lynds, peter- time and classical and quantum mechanics: indeterminacy vs. discontinuity

Upload: julio-caceda

Post on 04-Apr-2018

225 views

Category:

Documents


3 download

TRANSCRIPT

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    1/7

    :

    ^agf jbn Kej{{akje jbn Zvjb~vg Gfk`jbak{4 Abnf~fxgabjkq s{" Na{kib~abva~q

    \f~fx Eqbn{:

    ^agf% Kej{{akje Gfk`jbak{% Zvjb~vg Gfk`jbak{% Abnf~fxgabjkq% Na{kib~abva~q% Xfej~asa~q%

    Ki{gieioq% Agjoabjxq agf% K`xibib{% Tfbi{ \jxjnipf{"

    A~ a{ |i{~vej~fn ~`fxf a{ bi~ j |xfka{f {~j~ak ab{~jb~ ab ~agf vbnfxeqabo j nqbjgakje |`q{akje |xikf{{ j~ w`ak`

    ~`f xfej~asf |i{a~aib ic j hinq ab xfej~asf gi~aib ix j {|fkacak |`q{akje gjoba~vnf wiven ~`fixf~akjeeq hf

    |xfka{feq nf~fxgabfn" A~ a{ kibkevnfn a~ a{ fpjk~eq hfkjv{f ic ~`a{ ~`j~ ~agf (xfej~asf ab~fxsje j{ abnakj~fn hq j

    keikm! jbn ~`f kib~abva~q ic j |`q{akje |xikf{{ a{ |i{{ahef% wa~` ~`fxf hfabo j bfkf{{jxq ~xjnf icc ic jee

    |xfka{feq nf~fxgabfn |`q{akje sjevf{ j~ j ~agf% cix ~`fax kib~abva~q ~`xivo` ~agf" ^`a{ fp|ejbj~aib a{ je{i

    {`iwb ~i hf ~`f kixxfk~ {iev~aib ~i ~`f gi~aib jbn abcaba~q |jxjnipf{% fpkevnabo ~`f [~jnavg% ixaoabjeeq

    kibkfasfn hq ~`f jbkafb~ Oxffm gj~`fgj~akajb Tfbi ic Fefj" Zvjb~vg Ki{gieioq% Agjoabjxq ^agf jbn

    K`xibib{ jxf je{i ~`fb na{kv{{fn% wa~` ~`f ej~~fx ~wi j||fjxabo ~i hf {v|fx{fnfn ib j ~`fixf~akje hj{a{"

    :" Ab~xinvk~aib

    ^agf fb~fx{ gfk`jbak{ j{ j gfj{vxf ic ab~fxsje% xfej~asf ~i ~`f keikm kig|ef~abo ~`f gfj{vxfgfb~"

    Kibsfx{feq% je~`ivo` a~ a{ ofbfxjeeq bi~ xfjeatfn% ab jeekj{f{ j ~agf sjevf abnakj~f{ jb ab~fxsje ic ~agf%

    xj~`fx ~`jb j |xfka{f {~j~ak ab{~jb~ ab ~agf j~ w`ak` ~`f xfej~asf |i{a~aib ic j hinq ab xfej~asf gi~aib ix j

    {|fkacak |`q{akje gjoba~vnf wiven ~`fixf~akjeeq hf |xfka{feq nf~fxgabfn" Cix fpjg|ef% ac ~wi {f|jxj~f

    fsfb~{ jxf gfj{vxfn ~i ~jmf |ejkf j~ fa~`fx : `ivx ix :

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    2/7

    8

    kib~ix~fn {|jkf'~agf ofigf~xq{ |xf{fb~ |xfkfnabo \ejbkm {kjef (O`)k;!

    :)8dv{~ jc~fx ~`f hao hjbo (bfw

    abcej~aibjxq ginfe!% j{ `j{ ic~fb |xfsaiv{eq hffb ~fb~j~asfeq `q|i~`f{atfn"(8'?!

    Kib~abva~q wiven hf

    |xf{fb~ jbn bj~vxjeeq ab`fxfb~ ab |xjk~akjeeq jee aba~aje zvjb~vg {~j~f{ jbn kibcaovxj~aib{% xj~`fx ~`jb j

    {|fkacak cfw% ix {|fkaje ibf% xfojxnef{{ ic `iw gakxi{ki|ak ~`f {kjef" (>":! Cvx~`fxgixf% ~`f ki{gieioakje

    |xi|i{je ic Agjoabjxq ^agf%(8% ;% 6'?!

    a{ bi~ kig|j~ahef wa~` j kib{a{~fb~ |`q{akje nf{kxa|~aib% hi~`% j{ j

    kib{fzvfbkf ic ~`f jhisf kib{anfxj~aib% jbn {fkibneq% hfkjv{f a~ a{ ~`f xfej~asf ixnfx ic fsfb~{ ~`j~ a{xfefsjb~% bi~ ~`f naxfk~aib ic ~agf a~{fec" J{ j kib{fzvfbkf% a~ a{ bi~ |i{{ahef cix ~`f ixnfx ic j {fzvfbkf ic

    fsfb~{ ~i hf agjoabjxq (j~ xao`~ jboef{! xfej~asf ~i jbi~`fx {fzvfbkf ic fsfb~{" (6! Ej{~eq% K`xibib{%

    |xi|i{fn |jx~akef{ ic abnasa{ahef ab~fxsje{ ic ~agf%(8% 0!

    je{i j||fjx ~i hf {v|fx{fnfn ib j ~`fixf~akje hj{a{%

    j{ ~`fax |i{{ahef fpa{~fbkf a{ abkig|j~ahef wa~` ~`f {ag|ef kibkev{aib ~`j~ ~`f sfxq xfj{ib |`q{akje

    kib~abva~q a{ |i{{ahef ab ~`f cax{~ ab{~jbkf a{ nvf ~i ~`fxf bi~ hfabo j zvjb~vg ix j~ig ic ~agf"

