Generalizations

  • November 2019
  • PDF

This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA


Overview

Download & View Generalizations as PDF for free.

More details

  • Words: 11,473
  • Pages: 20
L_dkltl eim[ebdm\Zg\t\³NbehkhnkdbZel_jgZlb\b”, 2007, 4. _________________________________________________________________ ?CKL
1

ij_l_gpby gZc-fgh]h ^Z k_ ^h[eb`Z\Z ^h hgZab b^_ZegZdjZcgZp_egZl_hj_lbqghlhbake_^\Zg_” FZdkIeZgd Ijbgpbitl gZ gZc-fZedhlh ^_ckl\b_ _ \ hkgh\ZlZ gZ aZdhgbl_ aZ aZiZa\Zg_ j_ki gZ kbf_ljbbl_  dZdlh ih hlghr_gb_ gZ \tgrgbl_ ^\b`_gby lZdZ b ih hlghr_gb_ gZ ³\tlj_rgbl_´ ^\b`_gby1 kthl\ dZeb[jh\tqgbl_ kbf_ljbb  Hllmd lhcgZbklbgZfh`_^Z ij_l_g^bjZq__h[_^bgbl_egbylijbgpbigZkt\j_f_ggZlZ nbabdZ AZ baykgy\Zg_ gZ lh\Z fm agZq_gb_ j_rZ\Zsb kZ ^\_l_ l_hj_fb gZ ?fb Gvhl_j2 Itlyl aZ h[h[sZ\Zg_ gZ ijbgpbiZ gZ gZc-fZedhlh ^_ckl\b_ fbgZ\Z ij_a lyoghlhnbehkhnkdhhkfbkeyg_ Kfbktetl gZ itj\ZlZ l_hj_fZ k_ jZadjb\Z \ dhgp_ilmZegbl_ jZfdb gZ ki_pbZegZlZ l_hjby gZ hlghkbl_eghkllZ Ihke_^gZlZ hij_^_ey \jtadZlZ f_`^m ljbl_ ijhkljZgkl\_gb dhhj^bgZlb b \j_f_lh dZlh ijhkljZgkl\h-\j_f_ ijhkljZgkl\hlhgZFbgdh\kdb GZebp_kZke_^h\Zl_eghq_lbjbhkbkijyfhdhblh fh`_^ZbfZ^_k_lhkgh\gb^\b`_gbyq_lbjbljZgkeZpbbbr_kljhlZpbbLh\ZkZ ^_k_ll_hi_jZlhjZ3gZ]jmiZlZgZIhZgdZj_ihhlghr_gb_gZdhylhkihj_^itj\ZlZ 1 2

Kj\ k dhgp_ipbylZ aZ kdjblbl_ ^\b`_gby gZ O_efohep \` b [_e dtf l_dklZ gZ F IeZgd Itj\ZlZ l_hj_fZ ]eZkb :dh bgl_]jZetl I _ bg\ZjbZgl_g ih hlghr_gb_ gZ ]jmiZlZ r lh ρ  











 ³

´

































!



ebg_cgh g_aZ\bkbfb dhf[bgZpbb hl eZ]jZg`h\b bajZab k_ h[jtsZl \ ^b\_j]_gpbb b h[jZlgh hl ihke_^ghlh mkeh\b_ ijhbalbqZ bg\ZjbZglghkl gZ I ih hlghr_gb_ gZ gydZd\Z ]jmiZ r ´ G_l_j   
!

G_l_j :fZeb ?fb Gvhl_j _ g_fkdZ fZl_fZlbqdZ ba\tgsZl_g ij_ih^Z\Zl_e \ =vhlbg]_gkdby mgb\_jkbl_l k h]jhf_g ijbghk \ Ze]_[jZlZ b fZl_fZlbq_kdZlZ nbabdZ ihkj_^kl\hf pblbjZgbl_ ^\_ l_hj_fb 3 ?fb Gvhl_j jZa^_ey g_ij_dtkgZlbl_ ]jmib dhblh ihjZ^b lh\Z q_ kZ g_ij_dtkgZlb \bgZ]b kZ k [_adjZcgh b lh g_ba[jhbfh dhebq_kl\h _e_f_glb gZ djZcgb b [_adjZcgb IZjZf_ljbl_ g_aZ\bkbfbl_ ijhf_geb\b gZ nmgdpbbl_ ijb ^\_l_ l_hj_fb kZ djZ_g [jhc gh h[bdgh\_gh k_ baf_gyl \ [_adjZ_g bgl_j\Ze Ijb itj\ZlZ l_hj_fZ l _ ijb djZcgbl_ ]jmib l_ g_ihkj_^kl\_gh hij_^_eyl ]jmiZlZ ijb \lhjZlZ l_hj_fZ l _ ijb [_adjZcgbl_ ]jmib y hij_^_eyl qj_a ihkj_^gbq_kl\hlh gZ ijhba\hegb ^bn_j_gpbjm_fb nmgdpbb Ijhf_`^mltqgh iheh`_gb_ aZ_fZl ]jmibl_ dhblh aZ\bkyl hl [_adjZ_g [jhc iZjZf_ljb gh g_ aZ\bkyl hl gblh _^gZ ijhba\hegZ nmgdpby gZ dhc ^Z _ hl l_ab iZjZf_ljb G_ij_dtkgZlbl_ ]jmib h[bdgh\_gh k_ hibk\Zl qj_a hi_jZlhjb gZij ljZgkeZpbb jhlZpbb hljZ`_gby b ij \` gZij Weebhl >h[_j dhblh aZ djZcgbl_ ]jmib kZ djZ_g [jhc aZ ijhf_`^mltqgby \ZjbZgl \ h[sby kemqZc kZ ba[jhbfh dhebq_kl\h Z aZ [_adjZcgbl_ ]jmib kZ g_ba[jhbfh dhebq_kl\h ltc dZlh aZ \k_db iZjZf_ltj bfZ hi_jZlhjgZ nmgdpby b g_ gZ \k_db iZjZf_ltj dZdlh _ ijb djZcgbl_ ]jmib Z gZ \kydZ klhcghkl gZ iZjZf_ltjZ kthl\_lkl\m\Z bah[sh jZaebq_g hi_jZlhj ?^gZ b ktsZ [_adjZcgZ ]jmiZ fh`_ ^Z k_ ij_^klZ\b dZdlh kijyfh ijhba\hegb nmgdpbb hl djZcgby kb [jhc iZjZf_ljb dh_lh _ ih^oh^tl gZ Gvhl_j lZdZ b kijyfh dhgklZglb gZ [_adjZ_g [jhc iZjZf_ljb Ihke_^gZlZ _d\b\Ze_glghkl _ ]heyfh h[h[s_gb_ gZ Evh`Zg^jh\hlh ij_h[jZah\Zgb_ l _ gZ _d\b\Ze_glghkllZ gZ oZfbelhgh\h obe[_jlh\h ijhkljZgkl\h b eZ]jZg`h\h ik_\^hjbfZgh\h ijhkljZgkl\h ij_^klZ\yg_ gZ g_ij_dtkgZlZ ]jmiZ ]jmiZ gZ Eb qj_a hi_jZlhjbl_ gZ Z\lhfhjnbafZ gZ kthl\_lghlh ijhkljZgkl\h Lh\Z _ _^bg itl aZ

     



 













































 

































































 



































































  











´

´























































































³





















































 

 











































































































  













   





   









































