Chuong 2 Vu Tru Trong Vo Hat de - Smith.N Studio

8/3/2019 Chuong 2 Vu Tru Trong Vo Hat de - Smith.N Studio

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CHNG 2HNH DNG CA THI GIAN

Thuyt tng i rng ca Einstein cho thi gian mt hnh dngN c th tng hp vi thuyt lng t nh th no?

Smith Nguyen Studio.


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V T R T R O N G M T V H T

Ngi dch: [email protected], http://datrach.blogspot.com

(Hnh 2.1) M HNH THI GIAN GING NHNHNG NG RAY XE LA

Nhng ng ray chnh ch c tc dng v mtpha v tng lai hay n c th quay li nhpvi n ti cc giao im trc ?

Thi gian c th phn nhnhv quay li c khng?

ng ray xe la chnh chy tqu kh n tng lai

Cc vng nhnh kh c th xyra hay khng th xy ra?



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H N H D N G C A T H I G I A N


Thi gian l g? Mt bi thnh ca ni: thi gian l mt lungchy v tn cun theo bao m c ca chng ta. N c phil mt tuyn ng ray xe la hay khng? C th thi gianc nhng vng lp v phn nhnh v nh chng ta c th i tiv li cn c th quay li mt ga no trc trn ng ray (hnh2.1).

Mt tc gi th k 19 tn l Charles Lamb vit: khng c g lm tibi ri hn thi gian v khng gian, bi v ti cha bao gi ngh vn. Hu ht mi ngi trong chng ta chng mt th gi bn tmv thi gian v khng gian, chng l g cng c, nhng i lctt c chng ta t hi thi gian l g, n bt u th no v n angdn chng ta v u.

Theo ti, bt k mt l thuyt mang tnh khoa hc no v thi gianhoc v bt k mt khi nim no khc u da trn mt trit l

khoa hc hiu qu nht: phng php thc chng (positivism) donh trit hc Karl Popper v cng s a ra. Theo phng php tduy ny th mt l thuyt khoa hc l mt m hnh ton hc m tv gii m cc quan st m chng ta thu c. Mt l thuyt tt sm t c nhiu hin tng da trn mt s t cc gi thit v stin on c cc hin tng c th kim chng c. Nu cc tinon ph hp vi thc nghim th l thuyt s vt qua c tkim chng mc d c th ngi ta khng bao gi chng minh rngl thuyt l chnh xc. Mt khc, nu cc l thuyt khng phhp vi cc tin on th chng ta cn loi b hoc sa i l thuyt(t nht l nhng iu cn xy ra. Trn thc t, ngi ta thngt cu hi v chnh xc ca cc quan st v kha cnh o cca nhng ngi thc hin cc quan st ). Nu ngi ta ng trnquan im thc chng ging nh ti th ngi ta khng th ni thcs thi gian l g. Tt c nhng vic m ngi ta c th l m t ccs kin c tm ra cc m hnh ton hc v thi gian ph hptt vi thc nghim v tin on cc s kin mi.

Isaac Newton cho chng ta m hnh ton hc u tin v thigian v khng gian trong cun Cc nguyn l ton hc (Principia



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Mathematica), xut bn nm 1687. Newton tng gi gh gio sLucasian ti trng i hc Cambridge, v tr m ti ang gi hinnay, mc d lc chic gh ca Newton khng c iu khinbng in nh ca ti! Trong m hnh ca Newton, thi gian vkhng gian l khung nn cho cc s kin xy ra v khng gian vthi gian khng lm nh hng n cc s kin xy ra trong .Thi gian tch bit khi khng gian v c coi l n tuyn, hocc coi l ng ray tu ha di v tn theo hai hng (hnh 2.2).Bn thn thi gian c xem l vnh cu theo ngha n tn ti,

v n s tn ti mi mi. Nhng ngc li, phn ln mi ngi ungh rng v tr vi trng thi gn ging hin ti c sng to cchy vi ngn nm. iu ny lm cc nh trit hc nh ImmanuelKant, mt nh t tng ngi c, trn tr. Nu thc s v trc sng to ti mt thi im th ti sao li phi i mt khongthi gian v tn trc ? Mt khc, nu v tr tn ti mi mi thti sao nhng s kin s xy ra trong tng lai li khng xy ratrong qu kh, ng lch s kt thc? c bit l, ti sao v trli khng t n trng thi cn bng nhit trong mi vt u ccng nhit ?

Isaac Newton xut bn mhnh ton hc v khng gian vthi gian cch y 300 nm.

(Hnh 2.2)Thi gian ca Newton b tchkhi khng gian nh l nhngng ray xe la tri di nv tn theo hai hng.



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(Hnh 2.3) HNH DNG V HNG CA THI GIAN

Thuyt tng i ca Einstein l thuyt ph hp vi rt nhiu thc nghim cho thyrng thi gian v khng gian lin h cht ch vi nhau.Ngi ta khng th b cong khng gian m khng nh hng n thi gian. Do , thigian c mt hnh dng. Tuy vy, dng nh n ch c mt hng ging nh cc u myxe la trong hnh minh ha trn.



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Kant gi vn ny l mt s t mu thun ca l tnh thun ty(antinomy of pure reason), bi v dng nh l mt mu thunl-gc; n khng c li gii. Nhng n ch l mt mu thun trongbi cnh ca m hnh ton hc ca Newton, trong thi gian lmt ng thng, c lp vi cc s kin xy ra trong v tr. Tuynhin, nh chng ta thy trong chng 1, Einstein xut mtm hnh ton hc hon ton mi: thuyt tng i rng. K t khibi bo ca Einstein ra i n nay, chng ta b sung mt visa i nhng m hnh v khng gian v thi gian vn da trn mhnh m Einstein xut. Chng ny v cc chng sau s mt cc t tng ca chng ta pht trin nh th no k t khi bibo cch mng ca Einstein. l cu chuyn v thnh cng cart nhiu ngi, v ti t ho ng gp mt phn nh cng scvo cu chuyn .

Hnh 2.4: TM CAO SU VTR

Hn bi ln trung tm i dincho mt vt th nng nh l mt

ngi sao.Khi lng ca n lm cong tmcao su xung quanh. Nhng hnbi khc ln trn tm cao su s bnh hng bi cong v chuynng xung quanh hn bi ln, cchnh tinh trong trng hp dnca mt ngi sao cng chuynng xung quanh n ging nhtrn.



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Thuyt tng i rng kt hp chiu thi gian vi ba chiu cakhng gian to thnh ci gi l khng thi gian (spacetime hnh2.3). L thuyt gii thch hiu ng hp dn l s phn b ca vtcht v nng lng trong v tr lm cong v bin dng khng thigian, do khng thi gian khng phng. Cc vt th trong khng

thi gian c gng chuyn ng theo cc ng thng, nhng vkhng thi gian b cong nn cc qu o ca chng b cong theo.Cc vt th chuyn ng nh th chng b nh hng bi trnghp dn.