    Hfcixf |xikffnabo cvx~`fx `iwfsfx% A ~`abm a~ a{ ag|ix~jb~ ~i {~xf{{ ~`j~ je~`ivo` A `jsf j~~fg|~fn ~i hf

    j{ zvjb~a~j~asf jbn xaoixiv{ j{ |i{{ahef% ~`f {vhdfk~ ic ~agf nif{ bi~ xfjnaeq efbn a~{fec ~i {vk` j

    nf{kxa|~aib% |jx~akvejxeq ab ~`f kib~fp~ ab w`ak` a~ a{ ~xfj~fn `fxf% jbn xfjnfx{ gjq aba~ajeeq cabn ~`j~ ~`fq

    waee bffn ~i xfjeeq oxj||ef wa~` ~`f kib~fb~{ hfcixf ~`fq jxf jhef ~i jk`afsf j kefjx jbn ofbvabf

    vbnfx{~jbnabo" A j|ieioatf cix ~`a{% hv~ A kjb cabn bi i~`fx wjq ic kibsfqabo ~`f {jgf abcixgj~aib jbn

    ejqabo ~`f aba~aje civbnj~aib{ cix ~`f |`q{ak{ ~`j~ {vh{fzvfb~eq cieeiw% ic w`ak`% ab xfej~aib ~i ag|ix~jbkf%

    A kib{anfx ~i zva~f fj{aeq iv~wfao` jbq vbnf{axjhef% je~`ivo` vbjsianjhef jbn bfkf{{jxq j{|fk~{ ic ~`a{

    |j|fx"

    8" Gi~aib jbn Kib~abva~q

    _f hfoab hq kib{anfxabo ~`f {ag|ef jbn abbikviv{ |i{~vej~f4 ~`fxf a{ bi~ j |xfka{f {~j~ak ab{~jb~ ab

    ~agf vbnfxeqabo j nqbjgakje |`q{akje |xikf{{" Ac ~`fxf wfxf% ~`f xfej~asf |i{a~aib ic j hinq ab xfej~asf

    gi~aib ix j {|fkacak |`q{akje gjoba~vnf% je~`ivo` |xfka{feq nf~fxgabfn j~ {vk` j |xfka{f {~j~ak ab{~jb~%

    wiven je{i hq wjq ic eioakje bfkf{{a~q hf cxitfb {~j~ak j~ ~`j~ |xfka{f {~j~ak ab{~jb~" Cvx~`fxgixf% fsfb~{

    jbn jee |`q{akje gjoba~vnf{ wiven xfgjab cxitfb {~j~ak% j{ {vk` j |xfka{f {~j~ak ab{~jb~ ab ~agf wiven

    xfgjab cxitfb {~j~ak j~ ~`f {jgf |xfka{f {~j~ak ab{~jb~" (Abkanfb~jeeq% ~`f {jgf iv~kigf wiven je{i xf{ve~ ac

    {vk` j |xfka{f {~j~ak ab{~jb~ wfxf `q|i~`f~akjeeq cieeiwfn hq j kib~abviv{ {fzvfbkf ic cvx~`fx |xfka{f

    {~j~ak ab{~jb~{ ab ~agf% j{ hq ~`fax sfxq bj~vxf j |xfka{f {~j~ak ab{~jb~ ab ~agf nif{ bi~ `jsf nvxj~aib isfxab~fxsje ab ~agf% {i bfa~`fx kiven j cvx~`fx {vkkf{{aib ic ~`fg" ^`a{ {kfbjxai a{ bi~ |ejv{ahef `iwfsfx ab

    ~`f cax{~ ab{~jbkf% j{ ~`f bi~aib ic j kib~abviv{ |xioxf{{aib ic |xfka{f {~j~ak ab{~jb~{ ab ~agf a{ ihsaiv{eq

    bi~ |i{{ahef cix ~`f {jgf xfj{ib!" Xj~`fx ~`jb cjkaea~j~abo gi~aib jbn |`q{akje kib~abva~q% ~`a{ wiven

    |fx|f~vj~f j kib{~jb~ |xfka{f {~j~ak ab{~jb~ ab ~agf% jbn j{ a{ ~`f sfxq bj~vxf ic ~`a{ f~`fxfje bi~aib a"f" j

    |`q{akje |xikf{{ cxitfb {~j~ak j~ jb ab{~jb~% j{ ~`ivo` {~vkm ib |jv{f ix cxfftf cxjgf ib j gi~aib {kxffb%

    |`q{akje kib~abva~q a{ bi~ |i{{ahef ac {vk` j na{kib~abviv{ k`xibieioakje cfj~vxf a{ jb ab~xab{ak jbn

    ab`fxfb~ |xi|fx~q ic j nqbjgakje |`q{akje |xikf{{% jbn j{ {vk`% j gfjbabocve (jbn jk~vje |`q{akje!

    abnakj~ix ic j ~agf j~ w`ak` ~`f xfej~asf |i{a~aib ic j hinq ab xfej~asf gi~aib ix j kfx~jab |`q{akje

    gjoba~vnf a{ |xfka{feq nf~fxgabfn% j{ `j{ `a{~ixakjeeq hffb j{{vgfn" ^`j~ a{% a~ a{ ~`f `vgjb ih{fxsfx

    w`i {vhdfk~asfeq |xidfk~{% ag|i{f{ jbn j{{aob{ j |xfka{f ab{~jb~ ab ~agf v|ib j |`q{akje |xikf{{% cix

    fpjg|ef% ab ixnfx ~i ojab j gfjbabocve {vhdfk~asf |ak~vxf ix gfb~je {bj|{`i~ ic ~`f xfej~asf |i{a~aib ic j

    hinq ab xfej~asf gi~aib"J{ j bj~vxje kib{fzvfbkf ic ~`a{% ac ~`fxf a{ bi~ j |xfka{f {~j~ak ab{~jb~ ab ~agf vbnfxeqabo j nqbjgakje

    |`q{akje |xikf{{% ~`fxf a{ bi |`q{akje |xioxf{{aib ix ceiw ic ~agf% j{ wa~`iv~ j kib~abviv{ jbn

    k`xibieioakje |xioxf{{aib ~`xivo` nfcaba~f abnasa{ahef ab{~jb~{ ic ~agf isfx jb fp~fbnfn ab~fxsje ab ~agf%

    ~`fxf kjb hf bi |xioxf{{aib" ^`a{ gjq {ffg {igfw`j~ kivb~fx'ab~va~asf% hv~ a~ a{ fpjk~eq w`j~ a{ xfzvaxfn

    hq bj~vxf ~i fbjhef ~agf (xfej~asf ab~fxsje j{ abnakj~fn hq j keikm!% gi~aib jbn ~`f kib~abva~q ic j |`q{akje

    |xikf{{ ~i hf |i{{ahef" Ab~va~aib je{i {ffg{ ~i {voof{~ ~`j~ ac ~`fxf wfxf bi~ j |`q{akje |xioxf{{aib ic