2

l_hj_fZlZgZGvhl_js_bfZ^_k_laZdhgZaZaZiZa\Zg_dZdlhke_^\Zihhlghr_gb_ gZ ih^]jmiZlZ gZ ljZgkeZpbbl_ ih hklZ gZ \j_f_lh _ aZdhgtl aZ aZiZa\Zg_ gZ _g_j]bylZ ljbl_ ih^]jmib gZ ljZgkeZpbbl_ ih ijhkljZgkl\_gbl_ hkb kZ k\tjaZgb ktk aZdhgZ aZ aZiZa\Zg_ gZ bfimekZ ih^]jmibl_ gZ ljbl_ jhlZpbb f_`^m ljbl_ ^\hcdbijhkljZgkl\_gbhkbhij_^_eylaZdhgZaZaZiZa\Zg_gZfhf_glZgZbfimekZ Ih^]jmibl_gZljbl_jhlZpbbgZ^\hcdbl_hl\kydZijhkljZgkl\_gZhkb\j_f_\ZlZ hkhij_^_eyl qbklh ehj_gph\ZlZbg\ZjbZglghkl4blh\Z_kh[kl\_gbylijbghkgZ ki_pbZegZlZl_hjbygZhlghkbl_eghkllZ hklZgZebl_k_^_fbgl_]jZeZgZ^\b`_gb_ j_kiaZdhgbgZaZiZa\Zg_kZba\_klgbgZbk_ba\_`^ZlhldeZkbq_kdZlZnbabdZ 

Ki_pbZegh \gbfZgb_ ljy[\Z ^Z k_ h[tjg_ gZ hljZ`_gbylZ ijb \k_db hl pblbjZgbl_ ^_k_l iZjZf_ltjZ Ih hlghr_gb_ gZ lyo \_ebqbgbl_ k_ ^_eyl gZ ljb lbiZq_lgb kdZeZjgb -_g_j]bylZg_q_lgb \_dlhjgb –bfimektlbfhf_gltlgZ bfimekZ b bfZ]bg_jgb ehj_gph\bl_ jhlZpbb kijyfh ^\hcdbl_ bfZ]bg_jgZ hk gZ \j_f_lh b gydhy hl ljbl_ j_Zegb ijhkljZgkl\_gb hkb  hl dhblh ke_^\Z CPT

l_hj_fZlZ gZ IZmeb    BfZ]bg_jgbl_ hljZ`_gby ktsh lZdZ bfZl aZ ke_^kl\b_ki_pbnbqghlhkZfhaZd\Zglh\byk\ylgZebqb_gZfbdjhh[_dlbkihempye kibg gZjbqZgb n_jfbhgb dhblh ijb aZ\tjlZg_ gZ º ijhf_gyl agZdZ kb ih^qbgy\Zsb k_ gZ ijbgpbiZ gZ aZ[jZgZlZ gZ IZmeb b \ ]he_fb ZgkZf[eb jZaij_^_eysbk_ihklZlbklbdZlZgZN_jfb->bjZd:dh\kbqdbdeZkbq_kdbh[_dlb bd\Zglh\bl_hllbiZgZ[hahgbl_5ih^hljZ`_gb_³jZa[bjZl´aZ\tjlZg_gZº, lh aZ n_jfbhgbl_ hljZ`_gb_ hagZqZ\Z aZ\tjlZg_ gZ º, dZd\hlh aZ [hahgbl_ _ ^\_ (360º=180º+180º) hljZ`_gbybihjZ^blh\Zkt\iZ^_gb_ AZdhgbl_ aZ aZiZa\Zg_ fh]Zl ^Z k_ jZa]e_^Zl b dZlh gZmqgh ih-lhqgh nbabq_kdh baykgy\Zg_ dZd\h ljy[\Z ^Z k_ jZa[bjZ ih^ kts_kl\m\Zg_ Kts_kl\m\Z hgh\Zdh_lhk_aZiZa\ZMgb\_jkZeghkts_kl\m\Zshlhltdfhbmgb\_jkZeghs_k_

bgl_jn_jbjZg_ [_a kfms_gby gZ l_hjbylZ gZ hlghkbl_eghkllZ b d\Zglh\ZlZ f_oZgbdZ ltc dZlh l_ e_`Zl \ gZitegh jZaebqgb gZijZ\e_gby l _ ^Z k_ m^Z^_ [_a hkh[_g ljm^ ^Z k_ kta^Z^_ kbkl_fZ hl ihgylby dhylh ^Z h[o\ZsZ dZdlh LH lZdZ b DF LZab ljm^ghkl bfZ g_ nhjfZegh fZl_fZlbq_kdb Z4 ijbgpbi_g oZjZdl_j Rj_^bg]_j Dtf ehj_gph\bl_ ij_h[jZam\Zgby ijbgZ^e_`Zl ktsh lZdZ b h[bdgh\_gbl_ \tjl_gby hij_^_e_gb hl ^\_ ijhkljZgkl\_gb hkb gZij Weebhl >h[_j 5 G_ k_ ih^qbgy\Zl gZ ijbgpbiZ gZ IZmeb b ke_^h\Zl_egh ijhba\he_g [jhc hl lyo fh]Zl ^Z aZ_fZl _^gh b ktsh _g_j]_lbqgh ktklhygb_ AZ kf_ldZ gZ lh\Z ih\_q_ hl ^\Z [hahgZ g_ fh]Zl ^Z k_ gZfbjZl \ _^bg b ktsb fhf_gl hl \j_f_ \j_f_\h ktklhygb_ Zdh \j_f_lh _ d\Zglm\Zgh ih ih^h[b_ gZ _g_j]bylZ ?^gh\j_f_gghlh d\Zglm\Zg_ gZ \j_f_lh b _g_j]bylZ k_ aZ[jZgy\Z hl ijbgpbiZ gZ g_hij_^_e_ghkllZ JZaij_^_e_gb_lh gZ ]he_fb ZgkZf[eb hl [hahgb k_ ih^qbgy\Z gZ klZlbklbdZlZ gZ ;ha_-:cgsZcg Kj_sZgh ihgydh]Z l\tj^_gb_ q_ deZkbq_kdb h[_dlb kZ [hahgb _ g_dhj_dlgh :dh [yoZ [hahgb aZ lyo \j_f_lh s_r_ ^Z _ d\Zglm\Zgh b \t\ \kydh \j_f_\h ktklhygb_ [b [beh \tafh`gh ^Z bfZ g_ ih\_q_ hl ^\Z h[_dlZ Hk\_g lh\Z gyfZr_ ^Z k_ ih^qbgy\Zl gZ klZlbklbdZlZ gZ FZdkm_e;hepfZg j_ki gZ =b[k b syoZ ^Z h[jZam\Zl ihgydh]Z [ha_-dhg^_gaZlb ³



³

 



´





















































































































































 





























































 































































´











 









































 









´





´³  



























´

3

aZiZa\ZMgb\_jkZe_g_ ihg_^hk_]Z aZdhgtlaZaZiZa\Zg_gZ_g_j]bylZagZqbly_ nbehkhnkdZlZ iZgZp_y Z fZl_jbylZ s_ bfZ ^\_ nhjfb \_s_kl\_gZ b ihe_\Z ihke_^gZlZ qbklh _g_j]_lbqgZ
Kihj_^ Gvhl_j l_hj_fZ II fh`_ ^Z k_ kfylZ aZ gZc-]heyfh \tafh`gh h[h[s_gb_ hl ]e_^gZ lhqdZ gZ l_hjbylZ gZ ]jmibl_ gZ h[sZlZ l_hjby gZ hlghkbl_eghkllZ

6





    ³







































´

4

oZfbelhgh\ZlZnhjfmebjh\dZjZ\ghihklZ\ybg\ZjbZglZb]jmiZlZdZlh^\_]jmib b kthl\^\Zbg\ZjbZglZ dhblhkZ^\hcgkl\_gb\kfbkteZgZIhgljy]bg7. :dh k_ hklZg_ \ jZfdbl_ gZ eZ]jZg`bZgZ lh ij_^eZ]Zgbyl lmd ih^oh^ ba]e_`^Z dZlh h[h[sZ\Zg_ ih-kdhjh dhgdj_lbabjZg_  aZ kemqZy gZ bahi_jbf_ljbqgZlZaZ^ZqZ8 ihklhygkl\hgZ^_ckl\b_lhfbgbfmfgZ_gljhibylZgZ jZaij_^_e_gb_lh gZ ^_ckl\b_lh \ ijhkljZgkl\h-\j_f_lh  Kihj_^ f_g h[Zq_ ktsghkllZgZh[h[s_gb_lhg_fh`_^Zk_ij_^klZ\bhglheh]bqgh b^hjbZ^_d\Zlgh fZl_fZlbq_kdb9  \ eZ]jZg`h\hlh gZijZ\e_gb_ Ly k_ ktklhb \ lh\Z ^Z k_ \t\_^_ dZlh itj\hhkgh\Z b ke_^h\Zl_egh aZiZa\Zshlh k_) bgnhjfZpbylZ b ^Z k_ hij_^_eb dZlh g_kbf_ljbqgh hlghr_gb_ gZ ^\_ aZf_gbfb ]jmib10 GZ lh\Z \t\

