Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

Embed Size (px)

Citation preview

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    1/21

    3

    ^croj Tkeb`k~

    V`k Ahb`keRtkbak| v`kh|km oe s{cev{m mkb`ceobr7C t`ojhrht`obcj bhmmkev

    @oi`joi`vr7 Ehe-bhmm{voei s{cevovokr cef `offke tc|cmkvk|r Yc~k-bh|t{rb{jc| f{cjorm cef `offketc|cmkvk|rJhbcj h| ehejhbcj `offke tc|cmkvk|r T`crk rtcbk oe s{cev{m mkb`ceobr Ykj* Yoiek|*cef Mhcj ^he Ek{mceer v`kh|km clh{v v`k clrkebk hn `offke tc|cmkvk|r oe s{cev{m mkb`ceobr cef

    @k|mcee Lkjjr hlgkbvohe S{cev{m-mkb`ceobcj cef mcv`kmcvobcj oebhmmkcr{|clojov Ahb`ke Rtkbak|r ofkc clh{v v`ko| ks{o~cjkebkV`k ehvohe hn tc|vocj cjikl|cKmlkffclojov hn c s{lov oevh c lov

    S{cev{m bhmt{vk| or ehv V{|oei mcb`oek Or bhevoe{cjov {eo~k|rcj8 Fonnkhmh|t`orm cef ~kjhbov Koervkoer ikek|cj t|oebotjk hn |kjcvo~ov Mcb`r t|oebotjkV`k Rahjkmoce |kjcvo~ov hn v`k forb|kvk cefv`k bhevoe{h{rV`k bh{evk|kpcmtjk oe >Clh{v v`k bjcrrobcj vc{vhjhi y`ob` or {ev|{k lkoei |ktjcbkfl v`k rvcvkmkevr clh{v bhmmkcr{|cljk s{cev{m-mkb`ceobcj s{cevovokr Jhiobcj `offke tc|cmkvk|r V`k {efkbofclojov hn v`k `thv`kror clh{v `offke tc|cmkvk|r Yoiek|r yh|acef Ykjr t|k~oh{r hek

    Jok i|h{tr* |kt|krkevcvoher* cef-n{ebvohe N|hm c s{cjovcvo~k vh c s{cevovcvo~k kpt|krrohe hn |kjcvo~ov-n{ebvohe* h| v`k forb|kvk l v`k |cefhm Lc|vjkvvr ctt|hcb` -n{ebvohe cr v`k b`c|cbvk|orvob n{eb-vohe hn |cefhm s{cevovForb|kvk cef( h| bhevoe{cj fkrb|otvoheS{cevov cef ovr foiovcjowkf t|hgkbvohe

    V`k ofkc hn~kjhbovt|hlclojov V`k ehvohe hn t|hlclojov cef v`k joi`v rtkkf thrv{jcvk Ikek|cjowkft|hlclojov cef ovr t`robcj oevk|t|kvcvoheC s{cev{m fkrb|otvohe hn mcb|h-yh|jf V`k tk|ohf hn v`k cr-rhbocvkf fk L|hijok yc~k cef v`k jkeiv` hn ehy Bc{rcjov ks{o~cjkevj |ktjcbkf l b`cebk V`k t`ojhrh-

    t` hn s{cev{m oenh|mcvohe cef |kjoiohe Koervkoer v`kror clh{v v`k bher{lrvcevocjov hn oek|voc cevykoi`vCicoe clh{v v`k oevk|t|kvcvohe hn bhmtjkp ~kjhbov V`k rtkkf hn vomk Ekyvher jcy hn oek|voccef Jci|ceikr nh|m{jcvohe hnmkb`ceobrNh|bk cef knnkbvV`k v`kh| hn vcb`her cef ikek|cj |kjcvo~ov

    \okrwr |kt|krkevcvohe v`kh|kmV`k ehvohe hn bh~c|ocev yh|jf joekBhfoei c yh|jf joek l -n{ebvoheRtcbkvomk cef s{lov -n{ebvohe l s{lovr Clh{v v`k t`robcj oevk|t|kvcvohe hn lhv` v`k bhmtjkp cpkrhn c s{lov V`k oevk|t|kvcvohe hn v`k rkjn-cfghoev htk|cvh|r bhmthekevr V`k yh|jf joek hn ce c|lov|c|s{cevov V`k oe~c|ocebk hn v`k t`robcj jcyr vhyc|fr s{cev{m hlgkbv cef cttc|cv{r @ojlk|v rtcbk cefv`cv hn Moeahyrao V`k |kjcvoher`ot lkvykke v`k bhknnobokevr hn-n{ebvohe cef v`k s{lovr Yh|jf joek =-n{ebvohe ! rkjn-cfghoev htk|cvh| \kcjov cef fkrb|otvohe Fhkr b{|~kf @ojlk|v rtcbk kporv8V`k cpohm hn b`hobk* h| y`ke or thrroljk c njcvvkeoei hn @ojlk|v rtcbk8

    -n{ebvohe

    -n{ebvohe L{v y`

    ehv vh njcvvke cjrh trk{fh-\okmceeoce rtcbk8 V`k bhmm{vcvh| hn bheg{icvk s{cevovokr \kjcvo~k mcrr V`k rv|hakr hn rkjn-mh~kmkev cef ovr t`ojhrht`obcj oevk|t|kvcvohe V`k rkjn-tk|nkbvohe hn v`k {eo~k|rk V`k ikek|cjowcvohe hn s{cevov oe s{cev{m t`robr Ce cecjhi hn v`k Nkemce nh|mcjormNkemce cefmce-yh|jf oevk|t|kvcvohe V`k -n{ebvohe hn ~c|oh{r hlgkbvr Bh{evcljk cef {ebh{evcljk lcror Ik-ek|cjowkf bhevoe{{m cef c|ov`mkvowcvohe Nokjf cef kevceijkmkev N{ebvohe cr bhfoei V`k ofkc hnb{|~kf Fkrbc|vkr t|hf{bv V`k ke~o|hemkev hn c n{ebvohe Cehv`k| ~oky vh v`k ehvohe hn ~kjhbov-

    t|hlclojov \kcjov cef fkrb|otvohe @ojlk|v rtcbk cr c mhfkj lhv` hn hlgkbv cef fkrb|otvohe V`k eh-vohe hn `hjorvob jhiob T`robcj s{cevov cr v`k oenh|mcvohe clh{v ov B|hrr-vkmth|cj bh||kjcvoher V`k nh|kbcrvoei hn n{v{|k Fkrb|otvohe oe rktc|cljk cef oerktc|cljk @ojlk|v rtcbk Nh|bkr h|mo|cbjkr ^kjhbov h| vomkV`k ehvohe hn ehe-noeovk rkvFcrkoe h| FcwkovV`k v|cgkbvh| hn v`k y`hjk

    Hevhjhiobcj cef hevh-v`khjhiobcj fonnk|kebk Ce cecjhi hn v`k Nkemce cef mce-yh|jf oevk|t|kvcvohe -n{ebvohe cr t`robcj s{cevov V`oeir oe v`k yh|jf cef oervcebkr oe vomkV`k ikek|cvohe hn v`k t`ro-bcj l mcv`kmcvobcj V`k ikek|cjowkf ehvohe hn hlrk|~k|R{lgkbvo~k h| hlgkbvo~k t|hlclojovKek|i crv`k b`ceik hn t|hlclojov tk| v`k {eovk hn vomk V`k ikek|cjowkf t|oebotjk hn jkcrv cbvohe n|hm c eky ~oky-

    thoevV`k kpbktvohe hn vyh fomkeroher cef Nk|mcvr jcrv v`kh|km

    Ak yh|fr7 Ahb`keRtkbak| v`kh|km* ikek|cjowkf |kjcvo~ov* @ojlk|v rtcbk* Moeahyrao rtcbk* yh|jf joekl -n{ebvohe* -n{ebvohe l s{lovr

    Cv no|rv ijcebk* v`k yh|a hn Ahb`ke cef Rtkbak| |kovk|cvkrykjj-aehye |kr{jvr7V`k mcoe com hn v`or tctk| or vh io~k c t|hhn hn v`k ehekporvkebk hn `offke

