The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory - Lee...

7/30/2019 The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory - Lee Smolin

http://slidepdf.com/reader/full/the-bekenstein-bound-topological-quantum-field-theory-and-pluralistic-quantum 1/43

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http://arxiv.org/abs/gr-qc/9508064v2
































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68



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df|bè. wobco bs qh}qhshe|hl be |oh s|f|h `j s`dh lhgqhhs `j jqhhl`d besblh|oh àshqzhq% \oxs. wohe fe àshqzhq dfihs fe àshqzf|bè. b|s s|f|h dxs|cofegh. |` qhc ql |oh bej`qdf|bè gfbehl% Ax| bj |oh àshqzhq bs cè|fbehlbe |oh srs|hd. |ohe |oh s|f|h `j |oh srs|hd cofeghs cèshvxhe|nr. fs f qhsxn|`j |oh dhfsxqhdhe|. jq`d |oh dhfsxqhl s|f|h% \oh àshqzhq dfr f||hd}||` fgfbe dhfsxqh b|s s|f|h |` fschq|fbe |oh cofegh. ax| fgfbe |oh s|f|h dxs|cofegh. s` |of| |oh qhsxn| bs fe besteb|h qhgqhss% D`qh`zhq. j`q f c`d}nh|hshnj$dhfsxqhdhe| oh w`xnl ehhl fe besteb|h exdahq `j lhgqhhs `j jqhhl`d.ahcfxsh |ohqh bs f }qànhd `j besteb|h qhgqhss. hfco |bdh oh àshqzhs obdshnj oh ehhls f ehw }nfch |` }x| |oh bej`qdf|bè gfbehl s}hcbjrbeg obs }qhzb`xss|f|h%

\oxs. fs s`è fs wh fcch}| |oh }`be| `j zbhw |of| |oh vxfe|xd s|f|hc`qqhs}èls be s`dh hfc| wfr wb|o |oh bej`qdf|bè |of| fe àshqzhq dfrgfbe fa`x| |oh srs|hd fs |oh qhsxn| `j fe àshqzf|bè `j b|. wh dxs| fcch}|fns` |of| e` sxco lhscqb}|bè cfe gbzh f c`d}nh|h s}hcbstcf|bè `j |oh wo`nhxebzhqsh. fssxdbeg |of| b| fns` cè|fbes |oh àshqzhq% \oh ènr wfr |` ofzhf lhscqb}|bè wobco bs a`|o c`d}nh|h fel vxfe|xd dhcofebcfn bs |` xsh |ohjfc| |of| be jfc| |oh xebzhqsh bs c`d}nh he`xgo |of| |ohqh fqh dfer sxasrs$|hds |of| dfr ah cfnnhl àshqzhqs. fel |` |ohe }`s|xnf|h |of| |oh c`d}nh|hbej`qdf|bè j`q lhscqbabeg |oh s|f|h `j |oh xebzhqsh bs qh}qhshe|hl be f exd$ahq `j Obnahq| s}fchs. hfco `j wobco qh}qhshe|s |oh bec`d}nh|h bej`qdf|bè|of| f }fq|bcxnfq àshqzhq dfr ofzh fa`x| |oh xebzhqsh%

Wh dbgo| fns` e`|h |of| |fibeg |oh Obnahq| s}fch |` c`qqhs}èl |` |ohbe|hqfc|bè `j fe àshqzhq fel f srs|hd aqbegs |oh be|hq}qh|f|bè `j |ohj`qdfnbsd be|` c`d}nh|h c`qqhs}èlhech wb|o wof| wh fc|xfnnr l` wohewh f}}nr vxfe|xd |oh`qr |` |oh qhfn w`qnl% J`q be qhfn }qfc|bch. }orsbcbs|slhscqbah lbhqhe| bs`nf|hl srs|hds wb|o lbhqhe| Obnahq| s}fchs fel fnghaqfs`j àshqzfanhs% @eh |obeg |of| |obs be|hq}qh|f|bè fcc`d}nbsohs bs |oxs |`dfih |oh |oh`qr c`qqhs}èl lbqhc|nr |` fc|xfn }qfc|bch% Wh e` nèghq ehhl|` bdfgbeh |of| fnn |oh fc|xfn f}}nbcf|bès `j vxfe|xd |oh`qr fqh |` f gqhf|hq`q nhss`q h|he| f}}q`bdf|bès |` s`dh „qhfn vxfe|xd lhscqb}|bè— be |hqds`j s`dh blhfn „Obnahq| s}fch `j |oh xebzhqsh%—

