H APXH THE E/\AXIETHE APA>HE

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1 Keg6lcrto 19 H APXH THE E/\AXIETHE APA>HE 19.1 Mrq er6u<4 6rolel4 - o1e66v roro 16( Mio olpeioo4 nou npoor694xe pero 14 6roLe( I I 19.1 Mto etotxri Otdr.Lelq - o1e66v xcrtd 1,6[4' "'Orov n{yorvo oro Auxero, o 6ooxo-L6g pou mq quorxq - tou onoiou to ovopo rpov K0p1oS Bader - 'pe qrirvole pro pepo peto to pooqpo xor pou 'Feynrnan, eine, <poiveror na6 popr6ool xor yro our6 96lo vo. oou rro xdrr ev6roqipov. Ko1 Fou eine xcn nou to pprlxo oniorsuro ouvopnoorrx6 Kor rrou ro ppior,: on6 r6te xor p61pr o{pepo to i6ro yoqreunx6. Duv40cog, xooe qopo nou dplopor oltqr6tr,:nog pe xonoro np66lr1po, opxi(o vo epyo(opor nqvo oe our6. A-Lla out{ q qopo, otov opxroo vo npoerorpo(opor yro ouul rq 6rolel4, 6mooo rov eaut6 pou vo 6ivsr mo nolu dpqoorl oe xou 6roqopeur6 ono out6 yro to onoio npoxeror vo oog prl4or,l. Kor 6ror, owi vo ov4ou14oo yro ro ncog 9o noer q drotrelq epn.tr do pe evo xorvoupro np66lqpo. To owrxeipevo cutqg rrlg Orolelqg eivor q oplq qg slolrorrlg 6pooq9. rto en6pevo xeqoloro 6ev doptrintor dno ro ulft6 ouuls lrls 1611<45 610L44S. q onoio oroxeuer orri.a oro vo oog "610oKeoooer"

2 334 S MIA EIAIKH AIAAEOH - DXEAON KATA AEEH "O ruprog Baderpou eine ro el49: qowooou nr,rg dlerg dvo orlpori6ro (yro nopooerypo, Fdoo oe dvo popuuro ne6io) nou lexrvd ono xonou xor xrveiror e.leu epo npog xonoro o-l.lo orlpeio' 6qlo64 ro nerog xor our6 op4xo oxo.lou0ei ovo6xrl nopeio evrir or1 ouv6xero ndqter npog to xoro: no vq erooal ro o\rrkeiuevo ono rrlv opxrkrl or4v relrxrl rou 9do4 np6ner vo nepooer xonorog 1p6vog. Tripo, $erbpqoe Fro 6roQoperrKrl ylo vo noer m4v relrx4 rou, 96o11 ro(iderpe xonr,4 6tor q-l-lo om6oo, 6qrooe exei xovowog oxpr6<bg rov i6ro Xp6vo. Kor ouvexroe l,iyovrog: eov unoloyioerg rqv xrvqux4 evdpyero yro xooe Xpovrxrl orrypr; tqg Oto6popqg, oqorp6oerg t1 6uvoprxrl ev6pyero xor oloxlqprboerg yro olo ro xpovrxo 6rooqpo nou Orqpxqoe 4 xiv4o4, 9o 6ronrotriroerg nog o opt0p6g nou noipverg eivor peyo-lurepog on6 our6v nou ouoxeri(eror pe r4v npollonxrl xivr;oq. "Me ol-lo l6yro, or v6por rou Neurovo 0o pnopouoov vq 6rqrun<,:0ouv 6p or1 popqq F = rrta ol.}.o leyowog on: q pdoq xrvqnxrl evdpyero elonoupev4 xoro t4 pdoq 0uvoprxrl ev6pyero eivor q prxp6rep4 6uvoq yro rq 6ro6popq nou oxo.lou0ei 6vo ortrxeipevo yro vo ro(r6dq.rer ono 6vo oqpsio rou yirpou oe xonoro o,l-lo. "Aoe pr vo oou {qyqorl xonrlg xo-lurepo n t4v nepinrr,rorl rou popurrxou ne6iou, eqv ro oopori6ro xrveiror xoro p4xog xonorog 6ro6pop4g:(f) (9o nepropr.oroupe yro tqv rirpo orq povo6roororrl nepirrroorl xor 9o pc.lerr;ooupe dvo oripo nou xrveitor npog to novr,r Kqr npos rq xoto ol-lo 6Xr npog to n-loyro) 6nou.r eivor ro irgog on6 ro 66oQoS, rl xrv4nx4 rou ev6pyero 9o eivor, 1 r / r.\t iaq pt jm(dx ldt)' rvcb 11 Duvoprxrl rou sv6pyero oe xo0e xpovrxq mrypq $o eivor ioq ps /t1gx. Tcbpo. noipvr,r r4v xrvqtrxq evepyero peiov rq Ouvopxq evepyero yro xooe Xpovrx4 orrlprl xoro p4xog tr;g

3 I I Oro6poprlg <or oi.oxlrlp6vo (,ts rpos ro Xpovo xor ono pio opxrxq p61pr pio relrxq lpovrxq onypq. AS unoeeooupe nog u1 lpovuq or1yf4 h opxioope vo xrvoupoore ono xonoto ur.pog xor rrroe rrl Xpovxi or1.!?4 12 otcporqoope vo xrvoupome exowog rprooer oe xonoro o_l_lo urpog. H APXH THE EAAXIDTHD APAEHD 339 t I '"fore ro oloxl4popq yro ro onoio oou pti.or,t eivor to [,"[l*(#)' -*g,,]a' H npolgonxq xivqoq eivor xonoro ei6og xopmilqg - eov rq oxe6roooupe ouvopu;oer rou Xp6vou eivor pio nopo6o.lr'1 - xor 6tver o'ro oloxlrlpclpo xonoro ouyrerprp6vq npr1. Atr-lo 9o pnopouoops va cpautamo'ys xonoro oltr4 xivqoq, og noupe yro nopooerypo, nr,rg ro oripo opxrxo ov66r1xe nolu qqlo xor orl ouvexero opxtoe vo oveboxore6oiver pe xonoro nepiepyo rp6no Mnopoupe vo uno.loyiooupe r4v xrv4rrx4 evipyero peiov rq 6uvollxr; evdpyero xor vo oloxl.qprir ooupe xoro p4r<og prog rerorog Oro6pop1g... 4 roro pqxog onotog otr-lqg 6ro0popqg 96.Loupe. To 9oupo eivor ngrs ll npoytrrorxq Oro6popq nou 9o oxo.louoqoet relrxo ro oripo, eivor exeivq yro r4v onoio q nf{ ourou rou oloxlqpcirporog eivor 11 eloxrorq. 'Ag npoonoorlooupe vo 6oupe eov or,tog eivor eror. ApXxo og 9er,lpqooupe rqv nepinrooq ev6g eleuoepou oopon6iou nou Oev 6ro0erer xooof,.ou Ouvoprxrl evepyero. T6re o rov6vog pog leer nog

4 340 Q MIA EIAIKH AIAAEEH. DXEAON KATA AEEH Ko06S Fero6oivoup qn6 ro 6vo orlfeio oto olio Faoo o Kqnolo XpovlK6 otoorrlpo, rl Kwnrlxq svepyalq eivor eldlm4 xor enopdvr,rg ro oopod6ro 9o npinei vo xrveitor pe xonoro orooeprl tolur4ro (yvopi(oupe nog our4 eivor 4 ooorl onovrqoq' 64lo0q to vo xleitcn to oripo pe otooepq topirrlto). A.l-lo yrori roluer xon riroro: Dner0q eov ro ooporibro r<rvourov pe onoro6qnore ollo tp6no, or tolur4reg omore 9o qtov ugrll6tepeg xor o.llote loprll6repeg os ox6oq pa 14 p6oq ro1ut4to. H p6o4 toxur4ro 9o eivor 4 i6ro oe xo0e nepimt':oq, enerdq ro o6lro 9o np6ner vo rolr66get on6 "e6dr" eog "exei" pdoo oro i6ro Xpovrx6 0rootrlpo. "Og 6vo nopo6erypo, 9uirpqoe ncog np6ner va lexrvqoerg ono e6rir Kot vo nqs oto cloleio pe ro outoxivqro pdoo oe 6vo ouyxexprp6vo lpovrxo 6roor4pq. Aur6 pnopeig vo ro xoverg pe nolloug rp6noug: Mnopeig oulv opxq vo emroluverg oov rpem6g xor peto vo em6po6uverg not6wog ro <ppdv o1e6ov pdxpr to dppo, pnopeis vo rolrodrperg pe orooepr] to1pr4to, oplrxo vo xwq0ei5 npog to nior,:, uorepo npog ro epnp6s, K-o.K. De xo0e nepirnoorl ro hrouflo eivor nr,rg q p6o4 roxurqro 9o npener rpuorxo vo eivor iorl pe tq ouvolrxrl on6oroo4 nou 6r6vuoeg 6ro to lpovrxo 6root4po nou rolibsrpsg. A-llo eov eo0 dkoveg orr64nore ol.l.o on6 to vo tp6letg pe ouoep4 tolurqto, rote peprxig rpop69 n4yorveg nro opyd evrb o-l-leg rpopdg nqyorveg mo yp4yopo. AMd lepetg opog ncog ro p6oo utpayauo ronorog noo6r4tog nou petogolletol yupo ono pio pdoq np4 eivot nowote peyo.lutepo ono to rerpoyovo rou p6oou 6pou' drm, ro olox.lrlpopo tqg xrvrlnxrlg evdpyerog 9o eivor novtore peyo-lurepo eov eou ove6oxor66o(eg rrlv rolur4ro rou, nopo eov 6tpexeg novro pe t4v i6ro roxutqto. 'Eror pllnoupe nog out6 ro o.lox.lqpopo 61er tqv eloxrmq trprl tou eov 11 roxur4to eivor mo0eprl fiopie <puorxo vo unopxouv Ouvoperg) xor 4 ocoorrl 6ro6poprl eivor xonrog eror: "Tcbpo, evo or.nxeipevo nou pometor npog to novo p6oo oe 6vo popunx6 ne6io, ovedoiver ypqyopo mqv opxq xor peto enr6po6uver. Auro yivetor l6yr,: rqg unoplrlg ulg OuvoprxrlS evdpyetog xor 9o npener vo eyoupe rrlv eloxroq 6laQopa tqg xrvrfrxrlg xor 6uvoFrx45 ev6pyerog ooov oqopo rr5 p6oee rrpeg roug. Ener6q 11 buvoprxq evepyero ouloveror 6oo ugrll6repo ove6oivoupe oto ppo, 9o.Lo6oupe pio prxp6teprl 6roqopo eov pnopoupe vo nope 6oo ro 6uvoro nro ypqyopo oe o4peio nou xoporc4pi(ovror on6 peyo-l4 Ouvoprxq evdpyero. Dul ouvilero pnopoupe vo oqotpiooupe rr1 6uvoprxq on6 u1v xrvrprxq evdpyero xor vo nopoupe pio prxp6tepq p6oq trpq. 'Erot eivor nponpdrepo vo em.leloupe pio 6ro6pop4 nou vq ovegoivet npog to novo ror vo 661eror pio nolu peyolq opv4rrx4 ouveroqopo loyr,l rqg peyolqs Ouvopxrls ev6pyerog " rqv ollq nleupo p66oro, Oev pnopeire va nots unepbohxo ypqyopo q poxpro, sner6rl r6te 9o dlers nopo nolu peyolq xrv4lxq ev6pyeto' 9o npdner vo tpi(ete nolu yprlyopo yro vo ovebeite