Mt cch hnh dung th thin, khng thi gian ging nh mt tmcao su. Khi ta t mt vin bi ln tng trng cho mt tri ln tmcao su . Trng lng ca vin bi s ko tm cao su v lm chon b cong gn mt tri. Nu by gi ta ln cc vin bi nh ln tmcao su th chng s khng ln thng qua ch vin bi ln m thay

vo chng s di chuyn xung quanh n, ging nh cc hnh tinhchuyn ng xung quanh mt tri (hnh 2.4).

S hnh dung khng hon ton ng bi v ch mt phn hai chiuca khng gian b b cong, v thi gian khng b bin i ging nhtrong l thuyt ca Newton. Trong thuyt tng i rng, l thuytph php vi rt nhiu thc nghim, thi gian v khng gian gnlin vi nhau. Ngi ta khng th lm cong khng gian m khnglm bin i thi gian. Do thi gian c mt hnh dng. Bngcch lm cong khng gian v thi gian, thuyt tng i bin

chng t khung nn th ng m trong cc s kin xy ra thnhtc nhn nng ng tham gia vo cc s kin . Trong l thuytca Newton thi gian tn ti c lp vi tt c mi s vt khc, tac th hi: Cha lm g trc khi sng to ra v tr? Nh thnhAugustin tr li rng, ta khng nn ni a v iu , nu c ai trthi vy th ng tr li Ngi chun b a ngc cho nhng k qut m. l mt cu hi nghim tc m con ngi suy ngh trongnhiu th k. Theo thnh Augustin, trc khi Cha to thin ngv tri t, Ngi khng lm g c. Thc ra tng ny rt gn vicc t tng hin i.

Trong thuyt tng i rng, khng thi gian v v tr khng tnti c lp vi nhau. Chng c xc nh bng cc php o trongv tr nh l s cc dao ng ca tinh th thch anh trong ngh hoc chiu di ca mt ci thc. Trong v tr, thi gian cnh ngha nh th ny cng l iu d hiu, n cn c mt gi trb nht v ln nht hay ni cch khc, c mt s khi u v ktthc. Vic hi ci g xy ra trc khi thi gian bt u v ci gs xy ra sau khi thi gian kt thc l v ngha v lc n khngc xc nh.

Thnh Augustine, nh t tngth k th nm cho rng thigian khng tn ti trc khith gii ra i.



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Vic xc nh m hnh ton hc ca thuyt tng i rng tin onv tr v bn thn thi gian c bt u hay kt thc hay khng hin

nhin l mt vn quan trng. nh kin cho rng thi gian lv tn theo hai hng l ph bin i vi cc nh vt l l thuyttrong c Einstein. Mt khc, c nhiu cu hi rc ri v s sngth, cc cu hi ny c v nm ngoi phm vi nghin cu ca khoahc. Trong cc nghim ca cc phng trnh ca Einstein, thi gianc bt u v c kt thc, nhng tt c cc nghim u rt cbit, c nhiu php i xng. Ngi ta cho rng, trong mt vtth ang suy sp di lc hp dn ca chnh bn thn n, th ccp lc hoc cc vn tc bin (sideway) trnh cho vt cht khngcng nhau ri vo mt im mt vt cht s tr nn v hn.

Tng t nh th, nu ngi ta theo di s dn n ca v tr trongqu kh, ngi ta s thy rng vt cht ca v tr khng xut phtt mt im c mt v hn. Mt im c mt v hn nh vyc gi l mt im k d v n l im khi u v kt thc cathi gian.

Nm 1963, hai nh khoa hc ngi Nga l Evgenii Lifshitz andIsaac Khalatnikov khng nh chng minh tt c cc nghim caphng trnh ca Einstein cho thy vt cht v vn tc c sp xpmt cch c bit. Xc xut v tr xp xp c bit nh th gn

nh bng khng. Hu ht tt c cc nghim biu din trng thi cav tr u trnh c im k d vi mt v hn: trc pha ginn, v tr cn phi c mt pha co li trong vt cht b ko vonhau nhng khng va chm vi nhau sau ri nhau trong pha ginn hin nay. Nu ng nh th th thi gian lin tc mi mi t vtn trong qu kh ti v tn trong tng lai.

Lun c ca Lifshitz v Khalatnikov khng thuyt phc c tt cmi ngi. Thay vo , Roger Penrose v ti chp nhn mtcch tip cn khc khng da trn nghin cu chi tit cc nghimca phng trnh Einstein m da trn mt cu trc bao trm cakhng thi gian. Trong thuyt tng i, khng thi gian khngch b cong bi khi lng ca cc vt th m cn b cong bi nnglng trong na. Nng lng lun lun dng, do khng thigian b un cong v b cong hng ca cc tia sng li gn nhauhn.

By gi chng ta xem xt nn nh sng qu kh (hnh 2.5), l ccng trong khng thi gian m cc tia sng t cc thin h xa xii n chng ta hm nay. Trong gin th hin nn ng sng, thi

(Hnh 2.5) NN NH SNGQU KH CA CHNG TA

Khi chng ta nhn cc thin hxa xi, chng ta ang nhn v trtrong qu kh v nh sng chuynng vi vn tc hu hn. Nuchng ta biu din thi gian bngtrc thng ng v hai trong bachiu ca khng gian bng trcnm ngang th nhng tia sng nvi chng ta ngy nay nm nhnn.

Chiu khng gian

Chiu

khn

ggian

Th

igian

Ngi quan st



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Ngi quan st nhn v qu kh

Cc thin h xut hin gn y

Cc thin h xut hin cch y 5 t nm

Bc x phng



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L thuyt v thc nghim trng khp vi nhau

gian c biu din bng phng thng ng v khng gian cbiu din bng phng nm ngang, v tr ca chng ta trong l nh ca nn ng sng . Khi chng ta i v qu kh, tc l i tnh xung pha di ca nn, chng ta s thy cc thin h ti ccthi im rt sm ca v tr. V v tr ang gin n v tt c mith tng rt gn nhau, nn khi chng ta nhn xa hn v qu khth chng ta ang nhn li vng khng gian c mt vt cht lnhn. Chng ta quan st thy mt phng bc x vi sng (microwavebackground) lan ti chng ta dc theo nn nh sng qu kh t ccthi im rt xa xa khi m v tr rt c, rt nng hn by gi.Bng cch iu khin cc my o v cc tn s vi sng khc nhau,chng ta c th o c ph ca bc x ny (s phn b ca nng

(Hnh 2.6) KT QU PHP OPH PHNG VI SNG

Ph (phn b cng theotn s) ca bc x phng visng ging ph pht ra t mtvt nng. i vi bc x trongtrng thi cn bng nhit, vtcht lm tn x bc x nhiuln. iu ny cho thy rng c mt lng vt cht trong nnnh sng qu kh b cong nhsng.