<%3 \oh dhfsxqhdhe| }qànhd fel |oh cèshesxs cèlb|bèBj wh fcch}| |oh afsbc blhf `j }nxqfnbs|bc vxfe|xd c`sd`n`gr. wh e` nèghqofzh |` feswhq vxhs|bès fa`x| wobco s}nb| `q wobco afsbs `q wobco sh| `j obs|`qbhs c`qqhs}èls |` qhfnb|r% Bes|hfl. wh ofzh |` feswhq f ehw ibel `j

6:



vxhs|bè. wobco bs wof| qhnf|bèsob}s dfr ah h}hc|hl |` o`nl ah|whhe fer

|w` }`ssbanh Obnahq| s}fch lhscqb}|bès. hfco gbzbeg fe bec`d}nh|h lhscqb}$|bè `j |oh w`qnl fqbsbeg jq`d f lbhqhe| lbzbsbè `j |oh xebzhqsh be|` |w`sxasrs|hds% \obs ahc`dhs |oh ihr vxhs|b e j`q |oh |oh`qr9 wh wbnn shh. be$lhhl. |of| |oh wo`nh `j |oh |oh`qr. fel belhhl. hzhe b|s lrefdbcs. dfr ahh}qhsshl be |hqds `j |ohsh qhnf|bèsob}s%

\oh stqs| vxhs|bès |of| dxs| ah fsihl fa`x| |ohsh qhnf|bèsob}s bs woh|ohq|oh hbs|hech `j lbhqhe| bec`d}nh|h lhscqb}|bès `j |oh sfdh srs|hd cfe ahcèsbs|he| wb|o |oh }qbecb}nhs `j vxfe|xd dhcofebcs. fel be }fq|bcxnfq wb|o|oh xechq|fbe|r }qbecb}nh% Jxq|ohq. l`hs |obs }`be| `j zbhw sohl fer nbgo| è|oh dhfsxqhdhe| }qànhd0 Fe fqgxdhe| `j Q`zhnnb sxgghs|s |of| |oh fe$swhq bs rhsY1T% B w`xnl nbih e`w |` qhzbhw Q`zhnnb‒s fqgxdhe|. fs b| sxgghs|s

|oh ehhl j`q f chq|fbe cèsbs|hecr cèlb|bè. wobco B wbnn cfnn |oh cèshesxs cèlb|bè%

Sx}}`sh |of| |ohqh bs f vxfe|xd srs|hd F sxqq`xelhl ar f |w` sxqjfchS 6. wobco wh dfr bej`qdfnnr cfnn |oh „a`— |of| cè|fbes F% Sxqq`xelbeg|of| a` bs shcèl. S 1. wobco cè|fbes |oh srs|hd F fel fe àshqzhq. @6%@x|sblh `j |of| bs f shcèl àshqzhq. @1% \oh dhfsxqhdhe|s |oh |w` à$shqzhqs. @6 fel @1 dfih fqh qhc`qlhl be |oh s|f|hs be |w` Obnahq| s}fchs whdfr cfnn OS 6 fel OS 1 %

E`w. nh| xs fssxdh |of| @6 dhfsxqhs |oh s|f|h `j F. xsbeg f dhfsxqbegbes|qxdhe| |of| dhfsxqhs sthnls è |oh sxqjfch S 6% \oh qhsxn| bs lhscqbahllbhqhe|nr ar |oh |w` àshqzhqs. xsbeg |oh |w` Obnahq| s}fchs% \oh stqs|

àshqzhq‒s bes|qxdhe|s qhgbs|hq f lhsteb|h zfnxh. ι6 wobco dhfes |of| sohwbnn }q`khc| |oh s|f|h |of| lhscqbahs F be|` f lhsteb|h s|f|h ~6 5∏ OS 6% \ohshcèl àshqzhq dhfsxqhs |oh c`dabehl s|f|h `j F fel |oh dhfsxqbeg bes|qx$dhe|s fel àshqzhq @6. fel nhfqes ènr |of| fs f qhsxn| `j |ohbq be|hqfc|bè|ohr fqh be s`dh c`qqhnf|hl s|f|h.

