(da trn bi ging ca Lubos Motl, Harvard 2007; dch bi Trung Phan, MIT 03/20/2015)

NN MNG CA C HC LNG T V S R LNG T

NHNG CCH GII THCH

Nhng cch gii thch v th gii lng t sau y l t ph v quan trng nht:

1. Hy cm cha my li v lm tnh con m n i ca Richard Feynman

2. Cch hiu Copenhagen I (hm sng l khng c thc)

3. Cch hiu Copenhagen II (hm sng l c thc)

4. Cch hiu t vai tr c bit ca nhn thc (su v trit hc)

5. Cch hiu chuyn giao

6. Cch hiu Bohm - de Broglie

7. V tr song song ca Everett

8. Cch hiu lch s cht ch

Nhiu cch hiu c kh l ging nhau, ch c hi khc bit mt cht v tnh cht trit hc.

Trong nhng cch gii thch lit k trn trn, cch hiu ca Bohm-de Broglie tr

thnh l bch k t khi bt ng thc Bell c hiu v chng minh qua thc nghim: n

c v nh vi phm thuyt tng i hp, v c th gii thch hin tng s vng

lng t, cch hiu Bohm-de Broglie ny phi cn ti nhng tn hiu i nhanh hn nh

sng. Bn cnh , cch hiu lin quan ti vai tr c bit ca nhn thc l hon ton

v vn (nh nhng gii thch mang tnh trit hc vin vng khc) v khng cn thit sau

khi chng ta hiu c v s r lng t, t nhng nm 1980s. Cn ng lc dn n

cch hiu chuyn giao l kh ti ngha, i vi cc nh Vt L l thuyt hin i, nn

ta s ch dng li mc gii thiu n m thi.

C l, trong cc cch hiu v th gii lng t, lch s cht ch l hin i v hon

thin nht. Cng bng m ni, cch hiu ny cng ch l mt bn nng cp (v cht ch)

ca cch hiu Copenhagen m thi, khi mt s im kh hiu c gii thch k hn

v s r lng t c thm vo trong bc tranh ton cnh. Cch hiu ca Everett v

nhng v tr song song , tuy mc d c v chng khc g khoa hc vin tng, nhng

thc s li v cng ph bin trong gii lm khoa hc ng ti, v cng chnh Everett l

ngi chm ngi cho cuc cch mng v s r lng t.

Cch hiu Copenhagen cho c hc lng t l ph bin nht.

CNG NHAU TM HIU SU THM V CC CCH GII THCH

Hy cm cha my li v lm tnh con m n i

Cu ni ni ting ny ca Feynman thc s m t ng hin trng ph bin trong nghin

cu l thuyt hin ti, v n l thc dng v hiu qu nht. Rt rt rt quan trng trong

cuc sng ca ngi lm khoa hc l phi hiu c cch s dng nhng cng c Ton

hc, bit cc c ra xc sut c d bo bi nhng l thuyt lng t, v thm c

phng php so snh chng vi kt qu thc nghim, v l th duy nht c ngha Vt

L v kim tra c. Mt nh Vt L th nn nhng cu hi tm pho v vn cho my

thng thiu nng ri hi mang lt trit hc gia, hoc nhng tn ngh s na ma, hoc l

in i ca Feynman l nh vy.