BC SNG/mm

SNG(I/10-7

Wm-2sr-

1c

m)



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lng theo tn s). Chng ta tm thy mt ph c trng cho bcx t mt vt th vi nhit 2,7 K. Bc x vi sng ny khng mnh lm nng chic bnh piza, nhng ph ny ph hp mt

cch chnh xc vi ph ca bc x t mt vt c nhit 2,7 K,iu ni vi chng ta rng bc x cn phi n t cc vng cvt cht lm tn x vi sng (hnh 2.6).

Do chng ta c th kt lun rng nn nh sng qu kh cachng ta cn phi vt qua mt lng vt cht khi ngi ta i ngcli thi gian. Lng vt cht ny lm cong khng thi gian,do cc tia sng trong nn nh sng qu kh ca chng ta b bcong vo vi nhau (hnh 2.7).

(Hnh 2.7)LM CONG KHNG THIGIAN

V lc hp dn l lc ht nn vtcht lun lm cong khng thigian sao cho cc tia sng b bcong li vi nhau.



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Ti thi im ny, ngi qst ang nhn v qu kh

Cch thin h cchy nm t nm

Phng vi sng

Mt vt cht lm chonn nh sng b b cong

K d v n ln

KHNG GIAN

THIGIAN



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Khi chng ta i ngc li thi gian, cc mt ct ca nn nh sngqu kh t n mt kch thc cc i v sau li tr ln nhhn. Qu kh ca chng ta c hnh qu l (hnh 2.8).

Khi ta tip tc i theo nn nh sng v qu kh th mt vt chtnng lng dng s lm cho cc tia sng b b cong vo vi nhaumnh hn na. Mt ct ca nn nh sng s co li v 0 ti mt thiim hu hn. iu ny c ngha l tt c vt cht trong nn nhsng qu kh ca chng ta b by trong mt vng khng thi gianm bin ca n co li v 0. Do , khng ngc nhin khi Penrose vti c th chng minh bng cc m hnh ton hc ca thuyt tngi rng rng thi gian cn phi c mt thi im bt u c gil v n ln. L lun tng t cho thy thi gian cng c im kt

thc khi cc ngi sao hoc cc thin h suy sp di lc hp dnca bn thn chng to thnh cc h en. By gi chng ta phiquay li mt gi thuyt ngm ca Kant v s t mu thun ca ltnh thun ty m theo thi gian l mt thuc tnh ca v tr. Bitiu lun ca chng ti chng minh thi gian c mt im khi u t gii nh trong mt cuc thi do Qu nghin cu v hp dn titr vo nm 1968. Roger v ti cng chia nhau s tin thng 300USD. Ti khng ngh rng vo nm cc bi lun t gii khc cgi tr lu di hn bi ca chng ti.

c rt nhiu nhng phn ng khc nhau v cng trnh ca chngti. Cng trnh ca chng ti lm bun lng nhiu nh vt l, nhngn li lm hi lng cc nh lnh o tn gio, nhng ngi tin vohnh vi sng th v cho y l mt minh chng khoa hc. Trong khi, Lifshitz v Khalatnikov ang trong mt tnh trng rt kh x.H khng th tranh lun vi cc nh l ton hc m chng ti chng minh, nhng di h thng X Vit h khng th chp nhnl h sai v khoa hc phng Ty ng. Tuy vy, h thotc tnh trng bng cch tm ra mt h nghim vi mt im kd tng qut hn, nhng nghim ny cng khng c bit hn ccnghim trc m h tm ra. iu ny cho php h khng nhcc k d v s khi u hoc kt thc ca thi gian l pht minhca nhng ngi X Vit.

(Hnh 2.8, hnh trc) THI GIAN C HNH QU L

Nu ta i theo nn ng sng v qu kh th chic nn ny b b cong dovt cht nhng giai on rt sm ca v tr. Ton b v tr m chng taquan st nm trong mt vng m bin ca n nh li bng khng ti thiim v n ln. y c th l mt im k d, mt vt cht ln vhn v thuyt tng i c in khng cn ng na.



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M

t bc tin quan trng trong thuyt lngt l xut ca Max Plank vo nm 1900

l nh sng truyn i vi tng b nh gi llng t. Mc d gi thuyt lng t ca Plankgii thch rt tt tc bc x ca cc vt nngnhng phi n tn gia nhng nm 1920 khinh vt l ngi c Werner Heisenberg tm ranguyn l bt nh ni ting ca ng th ngi tami nhn thy ht ngha ca n. Theo Heisen-berg th gi thuyt ca Plank ng rng nu ta

mun o v tr ca ht cng chnh xc bao nhiuth php o vn tc cng km chnh xc by

nhiu v ngc li.

Ni chnh xc hn, Heisenberg chng minh rng bt nh v v tr ca ht nhn vi bt nhv m men ca n lun ln hn hng s Plank mt i lng lin h cht ch vi nng lngca mt lng t nh sng.

NGUYN L BT NH

Bc sng tn s thp lm nhiulon vn tc ca ht t hn

Bc sng tn s cao lm nhiu lonvn tc ca ht nhiu hn

Bc sng dng quan st ht cngdi th bt nh v v tr cng ln Bc sng dng quan st ht cngngn th bt nh v v tr cngnh



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Phn ln cc nh vt l u cm thy khng thch tng v skhi u v kt thc ca thi gian. Do , h ch ra rng cc mhnh ton hc s khng m t tt khng thi gian gn im k d.L do l thuyt tng i rng m t lc hp dn l mt l thuyt cin v khng tng hp vi nguyn l bt nh ca l thuyt lng

t iu khin cc lc khc m chng ta bit. S mu thun nykhng quan trng i vi phn ln v tr v thi gian v khng thigian b b cong trn mt phm vi rt ln cn cc hiu ng lng tch quan trng trn phm vi rt nh. Nhng gn mt im k d,hai phm vi ny gn bng nhau v cc hiu ng hp dn lng t(quantum gravity) s tr ln quan trng. Do cc nh l v imk d do Penrose v ti thit lp l vng khng thi gian c in cachng ta lin h vi qu kh v c th l c tng lai na bi ccvng khng thi gian m hp dn lng t ng vai tr quantrng. hiu ngun gc v s phn ca v tr, chng ta cn mt

L thuyt hp dn lng t (quantum theory of gravity), v y sl ch ca phn ln cun sch ny.