b ~b 56 ⊗~b 51∏ OS 6 wohqh |oh s|f|hs

~b 5b fqh |oh vxfe|xd s|f|hs `j |oh stqs| àshqzhq be wobco soh ofs àshqzhl|oh srs|hd F |` ofzh hbghezfnxh ιb%

\oh }`be| bs |of| |ohqh bs e` cè|qflbc|bè ah|whhe |ohsh |w` qhc`qls `j |oh àshqzf|bè% \oh dhfsxqhdhe| `j |oh shcèl àshqzhq fschq|fbes |of||oh c`dabehl srs|hd `j F fel |oh stqs| àshqzhq bs be f c`qqhnf|hl s|f|h.c`qqhs}èlbeg |` f dhfsxqhdhe| ofzbeg a hhe dflh% Ax| oh bs xefanh |`fchq|fbe wof| |oh qhsxn| `j |oh dhfsxqhdhe| wfs% Be |oh dhfe|bdh. |ohstqs| àshqzhq. ofzbeg dflh |oh dhfsxqhdhe|. ofs àshqzhl f lhsteb|h zfnxhι6. fel ofs qhlxchl ohq lhscqb}|bè `j |oh srs|hd F |` |oh c`qqhs}èlbeghbghes|f|h%

\obs hfd}nh so`ws |of| b| dfr ah }`ssbanh |` ofzh lbhqhe| Obnahq|

67



s}fchs wobco lhscqbah |oh qhsxn|s `j àshqzf|bès dflh ar lbhqhe| àshqzhqs.

be f wfr |of| fnn`ws |oh lbhqhe| s|f|hs |` ah lbhqhe| jq`d hfco `|ohq. ax|fns` cèsbs|he| wb|o hfco `|ohq% \obs hfd}nh fns` so`ws xs |oh wfr |`f cèlb|bè `j cèsbs|hecr wobco dxs| ah bd}`shl è |oh vxfe|xd s|f|hsfssbgehl |` lbhqhe| a`xelfqbhs% \oh s|f|h ~b` 5 è |oh beehq sxqjfch shhear |oh àshqzhq dxs| e`| ah }qhcnxlhl ar |oh s|f|h

b cb~b 56 ⊗~b 51 shhe

ar |oh shcèl àshqzhq. b%h% |oh fd}b|xlh cb= cfee`| ah {hq`% Wh wbnn cfnn|obs |oh cèshesxs cèlb|bè % S|f|hl j`qdfnnr. b| dhfes |of|

\ q6

φ6Y\ q1φ6)1T

4 = /3"

wohqh φ6 bs |oh s|f|bs|bcfn s|f|h |oh àshqzhq ofs |of| qh}qhshe|s obs bej`q$

df|bè fa`x| |oh srs|hd. φ6)1

bs |oh s|f|bs|bcfn s|f|h lhscqbabeg |oh wo`nhs|f|h `j |oh àshqzhq fel srs|hd fel \ q1 dhfes f |qfch `zhq |oh àshqzhqslhgqhhs `j jqhhl`d. wobnh \ q6 dhfes f |qfch `zhq |oh srs|hd‒s s|f|h s}fch%

<%< @|ohq cèsbs|hecr cèlb|b es

\ohqh fqh |w` `|ohq cèsbs|hecr cèlb|bès |of| b| bs ef|xqfn |` bd}`sh f||obs s|fgh% \oh stqs| bs |of| bj |oh sxqjfch bs c`d}`shl `j |w` lbscèehc|hl}fq|s. S 6 fel S 1. wh dxs| ofzh

OS 6∫S 1 4 OS 6 ⊗ S 1 /<"

fel. shcèlnr. qhzhqsfn `j `qbhe|f|bè bs fss`cbf|hl wb|o Ohqdb|bfe cèkxgf$|bè. s` |of|. bj S bs |oh sfdh sxqjfch. wb|o `qbhe|f|bè qhzhqshl.

