degrees of freedom,with a‘shifty split’between them[7].This split is convenient for conventional quantum theory,but there is no evidence that the world is divided in this way into purely classical and purely quantum domains.Modern nonrelativistic dynamical theories of measurement have neither of these problems,but the theory of the measurementfield has not yet been extended to relativistic versions of these theories.8Discussion and conclusionsIt may seem surprising that tachyons have played no role[27].There is a rea-son for this.The usual theory of tachyons has no preferred frame[17].This is normally considered an advantage,but without the preferred frame,interaction with normal matter leads to causal loops.Hence the difficulty of giving a phys-ical interpretation to such interaction.Here the preferred frame is a necessity, through a a nonlocal interaction with the measurementfield,and without using tachyons.There are many versions of nonrelativistic measurement dynamics without the faults of the L¨u ders theory discussed in section7.All of them are nonlocal, following Bell’s theorem.Thefirst was the pilot wave theory of de Broglie and Bohm,in which there are both waves and particles,and measurement dynamics is the result of the effect of the quantum waves on the classical particles[23,10]. Since then there have been dynamical theories based on waves alone,in which the Schr¨o dinger equation is modified by a weak stochastic process of localization, leading to the‘collapse’of the quantum wave.Particles are just very localized waves[28].The nonlocal processes depend on simultaneous changes that take place at spacelike separated points,where the simultaneity is determined by the universal time variable t.The theory presented here assumed that events like the orientation of a polarizer or the recording of a spin take place at spacetime points.In fact preparation and recording occupyfinite regions of space and take afinite time.This complicates the theory,but quantum state diffusion models of nonrelativistic measurement show that this complication leads to no fundamentally new problems.[28].To each of the nonrelativistic dynamical theories there corresponds a relativistic theory in which the definition of simultaneity is provided by the measurement field variableµ,just as in the case of L¨u der’s dynamics.But none of these14。