    ~agf% ~`f fb~axf vbasfx{f wiven hf cxitfb gi~aibef{{ j~ jb ab{~jb~% jojab j{ ~`ivo` {~vkm ib |jv{f ib j

    gi~aib {kxffb" Hv~ ac ~`f vbasfx{f wfxf cxitfb {~j~ak j~ {vk` j {~j~ak ab{~jb~% ~`a{ wiven hf j |xfka{f {~j~ak

    ab{~jb~ ic ~agf4 ~agf wivenhf j |`q{akje zvjb~a~q" ^`v{% a~ a{ ~`fb nvf ~i bj~vxf{ sfxq fpkev{aib ic j ~agf

    j{ j cvbnjgfb~je |`q{akje zvjb~a~q% ~`j~ ~agf j{ a~ a{ gfj{vxfn ab |`q{ak{ (xfej~asf ab~fxsje!% jbn j{ {vk`%

    gi~aib jbn |`q{akje kib~abva~q jxf abnffn |i{{ahef"

    A~ gao`~ je{i hf jxovfn ab j gixf |`aei{i|`akje {fb{f ~`j~ j ofbfxje nfcaba~aib ic {~j~ak wiven fb~a~ef j

    kfx~jab |`q{akje gjoba~vnf j{ hfabo vbk`jboabocix jb fp~fbnfn ab~fxsje ic ~agf" Hv~ ac ~`a{ a{ {i% `iw

    ~`fb kiven ~agf a~{fec hf {jan ~i hf cxitfb {~j~ak j~ j |xfka{f ab{~jb~ ac ~i ni {i je{i nfgjbn{ a~ gv{~ hf

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    3/7

    ;

    vbk`jboabo cix jb fp~fbnfn ab~fxsje ic ~agf9 J{ j ofbfxje jbn {fb{ahef nfcaba~aib ~`a{ a{ bi nivh~ kixxfk~%

    j{ wf easf ab j wixen w`fxf abnffn ~`fxf a{ ab~fxsje ab ~agf% jbn {i cix j kfx~jab |`q{akje gjoba~vnf ~i hf

    {~j~ak jbn vbk`jboabo a~ wiven bj~vxjeeq je{i `jsf ~i xfgjab {i cix jb fp~fbnfn nvxj~aib% `iwfsfx {`ix~"

    ^`fxf a{ {igf~`abo ic j |jxjnip `fxf `iwfsfx" Ac ~`fxf wfxf j |xfka{f {~j~ak ab{~jb~ vbnfxeqabo j

    nqbjgakje |`q{akje |xikf{{% fsfxq~`abo% abkevnabo keikm{ jbn wj~k`f{ wiven je{i hf cxitfb {~j~ak jbn

    na{kib~abviv{% jbn j{ {vk`% ab~fxsje ab ~agf wiven bi~ hf |i{{ahef fa~`fx" ^`fxf kiven hf bi ab~fxsje ab

    ~agf cix j kfx~jab |`q{akje gjoba~vnf ~i xfgjab vbk`jboabo" ^`v{ ~`a{ ofbfxje nfcaba~aib ic {~j~ak hxfjm{niwb w`fb ~`f bi~aib ic {~j~ak a{ j||eafn ~i ~agf a~{fec" _f jxf {i ~`fb cixkfn ~i {fjxk` cix j xfsa{fn

    nfcaba~aib ic {~j~ak cix ~`a{ {|fkaje ~fg|ixje kj{f" ^`a{ a{ nibf hq zvjeacqabo ~`f v{f ic {~j{a{ ab ~`a{

    |jx~akvejx kaxkvg{~jbkf hq bi~abo {~j~ak jbn vbk`jboabo% wa~` {~j~ak jbn vbk`jboabo j{ bi~ hfabo isfx

    ab~fxsje% j{ ~`fxf kiven hf bi ab~fxsje jbn bi~`abo kiven k`jbof ab ~`f cax{~ ab{~jbkf" J~ ~`f {jgf ~agf

    `iwfsfx% a~ {`iven je{i hf fbivo` dv{~ ~i hf jhef ~i xfkiobatf jbn jkmbiwefnof ~`f cjve~ jbn |jxjnip ab

    ~`f nfcaba~aib w`fb j||eafn ~i ~agf"

    A~ gao`~ je{i hf jxovfn hq jbjeioq wa~` ~`f kejag hq {igf |fi|ef ~`j~ ~`f {i'kjeefn /heikm vbasfx{f

    ginfe% a"f" j >'nagfb{aibje ginfe ic |`q{akje xfjea~q% abkix|ixj~abo ~agf j{ wfee j{ {|jkf% a{ {~j~ak ix

    vbk`jboabo" ^`a{ kejag `iwfsfx absiesf{ ~`f kiggib ga{~jmf ic cjaeabo ~i xfkiobatf ~`j~ vbef{{ ~`fxf a{

    jbi~`fx~agf nagfb{aib% a~ {ag|eq nif{b/~ gjmf {fb{f ~i {jq ~`j~ ~`f heikm vbasfx{f a{ {~j~ak% cix ~`fxf a{

    bi /fp~fxbje/ ~agf ab~fxsje isfx w`ak` a~ xfgjab{ ~`f {jgf" Ac wf ~`fb j||eq ~`f {jgf eabf ic xfj{ibabo ~i

    ~`f `q|i~`f~akje kj{f hfabo na{kv{{fn |xf{fb~eq% wf kiven {jq4 A~ nif{b/~ gjmf {fb{f ~i {jq ~`j~ fsfxq~`abowiven hf {~j~ak j~ jb ab{~jb~% (wa~` |`q{akje kib~abva~q jbn ab~fxsje ab ~agf bi~ hfabo |i{{ahef!% j{ ~`fxf

    wiven hf bi ~agf ab~fxsje cix {vk` jb j{{fx~aib ~i hf xfej~asf ~i% xfcfxfbkfn cxig% ix isfx w`ak` {vk` jb

    ab{~jb~ wiven xfgjab ~`f {jgf f~k" `a{ ihdfk~aib a{ sjean" @iwfsfx% j{ a~ j||eaf{ ~i ~`f `q|i~`f~akje kj{f

    vbnfx absf{~aoj~aib% a~ {`iven je{i hf kefjx ~`j~ a~ a{ bi~ jbq gixf j||eakjhef ix xfefsjb~ ~`jb hfabo j