Fgh`_kl\hlh hl \kbqdb g_ij_dtkgZlb oZjZdl_jb gZ ^Z^_gZ lhiheh]bqgZ Z[_e_\Z ]jmiZ G h[jZam\Z ]jmiZ G* hlghkgh h[bqZcghlh mfgh`_gb_ gZ hljZ`_gby G _ ^\hcgkl\_gZ beb ^mZegZ gZ G*. hij_^_eyg k nhjfmeZlZ φ(x): (χ)=χ(x) aZ x∈G, Kts_kl\m\Z dZghgbq_g ohfhfhjnbatf φ(x): G: χ∈G* Ijbgpbitl gZ ^\hcgkl\_ghkllZ gZ Ihgljy]bg l\tj^b q_ aZ ehdZegh dhfiZdlgZ ]jmiZ G dZghgbqgbyl ohfhfhjnbatf φ _ bahfhjngh lhiheh]bqgZ ]jmiZ 8 Kj\ k Dhghie_\Z Ihih\ Bah[sh fh`_ ^Z k_ dZ`_ q_ bfZ ^\_ ]he_fb gZijZ\e_gby \ jZa\blb_lh gZ d\Zglh\ZlZ f_oZgbdZ eZ]jZg`h\h b ]_hf_ljbqgh oZfbelhgh\h b ^bgZfbqgh EZg]jZ`h\ZlZ nhjfmebjh\dZ gZ d\Zglh\ZlZ f_oZgbdZ kZfbl_ l_hj_fb gZ Gvhl_j ki_pbZegZlZ b h[sZlZ l_hjby gZ hlghkbl_eghkllZ dZeb[jh\tqgbl_ l_hjbb h[_^bg_gbl_ l_hjbb gZ \aZbfh^_ckl\bylZ ijbgZ^e_`Zl gZ itj\hlh gZijZ\e_gb_ AZ lyo _ oZjZdl_jgh q_ jZa]e_`^Zl h[_dlbl_ b \aZbfh^_ckl\bylZ f_`^m lyo kZfh dZlh jZaebqgb lbih\_ h[_dlb \ _^gh h[sh fgh]hh[jZab_ Z [_e_] _ \h^_sZlZ jhey gZ eZ]jZg`bZgZ Dtf \lhjhlh ijbgZ^e_`Zl Gxlhgh\ZlZ b OZfbelhgh\ZlZ nhjfmebjh\dZ gZ deZkbq_kdZlZ f_oZgbdZ klZlbklbq_kdZlZ f_oZgbdZ b klZlbklbq_kdZlZ l_jfh^bgZfbdZ klZg^Zjlgbyl nhjfZebatf gZ d\Zglh\ZlZ f_oZgbdZ gZijZ\e_gb_lh gZ d\Zglh\ZlZ bgnhjfZpby AZ lyo _ oZjZdl_jgh q_ \t\_`^Zl ^\_ ebg_cgb fgh]hh[jZaby ]_hf_ljbqgh gZij kt^ b ]_hf_ljh-^bgZfbqgh gZij b^_Ze_g ]Za \ kt^Z - dZlh kthlgZkyg_lh f_`^m lyo k_ h[kt`^Z \ l_jfbgbl_ gZ ^bgZfbdZlZ gZ klZlbklbdZlZ b \_jhylghklbl_ Hlebqbl_e_g [_e_] _ ^hfbgbjZg_lh gZ oZfbelhgbZgZ JZa^_eyg_lh _ ih-kdhjh ih klbe gZ fbke_g_ gZ bake_^h\Zl_ebl_ lbi :cgsZcg b lbi ;hj ltc dZlh Evh`Zg^jh\hlh ij_h[jZah\Zgb_ b g_]h\bl_ h[h[s_gby g_ij_dtkgZlh ih^^tj`Z dhfmgbdZpbylZ f_`^m ^\ZlZ lbiZ nhjfZebafb gZ jZ\gbs_lh gZ _d\b\Ze_glghkl Kj\ b k DeZcgh\ZlZ b JbfZgh\ZlZ dhgp_ipby gZ ]_hf_ljbylZ [b^_cdb ijbeh`_gb dtf nbabdZlZ Dhghie_\Z Khdhebd -126). 9 Kj\ k [_e 3. Kihj_^ baykg_ghlh \ lZab [_e_`dZ fZl_fZlbq_kdb h[h[s_gb_lh k_ ktklhb \ lh\Z ^Z k_ fbg_ dtf ijhba\hegb nmgdpbb gZ [_adjZ_g [jhc iZjZf_ljb dh_lh _ fgh]h ih-e_kgh ^Z k_ gZijZ\b \ obe[_jlh\h ijhkljZgkl\h b ^Z k_ h[kt`^Z dZd\h s_ k_ aZiZa\Z \ lhab kemqZc FZl_fZlbq_kdZlZ ljm^ghkl k_ ktklhb \ lh\Z ^Z k_ gZf_jb ite_g [Zabk aZ ijhba\hegh badjb\_gh Obe[_jlh\h ijhkljZgkl\h k ijhf_geb\Z djb\bgZ dhclh ih \tafh`ghkl ^Z _ ba[jhbf k_iZjZ[_e_g 10 Kj\ k [_e GZijbf_j ^Z jZakt`^Z\Zf_ lZdZ Ijhba\hegh fgh`_kl\h ktk ktshlh dZj^bgZegh qbkeh fh`_ ^Z k_ jZa]e_^Z dZlh nemdlmZpby gZ ]jmiZ dhylh _ k fZdkbfZegZ _gljhiby l _ jZ\ghf_jghkl ih hlghr_gb_ gZ \kydZ k\hy nemdlmZpby Fh`_ ^Z k_ kjZ\gb b k _gljhibylZ gZ Dhefh]hjh\-KbgZc Dhedhlh nemdlmZpbylZ bglmblb\gh _ ih-]heyfZ lhedh\Z ]jmiZlZ gZ oZjZdl_jbl_ gZ lZab ]jmiZ s_ gZfZey\Z k\hylZ kltidZ gZ ^bkdj_lghkl \k_ _^gh s_ kZ g_h[oh^bfb ih\_q_ jZajy^b aZ dh^bjZg_ gZ nemdlmZpbbl_ H[bqZcgZlZ \_jhylghklgZ fyjdZ aZ bgnhjfZpby dZlh [bnmgdpbhgZe hl nmgdpby b eh]Zjbltf gZ ^jm]Z nmgdpby ijb gydZd\Z fyjZ fh`_ ^Z k_ ltedm\Z dZlh iehs gZ badjb\_gh ^_dZjlh\h ijhba\_^_gb_ hl nemdlbjZsZlZ ]jmiZ b ]jmiZlZ gZ oZjZdl_jbl_ gZ ^jm]Z nemdlmbjZsZ ]jmiZ \tjom gydZd\Z ih\tjoghkl Ke_^h\Zl_egh bgnhjfZpbylZ _ fyjdZ aZ ^_nhjfZpbylZ gZ \j_f_lh b g__j]h^bqghkllZ gZ kbkl_fZlZ BgnhjfZpbylZ fh`_ ^Z k_ hij_^_ey b lZdZ l _ dhgljZ\ZjbZglgh qj_a baf_g_gb_ gZ nemdlmZpbbl_ ijb aZ^Z^_g [Zabk oZjZdl_jb keh`ghkl b h[jZlgh dh\ZjbZglgh qj_a baf_g_gb_ gZ keh`ghkllZ ijb aZ^Z^_gZ nemdlmZpby 7































