a rXiv:g r-qc/93228v 122Feb1993KFKI-RMKI-16-FEB-1993K´a rolyh´a zy’s quantum space-time generates neutron star density in vacuum Lajos Di´o si 1and B´e la Luk´a cs 2KFKI Research Institute for Particle and Nuclear Physics H-1525Budapest 114,POB 49,HungaryAbstractBy simple arguments,we have shown that K´a rolyh´a zy’s model overestimates the quantum uncertainty of the space-time geometry and leads to absurd physi-cal consequences.The given model can thus not account for gradual violation of quantum coherence and can not predict tiny experimental effects either.In a pioneering paper[1],it was suggested that the quantum mechanics of macroscopic objects ought to be modified due to a certain eventual unsharpness of space-time ter on,the possibility of experimental verification of the model,too,has been developed[2,3].The idea went as follows.By combining Heisenberg’s uncertainty principle with gravitation,the following relation has been obtained for the minimum uncertainty∆s of a single(timelike) geodesic:∆s2=α4/3s2/3,(1) where s is the length of the geodesic andαis the Planck length[c.f.Eq.(3.1)of Ref.1].Then this uncertainty is believed to be a universal lower bound,and so must appear in the space time in an objective way.This was done via random ”gravitational waves”.The present authors[4]reanalysed the concept leading to Eq.(1).A result is that in Refs.1and2the value M of mass realizing the least uncertainty along the given geodesic takes irrealistically high values∼¯hThe random coefficients c k are uncorrelated.Their average is zero while the spreads are given byL3¯c2k=α4/3k−5/3(4) where L is the normalization volume[c.f.Eqs.(3.4)and(3.5)of Ref.1].The above equation is the only one which is conform to the uncertainty relation(1).According to the intentions implicit in Refs.1and2,the space-time geometries defined by Eqs.(2)and(3)must be approximate solutions of the Einstein equations. However,it turns out that they will not.Though they satisfy,by construction,the linearized vacuum Einstein equations(2),the conditions for the linear approxima-tion will seriously fail.We are going to test two rather trivial conditions.Thefirst will hold but the second will not.Let us calculate the mean squared deviation of the metric tensor from its Minkowski value.Squaring both sides of the Eq.(3)and taking stochastic aver-ages of the coefficients c k,one obtains:¯γ2∼k ¯c2k∼α4/3L−3 k k−5/3∼(αk max)4/3.(5)One needs afinite cutoffon k otherwise the amplitude of the random waves would diverge.K´a rolyh´a zy suggests k max=1013cm−1and this assures thatγis much smaller than the unity.This was thefirst condition for applying the linear form(2) of the Einstein equations.As for the second condition,let usfirst invoke the expansion of the scalar curvature R up to the second order inγ[c.f.Ref.5]:R=12γij¯⊔γij+14(γij,k−γik,j)(γij,k−γik,j)+ (6)Now,by substituting the waves(3)into this equation,thefirst order term indeed vanishes.The magnitude of the average of the remaining terms can be estimated by invoking Eq.(4);one obtains:¯R∼α4/3k10/3max.(7)This curvature is extremely ing the previous cutoffwe are led to¯R∼1cm−2.So the correspondingfluctuating metric is not at all the”extremely small smearing”[1]of theflat space-time,thought before.According to the exact Einstein equation R=8πα2∼1026g/cm3,(9)c2i.e.11orders of magnitude above neutron star density.In Ref.1the details of the cutoffwere thought of no importance.We have, however,pointed out that the original cutoffwould imply absurd results for cosmo-logical mass density.Since the cutoffk max is the only free parameter in the model one may hope to save the theory by choosing a lower value for it.Unfortunately, the choice k max=105cm−1,familiar from e.g.the model of Ghirardi et al.[6], yields still water density.Further decrease of k max is needed.Then,however,there would be only macroscopic wavelengths1/k and the gravitationalfluctuations(3) would not play a rˆo le in the quantum-classical transition anymore.The trace(9) in itself could be removed by means of an incredibly high cosmologic constantΛ, but in the Robertson-Walker Universe geometries two nontrivial components of the Einstein equations survive,and one cannot remove the problem from both.Obviously,the K´a rolyh´a zy model[1]has shown to overestimate something in the assumed quantum smearing of the space time.The spectrum(4)of gravitational fluctuations is certainly wrong whatever cutoffis chosen.The proposals outlined in Refs.[2,3]derive extremelyfine effects to observe experimentally.In the light of the cosmological absurdity of the model we wonder if such tiny effects would have to be taken serious.The necessity and timeliness to perform the present research were recognized in a discussion with Prof.P.Gn¨a dig of the E¨o tv¨o s University.This work was supported by the Hungarian Scientific Research Fund under Grant No1822/1991.References[1]F.K´a rolyh´a zy,NuovoCim.XLIIA,1506(1966)[2]F.K´a rolyh´a zy,A.Frenkel and B.Luk´a cs,in:Physics as natural philosophy,eds.A.Shimony and H.Feschbach(MIT Press,Cambridge,MA,1982)[3]F.K´a rolyh´a zy,A.Frenkel and B.Luk´a cs,in:Quantum concepts in space and time, eds.R.Penrose and C.J.Isham(Clarendon,Oxford,1986)[4]L.Di´o si and B.Luk´a cs,Phys.Lett.142A,331(1989)[5]C.W.Misner,K.S.Thorne,J.A.Wheeler:Gravitation(Freeman,San Francisco, 1973)[6]G.C.Ghirardi,A.Rimini and T.Weber,Phys.Rev.D34,470(1986)。

黑洞介绍英语作文带翻译Title: Exploring the Enigma of Black Holes。

Introduction。

Black holes have long captured the imagination of scientists and the public alike. These enigmatic cosmic entities, formed from the collapse of massive stars, possess gravitational forces so intense that not even light can escape their grasp. In this essay, we will delve into the fascinating world of black holes, exploring their properties, formation, and the profound implications they hold for our understanding of the universe.Properties of Black Holes。

At the heart of every black hole lies a singularity, a point of infinite density where the laws of physics, as we currently understand them, break down. Surrounding this singularity is the event horizon, the boundary beyond whichnothing can escape the black hole's gravitational pull. It is this event horizon that gives black holes their name, as it appears "black" to outside observers.Formation of Black Holes。