Cch hiu Copenhagen I v II

c t tn theo thnh ph ni m Niels Bohr m hoc c nhng ngi lm Vt L

l thuyt khc v i ca ng, cch hiu ny l c in (theo nh ngha t in, c in

l mt tnh t m t s xut chng v khc bit trong khong thi gian di cho mt s vt,

hin tng hoc gi tr vt cht hay tm l no ). Max Born l ngi u tin nhn ra

hm sng c c th m t c nh l tnh cht xc sut. Cch hiu Copenhagen pht

biu rng, nhng vt th lng t (thng l ht c bn v cc h vi m) th phi b chi

phi bi c hc lng t, cn nhng vt th c in (thng l nhng th to to nhn

nhn v m) th s i theo quy lut ca c hc c in. Cc vt th c in c th c

dng o c nhng tnh cht ca l vt th lng t. o c l s tng tc gia vt

th lng t v c in, v trong qu trnh hm sng ca vt th lng t (m t trng

thi ca vt ) s b suy sp vo hm sng ring (m t trng thi sau ) vi gi tr o

c xc nh chnh xc (VD: v tr ca electron p ln trn mn hunh quang). Xc sut

ca nhng trng thi, nhng hin tng, nhng kh nng khc nhau, c tnh ton t

hm sng. Hm sng, ta c th hiu n nh l tnh trng v hiu bit hoc mt sng

thc s, c th suy sp bt thnh lnh, tuy nhin vic hi v ngun gc ca s suy sp l

khng c ngha Vt L. Hmm, mc d vy, ta vn c th tng tng rng s tin ha

ca hm sng l c 2 qu trnh: s tin ha lin tc v tri chy (tun theo phng trnh

cho hm sng ca Schordinger) v s suy sp bt thnh lnh ca n khi b o c. Hin

tng suy sp k qui ny c nghin cu nh l mt vn ca o c.

Cch hiu Copenhagen l gii thch v hiu c kt qu ca tt c nhng th

nghim v lng t tng c tin hnh (ngoi tr mt s th nghim c lin quan ti

s r lng t, s c cp sau). Tuy vy, n c mt s l hng v logic nh sau:

Khng c s phn bit r rng v mch lc gia vt th c in v lng t.

Nu c ai tm cch nh ngha ranh gii c in v lng t, n s c v ty tin

v thiu t nhiu.

Ngay c nhng vt th v m cng c th tun theo c c hc lng t, nhng

khng r rng lm l s trong trng hp nh th no (xem thm v con mo

Schordinger, nyan nyan )

V cc vt th v m u c cu to t nhng vt th vi m, cho nn cn phi c

mt gii thch no cho vic th gii c in l mt mng con, mt s gn ng,

mt gii hn no ca th gii lng t. V c qu trnh o c na.

Nu hm sng l tht, th ngun gc ca s suy sp hm sng l cha c gii

thch, v cng khng c l do no cho vic s suy sp l phi xut hin trong l

thuyt.

Suy sp hm sng c v khng nh x.

Phn ln nhng l ny c trm li bi s r lng t. Hy cng nhau nhn vo mt

nghch l ni ting:

Schordinger, theo nguyn tc, xt mt con mo di mt h thng ba t s hot ng

bt c khi no phn r cu mt ht neutron c o c thy. S phn ca con mo ph

thuc vo mt qu trnh ngu nhin c m t bi c hc lng t (phn r ht). Hm

sng ca neutron (lng t) l s chng chp gia |cha t> v |t ri>, v bi v 2 trng

thi khc nhau ny cng biu th cho t 2 trng thi c th xy ra vi h thng ba (bt

hoc tt), nn con mo, biu din theo tinh thn ca Schordinger, s cng c hm sng:

|i mo> = a |cht m> + b |sng nhn>

Trn thc t, c rt nhiu trng thi phc tp c th c dung t kt cc ca con mo

chi tit hn, tuy nhin 2 trng thi l cho v d ca ta ri. Nu ta nhn vo con mo, ta

s thy n, , mt l cht v hai l sng. Ta s chng bao gi nhn thy rng con mo l:

0.8 |cht m> + 0.6 |sng nhn>

iu c phi ngha l ngay trc khi ta nhn, th con mo thc s trong mt trng

thi chng chp gia sng v cht khng? Nhng quan trng hn c, l trng thi |sng

nhn> hoc |cht m> s l kt qu ca o c, ch s khng phi l trng thi chng

chp. Clgt? Sao li vy? C g |sng nhn> hoc |cht m> ng u tin hn ( d

hiu, tng tng |sng nhn> v |cht m> l 2 phng vung gc nhau trong mt

phng, v trng thi chng chp ca chng l nhng phng cn li trong mt phng ;

th th c l do o g mt s trng thi s o c c, cn ng cn li th khng )?