L thuyt lng t ca cc h nh nguyn t vi mt s lng huhn cc ht c xy dng vo nhng nm 1920 do cng caHeisenberg, Schrodinger, v Dirac (Dirac cng l mt ngi tnggi gh m hin nay ti ang gi, nhng khng phi l chic ght ng!). Mc d vy, con ngi vn gp kh khn khi c gngm rng tng lng t vo trng in, t, v nh sng caMaxwell.

TRNG MAXWELL

Nm 1865, nh vt l ngiAnh Clerk Maxwell kt hp cc nh lut inv t bit. L thuyt caMaxwell da trn s tn tica cc trng, cc trng

truyn tc ng t ni nyn ni khc. ng nhn thyrng cc trng truyn nhiulon in v t l cc thc thng: chng c th dao ngv truyn trong khng gian.

Tng hp in t ca Maxwellc th gp li vo hai phngtrnh m t ng hc ca cctrng ny. Chnh ng cng

i n mt kt lun tuyt vi:tt c cc sng in t vi ttc cc tn s u truyn trongkhng gian vi mt vn tckhng i vn tc nh sng.

bt nh v vtr ca ht

bt nh vvn tc ca ht

Khi lng caht

X X = Khng nh hn hng s Plank

PHNG TRNH BT NH HEISENBERG



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Ta c th xem trng Maxwell to thnh t cc sng vi cc bcsng (khong cch gia hai nh sng) khc nhau. Trong mt sng,trng s dao ng t gi tr ny n gi tr khc ging nh mtcon lc (hnh 2.9).

Theo l thuyt lng t, trng thi c bn hay trng thi nng lngthp nht ca con lc khng ch ti im nng lng thp nhthng thng t trn xung. im c v tr v vn tc xc nh lbng khng. iu ny vi phm nguyn l bt nh, nguyn l khngcho php o mt cch chnh xc v tr v vn tc ti mt thi im. bt nh v v tr nhn vi bt nh v m men cn phi lnhn mt i lng xc nh c bit vi ci tn l hng s Plank mt con s nu vit ra s rt di, do chng ra dng mt biutng cho n: .

(Hnh 2.9)SNG LAN TRUYN VICON LC DAO NG

Bc x in t lan truyn trongkhng gian ging nh mt sngvi in trng v t trng daong ging nh mt con lc vhng truyn th vung gc vihng chuyn ng ca sng.Bc x cng c th c tothnh t nhiu trng vi ccbc sng khc nhau.

Bc sng l khong cchgia hai nh sng

Hng dao ng ca con lc

Hng sng truyn

Bcs

ng



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Do , nng lng ca con lc trng thi c bn hay trng thic nng lng cc tiu khng phi bng khng nh ngi ta trngi. Thay vo , ngay c trng thi c bn ca n, mt con lchay bt k mt h dao ng no cng c mt lng nng lng cctiu nht nh ca ci m ta gi l dao ng im khng (hay thngging im khng - zero point fluctuation). iu ny c ngha l

con lc khng nht thit phi nm theo hng thng t trn xungm n s lm vi phng thng ng mt gc nh vi mt xcxut nht nh (hnh 2.10). Tng t nh vy, ngay c trong chnkhng hoc trng thi nng lng thp nht, cc sng trong trngMaxwell s khng bng khng m c th c mt gi tr nh no .Tn s (s dao ng trong mt pht) ca con lc hay sng cng lnth nng lng trng thi c bn cng ln.

Cc tnh ton thng ging trng thi c bn trong trng Maxwellcho thy khi lng v in tch biu kin ca in t ln v cng,

(Hnh 2.10) CON LC VPHN B XC SUT

Theo nguyn l bt nh Heisen- berg, con lc khng th hngthng ng tuyt i t trnxung di vi vn tc bngkhng c. Thay vo , c hclng t cho thy rng, ngay c trng thi nng lng thp nht

con lc cng c mt lng thngging cc tiu.iu ny c ngha l v tr cacon lc s c cho bi mt phnb xc sut. trng thi c bn,trng thi kh d nht l hngthng t trn xung, nhng cngc xc sut tm thy con lc lmmt gc nh vi phng thngng.

Phn b xc sut

Hng



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iu ny khng ph hp vi cc quan st. Tuy vy, vo nhngnm 1940, cc nh vt l Richard Feynman, Julian Schwinger vShinichiro Tomonaga pht trin mt phng php cht ch loi b gi tr v hn v thu c gi tr hu hn ca khi lng vin tch ging nh quan st. Tuy nhin, cc thng ging trng thic bn vn gy cc hiu ng nh c th o c v ph hp vithc nghim. Cc s loi tr cc gi tr ln v hn tng t cngng i vi cc trng Yang-Mills trong l thuyt do Chen NingYang (Yang Chen Ning Dng Chn Ninh) v Robert Mills xy

dng. L thuyt Yang-Mills l m rng ca l thuyt Maxwell m t tng tc ca hai lc khc gi l lc ht nhn yu v lc htnhn mnh. Tuy vy cc thng ging trng thi c bn c hiu ngng k hn trong l thuyt hp dn lng t. Li na, mt bcsng c mt nng lng trng thi c bn. V bc sng ca trngMaxwell c th nh bao nhiu cng c nn c mt s v hn ccbc sng khc nhau v mt s v hn cc nng lng trng thic bn trong bt k vng no ca khng thi gian. V mt nnglng cng ging nh vt cht l ngun gc ca hp dn nn mt nng lng v hn ny c ngha l c lc ht hp dn trong

v tr lm cong khng thi gian thnh mt im m iu rrng l khng xy ra.

Ngi ta cng c th hy vng gii quyt bi ton c v mu thungia l thuyt v thc nghim ny bng cch cho rng cc thngging trng thi c bn khng c hiu ng hp dn, nhng gi thitny khng ng. Ngi ta c th ghi nhn nng lng ca thngging trng thi c bn bng hiu ng Casimir. Nu bn t hai tmkim loi song song vi nhau v rt gn nhau th s c mt ca haitm kim loi s lm gim s cc bc sng c th khp gia haitm kim loi so vi s cc bc sng bn ngoi hai tm mt chtt. iu ny c ngha l mt nng lng ca thng ging trngthi c bn gia hai tm, mc d vn l v hn, vn nh hn mt nng lng bn ngoi hai tm mt lng hu hn (hnh 2.11). Skhc bit v mt nng lng ny lm xut hin mt lc ko haitm kim loi vo vi nhau v lc ny c quan st bng thcnghim. Trong thuyt tng i, ging nh vt cht, cc lc cngto nn hp dn, do , chng ta khng th b qua hiu ng hp dnca s khc bit v nng lng ny.



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(Hnh 2.11) HIU NG CASI-MIR

S tn ti ca thng ging trngthi c bn c khng nh bngthc nghim thng qua hiu ngCasimir v s c mt ca mt lcnh gia hai tm kim loi songsong.