 





 









































  







 





































































































 

































































































 





















 

























 

































 



























 































































































 

































 



































































 ³

´























































































































































































































  







*













































 

5

nhjfZebafZ gZ eZ]jZg`h\hlh gZijZ\e_gb_ dhclh _ gZ jZakeh_ghlh ijhkljZgkl\h  kthl\_lkl\m\Z g_kbf_ljbqghlh hlghr_gb_ f_`^m [ZaZ b kehc dZdlh b k_q_gb_  LZdZ bgnhjfZpbylZ _ g_ebg_cghlh b j_eZpbhggh h[h[s_gb_ gZ km[klZgpbhgZebabjZgZlZ _g_j]by Lh]Z\Z ihklmeZltl gZ IeZgd E= «ω = hν)11 k_ ltedm\ZdZlh_d\b\Ze_glghklgZ_g_j]bylZk[_ajZaf_jgZlZbgnhjfZpbyaZ_^bgbpZ \j_f_ Z aZiZa\Zg_lh gZ bgnhjfZpbylZ nbabq_kdb k_ ij_^klZ\y dZlh dhgklZglgh ^_ckl\b_ [jhc d\Zglb Nh  Z d\Zgltl k_ jZa[bjZ dZlh _e_f_glZj_g ba[hj f_`^m ^\_ jZ\gh\_jhylgb \tafh`ghklb bit  Ba[hjtl _ f_`^m fZdkbfZegZ b fbgbfZegZ _gljhiby :dh ba[hjtl k_ hkts_kl\y\Z hl ³^_fhgZ gZ FZdkm_e´12 beb hl ohjZlZ _gljhibylZs_gZfZey\Zj_kibgnhjfZpbylZs_k_m\_ebqZ\ZQ_ohjZlZ–ltdfhb ^hjb kZfh k lh\Z k_ aZgbfZ\Zf_ _^\Z eb [m^b ktfg_gb_ \tijhktl _ ^Zeb kts_kl\m\Zl ijbjh^gb aZdhgb beb f_oZgbafb dhblh ^_ckl\m\Zl dZlh hgh\Z

H[sbyl kemqZc _ lhab ijb k^\hy\Zg_ entanglement) – baf_g_gb_ b gZ keh`ghkllZ b gZ nemdlmZpbbl_ – kh[kl\_gh \babjZg hl nemdlmZpbhggh-^bkbiZlb\gZlZ l_hj_fZ Ijb g_]h fh`_f ^Z \t\_^_f bgnhjfZpbhggZ fyjZ h[Zq_ aZ kt`Ze_gb_ k bgl_]jZe_g eh]Zjbltf ih^ agZdZ gZ ^bn_j_gpbZeZ < kemqZy gZ k^\hy\Zg_ _ gZebp_ f_`^bg_g kemqZc hν b dL kZ hl _^gZdt\ ihjy^td \t\ nhjfmeZlZ gZ IeZgd IhieZ\kdbc beb GZcd\bkl =bga[mj] aZ kj_^gZlZ _g_j]by j_ki kj_^gZlZ q_klhlZ l gZj kj_^gZ ki_dljZegZ ietlghkl IhieZ\kdbc -42). <_jhylghkllZ aZ k^\h_gh ktklhygb_ fh`_ ^Z k_ ihemqb ih itly dtf jZaij_^_e_gb_lh gZ =b[k Zdh g_ k_ ij_g_[j_]g_ dZlh g_agZqbl_egZ _g_j]bylZ gZ d\Zglh\ZlZ kbkl_fZ \ kjZ\g_gb_ k lZab gZ kj_^ZlZ EZg^Zm Ebrnbp 1976: 101hkh[ nhjf 28.2). :dh k^\hy\Zg_lh k_ jZa]e_^Z dZlh bgnhjfZpbhg_g dZgZe lh kihj_^ l_hj_fZlZ gZ R_ghg b ke \` b IhieZ\kdbc aZ ijhimkdgZlZ kihkh[ghkl ijb rmf lh ly ihemqZ\Z fZdkbfZegZ klhcghkl ijb fZdkbfZegh k^\hy\Zg_ l _ aZ gZk ijb hν=ln3.kT L_hj_fZlZ gZ R_ghg bfZ badexqbl_egh ^te[hd nmg^Zf_glZe_g nbehkhnkdb kfbkte \ kemqZcghlh \ta^_ckl\b_ k \tgr_g ba]e_^ gZ [ye ]Zmkh\ rmf fh`_ ^Z _ dh^bjZgZ fZdkbfZegZ bgnhjfZpby sapienti sat) ke_^ dZlh rmftl _ g_ba[_`_g 11 Ihgydh]Z g_hkgh\Zl_egh gZjbqZg ihklmeZl gZ :cgsZcg g_hkgh\Zl_egh ltc dZlh IeZgd ]h nhjfmebjZ ] \t\ \jtadZ k h[ykgy\Zg_ gZ baetq\Zg_lh gZ Z[khexlgh q_jghlh lyeh Z :cgrZcg ]h ijbeZ]Z \t\ \jtadZ k l_hjbylZ gZ nhlh_n_dlZ 12 Gh Zdh kb ij_^klZ\bf kts_kl\h qbblh kihkh[ghklb kZ lZdZ bahklj_gb q_ lh [b fh]eh ^Z ke_^b \kydZ fhe_dmeZ \ g_cghlh ^\b`_gb_ lh lZdh\Z kts_kl\h qbblh k\hckl\Z kZ ktsghklgh djZcgb dZdlh gZrbl_ kh[kl\_gb [b [beh \ ktklhygb_ ^Z gZijZ\b hgh\Z dh_lh _ g_\tafh`gh aZ gZk Ltc dZlh \b^yof_ q_ fhe_dmebl_ \ kt^ ite_g k \ta^mo ijb _^gZd\Z l_fi_jZlmjZ k_ ^\b`Zl ktk kdhjhklb ih gbdZdt\ gZqbg _^gZd\b fZdZj kj_^gZlZ kdhjhkl aZ \k_db ]heyf [jhc hl lyo ba[jZgb ijhba\hegh ihqlb lhqgh _^gZd\Z >Z ij_^iheh`bf k_]Z q_ lZdt\ kt^ _ jZa^_e_g gZ ^\_ qZklb : b < qj_a ij_]jZ^Z \ dhylh bfZ fZedZ ^midZ b q_ kts_kl\h dh_lh fh`_ ^Z \b`^Z hl^_egbl_ fhe_dmeb aZl\Zjy b hl\Zjy lZab ^midZ lZdZ q_ ^Z iha\hey\Z gZ kZfh gZ ih-[tjabl_ fhe_dmeb ^Z ij_fbgZl hl : \ < Z kZfh gZ ih-[Z\gbl_ ^Z ij_fbgZl hl \ : LZdZ lh - [_a jZaoh^ gZ jZ[hlZ - s_ ih\brb l_fi_jZlmjZlZ gZ B b s_ ihgb`b l_fi_jZlmjZlZ gZ : \ ijhlb\hj_qb_ k \lhjby aZdhg gZ l_jfh^bgZfbdZlZ Maxwell (1871): 4 (308)). Ke_^ fbke_g _dki_jbf_gl FZdkm_e ijZ\b l\tj^_ ^te[hdhlh b ijhgbpZl_egh aZdexq_gb_ q_ Zdh lhiebgZlZ _ ^\b`_gb_ gZ qZklbl_ gZ lyehlh lh hl^_egbl_ ^\b`_sb k_ qZklb gZ lyehlh ljy[\Z ^Z [t^Zl lhedh\Z fZedb beb lhedh\Z g_hk_aZl_egb q_ ih gbdZdt\ gZqbg g_ fh]Zl ^Z [t^Zl kij_gb Dmag_ph\Z dmjkb\tl fhc – < I AZ \kbqdb jZa]e_^Zgb fh^_eb gZ ijhp_kZ gZ mijZ\e_gb_ k_ ihdZa\Z q_ g_]_gljhibcgbyl _n_dl _ agZqbl_egh ihfZetd hl jtklZ gZ _gljhibylZ ij_^ba\bdZg hl jZak_c\Zg_lh gZ _g_j]bylZ b ijhp_kZ gZ ihemqZ\Zg_ gZ bgnhjfZpby b kh[kl\_gh gZ mijZ\e_gb_ Ih lZdt\ gZqbg hlgh\h k_ ihl\tj`^Z\Z ba\h^tl aZ kts_kl\_gZlZ g_h[jZlbfhkl gZ bgnhjfZpbhggbl_ ijhp_kb IhieZ\kdbc Hlghkgh d\Zglh\h-f_oZgbqgby \ZjbZgl gZ ^_fhgZ Lloyd 1997. 

