    ~c|ocljkr% V`or |ks{o|kr v`cv yk io~k cv jkcrv c t|kbork ekbkrrc| bhefovohe nh| v`ko|kporvkebk(Ahb`ke* Rtkbak| 3?>97 ;?/%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    2/21

    97 ;?->4/%

    Ek~k|v`kjkrr* cjv`h{i` lkoei bhmmker{|cljk cef bhmm{vcljk* v`k fh ehv cj-

    jhy `offke tc|cmkvk|r cr Ahb`ke cef Rtkbak| r`hykf* roebk v`k oefortkercljk bhefovohe

    nh| v`ko| t|krkebk or ehv n{jnojjkf7 kpcbvj v`k kmlkffclojov hn tc|vocj cjikl|c cbbh|foeivh vyh c{v`h|r bhebktv* l y`ob` v`k nh|mcjork bhmmker{|cljk s{cevovokr hn s{cev{m-

    mkb`ceobcj s{cevovokr oe bhmm{vcvo~k cjikl|c% \krtkbvo~kj v`k rvcvkmkevr he r{b` s{ce-

    vovokr rh-bcjjkf tc|vocjLhhjkce cjikl|c or ehv kmlkffcljk oe Lhhjkce cjikl|c* h| oe

    hv`k| yh|fr* mh|k bhevkmth|c|oj rcof* heks{lov or ehv kmlkffcljk oe hek lov* s{cev{m

    bhmt{vk| or ehv V{|oei mcb`oek%

    C ekbkrrc| bhefovohe v`ke nh| v`k kporvkebk hn `offke ~c|ocljkr or v`cv v`or

    tc|vocj cjikl|c lk omlkffcljk oe c bhmm{vcvo~k cjikl|c (r{b` cr v`k cjikl|c hn cjj |kcj-

    ~cj{kf n{ebvoher he c t`crk rtcbk/ (Ahb`ke* Rtkbak| 3?>97 >4/%

    V`ke

    ov or r`hye v`cv v`k|k kporvr c noeovk tc|vocj cjikl|c hn s{cev{m mkb`ceobcj hlrk|~cljkr

    nh| y`ob` eh r{b` omlkffoei kporvr% V`k t`robcj fkrb|otvohe hn v`or |kr{jv mc lk

    {efk|rvhhf oe ce oev{ovo~k ncr`ohe s{ovk oefktkefkevj hn v`k nh|mcj mcb`oek|

    oev|hf{bkf(Ahb`ke* Rtkbak| 3?>97 >4/%

    Rh ov bhmkr ecv{|cj vh cra `hy bce lk kptjcoekf v`k fonnk|kev lk`c~oh{| hn

    t`robcj s{cevovokr oe bjcrrobcj cef oe s{cev{m mkb`ceobr v`k fkvk|moeorm hn v`k nh|mk|cef v`k oefkvk|moeorm hn v`k jcvvk| on v`k fkmc|bcvohe7 bhmm{vclojov ehe-

    bhmm{vclojov mcakr eh cj|kcf rkerk% Hl~oh{rj v`k hej fonnk|kebk jknv or v`k bhevoe{cjo-

    v hn v`k s{cevovokr oe bjcrrobcj t`robr cef v`ko| forb|kvk b`c|cbvk| cr c |{jk oe s{cev{m

    mkb`ceobr* h| oe hv`k| yh|fr v`k ~cjofov hn ovr nokjf hn v`k t|oebotjk hn s{cev{m-

    mkb`ceobcj f{cjorm% V`k |kcj t|kmork nh| v`k clrkebk hn `offke tc|cmkvk|r bh{jf lk nh|-

    m{jcvkf cr oe~cjofov hnKoervkoer t|oebotjk hn |kjcvo~ov (Koervkoe 3?307

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    5/21

    ;

    Rahjkmoce |kjcvo~k* oebj{foei v`k mceek| hn v`ko| kpthrovohe oe Ahb`ke cef Rtkbak|r c|-

    vobjk% Cnvk| t|h~oei v`ko| ncmh{r v`kh|km cef ovr omtjobcvoher* v`k ic~k c bh{evk|-

    kpcmtjk oev|hf{boei `offke tc|cmkvk|r jomovoei v`ko| bherofk|cvohe vh vyh-fomkerohecj

    @ojlk|v rtcbk cef c mhfkj hn c roeijk kjkbv|he rtoe kmt`crowoei v`cv ov or bhmtjkvkj c|vono-

    bocj cef k~ke oe~cjof oe v`k bcrk hn vyh kjkbv|her oe c thvkevocj nokjf cbbh|foei vh v`ko|

    yh|fr% @hyk~k|* v`ko| oevkevohe ycr v`{r vh r`hy v`cv ~he Ek{mceer v`kh|km |ks{o|kr oev`cv bcrk v`k clrkebk hn `offke tc|cmkvk|r* y`ojk v`ko| hye bherofk|cvohe yh{jf fkmhe-

    rv|cvk v`k thrrolojov hn lkoei oev|hf{bkf%

    Oe v{|e* yk mc kcroj r`hy v`cv v`or bh{evk|-kpcmtjk or orhmh|t`ob vh c s{lov*

    roebk ov |kt|krkevr c rt`k|k oe v`|kk-fomkerohecj K{bjofkce rtcbk* cef lkbc{rk hn

    v`k s{lov cffovo~ov ov bce lk v|cernk||kf cef bherhjofcvkf nh| v`k y`hjk @ojlk|v rtcbk%

    Oe hv`k| yh|fr* v`or or c bh{evk|-kpcmtjk cjrh vhyc|fr v`k ~k| mcoe v`kh|km hn v`ko|r

    cef or oe fo|kbv bhev|cfobvohe vh v`k ommkfocvk bh|hjjc|% V`cv or y` v`k v`kh|km r`h{jf

    hlvcoe v`k rvcv{vk hn hek mh|k bjcom {erhj~cljk oe s{cev{m mkb`ceobr v`k hek rofk hn c

    bhmtjkmkevc|* f{cj |kjcvohe y`hrk hv`k| rofk or t|kborkj ovr ekicvohe% V`k vhikv`k|fkmherv|cvk v`k rcmk r{iikrvoei v`cv ov or hej hek rtkbocj bcrk1 he v`k lcror hn Rahjk-

    moce vtk |kjcvo~ov yk bce vcja clh{v c rtkbocj aoef hn s{cev{m f{cjorm7 clrkebk t|kr-

    kebk hn `offke tc|cmkvk|r% L{v `hy v`ke r`h{jf yk oevk|t|kv `offke tc|cmkvk|8 Cbbh|f-

    oei vh v`k ojj{rv|cvohe v`cv Ahb`ke cef Rtkbak| `c~k io~ke* v`or or c |cefhm throvohe he c

    forb* o%k% hn c jc|ik bo|bjk hn v`k rt`k|k% Oe v`k ikek|cj bcrk hn h|fk|kf r{m hn s{lovr |kt-

    |krkevoei @ojlk|v rtcbk* v`k `offke tc|cmkvk| yojj lk v`k ceijk nh|mkf n|hm v`k ,cpkr, hn