5 H APXH TH' EAAXI'THD APADHD 347 Vrllo Kor orq ouv6xslo vo Kore6eire pdoo mo 6ro0dotpo Xpovrx6 6romqpo. 'Dtor 6ev 96Lete va nore unepgo.hxo poxpro o-l-lo vo rptooere pexpr xonoro oqpeio. Arro6errvueror.Lorn6v, nrog q Luo4 pog 9o dler vo xover pe xonoro ei6og roopponiog 6oov oqopo rqv npoonooero pog vo ortl4ooupe neproo6repq 6uvoprxq evepyero oltro pe ulv eloxroq noo6rr'1ro emnlfov xw4uxqg evepyerog' 641o011, npoono0rirvrog vo xovou'pe tq Droqopo rqg xrvqnxrlg peiov q 6uvoprx4 ev6pyero 6oo ro 6uvor6v nro F1KP4. 'Auto eivor olo ooo pou eine o 6ooxoL6g poll, ener6q qrov dvog xo-l6g Oooxo-log xor qlepe n6rs enpene vo mopotqoer vo prloer. AMo eyri pegoro 6ev l6pco n6re npdner vo oropot4oo xor dror ovd vo oos oqrlor^r pe olo 6oo oog eino vo nopolreivouv pia ev6roqepouoo nopor4p4oq, oxoneuo vo oog npoxoldoo rp6po Kol onoorpoqrl pdrirwog oos yro ns no.lunlox6rqreg tqg (o4g xor ono6erxvuor.rog oog ouro nou oog eino. To ei6og rou pooqponxot npo6.l4p.orog nou dxoupe, eivor e(orpenxo nolunloxo xor eivor xou nou 6ev 61oupe lovo6ei. E6ri 6Xoupe xonoro ouy<exprpdv4 noo6trpo nou rrlv ovolro(oupe 6paon, r\ oupgoli(oupe ps to S xor tqv opi(oups og rq Oroqopo tqg xw4txqg peiov rq 6uvoprx4 evipyero olox.lqpcopevq r,lg npog to lpovo: ctz 6pooq = 5 = (rrvrpxn cvepyrro - Ouvoprxq evepysro) nog t6oo 4 xrv4uxrl 6oo xor q 6uvo1lx4 evdpyero eivor xor or 6uo ouvoprqoerg rou 1povou. I.o xooe nroov4 6roqoperx4 6ro6poprl 9o exer, Ko Fio 8loQopsnxq uprl yro ourrl rq 6poo4. Enopdvog to 'po04ponx6 pog np66l4po eivor va npoo6ropiooupe t4v xopnul4 yro rrlv onoio ourog o opr0pog ixcr r4v r,\oxrorrl rrpr; tou. "@o neire oiyoupo: "o vor, npoxertor yro ro ouvqoropevo loyropo nou 61er vo xover pe ro peytoro xor ro unoloyioerg rq 6pooq xor pera onlo 9o 14 Oroqopioerg yro vo ppsrg ro e.lo1roro". "A-L.Lo 6eire 6pog. Etrg ouvq0ropeveg neprnrrioerg 6Xoupe pro ouvoprqoq xonorog pero6lqr4g xor npener vo ppoupe tqv n'pr1 ourrlg rqg Wta6nr94g yro r4v onoio 11 ouvoprqorl e.loxroronoreiror1 peyroronoreiror. I'o nopo6erlpo, neite nog dloupe pro po66o nou iler 9sppovOsi mo p6oo r4g xor q 9epp6r4ro 6raX6eror orov nepr6ol-trowo Xrirpo. fro xo0e orlpeio ulg po60ou ldpoupe rq Seppoxpooio xor $eloupe vo Bpoupe to oqpeio 6nou 11 $eppoxpooio eivor p yror4. A.l.l.a r<bpo, yta rcade 6n6polrn mo yrbpo dloupe 6vo opr0p6 - nou eivor xorr evre.lrig 6roqoperrx6 - xor 9eLoupe vo ppoupe q 6ro6popq yro rqv onoio out6g o opr0pog 6Xer rqv eloxrmq rrpq rou. Auro onotalei 6vo ertelrirg (eloproro x.lo6o rr,rv poo4porrxrbv. Aev exer vo xover oe rinore pe ro ouvrlorop6vo troyrop6. Eulv npo4rorrxorqro, eivor l"vroorog pe ro 6votto fttytoptog 1nta6oflr,tv.

6 9, T. MlA EIAIKH AIAAEEH - DXEAON KATA AEEH 'Ynopxouv nomo npo6lrlporo nou ouoleti(ovrot pe our6 ro ei6og tov po0qpoux6v. I.o nopo6erypo, o rux-log opi(eror og o yeoperpr<69 r6nog 6Lov rov o4peir,rv nou ppioxoltor oe xonorq orogepo onoorooq ono 6vo oro0epo orlpeio' r,:ot6oo, ivog evomortrxog oprop6g rou xux.lou eivor o elqg: evog ruxlog eivor pio r<opnulq 6e6oyiuou ltikoug q onoio neprxleisr rq p6yroq 6uvor4 enrqovero. Onoro0qnote omrl tiroro xopnulq, neprxi.eier prxporepq emeqvelo yro pio 6e6op6v4 npq neprp6rpou oe o;6o11 pe out4 nou neprx.lsi rol on6 rov r<6x.lo. 'Eror eov oog (rltqooupe vo emluoete ro np66.l4po: "ppeire erceivrl rqv xopmll4 nou neprxleisr q peyo-l\utsp4 anl(povero yro 6e6opev4 nepiperpo", orqv npoypouxdrqto oog 6;1ou1re Orboer 6vo np66.?\4po.loyropors pero6o.l6v' evo.loyrop6 Oroqoperrxou r0nou oe oxsorl pe our6v nou eilore ouvqoioei. "'C)ore lorn6v exeivo nou 9i:loupe, eivor o unoloyropog rrlg 6ro0pop4g ev6g ovnxerpdvou. O rp6nog pe rov onoio 9o ro xovoupe eivor o e(4g: H xer.rprxq 1660 ivo1 vo uno06ooupe nr,rg unopler xonoro oom{ bro6popq Kol nros xd0e o-ll4 6ro6pop{ nou oxe6ro(oupe eivor pio eoeol}revn 6ro6pop4' enop6vog, eov unoloyiooupe u1 6pooq ylo qv eoeo-i,]rdvq 6ro6pop{ q trp4 nou 9o.Lo6oupe 9o eivor peyotrurep4 on6 exeivq nou 9o unoloyiooups yrq trl ooodl 6ro6popq. "Enop6vr,:9 to np66lqpo pog etvor: "ppeite tq or,lorrl 6ro6popq". llou ppioxeror ourq; flpoqovrirg, 6vog tp6nog ylo vq ro xcvoupe, eivor vo unoloyiooupe rq 6poo4 yro exoroppupro exoroppupit:v Oto6popSg xor vo 0oupe ylo noro on6 outig 4 6pooq 6xer rr1 prxp6repq rrp4. 'orov npoo6ropioere our4 rqv elolrorq up4, 9o 61ere npoo6ropioer xor 14 ooror4 Orobpopq. I I I "Aur65 rpuorxo eivor 6vog 6uvor6g tponog pe tov onoio pnopoupe vo emluooupe ro np66lrtfd FoS. A.LLo unopxouv xor ol.lor tpdnor xolutepor on6 our6v. 'Orov dxoupe pro noo6rrlto q onoio 6ro0dter ivo etr oxroro - 6nog eivor yro nopooerypo pio runxq ouvoprqor; oov xor outq nou neprypoqer r4 9eppoxpooto - 'pio on6 ug r6r6trpes rou eloliotou tqg eivor 116)S qv qnopqxpuvooupe on6 ro sloxuo oe nprin4 rolq, 4 on6xhoq r4e ouvoprqorlg on6 out4 r4v eldlroq up4 t4g eivor p6vo 6eutepqg ro(49. Ee onoro6qnore ollo o4psio ulg xopnulqg, eov petoxrvqooripe xoro pio prxpr] on6moo4. 4 rrp4 qg ouvoptqoqg omo(sr enioqg og peyeoog nprir4g rol49. Allo oxpr665 oq 9ioq tou eloliorou, pic prxpooxomxq xiv4oq 6ev rover - roulopmov oe pio np<btq npoo6yyro4 - xopio 6roqopo. ''Aurr1 Lornov eivor 4 p60o6og nou npoxerrot vo Xp4orponorrloouFE ylcr vo unoloyiooupre 14 orlmrl 6ro6pop{. E6v lepoupe 14 ooorq 6ro6poprl, pio xopntlrq nou 6roqiper povo xoro liyo on6 our4, 6ev 9o 66oer - oe pio nprirtq npoodyyroq - xopio 6roqopo or4v rtp4 tqg 6pdoqg. Kd0s Otoqopo 9o epqovi(eror oq 6eureprl npooriyyrorl, eov npoypotr 61oupe ivo eloxroto. 'Aur6 eivor euxolo vo rd onobeiloupe. Eov unopler pio perogolq nprirqg ro(49 orov onor.livo rrlv

7 H APXH THD EAA)(ETHE APAEHD KoFnulrf Koro dvo oprofivo tp6no, unopxtl Kor pio psrctbolrl orn 6pqon rl onoio eivql avanoynrqs on6k.llorls. Aurq q peto6olq ovopiveror vo xoromrloer 14 6poo4 ox6pq peyo-lureprl' Oroqopenxo, 6ev 9o unrlpxe xonoro eloxroul upr]..allo dneto, eov r1 6poo4 xivor avaloyn qg on6xhoqg, q owrmpoqq rou npoo4pou rqg on6<tr roqg 9o 6xove rq 0poo4 pnoporsoope lorn6v vo 61oupe r4 Opooq vo oulover pe tov 6vo rpono xor vo elorriveror pe rov ollo. O p6vog tp6nog nou 9o o6qyouoe npollouxo oe 6vo eloxroto, eivor nog t trpdr\ npoo6yyro4 6ev emqeper xopio 6roqopo, 6u 611lo64 olpero6ol6g eivor ovoloyeg rou crpoyrbvou rr15 on6xlrorlg ono 14 o<oor1 6ro6pop4. "Enop6vog 9o ruv4ooupe pe rov oxol,ou0o ovopoooupe x(f) (pe pio unoypopprorl) t4v npoypotrx4 6ro6poprl' 611lo611 our4 nou enr upoupe vo npoo6ropioo-upe. Dr4 ouv6xero 9o $eopilooupe pio ollrl Doxrpomrxrl 6ro6pop4 nou 6roqeper on6 14 or^ror4 6ro6poprl <oro pio prxp4 noo6r4ro rqv onoiq 9q oup6oliooupc pe 4(f) 'Tcbpo, q r6io eivor nog ov unoloyiooupe r4 6pooq S yro rq Oro6popq x(l) rore q Oroqopo ovopeoo fin 6poon 5 xor ot4 0poo4 nou unoloyi(oupe yro 14 ooor4 6ro6pop4 r(f) - xor tqv onoio yro loyoug ontr6tqtog 9o tq oupboli(oupe pe S - 64fo6q q 6roqopo pero$.r rov S id 5, 9o eivor io4 pe ro pq66v mnv np6rrl npoo6yyroq xor yro prxpdg npdg r4g nopop6rpou 4. Aurrl pnopei vo Oroqdper or1 Oeurepq tolq, ollo orqv nprbrq ro(r1 q 6roqopo outrl eivor iorl pe to pr;6dv.

8 344 \ MIA EIAIKH AIAAEEH - DXEAON KAIA NEEH "Auro eivo.r xqtr nou 9o np6ner vo eivor olq0eg yro xooe 4. I-1o trlv oxpigero, oxr yro er,telcilg ou0airepo 4. Aur4 q p60o6og 6ev o4poiver rinore ono.lurog, srcoe ov $eopqoere 6ro6popdg nou opli(ouv o.leg ono to i6ro o4peio xor relerclvouv o.leg enio4g oro i6ro oqpeio xo0e 6ro6pop4 opxi(er ono xonoro oqpeio 14 Xpovtx4 onyprt f1 Kqr rrlslover oe xonoro o.l-lo oqpeio rq lpovrx4 onyp.4 f2 xor outo ro oqpeio xor or lpovrxdg on1p6g 6torrlpouwor mooepo. Enop6vc4 or onox-lioerg poe So npener vo eivor pqoevr<eg oe xooe oxpo, xon nou pooqpouxo Ororunoveror og 4(f1) = 0 xor l7(fz) = 0. Me our4 rq ouv0rlxq dyoupe npoo6ropioer n-l4poe ro po04porrxo pog npo6l4po. "Eov 6sv (6pere tinote ono ro ouvqoq loyropo, pnopeire vo xqvere oxpr6<bg ro i6ro npolgo yro vo npoo6ropioere to aloxroro prog runrx4g otrvoprqoqg pnopouoote va ou(qr4oere ro n oupgoiver eov nopete rq ouvaprqoq /(r), npooodoere oro.x xonorq prxp4 upq h xor unoorrlpi(ere norg 116rop0ooq otrlv /(r) yro rqv nprirrq ro(4 tou h go npener vo eivor io4 pe to pr;6dv or4 96oq rou npener vo ovnxoroorqoete ro,t p ro r+ft xor vo to ovonrulere pdxpr m4v nprilul rol4 os npos ro h... xor ouro eivor oxpr6cbg exeivo nou 9o xovoupe yro ro 4. "Ag npolopqooupe lornov m4v or,uxotooroon r(f) = 'x(t) + 4(f) mlv e(ioclo4 pog yro rr1 LoBoupe rore '= Itt(#f -v61)a, onou oup6oli(o t4 6uvoprx4 evspyero lre y("'r). H nopoyclyog dxldt dvot, <puorxo q nopoy<,ryog rou r(f) ouv r4v nopoy<oyo rou 4(i) enop6vorg, q eliooorl nou noipvo yro rq 6poo4 61er t4 popqq ' = I,'' [t(#. #)' - v 1y+,1fat Tcbpo 9o yporgo rqv noponovo r(ioooq pe psyolurep4 lenrop6pero. flo rov trpoyovrxo opo So ixcl tdxl \d,).zii.\i) dxdn rdnl A.l-Lo neprpevere. Aev ev6roq5popor yro rolerg urp4lotepeg on6 tq 6eurepq yro ro Loyo ouro, pnopco vo nopco o.loug roue opoug nou n pnxouv ro ry2 xot oi S r1s upnlorepeg Ouvoperg xor vo trg po.lcl oe 6vo ptxpo xouri nou ovopo(eror "6eurepl xor urpqldtepeg ro(erg". An6 our6v rov opo 9o xporqor,r povo r4 6eutep4 tol4 yvctpi(ovrog 'Eror op<og nog exei ;reoo unopxouv xor neproodrepo npolgoro. ro rprlpo rqg xrvrlrrx4g ev5pyerog So lo6er rn popen m t )*,2 s- ),. - + m=. + (6rurcpn ror uqrq,\orrpe5 toln5) ItI AI AI 'Ttirpo, Xpero(opor ro 0uvoprx6 7 orq 0eoq x + nc)s ro 4 eivor nolu prxp6, xor riror pnop<b vo ovorrulr,r 14 ouvoprqoq V oe oerpo Taylor. Auto eivor npooelyrmrro ioo pe V(.r) or4v enopevq npooeltlol (ono tq ouv4oq rpio4 rov nopoydrycov), 4 6rop0oo4 eivor 4 rpopeg o puefos pero6ol49 rou V rog flpos ro.x. K.o.K.:.-2 v(x + rl = V(1) + qv' (a) + (t) + ;v" "' 'EXo Xp4orlronorqoer ro oupgolo 7'yro r4v nopoyr,ryo tou 7 rog npog rq pero6i.qr4 -t npoxerpfvou vo y.lurcioo Xp6vo. O opog oro 172 xor ouroi nou oxolouoouv, eprtirtrouv or4v xarrlyopio rqg "6curuprl5 xot utpllorepqg to(qg" xot 6ev lpero(eror vo ovqouloupe yro outoug. Bo(ovrog ro olo po(i go nooouue '= 1,,'' lr(#)' - yg) + ^#H - ly'(x) +(6eurepq xor ur.pq.l6repee.a!"'e)],ir