 

























































































 %









































































´



















 































































































































































 













































 













 















































































´











































 











 





















  









  















































































   









 





  











































































  









 

























































   





³































 

























 ³

 





















   



´

6

´fbgbZlxjgh kts_kl\h´ LZdZ g_ aZiZa\Zg_lh gZ _g_j]bylZ dh_lh hklZ\Z \Zeb^gh dZlh qZkl_g kemqZc Z aZiZa\Zg_lh gZ bgnhjfZpbylZ13 b g_cghlh ³^_fhgbqgh´ jZa^_eyg__ktsghkllZgZijbjh^ZlZ Fgh]h bgl_j_kgb kZ nbabdh-nbehkhnkdbl_ \ta]e_^b gZ jmkdbl_ bake_^h\Zl_eb Dhghie_\Z b Khdhebd  -   hkgh\Zgb gZ l_hj_fbl_ gZ Gvhl_j b gZ l_abkZ gZ DZgl aZ [blb_lh aZ nbabq_kdh bgl_jij_lbjZg_ gZ kts_kl\m\Zg_lh dZlh :cgsZcgh\ZlZ h[sZ dh\ZjbZglghkl h[sZ hlghkbl_eghkl  aZ jZaebdZ hl deZkbnbpbjZsbl_ ij_^bdZlb aZ kts_kl\m\Zshlh ltedm\Zgb dZlh kbf_ljby \ kh[kl\_g kfbkte qZklgZ hlghkbl_eghkl  Ijb lh\Z ³ij_^bdZlbl_ g_ ^Z\Zl gbdZdt\ ijbghk \ hglheh]bylZ´ k   Z\Zl ijbf_j k   kihj_^ dhclh djb\bgZlZ gZ ijhkljZgkl\hlh \ h[sZlZ l_hjby gZ hlghkbl_eghkllZ _ nbabdh-hglheh]bq_g djbl_jbc aZ kts_kl\m\Zg_ bfZ djb\bgZ  bfZ_g_j]by fZkZ  bfZkts_kl\m\Zg_bh[jZlghlhDjb\bgZlZh[Zq_g_fh`_^Z k_ hibr_ k g_ij_dtkgZlZ ]jmiZ k djZ_g [jhc hi_jZlhjb dZdlh babkd\Z itj\ZlZ l_hj_fZgZGvhl_jg__kbf_ljby\kh[kl\_gkfbkteke_^h\Zl_egh-ltdfhihDZgl - g_ _ ij_^bdZl DZd\h h[Zq_ baebaZ dZlh ijh^te`bf ^Z fbkebf"Hlktkl\b_lh gZ djb\bgZ l_ gme_\ZlZ djb\bgZ b hllmd \ l_jfbgbl_ gZ Z\lhjbl_ g_kts_kl\m\Zg_lh _ kbf_ljby b ke_^h\Zl_egh ij_^bdZl Hldt^_lh itd ke_^\Z ijhqmlbyll_abkgZO_]_edhf_glbjZgbihkts_kl\hijb_fZgbhlOZc^_]_jbhl KZjltjbhlfgh`_kl\h^jm]bZ\lhjbq_qbklhlh[blb_bqbklhlhgbshkZ_^ghb ktsh Qbklhlh [blb_ k_ fbkeb dZlh ij_^bpbjm_fhlh [blb_ dZlh g_[blb_lh Gh ke_^\Zcdb \ h[jZlgZ ihkhdZ nbabdh-nbehkhnkdby fh^_e gZ bgl_jij_lZpby gZ jmkdbl_ bake_^h\Zl_eb lh\Z _ hglheh]bqghlh kt^tj`Zgb_ gZ \lhjZlZ l_hj_fZ gZ Gvhl_j gZ \kydh kts_kl\m\Zg_ fZdZj b g_kbf_ljbqgh gh h]jZgbq_gh ^h djZ_g [jhciZjZf_ljbkthl\_lkl\Zb^_ZegZl_hjbyl_ij_^bpbjm_fh[blb_hkgh\Z\ZsZ gZkbf_ljbylZkijyfhl_abiZjZf_ljb LZdZ :gsZcgh\ZlZ h[sZ l_hjby _ l_hjby \ h[h[s_g kfbkte ^hdhedhlh k_ h]jZgbqZ\Z ^h q_lbjbl_ iZjZf_ltjZ gZ ijhkljZgkl\h-\j_f_lh fZdZj b jbfZgh\h ih-lhqgh ik_\^hjbfZgh\h b ke_^h\Zl_egh ijhba\hegh djb\h b agZqb kt\k_f

Oj_ggbdh\ Khrennikov, A. 200 baeZ]Z obihl_aZlZ q_ \h^_sh mkeh\b_ aZ ba[hj gZ nhjfZebafZ gZ d\Zglh\ZlZ f_oZgbdZ _ mkeh\b_lh aZ Z^blb\ghkl gZ \_jhylghklbl_ :^blb\ghkllZ _ g_h[oh^bfh mkeh\b_ aZ aZiZa\Zg_ < lZab \jtadZ \tagbd\Zl ke_^gbl_ \tijhkb :dh d\Zglh\ZlZ f_oZgbdZ ij_^iheZ]Z Z^blb\ghkl aZiZa\Zg_ dZdlh gZ _g_j]bylZ lZdZ b gZ _gljhibylZ \j_f_\Z h[jZlbfhkl lh fh]Zl eb l_ab ^\Z gZqZeZ ^Z \eyaZl \ dhgnebdl :dh y\e_gbylZ gZ k^\hy\Zg_ ihdZa\Zl g_Z^blb\ghkl gZ _gljhibylZ lh ke_^\Z eb hl lh\Z g_Z^blb\ghkl gZ _g_j]bylZ 13





  























































"



















































































"

7

g_kbf_ljbqgh \b`_gb_lhihijZ\Zebgbyf_`^m^\_lhqdbhagZqZ\Zq_ijhkljZgkl\hlh k_ ljZgknhjfbjZ k ebg__g hi_jZlhj hij_^_e_g hl l_ab ^\_ lhqdb Ijbgpbitl gZ gZc-fZedhlh ^_ckl\b_ dZa\Z q_ ljZ_dlhjby \ h[sby kemqZc g_ _ ijZ\ZlZ ebgby 8