    {fgjb~akje |xihefg ic ~`f wixn{ ibf fg|eiq{ ~i hf{~ ~xq ~i |v~ jkxi{{ j |iab~ jbn j{ hfabo j kib~xjnak~aib

    ab ~fxg{% xj~`fx ~`jb |fx~jababo ~i jbq kib~xjnak~aib ab ~`f jk~vje (ab ~`a{ kj{f% `q|i~`f~akje! |`q{ak{

    absiesfn" Ibf kiven kfx~jabeq je{i j{{fx~ ~`j~ ~`fxf wfxf bi ab~fxsje ab ~agf% jbn {i ac ibf wa{`f{% ~`fxf

    wfxf j |xfka{f {~j~ak ab{~jb~ vbnfxeqabo j |`q{akje |xikf{{% wa~`iv~ a~ hfabo nf|fbnfb~ ib ~`fxf jk~vjeeq

    hfabo ab~fxsje4 j{ a{ ~`f kj{f wa~` ~`f `q|i~`f~akje jh{fbkf ic gj{{ jbn fbfxoq% jbn ~`f xf{ve~abo jh{fbkf

    ic ; {|j~aje nagfb{aib{"

    A~ a{ je{i ag|ix~jb~ ~i bi~f ~`a{ kibkev{aib a{ kig|j~ahef wa~` ~`f nqbjgakje gjbbfx ab w`ak` ~agf

    fb~fx{ ~`f fzvj~aib{% ofigf~xq jbn nf{kxa|~aib ic ~`f vbasfx{f ab Jehfx~ Fab{~fab{ ~`fixaf{% {|fkaje jbn

    ofbfxje xfej~asa~q"(1!

    A~ a{ xfej~asf ab~fxsje j{ gfj{vxfn hq jee keikm{ (w`f~`fx naoa~je% j~igak% eao`~%

    haieioakje ix i~`fx! ~`j~ a{ wjx|fn jbn gv~jhef j~ xfej~asa{~ak sfeika~af{ jbn ab ~`f {|j~aje sakaba~q ic

    oxjsa~q% bi~ jbq |`q{akje |xioxf{{aib ic ~agf" Abnffn% a~ kiven hf {jan a~ a{ nvf ~i ~`fxf bi~ hfabo j

    |`q{akje ab{~jb~ jbn |`q{akje |xioxf{{aib ic ~agf% ~`j~ ~`f kib~abva~q% |xi|joj~aib jbn kib{~jb~ xfej~asf

    sfeika~q ic fefk~xigjobf~ak xjnaj~aib% jbn ~`v{% j wjx|abo ic xfej~asf nvxj~aib a{ |i{{ahef ab ~`f cax{~

    ab{~jbkf" [vh{fzvfb~eq% ~`a{ kibkev{aib a{ je{i kib{a{~fb~ jbn kig|j~ahef wa~` Gabmiw{ma {|jkf'~agf4

    ~agf j{ j nagfb{aibje xf|xf{fb~j~aib j||eaf{ ~i ~`f vbasfx{f4 ~`f vbasfx{f a{ bi~ ab ~agf" Eamfwa{f% {|jkf

    a{ ab ~`f vbasfx{f4 ~`f vbasfx{f a{ bi~ ab j xfoaib ic {|jkf" ^agf (~`f nagfb{aib! ~jmf{ {|jkf% jbn {|jkf

    (~`f nagfb{aib{! ~jmf ~agf% jbn {|jkf'~agf a{ abnf|fbnfb~ jbn vbjccfk~fn hq ~`f jh{fbkf ic j |`q{akje

    ab{~jb~ jbn |`q{akje |xioxf{{aib ic ~agf" ^i ~`f kib~xjxq% j{ gjbq xfjnfx{ waee hf jwjxf% Gabmiw{ma

    {|jkf'~agf je{i aeev{~xj~f{ ~agf ~i hf j nfxasj~asf bi~aib% bi~ jk~vjeeq ceiwabo j{ ivx {vhdfk~asf

    kib{kaiv{ |fxkf|~aib{ ic~fb {ffg ~i {voof{~"

    ;" ^agf jbn Kej{{akje jbn Zvjb~vg Gfk`jbak{4 Abnf~fxgabjkq s{" Na{kib~abva~q

    ^`f jh{fbkf ic j |xfka{f {~j~ak ab{~jb~ ab ~agf vbnfxeqabo j nqbjgakje |`q{akje |xikf{{ gfjb{ ~`j~ j

    hinq (gakxi jbn gjkxi{ki|ak! ab xfej~asf gi~aib nif{ bi~ `jsf j |xfka{feq nf~fxgabfn xfej~asf |i{a~aib j~

    jbq ~agf% jbn ~`j~ jee |`q{akje gjoba~vnf{ jxf bi~ |xfka{feq nf~fxgabfn j~ jbq ~agf% je~`ivo` wa~` ~`f

    |jxjgf~fx jbn hivbnjxq ic ~`fax xf{|fk~asf |i{a~aib jbn gjoba~vnf hfabo nf~fxgabjhef v| ~i ~`f eaga~{ ic

    |i{{ahef gfj{vxfgfb~ j{ {~j~fn hq ~`f zvjb~vg `q|i~`f{a{(:!

    % hv~ wa~` ~`a{ abnf~fxgabjkq ab |xfka{f sjevf

    bi~ hfabo j kib{fzvfbkf ic ` jbn zvjb~vg vbkfx~jab~q" ^`f xfj{ib w`q kjb hf nfgib{~xj~fn hq

    fg|eiqabo Jehfx~ Fab{~fab{ cjgiv{ :1

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    4/7

    >

    ~`f ~xjab |j{{f{ ~`a{ |iab~ nvxabo ~`f gfj{vxfn ~agf ab~fxsje ic :

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    5/7

    6

    (G:g

    8)x

    8!% cixkf C7gj% {i bfa~`fx a{ |xf{{vxf |7C)J% fefk~xak cafen {~xfbo~` F7C)Z% ag|ve{f C~7gs%