    @ojlk|v rtcbk* y`ob` |kt|krkev ce oenoeovk e{mlk| hn kmlkffkf oevh hek cehv`k| fkb|kcr-

    oei hrbojjcvh|r% V`cv ceijk mc lk oevk|t|kvkf cr ce oeovocjmhmkev oe vomk7 nh| kpcmtjk*on yk `c~k b`hrke c wk|h thoev hn vomk nh| cjj hrbojjcvh|r* v`ke @ojlk|v rtcbk cr ce h|fk|kfrkv hn s{lovr yojj lk fortjckf oe c romtjk cef fkvk|moekf mceek| l v`k `offke tc|cmk-

    vk|r cr ce oenoeovk rv|ot% V`cv or cjrh c |krtkbvo~kjh|fk|kf rkv hn wk|hr cef hekr cbbh|foeivh v`k nhjjhyoei (ehv hej thrroljk/ |{jk7 * on v`k `offke tc|cmkvk| fkvk|moekr c tcrvmhmkev oe vomk bh||krthefoei vh v`k b`hrke wk|h lkeb`mc|a* cef * on ov fkvk|moekr t|k-rkev h| n{v{|k mhmkev% Cjhei yov` v`or* b{|~kf@ojlk|v rtcbk bce lk bhmtc|kf oe c rom-

    tjk mceek| yov` trk{fh-\okmceeoce rtcbk cef v`{r lk rh oevk|t|kvkf% V`k|knh|k v`k tc-

    |cmkvk| bce lk bherv|{kf cr i|c~ov% V`krk vyh oevk|t|kvcvoher hn v`k `offke tc|cmkvk|

    vomk cef i|c~ovcvohecj cicoe t|h~kf vh lk f{cj* y`ob` v{|er h{v vh lk c eh|mcj kptkbvc-

    vohe oe s{cev{m mkb`ceobr%

    Cv v`k kef hnv`ko| c|vobjk* oe v`k jcrv 9 lhv` c{v`h|r r{iikrv v`cv v`ko| bhe-

    rofk|cvohe mc lk jhiobcjj fkmherv|cvkf cr v`k omthrrolojov vh lk kmlkffkf (|krt% ykca

    kmlkffoei `hmhmh|t`orm/ v`k tc|vocj Lhhjkce cjikl|c hn s{cev{m-mkb`ceobcj hlrk|~-

    cljkr oe Lhhjkce cjikl|c%

    Ov or t|h~kf v`k|k v`cv v`k omlkffoei t|hljkm yk bherofk|kf kc|jok| or

    ks{o~cjkev vh v`k s{krvohe hn y`kv`k| v`k jhiob hn s{cev{m mkb`ceobr or krrkevocjj v`k

    rcmk cr bjcrrobcj jhiob(Ahb`ke* Rtkbak| 3?>97 >4/%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    6/21

    >

    V`kebk v`k fkf{bk v`cv v`k|k or c bjcrrobcj vc{vhjhi * y`ob` or ncjrk k~ke oemkceoein{j r{lrvov{vohe* o%k% v`k r{lrvov{vohe yov` rvcvkmkevr bhebk|eoei bhmmker{|cljk

    s{cev{m-mkb`ceobcj ~c|ocljkr7

    \h{i`j rtkcaoei c t|hthrovohecj nh|m{jc or ~cjof oe s{cev{m

    mkb`ceobr on nh| k~k| ,mkceoein{j, r{lrvov{vohe hn s{cev{m mkb`ceobcj t|hthrovohernh| v`k ~c|ocljkrv`or nh|m{jc or v|{k* y`k|k c mkceoein{j r{lrvov{vohe or hek r{b` v`cvv`k t|hthrovoher * c|k hej bheghoekf l v`k jhiobcj bheekbvo~kr oe onv`k c|k rom{jvcekh{rj mkcr{|cljk% Ov v`ke nhjjhyr n|hm h{| |kr{jvr v`cv v`k|k or c

    nh|m{jc y`ob` or c bjcrrobcj vc{vhjhi l{v or ncjrk nh| rhmk mkceoein{jr{lrvov{vohe hn s{cev{m mkb`ceobcj t|hthrovoher% Oe v`or rkerk v`k jhiob hn s{cev{m

    mkb`ceobr fonnk|r n|hm bjcrrobcj jhiob(Ahb`ke* Rtkbak| 3?>97 >4/%

    Cef v`k ommkfocvkj io~k c romtjk kpcmtjk hn r{b` c vc{vhjhi% Cbbh|foei vh

    h{| t|oebotjk throvohe yk yojj tc cvvkevohe hebk cicoe vh v`k cjjkikf |kjcvo~ov hn v`orrvcvkmkev* o%k% n|hm y`cv aoef hn f{cj* bhmtjkmkevc|* l{v cjrh s{ovk jkiovomcvk throvohe

    v`k htthrovk or v|{k7 v`k ehe-kporvkebk hn r{b` c bjcrrobcj vc{vhjhi h| eh r{lrvov{vohe hn

    v`k s{cev{m mkb`ceobcj hlrk|~cljkr* y`ob` mcakr v`cv bjcrrobcj vc{vhjhi ncjrk%

    Nh| v`or t{|thrk v`k bhebktv hn `offke tc|cmkvk| r`h{jf lk v|cernk||kf vh

    t|htk|j jhiobcj bherofk|cvohe% V`cv yh{jf lk v`k t|krkebk hn c `offke {erhj~cljk rvcvk-

    mkev* oe hv`k| yh|fr* c `offke cpohm% V`{r y`kv`k| ov h| ovr ekicvohe or cbbktvkf yojj fk-

    vk|moek y`kv`k| v`k bhebk|ekf rvcvkmkev he s{cev{m mkb`ceobcj hlrk|~cljk or v|{k h|

    ncjrk% Kmlkfclojov (ykca kmlkfmkev* `hmhmh|t`orm/ or v`k ekbkrrc| bhefovohe nh| v`k

    kporvkebk hn r{b` c jhiobcj `offke tc|cmkvk|% \krtkbvo~kj v`k clrkebk hn r{b` kmlkfcloj-ov ker{|kr ovr ehe-kporvkebk% V`ke h{| t|hthrovohecj nh|m{jc y`ob` or c bjcrrobcj vc{vhj-hi yojj cttkc| vh lk v|{k cjrh oe r{lrvov{vohe nh| bhmmker{|cljk s{cev{m-mkb`ceobcj

    hlrk|-~cljkr% V`k|knh|k* v`k ~k| nh|m{jc or n|hm v`k fkro|kf vtk hn {erhj~cljk rvcvk-mkev h| c jhiobcjj `offke tc|cmkvk|% Oe v`or bcrk ce t|hthrovohecj nh|m{jc v`cv or v|{k oe

    c bjcrrobcj rkerk cef ncjrk oe c s{cev{m-mkb`ceobcj r{lrvov{vohe* cr rvcvkf clh~k* or r{b`

    c jhiobcjj `offke tc|cmkvk|* ce {erhj~cljk rvcvkmkev%

    V`k|k kmk|ikr c bhmmhe cef n{efcmkevcj `offke tc|cmkvk| hn r{b` jhiobcj

    vtk* ce {erhj~cljk rvcvkmkev7 y`kv`k| |cefhmj io~ke nh|m{jc yojj lk bherofk|kf crbjcrrobcj h| cr s{cev{m-mkb`ceobcj% V`cv bceehv r{|t|ork {r cv cjj* cr ov or l{ojv oe v`k ~k|nh{efcvohe* oe v`k rv|{bv{|k cef mcv`kmcvobcj nh|mcjorm hn s{cev{m mkb`ceobr cr c v`kh-

    | clh{v v`k rrvkm hn c bjcrrobcj fk~obk cef c s{cev{m hlgkbv% Cbbh|foeij* r{b` oerhj{-

    ljk* f{cjj v|{k t|hthrovoher clh{v v`k rrvkm bce lk rhj~kf y`ke |knk||kf kov`k| hej vh

    v`k cttc|cv{r* h| hej vh v`k mob|h-hlgkbv%L{v v`k ~k| rkbhef |knk|kebk bhevcoer ce kjk-mkev hn oerhj{lojov cef or `thv`kvobcj cr c v`kh| hn v`k mob|h-hlgkbv l ovrkjn fhkr ehv

    rkkm thrroljk%

    Yov` c romojc| |krk|~cvohe |kf{boei v`k mk|k rvcvkmkev clh{v v`k kporvkebk hn

    `offke tc|cmkvk|r vh oerhj{lojov* `hyk~k|* v`k htthrovohe h| v`k f{cjorm lkvykke fk~obk

    cef s{cev{m hlgkbv mc lk crr{mkf cef v`k|knh|k oevk|t|kvkf oe ce rtkbocj bcrk cr c{eo~k|rcj `offke tc|cmkvk| oe v`k jhiobcj rkerk%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    7/21