Bc sng bn ngoi

S bc sng bn trongkhong khng gian bgii hn bi hai a bgim i v phi va khpkhong cch gia hai a

Mt nng lng ca thngging trng thi c bn giahai a nh hn mt bnngoi a lm cho hai a bht li gn nhau

Mt nng lng ca thngging trng thi c bn bnngoi hai a ln hn bntrong



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(Hnh 2.12) SPIN

Tt c cc ht c mt tnh cht gi l spin,tc dng ca spin l lm cho cc ht cthy nh nhn t cc hng khc nhau. Ngita c th minh ha iu ny bng mt b bi.Trc tin hy xem con t pch, nu bn quayng mt vng hay 360 th bn s thy nging nh trc khi quay. Do , con t pch cspin bng 1.Ngc li, con qui c c hai u. Nu bn quaymt na vng hay 180 bn s thy n ging

nh ban u. Con qui c c spin bng hai. Tngt, ta c th tng tng cc vt th c spin bng3 hoc nhiu hn nu hnh dng ca n gingnh ban u khi quay mt phn nh hn ca mt

vng quay.Spin cng cao th gc quay vt th c hnhdng ban u cng nh. Nhng c mt iung ch l c cc ht m hnh dng ca chngging nh ban u ch khi bn quay hai vng. Ngi ta gi nhng ht nh vy c spin bng1/2.

180 360

90 180

360 360

360

Ht c spinbng 1

Ht c spinbng 2

Ht c spinbng 1/2



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Ht c spin = 1

Ht c spin = 2Ht c spin = 1/2

Mt nghim khc ca bi ton m c th i hi c mt hng s v trging nh Einstein a ra c c m hnh v tr tnh. Nu hngs ny c gi tr m v cng th n c th loi tr chnh xc gi tr dngv cng ca nng lng trng thi c bn trong khng gian t do, nhnghng s ny c v nh khng c d tnh trc (ad hoc) v n c thc iu chnh mt cch cc k chnh xc.

Tht may mn, ngi ta pht hin mt loi i xng hon ton mivo nhng nm 1970, n cung cp mt c ch vt l t nhin loitr cc gi tr v hn xut hin t thng ging trng thi c bn. Siu

i xng l mt c im ca cc m hnh ton hc hin i ca chngta m c th c m t theo nhiu cch. Mt trong nhng cch nirng khng thi gian c thm cc chiu khc bn cnh cc chiu mchng ta ang tri nhim. Nhng chiu ny c gi l nhng chiuGrassmann bi v chng c o bng cc con s c gi l cc bins Grassmann ch khng phi l nhng con s thc bnh thng. Ccs bnh thng giao hon vi nhau; tc l; bn c th nhn chng theomt trt t no cng c: 6 nhn vi 4 cng bng 4 nhn vi 6. Nhngnhng bin Grassmann th li phn giao hon (anticommute) vi nhau:x nhn vi y bng y nhn vi x.

Ln u tin, siu i xng c nghin cu khi loi tr cc gi tr v hntrong cc trng vt cht v trng Yan-Mills trong khng thi gian c cc chiu s thc v cc chiu Grassmann u phng, khng b cong.Vic m rng siu i xng vo cc chiu s thc v chiu Grassmannkhi cc chiu ny b un cong l mt iu rt t nhin. S m rng nydn n mt s cc l thuyt c gi l siu hp dn (supergravity) vis lng cc i xng khc nhau. Mt h qu ca siu i xng l mitrng hoc mi ht u c mt siu i tc (superpartner) c spin lnhn hoc nh hn spin ca n 1/2 (hnh 2.12).



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Ht Boson l nhng ht c spinnguyn (v d: 0, 1, 2) ca siu hpdn N=8. Nng lng trng thi cbn ca chng l dng.

Ht Fermion vi spin bn nguyn(nh l 1/2) to nn vt cht thng. Nng lng trng thi c bn cachng l m.

(Hnh 2.13) SIU I TCTt c cc ht trong v tr u thuc mt tronghai nhm: Fermion hoc Boson. Ht Fermionl cc ht c spin bn nguyn (nh l 1/2) tonn vt cht thng. Nng lng trng thi cbn ca chng l m.Ht Boson l nhng ht c spin nguyn (v d:0, 1, 2) lm tng lc xut hin gia cc ht Fer-mion nh l lc hp dn v nh sng chnghn. Nng lng trng thi c bn ca chngl dng. Thuyt siu hp dn gi thuyt rngtt c cc ht Fermion v Boson u c mtsiu i tc c spin ln hn hoc nh hn spin

ca ht 1/2. V d mt photon (l ht bo-son) c spin l 1, nng lng trng thi c bnl dng. Siu i tc ca photon l photionc spin bng 1/2 l mt fermion. Do nnglng trng thi c bn l m.Trong s siu hp dn ny, chng ta s cs cc ht fermion v boson bng nhau. Nnglng trng thi c bn ca cc ht boson lmnghing cn cn v pha dng v nng lngtrng thi c bn ca cc ht fermion lm ng-hing cn cn v pha nng lng m, nnglng trng thi c bn s trit tiu ln nhau vloi b gi tr ln v hn.



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M HNH TNH CHT CC HT

1Nu cc ht im (point particle) thcs tn ti nh l cc yu t ring bit

ging nh cc qu bng bi-a th khi haiqu bng va chm vi nhau th l trnhca chng b lch theo hai hng mi.

2 chnh l iu xy ra khi hai httng tc, ch khc hin tng nykch tnh hn.

3L thuyt trng lng t chngminh rng hai ht v d in t vphn in t va chm vi nhau th chngs hy ln nhau to ra mt t bng nnng lng rt ln v to ra mt quangt. Quang t ny gii phng nng lngto ra mt cp in t-phn in t khc.iu ny lm cho chng ta thy nh l ltrnh ca in t-phn in t b lch itheo hng mi.

4Nu cc ht khng phi l nhng htim m l cc dy mt chiu trong cc vng dao ng ging nh mtin t v phn in t th khi chng vachm v hy ln nhau, chng s to mtdy mi vi mt kiu dao ng khc.Khi gii phng nng lng, dy ny b

chia thnh hai dy i theo hai l trnhmi.

5Nu cc dy ban u ny khng cxem l nhng khong thi gian rirc m l mt lch s thi gian khng bgin on th cc dy c thy nhl mt tm gm nhiu dy to nn.

im tng tc

im tng tc

im va chmvo nhau



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Nng lng trng thi c bn ca cc ht boson, trng c spin lmt s nguyn (0, 1, 2, v.v.), l dng. Ngc li nng lng trngthi c bn ca cc ht fermion, trng c spin bn nguyn (1/2,3/2, v.v.), l m. V c mt lng ln cc ht boson v fermion bngnhau, cc gi tr v hn ln nht trit tiu nhau trong cc l thuytsiu hp dn (hnh 2.13).