9 H AP)GI THD EAAXDTHD APA>HD 345 Tcbpo, eov pe.lerrlooupe npooernxo u1v noponovo elioooq So xotolo6oupe nog or npcbrot 6uo 6por nou i1o xorooxeucroer, ovnotorxouv mq 6pooq S nou 9o eixo uno.loyioer yro u1 orootq 0ro6popq l. Auro mo onoio 0dLco vo enrxewpoocb eivor 4 pero6olq rqg S: 11 Oloeopo ovopeoo ong 6pooerg S xor S nou 9o pog e6rve xor rq oromq Oro6poprl. Aurq q 6roqopo, nou go 14 oupgoliooupe pe 65 ovopo(erot "q pstooolrl rou 5". Ayvorbrtog rov 6po nou ouoxed(eror pe 14 6eurep4 xor rrg ovrirrepeg to(erg uno.loyi(ro ro 65 on6 rqv elioooq "AMo t<bpo ro np66lqpo 6rqruncoverorig e(rtg: our6 eivor 6vo ouyrexprp6vo oloxlqpopo. Aev yvopi(r,l ox6po noro eivor ro l o-l-lo 1ryopi(or oot6oo, nog 6noro xor ov etvor to 4, q np4 rou noponovr^r oloklrlp6foros 9o npdner vo eivor io4 pe ro pq6ev. Aornov, 9o oxeqcite, o povog rpdnog yro vo oupgoiver xou 16roro, eivor nog 6,n nomon-looro(etor pe ro 4 90 np6ns1 vq eivor ioo pe ro pq66v. Ai,i.o rr yiveror pe rov nprirro 6po nou neptdxer rqv nopoyr,:yo dtlldt: Iton6v, ent6.loug, eov ro 4 pnopei vo eivor onorodqnore, q nopoyoy6g rou npoqovrirg So pnopei vo eivor xor ouul onoro6qnote ror enopevc,re 9o pnopouoote vo oupnepovere nog o ouvte.leotrlg rcu drlldt 9o npdner vo eivor xot out6g ioog pe ro pq66v. Allo our6 Oev eivor eltel6g ooo16. Aev eivo.r ooo16, ener6rl 9o npdner vo unopxer xonoro ouo;6noq ovopeoo mo ry Kol oqv nopayoy6 rou ourq 6ev pnopei vo eivor te.leioe oveloprqro perof0 roug, oqou q ouvoprqorl 4(i) 9o npener vo eivor iorl pe ro pq6dv, rooo rq Xpovrxrl mryrn t1 6oo xor rq Xpovrxrl onyprl f2. "H pe0o6og t4g eniluoqg olc)v rov npo6lqporcov rou Loyropou petobotr cbv, novto xover Xpqo4 rqg i6tog yevtxqg ap1qg. Mnopeire vo eqopp6oere pio peror6nrorl orqv ovrorqro nou $dlere vq perogo-lera (onr,5 xovope xor e66 npoo06rowog 14 ouvopulorl 4) Ko1 mrl ouvixero vo pel,et4oere toug opoug npcbrqg roler,lg' uotepo, 9a pnopeirs nowore vq 6reuOerrloete ro npogroro pe rdtoro tp6no rirote vo nopec 6vo olo<i.qpopo qs ]ropens "xon nou eivor nomord.ooroop6vo eni rq petot6moq 4" oi'lo Xr,rpig vo ixere omeg nopoyriyoug (6111o611, vo pqv unopxer q nopdyoyog drl ldf). Aut6 or;poiver nog ourq r; elior,:o4 9o npener vo ovo6rorox0ei ex veou etor rirore vo rioer or4 popen "Kor1 nou eivcrr nomonlooroopevo eni rq perotdnlon 4". H peyolq pog onlpq 9o tloei oe evq lemo (unopxouv po0rlponxlg ox6oerg nou oog Leve ro nog vo npollroronorqoere ourq rr1 bto6rxooio yro xonoreg er6rx g neprntrioerg Xr,:pig mqv npolponroupo vo unoloyioete rinore, ol.}.o 6ev eivor opxero yevrxeg 6ror r,rore vo ofi(er rov xono va aoxo.lrl0oupe pe oudg o xoluupog rponog yro vo xovoupe roug unoloyropoug pog, eivor outog nou neprypoqoupe e66). "flog pnopdr vo enovo6rorolo rcv opo dtl ldt 6tor 6me relrxo vo peiver povo 6vo 4; Mnop6 vo ro xovco oi.oxi.4pcbvortog xora nopoyoweg. Aro6errvuetor nog 6lq q ouo'io tou Loytopou perobolriv 6yxerrar mo vo npoo6ropiooupe 14 peto6olr; rqg 6poo4g S xor or4 ouvexero, oloxlqprirvorto5 xoro pepq vo eloqoviooupe rrlv nopoyoyo rrlg peroronrorlg 4. Auri rl pe0o6og eivqr no\,tq q i6ro, oe 6.Lo ro npo6l4poro mo onoio unopxouv nopoyr,ryor. 'Yno06ro n<og $upoore rq yevrx4 opxrl oloxlr;pooqg xoro nopoyoweg: Eov 6Xere pio onoro- Oqnore ouvoptrlorl / nomonlooroop6vq eni u1v nopoycoyo dqldt xar 6Lo our6 ro yrv6psvo etvor olox.l4popevo ors npos ro Xpovo f, pnopeire vo 6rorun6oere rqv nopoyoryo r4g nopoorooqe rlf pt tl POPQTI ur= I,'I-#H-qv,@1]at d.. df.dn E(nJl =,1,it * J d, To ol,oxl.qp<opo nou 9elfle eivor outo eni rou releuroiou 6pou xor 6ro1 9o 6Xoupe It#"=r-[n4[at

10 346 [ T9.T. MIA EIAIKH AIAAEEH - D(EAON KATAAEAH " Drqv eliocoorl pos ylq rrl 6roqopo 65, q ouvopr4oq / eivor 4 Fo3o m nollonlooroop6v4 eni rrlv nopoyoyo dxldt tnoptvrog,9o dy,: rqv ox6lou0q oldoq yro ro 55: as=*ftnol", t *@ff)rov'- l,' v'@)tt\dt O nprirrog 6pog rqg noponcvr,r ox6oqg, 9o np6ner vo unoloyrotei oro 6pro t-r Kor t2. Mero on6 qur6, 9o np6ner vo dxco ro oloxlqpr,r'po on6 ro un6lorno qr4po rqe oloxlqpcloqg xoro p6pq. O releuroiog 6pog 9o peiver Xcopig omoyeg. 'Trbpo, dxoupe xotr nou oupgoiver nowo: o o.lox.lqpcopevog 6pog dqqovis*or (mr1v npoyponxorqro, eov aur6g o 6pog 6ev doqovr(otov, 9o enpene vo enovo6rotunriroete r4v oplr] ror vo npoo0i:oete ouv0qxag ftor rirore vo 6rooqo-Lioere nog npoypou eloqovi(etor!) Eloupe ner 464 6n ro 4 9o npanrl,/ vo eivor pq66v xor orq 6uo oxpo t4g 6ro6popig, ener6q q op14 6qkivet nog 4 6poor1 eivor q elo- Xtor4 un6 rqv npoun60soq nog q peroblqtrl xopnulq opli(er xor teler6ver oto emle11:6vo oqpeio. H ouvor1xr1 pog eivot on 4(11) = 0 xor 4(12) = 0 xor enop6vog o oloxl4popevog 6pog p46evi(eror. Olro6onorrirwog roug unolornoug opoug pnopoupe vo yporpoupe rqv eliocrq pe q popqq 6s= f,,"[-^#-v'@lqoat H peto6ol4 rou S eivor tripo oq popqq nou tq $dlope: unopxer q noo6t4ro ong oyxu.l.eg (og tqv ovopoooups F) nol.lon-looroop6vq eni r4 peroronlon 4(l) Kol oloklqpr^lp6vq on6 u1 lpovrx4 onyp4 f1 6cog u1 lpovrxrl orryprl f2. "Koml{(ope lorn6v oro oupnepoo}ro rros ro oloklqpopo xonorog noo6rqrog nomonlooroopdvrl eni 4 eivor ndwo ioo pre to p46dv : [,6,t(,ya, = o 'EXco 611lo64 pio ouvoptqoq rou Xpovou f, tqv onoio nomonlooro(r,l eni tr1 ouvoptqoq 4(f) xor pero o.lox-lrlptbvo ono ro evq oxpo oro s-tr-tro. Enrn-Ldov onoro64norc xor qv eivor 4 ouvopt4o4 r1(f), ro onord:l\eopo eivor novro ioo pe to p46iv. Al.l.d outo oqpoiver rtc4 4 ouvopr4o4 F 9o eivor pq6iv, Korr fiou eivor npoqov6g, o.l.lo ourr,lg r1 omrog 9o oog nopouoroor,: 6vo rp6no on66erlqg outou tou oupnepqopqros. "Yno06orc rrbpo nclg r,:g ouvoprqoq 4(/) 6ro-lela xon nou rpov ioo pe ro pq66v yro xooe lpovrx4 orryp4 cnog on6 14 yctrovto xonorog ouyxexprpdvrlg Xpovrxqs ml\?rls xorr oov xor ouro nou rgoiveror nopororr,l (E.r.p. 6eire ro endpevo oxrlpo): A4lo64, 4 4(l) eivor p46evrx4 p61pr vo npooeyyioer ekeivrl rrl onl'fn, or4 ouv6lero ove6oiver npog ro novo xor ralog xoreboiver xor p46evi(eror ex veou. 'Oro.v unoloyi(oupe ro oloxtrrlpopo ouror! rou 4 nomonlooroopdvo ps onoro6rlnore ouvopr4oq F, ro p6vo 6romqpo oro ofloio 9o ppeire Korl q-l-lo ekr6s on6 p46ev 4tov exei nou epqoviorqxe 11 onoropq psrobolrl, xorpero, 9o nopec r4v npq u1g ouvoprrloqg F yro exeivq rqv neprolrl nol,.lonl,ooroopevl ps ro oloklnpcopo eni tou noponovco 6r.oor4porog. To oloxl4pr,lpo ourqg tqg perogolqg, ono p6vo rou 6ev eivor p46ev r,rm6oo, ouro to ro olorlrlpr,lpo nomonlooroopevo pe 14 ouvopulo4 F, 9o np6ner vo p46evi(eror. 'Dror ror q ouvopt4orl F So npdner vo eivor ior; pe to pr166v orq 9io4 rqg on6ropqg perogolqg. A.L.Lo oudl { F ro6o.lrl 90 lrnopouos vq rpeovrmei onou0qnots xor sror q ouvopr4o4 F 9o np6ner xor our4 vo eivor onou6qnore io4 pe to pq66v. "B.L6noupe lorn6v, nr,rg ov ro ol.ox.l4propo pog eivor ioo pe ro pqbiv yro xooe 4, rore or oulrelsordg rou 4 9o npiner vo eivor ioor ps ro p46ev. To oloxl4pcopo r49 6poo4g 9o 6Xer t4v elolrorq np4 rou yro axeiv4 u1 6ro6popq 4 onoio rxovonoui tqv nolunlox4 Droqoprxrl elior,rrl rd2xl l-. d,, - Y'(r)l = o