    9

    Noecjj* v`k rcmk rov{cvohe bce lk fkmherv|cvkf l v`k bh{evk|-kpcmtjk io~ke

    l v`km* oe y`ob` c rt`k|k cr c s{lov yojj lk bhmtc|kf vh v`k t|hthrovohecj nh|m{jc hns{cev{m-mkb`ceobcj hlrk|~cljkr cef c {r{cj lov* o%k% c loec| {eov* vh v`k v|{k ~cj{k hn

    v`k t|hthrovohecj nh|m{jc bjcrrobcjj oevk|t|kvkf%V`k bhebj{rohe hn Ahb`ke cef Rtkbak| oefobcvkf v`k roieonobcebk hn v`ko| yh|a

    vh v`k h~k|cjj fk~kjhtmkev hn v`h{i`v oe s{cev{m mkb`ceobr* y`ob` yk `c~k cj|kcf v|okfvh rakvb` l|oknj7

    V`or yc hn ~okyoei v`k |kr{jvr hn Rkbvoher 2 cef 6* rkkmr vh {r vh fortjc c

    eky nkcv{|k hn s{cev{m mkb`ceobr oe ovr fktc|v{|k n|hm bjcrrobcj mkb`ceobr% Ov or hn

    bh{|rk v|{k v`cv v`k [ebk|vcoev T|oebotjk* rc* cj|kcf mc|ar c fktc|v{|k n|hm bjcrrobcj

    t`robr% @hyk~k|* v`k rvcvkmkev hn v`k [ebk|vcoev T|oebotjk oe~hj~kr vyh hlrk|~cljkr

    y`ob` c|k ehv bhmmkcr{|cljk* cef rh mc lk |kn{vkf oe v`k n{v{|k yov` v`k cffovohe hn

    eky rvcvkr% V`or or v`k ~oky hn v`hrk y`h lkjok~k oe `offke ~c|ocljkr% V`{r* v`k

    [ebk|vcoej T|oebotjk cr cttjokf vh v`k vyh-fomkerohecj rov{cvohe fkrb|olkf oe Rkbvohe >lkbhmkr oecttjobcljk hebk v`k rrvkm or omlkffkf oe v`k bjcrrobcj hek% V`k

    rvcvkmkev * yk `c~k bherv|{bvkf fkcjr hej oe kcb` hn v`k rvktr hn ovrbherv|{bvohe yov` bhmmkcr{|cljk hlrk|~cljkr* cef rh bceehv lk |kn{vkf cv c jcvk| fcvk

    (Ahb`ke* Rtkbak| 3?>97 0>/%

    Jkv {r rvc|v h{| fkvcojkf forb{rrohe hn v`k yh|a hn Ahb`ke cef Rtkbak| n|hm

    v`k thrrolojov* v`k fonnob{jvokr cef v`k ycr vh {rk v`k t`crk rtcbk hn bjcrrobcj mkb`ceobr

    cef v`k|mhfecmobr roebk ov cbvr cr c l|ofik lkvykke v`k rvcvorvobcj oevk|t|kvcvoher hn

    v`k jcvvk| l v`k nh|mk|* cef v`{r rkvr c r{bbkrrn{j kpcmtjk nh| v`k oev|hf{bvohe hn ,`of-fke tc|cmkvk|r,% V`k|knh|k* ce bheno|mcvohehn r{b` omthrrolojov m{rv bjc|on t|kborkjy`cv kpcbvj or v`k fonnk|kebk lkvykke bjcrrobcj cef s{cev{m mkb`ceobr* y`ob` fkvk|r{rn|hm nhjjhyoei v`or mkv`hf% Yk cjrh `c~k v`k mcgh| yh|ar hn Ykj (3?

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    8/21

    0

    V`k mcoe ofkc hn v`k v`kh| hn |kt|krkevcvoher v`k ofkevonobcvohe {efk| bk|-

    vcoe bhefovoher* ecmkj v`k c~cojclojov hn |kt|krkevcvohe oe ikek|cj* hn v`k i|h{tr cef hn

    (v`k v|cernh|mcvoher hn/ @ojlk|v rtcbk yojj cjjhy {r vh mcak c fkboro~k rvkt nh|yc|f oe

    rv{foei v`k |kjcvo~ov hn v`k bhevoe{h{r cef forb|kvk oe c mcv`kmcvobcj cef oe c t`robcj*

    cef oe c t`ojhrht`obcj rkerk cr ykjj% On v`k i|h{t or ehv hej bhevoe{h{r l{v cjrh rmhhv`*

    o%k% fonnk|kevocljk* r{b` cr Jok i|h{tr c|k* yk bh{jf ks{cvk ov* cv jkcrv mcv`kmcvobcjj* lovr t|krkevcvoher* vh @ojlk|v rtcbk hn -n{ebvoher* o%k% hn s{cev{m* v`k|knh|k forb|kvkrvcvkr% On v`k ~k| Jok i|h{t kmlhfokr Koervkoe r t|oebotjk hn ikek|cj bh~c|ocebk (|kjcvo~o-

    v/* yk r`h{jf bjc|on `hy kpcbvj (h| ecmkj/ -n{ebvohe t|krkevr c s{cev{m* forb|kvkrvcvk% Ov yojj `kjt {r vh mh~k nh|yc|f n|hm c mk|kj s{cjovcvo~k|kjcvo~ov hn bhevoe{ov cef

    forb|kvkekrr vh c s{cevovcvo~k(oe c l|hcf rkerk* l mcv`kmcvobcj rv|{bv{|kr/ fkrb|otvohe

    hn v`ko| {eov cef v`k v|cerovohe lkvykke v`km%

    -n{ebvohe t|krkevr v`k forb|kvk l v`k |cefhm cr nhjjhyr% Ov or cjycr c n{eb-vohe hn c|i{mkevr bherorvoei hn kpcbvj `cjn v`k tc|cmkvk|r oe v`k bhenoi{|cvohe rtcbk

    v`ce oe v`k bjcrrobcj bcrk cef v`hrk tc|cmkvk|r mc lk bherofk|kf cr bhevoe{h{r hekr%V`k hv`k| `cjn cbbh|foei vh @korkelk|ir {ebk|vcoev t|h~kf vh lk bhmtjkvkj ~ci{k*

    |cefhm* cef forb|kvk% Roebk v`k|k or c s{cev{m jkct* forb|kvkekrr* v`cv rkbhef `cjn hn

    v`k tc|cmkvk|r cttkc|r vh lk c rkv hn |cefhm ~c|ocljkr* y`ob` mc vcak hek h| cehv`k|

    ~cj{k yov` fonnk|kev t|hlclojov%

    V`ke yk yojj oevk|t|kv -n{ebvohe* oe v`k rto|ov hn Lc|vjkvv (3?6;/)r ctt|hcb`* crv`k b`c|cbvk|orvob n{ebvohe hn v`k forb|kvk cef v`k|knh|k |cefhm bhh|foecvkr oe bhenoi{|c-

    vohe rtcbk% V`k hv`k| `cjn hn bhh|foecvkr oe bhenoi{|cvohe rtcbk romtj fh ehv ekkf c fk-

    rb|otvohe l - n{ebvohe* roebk lkoei bhevoe{h{r* v`k c|k ehv |cefhm%

    N|hm v`or thoev hn ~oky ,v`k t|hljkm hn `offke tc|cmkvk|r, cttkc|r vh lk c |k-r{jv hn mor{efk|rvcefoei7 -n{ebvohe fhkr ehv r{mmc|owk* l{v hej bhmtjkmkevrv`k bhevoe{cj fkrb|otvohe hn bjcrrobcj t`robr yov` ovr forb|kvk ,mcvk,* y`k|k v`k forb|kvk or

    |kt|krkevkf l v`k cbbofkevcj% V`k hv`k| ,`cjn,* o%k% v`k bhevoe{cj fkrb|otvohe ovrkjn or io~ke

    l v`k oek~ovcljk oe s{cev{m mkb`ceobr t|krkebk hn bjcrrobcj fk~obk% @kebk v`k om-

    th|vcebk hn v`k v`kh| hn |kt|krkevcvoher nh| v`k oevk|t|kvcvohe h| b|kcvoei v`k hevhjhi hn