英语关于黑洞的作文The Mysterious and Fascinating Black Holes.In the vast and enigmatic universe, black holes standas one of the most intriguing and perplexing phenomena. These regions of space, characterized by their intense gravity and complete absence of light, have captivated the imagination of scientists and laypeople alike for centuries. Despite their otherworldly nature, black holes play acrucial role in understanding the evolution and structureof our universe.The concept of black holes emerged in the late 18th century, with the pioneering work of scientists like John Michell and Pierre-Simon Laplace. They theorized the existence of objects so massive that not even light could escape their intense gravitational pull. However, it wasnot until the 20th century that astronomers began to gather evidence that supported the existence of these mysterious objects.One of the most significant milestones in the study of black holes was the work of Albert Einstein. His theory of general relativity provided a mathematical framework to describe the behavior of gravity and its interaction with matter. This theory laid the foundation for understanding the properties of black holes, including their formation, evolution, and interaction with their environment.Black holes are formed when a massive star collapses under its own weight at the end of its life cycle. This collapse compresses the star's matter into a tiny, ultra-dense region known as a singularity. The gravity around this singularity is so intense that nothing, including light, can escape its pull. The boundary of this region, known as the event horizon, marks the point where the escape velocity exceeds the speed of light.There are two main types of black holes: stellar-mass black holes and supermassive black holes. Stellar-mass black holes are formed when a star of about 10 to 30 times the mass of the Sun collapses. These black holes have adiameter of only a few kilometers but possess a mass comparable to that of a small star. On the other hand, supermassive black holes have masses ranging from millionsto billions of times the mass of the Sun. They are believed to reside at the centers of most galaxies, including ourown Milky Way.The study of black holes has revealed much about the structure and dynamics of the universe. For instance, black holes play a crucial role in the evolution of galaxies. By accreting matter and emitting radiation, they can significantly impact the star formation and gas dynamics of their host galaxies. Additionally, the merging of black holes, a common occurrence in the universe, can emit gravitational waves, ripples in the fabric of spacetimethat can be detected by advanced telescopes like the Laser Interferometer Gravitational-Wave Observatory (LIGO).Despite their otherworldly nature, black holes are not entirely devoid of life. In fact, there are theories that suggest the existence of accretion disks around black holes. These disks are formed when matter from a nearby star orgas cloud is attracted to the black hole and begins toorbit it. As the matter spirals inward, it heats up and emits radiation, creating a bright and energetic environment.The study of black holes also holds the key to understanding some of the most fundamental questions about our universe. For instance, black holes provide a unique laboratory to test the limits of Einstein's theory of general relativity. By studying the behavior of matter and light near the event horizon, scientists can gain insights into the nature of gravity and its interaction with quantum mechanics.In conclusion, black holes are one of the most mysterious and fascinating phenomena in the universe. They challenge our understanding of gravity, matter, and the structure of the cosmos. As we continue to explore and study these enigmatic objects, we may unlock the secrets of the universe and gain a deeper understanding of our placein the cosmos.。

中考英语太空探索成就单选题40题1. The first artificial satellite was launched by the Soviet Union in 1957. What was the name of this satellite?A. Sputnik 1B. Explorer 1C. Apollo 1D. Shenzhou 1答案：A。

解析：1957年苏联发射的第一颗人造卫星叫斯普特尼克1号。

选项B“Explorer 1”是美国发射的第一颗人造卫星；选项C“Apollo 1”是美国阿波罗计划中的一艘飞船，但不是第一颗人造卫星；选项D“Shenzhou 1”是中国发射的神舟一号飞船，与苏联发射的第一颗人造卫星无关，所以正确答案是A。

2. In which year did the United States send the first man to the moon?A. 1961B. 1969C. 1971D. 1979答案：B。

解析：1969年美国实现了首次载人登月。

1961年是苏联宇航员加加林首次进入太空的年份；1971年不是首次载人登月的时间；1979年与首次载人登月事件无关，所以正确答案是B。

3. Who was the first man in space?A. Neil ArmstrongB. Yuri GagarinC. Buzz AldrinD. Alan Shepard答案：B。

解析：尤里·加加林是第一个进入太空的人。

尼尔·阿姆斯特朗是第一个登上月球的人；巴兹·奥尔德林是第二个登上月球的人；艾伦·谢泼德是美国第一位进入太空的宇航员，但不是世界上第一个进入太空的人，所以正确答案是B。

4. The Apollo program was carried out by the United States. How many manned lunar landings were there in this program?A. 5B. 6C. 7D. 8答案：B。