11 H AP)GI THD ENAXIDTHD APA>HE 347 Erlv npolponx6rqto p66oro 6ev eivot xor rooo nolun.loxq. T4v elere 6er xor o-l-leg <pop6g. Eivor ordo 11 oleoq F = ma. O nprirog 6pog eivor ioog pe rq po(o nollon-looroopevrl Fe rr1v emroluvo4, evcb o Oeutepog eivor q nopoycoyog tr;g Duvopr<qg evipyerog nou eivor 116uvopq. "'Etor, toulolrorov yro 6vo ouwqpqnxo o0m4po, dxoupe 6ei(et ncog q oplq r4g elopoiqg 6pooqg 0iver rq or,rmrl onortqoq: pog.l6er nog 11 Oro6popq nou ouoleri(eror pe qv ei.axroq 6pooq, eivor ouul nou rxovonorei ro vopo tou Neurr,rvo. "Dro oqpeio ouro 9o npdner vo xovoupe pio noporrlpqoq: Aev e1o ono6ei(er nr,:g ourrl rl bpoo4 rlrov q eloxroq' 9o pnopouoe xol'l.roro vo qrov 4 pdyroq. Erqv npoyporrx6rqro Oev lpsrd(etor vo sivor 11 eloxroq. Aurq r1 xotoorooq eivor ewel,rig ovoloyq pe exeivq mr;v onoio eilopa ovotruoer r4v "op1q tou aloxrorou Xp6vou" nou ou(4rrloope orqv omrxq. Kor exei enioqg opxrxo eilope ovoqep0ei mol " efiaytmo" Xpovo. Ootooo opyorepo npodrupe nr,tg unqpxov neprmriroeig mrg onoieg our6g 6ev ipav o eiaytmog Xp6vog. H 9e'pefudr6qg opx4 pog 4rov nog yro ro9x pemdotrq zpoz4g zriplg poxpro ono rqv omrxrl 6ro6pop4, q yen6olrl oro Xpovo 4rov ioq pe ro pr16ev. xor eodr, fxoupe tqv i6ro roropio. Exsivo nou npolponr<o ewoupe pe ro " efiaytmo" eivor nc5 4 pero6o.lrl nprirqg tolr;g otqv np4 rou 5 6tov omolore rq 6ro6popq eivor ioq pe ro pq6ev. Aev eivor Lornov unoxpeouko evo "eloxroto". "Du1 ouvexero $dlo vo emoqpovo xonoreg yevrxeuoerg. np(ito on6 6.Lo, outq 11 roropio pnopei vo enovo-lr1qoei ons rpers Orootooerg. Avti vo Xpqorponorqooupe Fovo ro :r, 9o pnopouoo vo 6Xr,r ro x/ r/ Kql z og ouvoprqocrg rou l' oqv nepimr,roq our4 pe6oro, 4 6poor; yiveror nro noluntroxq. ho tqv tprobroororq xivqoq, 9o npener vo Xp4orponor4oere rqv n.l4p4 xtvqnxq ev6pyero, 6qlodr.1 u1 ouvolrxq rolurqto urpopev4 erg ro rerpoyr,rvo xor nomonlooraop6v4 eni ml2. L\?'c6i Krvqn<q ev6pyero = ;l(#f.(h)'.(#)'l Eniof S Ouvopxr; ev6pyero eivor nleov ouvapr4orl rr,rv r, y Kor z. A.l.}.a n oupboiver pe rq Oto6popq ; H 6to6popq 9o eivor xonoro yevrxrl xopnui,q oro ybpo nou yevtxo Oev eivor euro.lo vq oxa8roorei. ootooo, 11 r6eo eivor q i6ro. Tilog, u oupgoivet pe ro 4: Aorn6v, to 4 pnopei va elsr rperg pnopouoore vo peroronioere ug Oro6popeg os npos x, r,ls npos y r1 c5 npog z, 4 9o pnopouoorc vo rls peroronioerr Kqr npos ng rperg 6reu0uvoerg routolpovo. 'Eror ro 4 otqv npoypotrxor4ro eivot 6vo 6ror,'uopo, xon nou om6oo 6ev neprn-lixer ro npolpoto rotoirepo. Ener6rl povo q pero6olq rprbutg taf4g rl.piner vo eivor ior; pe ro p46ev, pnopoupe va npolporonorrlooupe roug unoloyopoug npolloronorrirvrog rperg 6ro6olrxig peroronioe,re. Mnopoupe vo peroroniooupe ro 4 povo xoto t4 6reu0uvo4 rc)v.,r, Ko1 vo noupe nctg o ouwe.lemrlg 9o npiner vo eivor pr16ev. Me rov rp6no ouro go

12 348 Q 19.I. MIA EIAIKH AIAAEEH - DXEAON KATA AEEH nopoulre rrlv np6rn e(iooorl. Er4 ouvexero peroronr(opoora xoto rq 6reu0uvol r<ov y Kql noipvoupe ox6po pio s(ior,lo4. Kovowos ro i6ro yro rq 6reu0uvoq rrlv z noipvoupe xor ol.l.q eliooo4. <Duorxo pnopeire vo npolgoronolqoere our6g ng peroronioetg pe 6noro oerpo 96.lere. T6.Log nowov, orlv ncpinrr,lo4 ourq 61ere rperg elrorboerg' xor rpuorxo, o vo'pog tou Neurovo ylq ns rpels 0roorooerg nepr-lop6over npollron tperg elrodroerg: pio yro xooe ouvrotrioo. Nopi(o nog orrlv npolq 61ere 6er nog outo nou.lripe eivor or,roro, o-llo 9o oq{ooupe oe eoo5 vo ono6ei(ere nog outrl q pe0o6og 9o Oouldger oooro yro ng tpsrg Orooroosrg. llopepmmowog, 9o pnopouoore vo Xp4orponor4oere 6noro ouor4po ouvteroypevov 9ill.ere, n.1. no.lrx6 r1 onoro6rlnora o-l-lo xor vo nopec op6o<og roug vopoug tou Neurrlvo m4 popqrl nou eivor Koro-Llqlq yro to ototr;po ouvreroyp6v<.rv nou Xp4orponoreire noporqpcivrog on-lo ro ri oup6oiver eov eixore u1 peror6nrorl 4 m4v ordva, oe xonoro yovio, x.l.n. "Me nop6poro rp6no, 4 peeo6os pnopei vo yevrxeurei yro ouooipero nlrloog oopondicov. Eov 6Xete, og noupe, 6uo oopotioro, perolu rov onoiov ooxsiror pio 6uvo'pr1 dror cbore vo unopxer pio opor6oio 6uvaprx4 svdpyero, exeivo nou 9o npiner vo xovere 9o eivor on-lo vo npoo0doere ug 6uo xrvqnxeg evepyereg Kor vo onolrokpuvere rq 6uvollxq evdpyero tqg oporboiog o-@leni6pooqg. Kot ri eivor outo nou 9o pero6o-l-lete ng Dro6popig rcat tau 6uo oopor6ir,rv. Allo our6 o4poiver - yro ro 6uo ooporioro nou xrvouwqr mls rprls Oroorooerg - nog 9o unoplouv ouvol,rxo elr elrodloerg. Mnopeire vo pero6omste rr1 960q rou ocopon6iou I Koro rn r Oreueuvon, ulv y 6reu0uvorl Kqr rlv z 6reuguvoq xor uotepo vo xqvere ro i6ro xor yro ro oopori8ro 2 pe rov rpono our6, 9o ppeits elr e(rorioerg, 6nog otrlv npo.lgoux6rqro 9o enpene vo oupboiver. YnopXouv or rperg elrorioerg nou xooopi(ouv rqv entoxuvoq rou oopon6iou I oe ouvopt4or; pe rq 6uvop4 rcor omeg rperg elroriroerg yro rqv enrroxuvoq tou or,rponoiou 2 ono rq 6uvopq nou ooxeirqr eni qurou. Mnopeire vo noi(ete ouvilero out6 ro noryvior xor vo ppioxere roug vopoug rou Neurovo mrg rperg Oroorooerg xor yro xo0e ntr4oog oopon6ir,rv. "Eixo ner npo4youp6vog, nog p6oo on6 ourrl rrl 6rq6rKooio, xoro-lqyoupe re}rxq oro v6po tou Neurcovo. Aur6 r,ro16oo 6ev eivor on6luro ooor6 enei6rl o v6po5 rou Neurovo nepr-lopbover xor pr; ouvqp4nx6g 6uvoperg 6nrog eivor q rpr6q. O Ncutovog eins nog ro ytvopevo ma eivot ioo pe xo0e F. Oorooo, I opxi rrls elaporqg 8pooqg roxuer p6vo yro to ouutryc4ttrca oum4poro, onou oleg or 0uvolrerg npo6plovror ono xonoro ouvoprqorl Ouvoprxou. fvr,lpi(ere r,lm6oo nog oe evo prxpooxonrx6 enine6o. mo mo pooro eninedo r4g quorxrlg 6ev spqovi(owol F4 ouwrlpnnkdg 6uvoperg. Autou tou runou or buvdperg, onr,5 I tpr6q, epqovi(ovtor povo ener6q olvooupe trg nolunlox6rrlreg rou prxp6xoolrou' unopxouv 16oo nomo oopori6ro yro vo ovo-truooupe. ALlo coot6oo, or 9epstr66etg r.ro;ror, pnopouv vo 6roruno0ouv pe pio v6o popqrl nou vo eivor ouf6orrl pe rrlv opx4 qg eloxrorng 6poo19. "Ag yevrxeuoco oxopq neproo6cpo. Yno0dore nog ovopotr6lrome n oup6oiver eov ro o<,rpori6ro xrveiror pe olerrxronr<o rpono. Dr4v nepimoo4 ourq 6ev 9o noipvope 14 orom4 oxerrxrmrxq elior,:or1 tqg xivqo4g 4 elioooq F = ma xivan oclorq povo yro rrl F.rl oxertxrmrxq nepintr,loq. To eprirr4po }or nov eivqr ro e(qg: unopxer pio ovriororx4 opxrl rrlg eloxrorq5 Opooqg yro q olenxrmrx4 nepinrc,:ory: H onovr4o4 civqr. vor. unopler. H po0rlpouxrl o16o11 yro r4v nepinroo4 r4g oleuxol4log eivor q oxolou0n : t - ^1, - S = -*or',lt - u2lcz fr, at - q l. lrf(x,y,z,tl Jlr t I - u.a(x,y,z,t)ldt To nprirto pd:trog oto noponovo olox-l4pclpo rqg Opooqg eivor 1td3?_!!!+S r70 noli.onloorooprvrl lre ro c2 eni ro ol.oxlrlpr,lpo pros ouvqprrlorls rrls rqxurrfqs,.ls Vl - u2lc2. Lrq ouvelero, ovti vo dxoupe on-lo rq 6uvopr<r1 evdpyero, Xoupe 6vo olox.lrlpopo eni evog pooptorou xor eni prog nooot4rog nou eivor to yrvopevo rqg roxur4rog u pe to Orowoponxo 0uvoprxo pe rov tpono out6 9o oupnepr-logoupe p6vo ug 4Lerrpopo1ryr1nx69 Ouvoperg. 'OLo ro rl.lercprxo xor ro poyvquxo ne6io 6i6ovtor ouvopt4oer tcov 6uvoprxr,lv rp xor A. Aurq 4 ouvoprqon Opooqs 6iver t4v nlqpq $ecopio r4g cxenxrotrxqg xivqoqg ev6g onlou ocopou6iou oe 6vo 4lercrpopol.v4ux6 ne6io.