Rt k diu, s r lng t gii thch c iu ny.

S khc bit gia cch hiu Copenhagen I v II l khng ln lm, v ta b qua chi tit ny.

Cch hiu t vai tr c bit ca nhn thc

ch, li l cc thnh trit ?

Hy cng nhau quay tr li v s khc bit gia nhng vt th v m v vi m. Wigner v

von Neumann tng c gng l lun rng, mi th to hay nh th u tun theo s

chi phi ca phng chnh hm sng Schordinger ht, v s suy sp ch xut hin khi ta

thc s mun quan st v o c mt ci g , tc l cn nhn thc. Tc l, ta c th

cng tin rng, nhng ngi khc xut hin trong cuc i bn, hoc trn th gii ni

chung, hay c v tr ny, thc s l s chng chp ca v vn nhng trng thi vi hm

sng khc nhau, v chnh ta ngi quan st, vi nhn thc ca ring ta l nhn thc

mt thc ti no trong nhng kh nng c th (v c hiu nh l hm sng suy sp).

Thut ng trit hc, th cch hiu ny (thc duy nht l thc, th ch c mi chnh ta) c

gi l duy ng.

Th tc l Sp Vng v B Tng l sn phm ca nhn thc ca ring mnh ? i, ci

$%^&*($%^&R%

Tm li th, ta c th thy rng cch hiu ny kh ging d gio, v cm n hiu bit hin

i v s r lng t, chng ta c th thoi mi vt cch hiu ca cc thnh trit ny vo

st.

Cch hiu chuyn giao

c a ra bi John Cramer nhm xo nu li tng ca Wheeler v Feynman v cc

ht di chuyn xui v ngc chiu thi gian v ci tin n ln thnh mt cch hiu mi

ca c hc lng t, tuy nhin chng ai hiu ni tng ny c th gii quyt c

nhng l hng ca cch hiu Copenhagen ( cp pha trn), cho nn xin mn php kt

thc mc ny y.

Cch hiu Bohm - de Broglie

Vo nm 1927, Hong t ca nh Broglie (mt gia tc v cng ni ting v quyn lc

Php) xut mt cch hiu khng cn dng n xc sut, cho c hc lng t, da

vo u sng. , ng ri, chnh Broglie c gii Nobel l ng ny y, Louis de Broglie.

tng ny c khm ph li v nng cp vi Bohm vo nm 1952, v c gi bng ci

tn c hc Bohmian. Mc d mc ch l an i Einstein (ng bo Cha l g, cng.

ng o chi xc xc u.), nhng cu trc Ton hc ca n th v cng xu x (v cng

ch c d on g vt qua kh nng m t ca c hc lng t c), nn ng ny b

Einstein ph l phc tp ha mt cch khng cn thit.

Theo c hc Bohmian, mt vt th -- ht -- cu to bi C mt cht im v hm sng

c m t nh mt sng c. Bi v cht im, nh tn gi, ng ti mt im duy nht,

nn s khng c g l l khi quan st v o c th n cho ta mt gi tr v tr duy nht (,

ang ni n th nghim kiu giao thoa electron trn khe hp v xem kt qu trn mn

hunh quang). Mt khc, hm sng trong c hc Bohmian l u sng, c th b sung

thm lc vo ht, v do th nng lng t c th c nh ngha sao cho ht c th b

n y ra ngoi khi nhng v tr giao thoa sng cc tiu v ht li ch cc i. V chng ta

khng hon ton hiu r v u sng (c th hiu nh bc t do ny l mt kiu yu t

khng bit, nh gi nh ca Einstein v ng nghip t trc , cho lng t), nn gy

nn s bt nh, dn n nhng kt qu vi ngha xc sut, xut hin.