Vn cn li xc xut c gi tr v hn mc d rt nh nhng vntn ti. Khng ai c s kin nhn cn thit tnh ton xem cc

l thuyt ny c thc s l hon ton hu hn hay khng. Ngi tatnh rng lm iu mt sinh vin gii phi mt 200 nm, vlm sao bn c bit sinh vin khng phm phi sai lm ngay trang th hai? n nm 1985, phn ln mi ngi vn tin rng huht cc l thuyt siu hp dn siu i xng (supersymetric) khngc cha cc gi tr v hn.

Sau th t nhin mt thay i. Ngi ta tuyn b rng khngc l do g khng trng i cc gi tr v hn trong cc l thuytsiu hp dn, iu ny c ng rng cc l thuyt siu hp dn

cng c cc sai lm cht ngi nh cc l thuyt khc. Thay vo ,ngi ta qu quyt rng mt l thuyt c gi l l thuyt dy siui xng l cch duy nht kt hp l thuyt hp dn v l thuytlng t. Cc dy, ging nh cc dy trong kinh nghim hng ngy,l cc vt th mt chiu. Chng ch c chiu di. Cc dy trong lthuyt dy chuyn ng trong khng thi gian. Cc s dao ng cady th hin cho cc ht (hnh 2.14).

Nu cc dy ny c cc chiu Grassmann v cc chiu s thngth cc dao ng s tng ng vi cc ht boson v fermion. Trongtrng hp ny, nng lng trng thi c bn m v dng trit tiumt cch chnh xc n ni s hon ton khng c cc gi tr v hn.Cc siu dy (superstring) c gi l l thuyt v vn vt (theoryof everything).

Cc nh vit lch s khoa hc trong tng lai s thy rt th v khilp biu biu din xu hng thay i t tng ca cc nh vt ll thuyt. Ch trong vi nm, l thuyt dy ng tr tuyt i vthuyt siu hp dn b ging xung thnh mt l thuyt gn ng,ch ph hp nng lng thp. i lng nng lng thp b coi

(Hnh 2.14, hnh k)DAO NG CA DY

Trong l thuyt dy, cc thcth c bn khng phi l cc htchim mt im trong khng gianm l cc dy mt chiu. Cc dyny c cc u khc nhau hoccc u c th ni vi nhau to thnh cc vng dy.

Ging nh cc si dy ca n vi-olon, cc day trong l thuyt dyc cc kiu dao ng hoc tn scng hng nht nh, bc sngca cc kiu dao ng ny trngkhp chnh xc vi khong cchgia hai u dy.Nhng trong khi cc tn s cnghng ca dy n khc nhau tonn cc nt nhc khc nhau thdao ng cng hng ca mt

dy s to ra khi lng, lc khcnhau nhng thc th c giithch l cc ht c bn. Ni nmna l bc sng dao ng ca dycng nh th khi lng ca htcng ln.



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nh mt s ch bai, d l trong ng cnh ny cc nng lng thpng cc ht vi nng lng nh hn hng t t ln so vi cc httrong mt v n TNT. Nu siu hp dn ch l mt php gn ngnng lng thp th n khng th l l thuyt c bn cho v trc. M thay vo , l c bn c xut c th l mt trongnm l thuyt siu dy. Nhng l thuyt no trong nm l thuytsiu dy m t v tr ca chng ta? V thuyt dy s c pht biunh th no vt qua c php gn ng trong cc dy cm t nh l cc mt vi mt chiu khng gian v mt chiu thigian dao ng trong mt phng khng thi gian phng. Liu ccdy c lm cong phng khng thi gian hay khng?



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Vo nhng nm sau 1985, ngi ta dn nhn thy rng, thuyt dykhng phi l mt bc tranh hon ho. Khi u l vic ngi tanhn ra rng cc dy ch l mt thnh phn ca mt lp cc thcth bao qut hn, cc thc th ny c th c m rng vo nhiuhn mt chiu. Paul Townsend, mt ngi cng l thnh vin cakhoa Ton ng dng v Vt l l thuyt ging nh ti i hcCambridge, mt ngi thc hin nhiu cng trnh c bn v ccthc th ny, t cho chng mt ci tn l cc mng-p (p-brane).Mt mng-p c chiu di theo p hng. Do , mng c p=1 l mt

dy, mng c p=2 l mt mt hay mt mng bnh thng, v v.v.(hnh 2.15). Cc mng vi p=1 trong trng hp ca cc dy c vnh khng c u tin hn so vi cc gi tr c th khc ca p.Thay vo , chng ta thng qua mt nguyn tc dn ch cho ccmng-p: tt c cc mng-p sinh ra u c quyn bnh ng.

Tt c cc mng-p u c tm thy l nghim ca cc phngtrnh trong thuyt siu hp dn vi 10 hoc 11 chiu. 10 hoc 11chiu c v nh khng ging khng thi gian m chng ta ang tringhim nhng tng l 6 hoc 7 chiu trong s cc chiu b

cun li nh n ni ta khng th thy chng, chng ta ch c thnhn ra 4 chiu ln v gn nh phng cn li m thi.

Vi t cch c nhn m ni, ti rt min cng khi tin vo cc chiub sung. Nhng v ti l mt ngi theo ch ngha thc chng nncu hi Cc chiu b sung c thc s tn ti hay khng? khngc ngha g c. Tt c nhng iu m ngi ta c th hi l mhnh ton hc vi cc chiu b sung c m t tt v tr ca chngta hay khng. Chng ta vn cha c quan st no m gii thchn ngi ta cn n cc chiu b sung. Tuy vy, chng ta c th cc hi quan st chng trong my va chm Hadron (Large Hadron

(Hnh 2.15) MNG-P

Cc mng-p l cc thc th kodi theo p chiu. Trng hp cbit l cc dy vi p=1 v cc tmvi p=2, nhng cc gi tr kh dca p c th ln hn ti 10 hoc11 chiu. Nhng thng th mts hoc tt c p chiu b cunli ging nh nhng vng xuyn.

Chng ta tin mt s tht hinnhin l tt c cc mng-p sinhra u c quyn bnh ng.



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Paul Townsend, chuyn gia v mng-p

Kt cu khng gian ca v tr ca chng ta c th c cchiu m rng ln chiu b cun li. Cc mng-p c thc xem xt d dng hn nu chng b cun li.

Mt mng 1 chiuhay mt dy b cunli

Mt mng hai chiub cun li thnh mthnh xuyn



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(Hnh 2.16) M HNH THNG NHT

C mt mng li cc mi lin h c gi l tnh i ngu kt ni nm l thuyt dy v siuhp dn mi mt chiu. Tnh i ngu cho thy rng cc l thuyt dy khc nhau ch l nhngbiu din khc nhau ca mt l thuyt c bn c gi l thuyt-M.Trc thp nin 90 ngi ta cho rng 5 l thuyt dy l cc l thuyt ring bit v hon tonkhng lin h vi nhau.Thuyt-M thng nht 5 l thuyt dy vo mt m hnh l thuyt duy nht, nhng ngi ta vncha hiu rt nhiu tnh cht ca m hnh ny.