    s{cev{m mkb`ceobr7 ov t|h~ofkr v`k thrrolojov* {eov cef s{cevovcvo~k ks{o~cjkebk hn v`k

    forb|kvk fkrb|otvohe hn s{cev{m t`kehmkec oe vk|mr hn mob|h-hlgkbv cef v`ko| bhevoe{cj

    fkrb|otvohe oe vk|mr hn fk~obk%

    Oe r{b` ,v|cerjcvoher, lkvykke lhv` jcei{cikr* yk r`h{jf tc rtkbocj cvvkevohe vh

    v`k bher{lrvcevocjov cef v`k ks{o~cjkev v|cernh|mcvohe hn v`k rtkkf n|hm c rmhhv` fk-

    rb|otvohe (o%k% ehv hej mcv`kmcvobcjj bhevoe{cj l{v cjrh fonnk|kevocljk/ oe v`k t|hlclojov

    n|hm c forb|kvk fkrb|otvohe% V`k|k bhmkr v`k bhebj{rohe v`cv Jh|kevw oe~c|ocebk (cef |k-

    rtkbvo~kj v`k thrv{jcvk hn eh kpbkkfoei v`k rtkkf hn joi`v oe n|kk rtcbk/ or c fo|kbv |kr{jv

    hn c t|oebotjk cj|kcf oe~hj~kf oe v`k t|k~oh{r rkevkebk* y`ob` or ~cjof nh| v`k omthrkf

    ikek|cjorcvohe hn Koervkoer |kjcvo~ov t|oebotjk cjrh nh| forb|kvk mhvoher7 cr i|c~ov cef oe-

    k|voc c|k v|kcvkf ks{cjj oe ikek|cj |kjcvo~ov* cr ~kjhbov cef t|hlclojov r`h{jf bhoebofk cr

    vh v`k rakvb`kf mh|k ikek|cj ~oky% @hyk~k|* v`or yh{jf lk thrroljk hej on v`k|k or c n{e-

    fcmkevcj bhervcev hn mcpomcj ~kjhbov* oe |kjcvohe vh y`ob` ce ~kjhbov or bhe~k|vkf vh c

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    9/21

    ?

    fomkerohejkrr e{mlk| v`cv nh| cjj jkrr h| ks{cj vh v`k mcpomcj ~kjhbov or |krtkbvo~kj jkrr

    v`ce h| ks{cj vh hek cef bce v`k|knh|k lk oevk|t|kvkf cr c rvcefc|f t|hlclojov%

    On `hyk~k|* {roei Lc|vjkvvr ctt|hcb`* yk `c~k oev|hf{bkf ekicvo~k t|hlclojovokr

    (cef `kebk v`hrk y`ob` c|k i|kcvk| v`ce hek/* v`ke v`k r`h{jf lk forb{rrkf cjrh rtkkfr

    kpbkkfoei v`cv hn joi`v cbbh|foei vh c t|oebotjk hn ks{o~cjkebk hn ~kjhbov cef t|hlclojov%

    Bhe~k|rkj* v`k kmk|ioei n|hm v`k mcv`kmcvobcj nh|mcjorm hn rtkbocj |kjcvo~ov bhmtjkprtkkf h| hv`k| aoekmcvob t`robcj s{cevovokr ikvvoei bhmtjkp ~cj{kr c|k ommkfocvkj oevk|-

    t|kvkf cr v`k kptjcoekf clh~k bhmtjkp t|hlclojovokr h| v`k t`robcj s{cevovokr hn kevceijkf

    rrvkmr rv{fokf l s{cev{m oenh|mcvohe7 V`k vcb`her v`kh| fk~kjhtkf oe v`k rkbhef

    `cjn hn jcrv bkev{| bh{jf lk ofkevonokf yov` s{cev{m oenh|mcvohe h| mh|k kpcbvj* yov` ovr

    v|cerjcvohe oevh v`k fonnkhmh|t`orm jcei{cik hn bjcrrobcj t`robr% Rh Yoiek| n{ebvohe

    (Yoiek| 3?2

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    10/21

    34

    v`km* vhh% Bjkc|j* v`k v`kh| hn |kt|krkevcvoher* hnnk|oei c mcv`kmcvobcj jcei{cik vh

    ofkevon cef kptjcoe v`k orhmh|t`orm hn thvkevocj (i|c~ovcvohecj/ cef s{cev{m |cefhm-

    ekrr* cjhei yov` v`cv* i{ofkr {r vh v`ko| k~kev{cj bher{lrvcevocjov% On s{cev{m mkb`ceobr

    l -n{ebvohe r`c|kr ce ks{o~cjkev forb|kvk fkrb|otvohe hn ce thvkevocj nokjf* cef ikek|cj|kjcvo~ov `cr cj|kcf kecbvkf v`k oeforvoei{or`clojov hn c|lov|c| thvkevocj cef i|c~ovcvohecj

    nokjf* yk `c~k eh mh|k b`hobk kpbktv bhebj{foei v`cv -n{ebvohe r`h{jf lk ce ks{o~cjkev*l{v forb|kvk fkrb|otvohe hn i|c~ovcvohecj nokjf7 Nh| kpcmtjk* v`ke v`k fkrb|otvoher hn v`k

    {eo~k|rk l ovr -n{ebvohe h| l mkv|obcj vkerh| oe ce thoev hn rtcbk-vomk c|k cv jkcrvorhmh|t`ob* cef nhjjhyoei ce Koervkoeoce aoef hn Tv`cih|kce hevhjhi (

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    11/21

    33

    Ov or {rkn{j vh kmt`crowk c |kjcvoher`ot yov` v`k |kt|krkevcvohe v`kh|km (\okrw

    3?49/ vh v| vh bjc|on `hy v k cj|kcf rakvb`kf ofkevonobcvohe hn I\ yov` v`k r{tk|j{moecj

    kpvkerohe hn R\ (v`k v`kh| hn vcb`her/* no|rv* or kcr vh lk v|cernk||kf cr orhmh|t`orm

    lkvykke trk{fh-\okmceeoce cef Moeahyrao rtcbk* cef rkbhefj* icoer rhmk |kf{efceb

    hn v`k v`h{i`v hn b{|~kf@ojlk|v rtcbk* roebk v`cv orhmh|t`orm bce lk bhef{bvkf* ecmk-

    j l v`k \okrw v`kh|km* cjrh lkvykke {r{cj rvcefc|f cef cjjkikf b{|~kf @ojlk|v rtcbk%R{nnobk ov vh oev|hf{bk v`k bhebktv hn bh~c|ocev yh|jf joek mcvb`oei v`k {r{cj

    bhev|c~c|ocev hek on cef hej on v`k b{|~cv{|k hn trk{fh-\okmceeoce rtcbk oe ce thoev hn

    v`k yh|jf joek or wk|h% Hl~oh{rj* v`k bhefovohe or mkv nh| kcb` yh|jf joek oe Moeahyrao

    rtcbk%

    On h{ oev|hf{bk c mh|k ecv{|cj cef |kcrhecljk* cef hek bce rc* cef v|cfo-

    vohecj t|oebotjk hn oe~c|ocebk hn t`robcj jcyr oe v`k v|cerovohe n|hm s{cev{m mob|h-hlgkbv

    vh mkcr{|oei oerv|{mkev (oe tc|vob{jc|* ov omtjokr v`k mkic-oevk|t|kvcvohe hn s{cev{m mk-

    b`ceobr/* y`ob` krvcljor`kr v`k ks{o~cjkebk hn ce {r{cj bhevoe{cj cef c eky* forb|kvk

    fkrb|otvohe hn v`k r{||h{efoei mcb|h-t`robcj |kcjov oe |kjcvohe vh mkic* o%k% {eo~k|rk hl-gkbvr% V`k |kr{jvoei bhmmhe mob|h cef mkic-oevk|t|kvcvohe or bcjjkf |kjcvo~k oevk|t|kvcvohe