V c bn, c hc Bohmian gii thch ngha cc thnh phn trong c hc lng t theo

cch ca ring n, tuy nhin cc phng trnh Ton hc th hu nh y ht. Cng cn phi

bit thm l c hc Bohmian khng h gii thch l u sng, s bin i u mt khi ht b

hp th, nh khi ht electron c ht bi mn hunh quang. Hn na, mn c hc ny

cng gp nhiu vn khi m t tnh cht ca h gm nhiu ht ring bit, v cn bt cp

nhiu hn khi s dng gii thch ngha ca spin, cng nh khi t n vo vo thuyt

tng i hp (mu thun xy ra, vi vic cc bc t do trong c hc Bohmian ht v

sng u l c in, m vng lng t l mt hiu ng nhanh hn nh sng). Ni

chung l th, cc nh Vt L thng ci khy v vt x mt bn, v bn c khi qua mc

ny cng c th thy n phc tp, ri rm v lng nhng nh th no.

Nhng tt nhin, v v vn nh vy nn dn lm v trit hc rt yu qu hc thuyt ny

(nn vkl ), c bit l nhng ngi tin rng th gii vn ng khng theo xc sut, m

mi th u xc nh ht.

V tr song song ca Everett

Lun vn ca Everett, v cch hiu v cng sng to (v c phn t ph) ny, c vit

vo nm 1956. Nu ta o c mt vt th lng t v thu c kt qu A, th bi v lc

trc khi o c, mt kt qu B no khc cng c kh nng xy ra (vi xc sut khc 0),

cho nn Everett gi nh rng s c th tn ti mt v tr no khc, song song vi

chng ta, vi kt qu thu c l B. C mi ln th gii c mt tng tc vi xc xut

trong (tng tc gia vt th c in v lng t, vi s suy sp hm sng v xc sut

cho cc suy sp c th), th n s r nhnh t v tr ban u ra thnh nhng v tr song

song khc nhau. cc v tr , cuc sng ca ta s khc so vi v tr m ta ang cm

nhn, v c th bn cn khng tn ti mt trong s cc v tr , do con tinh trng

mang thng tin ca bn chy chm hn chng hn. V cn nhiu tng th v bn l na.

Mt s nh Vt L l thuyt tin rng tng ny rt tuyt vi v c th m ra nhng con

ng mi, nhng mt s khc th v cng nghi ng nhn nh ny, c th l v vic n

rt rt rt kh thnh lp di dng mt ngn ng v h lp lun Ton hc cht ch.

Lch s cht ch

Trc ht, cm n Gell-Mann, Hartle v Omnes v cch hiu lng t ny. V c bn, vn

l Ton hc t nhng tng c hc lng t i trc (c th, cch biu din v tin

ca phng php biu din thng tin lng t), nhng vi gii thch khc bit v ngha

trit hc su sa.

Th chng ta biu din thng tin lng t nh th no? V thng tin v trng thi m t

vt th l tp hp ca nhng tnh cht, cho nn ta s biu din trng thi lng t (biu

din []) v tnh cht lng t P (biu din [P]) tng t nhau, v c th l dng nhng

ton t php chiu biu din (c th hiu chng nh nhng ma trn Hermittian):

[]* = [] , []2 = [] , Tr( [] ) = 1 v [P]* = [P] , [P]2 = [P] , Tr( [P] )

Hay, biu din theo bra-ket (pht trin bi Dirac, thn thuc vi sinh vin chuyn ngnh):

[] = |>

Vi cc tnh cht khc nhau, ta c cc tnh cht P v Q dung ha c vi nhau khi tc

dng giao hon c, tri ngc vi nhau khi tc dng bng 0, v khng dung ha c

khi tc dng khng giao hon v khc 0:

Dung hp: [P][Q] = [Q][P] 0 , Tri ngc: [P][Q] = [Q][P] = 0

Khng dung hp: [P][Q] [Q][P] 0

o c c nh ngha kh n gin, l s xc nh xem vt th c tnh cht g, v nu

vt khng c nhng tnh cht P, Q, R (dung ha c vi nhau) th ta s ni rng rng n

c tnh cht 1 - PQR (vi biu din 1 [P][Q][R]).Khng c bt c iu g lin quan ti s

suy sp hm sng hay trng thi hay g y c. Gi ta s nh ngha th no l lch s.