O S 4 O†S /8"

\oh s|f|hs fss`cbf|hl wb|o „|oh àshqzhq— |ohe c`qqhs}èl |` nbehfq jxec$|bèfns `j |oh s|f|hs |of| c`qqhs}èl |` „|oh srs|hd—. wobco bs ef|xqfn gbzhe|of| |oh s|f|h s}fch bs f lhscqb}|bè `j |ohbq be|hqjfch%

F sbd}nh àkhc|bè dfr ah qfbshl |` |obs. wobco cèchqes |oh cfsh bewobco |oh fqhf `j |oh sxqjfch bs sdfnn c`d}fql |` |oh sb{h `j |oh wo`nh xeb$zhqsh% Be |obs cfsh |oh sxqjfch dfr cè|fbe f sdfnn àshqzhq n`ìbeg f| fnfqgh xebzhqsh. ax| dbgo| b| fns` e`| sxqq`xel f sdfnn srs|hd ahbeg s|xlbhlwb|o fnn |oh qhs`xqchs fzfbnfanh be f nfqgh xebzhqsh0 \oxs. be |oh nbdb| |of||oh sxqjfch soqbeis l`we. so`xnle‒| èh `j b|s fss`cbf|hl Obnahq| s}fchs gh|zhqr abg. wobnh |oh `|ohq ahc`dhs zhqr sdfnn0 \oh feswhq |` |obs bs |of|whqh |obs |` of}}he b| zb`nf|hs `xq ]qbecb}nh `j |oh bd}`ssbabnb|r `j fe be|hq$

}qh|f|bè `j f c`sd`n`gbcfn |oh`qr ar fe àshqzhq `x|sblh `j |oh xebzhqsh% Wh

6?



dxs| ihh} be dbel |of| |oh s|f|h s}fch fss`cbf|hl |` f a`xelfqr lhscqbahs

|oh bej`qdf|bè |of| fe àshqzhq è èh sblh dfr ie`w fa`x| |oh }fq| `j |oh w`qnl be |oh `|ohq sblh% Fs sxco. wohe |oh fqhf `j |oh sxqjfch lhcqhfshs.|oh lbdhesbè `j |oh fss`cbf|hl s|f|h s}fch dfr lhcqhfsh. qh}qhshe|beg hb$|ohq |oh nbdb|hl bej`qdf|bè cf}fcb|r `j |oh àshqzhq. be |oh cfsh |of| |oh„àshqzhq dfr ah shhe |` ah ahc`dbeg sdfnn— `q |oh lhcqhfsbeg exdahq `j lhgqhhs `j jqhhl`d `j |oh „srs|hd— be |oh cfsh |of| b| dfr ah ahc`dbegsdfnn%

O`whzhq. wobnh b| dfr ohn} |` |obei |obs wfr. wh so`xnl fns` qhdhdahq|of| |ohqh bs e` gxfqfe|hh |of| |oh z`nxdh be èh qhgbè `q |oh `|ohq bs fg``l }orsbcfn àshqzfanh be vxfe|xd gqfzb|r%

8 ]`s|xnf|hs `j }nxqfnbs|bc vxfe|xd c`sd`n`gr

Be |oh eh| shc|bè wh wbnn |xqe |` |oh df|ohdf|bcfn s|qxc|xqh wobco bsfzfbnfanh |` bd}nhdhe| |ohsh blhfs% J`q |oh }qhshe| wh dfr sxddfqb{h |ohqhsxn|s `j |oh qhfsèbeg x} |bnn |obs }`be| be f nbs| `j }`s|xnf|hs. |of| whw`xnl nbih f vxfe|xd |oh`qr `j c`sd`n`gr |` sf|bsjr%

6" Lhsteb|bè `j s|f|h s}fchs; F vxfe|xd c`sd`n`gbcfn |oh`qr fs$s`cbf|hs |` hzhqr `qbhe|hl |oqhh lbdhesbèfn sxqjfch ∊ 4 S × Q. wb|o S f c`d}fc| |w` sxqjfch wb|o`x| a`xelfqr. f Obnahq| s}fch OVG∊ . wobco bs f

qh}qhshe|f|bè `j fe fnghaqf `j `}hqf|`qs FVG∊ % \ohsh fssbgedhe|s `j Obnahq|s}fchs sf|bsjr |oh cèlb|bès /<" fel /8"% Jxq|ohqd`qh. j`q hzhqr cà`qlbsd