f_`^m ^\_ lhqdb \ _\deb^h\hlh ijhkljZgkl\h Z ijZ\ZlZ ebgby \t\ nZah\hlh ijhkljZgkl\h :gZeh]bqgh h[h[s_gb_gZ ke_^\Zsh kltiZeh k_ ijZ\b \ d\Zglh\ZlZ f_oZgbdZ ^\b`_gb_lh k_ hkts_kl\y\Z ih ijZ\Z ebgby l_ qj_a ebg__g hi_jZlhj \_q_ \ obe[_jlh\hlh ijhkljZgkl\h KZfZlZ gZkhdZ iha\hey\Z ^Z k_ h[h[sb ijbgpbitl gZ gZc-fZedhlh ^_ckl\b_ dZlh _\jbklbq_g \ ltjk_g_lh gZ gh\b ihh[o\Zlgb l_hjbb Z bf_ggh ^Z k_ gZf_jb ijhkljZgkl\hlh \ dh_lh h[h[s_ghlh ij_h[jZah\Zgb_ _ ebg_cgh < lZab kb nhjfZ lhc fh`_ ^Z k_ gZj_q_ _\jbklbq_g ijbgpbigZebg_cghkllZ. 
kljh]h baihea\Zg_ gZ aZdhgbl_ aZ aZiZa\Zg_ Lh\Z k_ ij_^ba\bd\Z hl ijbgpbigZlZ g_dhgljhebjm_fhkl gZ h[f_gZ gZ _g_j]by b bfimek f_`^m bake_^\Zgby h[_dl b l\tj^bl_ l_eZ b qZkh\gbpbl_ hij_^_eysb ijhkljZgkl\_gh-\j_f_\ZlZ hlijZ\gZ kbkl_fZ B h[jZlgh kljh]h hij_^_e_ghlh baihea\Zg_ gZ aZdhgbl_ aZ aZiZa\Zg_ \ d\Zglh\bl_ y\e_gby ij_^iheZ]Z kts_kl\_g hldZa hl ijhkljZgkl\_gh \j_f_\Z dhhj^bgZpby´ ;hj  LtcdZlhN = 1 _fbgbfZegZlZklhcghkl(log N = log 1 = 0 lhfbgbfmftl fh`_ _^gZd\h ^h[j_ ^Z k_ ltedm\Z dZlh fbgbfmf b gZ bgnhjfZpby l_  [bit] bgnhjfZpby  b gZ _gljhiby l_ ktklhygb_ k \_jhylghkl   b dZlh fbgbfZegZ bgnhjfZpby b ke_^h\Zl_egh fZdkbfZegZ _gljhiby jZ\gh\_kghlh ktklhygb_ ijb ijhba\hegZ iheh`bl_egZ Z[khexlgZ l_fi_jZlmjZ b g_gme_\Z _g_j]by  b dZlh fZdkbfZegZ bgnhjfZpby b ke_^h\Zl_egh fbgbfZegZ _gljhiby lj_lhlh gZqZeh gZ l_jfh^bgZfbdZlZ ijb gme_\Z Z[khexlgZ l_fi_jZlmjZ _gljhibylZ _ gmeZ hl g_]h ke_^\Zq__g_j]bylZdehgbdtfgmeZih-[tjahhl_gljhibylZ  DZdlh k_ dZa\Z \ lZdb\Z kemqZb lh\Z _ l\tj^_ bgl_j_kgh iheh`_gb_ gZ g_sZlZ >\_l_ ltedm\Zgby kthl\_lkl\m\Zl gZ dehg_g_ gZ ^_ckl\b_lh dtf dhgklZglZlZgZIeZgdhl]hj_bhl^hem S :K6!Kb S:K6K ^hdZlhaZdhgtlaZ aZiZa\Zg_ gZ _g_j]bylZ _ \Zeb^_g kZfh aZ _dklj_fZegby kemqZc gZ jZ\_gkl\h gZ ^_ckl\b_lhkdhgklZglZlZgZIeZgd S = h). Hllmd g_hljbpZl_eghkllZgZ\_ebqbgbl_ fZkZ _g_j]by Z[khexlgZ l_fi_jZlmjZ ke_^\Z ^Z k_ fbkeyl dZlh lZ\lheh]bqgb ktk kthlghr_gb_lhaZg_hij_^_e_ghklgZOZca_g[_j] S •h). Ijb lZdh\Z ltedm\Zg_ ljy[\Z ^Z ijb_f_f q_ \lhjhlh gZqZeh gZ l_jfh^bgZfbdZlZ _ ih-h[shlh hl itj\hlh dZlh ihke_^ghlh \babjZ kZfh _^bg qZkl_gkemqZcgZ_dklj_fmf14LZabb^_y_gZebp_g_y\ghhs_m;hepfZg 29; 190- \hiblbl_fm^Zba\_^_\lhjbyaZdhggZl_jfh^bgZfbdZlZhlijbgpbiZ gZgZc-fZedhlh^_ckl\b_:dhgZijhlb\ijb_f_fq_itj\hlhb\lhjhlhgZqZehkZk _^gZd\Z h[sghkl dZd\Zlh _ h[shijb_lZlZ ]e_^gZ lhqdZ lh lh\Z gb hl\_`^Z \ ltedm\Zgb_lh gZ h[sZlZ l_hjby gZ hlghkbl_eghkllZ aZ aZiZa\Zg_lh gZ _g_j]bylZ dZlh kbe_g aZdhg aZ aZiZa\Zg_ < lhab kemqZc ke_^ dZlh _g_j]bylZ k_ aZiZa\Z lh kihj_^ \lhjhlh gZqZeh k m\_ebqZ\Zg_lh hl kZfh k_[_ kb gZ _gljhibylZ bgnhjfZpbylZbaq_a\Z[_ake_^ghLh\Zh[Zq__]e_^gZlZlhqdZkZfhgZl_hjbylZgZ hlghkbl_eghkllZ














































    

 









































     





























10

:dh ijb_f_f k_]Z klZgh\bs_lh gZ d\Zglh\ZlZ f_oZgbdZ b aZdhgtl aZ aZiZa\Zg_ gZ _g_j]bylZ _ keZ[ aZdhg aZ aZiZa\Zg_ lh aZ ijhba\hegb klhcghklb gZ ^_ckl\b_lh j_ki aZ ijhba\hegb iheh`bl_egb Z[khexlgb l_fi_jZlmjb l_ aZ _g_j]_lbqgh g_h[jZlbfb ijhp_kb dZd\blh k_ \babjZl \t\ \lhjhlh gZqZeh gZ l_jfh^bgZfbdZlZ_g_j]bylZk_]m[bbaq_a\ZghfZdZjq_k_]m[blyg_fh`_^Z k_ kta^Z^_ < lZab j_^Zdpby h[_^bgy\Zg_lh gZ itj\by b \lhjby aZdhg l_jfh^bgZfbdZlZhagZqZ\Z_g_j]byfh`_kZfh^Zk_]m[bl_beb^Zk_]m[bbeb ^ZhklZ\ZihklhyggZghg_b^Zk_ihy\y\Z@_jl\Zcdb_g_j]bylZh[Zq_ihemqZ\Zf_ ijZ\hlh ^Z aZiZa\Zf_ bgnhjfZpbylZ m\_ebqZ\Zg_lh gZ _gljhibylZ k_ ktijh\h`^Z g_h[oh^bfh k g_cghlh gZfZey\Zg_ f_`^m \tafh`gbl_ k\_lh\_ \ djZcgZ kf_ldZ \h^_sh dtf lyogZlZ j_^mdpby ^h ^_ckl\bl_egby15 Kt\j_f_gghlh ktklhygb_ gZ gZmdZlZ \_q_ iha\hey\Z ^Z k_ h[kt`^Z _^gZ k^\h_gZ entanglement) l_hjby gZ lhiebgZlZ dZlh dhgdj_l_g f_oZgbatf qj_a dhclh k_ hkts_kl\y\Z lhab ij_ghk gZ d\Zglh\Z bgnhjfZpby ij_a k\_lebggZlZ [Zjb_jZ Fgh`_kl\h \tajZ`_gby kj_sm ;hepfZgh\ZlZ klZlbklbq_kdZ bgl_jij_lZpby gZ \lhjby aZdhg gZ l_jfh^bgZfbdZlZ k_ hlgZkyl ^h ^be_fZlZ gZij hs_ P_jf_eh  ;hepfZg   \j_f_\Z  h[jZlbfhkl gZ f_oZgbqgbl_ y\e_gby \ lq b d\Zglh\h-f_oZgbqgbl_  b g_h[jZlbfhklgZl_jfh^bgZfbqgbl_bijblh\Zba\h^bfhklgZ\lhjbl_hlitj\bl_
< jZfdbl_ gZ fgh]hk\_lh\ZlZ bgl_jij_lZpby fh`_f ^Z ^himkg_f q_ ^_ckl\bl_egZlZ \k_e_gZ ih]etsZ \_jhylghklbl_ aZ j_ZebabjZg_ gZ iZjZe_egbl_ kj\ k DeWitt 1970; 1968; Jarmer 1974: ] 507-521). Fh`_f ^Z dZ`_f q_ dZlh ^_ckl\bl_e_g k_ j_ZebabjZ gZc-keh`gbyl k\yl < : G Dhefh]hjh\ \t\_`^Z ihgylb_ aZ keh`ghkl gZ djZ_g h[_dl Keh`ghkllZ hij_^_ey dZlh fbgbfZegby [jhc ^\hbqgb agZpb kt^tj`Zsb pyeZlZ bgnhjfZpby aZ aZ^Z\Zgby h[_dl ^hklZltqgZ aZ g_]h\hlh \taklZgh\y\Zg_ ^_dh^bjZg_ Lh\Z hij_^_e_gb_ kts_kl\_gh aZ\bkb hl f_lh^Z gZ ^_dh^bjZg_ h[Zq_ k h[sZlZ l_hjby gZ Ze]hjblfbl_ : G Dhefh]hjh\ mkiy\Z ^Z ^Z^_ bg\ZjbZglgh mgb\_jkZegh hij_^_e_gb_ gZ keh`ghkllZ A\hgdbg E_\bg >hdhedhlh h[bqZcghlh \_jhylghklgh hij_^_e_gb_ gZ bgnhjfZpbylZ b lh\Z gZ Dhefh]hjh\ dZlh keh`ghkl kZ lykgh k\tjaZgb iZd lZf b ih^h[gZ \jtadZ kts_kl\m\Z aZ ijhba\he_g klZpbhgZj_g _j]h^bq_g ijhp_k iZd lZf lh h[h[s_gb_lh aZ g__j]h^bq_g ijhp_k iZd lZf _ ^jm] ih^oh^ dtf ltjk_ghlh hl gZk h[h[s_gb_ gZ l_hj_fbl_ gZ Gvhl_j dZdlh b h[h[s_gb_ gZ ijbgpbiZ gZ Ihgljy]bg <` b [_e JZa]e_`^Zg_lh _ k\tjaZgh b k nemdlZpbhggh-^bkbiZlb\gZlZ l_hj_fZ EZg^Zm Ebrnbp 431Julh\ =bga[mj] Kfbktetl gZ \jtadZlZ _ ke_^gbyl ijhfygZlZ gZ nemdlmZpbbl_ dZlh iZjZf_ltj oZjZdl_jbabjZs ^_nhjfZpbylZ gZ \j_f_lh fhghlhggh kthl\_lkl\m\Z gZ keh`ghkllZ gZ kbkl_fZlZ <` [_e b >_nhjfZpbylZ gZ \j_f_lh j_ki hldZatl hl _j]h^bqghkl \h^b ^h jZa]e_`^Zg_ gZ [_adjZ_g [jhc nmgdpbb.