Lch s l tp hp nhng tnh cht ca vt th o c nhng thi gian khc nhau (l At

cho tnh cht thi im t), v trn mi thi gian khc nhau ta ch c th thu c

nhng tnh cht dung ha vi nhau m thi (vic thu c kt qu l tnh cht khng dung

ha vi nhau l khng th, bi v, gi s c 2 tnh cht khng dng ha, th th nu c tnh

cht ny th chc chn tnh cht cn li phi khng xc nh, nh pht biu t trc, v

iu tng t i vi nhng tnh cht hon ton tri ngc).

Mt lch s A (vi nhng o c thi im t1, t2, , tN) th s c biu din l:

AtN,t1 = AtN AtN-1 At1

Gi, hy ch rng, tt c nhng tnh cht lng t u tin ha theo thi gian, vi ton

t (ma trn) tin ha U ph thuc vo Halmintonian H, lin kt cc thi im khc nhau li

vi nhau. C th biu din ca lch s di dng ton t (hoc ma trn) s l:

[AtN,t1] = [AtN] [UtN,tN-1] [AtN-1] [UtN-1,tN-2] [Ut1,t2] [At1] vi [Utf,ti] = ei[H](tf-ti)

Xc sut lch s (vi nhng gi tr c th o c c nhng thi im khc nhau)

xy ra, nu vt th trng thi ti thi im t0:

Pr{A} = D{AtN,t1; AtN,t1|t0,} = Tr( [AtN,t1] [Ut1,t0] [] [Ut1,t0]* [AtN,t1]* )

2 lch s khc nhau, A v B, s c gi l cht ch so vi nhau, nu ta c lin h:

AtN,t1 BtM,t1 , D{AtN,t1; BtM,t1|t0,} = Tr( [AtN,t1] [Ut1,t0] [] [Ut1,t0]* [BtM,t1]* ) = 0

C th thy php tnh ny cho cc lch s (ging hoc khc nhau) c mt s tng t vi

tch phn ng Wilson trong trng lng t. Tht s th, lin h ny c ngha kh

th v, nhng rt tic l chng ta s phi ni v n mt dp khc

H qu ca 2 lch s cht ch so vi nhau s l:

Pr{A hoc B} = Pr{A} + Pr{B} Pr{A v B}

V, l nhng khi nim c bn nht ca cch gii thch lng t thng qua lch s cht

ch. Logic chi phi chnh y l, tt c nhng cu hi c ngha Vt L u c th c

pht biu li thnh nhng cu hi v cc kh nng c th v xc sut tng ng ca

nhng lch s cht ch khc nhau. hiu r hn v pht biu ny, xin mi cc ban tham

kho quyn Consistent Quantum Histories ca Griffiths hoc Understanding Quantum

Mechanics ca Omnes mt cch chi tit. C th thy, trong sut qu trnh thnh lp

nhng ngha, nhng i lng, nhng lin h, nhng tnh ton, khng mt ln no

chng ta phi s dng ti khi nim suy sp hm sng hay s chuyn giao do s o c c

in ln vt th lng t c. V vi gip t nhng hiu bit v s r lng t, chng ta

s c mt bc tranh hon chnh hn, v chuyn giao gia th gii c in thn thuc v

th gii lng t k b.

S R LNG T

Qu trnh r lng t

Trc ht, ch rng, y l mt khi nim v cng lng nhng v kh hiu, nn do ,

cng ging nh lch s cht ch, cc ban nn tham kho quyn Consistent Quantum

Histories ca Griffiths hoc Understanding Quantum Mechanics ca Omnes cho nhng

l lun cu k, phc tp nhng c th v hon thin hn. Ngoi ra, tham kho thm v ch

ny nhng cun snh v my tnh lng t, VD Quantum Computation and

Quantum Information ca Niesel v Chuang, v mt l do s cp sau.