13 H APXH TH' EAAXIDTHD APA>H> 349 "<Duorxo, xoge gopo nou Xpqorponor6 ro oupgolo u, 6xere ovrdrlq0ei nog nprv npoonooqoec vo unoloyioere ou6qnore, 9o npdner vo owr<oroorrloara ro u,' pe rc dxldt xor vo xovere ro i6ro xor yro rrg o-l-leg ouvrmooeg. Enio4g 9o npener vo ouver0qtonorqoere nos or ouvreroypdveg xty Kr:r z rou xqoe orlpeiou rqe 6ro6pop4g, orqv npolgorrx6rqto eivor ouvoprrloerg rou lpovou rns FopQrlS x(t), y(t) xot z(t). M6vo pero ono ourig rrg owrxoroorooerg, 9o 61ere rq oclm4 pooqpotrxrl o1eo4 yro rq 6poo4 evoe oxerrxronxou oqloo yro roue nro elunvoue ono eoog ro npo6l4po rrlg an66sr(qg nog ourrl 4 ox6oq yro rq 6pooq oqv npolpouxorqro o6rlyei mrg ooordg elroriroerg xivrlo4g yro u1 pou enrrp6pere vo oog xovr,r rqv uno0er(q, nog opxrxo 9o np6ner vo 6ouLdgere X<,rpig vo Lo6ete un' orprv ro po1ryr1n<o Ouvoprxo A, 6qlo64 vo uno06ore nr,rg 6ev unopler po1ruqnx6 neoio. Drq ouv6xero pnopeire vo nopete ng ouvrmdroeg rqg e(ior,loqg xivqoqg, dplttt = -qyq 6now rpuorxo 9o tro6rrc un otprv orr p = *ttl,lt -tw. "An6 rqv ol-lq n.leupo, q petr eq t4g nepinrooqe xoro tqv onoio to Orovuoponxo 6uvoprx6loppovetor un' 6rprv, eivor no.lu nro 6uoxo.Lq xor or pero6o.leg onortouv peyo-lo po0p6 no.lunloxorqrog. A.l-lo oro rilog, o 6pog rqg 6uvop4g nporurnei ioog pe 4 (E + u x B) 6no9 quouo 9o enpene vo oup6oiver. A.l-tro So oqloo ouro ro nor1.vi6r oe oog. "@o r1oelo va rovioo nr,:g orq yevuq nepimooq, yro nopo6er11ro mq pooqporurl o1do4 yro t4v nepinrr,:oq r49 oxenxdrqtog, q oi.oxlqpoteo nopoorooq 6ev 6Xer n-leov q FopQq rqg xrv4nxqe evepyerog peiov rq 6uvoprxq ev6pyero, xon nou ro;uer p6vo ylo rrl Frl oleuxronxq npoo61ryro4. fro nopo6erygo. o opog m0c2l ra -,2/a26.u ouonaproto rxeivo nou eixopr ovopooer rrvqrrr4 rvipyrro. To eprirqpo rou ncbg 9o npener vo poro(er q 6pooq yro rrlv xooe lexoprorq nepimr,roq, 9o npdner vo onovrqoei KoroQeuyowos mq p60o6o rr;g oorrpqg xor rou Loooug. Eivor onlo ro i6ro npoolqpo l-rs ro vo xooopiooupe npc,rto ono olo noror eivor or v6por rqg npener vo noilere pe ng slro<iosrg nou (6pere xor vo 6eire eov pnopeire vo ng rpdpere oe pio popqr; nou vo eivor oup6otq pe r r1v op1r1 rqg clolrorrlg 6poo4g. 'Ag toviooupe xor xou o}io 6oov oqopo rqv opoloyio. H ouvopqo4 nou otrox.lqprbverqr 6rs npos ro Xpovo yro. vo. pqs 6<boer tr1 6poor1 S, ovopo(eror Aoyrpor(rovq, oup6o.li(eror pe ro ypappo I xor eivor pio ouvopt4o4 povo rr,rv roxutrlrov Kol rov 96oeov rov oopou6iov. 'Etor q opxrl tqg etr oxr.orrlg 6poo49 pnopei snio{s vo ypoqsi xor pe 14 popqrl rtz s = L(xi,u)dt rti 6nou pe ro o0p6o.lo xi <or u; ewooupe o.lee ng ouvrorciroeg r<ov 96oer,rv xor rov rolurqrov. Enopevolg eov oxouoere xonoroug vo prlove yro 14 Aoyxpor(rovq 9o \epere nr,lg pulove yro t4 mrvopr4o4 nou Xpqorponoreiror yro rov npoooroprop6 rrlg 6poo49 S. frq rn ox r1krmlxr1 xivqoq oe dva qlertpopayvqnxd ne6io, q Aoyrpot(rav4 e1el q popqq C= -mocz ^lt - - q16 + r.e) "21& "Eniorlg 9o 40eLo vo oqs nr^r n<,ls ro 5 orqv npolgou<6rqro 6ev ovopo(eror "6poo4"' rouloxrorov ono roug mo oxpr6ol6youg xor oxolomrxoug ovopcbnoug. Avri0ero, ovopo(etor "4 npcbrq rupro ouvopr4o4 rou Hamilton". A-L.L onex0ovopo.r vq 8riroo pio 6role(q novo orqv "opxrl qs elolrmqg npri[qg xuprag ouvoptrloqg tou Hamilton". 'Etor, anla tqv ovopa(o "6pooq", xofl nou roxuer xor yro o.lo xor nepro6cpoug ovoprbnoue. Iotoprxo p.l6nete, ovopo(eror 6pooq xqn q-l-lo nou 6ev eivqr xqr rooo Xprlorpo' rdor6oo, nroreur^l nog eivor nro npornxo ro vo lpqorponorrlooupe yro ouro xonoto nto npooqoro oprop6. 'Eror rrilpo xor eoeig 9o onoxo-leire ourq rq ouvopqo4 6pooq xor no.lu otwopo ouro ro 6vopo 9o xo0repr,roei ror 9o lpqorponoreiror on6 6.loug. "Tripo. 9itrcl vo fic) oproprvo rpoyporo yro ouro ro ortrxriprvo nou rivor nopoporo pr rrcivo nou eixope ner yro rrlv opxq rou elolotou 1p6vou. YnopXer 6roqopo ovopeoo oro Xoporulpronxo evog v6pou nou pqs Leer nog evo ouyrexprpevo oloxlqpopo ono 6vo oqpeio oe xonoro o.l.lo 6Xer

14 350 s MrA EIAIKH AIAAEOH - D(EAON KATAAEAH rnv rloxrotq np{ rou - 611lo0rl nou pog L6er xdn yro rq 6ro6pop4, oro o0votr6 rrls - Ko1 oe 6vq o-ltro v6po nou Leer nrog xoorirg xrveiore unopler pio Ouvopq nou npoxolei emtoxuvoq. O Drurspos vopos qvo(piperor mov rpono pe tov onoio xrveiore omoopq npog omoopq xoro p4xo5 rrlg 6to6polrns, wd) o npcirog eivor pio 6qlooq nou oqopo oloxlr;pr; rq 6ro6poprj. Errlv nepimoorl rou qot69 pr-l4oope yro pio ouo;6no4 nou uqiorarol ovopeoo oe ouroug roug 6rio vopoug. Trirpo, 9o 40elo vo efqy4or,l ytori eivor o.lq06:g ro yeyovog nclg unoplouv broqopenxoi v6por xooe qopo nou un6pler pio opxrl elolotrlg 6poo4g ourou rou tunou. O l6yog eivor o e(qg: 9eopeire t4v npoyponxr] bro6popr] oro lirpo xor mo Xp6vo. 'Onr,rg xor npoqyoupdvog, og nepr.oproroupe m4 pio 6rooroorl xor og oxe6roooupe ivo Droypoppo nou vo 6eiXver4 perobolq tou.r oe ouvoptqoq pe to f. Koro p4xog rrlg or,lmrlg Oro6poprlg q 6poor1 S iler rqv eloxror4 npq r4g. Ag uno06ooupe n<,lg yvcopi(oupe t4 ooorq 6rodpop4 xor nr,:g ourq 6rdpleror on6 xonoro oqpeio a oro 16po xor mo 1p6vo xor enio4g on6 6vo yeuovrx6 o4peio b 6nog rpoiveror nopoxorr,r : Tripo, eov to oloxl{popo an6 t4 lpovrx4 onypi h er,rg r4 Xpovrxrl ony1r4 f2 iler tqv eloxroq np4 rou, em6olleror enioqg vo eivor e.ld1roro xor ro oloxl4popo on6 ro o4peio a oro o4peio b. Aev pnopei nopo vo eivor 6ror, yrori 6roqopenxo 9o pnopouoote vo noilere pe our6 to qrqpo qs Oro0pop;lg xor vo xovue rqv nprl rou olox.l4pcirporog ox6po prxp6rep4. "Enopdvog, xooe qrrlpo ulg oroor4g 6ro6popqg So o64yei enio4g oe e.tro1rmr1 upq, xon nou roluer ovelopr4ro on6 ro nooo pupo eivor out6 ro qrqpo. Auto pe rr1 oerpo rou o64yei mo oupndpoopo nog r; op14 o0pqovo pe ulv onoio q ouvofux4 6ro6pop4 6iver 6vo eloxroro, pnopei vo 6rotunro0ei enio4g Liyowog nrog evo onerpoor6 rprlpo rqg 6robpoprl5 enio4g eivor pio xopmil4 yro t4v onoio q upq qg 6pooqg vo eivor q eloxroq 6uvotr]. Trbpo, eov ger,lprlooupe evo opxero prxp6 xoppou qg 6ro6poprlg - perolu og noupe 6uo orlpeir,:v nou eivor nolu xolto ro 6vo mo o-l-lo v<borl rou rpdnou pe rov onoio pero6o.l.letor ro 6uvoprx6 on6 ivo o4peio npog xonoro dltro nou pptoretor opxero poxpro, 6ev eivor xor 16oo oqpowrxq, oqou 9o nopopeivere o1e66v oro i6ro onpeio Krvoupevor novo oe out6 ro prxp6 qrt'lpo rns 6ro6poprlg. To p6vo npoypo pe to onoio oli(er vo ooxo.lq0eire, eivor q peto6otrr1 nprbtqg to(qg tqg ouvoprrloqg tou Ouvoprxou. H anovr4orl 6ev pnopei vo e(oproror on6 dnore otrlo n6po on6 rqv nopoycoyo rou Ouvoprxou xor oiyoupo eivor oveldprqt4 on6 rrlv np4 rou Ouvoprrou onou6qnore oro lbpo. 'Eror 4 6rlLoor1 yro ng r6r6rrlreg rqg xopnulqg oro ouvol6 rqg, ovoyeror oro ep6rnpo tou oupociver oe nolu prxp6 rprlpo rrlg' xou nou qnore.lei pio 6roqopu4 6qloor; q onoio neptlopbover p6vo r4v nopoy<,ryo rou 6uvoprxou, 64tro0q q Ouvoprl nou ooreitor oe 6vo o4peio. Autrl eivor xor r1 norotxq efnvqoq rns ox6orlg ovopeoo mo pokpookorrlx6 xor mo 6roqopx6 v6po. "Er4v nepirnooq rou gr,x6g, eixope oufirqoer enioqg, to enopevo eprbulpo: nr,rg pnopei ro oopoti6ro vo npoobropioel q ooou1 6ro6popq ; An6 rq Oroqoprxq nleupo rou 96porog, our6 etvor euxoi.o