15





³





´

























  

































































































 

 

 



























































 













  









 ³

   













  





































´



  

































   









































































11

mqZkl\m\Zsbl_ K\_lebggZlZ [Zjb_jZ b]jZ_ jheylZ gZ ³^_fhg gZ FZdkm_e´ ³BfZ ^\Z _dki_jbf_glZegb nZdlZ dhblh jZa]e_^Zgb aZ_^gh agZqbl_egh h]jZgbqZ\Zl \kydZ \tafh`gZ nbabq_kdZ l_hjby aZ dhylh l_ kZ j_e_\Zglgb Itj\byl _ ihklhygkl\hlh gZ kdhjhkllZ gZ k\_lebgZlZ \t\ \kydZ hlijZ\gZ kbkl_fZ Hl lh\Z ke_^\Z q_ gyfZ kb]gZe ghk_s bgnhjfZpby dhclh fh`_ ^Z k_ jZaijhkljZgy\Z ktk kdhjhkl ih-]heyfZ hl lZab gZ k\_lebgZlZ 
AhjZg JZgl keh\_gkdb bg`_g_j mq_g b ij_ih^Z\Zl_e AZ g_h]jZgbq_gh ij_h[jZam_fZlZ qZkl gZ Zg_j]bylZ JZgl gZ dhgn_j_gpby \ ] \t\_`^Z ihgylb_lh _dk_j]by. IjbklZ\dZlZ _dk ij_^ dhj_gZ _j] oZjZdl_jbabjZ jZ[hlZlZ dZlh ijhlhlbi gZ ij_h[jZam_fZlZ _g_j]by dhylh fh`_ ^Z ba\tjrb kbkl_fZlZ >\_ ]h^bgb ij_^b lh\Z aZ g_ij_h[jZam_fZlZ qZkl hl _g_j]bylZ JZgl ij_^eZ]Z l_jfbgZ Zg_j]by HljbqZsZlZ ij_^klZ\dZ ij_^ _j] oZjZdl_jbabjZ hgZab qZkl hl _g_j]bylZ dhylh g_ fh`_ ^Z ba\tjrb jZ[hlZ ;Z_j G_y\gh ihgylb_lh h[Zq_ kts_kl\m\Z hs_ ijb FZdkm_e =b[k dZlh gZebqgZlZ _g_j]by gZ lyehlh b kj_^ZlZ b = =mb dZlh \tafh`ghkllZ aZ ihemqZ\Zg_ gZ jZ[hlZ L_jfbgtl _dk_j]by k_ baihea\Z ih ZgZeh]by b \ l_hjbylZ gZ bgnhjfZpbylZ aZ ^Z h[hagZqb h[jZlbfhlh baqbke_gb_ Kbghgbfb gZ _dk_j]by kZ gZebqghkl gZebqgZ _g_j]by _dk_j]bqgZ _g_j]by _k_j]by essergy) baihea\Z_fZ _g_j]by gZebqgZ jZ[hlZ fZdkbfmf jZ[hlZ h[jZlbfZ jZ[hlZ b^_ZegZ jZ[hlZ 17 Kihj_^ RZj]ml \ ijbjh^ZlZ gyfZ kbkl_fZ _dk_j]bylZ gZ dhylh ^Z _ lhqgh jZ\gZ gZ gmeZ b ke_^h\Zl_egh gme_\ZlZ lhqdZ gZ hlqblZg_ gZ _dk_j]bylZ k_ ba[bjZ mkeh\gh 18 Gydhb Z\lhjb jZa[bjZl ih^ _dk_j]by kZfh hgZab qZkl dhylh k_ hij_^_ey hl ]hjghlh mjZ\g_gb_ <_s_kl\h k iZjZf_ljb gZ ktklhygb_lh p0, t0 bfZ iheh`bl_egZ obfbqgZ _dk_j]by ]he_fbgZlZ gZ dhylh kthl\_lkl\m\Z gZ jZaebdZlZ f_`^m obfbq_kdby ktklZ\ gZ bake_^\Zghlh \_s_kl\h b obfbq_kdby ktklZ\ g dhfihg_glbl_ kj_sZsb k_ \ hdhegZlZ kj_^Z RZj]ml 16





 





 ³















































































´







 































´













´







 



















































´



























   

















³







´

  











    ³ 



³



























   



 

















´



















 ³







  













´



























 