D. wobco bs f j`xq dfebj`nl wb|o a`xelfqbhs ∁ D 4 ∊ ∫ ∊‱ |ohqh bs f nbehfqdf}. DΣ ; OVG∊ ↑ OVG∊‱ %

1" Cèshesxs cèlb|bè; F }nxqfnbs|bc vxfe|xd s|f|h `j |oh xebzhqsh

bs fe fssbgedhe| `j f s|f|bs|bcfn s|f|h φS×Q be|` hfco OVGS×Q. sxakhc| |`|oh cèshesxs cèlb|bè . wobco be lbh`d`q}obsd bezfqbfe| nfegfxgh bs h$}qhsshl fs j`nn`ws% Nh| |oh sxqjfch S ah `j |oh j`qd `j |w` lbscèehc|hl}bhchs S 4 S B ∫ S BB % \ohe wh ie`w jq`d /<" |of|

OVGS×Q 4 OVGS B ×Q ⊗ OVGS BB ×Q% /:"

\oh cèshesxs cèlb|bè bs |ohe |oh qhvxbqhdhe| |of|

\ qB /Y\ qBB φB ∫BB T φB " 4 = /7"

\oh be|hq}qh|f|bès `j |ohsh àkhc|s fqh |oh j`nn`wbeg% J`q hzhqr ∊ whdfr cès|qxc| f j`xq lbdhesbèfn qhgbè `j s}fch|bdh W sxco |of| ∊ ⊁

62



∁

W % \oh qhgbè

W dfr cè|fbe fe àshqzhq. |`gh|ohq wb|o cn`cis fel

dhfsxqbeg bes|qxdhe|s |of| fqh fanh |` dhfsxqh |oh zfnxhs `j sthnls belxchlè ∊% \oh fnghaqf `j àshqzfanhs FVG∊ |ohe dxs| ofzh f cnfssbcfn nbdb|wobco c`qqhs}èls |` fe fnghaqf `j sthnls be f cnfssbcfn s}fch|bdh belxchl èf sxqjfch ∊ /shh <. ahn`w%" F s|f|h φS×Q |ohe c`qqhs}èls |` |oh bej`qdf|bè|of| fe àshqzhq be W dfr ofzh fa`x| |oh sthnls belxchl è ∊ 4 S × Q%\ohsh. |`gh|ohq wb|o ie`wnhlgh `j |oh cès|qfbe|s fel lrefdbcs. dfr |oheah xshl |` bejhq bej`qdf|bè fa`x| |oh zfnxhs `j sthnls be |oh qhgbè è „|oh`|ohq sblh `j ∊—%

J`q hfd}nh. bj S 4 S 1 × Q wo`sh be|hqb`q bs W 4 S 3 × Q. |ohe wh dfrsfr |of| fe àshqzhq wo` nbzhs be |oh „w`qnl$|xah— W bs fanh. ar dhfes `j dhfsxqhdhe|s `j sthnls è |oh a`xelfqr S 1

×Q. |` gfbe bej`qdf|bè fa`x|

|oh xebzhqsh h|hqefn |` |oh a`xelfqr% \obs bej`qdf|bè bs |ohe qhc`qlhl be|oh zfnxh `j f s|f|bs|bcfn s|f|h φS 1×Q%

3" E` be|hq}qh|f|bè be |hqds `j h|hqefn àshqzhqs; OVGS×Q ↑ C .|oh c`d}nh exdahqs. be |oh nbdb| |of| |oh |w` sxqjfch S soqbeis |` f }`be|%

<" Bec`q}q`qf|bè `j vxfe|xd gqfzb|r; F∊ dxs| ofzh f sxafnghaqfFS . wobco becnxlhs àshqzfanhs |of| dhfsxqh |oh s}fch|bdh dh|qbc gfa felnhj| ofelhl s}be cèehc|bè FFAF }xnnhl afci be|` |oh |w` sxqjfch S % /\ohshwbnn ah lhe`|hl oζα fel fFAζ qhs}hc|bzhnr%"

8" \oh Ahihes|hbe cèlb|bè; Nh| OS .o ah |oh sxas}fch `j OVGS×Qcè|fbebeg hbghes|f|hs `j |oh |w` dh|qbc è S wb|o hbghezfnxhs lhe`|hl aro% \ohe. bj F/o" bs |oh fqhf `j |oh |w` sxqjfch dh|qbc wh qhvxbqh.

lbd/OS .o" 4 hcF/o"/n1]n /?"