    ~ixzvf ^7Cp% wixm_7C{% Cn% {i bfa~`fx a{ |iwfx\7_)~%F)~% Cs% SAf~k" Acg%ojbn xfej~asf |i{a~aib `jxf bi~ |xfka{feq nf~fxgabfn% bfa~`fx a{ oxjsa~j~aibje |i~fb~aje fbfxoqF

    |7go`% jbn ab kibdvbk~aib wa~` %

    jkkixnabo ~i Fab{~fab{ ofbfxje ~`fixq ic xfej~asa~q% bfa~`fx a{ j |xfka{f ab~fxsje ic ~agf j{ abnakj~fn hq j

    keikm vbnfx ~`f abcevfbkf ic oxjsa~q% xfej~asf ~i jbi~`fx keikm" Gixfisfx% acs%%Fjbn g jxf bi~ |xfka{feq

    nf~fxgabfn% bfa~`fx a{ jbq |`q{akje gjoba~vnf% jbn j{ ~`a{ abkevnf{ oxjsa~q% ~`a{ je{i j||eaf{ ~i ~`f sfxq{~xvk~vxf ic {|jkf'~agf" Kxvkajeeq `iwfsfx% ~`a{ vbasfx{je abnf~fxgabjkq ab|xfka{f |`q{akje gjoba~vnf a{

    bi~ j kib{fzvfbkf ic` jbn zvjb~vg vbkfx~jab~q"

    ;": Bfw~ib jbn Tfbi ic Fefj{ Gi~aib jbn Abcaba~q \jxjnipf{

    ^`f ibeq {a~vj~aib ab w`ak` j |`q{akje gjoba~vnf wiven hf |xfka{feq nf~fxgabfn wj{ ac ~`fxf wfxf j

    |xfka{f {~j~ak ab{~jb~ ab ~agf vbnfxeqabo j nqbjgakje |`q{akje |xikf{{ jbn j{ j kib{fzvfbkf j |`q{akje

    {q{~fg wfxf cxitfb {~j~ak j~ ~`j~ ab{~jb~" Ab {vk` j {q{~fg jb abnasa{ahef gj~`fgj~akje ~agf sjevf% f"o" 8{%

    wiven kixxfk~eq xf|xf{fb~ j |xfka{f {~j~ak ab{~jb~ ab ~agf% xj~`fx ~`jb jb ab~fxsje ab ~agf (j{ a~ a{ ofbfxjeeq

    j{{vgfn ~i ab ~`f kib~fp~ ic kjekvev{% jbn ~xjkfjhef hjkm ~i ~`f eamf{ ic Ojeaefi% jbn gixf {|fkacakjeeq%

    Bfw~ib% ~`v{ ovjxjb~ffabo jh{iev~f |xfka{fbf{{ ab ~`fixf~akje kjekvej~aib{ hfcixf ~`f cjk~ a"f" n)~7s!"

    Cix~vbj~feq ~`a{ a{ bi~ ~`f kj{f% j{ ~`a{ {~j~ak cxjgf wiven abkevnf ~`f fb~axf vbasfx{f" Gixfisfx% ~`f

    vbasfx{f{ aba~aje fpa{~fbkf jbn |xioxf{{aib ~`xivo` ~agf wiven bi~ hf |i{{ahef" ^`jbmcveeq% a~ {ffg{

    bj~vxf `j{ wa{feq ~xjnfn kfx~jab~q cix kib~abva~q"8

    Jbi~`fx wjq ~i eiim j~ ~`a{ a{ ac j |`q{akje sjevf wfxf |xfka{feq nf~fxgabfn j~ j |xfka{f ab{~jb~ ab ~agf%

    a~ kiven bfsfx k`jbof% j{ a~ wiven cax{~eq `jsf ~i |xikffn ~i jbi~`fx |xfka{f sjevf" Hv~ hfcixf a~ kiven ni

    ~`a{% a~ wiven cax{~eq `jsf ~i |xikffn ~i `jec ic ~`j~ sjevf" Hv~ hfcixf a~ kiven ni ~`a{% a~ wiven `jsf ~i

    |xikffn ~i `jec ic ~`j~ sjevf jojab% jbn {i ib% jbn {i ib% ~i abcaba~vg" ^`v{% ab ~`a{ gjbbfx a~ kjb hf

    nfgib{~xj~fn ~`j~ ac j |`q{akje sjevf wfxf |xfka{feq nf~fxgabfn% a~ kiven bfsfx k`jbof" ^`fxf a{ j

    bfkf{{jxq ~xjnf icc ic hf~wffb kfx~jab~q j~ j ~agf% cix kib~abva~q ~`xivo` ~agf" \efj{f bi~f ~`j~ ~`f

    fp|ejbj~aib |xisanfn `fxf jbn |xfsaiv{eq ~`xivo`iv~ ~`a{ |j|fx a{ je{i ~`f kixxfk~ {iev~aib ~i ~`f gi~aib

    jbn abcaba~q |jxjnipf{ ~`f Nak`i~igq% Jk`aeef{ jbn ~`f ^ix~ia{f% ~`f Jxxiw% jbn ~`fax i~`fx gixf ginfxb

    sjxaj~aib{% ixaoabjeeq kibkfasfn hq ~`f Oxffm gj~`fgj~akajb% Tfbi ic Fefj"(:

    ^`j~ a{% ~`fq jee `jsf ~`f

    {jgf ofbfxje {iev~aib ~`xivo` {vk` xfj{ibabo j{ `j{ hffb na{kv{{fn `fxf% jbn jxf bi~ na{~abk~ jbn

    naccfxfb~ |xihefg{ xfzvaxabo naccfxfb~ jbn na{~abk~ |xi|i{fn {iev~aib{ j{ `j{ `a{~ixakjeeq hffb j{{vgfn" ;

    ;"8 J Kib{a{~fb~ Kej{{akje jbn Zvjb~vg Gfk`jbakje Nf{kxa|~aib

    Ab xfej~aib ~i zvjb~vg gfk`jbak{ ~`fb% ~`a{ kibkev{aib aeev{~xj~f{ ~`j~ ~`f xfej~aib{`a| hf~wffb `%

    wjsf'|jx~akef nvjea~q% zvjb~vg fb~jboefgfb~ f~k% jbn ~`f kib{~jb~ abnf~fxgabjkq ab jee |xfka{f |`q{akje

    sjevf{ nvf ~i ~`f jh{fbkf ic j |xfka{f {~j~ak ab{~jb~ ab ~agf% je~`ivo` abna{~abova{`jhef cix jee |xjk~akje

    |vx|i{f{ w`fb zvjb~acqabo ~`f isfxjee {~j~f ic j |`q{akje {q{~fg j~ j gakxi{ki|ak efsfe% jxf ab cjk~