Nhng cu hi th v m s r lng t gii thch c l:

a. Ranh gii gia th gii lng t (m t bi s giao thoa ca hm sng) v th gii

lng t (m t bi trc gic)

b. Nhng tnh cht c u tin hn khi xt n nhng vt th v m v d trng

thi cht hoc sng, cho s phn ca ch mo c ngun gc nh th no?

S r lng t c th hiu nm na, tng t, gn ging nh s ma st, v n cho chng ta

thy nh hng t hng i c th ca chiu thi gian (s bt i xng gia qu kh v

tng lai). u tin, chng ta s xt h m -- chng ta s khng th ch ni ti mi ti mi

(h) vt th m chng ta tin hnh o c, vi Halmintonian Hc, m s thm c ng

gp t mi trng ngoi He v tng tc gia (h)vt th m ta ch vi mi trng Hi:

H = Hc + He + Hi

S r lng t l s mt mt v thng tin v nhng pha tng i ca giao thoa hay,

tng ng, s bin mt ca thnh phn khng nm trn ng cho ca ma trn mt

lng t sau khi ta ly ra ht nhng bc t do khng tnh ti phn mi trng bn

ngoi (ly phn vt ca ma trn trong khng gian trng thi lng t tng ng).

Thc s m ni, cc bc t do ca mi trng bn ngoi l v cng nhy, v ph ca chng

gn nh l lin tc. V d, nu nh ta c N nguyn t v mi trong s chng, ring l, c n

trng thi, th th ta s thu c nN trng thi khc nhau c thy. Nu s khc bit gia

nng lng ca trng thi nng lng t nht v cao nht l NE, th th khong cch trung

bnh gia cc mc nng lng s ch l:

= NE / nN , rt rt rt nh vi N (v n) ln

Gi, chng ta hy cng nhau quan st qu trnh r lng t (theo ngn ng thng dng

bra-ket). Bt u vi trng thi ca mt vt th vi m mt ht l c1|1> + c2|2>. Xt

dng c th nghim, dng o v ly thng tin v nhng tnh cht ca ht, trng thi

ngh |0>. Ngay sau khi o c, trng thi ca dng c ny s b thay i, v trng thi ca

ton b m t ca ta sau s l (ti thi im, chn l, t = 0):

|(t=0)> = c1|1>|1> + c2|2>|2>

Phn ln cc dng c th nghim u hot ng trn c ch da vo s hp th ca ht

c o c vo bn trong dng c, cho nn, ta cn phi coi thng tin ca ht cng l ca

dng cu ny. Theo ngn ng Ton hc:

|(t=0)> = c1|1> + c2|2>

n thi im ny, chng ta vn ang qun mt cha b sung vo nhng tnh cht t cc

bc t do m trng bn ngoi. Ngay sau khi o c, ta c th coi nh nhng tng tc

gia dng c o v mi trng l cha c my, v ta c th biu din trng thi ca mi

trng l chung chung |e> i vi mi trng thi ca dng c o:

|(t=0)> = (c1|1> + c2|2>)|e>

Sau , v tng tc gia dng c o v mi trng bt u th hin vai tr ca mnh

(iu khin bi Halmintonian Hi), nn iu ny s lm cho trng thi ca mi trng tin

ha da trn trng thi tng ng ca dng c o dng c o v mi trng bt u b

vng lng t vo vi nhau:

|(t=T)> = c1|1>|e1> + c2|2>|e2>

Qu trnh ny, thc s, rt ging vi tng tc tn nng lng nh ma st. Khi v nu

trng thi ca dng c o |1> v |2> l khc bit ln, tc vung gc vi nhau (tc

= 0) v d, ht c hp th nhng v tr khng ging nhau (cch nhau khong

c vi ng knh nguyn t) th chng s nh hng ti mi trng ngoi rt lch

nhau: trng thi |e1> v |e2> s dn tr nn vung gc (tc 0) vi nhau

v d, nhng trng thi ny c photon vi nng lng IR, s mang theo nhit ti nhng v

tr khc bit, to nn lin h vung gc. Tht vy, nh cp t trc, do s chnh

lch nng lng trung bnh gia cc trng thi khc nhau ca mi trng ngoi l rt n,

nn chng rt nhy.