    (

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    12/21

    3

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    15/21

    3;

    tc|vr hn ovr% Oe c ikek|cjowkf rkerk* v`k v|cgkbvh| hn c tc|v bce lk fkvk|moekf l ce cecj-

    hih{r vh v`k t|oebotjk hn jkcrv cbvohe* cbbh|foei vh y`ob` v`k v|cgkbvh| or cbbhmtjor`kf

    v`|h{i` v`k rmcjjkrv* oe tc|vob{jc| wk|h hevhjhiobcj fonnk|kebk% V`k tcv`yc hn jkcrv h| eh

    hevhjhiobcj fonnk|kebk mc lk oefobcvkf* {roei v`k vk|mr hn B`oekrk t`ojhrht`* y`ob`

    `c~k lkke kev|cevr cnvk| Lh`| oe v`cv hn s{cev{m mkb`ceobr* r{b` cr Vch* cef r{lgkbvo~k

    cef hlgkbvo~k t|hlclojov* h| r{lgkbvo~k cef hlgkbvo~k vomk* bh||kjcvk v`k bh{tjk hn _ceicef _oe;%

    Y`ke yk ikek|cjowk v`k bhebktv hn v|cgkbvh| n|hm v`|kk-fomkerohecj vh

    @ojlk|v rtcbk* yk |ktjcbk thoev (ce kjkmkev hn c n{ebvohe/ yov` n{ebvohe% V`k bhebktv hn

    bhevoe{h{r v|cgkbvh| m{rv v`k|knh|k lk |k~okykf% Oe h{| kpcmoecvohe l mkcer hn

    s{lovr* bhevoe{h{r v|cgkbvh| |knk|r vh cjj hn v`km cef v`{r or jomovkf vh v`k bhevoe{h{r

    tcv` hn thoevr%N{|v`k|mh|k* v`k b`ceik hn t|hlclojov tk| vomk {eov or fo|kbvj oevk|t|kvkf

    l v`k s{cev{m hn cbvohe* o%k% nh| v`k ~cj{kr rmcjjk| v`ce ov% Yk `c~k vh tc rtkbocj cvvke-

    vohe vh v`k vkpv oe ovcjobr* lkbc{rk* l v`k crr{mkf cef oevk|t|kvkf |kjcvoher`ot lkvykke

    kek|i cef t|hlclojov* yk bce v|cernh|m r{l-s{cev{m oevh r{tk|-s{cev{m |kcjov oebj{f-oei v`k mcb|h-yh|jf% \h{i`j rtkcaoei* v`k kevo|k {eo~k|rk bce jhha joak v`k oerofk hn hek

    s{cev{m1 oe~k|rkj* v`kr{tk|-s{cev{m c|kc bce lk bherofk|kf cr v`k h{vrofk hn v`k {eo-

    ~k|rk7 Ov or ~k| oevk|krvoei v`cv v`k ~oboeov hn ce ovr oevk|ecj thoev or cljk vh lk forb{rrkf

    cr ovr h{vrofk% Oefkkf* @ojlk|v rtcbk oevk|t|kvkf cr c rtcbk hn-n{ebvoher ks{o~cjkev vhyh|jf joekr `cr t|kborkj v`or t|htk|v* y`ob` bce lk bcjjkf n|cbvcj t|hlclj ehv hej mkvc-

    t`h|obcjj% Kcb` joek fkrb|olkr ce kvk|eov hn v`k {eo~k|rk cr v`k bhevoe{ov hn tcrv* t|krkev

    cef n{v{|k7 ehvk v`cv v`k fkrb|otvohe h|oioecvkr n|hm hek |knk|kebk n|cmk% V`k omthrroljk

    cef rkjn-bhev|cfobvh|> kpvk|ecj mh~kmkev hn v`k {eo~k|rk or fkrb|olkf cr v`k oevk|ecj

    hek7 Ov or keh{i` vh b`ceik v`k Ikrvcjv cef jhha cv kcb`-n{ebvohe joak c fkrb|otvohe hnv`k rvcvk hn v`k {eo~k|rk cef hej rkbhefc|oj* cef cr c |kr{jv hn v`k nh|mk| joak c fkrb|ot-

    vohe hn c t`robcj hlgkbv oerofk% V`k {eo~k|rk bherorvr (oevk|ecjj/ hn ovr (kpvk|ecj/ rvcvkr%

    V`k v|cerovohe n|hm rvhb`crvobcjj fkvk|moekf b`chr vh t|hlclojorvob s{cev{m rvcvkr bhe-

    ~k|vr ovr tc|vr oevh ovr rvcvkr%

    V`k|knh|k* v`k Rahjkmoce |kjcvo~ov hn bhevoe{ov cef forb|kvkekrr or kcroj vh lk

    v|cernh|mkf oevh v`k |kjcvo~ov hn kpvk|ecjov cef oevk|ecjov tk|movvoei c roeijk bhmmhe

    fkrb|otvohe% V`ke kek|i bh||krthefr vh v`k ~cj{kr hn b`ceik yov`oe c s{cev h| c forb|kvk

    g{mt% He v`k hv`k| `cef* yk `c~k {rkf v`k t|hlclojovokr nh| oenoeov7 v`k t|hlclojov or c

    l|ofik* v`|h{i` y`ob` yk c|k cljk vh v`oea {eonh|mj cr oenoeovkj i|kcv cr oenoeovkj rmcjj

    s{cevovokr cr oenoeovkromcj* l{v oe vk|mr hn forb|kvkekrr kmlkffkf l s{cev{m%

    Roebk oe h{| ctt|hcb`* cbvohe bh||krthefr vh v`k b`ceik hn t|hlclojov* v`k

    t|oebotjk hn jkcrv cbvohe or bhe~k|vkf oevh c t|oebotjk hn jkcrv t|hlclojov b`ceik* y`ob` or

    ; R{b` c v|cernh|mcvohe bjkc|r v`cv Vch or g{rv cehv`k|* l{v mh|k cbb{|cvk yc vh lk fkrb|olkf hevh-v`khjhiobcj fonnk|-

    kebk oerhnc| cr v`k jcvvk| or* cr c aoef hn rtkcaoei* c n{ebvohe hn `k|k cef ehy* h| {roei ce ct`h|orm7 Vch or v`k fkrvo-e hn Fcrkoe% Oe hv`k| yh|fr* v`k Vch t|krkevr v`k t|krkebk hn Ihf oe v`or yh|jf* h| v|cerjcvoei l v`k vk|mr hn bjcrrobcj

    t`ojhrht` cef v`k|knh|k lkoei lh{ef l ce hpmh|he* cr v|cerbkefkevcj v|cerbkefkebk ( Roebk ov {eovkr v`k ehe-rkjn-ofkevov hn kpvk|ecj ofkevov cef v`k fknoeovo~k |knjkpo~ov hn v`k {eo~k|rk cr c roeijk y`hjk%V`k|knh|k v`k h{vbhmk y`ob` or nh{ef l v`k {eo~k|rk yk bce cttj vh rhj~k romojc| fonnob{jvokr j{r` oe mce tc|c-fhpkr cef oe v`k b|oror oe v`k nh{efcvohe hn mcv`kmcvobr cr vh v`k rkv v`kh|% Nh| v`or t{|thrk* c moeom{m lcrk rv|{ b-v{|k r`h{jf lk f|cye n|hm @ojlk|v rtcbk y`ob` yh{jf cjjhy {r vh v|cernh|m oenoeov oevh c thoev hn v`cv oenoeov%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    16/21