wohqh c bs f sthl lbdhesbènhss cès|fe|%Jbefnnr. wh qhvxbqh fe fb`d `j c`qqhs}èlhech wb|o nbehfqb{hl vxfe|xd

sthnl |oh`qr. wobco dfr ah j`qdxnf|hl fs j`nn`ws.:" C`qqhs}èlhech wb|o nbehfqb{hl VJ\; Nh| xs co``sh f c`sd`$

n`gbcfn cès|fe| Ι /wobco bs fssxdhl èh `j |oh }fqfd|hqs `j |oh |oh`qr".fe fqhf F= fel fe xn|qfzb`nh| cx|` q sxco |of|

n1] n >> q1 >> F= >> Ι∑6/1 /2"

\ohe. nh|Onbe

Ι.F.q.ǩah |oh Obnahq| s}fch `j nbehfqb{hl gqfzb|ès /fel `|ohq

dfssnhss sthnls. bj lhsbqhl" qhs|qbc|hl |` f qhgbè `j LhSb||hq s}fch|bdh wb|oc`sd`n`gbcfn cès|fe| Ι a`xelhl ar f |oqhh a`xelfqr S 1 × Q. wb|o |ohdh|qbc belxchl è |oh |w` s}ohqh ahbeg f |w` s}ohqh dh|qbc wb|o fqhf F ar|oh cèlb|bè |of| |oh nbehfqb{hl sthnls zfebso f| |oh a`xelfqr% Jxq|ohq. be

1=



|oh qhjhqhech jqfdh be wobco |oh a`xelfqr bs s|f|bc |w` cèlb|bès fqh }x|

è |oh s}hc|qxd% Jbqs|. |oh hehqgr `j |oh belbzblxfn gqfzb|ès fel `|ohqdfssnhss vxfe|f dxs| ah nhss |ofe |oh bezhqsh cx|` q∑6% Shcèl. |oh |`|fnhehqgr /lhstehl be |hqds `j |oh vxfsb$n`cfn sxqjfch be|hgqfn O 4

S 1 λ" dxs|

ah a`xelhl arH > ǩ

∛ F /6="

wb|o h}sbnè dxco nhss |ofe èh% Nh| FnbeΙ.F.q.ǩ ah fe fnghaqf `j àshqzfanhsfss`cbf|hl wb|o |obs s}fch%

\oh dhfebeg `j |obs s}fch fel fnghaqf bs |ohr lhsteh |oh nbehfqb{hlnbdb| `j fer vxfe|xd |oh`qr `j gqfzb|r wb|o sdfnn c`sd`n`gbcfn cès|fe|.qhs|qbc|hl |` |oh be|hqb`q `j f s|f|bc sxqjfch% \w` cx|`s fqh ehhlhl. èh |`nbdb| |oh hehqgr `j fer sbegnh gqfzb|è |` nhss |ofe |oh ]nfeci scfnh. |oh `|ohq|` nbdb| |oh |`|fn hehqgr |` ah dxco nhss |ofe |of| f| wobco gqfzb|f|bèfnabelbeg hehqgr. fel |oh c`nnf}sh |` f anfci o`nh. w`xnl ah qhnhzfe|%

J`q |oh vxfe|xd |oh`qr `j c`sd`n`gr |` ofzh fe fcch}|fanh nbehfqb{hlvxfe|xd sthnl |oh`qr nbdb| wh qhvxbqh |of| ohqh hbs|s f jfdbnr `j df}s.

E Ι.F.q.ǩ ; OnbeΙ.F.q.ǩ ↑ OVGS 1×Q /66"

E Ι.F.q.ǩ ; FnbeΙ.F.q.ǩ ↑ FVGS 1×Q /61"

sxco |of|

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31



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33



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FCIE@WNHLGHDHE\S

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38



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3:

http://arxiv.org/abs/gr-qc/9310006

http://arxiv.org/abs/hep-th/9409089


http://arxiv.org/abs/hep-ph/9410306

http://arxiv.org/abs/hep-ph/9410306






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37





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Y36T F% S|q`dbeghq. Dfssnhss anfci o`nhs fel cèbj`nls be s|qbeg |oh qr

}qh}qbeg oh}$|o28=<=2=9 A%Q% Gqhhe. L% Q% D`qqbsè fel F% S|q`$dbeghq. Anfci o`nh cèlhesf|b e fel |oh xebstcf|b e `j s|qbeg zfcxf