Ma trn mt lng t, hay c gi tn trong cch hiu lch s cht ch l thng tin v

tnh cht lng t ca vt th:

[] = |>|e1>< 1|

, chng ta cn phi ly vt ca ma trn ny vi khng gian lng t ca tnh cht trng

thi cc bc t do ny, v vi = 0:

[c] = Tre( [] ) = < e1|> + < e2|>

= |c1|2 |1> v

|1>, m ch chn lc ra ng 2 trng thi duy nht (c th o c) l |1> vi xc sut p1

= |c1|2 v |2> vi xc sut p2 = |c2|

2.

Vi p1 p2 th s lun lun tn ti c s duy nht cho trng thi ring (trng thi c

chn lc ) ca ma trn mt lng t vi bc t do m ta quan tm (bc t do m t

trng thi ca dng c o). Vi p1 = p2 th ta c th thy rng ma trn ny cho ha cho

mi c s, nhng trn thc t th ma trn ny t l ht nh ma trn n v l v cng

kh khn tuy nhin ta lun lun c th thit k mt th nghim sao cho trng thi ring

(trng thi chn lc) l mp m, khng hon ton xc nh r rng.

Bng vic tnh nhng tng tc vi mi trng ngoi vo nh hng ti thng tin

lng t, chng ta c c mt ma trn mt ng lng t cho ha vi thnh phn

cho p1 v p2 vi ngha xc sut c cch hiu ging nh Vt L c in (cc trng thi

chn lc v vung gc vi nhau ). S giao thoa thng xut hin trong logic lng t

bin mt, v trng thi c chn lc (m cch hiu v vai tr c bit ca nhn thc

cho c hc lng t coi nh l s chn la ca nhn thc mi ngi) c ngun gc rt

r rng. Mt cht su hn v nhng chn thi c chn lc, th v c bn, chng l

nhng trng thi c th nh hng mnh vi mi trng bn ngoi chng cht ch v

bn vng. Ranh gii gia th gii lng t v th gii c in cng b xa b , v

nguyn nhn chnh l nh hng t nhng tng tc phc tp ca nhng bc t do khng

c quan tm n, hay ni cch khc, l nh hng t tnh cht m ca i tng c

ch .

Thi gian cn thit r lng t

Th chng ta cn phi mt bao lu mt h m trong thc t b r lng t, v cch

hiu c in tr nn chp nhn c (cho mng tr li vi th gii c in t th gii

lng t!)? Thng th, s tin ha ca trng thi mi trng ngoi gn vi nhng trng

thi khc nhau ca dng c o c, ph thuc theo thi gian theo dng l:

exp( -t / td)

C th hn, hy xt mt con lc vi ng lng p, di nh hng ca lc n phc F v

ma st up, vi 1/u l c thi gian ca s tt dn. Phng trnh chuyn ng ca con lc:

dp / dt = F up

Vi bin dao ng ban u l a v nhit mi trng ngoi l T, th th thi gian c

trng bi s r lng t, c tnh ton chi tit bi nhng nh Vt L l thuyt hoc c

tnh t th nguyn l:

td = 2 / umkTa2

Ma st cng ln, tc tng tc vi mi trng ngoi cng mnh, s dn n vic s r

lng t xy ra nhanh chng hn. iu tng t cng chnh xc vi nhit cao hn,

nng lng gia cc trng thi c ch tng ln, hay sc (khi lng) ca h c

xt tr nn nhiu hn. Cng thc pha trn kh a nng, ng cho nhiu nhng trng

hp khc nhau m khng qu ph thuc vo loi mi trng c th.