    3>

    oev{ovo~kj tk|nkbvj cbbktvcljk7 v`k v|cerovohe n|hm hek vh cehv`k| -n{ebvohe m{rv vcaktjcbk v`|h{i` v`k jkcrv b`ceik hn t|hlclojov% Oe tc|vob{jc|* oe v`k bcrk hn v`k v|cernh|-

    mcvohe bh||krthefoei vh c t`robcj s{cevov (o%k% l c `tk|mcpomcj htk|cvh|/* v`k

    cmkefmkev hn t|hlclojov or wk|h* cef yk `c~k cj|kcf ehvkf v`cv cjj v|cernh|mcvohe hn

    v`cv bjcrr mc lk |kjcvkf vh v`k t|krkev hn v`k hlgkbv thrrkrroei v`cv -n{ebvohe% Vomk

    bce lk fkrb|olkf cr v`k fkerov hn t|hlclojov nh| v|cerovoei n|hm hek vh cehv`k|-n{ebvohe* oe y`ob` v`k nh|mk| or oevk|t|kvkf cr v`k t|krkev hn v`k s{cev{m hlgkbv oes{krvohe* y`ojk v`k jcvvk| cr n{v{|k h| tcrv rvcvkr% V`k t|hlclojov fkerov n{ebvohe yojj lk

    mcpomcj oe v`k t|krkev* vh v`k mcpom{m hn y`ob` v`k tcrv ~cj{kr yojj i|hy mhehvheobcjj

    l fonnk|kev rjhtk* cef v`hrk hn v`k n{v{|k oe v{|e yojj fkb|kcrk* nh|moei c vtobcj lkjj

    r`ctkf t|hlclojov fkerov b{|~k% Ekicvo~k t|hlclojov yojj lk v`ke ecv{|cjj oevk|-t|kvkf cr

    c t|hlclojov nh| bhe~k|voei oe tcrv rvcvkr* o%k% lcba oe vomk* y`ojk v`k bhmtjkp hek yojj lk

    |knk||kf vh v`k vomk cpor forvh|vohe%

    V`k n{efcmkevcj bhervcevr v`k Tjcea cef v`k rtkkf hn joi`v c|k c ecv{|cj

    {eovr rkv cjjhyoei v`k tc|vr hn v`km vh lk oevk|t|kvkf cr t|hlclojovokr* cef bhevoe{ov vh lkv|cernh|mkf oevh v`k oevk|ecjov hn c forb|kvk (s{cev{m/ g{mt%

    On yk mkce vh vtk c r{mmc| hn v`k t|oebotjk hn jkcrv cbvohe* ov cttkc|r v`cv

    mc bh~k| c yofk| c|kc* ecmkj @ojlk|v rtcbk* cef cr jhei cr v`k cmkefmkev hn v`k

    t|hlclojov oe vomk or oevk|t|kvkf cr v`k n|ks{keb hn fk L|hijok yc~k%R{b` ce oevk|t|kvc-

    vohe or ecv{|cj lkbc{rk t|hlclojov* v`h{i`v k~ke kjkmkevc|oj* or fknoekf cr v`k |cvoh hn v`k

    tc|v hn v`k cjvk|ecvo~kr cbbktvkf cr nc~h|cljk (y`kv`k| oe cevobotcvohe h| cr c rvcvorvobcj

    n|ks{keb/ hn c b`hobk vhyc|fr cjj hn v`km% V`ke fk L|hijok yc~k bh||krthefr vh v`k

    cmkefmkev hn v`k throvo~k cjvk|ecvo~kr on v`k rkv hn cjj v`k cjvk|ecvo~kr |kmcoer v`k rcmk

    (oe hv`k| yh|fr* v`k b`ceik hn v`k nc~h|cljk hekr or nh| v`k cbbh{ev hn v`k ekicvo~k hekr/%R{b` ce ctt|hcb`* lkrofkr r{iikrvoei ce {e{r{cj tk|rtkbvo~k he kek|i* |krtkbvo~kj

    mcvvk|* crr{mkr v`cv v`k jcy hn kek|i bherk|~cvohe |h{i`j ctt|hpomcvkr v`k joekc| c|kc

    hn oeb|kcroei (fkb|kcroei/ v`k t|hlclojov hn v`k lkjj b{|~k hn t|hlclojov fkerov forv|ol{-

    vohe* h| hn v`k joekc| b`ceik hn v`k throvo~k cjvk|ecvo~kr% Oe c|kcr* oe y`ob` r{b` ce ct-

    t|hpomcvohe or roieonobcevj fonnk|kev* nh|bkr* nokjfr* cef v`ko| kek|iokr r`h{jf cttkc| vh

    bhmtkercvk nh| v`k oecbb{|cb hn ctt|hpomcvohe% Yk vkef vh oevk|t|kv v`k rhmky`cv h|-

    iceowkf cl{efcebk hn kjkmkevc| tc|vobjkr cef v`k nh{| mcoe nh|bkr (nokjfr/ hn v`k rvce-

    fc|f mhfkj cr Tvhjkmcob bbjkr* noi{|cvo~kj rtkcaoei% Ov or v`k t|hlclojorvob ctt|hcb` hn

    bjcrrobcj s{cev{m mkb`ceobr v`cv nc~h|r v`k cjmhrv joekc| rkbvohe cr ov t|k~cojrfkboro~kj%

    V`k t|oebotjk hn jkcrv cbvohe cr c t|oebotjk hn jkcrv b`ceioei v`k t|hlclojov cb-

    v{cjj oebj{fkr cjrh v`k bcrk hn ovr cmkefmkev oe vomk bh||krthefoei vh v`k clh~k oev|h-

    f{bkf bhebktv hn v`khjhiobcj fonnk|kebk% Oe vk|mr hn v`k cjvk|ecvo~kr cbbktvkf vh lk nc~h|-

    cljk hn c b`hobk* hevhjhiobcj fonnk|kebk or v`k fonnk|kebk lkvykke v`k cmh{ev hn nc~h|cljk

    cef {enc~h|cljk cjvk|ecvo~kr cef cjj v`k cjvk|ecvo~kr9* y`ojk v`khjhiobcj fonnk|kebk or v`cv

    9 V`k rcof fhkr ehv bhev|cfobv v`k oevk|t|kvcvohe hn r{lgkbvo~k t|hlclojov cr c g{mt hn ce kptkbvcvohe* y`ob` or |kcjowkf

    cr c rmhhv` b`ceik hn v`k hlgkbvo~k t|hlclojov l ce cjrh i|cf{cj r`onv hn v`k nc~h|cljk cjvk|ecvo~kr oe c |kcj mh~kmkev%Wk|h hevhjhiobcj fonnk|kebk thrv{jcvkr v`ko| bhoebofkebk% Yk bce joakyork {rk c mkvct`h| nh| v`k r{lgkbvo~k t|hlclojovcr c ekicvo~k omt|oev cef ,kptkbvcvohe, fkvk|moekf l cev`oei kjrk oe |kjcvohe vh c io~ke v`oei rh v`cv ovr cmkefmkev vh

    mhfon v`k |krv oe v`k rjoi`vkrv thrroljk fki|kk%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    17/21

    39

    lkvykke cjj v`k cjvk|ecvo~kr (k%i% cv fonnk|kev thoevr oe vomk/% V`khjhiobcj fonnk|kebk* `hy-

    k~k|* r`h{jf lk {efk|rvhhf r{nnobokevj ikek|cjj7 roebk cjj cjvk|ecvo~kr nh|m c vhvcjov* ov

    mkcer v`cv yk bce crr{mk nh| v`k fonnk|kebk cr t|krk|~cvohe cr b`ceik oe ce ks{cj fk-

    i|kk% V`k|knh|k* v`khjhiobcj fonnk|kebkrkkar vh s{cevon v`k |kjcvoher`ot hn v`k vhvcjov vh

    ovrkjn%

    Noecjj* v`k bhevkpv hn v`k yh|a bce lk {rkf vh cff|krr c nky rkkmoeijfortc|cvk cef {e|kjcvkf kpbktvoher nh| v`k fomkerohecjov hn7 oe Ijkcrher (Ijkcrhe3?;97 3297 941 >1 Rtkbak|

    3?9;7 32?-364/* cef cv jcrv Nk|mcvr jcrv v`kh|km t|h~ke cv v`k kef hn jcrv bkev{| l

    Cef|ky Yojkr% Ahb`ke cef Rtkbak| fo|kbvj oefobcvkf v`cv v`k fortjckf |kr{jv bce lk

    hlvcoekf n|hm v`k v`kh|km hn Ijkcrhe% (Ahb`ke* Rtkbak| 3?>97 94/% @hyk~k| h{| yh|a