Loi I

Loi IIB

Loi IIA

Heterotic-EHeterotic-O

Siu hp dn 11 chiu

THUYT-M



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Collider) Geneva. Nhng iu thuyt phc nhiu ngi trong c ti nghim tc chn cc m hnh vi cc chiu b sung lc mt m cc mi lin h khng ng c gi l tnh i ngu(duality) gia cc m hnh. Tnh i ngu ny cho thy rng ttc cc m hnh u tng ng; tc l, chng ch l nhng khacnh khc nhau ca cng mt l thuyt c bn c gi vi ci tnl thuyt-M (M-theory). Nu khng ly tnh i ngu lm du hiucho thy chng ta i ng hng th iu cng gn ging nhcho rng Cha t cc ha thch vo trong lm Darwin

nhm ln v s tin ha ca s sng.

Tnh i ngu cho thy rng c 5 l thuyt siu dy u m t ccbn cht vt l ging nhau v chng cho thy rng v mt vt lchng cng tng ng vi l thuyt siu hp dn (hnh 2.16). Takhng th ni rng cc siu dy c bn hn siu hp dn hoc ngcli. ng hn, chng ch l nhng biu din khc nhau ca cngmt l thuyt c bn, mi l thuyt u tnh ton mt cch hiu qutrong cc tnh hung khc nhau. V cc l thuyt dy khng c chacc gi tr v hn, chng c dng tnh cc kt qu c th xy

ra khi mt s t cc ht nng lng cao va chm v tn x vi nhau.Tuy vy, chng khng hay c s dng m t nng lng camt s ln cc ht lm cong v tr nh th no hoc hnh thnh cctrng thi b tri buc (bound state), ging nh mt h en, ra sao.Vi cc trng hp ny, ngi ta cn n thuyt siu hp dn, vc bn l thuyt ny da trn l thuyt Einstein v khng thi giancong vi mt s loi vt cht b sung. y chnh l bc tranh ti sdng ch yu trong cc phn sau.

Loi I

Loi IIB

Loi IIA

Heterotic-O Heterotic-E

Loi I

Loi IIB

Loi IIA

Heterotic-O Heterotic-E

Thuyt-M thng nht 5 lthuyt dy thnh mt lthuyt c bn duy nht,nhng ngi ta vn chahiu rt nhiu tnh cht cal thuyt ny.



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(Hnh 2.17)

Ta c th xy dng mt m hnh trong trc thi gian o nm vung gcvi trc thi gian thc. Cc qui tcca m hnh ny s xc nh lch sthi gian o da theo thi gian thcv ngc li



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m t l thuyt lng t to hnh dng cho khng thi gian nhth no, vic a tng thi gian o s rt hiu qu. Thi gian o

nghe c v nh mt ci g n t nhng cu chuyn vin tngkhoa hc, nhng n l mt khi nim ton hc c nh ngha rtr rng: thi gian c o bng cc s m ta gi l cc s o. Ta cth ngh v cc s thc bnh thng nh cc s 1, 2, -3,5, v. v. tngng vi cc v tr trn mt ng thng ko di t tri sang phi:im 0 gia, cc s thc dng nm bn phi v cc s thc mnm bn tri (hnh 2.17).

Cc s o c th c biu din l cc v tr nm trn mt ngthng vung gc: im 0 vn nm gia, cc s o dng nm

pha trn v cc s o m c v pha di. Do , cc s o cth c coi nh mt loi s mi nm vung gc vi cc s thcbnh thng. V chng l cc thnh phn ton hc nn chng khngcn phi tng ng vi thc ti vt l no; chng ta khng th cmt s o cc qu cam hoc mt ha n in thoi o c (hnh2.18).

Ngi ta c th ngh iu ny ng rng cc s o ch l mt trchi ton hc m chng c g lin quan n thc ti. Tuy vy, trnquan im trit hc thc chng, ngi ta khng th nh ngha thc

ti l g. Tt c nhng iu m ngi ta c th lm l tm ra m hnhton hc no l m hnh m t v tr m chng ta ang sng. Ha ramt m hnh ton hc c cha thi gian o khng ch tin on cchiu ng m chng ta quan st c m cn tin on c nhnghiu ng m chng ta vn cha th o c. Tuy cha o cnhng v cc l do khc m chng ta vn tin vo cc hiu ng .Vy th thc ti l g v o nh l g? Liu s khc bit gia chngch c trong u c ca chng ta hay khng?

(Hnh 2.18)

S o l mt khi nim ton hc.Bn khng th c mt ha nth tn dng o.



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L thuyt tng i rng c in (tc l khng c tnh lng t) caEinstein kt hp thi gian thc v ba chiu khc ca khng gianthnh mt khng thi gian bn chiu. Nhng chiu thi gian thc

vn khc bit vi ba chiu ca khng gian. V tr tuyn (world line)hay lch s ca ngi quan st lun tng theo thi gian thc (tcl thi gian lun chuyn ng t qu kh n tng lai), nhng vtr tuyn li c th tng hoc gim theo bt k chiu no ca khnggian. Ni cch khc, ngi ta ch c th quay ngc li trong khnggian ch khng th quay ngc li trong thi gian (hnh 2.19).

Mt khc, v thi gian o vung gc vi thi gian thc, nn thigian hnh x nh mt trc khng gian th t. Do vy, thi gian ny

(Hnh 2.19)

Trong khng thi gian ca thuyt

tng i rng c in, thi giankhc bit vi cc hng cakhng gian v n ch tng theolch s ca ngi quan st chkhng ging nh cc chiu cakhng gian c th tng hoc gimtheo lch s . Ngc li, hngca thi gian o ging nh mttrc khng gian, c th tng hocgim.

Hng ca thi gian Lch s ca ngi quan st Nn nh sng



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(Hnh 2.20) THI GIAN O

Khng thi gian o l mt hnhcu, trong , hng thi gian oc biu din l khong ccht cc nam. Nu ta i v hngbc th cc v tuyn (nhng imnm trn cch u cc nam)

s ln dn tng ng vi vtr gin n trong thi gian o.V tr s t kch thc cc iti xch o v sau nu ta tiptc tng thi gian o th v tr sco li cho n kch thc bngkhng ti cc bc. Mc d kchthc ca v tr bng khng ticc cc, nhng nhng im nykhng phi l nhng im k d,cng ging nh bc cc v nam

cc ca tri t l nhng imhon ton bnh thng. iu nygii rng, ngun gc ca v trtrong thi gian o c th l nhngim bnh thng trong khngthi gian.