}qh}qbe| oh}$|o28=<6<89 I% Ahcihq. D% Ahcihq fel F% S|q`dbeghq.Jbzhaqfehs. Dhdaqfehs fel eè$}hq|xqaf|bzh s|qbeg |oh qr }qh}qbe|oh}$|o28=768?%

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Y31T \% Kfcàsè fel N% Sd`nbe. Excn% ]ors% A 122 /62??" 128$3<8%

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Y38T Q% A`qbss`z. C% Q zhnnb fel N% Sd nbe. Eè}hq|xqaf|bzh lrefdbcs `j

vxfe|xd ghehqfn qhnf|bzb|r }qh}qbe| be }qh}fqf|bè9

Y3:T N Sd nbe; be Lbqhc|bès be Ghehqfn Qhnf|bzb|r. z% 1. }f}hqs be oè`xq

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Y37T S% Dfk`q fel N% Sd nbe. Vxfe|xd s}be eh|w`qis be vxfe|xd gqfzb|r

}hq}qbe| be }qh}fqf|bè%

Y3?T D% Gqhhe. Scowfq|{ fel H% Wb||he S|qbeg \oh`qr /Cfdaqblgh Xebzhq$sb|r ]qhss"

Y32T L Gq`ss fel ]J Dhelh. ]ors Nh|| A627 /62?7" 612 9 Excn ]ors A3=3/62??" <=7

Y<=T K K F|bci H Wb||he. Excn ]ors A36= /62??" 126

Y<6T D If|`; ]ors Nh|| A1<8 /622=" <3% I Ièbsob G ]fx|b ] ]q zhq ;

]ors Nh|| A13< /622=" 17:% G Zheh{bfe`; Hxq`}ors Nh|| 1 /62?:"622%L Fdf|b D Cbfjfnèb G Zheh{bfe` ]ors% Nh||% A16: /62?2" <69 Q GxblfI Ièbsob ] ]q`zhq`; D`l ]ors Nh|| F: /6226"6<?7

Y<1T B Inhafe z N Sxssibel; Excn ]ors A3=2 /62??" 678

Y<3T \% Kfc asè. „\oh Hbes|hbe hvxf|b e `j s|f|h—. Dfqrnfel }qh}qbe|.6228%

Y<<T N K Gfqfr; „Vxfe|xd gqfzb|r fel dbebdxd nheg|o—. Bd}hqbfn C`nnhgh}qh}qbe|\]23$2<1=. gq$vc2<=3==? /622<"

Y<8T O% Hzhqh||. Qhz% D`l% ]ors% 12 /6287" <8<%

Y<:T A% LhWb|| fel Q%E% Gqfofd. hls% \oh Dfer W`qnls Be|hq}qh|f|bè `j

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Y<7T Q%A%Gqbffi|os. K% S|f|% ]ors% 3: /?<" 1629 J`xel% ]ors% 13 /23" 6:=6%

32





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|bè `j b|s ]qbecb}nhs /@}he C`xq|.Nèlè.6?23"

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s|hbe fel |oh Obs|`qr `j Ghehqfn Qhnfzb|r hl% ar L% O`wfql fel K%S|fcohn. Hbes|hbe S|xlbhs. Z`nxdh 6 /Abqiofxshq.A`s|è.62?2"%

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6839 Aqb|% K% ]obn% Scb% 33 /62?1" 1869 Fas nx|h `q Qhnf|bzh D`|bè0 FS|xlr jq`d |oh Dfcobfe ]`be| `j Zbhw `j |oh Lbsc`zhqr fel S|qxc|xqh

`j Lrefdbcfn \oh`qbhs /Cfdaqblgh Xebzhqsb|r ]qhss.Cfdaqblgh.62?2"%

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s|felbeg `j S}fch fel \bdh hl% B% @% S|fdf|hscx /Inh|| C`||f"9 \oh

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Y:?T \% Aqxhq. @e |oh bd}`ssbabnb|r `j shnj$dhfsxqhdhe|

Y:2T A% S% LhWb||. ]ors. Qhz. 6:= /62:7"%

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Y71T K% Ofq|nh. Fd% K% ]ors% 3: /62::" 7=<%

Y73T E% Aòq. Lbscxssbès wb|o Hbes|hbe è H}bs|hd`n gbcfn Vxhs|bès beSconb}} `}% cb|%%

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Y?:T K% Afh{. Cnfss% Vxfe|% Gqfz% 6= /6223" 6=6%

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<3

The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory - Lee...

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