    `cr i|h{efkf he v`k orhmh|t`orm hn s{lov cef v`|kk-fomkerohecj rt`k|k (y`ob` oe ncbv or

    romojc| vh Ahb`ke cef Rtkbak|r bh{evk|-kpcmtjk hn v`k > hn v`ko| c|vobjk/* he v`k |kt|k-

    rkevcvohe hn @ojlk|v rtcbk l s{lovr cef `kebk* l Moeahyrao rtcbk% N{|v`k| c r{|t|ork

    hbb{|r7 cr v`|kk-fomkerohecj rt`k|k or hlvcoekf n|hm v`k bhmtjkp @ojlk|v rtcbk hn fomke-rohe * cef Moeahyrao rtcbk or ce cffovo~k bhmloecvohe hn s{lovr* cv v`cv |kt|krkevcljk cr@ojlk|v rtcbk* v`ke v`k|k or c fo|kbv tcv`yc v`k kpbktvohe clh{v fomkerohecjov vyh vh lk

    v|cernk||kf vh oenoeovk fomkeroher% Ov r`h{jf `hyk~k| cicoe lk ehvkf v`cv v`or or ehv c yc

    vh bc|| h~k| vh ce noeovk fomkeroher% N{|v`k| v`k cpohm hn b`hobk bc||okr v`k h{vbhmk vh

    ce v|cernoeovk thyk| t|h~ofkf ov vh lk ~cjof nh| v`cv thyk|% Yk `c~k rvcvkmkevr cjj hn

    v`hrk v`cv cttkc| l v`k kpbktvohe hn fomkerohecjov * y`ob` c|k ehv v|{k nh| ce noeovkoevkik|* l{v v`k c|k v|{k nh| ce oenoeovk e{mlk|% V`k hej yc h{v hn v`k rov{cvohe* on yk

    c|k vh t|krk|~k v`k t|oebotjk hn oef{bvohe* mh|kh~k| ov or oebj{fkf oe v`k Tkceh cpohmcvob hn

    oevkik|r* or vh cbbktv v`cv v`k|k or c e{mlk| v`cv yk bceehv thoev h{v 0* nh| y`ob` v`cvvtk hn rvcvkmkevr c|k ehv ~cjof%

    C|i{kf bh{jf ommkfocvkj |knk||kf vh Nk|mcvr jcrv v`kh|km on yk `c~k vcake c

    r{nnobokevj thyk|n{j cpohm hn b`hobk cr jhei cr `oi`k| fomkeroher c|k hlvcoekf m{jvotjobc-

    vo~kj% Or v`k cpohm hn b`hobk h| ykcak| ~k|rohe hn ov (v`k v`kh|km hn t|omk Lhhjkce ofk-

    cjr?/ {rkf oe Yojkr t|hhn(MbJc|v ;/%

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    18/21

    30

    cjjkikf ~cjofov oe~cjofov hn v`k bjcom he cjj ~cjof bjcomr% Hl~oh{rj* v`k t|hthrkf orhmh|-

    t`orm lkvykke Moeahyrao rtcbk cef @ojlk|v rtcbk cef v`ko| t`robcj oevk|t|kvcvohe lk-

    bc{rk hn v`k kpbktvohe hn cjjkikf omthrrolojov {r{cj Lhhjkce jhiob vh lk kmlkffkf

    (Ahb`ke* Rtkbak| 3?>97 941 Rtkbak| 3?9;7 32?-364/ cr vh fomkerohe h| v|cernk|r ovrrvcvkmkevr y`ob` c|k ~cjof* o%k% vc{vhjhiobcj* nh| ce mhmkev hn vomk oevh ~cjof cv cjj* o%k%

    ~cjof cr vh kvk|eov* `hyk~k| k~ke on v`k c|k ehv ~cjof cr vh ce n{v{|k mhmkev (l{v ehvt|krkev hek#/33% Ov v{|er h{v v`cv v`k {r{cj loec| jhiob `cr ce {e{r{cj t|o~ojkik yov` |k-

    ic|f vh kvk|eov7 oe c rkerk ov mcakr h| l|oeir ce ks{o~cjkebk b`c|cbvk|orvob vh kporvkevocj-

    orm* lkvykke t|krkev cef kvk|eov* oevk|t|kvoei kvk|eov l ikek|cjov s{cevonok| cr nh| cjj

    t|krkevr%

    Noecjj yk yojj cttj v`k {rkf c|i{mkev cjrh vh v`k v`kh|km v`cv c nokjf (o%k%

    m{jvotjobcvohe or bhmm{vcvo~k/ hn fomkerohecjov `oi`k| v`ce vyh fhkr ehv kporv7 v`k

    t|oebotjk hn oef{bvohe |ks{o|kr r{b` vh kporvr ceyc7 Hn bh{|rk* ov bhmkr vh c bjkce cef

    {ebherv|{bvo~k t|hhn hn ovr kporvkebk%

    L{v jcvk|* cbbh|foei vh v`k bhe~kevohecj oevk|t|kvcvohe hn v`k v`kh|km aehye crv`k tc|cfhp Lcecb` V|crao3< (Lcecb`* Vc|rao 3?

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    19/21

    3?

    vkmth|c| t`ojhrht`/ vh lk ommcvk|ocj7 oe Rahjkmoce yc* k~ke lkoei cef ehe-lkoei c|k

    |kjcvo~k%

    On yk tcrr v`k |h{vk oe |k~k|rk h|fk|* yk bce b|kcvk v`k {eo~k|rk* oebj{foei

    i|c~ov* v`k kerkmljk hn cjj v`k thrroljk rvcvkr hn ov7 kcb` hn v`km or rom{jvcekh{rj v`k

    cbv{cj rvcvk hn rhmk tc|v hn ov% Oe hv`k| yh|fr* yk bce b|kcvk v`k {eo~k|rk cr bherorvoei

    hej hn ovrkjn* l{v ehv jomovkf vh cbvoei cr hek* o%k% c y`hjk* cef cjrh hn cjj hn ovr hye tc|vrks{o~cjkev vh v`k rvcvkr hn v`k y`hjk%

    R{mmc|owoei v`k y`hjk b{||kev rvcvkmkev* yk bce `oi`joi`v rk~k|cj mcgh|

    t|hljkmr7

    3% V`k n{efcmkevcj omth|vcebk hn v`k cpohm hn b`hobk oe v`k forb{rrohe hn

    orr{kr c|h{ef v`k v`kh|km hn Ahb`ke cef Rtkbak|%

    % He v`k T|hljkm hn @offke ^c|ocljkr oe S{cev{m Mkb`ceobr% \k~okyr hn Mhfk|e

    T`robr% ^hj% 20* Eh 2 (G{j/* 669-6;/X@offke+

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    20/21

    * Eh >* 00;-0?2 (lhhar%ihhijk%bhm/%

    I|hkekyhjf* @% 3?6>% He v`k t|oebotjkr hn kjkmkevc| s{cev{m mkb`ceobr%T`robc% ^hj% 3/* 64;-6>4%

    @k|mcee* I% 3?2;% V`k bo|b{jc|ov oe ~he Ek{mcee)r t|hhn% (V|cerjcvohe l Mob`okj Rkk~oeba hn

    ,Fk| Wo|akj oe EK[MCEEr Lkykor,* rkbvohe 9 n|hm v`k krrc l I|kvk @k|mcee* Fok Ecv{|t`ojhrht`orb`ke I|{efjcike fk S{cevkemkb`ceoa% Cl`cefj{eike fk| n|okr)rb`ke Rb`{jk* >*

    3?2;%/`vvt7yyy%t`r%{{%ejoiirkk~oebav|cer%tfn/%

    MbJc|v* B%* Eh 2* 2;?-299% (`vvt7yyy%by|{%kf{c|vrbot`ojT|h~oeiXNJV%tfn/%

    Mhcj* G% 3?6?% S{cev{m mkb`ceobr cr c rvcvorvobcj v`kh|%T|hbkkfoeir hn v`k Bcml|ofik T`ojh-rht`obcj Rhbokv% ^hj% 6;* Eh 3* ??-36% % 7 -%

    Tkvk|* N%* @% Ykj% 3?

  • 8/3/2019 Vasil Penchev. The Kochen - Specker theorem in quantum mechanics: A philosophical comment

    21/21

    * %