15 H APXH THE traaxiethe APAEHD 351 vo yiv r Kqrqvorlro: or Koer XpovrKn orrl?q onokto Fio sntroxuvorl Kor tv6)pi3et Fovo Lo Lr vo KqvEr oe eksivq rl XpovlK4 orlyfrl. A-l-lo quolko otro ro rvonkr6 oos 6oov oeopo lrl o-xdorl orriou - onor,tr rioporos nqrl nepinoro, otov roxupi(eore nc,rg ro ooporidro ortoqcoi@l vo oxolou0rloer exeiv4 14 6ro0popq nou o6qyei m4v eloxroq 6poo4. Mqnc4 "ooqpoiveror" ng yertovrx6g Oro6popdg yro vo 6ronrmooer eov aut6g 6Xouv neproo6repq 4 hy6repq 6pooq ; Erqv nepimoo4 rou rpor69 nou ronooerqoope epn66ro oro 6popo 6ror oore ro rpr,xovro vo pqv pnopioouv vo r-ldy(ouv 6i.eg ug 6ro6popeg, 0ronrotr,roope nc,rg ouro 6sv xoroqepov vo npoo6ropioouv ro nou 9o nove, o0uvopio nou pog o64yr1oe ralrxo oto rporv6pevo rqg nepio.looqg. "Icxusl o1ros xan teroro Kor orrl FqxovrKrl; Anlo6q, eivor o-lr1oero nog ro o<,rpori6ro 6ev pnopei onlo vo "6ro-leler 14 or^rotr1 6ro6popq", oi,lo onevovtiog Ooxrpo(er xo.r oleg rrg amsg mooveg rpolreg: Me amo loyro, ncog eov 6wog ro npoqroto eivqr ror, rote, ov Oev emrpdrgoupe oro oopori0ro vo npoypotonorqoouv oleg ourdg ug 6oxrpdg, 9o nopoupa xonoro rporvopevo ovo-loyo pe exeivo t4g nepio.looqg; To Soupo eivor nog guorxo, to npolgoro 9o yivouv oxpr66g pe our6v rov rpono, ron nou npog.ldneror xqt qno roug xovoveg rqg x6or,.rop4xovuqg. Enopevog q 6rorunoor'1 qs opxls r49 elopotqg Opooqg Oev eivor nlrlpqg. lho ouyxexprpdvo, q nopo6oxq n<og 6vo ocopori6ro on-lo enddyer 14 6ro6pop4 nou ovtrmorxei orqv e.loxrorq Opooq Oev eivor or,tmq or,ti0eto, exeivo nou yiveror orqv npoyponxorqro, eivor no:g ro oopori8ro "ooqpoiveror" 6leg rrg 6ro6popdE nou Bpioxortor orq yerrovro rou xor 6roL6yer ereivq nou o64yei m4v aloxrorq 6poo4, pe pio pe0o6o ovo,loy4 pe exeivrl pe rqv onoiq ro cprog 6ro,L6yer q 6ro6popq rqv onoio Orovuer orov e.lolroro Ouvoro Supoore nos ro qos 6roL6yer ro prxpdrepo 1p6vo olg elrlg: eov nqyorve on6 pio 6ro6pop4 nou So onotrouoe 61oqop lx6 Xpovo, 9o eqrove exei pe Oroqopenx4 rgooq. lvcopi(oupe nos ro ouvolrxo n-lotos oe xonoro or;peio eivor orllo ro ooporopo r@v ouvsroqop6v orqv npq rou n.loroug, 6.lov tr,rv 61oQop r1kov rp6nov pe roug onoioug ro <pr,5 pnopei vo rpraoer oro ouyxexprpdvo o4peio. 'OLsg or Oro6popeg nou o6qyouv oe no.lu Droqopenxeg upeg qooqg ouoramrxo 6ev ouveroqdpouv rinore. A-llo eov pnopeirs vo ppeire pio o.lox.l4p4 oxo.lou0io 6ro6popriv yro rre onoieg or cgoolg rivor oxe6ov or i6reg, rote ourdg or prxp6g ouveroqopdg npoorioewor pero(rl rous Ko.1 nporunrer 6vo.Loyr<6 ouvo.l.r<6 n-lorog ruporog oro o4peio npooproprou. Og oqpoi,trx4 6ro0poprl emldyetor exeivrl yro rqv onoio unopxouv nomdg yertovrx6g 6ra6popeg nou Divouv novo xorr,: rqv i6ro <pooq. "To i6to oxpr6rirg npoypo roxuer Kol oulv x6or,trxr'1 FqxovlKl. H r qpls $eopio rqg x6ovtopq- Xovrxqg (yro rl F.rl oxtrrxlorlx4 nepirncooq xor olruoril.rog ro onlv rou qlercpoviou) ).etoupyei og e(qg: q m0ov6rqto nou 6Xer ivo ooporidro va (env4oer an6 ro oqpeio 1 rq lpovu<q otrlprl f1 xor vo rgtooer oto orlpeio 2 rq lpovrkq mr1?q,2, opis crl (,)S ro rerpoyovo xonorog nurcv6rqtog nroovorqrog. To ouvotr rx6 n-lotog pnopei vo exqpoorei og ro ooporopo rr,lv rd.orrbv rqg xooe moovqg 6ro6pop4g, yro xo0e Oroqopenxo rp6no oqr(4g. I'o <ooe 6ro6poprl :r(f) - 6qfo6l yro xooe duvorq rpovroorrxq rpoxro - 9o rrpartar vo unoloyiooupe xonoro rr-lorog ror orq ouv6xero vo npoo06ooupe 6lq qurq rq rr-lorr1 perolu roug. Al,\o rr Seopoupe og nlorog yro rrlv Ko0s Dlo6popn i To oloklrlpopo rqg Dpooqg pos Ldsl pe, u 9o poro(er ro ni.otog rqg xooe rpoxrog. To n-lorog eivor ovoloyo xonorog orooepog no.l-lon-looroop6vl Fs rlv nooor4ro eislft onou S eivor 4 6poor1 yro ourq ulv rpolo. A4lo0q, eov ovonopooulooupe rq rpooq tou nloroug pe ivo pryo6rxo opr0p6, q yovio rqg rpooqg eivor ioq pe S//?. H Opooq S 6Xer povooo pdrpqoqg r4v ev6pyero eni ro Xpovo xorr nou roxuer enioqg xor yro t4 otooepo rou Planck q onoio yevrxo xooopi(er ro nore 4 x6or,trxq pqlovrxq eivor o4powrxrl. "Ag Ooupe tripo nrirg orpr6rbg 8ouLeuer ourq q opx4: unooeotr nos y1o xo0e 6ro6polrq, q 0pooq S eivor no.lu peyolq ouyxptrxo pe r4v npq rqg oro0epog ft. Konoro 6ro6poprl 9o ouveroqeper xonoro nlorog. lta pro yerrovrxq 6ro6poFrl, q rpoo4 9o eivor evte.lri4 oroqopenxq, oqou yto pio repomro up4 rou S, ox6pr1 xor pro pu<pr; perobolrl mo 5 9o o6qyouoe oe pio ewalrbg 8lcrqoperrxi qao{' oqou 11 trpq rqg orooepog ft eivor e(orperxo pxprl. Enopdvog or yertovrxeg rpoxrig 9o oruprirvouv ug ouveroqop6g roug xoro rov unoloyropo tou aopoioporog, err6g on6 pio neproxrl: ourrl q neprolq eivor exeivq orqv onoio pio 6ro0pop4 r<or xonoto yetovrxq cog npog outr; Oivouv rqv i6ro rpoorl oe nptbrrl npooeyyroq [xor rro oup<exprpdvo rqv i6to lpq Opoorlg p6oo oro opro rou D). Movo exeiveg or

16 9, MIA EIAIKH AIANEEH - DXEAON KATA AEEH oro6popig $et:pouwor oqpovtrxdg. Enop6vc,r5, oqv oprox4 nepinrr,ro4 yro ulv onoio q orooepo rou Plank teiver oro Unoev, or octotot x8ouop4xovrxoi v6por pnopouv vo ouvorprmouv on-lo ldyovtos:,,oexoote 6lo 6oo!6pore yro ro n_lorr; nrgov6ufos. To ooforioro 9o oxolouoqoer pio erorxrl 6ro6popq Kor nlo ouyr<skprpcvo exeiv4 yro rqv onoio r; opoorl s 6ev pero6o-l.leror oe nprinq npooeyyrorl". Aurrl eivor 4 ouox6troq ovopeoo mqv qpxi tqg eloxroqg 6poo45 xor orqv x6ovrop4lovrx{. To yeyov6g nr,:g 4 xbovnxq p4xovrx4 pnopei vo gepe.lro0ei pe cut6v rov tp6no ovoxoluqoqxs Ytq npdfin qopo to 1942 on6 6vo qou4tq nou eile xol outog og Oooxolo tov x. Bader' yro rov onoio pi.lqoo oqv opxrl our49 t49 6roi,e!49 In xgovnxq pqxovrxrl oplrxo 9epa\rrb04xe 6t6ovtog pro 8roqoprxrl elioclorl yto ro nlorog (Schrddinger) xor enio4s xonoto poonpotrxo nou oqopouoov nivoxeg (Heisenber$1. 'Trirpo 9i-\o vo oog pr-lqoo yro pto o-ll4 op14 elolimou oq quorxrl. YnopXouv no.tr.tris r6rores opxig nou eivor nolt ev6roq6pouoeg. Aev 9o npoono0rloo vo ug onoprop{oo e66' q-l.-l.o povo vo nepryporpo oxopo pio. Apy6cpo, 6tov 9o neprypotpoupe evo quorx6 gorv6pevo nou oqpi(eror oe pio 6popqq oplq elolimou 8o oog pr-lqoo t6re yro trbpo vo oog 6eilo nos FnopouFo vo nepryporpoupe r4v qlertpootonx4, 61r xo0opi(ovtog rq 6roqoprx4 e(ioooq rou ne6iou, oma leyovtog nog xonoro ouyxexprfdvo oloklrlpopo 9o npiner vo eivor p6yrmo 11 eloxrmo. flp<irro ono olo, o9 geop4ooupe t4v nepirnooq 6nou xqnorq m.rxvdt4ro <poptiou eivor yvoor4 oe xo0e oqpeio xor ro np68l4po eivor vo ppoupe to 6uvoPrK6 nou 6qproupyeiror on6 out{ oe xooe oqpeio tou Xcbpou' t\,ropi(e te nog 4 onow4o4 9o np6ne r eivot : ^p v.q=_ o Qor6oo, dvog evo-l-lornx6g rp6nog 6torunoro4g tou t6iou npollrorog eivot o e(49: unoloyior ro oloxl4popo U* nou 6i6etor on6 t4 ox6o4 c^f ^ f u'=+ l(vf)'dv- I pqdv ZJ J 4 onoio neprypoqer evo oloxlqpr.rpo oyxou nou unol,oyi(sror yro 6lo ro X6po. Auro to oloxtr4pclpo 9o np6ner vo iler tqv eloxrmrl np4 rou Ylo trl ooorq xorovoprl tou Duvcprrou Q@,y,z,t). "Mnopoupe vo oeiloupe nr,:5 or 6uo noponovo 64lcioerg yro t{v 4Lertpootorrxq eivor roo6uvopeg' Ag uno06ooupe nog 6ro-L6youpe pio onorobqnore ouvopt4oq vo onooeiloupe nr':g 6tov 6ro-\6!oupe yro 14 p 14 oclm4 npooou!4piv4 xoto pio prxprl onoxfuo4 /. r6re, oe np6trl ro!4, 11 pero6ol4 rr19 evepyerog U* 9o eivor ior; pe to pr166v. fpdqoupe Lornov Q=9*r H eivor our4 nou rpolvoupe, o_l_lo 9o oer,tprlooups povo pio perooolrl rrls 6to16o.ts vo npoobropiooupl noro So npener vo eivor, yro vo o64yei oe peto6olrl nprbtqg to(45 rou U* ioq pe ro p466v. fro rov np6ro 6po r4g U, to ovorm:1po So pog Driroer (VOF = WOF +2vQ.vf + (vfl2 'O p6vog opog nprbrqg to(etog nou 9o perobo-lletor eivor o 2vQ-vf Dro 6eurepo opo rqg evepyerog U'q ouvopqo4 npo5 olox.lqpoorl eivor 11 ro pero6lqto p6pog tou onoiou sivor rc pf. xpero(6poote to otroklr1popo pq=pq+pf 'Erot, geopcbwos povo ro rpqporo nou petooollortot. ^u'= lgsvq.vf -pf)dv.l-

17 H AP)GI THE EAAXIETHE APAEHD 353 " Tcbpo, o<o.louoriwog rov no-lr6 yevrx6 <qv6vq, 9q npdner vo onoleir.potpe rtg nopoytbyoug r4g ouvoptqoqg /. Ag 6oupe opxrxo noreg eivor ourdg or nopoyr,ryor. To eooreprx6 yrv6pevo ypoqeror org aq ar aq ar aq ar dx 0x dy dy dz 0z onou <puorxa 9o npdner vo o.lox.l4ptbooupe os npos x, y Kor z. no vo to xovoupe ouro 9o xotoquyoupe mo el4g r6pootrro: yro vo onoltroyoupe ono n }fldx 9o oloxlrlp<irooupe xoro nopoyovreg os npos q pero6l4rq.t xon nou 9o' Feroq6pel rov relem4 t4g nopoyrbyou oq ouvopt4oq 0. Aurrl 6ev eivqr oll4 ono 14 yevrx4 r66q nou lp4orponor4oope yro vo onomoyoups ano rr'g nopoyr,lyoug r,rg npog ro Xpovo f. Ag Xpqorponorrqooupe Lonov rqv roor4ro rdbsr ab r d2d -2a"= r- - r -dx J axax-*-rax Jtnr' O o.lox.lqpopevog 6pog eivor ioog pe ro p46ev, enerbq dloupe uno06oer nog q ouvoprrloq / eivar io4 pe ro pq66v oe onerpq on6mooq (ouro cvnotorlei mo vo 96ooupe q ouvoprqoq 4 ioq pe to pq66v yro T1g Xpovrxdg mrlpeg f1 xor f2. 'Eror n opxrl FoS ororunriverqr pe peyolureprl oxpibero cog elqg: to U* eivor pxp6repo yro ro nopo yro onoro64nore dl'}',o Q@,y,2) nou dxer ug i6reg npfg oe onerpq onoorooq). Dtq ouvelero xovoupe to i6ro npoypo yro ng pero6tr4re9 y xor z xor re.l.rxo ro olox.lqpopo pog 9o tro6er rrl popqq AU'= I eeovzq - ilf dv llpoxerpdvou ourq q perogolq vo eivor iorl pe to pr166v yro xo0e;[ 6noro xor eqv eivor ourl, 9o npiner o our,te.lem4g tou / vo eivor ioog pe ro pq66v ono onou nporunrer ot YzQ = -plen Koro-L4(ope Lorn6v m4v opxrxrl pog elior^ro4. Enopevc,rg rl okeprl pos'!.1o ro " Loxlmo" eivor ot:or1. "Mnopoupe vo yevrxeuooupe our4 pog rqv nporooq eov npcllotonorqooupe ug olye6prxeg npo- (erg pe eloqpo 6roqopenr6 tpono. Ag y:piooupe nior,: Ko1 os npol'l,loronorrlooupe ulv oloxlqpooq roro napoyoueg lclpig vo Karoquyoupe mrg eni pdpoug ouvrorriroeg. Ag lexrvqooupe ono u"1v ovro6- Irlrq v.(/v@) =vf vq+fv2q Eov Oroqopioo ro oprorsp6 pslog, pnoprb va 6eilo nc5 ouro eivar onlo ioo pe ro 6eli pelog. Dtq ouvdlero, 'pnopoupe vo Xpqorponorrlooupe aut4 rqv elioooq yro vo oloxi.qprirooupe xoro nopoyovreg. Auro oqpoiver nr,rg mo oloxlqpclpo pog yro rqv nopootooq AU. 9o ovtrxotootrlooupe r4v nopoorooq -V4.V/ pe r{v /V20-V.(/V@) rrou So o.lox.lqpo:0si oe ol6r.lqpo rov 6yxo. O opog qg an6x.lroqg nou olox.lqpcirvetor oe otr 6x.Lqpo rov ol.xo, pnopei vo qltrxqrqorqoei qn6 6vo efllqovetoxd o.lox.lqpopa orjl,1q6)vo pe rq oxeorl rr I v.(rva)dv = fvq.n da.j-.j- Ener64 oloxl4pcbvoupe oe oldxlqpo rov oyxo, rl enrqovsro eni tr;g onoiog oloklqpd)voupe 9o eivol onerp4. A-l-Lo exei 11 ouvoprqoq / eivor ioq pe ro p46ev ror retrlrcr 9o nopoupe ro i6ro onori:.leopa onog xor npo4youpdvog. "Movo rrbpo dxoupe tqv rxovorqro vo xoto-lo6oupe rov rp6no pe rov onoio 9o npener vq enduooupe evo npo6lrlpo 6tov deu yuapi(ouyz nou ppioxovror 6Lo ro rpoprio. Yno0eore nog 6ro06roupe