Khng nhng th, sau khi thnh phn khng nm trn phn cho ca ma trn mt

lng t gim qu mt t l nht nh, chng s tip tc gim mnh vi c thi gian c

trng khc td. nhn ra c iu ny, cn phi ch rng, ch cn duy nht 1 photton

c pht x ra hoc mt thnh phn no ca mi trng thay i th cng

cho h b r lng t vi tc ca hm m, nhng thm na l s lng ca nhng

photon hoc cc thay i tng t cng s tng theo thi gian, tc ca r lng t

chnh xc hn s l tch ca hm m vi hm m, tc mt hm m nhanh hn na. Nhanh

vl ra, cc bn .

Mt s con s th v: xt mt vt nng 10g, c thi gian tt dn ca dao ng 1/u tm 1

pht, v bin dao ng l khong 1m, th th thi gian ca s r lng t l c 10-26s.

C th i h c hc thnh h mch dao ng RLC vi hin in th xoay chiu c bin

V l 100mV, dung khng C l 10pF v in tr 100:

td = 2 / RkTC2V2 10-26s

Bn cng hon ton c th c tnh thi gian mt ht bi va chm vi mt vt th yu

yu bc x nn ca v tr chng hn, v bn vn ch cn c 10-12s cho s r lng t.

Bi hc qua nhng tnh ton ny l rt r rng: s r lng t xy ra gn nh lp tc i

vi nhng h v m (hay k c kch thc nh nh). C 2 trng hp chnh trong Vt L,

khi m tnh cht lng t vn c gi, k c khi h l v m:

H siu lng

H siu dn

Trong nhng trng hp ny, h c m t v m bi cc trng c cu trc v tnh cht

rt ging vi hm sng, hay ni cch khc, chng ta nhn li c c hc lng t trong

th gii v m.

My tnh lng t, v l thuyt, l mt h v m nhng vn hnh theo c ch ca c hc

lng t, vi nhng dao ng phc v giao thoa, trong mt khong thi gian rt di. S r

lng t l k th v cng ng ght ca cng ngh tng lai ny y cng l l do chnh

ti sao rt nhiu gio trnh v khoa hc my tnh li cp rt su v s r lng t, thm

ch cn hn c nhng ti liu Vt L chuyn ngnh. Mc tiu chnh ca ngi ch to loi

my tnh ny l lm th no gim thiu ti a s r lng t m vn c c nhng

tng tc ti thiu gia cc b phn khc nhau ca my tnh.

Nhng th nghim v r lng t c tin hnh, v kt qu thu c l v cng chnh

xc vi nhng d on t l thuyt.

Tn mn cui cng v tnh cht xc sut ca th gii lng t

Xin ch rng, sau khi s dng nhng l lun tin tin nht ca cch hiu lch s cht ch

v cc thnh tu t l thuyt v s r lng t, chng ta vn cha th hiu c ct li

ca tnh cht xc sut ca th gii lng t: nu c 2 kt qu c th xy ra, c ch g quyt

nh kt qu ngu nhin m ta thu c? Chng ta bit rng, nu c ch ny c ngun

gc t nhng bc t do c in cha c khm ph (nh u sng trong c hc

Bohmian), th s c mt s vi phm v tnh cht nh x v s di chuyn nhanh hn nh

sng (gy hn vi thuyt tng i hp). Tt nhin, rt rt rt nhiu nhng thnh trit c

gng t nhng cu hi v c ch ny, nhng cc nh Vt L l thuyt hin i, v c bit

l Omnes, l lun rng, cu hi ny l phi khoa hc. Tht s g, cng kh ging Feynman

vi chn l Hy cm cha my li v lm tnh con m my i, khng my ai quan tm ti

nhng l lun trit hc gn gn vi tn gio lm, v dn nghin cu ch quan tm ti kt

qu Ton hc v nhng d on em li, k m cch hiu v l thuyt lng t ca tng

ngi. c l l l do cch hiu Copenhagen vn cn rt ph bin v cha c hon

ton thay th bi cch hiu lch s cht ch, vi s gip t s r lng t.