    {f|jxj~f jbn na{~abk~ sjxajhef{% |ejqabo zva~f {f|jxj~f jbn na{~abk~ xief{" J{ {vk`% j xfsa{fn jbn {ffgaboeq

    gixf j||xi|xaj~f nf{kxa|~aib a{4 jee |`q{akje gjoba~vnf{ jxf bi~ fsfx |xfka{feq nf~fxgabfn nvf ~i ~`f

    jh{fbkf ic j |xfka{f {~j~ak ab{~jb~ ab ~agf vbnfxeqabo j nqbjgakjeeq |`q{akje |xikf{{% je~`ivo` wa~` ~`f|jxjgf~fx jbn hivbnjxq ic ~`f ~`fax xf{|fk~asf sjevf hfabo nf~fxgabjhef v| ~i ~`f eaga~{ ic |i{{ahef

    gfj{vxfgfb~ j{ {~j~fn hq ~`f zvjb~vg `q|i~`f{a{ jbn @fa{fbhfxo{ vbkfx~jab~q |xabka|ef%(:!

    hv~ wa~` ~`a{

    abnf~fxgabjkq ab |xfka{f gjoba~vnf bi~ hfabo j kib{fzvfbkf ic` jbn zvjb~vg vbkfx~jab~q" Cieeiwabo

    wa~` ~`f ab~xinvk~aib ic vbkfx~jab~q jbn)ix {~j~a{~ak{ ab zvjb~vg sjevf{ nvf ~i `% wjsf'|jx~akef nvjea~q%

    zvjb~vg fb~jboefgfb~ f~k" ^`a{ aeev{~xj~f{ ~`j~ ab xfej~aib ~i abnf~fxgabjkq ab |xfka{f |`q{akje gjoba~vnf%

    ~`fxf a{ bi~ j na{~abk~aib hf~wffb ~`f ejxof jbn gjkxi{ki|ak jbn ~`f gakxi{ki|ak xfjeg ic zvjb~vg

    gfk`jbak{% ab ~`f {fb{f ~`j~ hi~`% ~`f gakxi jbn gjkxi{ki|ak% jxf naxfk~eq {vhdfk~ ~i ab`fxfb~

    abnf~fxgabjkq% xj~`fx ~`jb dv{~ j kj{f ic ~`f cixgfx vbnfxeqabo jbn kib~xahv~abo ~i ~`f ej~~fx" Ab ~`a{

    xfojxn% ~`fq jxf hi~` jk~vjeeq j |jx~ ic ~`f {jgf |jxkfe% hfabo abfp~xakjheq eabmfn"

    8 \efj{f bi~f ~`j~ ~`fxf a{ ihsaiv{eq bi cjve~ ab ~`f jk~vje gj~`fgj~ak{ `fxf% hv~ xj~`fx ab ~`f `a{~ixakje j{{vg|~aib

    vbnfxeqabo ~`fg xfojxnabo nf~fxgabfn |`q{akje gjoba~vnf{ j~ j ~agf jbn)ix ab{~jb~"; Cix j nf~jaefn fp|ejbj~aib ic Tfbi{ |jxjnipf{ jbn ~`fax xf{iev~aib% |efj{f {ff% Eqbn{% \" Tfbi{ \jxjnipf{4 J^agfeq [iev~aib" \xf{fb~eq vbnfx kib{anfxj~aib wa~` \`aei{i| q ic [kafbkf"

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    6/7

    3

    A wiven {voof{~ ~`j~ ~`fxf a{ |i{{aheq gvk` gixf ~i hf oefjbfn cxig ~`f kibbfk~aib hf~wffb zvjb~vg

    |`q{ak{ jbn ~`f ab`fxfb~ bffn cix |`q{akje kib~abva~q% jbn fsfb oi j{ cjx ~i {|fkvej~f ~`j~ ~`f nf|fbnfb~

    xfej~aib{`a| gjq hf ~`f vbnfxeqabo fp|ejbj~aib cix zvjb~vg dvg|abo jbn wa~` {~j~ak abnasa{ahef

    gj~`fgj~akje ~agf sjevf{ naxfk~eq xfej~fn ~i ~`f |xikf{{ ic zvjb~vg kieej|{f" ^agf waee ~fee">

    >" ^agf jbn Zvjb~vg Ki{gieioq

    Nf~jaefn kjekvej~aib{ `jsf hffb kig|ef~fn ab ~`f ~`fixf~akje cafen ic zvjb~vg ki{gieioq ab jb j~~fg|~

    ~i fevkanj~f `iw ~agf gjq `jsf fgfxofn jbn kibofjefn iv~ ic ~`f zvjb~vg cijg jbn `ao`eq

    kib~ix~fn {|jkf'~agf ofigf~xq{ jbn k`ji~ak kibna~aib{ |xfkfnabo \ejbkm {kjef (O )k;!:)8

    dv{~ jc~fx ~`f

    hao hjbo (bfw abcej~aibjxq ginfe!"(8'?!

    Gixf {|fkacakjeeq% a~ `j{ hffb ~fb~j~asfeq `q|i~`f{atfn ~`j~ a~

    wiven xfzvaxf |jx~akvejxeq {|fkaje aba~aje zvjb~vg kibcaovxj~aib{ cix ~`f kxq{~jeeatj~aib ic ~agf jbn ~`f

    fgfxofbkf ic gjkxi{ki|ak (bib'zvjb~vg! |`fbigfbj ~i hf |i{{ahef"(8'?!

    ^`a{ kibkev{aib `iwfsfx%

    aeev{~xj~f{ ~`j~ ~fg|ixjea~q wivenb~ bffn ~i fgfxof j~ jee% hv~ wiven hf |xf{fb~ jbn bj~vxjeeq ab`fxfb~

    ab |xjk~akjeeq jee aba~aje zvjb~vg {~j~f{ jbn kibcaovxj~aib{% xj~`fx ~`jb j {|fkacak cfw% ix {|fkaje ibf% jbn

    xfojxnef{{ ic `iw gakxi{ki|ak ~`f {kjef"