18 35,4 E 19.I. MIA EIAIKH AIAAEEH - D(EAON KATA AEEH oyr,lyous Fe eoprio nou eivol Orooxopmop6vo novo roug pe r<onoro rpono. Mnopoupe ox6prl vo lpqorponorrlooupe rqv oplq tou e.loxiorou eov to 6uvopr<o o.lorv tov oyoyrbv eivor orooepo. Dulv nepinrooq ouul 8o unoloyiooupe to olox.lqpc)l,ro ylo ro U- p6vo yro ro 1r,5po 6lcl ono 6loug rous oyoyoug. Dr4 ouv61ero, ener6rl 6ev pnopoupe vo pero6o-l-loupe to tou oyoyou, q ouvoprqoq / So eler pq ior; pe ro pq66v oe 6Leg ourdg ng enlqovsles Kol ro n1(pova1ox6 oloxlqpopo 1vq.n aa 9o eivor xor our6 ioo pe to pr;66v. To p6vo rpqpo rou oloxlrlprbporog nou nopopdver eivor ro, -r, zru = I t- ]v-q - p)jav ro onoio 9o' npdner vo uno.l.oyrmei r,o.,r riro,o*r, ovopeoo moug 9o xoro.lqloupe xqr nq-lr orqv e(ioooq rou Poisson Y2Q - -p les 'EXoupe Lorn6v 6eiler, ncog ro opxrx6 pog oloxlqpopo U* eloxroronoreitor eniorlg eov ro unoloyiooupe novrl oe 6.leg rrg nsprol6g err6g rov oyoyriv or onoior unori0swor nog ppioxortor oe oro0ep6g rrp g 6uvoprxou [our6 pe ol-tro troyro o4poiver ncog xooe Ooxrpoonxrl ouvopqorl Q@,y,2) 9o np net vo eivot toq pe ro 6e6op6vo 6uvoprx6 oroug oyoyoug 6rov ro x,y,z qvqqdpo\tqr oe o4peio nou ppio<eror novr,r m4v enleovero rou oyoyou). "YnopXer pio ev6roqdpouoo nepirnrooq, otqv onoio ta povo6rxo rpoptio nou unopxouv, ppioxovtor novo oroug oyoyoug. Lqv nepinrr,ro4 ourrl ro oloxl4pr,rlro rqg evdpyerog U- $o lo6er rq popqq u.--} [tvofav Drqv nepintooq ouul 4 oplq rou eloxiorou pog o6qyei oro qupnepqolrq rttos oe neplqlqoels olr9 onoieg unoplouv oyoyoi nou 61ouv reosi oe ouyxerprp6veg 6e6op6veg np6.9 6uvoprxou, ro 8uvoprxo ovopeoo oe auroug ouronpooopp6(eror pe tetoro rpono rbme ro noponovr,: oloxl4popo vo LopBover r4v elopoq npq rou. Altro n exqpo(er our6 ro oloxlqpclpo; O 6pog V@ eivor to qlercprxo ne6io xor enopevr,:g ro noponov<o oloxlqpopo ovonoproro rqv 4.lerrpooronxrl ev6pyero. Ano 6Lo.Lorn6v rq ne6iq nou npoepxovtor on6 qv x.lioq rou 0uvoprxou, ro oom6 ne6io eivor exeivo nou or,trmorlei oqv eloxroq ouvo.luq ev6pyero. "@o Xpqorponorqor,r our6 ro onoreleopo ylo vo oos Oeilo xon ouyxexprp.evo p6oo ono to onoio 9o 6eire yrori 6Lo ouro to npoypoto axouv oqv npoyponx6ulro peyo.lq nporuxrl o(io. Yno0eoe nog 9eop6 Ouo oyoyoug or onoior ilouv tr; popqi evos xu}rv6prxou nuxvorrl onog rpoiveror mo arrofevo ox{}ro. O eor,xeprx6g oyoy6g ppioxeror oe dvo 6uvoprx6 V ev<iro 6uvopr<o rou el'rorepr<ou oyoyou eivor ioo pe ro p46ev. Ag unooeooupe eniorlg nog q orcivo rou eooreprxou oyr,ryou eivot io4 pe a evrir e- xeivq rou efotepxou oyoyou sivor ioq pe b. Toipo, pnopoupe vo 9eop4ooupe otrota6rlnote xorovoltcl rou Ouvoprxou ovopeoo oe ouroug roug 6uo oyoyous. Eov Xpqorponor4ooupe ro ooor6 xor uno.loyiooupe rqv noo6rrp q ( 012) J FQ)2dV, ouul 9o np ner vo eivor io4 pe rqv qlerrpoororlr4 cvipytro rou ouotrlporog. \114CV2. Enopevog. Xprlorponortivrog r4v op14 pog pnopo0;-re vo unoloylooupe rq Xopqm6rqro C rou nurvor4. Allo eov npoonogouoope vo unoloyiooupe rq y,rpqtrxorqro pe outrl t4 pi0o6o, lpqorponor6vrog eopalpdvq xorovoprl Duvoprxou, 4lopqnxo rrlro nou 9o noipvope 9o qrov nolu peyolq, oqou q npq rou 0uvollxou V eivor ouyxexprpivq. Onoro0qnore unon06pevo nou 6ev rouri(eror n-lqpog pe ro oooro 6uvopr<6 9o 6r^roer pio

19 H APXH THD ENA)CDTHD APA'HD 355 n-loqrortxq npq Xopqnxotr;ros, nou 9o eivor peyolurep4 ono exsivr; nou.9q 66rve q oom4 ouvoprqoq Ouvoprxou. Oorooo, eov I soeoltrr.6vl pca npooelyro4 yro eivor oxerrxo xowo orq ooorl rtprl, rore 4 npooelyto4 rqg 1<,:pqnxor4rog nou go LoBoupr 9q rivqr r<ovonorqrtxq, oeou ro oeolpo otq Xopqux6rqro C eivor 6eurepqg roiqs mo oeo.lpo yro ro "Yno06ore nog 6ev.i,.vopi(o tq lcopquxorqro rou xufuvoprxou pou rturvrorrl. Drqv nepimooq ourq, pnopril vo lp4orponorqoo ourrl rqv opxrl ylq vo rqv npoo6ropior,t. Exeivo nou 9o Kov(,) 90. sivor vo povreu<,r rrl ouvopuloq rou 8uvoprxou pdxpl rshko vo nopo t4 lopql6repq rlpl y1o rrl 1r,lpqrrx6r4ro C. Yno06ore yro nopo6rlyfo nr,ls DroLeyr,t evo 6uvopx6 nou or,'uororyei oe 6vo mogepo ne6io (1'vr,lpi(ere rpuorxo, nc4 otrlv npoylj.oflxorqro ro ne6io e6(5 6ev eivot oro0ep6: Uero6o.L.L rq.l ovoloyo pe ro 1/r). 'Evo oro0rpo ne6io o4poiver nog to 6uvoprx6 9o ouloveror ypopprxo pe rqv onooloon, flpoktllrdvou vo npoooppooo ourdg ug ouv0qxeg oro ouorqpo tr,tv 6uo oyr,ry6v 9o npener vo 9sr,lp{oo evo 0uvo}rx6 rls }roperls 6=v :l, \ b_ltj Aut4 4 ouvoprqoq eivor ioq Fr yytorrlvrrfn r = axoriol petop466vyro rqv upq r = b evci ovofeoo oe oureg trg Ouo 96oerg 6Xer pio oro0epo xlio4 Ve q)rt -Vl(b a). 'Eror exeivo nou 9o npener vo xover xonorog yro vo npoobropioer to oloxlrlpopo U*, eivor vo nollonlaorooer to rerpoyr,rvo rqg x.lioqg pe rqv noodrqro e6/2 <or oul ouvexeto vo olor.lqprboer yro oloxlrlpo rov oyrco. Ag npolloronor4ooupe outq rq oroorxooio yro evo xuhvopo povooroiou evo ororlsio 6yxou orqv orctivo r our6 9cr eivor ioo pe znrdr. Yno.Loyi(or,'toE ro olox.l4popa, ppio<o noe 4 npcbt4 pou npoono0ero vo uno.troyioo rq lopqnx6rqro pe ooqyei oro orori.leopo l -,,,. ca lh V2 v-lnpotn npoonqurro) -, tl O unoloyrop6g rou oloxi.4prilporog eivor euxolog <or ro onorileopo nou npok0nret eivor ioo pe --alb+d\,rv'\b _ ^) EnopevcS 6Xo pio e(iocooq yro rq 1r,rpqnx6r4ro nou 6ev eivor pi6oro q otuq oi-\o loxuel p6vo Koro