(Hnh 2.21)Thay cho v , ta c th tngtng hng thi gian o tronghnh cu khng thi gian ging

nh cc kinh . V tt c ccng kinh tuyn u gp nhauti cc bc v cc nam nn thigian s dng ti cc cc, nu tamun tng thi gian o ti thta ng yn ti ch, ging nhta ng bc cc ca tri t vi v hng ty th ta vn s nguyn ch .



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Cng thc din tch entropy hay ls cc trng thi ni ca mt h engi rng thng tin b ri vo trongmt h en c th c lu tr trong ging nh mt my ghi m vc phc hi khi h en bay hi.

Thng tin ri vo h en

Thng tin c lu tr



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c rt nhiu s kin c th xy ra hn ng ray xe la ca thigian thc (thi gian thc ch c mt im khi u hoc kt thc

hoc i thnh cc ng vng). Vi ngha o ny, thi gian cmt hnh dng.

thy cc s kin c th xy ra, hy coi khng thi gian o nhmt qu cu, ging nh b mt tri t. Gi thit rng thi giano l v ca cc v tuyn (hnh 2.20). Khi y lch s ca v trtrong thi gian o s bt u ti Nam Cc. Cu hi Ci g xyra trc khi v tr hnh thnh? s tr nn v ngha. n gin lthi gian trc khi v tr hnh thnh khng c nh ngha, gingnh khng c im no nm pha nam ca Nam Cc. Nam Cc

l mt im hon ton bnh thng trn b mt tri t, v cc nhlut khoa hc cng ng Nam Cc ging nh ng cc imkhc trn tri t. iu ny gi rng s khi u ca v tr trongthi gian o c th l mt im bnh thng ca khng thi gian,v n cng gi rng cc nh lut khoa hc cng ng ti imkhi u ca thi gian ging nh ti cc thi im khc ca v tr(ngun gc lng t v s tin ha ca v tr s c tho luntrong chng sau).

Ta c th thy mt s kin khc c th xy ra khi coi thi gian o

l ca cc ng kinh tuyn trn tri t. Tt c cc ng kinhtuyn u gp nhau Bc Cc v Nam Cc (hnh 2.21). Do , ticc cc, thi gian s dng nu ta coi thi gian o tri tng t nhkinh ca cc kinh tuyn tng ln. Hnh dung mt ngi ng mt trong hai cc v i v hng ng hoc hng ty (theo hngkinh tuyn tng) th anh ta s t quay quanh mnh v ng yn mtch. iu ny tng t nh cch m thi gian thc dng li chntri ca h en. Chng ta cn nhn thy rng s dng li ca thigian thc v o (hoc c thi gian thc v o cng dng, hoc khngc thi gian no dng) c ngha l khng thi gian c mt nhit ,ging nh ti pht hin ra iu cho h en. H en khng chc nhit m n cn hnh x nh l n c mt i lng gi lentropy. Entropy o s cc trng thi ni (s cc cch m bn trongh en c nh hnh) m h en c th c. Mt ngi quan stbn ngoi khng nhn thy c s khc bit no v s cc trng thini ny ca h en. Ngi quan st ny ch c th quan st ckhi lng, s quay v in tch ca h en m thi. Entropy cah en ny c cho bi mt cng thc rt n gin m ti tmra vo nm 1974. N t l vi din tch ca chn tri ca h en: cmt cht thng tin v trng thi ni ca h en i vi mi n v

S = Akc3

/4hGCng thc tnh Entropyca h en

A: din tch chn tri skin ca h en

h: hng s Plank

k: hng s Boltzman

G: hng s hp dn New-ton

c: vn tc nh sng

S: entropy



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Thm ch mt mnh nh trna nh hai chiu cng cha

thng tin ti xy dngnh ba chiu ca qu to.

din tch c bn ca chn tri. iu ny cho thy rng c mt miquan h su sc gia hp dn lng t v nhit ng hc mt mnkhoa hc v nhit (mn ny c nghin cu v entropy). N cng gi

rng hp dn lng t c th cho bit mt ci m ngi ta gi lphng php chp nh a chiu (holography) (hnh 2.22).

V mt l do no m thng tin v cc trng thi lng t trongmt vng khng thi gian c th c m ha bin ca vngkhng thi gian . S chiu bin ca khng thi gian t hn haichiu so vi vng bn trong. iu ny ging nh vic chp nh bachiu trn mt mt phng hai chiu. Nu hp dn lng t kt hpcht ch vi nguyn l chp nh a chiu th iu ny c th chophp ta theo di cc s kin bn trong h en. Vic chng ta c th

tin on bc x thot ra khi h en hay khng l iu rt quantrng. Nu ta khng lm c iu th chng ta khng th tinon c tng lai mt cch y nh chng ta ngh. Vn ny s c tho lun trong chng 4. K thut chp nh a chius c bn lun li trong chng 7. Dng nh l chng ta angsng trong mt mt mng-3 chiu (3-brane) l mt mt bnchiu (ba chiu khng gian v mt chiu thi gian). Mt bn chiuny li l bin ca mt vng nm chiu vi chiu cn li b cun lirt nh. Trng thi ca v tr trn mt mng s gii m nhng skin xy ra trong mt vng nm chiu.

NGUYN L NH ACHIU

Ngi ta thy rng din tch bmt chn tri bao xung quanhh en l mt php o entropyca h en. iu ny lm chongi ta gi thit rng entropycc i ca bt k vng khnggian ng no cng khng thvt qu mt phn t din tch b mt gii hn vng khnggian . V entropy khng lg khc hn l php o thng

tin ton phn c trong h, do, thng tin lin quan ntt c mi hin tng trongth gii ba chiu c th clu tr trn bin hai chiu can ging nh mt bc nh achiu. Theo mt ngha nhtnh, th gii c th l haichiu.



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(Hnh 2.22)V nguyn tc, nh a chiu l mt hin tng giaothoa ca cc loi sng. nh c to ra khi nhsng t mt chm laser n b tch thnh hai chm(a) v (b). Chm (b) p vo vt th (c) v phn xln a nhy nh sng (d). Chm (a) s i qua mtthu knh (e) v chm vo nh sng phn x (b) tora vn giao thoa trn a.Khi mt chm laser c chiu qua a th ngi ta

thu c hnh nh ba chiu y ca vt th. Mtnh quan st c th nghin cu bc nh a chiuny v c th nhn thy nhng mt m nhng bcnh thng khng th cho thy c.B mt hai chiu ca a bn tri, khng ging nhmt bc nh bnh thng, c mt tnh cht ngch l bt k mt phn nh no trn b mt can u cha tt c cc thng tin cn thit ti cutrc ton b hnh nh.



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