    J{ {iib j{ ~`fxf a{ jbq gjoba~vnf ic {|jkf (j{ j |xi|fx~q ic gj{{'fbfxoq!% qiv bj~vxjeeq of~ ~`f ~agf

    nagfb{aib hq nfcjve~" Ac ~`fxf a{ bi gj{{'fbfxoq% ~`fxf a{ bi {|jkf'~agf" Hfkjv{f ~`f xfj{ib kib~abva~q a{

    |i{{ahef a{ nvf ~i ~`fxf bi~ hfabo j |`q{akje ab{~jb~ jbn |`q{akje |xioxf{{aib ic ~agf% a~ a{ bi~ bfkf{{jxq

    cix ~agf ~i fgfxof ab ~`f cax{~ ab{~jbkf" ^`f gixf j||xi|xaj~f zvf{~aib xfgjab{4 `iw kjb gj{{'fbfxoq%

    jbn j{ {vk`% {|jkf'~agf fgfxof9% {agve~jbfiv{eq hxaboabo kib~abva~q wa~` a~ nvf ~i ~`f jh{fbkf ic j

    |`q{akje ab{~jb~ jbn |`q{akje |xioxf{{aib ic ~agf% a"f" ~fg|ixjea~q ix kib~abva~q wiven ibeq hf xfzvaxfn ~i

    fgfxof cxig |i{{ahef aba~aje zvjb~vg kibcaovxj~aib{% {~j~f{ ix `a{~ixaf{ ab w`ak` ~agf wfxf j |`q{akje

    zvjb~a~q"

    >": Agjoabjxq ^agf

    ^`a{ kibkev{aib a{ je{i bi~ kib{a{~fb~ wa~` ~`f ki{gieioakje |xi|i{je ic Agjoabjxq ^agf jbn bi

    hivbnjxq kibna~aib%(8% ;% 6'?!

    hi~`% j{ j kib{fzvfbkf ic ~`f jhisf kib{anfxj~aib% jbn {fkibneq% hfkjv{f a~ a{~`f xfej~asf ixnfx ic fsfb~{ ~`j~ a{ xfefsjb~% bi~ ~`f naxfk~aib ic ~agf a~{fec" A~ a{ bi~ |i{{ahef ~i j{{fx~ v{abo

    j ginfe ic ~`f vbasfx{f ~`j~ abkevnf{ j nf{kxa|~aib ic ~`f {vg isfx `a{~ixaf{ ix |j~` ab~foxje{ ic ~`f jk~vje

    {~xvk~vxf ic {|jkf'~agf% ~`j~ ~agf oif{ ab jbq naxfk~aib% ef~ jeibf j~ 1< nfoxff{ ~i xfje ~agf ix eabfjx ~agf

    jbn ~jmf{ ib {igf ic ~`f |xi|fx~af{% ix a{ anfb~akje ~i ~`j~ ic {|j~aje nagfb{aib{ j~ j||xipagj~feq \ejbkm

    {kjef (O`)k;!

    :)8r :;{% w`aef {~aee hfabo hivbnfn hq ~`f hao hjbo (ix |i{{ahef hao kxvbk`% ab j

    biw {ffgaboeq ih{ief~f kei{fn vbasfx{f! {abovejxa~af{ ab xfje ix eabfjx ~agf% hv~ `jsabo bi hivbnjxaf{ ab

    agjoabjxq ~agf" Bfa~`fx xfje bix agjoabjxq ~agf fpa{~ ab j kib{a{~fb~ |`q{akje nf{kxa|~aib% j{ ~agf nif{

    bi~ oi ab jbq naxfk~aib"

    A~ a{ ~`f xfej~asf ixnfx ic fsfb~{ ~`j~ a{ xfefsjb~% bi~ ~`f naxfk~aib ic ~agf a~{fec" ^`f ixnfx ic j {fzvfbkf

    ic fsfb~{ kjb ~jmf |ejkf ab fa~`fx ibf ixnfx xfej~asf ~i a~{ xfsfx{f ixnfx% ix ab ~`f xfsfx{f ixnfx% xfej~asf ~i

    ~`f cax{~" A~ a{ bi~ |i{{ahef cix ~`f ixnfx ic j {fzvfbkf ic fsfb~{ ~i hf agjoabjxq ab ~`f gj~`fgj~akje {fb{f

    j{ a~ a{ eioakjeeq kib~xjnak~ixq jbn gfjbaboef{{ ~i nf{kxahf ~`f ixnfx ic j {fzvfbkf ic fsfb~{ j{ hfabo j~xao`~ jboef{ xfej~asf ~i ~`j~ ic jbi~`fx {fzvfbkf ic fsfb~{" ^`f i||i{a~f ~i ~`a{ kiven hf |i{a~fn cix ~`f

    > Kib{anfxj~aib{ ~i ni wa~` ~agf na{kib~abva~q |xf{fb~fn ab ~`a{ |j|fx je{i `jsf xfej~aib ~i {agaejx absf{~aoj~aib{|fxcixgfn ab ~`f cxjgfwixm ic |'jnak gj~`fgj~akje |`q{ak{" Hq v{abo |'jnak bvghfx{% ab{~fjn ic kib~abviv{ xfjebvghfx{% wf kjb of~ ginfe{ (wa~` |'jnak bibkib~abviv{ ~agf! ~`j~ `jsf hi~` kej{{akje jbn zvjb~vg cfj~vxf{" \efj{fxfcfx ~i4

    J" Q" M`xfbbamis% Bib'Jxk`agfnfjb jbjeq{a{4zvjb~vg |jxjnipf{% nqbjgakje {q{~fg{ jbn haieioakje ginfe{"Mevwfx Jkjn" \vhea{`fx{% Nixnxf`~% (:11?!" F{|fkajeeq K`j|~fx >" jbn |o" :3>':33 ib @fa{fbhfxo vbkfx~jab~q

    xfej~aib"[" Jehfsfxai jbn J" Q" M`xfbbamis% Xf|xf{fb~j~aib ic ~`f _fqe oxiv| ab {|jkf{ ic {zvjxf ab~foxjhef cvbk~aib{ wa~`xf{|fk~ ~i |'jnak sjevfn Ojv{{ajb na{~xahv~aib{" D" ic \`q{" J% s" 81% |o" 66:6'668?% (:113!"