20 356 Q T9.T. MlAEIAIKH AIAAEAH - EXEAON KATANEOH npooeyrloq : c b+d znes = 2(b - a) H rfloooq ourq eivor quorxo 6roqopetu<4 on6 rq oclodl elior^loq nou opi(er 14 y,rp4rx6r4ro an6 rq oxsoq C = 2neolln(bla) om6 r,:ot6oo 6ev eivqr xor 16oo xox4. Ag ouyxpivoupe ro onoreleopo nou noipvoupe on6 ourrq pe rr1 oomq onoltrlor;, yro 6roqopeg rtp6g rou l6you b/a. Auto ro onoteldoporo rixouv unoloyrorei xor epqovi(ovror mov en6pevo nivoxo: loo 1.1 C (ooo16) 2neg o.721 o.434 o ro C (nprilrrl npoodyfrorl) 2nen r o.6t2 0.5r 2-5U r Ax61lo xor ov o L6yog b/a 61er rrp4 iorl pe 2 - nou 6iver pio oqpowrrrl petobolq oto ne6io ouyxprtrxo pe 6vo ypopprxo petobo-llogevo ne6io - noipvo pio xolq npooeyyro4. H onovrlorl rpuorxo etvor ltyo peyolurep4 on6 6tr neprpivolre. To npoypoto yivovror nolu lerpotepo eov ono0etrloere 6vq.Lern6 otppo mo eor,xeprx6 ev6g psydlou ruliv6pou. Ee ourq rqv nepirnoo4 ro ne6io 9o Xoporr4pi(etor on6 nolu peyd-leg pero6ol65 xor ov npoonoorloete vo ro ovqrropqorrjoete pe pio orooepo, 6ev 9o xovec ro06lou xqlq. Me 6vo l6yo bla = 100 eilroore ekr6s np66leq49 xoto 6vo nopoyovto ioo pe 2. To npoyporo eivor no.lu xo-luupo go prxpeg npi:5 rou }$you b/a. Eov nope oro ollo oxpo, eov yro nopo6erypo or oyoyoi 6ev eivor nol,u poxpto o dvog on6 rov ol}o - og noupe yro nopo6erg:o nr4 o L6yog b/a exsr npq iorl pe I.I - r6re rl npoo6lryroq rou oto0epou ne6iou eivor nopo nolu xolr; ror 9o nopoupe rq ooorq npq yro 14 xarprlnxot4ro pe pto on6xlrorl rrlg tolqg tou 0.10lo. "AS oos no enio4g nog vo pelncboete neporripo roug unoloyopoug oog (quotxo, yuopl(erc 464 u1 ooodl onowrlorl yro rov xulrv6po, omo 11 pd0o6og eivor oxpr6rig q i6ro yro onoro64nore d-l-l.o nopolevo oxrlpo yro to onoio nroovdv vo pqv yvr^lpi(ere q or,:ou1 onovqoq). To enopsvo pqpo eivor vo npoonoo{ooupe vo ppoupe pio r<o-lurepn npoo6yyro4 yro tqv o1'vootq or,loul fro nopo6erlpo pnopoupe vo npoonoo{ooupe vo 6oxrpoooupe pio orooepo po(i pe pio exoeur<4 ouvoprqo4 0, A-llo nog (6peu nog our6 onorelei pio xo-lt'1 npooiyyroq ov 6ev yvopi(ere r4 oom{ H onovr4cq eivor q drlg: unoloyl(ete u1 1opr1nx6ulro C xot 6oo mo prxprl eivor r; upq nou ppioxers t6oo mo xovro otqv olr]oero eivor oudl rl npn. AS 6oxrpoooupe ourq rr;v 166o. Yno06ore nc:g ro 6uvoprx6 pog 6ev eivor ypopprr6, ollo og noupe nr,rg eivor 6eutepo6o0ilo ouvoprrloq rou r xon nou oqpoivsr, rrc)s Ko1 ro qlertpx6 ne6io 6ev eivor rddov otoeep6 ollo pero6o-trtreror ypopprxo og ouvopr4orl pet4v on6orooq. H nro yeuaoi 6eurepo6o0pro popqrl nou 6xei rlprl 0 = 0 yro r = b = V yn r = a sivor q o = vl +' (i-?') - tr. - "{: " f I L \b-dl \b-dl l onou a eivor ivog onoroo6rlnore oro0ep6g opr0p6g. Aur4 4 o11io4 eivor.liyo nro nol\unloxq. llepr 1et 6vo 6eurepo6o0pro 6po oro 6uvoprx6 xoorbg enio4g xor ivo ypopprxo dpo. Eivor nolu euxolo vo ppoupe ro ne6io qno ouu] t4 ox3oq. To ne6io onlo eivor ioo pa E ---ry = -! + 2(t + dy:9i dr b-a '(b-s1z

21 H APXH THD EAAXIDTHE APAEHD 357 Tripo, 9o npdner vo urp6ooupe erg ro terpoyovo our4 q oxeo4 xor vo o.lox.l4prirooupa yro ol6xlrlpo rov oyxo. A.l.l.o pio mrypq. lloro upq 9o npiner vo 6ro-ld{o y1o ro pnopouoo vo nopo pro nopobolq yro ollo noro nopogolq; Exeivo nou xovo eivor ro el49: Ynotroyi(ro 14 lopqrrxorqro yro 6vo ouooipeto a xor xorol{yo oqv e(ior,ro4 C a lblaz 2a -\ 1.' 1l 2"r, = b - ^l;\ 6 * T * + )+ Aa- 5) Aurq 4 diooo4 poro(er opxero nolurrloxrl o-l.lo nporurcsr euxol.o oloxlqprilovrog to rerpoycovo rou ne6iou. Trirpo 9o Orotrilcl r4v rrprl pou yro r4v nopopcrpo a. fvt^rpiso nog 4 ol40ero ppioxeror laprll6repo ono o,rr64nore np6xerror vo unol\oyioo xor enopdvog 6noro xor eov eivqr q nprl rou a out6 nou 9o nopo 9o eivor peyolutepo on6 ro or,lm6. Ai\-tro eov ouveli(o vo noi(r,r p ro 4 610r 6ore vo nopo rq pxporepq 6uvorr; nprl nou pnoprir, outq 4 Xop4trotepq upq 80 rivqr notru rtlo xowo mqv olqoero oe ox6oq pe 'Eror onoro6qnoc ollq up{. exeivo nou rovo orq ouv6xero eivor vo xpqorponorr'1or,l og uprl yro ro a exeiv4 nou eloxrmonorai rr1 1o:pqtrx6r4ro C. Epyo(6pevog o0pqr,:vo pe ne rexvrx6g rou ouvqoropdvou loyropou, ppioxo etxolo nclg 4 trpq rou A y1o rrlv onoio 4 lop4trx6upo 61er t4v etrdxrorl np{ t4g eivor r1 a = -2b(b + a). Avnxo rouirvrog ourq trlv npq m4v noponovra ox6.o4 ppioxo: nog q eloporq Xr,rpqnx6tqto eivor ioq pe b2+4ab+a2 2nes 3(b2 - d2) "'EXo unoloyioer ng up6g rqg xr,lpqnx6t4rog nou 6iver 11 noponovr,r oxd.oq yro Oroqopeg np6g tou troyou bla. Ovopo(o ouroug roug opropou5 C (6eutepo6o0pro). AxoLou0ei dvog nivoxog nou nepriler trlg npeg tqg lopr;ux6qtog C (6eurepo6o0Fro) oe olior1 pe ug oo:ordg npdg rqg Xop4nx6qtog C. 2 lo 100 C (oroo16) 2nen t.4423 o.721 o.434 o.267 C l6rurepo6o0pro) 2ne6 r.444 o.733 o.475 o t.l ro ro "fro nopo6erypo, otov o l6yog rov ordvov eivor ioog pe 2 npog 1, 6p rtpq lclprpx6rqtog io4 pe or eivor pio nolu xolrl npooiyyro4 yro rr; or,lmq onowqoq nou eivor Axopo xor yro peyoleg upi:g tou L6yor,: bla q npoodyyroq nopolrdver nolu Kq-h' xor po-lroro nolu xo-lutepq oe ox6oq pe rqv npdrrq npoodyyroq. E(oxolou0ei enio4g vo eivor xol4 - pe on6xi.rorl povo l0olo - ox6p4 xor 6rov o l6yog bfa eivot ioog pe lo npog l. AMo otov o.loyog yivsr ioog Fe IOO npos l, ro npolloro opli(ouv vo oypreuouv xor 11 Xopqrxorqro nou unoloyi(o eivor iorl pe owi yro r4 oooul npq nou eivor ioq pe Art6 rqv oll4 nleupo, yro ivo loyo orrivcov ioo pe I.5, I onovrqoq eivor oprmq yto tr1-rq L6you 6e ioq pe I.t, 4 onovrqoq nou npor0ncr eivor ioq pe owi yro tq ooot4 nou eivor , 6nou 4 onort4o4 eivor no.lu xo.lq, nopo no.lu Kolrl. "Eog 66r,:oo ouro to nopo6eiyporo nprbtov yro vo oos Oeilcl rq 9eclp4uxrl olio ulg oplqg r4g elolrotqg Opooqg xor yevrx6repo rov opxrirv eloxiorou xor 6eutepov yro vo oog 6eilt: tqv npogronxrl lpqorp6trlto roug' xor o1 p6vo yro rov unoloyropo prog Xr,rp4trxot4rog xor po-lroro 6rov rl6rl \.vopi(o rqv onovr4o4. fro xo0e ollo oxqpo, pnopeire vo powdgete xonoro ouyxexptp6vo ne6io pe xonoreg oyvc:oreg nopop6rpoug 6nog eivor 11 a xor m4 ouv6lerq vo rls npooopf6oere yro vo ppeire rrlv eloxrorrl Lo6ec oprmo nerpoponxo onorel6oporo yro Oroqopo o.l-lo 6uoxo.Lo npo6lqporo.

22 35A 8 I9.2. MIA DHMEIC'DH IIOY IIPODTE@HKE META TH AIAAE@H 19.2 Mic o4petooon rrou npootd04xe petri 14 6tdle[4 "@o 40elo vo npoo06oo xdn yro ro onoio 6ev eilo ro 1p6vo vo ro no ot4 6rd-lel4. (<Doivopor nowo vo npoerorpo(opor vo no neproo6repo on6 ooo npologoivro vo n(,)). 'OnoS ov6qepo xor nporlyoupiv<og, ev6roq6p0qxo yro 6vo npo6l4po evri epyo(61rouvq ndvo oe oudl 14 6rd-lefq xor rrbpo 9d:ko vo oog no nor6 eivor our6 ro np66l4po. Avdpeoo mrg op16g eloxiorou nou So pnopouoo vo ovoqepr,l noporqp4oo nog or nro noll65 on6 our6g npo6pxoltor pe rov 6vo q pe tov oi,-lo rp6no on6 r4v op1r1 t4g elo4m4g 6pooqg r49 prlxovrxqg xor tqg qlertpoouvopuqg. A-tr-Lo unopxer eniorlg pio xor4yopio oplriw or onoieg 6ev epninrouv oe out6 rov xqv6va. Og 6vo nopo6erlpo, eov elovoyxoooupe xonoro peuporo vo xrvqoouv p6oo on6 6vo roppon ufuxou yro ro onoio roxuer o v6pog rou Ohm, to peuporo 9o xoroveprloouv on6 p6vo roug p6oo mo ulff6 xor pe rdroro tp6no riroe 4 9epp6r4ro 4 onoio 9o Drlproupyq0ei vo eivor 11 eloymq 6uvorr1. Enioqg pnoporipe vo 6oupe (eov ro npoypoto nopopsivouv oe pio roo0epprxq roroorooq) n<,rg o pu0ir6g pe rqv onoio lopgover Xrbpo 11 Drlproupyto ev6pyetog eivor o e?lolrotog 6uvor69. Tripo, our4 4 op1{ pnopei vo lp4orponorrl0si enioqg, oupqovo pe tqv xlootxq 9er,:pio xor yro rov xo0oprop6 r4g xorovopqg rrov rolurqrov tov 4lercpoviov pdoo oe 6vo piro-l-l.o nou UeroQaperonoro peupo. H xorovofrl ourrirv rov rolur4rov 6ev eivor oxprorig pio KqrovoFrl oe roopponio [Keqoloro 40 rou np6rou ropou, eliocooq (40.6)] lovr,l rcov n-leuprx6v xrv4oeov nou ng loporrqpi(ouv. H v6o xotovopq pnopei vo ppeoei yp4orponorcbwog qv oplq o0pqr,:vo ps tqv onoio q oc,rm4 rorovoprl yro 6vo 6e6op6vo peupo 9o np6ner vo eivor exeivq yro tqv onoio rl $'lportiq nou ovonruooeror orq povobo rou 1p6vou.L6yo rov ouyxpouoec,rv nou nopot4pourtor, vq ivol rl stroxlotrl 6uvot4. Oorooo, 4 oomq neprypoqq qg or:pneprqopog rr,:v qlsrrpoviov, 9o np6ner vo 6i6eror on6 r4v x6owopqxovrxq. H eprin4oq eivor: pnopei q i6ro opxq rqg Oqproupyiog qg eloxroqg evtponiog vo roluer enioqg xor yro ng xotoorooerg nou neprypoqowor ono tqv rgovnxq Urlxovxn; Aev 6xor pper ox6po xonoro onowqo4 yro ouro to eprinqpo. "Bi6oro, ouu] 4 eprit4o4 6;1er ro16 x0pro l6yo oxo64poix6 ev6roqdpov. T6roles opxis lvol ouvopnoonx6g xor ndvrote o(i(er rov x6no vq npoonoeoupt vo 6oupe to n6oo yevrxig eivor. A.l-Lo enioqg, on6 pio ox6p4 nro npornx4 ormxrl yr,:vio, 9eiar vo lvr,lpi(co. Mo(i pe xonoroug ouvepydreg pou 61o Oqpooreuoer pio epyooio orqv onoio dxoupe unoloyioer npooel'ytotrxo xor pe t4 po40ero rr,rv opxriv rqg x6owop4xcvrxqg, ulv 4Lercprxr1 owiotoorl nou ortrlopbovetor 6vo rl.lertpovro orov 6r6p1eror p6oo on6 dvo 1ov1Ko KpumoMo 6nr,:9 ro NaCl lfe]mman, Hellworth, Iddings, and Platzman, "Mobility of Slow Electrons in a Polar Crystal", Phys.Rev.127,1OO4 (1962)1. Al,\o eov unrlple pio opxrl eloliorou, 9o pnopouoops vo xotoorqooupe to onotel6oporo pog oxoprl nto oxpr6rl, pe tov i6ro oxpr&bg rpono pe rov onoio 11 opxq elolimou yro r4v nepirnoo4 rqg lclprprxotqtos rou nukvorrl, pog en6rperpe vo emru;1oupe pio reroro oxpigero ox6pr1 xor eov eilope p6vo pio xowprxrl onoprl yro to 4lercprx6 ne6io."