    J" Q" M`xfbbamis% Ve~xjgf~xak @aehfx~ {|jkf xf|xf{fb~j~aib ic zvjb~vg gfk`jbak{ wa~` j caba~f fpjk~bf{{" Civbn" ic\`q{ak{% 83% Bi" 0% :

  • 7/30/2019 Lynds, Peter- Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity

    7/7

    ?

    xfej~asf {|j~aje naxfk~aib ic fsfb~{% hv~ fsfb~{ ~jmf |ejkf j~ xao`~ jboef{ xfej~asf ~i i~`fx{ ib j xfovejx

    hj{a{% jbn ~`a{ `j{ bi~`abo ~i ni wa~` ~`fax naxfk~aib% ix ~`f naxfk~aib ic ~agf hfkigabo agjoabjxq"

    ^`f cjk~ ~`j~ agjoabjxq bvghfx{ j||fjx w`fb kig|v~abo {|jkf'~agf ab~fxsje{ jbn |j~` ab~foxje{ nif{

    bi~ cjkaea~j~f ~`j~ w`fb gve~a|eafn hq a% ~`j~ ~agf ab~fxsje{ hfkigf hj{akjeeq anfb~akje ~i nagfb{aib{ ic

    {|jkf" Agjoabjxq bvghfx{ {`iw v| ab {|jkf'~agf ab~fxsje{ w`fb {|jkf jbn ~agf {f|jxj~aib{ jxf kighabfn

    j~ bfjx ~`f {|ffn ic eao`~% jbn {|j~aje {f|jxj~aib{ jxf {gjee xfej~asf ~i ~agf ab~fxsje{" _`j~ ~`a{ aeev{~xj~f{

    a{ ~`j~ je~`ivo` {|jkf jbn ~agf jxf ab~fxwisfb ab Gabmiw{ma {|jkf'~agf% jbn ~agf a{ ~`f civx~`nagfb{aib% ~agf a{ bi~ j {|j~aje nagfb{aib4 ~agf a{ jewjq{ ~agf% jbn {|jkf a{ jewjq{ {|jkf% j{ ~`i{f a{

    mff| {`iwabo v{" ^`fxf a{ jewjq{ j naccfxfbkf" Ac ~`fxf a{ jbq nfoxff ic {|jkf% xfojxnef{{ ic `iw

    gakxi{ki|ak% ~`fxf wiven j||fjx ~i hf ab`fxfb~ kib~abva~q a"f" ab~fxsje ab ~agf"

    6" K`xibib{

    K`xibib{% |xi|i{fn ~`fixf~akje |jx~akef{ ix j~ig{ ic abnasa{ahef ab~fxsje{ ic ~agf%(8% 0!

    jxf je{i bi~kig|j~ahef wa~` j kib{a{~fb~ |`q{akje nf{kxa|~aib" ^`fxf a{ bi~ j bffn cix zvjb~vg ix j~igak abnasa{ahef~agf i|fxj~ix{ ~i {~a~k` gakxi{ki|ak fsfb~{ ~iof~`fx ~i cjkaea~j~f |`q{akje kib~abva~q% j{ ~`a{ isfxjee

    kibkev{aib aeev{~xj~f{ ~`j~ ~`f sfxq xfj{ib fsfb~{ jxf kib~abviv{ ab ~`f cax{~ ab{~jbkf a{ nvf ~i ~`fxf bi~hfabo jb j~ig ix zvjb~vg ic ~agf" [ag|eq% ac ~`fxf wfxf% |`q{akje kib~abva~q% gi~aib jbn ~agf (xfej~asf

    ab~fxsje! wiven bi~ hf |i{{ahef"

    3" Kibkev{aib

    Ab {vggjxq% a~ wj{ {`iwb ~`fxf a{ j bfkf{{jxq ~xjnf icc ic jee |xfka{feq nf~fxgabfn |`q{akjegjoba~vnf{ jbn sjevf{ j~ j ~agf% cix ~`fax kib~abva~q ~`xivo` ~agf% je~`ivo` wa~` ~`f |jxjgf~fx jbn

    hivbnjxq ic ~`fax xf{|fk~asf gjoba~vnf jbn sjevf hfabo nf~fxgabjhef v| ~i ~`f eaga~{ ic |i{{ahef

    gfj{vxfgfb~ j{ nf{kxahfn hq ~`f zvjb~vg `q|i~`f{a{%(:!

    hv~ wa~` ~`a{ abnf~fxgabjkq ab |xfka{f sjevf bi~

    hfabo j kib{fzvfbkf ic` jbn zvjb~vg vbkfx~jab~q" ^`a{ aeev{~xj~fn ~`j~ ab xfej~aib ~i abnf~fxgabjkq ab|xfka{f |`q{akje gjoba~vnf% ~`f gjkxi jbn gakxi{ki|ak jxf abfp~xakjheq eabmfn% xj~`fx ~`jb hfabo j

    sjxajhef ibeq naxfk~eq j{{ikaj~fn wa~` ~`f zvjb~vg wixen" ^`f fp|ejbj~aib |xisanfn wj{ je{i {`iwb ~i hf

    ~`f kixxfk~ {iev~aib ~i ~`f gi~aib jbn abcaba~q |jxjnipf{% fpkevnabo ~`f [~jnavg% ixaoabjeeq kibkfasfn hq~`f jbkafb~ Oxffm gj~`fgj~akajb% Tfbi ic Fefj"

    (1!A~ a{ bi~ bfkf{{jxq cix ~agf ~i fgfxof cxig ~`f

    zvjb~vg cijg |xf{fb~ dv{~ jc~fx ~`f hao hjbo j~ j||xipagj~feq (O`)k;!

    :)8{kjef%

    (8'?!jbn ~`f |xi|i{je{ ic

    Agjoabjxq ^agf%(8% ;% 6'?!

    jbn K`xibib{%(8% 0!

    `jsf hffb {`iwb ~i hf abkig|j~ahef wa~` j kib{a{~fb~|`q{akje nf{kxa|~aib% jbn wiven j||fjx ~i hf {v|fx{fnfn ib j ~`fixf~akje hj{a{"

    Kibsfx{j~aib{ jbn kixxf{|ibnfbkf wa~`% jbn fbkivxjoabo wixn{ xfkfasfn cxig D" J" _`ffefx ic \xabkf~ib% D" D" K"

    [gjx~ jbn @" \xakf ic Jv{~xjeaj% K" Oxao{ib ic Bfw Tfjejbn% J" \" Cxfbk` ic GA^% jbn _" H" Qaoa~it ic Kjbjnj% j{

    wfee j{ cxig ~`f ~wi sfxq `fe|cve vbjbagiv{ xfcfxff{ ic ~`a{ |j|fx% jxf gi{~ oxj~fcveeq jkmbiwefnofn"

    Xfcfxfbkf{

    :" D" J" _`ffefx jbn _" @" Tvxfkm (Fn{"!% Zvjb~vg ^`fixq jbn Gfj{vxfgfb~" \xabkf~ib Vbasfx{a~q

    \xf{{ (:10;!"

    8" \" K" _" Njsaf{%Jhiv~ ^agf4 Fab{~fab{ Vbcaba{`fn Xfsiev~aib" Samabo% Eibnib% (:116!"

    ;" [" _" @jwmabo% Zvjb~vg Ki{gieioq" Ab ;