12

>Z h[tjg_f \gbfZgb_ q_ nbabq_kdZlZ _dk_j]by \ ]hjghlh jZ\_gkl\h k_ hij_^_eyZgZeh]bqghgZk\h[h^gZlZ_g_j]by bebgZ=b[kG,bebgZO_efohep F, \ aZ\bkbfhkl hl lh\Z  ^Zeb mqZkl\m\Z  _glZeibylZ H beb \tlj_rgZlZ _g_j]by U19). Lh]Z\Z\_ebqbgZlZT0.sn [bljy[\Zeh^Z_jZ\gZgZZg_j]bylZ a –_g_j]bylZdhylhk_ ]m[b ihjZ^b g_h[jZlbfhkllZ G_dZ k_]Z ^himkg_f q_ sn  sa dt^_lh sa=a/T0  b ihki_pbZeghsn > salh\Zs_\h^b^h m\_ebqZ\Zg_gZ_n_dlb\gZlZaZ]m[ZgZ_g_j]by qZkls_k_baetq\Z\hdhegZlZkj_^Zih^_^gZbeb^jm]ZnhjfZgZ _g_j]byZqZkl s_ k_ ]m[b ihjZ^b m\_ebqZ\Zg_ gZ _gljhibylZ j_ki ³baetq\Zg_ gZ bgnhjfZpby´ DZlhdhgdj_l_gf_oZgbatfgZlh\Zbaetq\Zg_gZbgnhjfZpbyfh`_^Zk_ij_^eh`b \tagbd\Zg_lh gZ k^\hy\Zg_ f_`^m fhe_dmebl_ b Zlhfbl_ ijb m^Zj ijb dhclh l_ h[f_gyl _g_j]by b bfimek K\_lebggZlZ [Zjb_jZ b]jZ_ jheylZ \k_ _^gh gZ _^bg ³^_fhg gZ FZdkm_e´ dhclh ijhimkdZ  d\Zglh\Z bgnhjfZpby qj_a d\Zglh\bl_ dhj_eZpbb hl _^gZ kljZgZ b aZ^tj`Z deZkbq_kdZ bgnhjfZpby dZlh _gljhiby hl ^jm]Z kihj_^ pblbjZgbl_ ih-]hj_ ^\Z hkgh\gb nZdlZ k dhblh ljy[\Z ^Z k_ kth[jZay\Zl\kbqdbkt\j_f_ggbnbabq_kdbl_hjbbLZabbaetq_gZbaZ^tj`ZgZ³hl ^jm]ZlZ kljZgZ´ gZ k\_lebggZlZ [Zjb_jZ bgnhjfZpby iha\hey\Z k\_lZ ^Z \tagbdg_ dZlh fgh]h g_\_jhylgh ktklhygb_20 \k_e_gZlZ k_ hdZa\Z _^gh bgnhjfZpbhggh perpetuum mobiledh_lhjZa]e_^ZghkijyfhgZklhys_lh_^hjbhl³itj\bjh^´ltc dZlh aZ_fZ bgnhjfZpby hl [t^_s_lh l_ _^\Z ih hlghr_gb_ gZ \_qghkllZ _ hl ³\lhjbjh^´  >Z k_ \tjg_f dtf ´l\tj^_ bgl_j_kghlh iheh`_gb_ gZ g_sZlZ´ qbylh bgl_j_kghkl hs_ g_ _ baq_jiZgZ Lj_lhlh gZqZeh gZ l_jfh^bgZfbdZlZ kh[kl\_gh l\tj^b q_ ijb l_fi_jZlmjZ dehgysZ dtf gmeZ _gljhibylZ dehgb dtf gmeZ hldt^_lh ke_^\Z ltc dZlh l_fi_jZlmjZlZ _ hlghr_gb_ gZ _g_j]by  b _gljhiby q_ _g_j]bylZktshdehgbdtfgmeZijblh\Zih-[tjahhl_gljhibylZ>Zebh[Zq_gyfZ l_hj_lbqgb h[_dlb k ZgZehab \ ijbjh^ZlZ dhblh ijbl_`Z\Zl _^gh\j_f_ggh g_gme_\Z_g_j]byb[_adjZcgZ_gljhibybke_^h\Zl_eghgme_\Zl_fi_jZlmjZ">Zeb Zdh kts_kl\m\Zl l_ g_ gZjmrZ\Zl lj_lhlh gZqZeh gZ l_jfh^bgZfbdZlZ ltc dZlh 



F=U-TS; G=H-TS Kihj_^ l_hj_fZlZ gZ G_jgkl ijb L: , F=U b G=H Ijb lh\Z F b G hl _^gZ kljZgZ b U b X hl ^jm]Z k_ ihemqZ\Zl _^gh hl ^jm]h qj_a ljZgknhjfZpbylZ gZ Evh`Zg^tj qj_a dhylh h[_ftl V kthl\_lkl\m\Zs gZ ijhkljZgkl\_gbl_ dhhj^bgZlb k_ ij_h[jZam\Z \ gZey]Zg_lh p, kthl\_lkl\m\Zs gZ bfimekbl_ b h[jZlghlh Z _gljhibylZ S b [jhyl qZklbpb N hklZ\Zl bg\ZjbZglgb ijb ij_h[jZah\Zgb_lh gZ Evh`Zg^tj Ke_^\Z ^Z k_ ih^q_jlZ_ q_ _gljhibylZ j_ki bgnhjfZpbylZ _ bg\ZjbZglgZ ijb ij_h[jZah\Zgb_lh gZ Evh`Zg^tj 20 Kj\ k Hl]h\hjtl gZ \tijhkZ dZd _ klZgZeh lZdZ q_ ihgZklhys_f hdjt`Z\Zsbl_ l_eZ k_ gZfbjZl \ fgh]h g_\_jhylgh ktklhygb_ fh`_ ^Z k_ ^Z^_ g_ \ ih-]heyfZ kl_i_g hldhedhlh ^Z k_ qZdZ hl gZmdZlZ ^Z gb dZ`_ aZsh \th[s_ kts_kl\m\Zl y\e_gby b aZsh l_ k_ hkts_kl\y\Zl ih hij_^_e_gb aZdhgb ;hevpfZg 19





































´

















































 

































 









 



























 ³









































































 

13

kihj_^ g_]h Zdh lyogZlZ _gljhiby ljy[\Z ^Z g_ _ [_adjZcgZ Z gme_\Z" >Zeb lh\Z gyfZ g_sh h[sh k \_q_ \babjZghlh ih-]hj_ iheh`_gb_ aZ fbgbfmfZ ^_ckl\b_ dhclh fh`_r_ ^Z k_ ltedm\Z b dZlh gme_\Z _gljhiby b dZlh gme_\Z bgnhjfZpby" >Zeb jZa]e_`^Zg_lh g_ _ k\tjaZgh k baetq\Zg_lh gZ Z[khexlgh q_jghlh lyeh aZjZ^bdh_lhFZdkIeZgd\t\_`^ZdZdlhdhgklZglZlZgZIeZgdlZdZbihklmeZlZgZ IeZgdbaltedm\Zgih-]hj_dZlhaZdhgaZaZiZa\Zg_gZ^_ckl\b_lh" Fh`_ ^Z k_ ij_^iheh`b q_ k\_lebgZlZ \  l_hjbylZ gZ hlghkbl_eghkllZ21 _ ltjk_gbyl nbabq_kdb h[_dl
Kihj_^ I_j_i_ebpZ ijbgpbitl gZ ijbqbgghkllZ jZaj_rZ\Z kts_kl\m\Zg_lh -61; 46gZ k\jtok\_lh\b qZklbpb \ jZfdbl_ gZ HLH ^hdZlh lhc aZ[jZgy\Z k\jtok\_lebggbl_ kb]gZeb \ jZfdbl_ gZ KLH Kj\ b k L_je_pdbc 22 FboZbe B\Zgh\bq RZoiZjhgh\ aZ\_`^Zs eZ[hjZlhjbylZ ih jZal\hjb dtf dZl_^jZlZ ih nbabq_kdZ obfby gZ Obfbq_kdby nZdmel_l gZ Fhkdh\kdby ^tj`Z\_g mgb\_jkbl_l 23


 











´









 















 





































  























 















  



























































































 









































 











´

 















 





















   





















   





´



















  ³



























14

HgkZ]_j25 l_ _^gZ hl nhjfmebjh\dbl_ gZ l gZj q_l\tjlb aZdhg gZ l_jfh^bgZfbdZlZ  iZdlZf- g_h[jZlbfhkllZgZ\j_f_lh iZdlZf ³^Zk_ j_rb \ h[sZ nhjfZ hl^Z\gZ ihklZ\_gby hl gZmdZlZ \tijhk aZ lh\Z dZd \ fZdjhkdhibqgbl_kbkl_fb\tagbd\Zly\e_gbygZ[Z ]kZfhhj]ZgbaZpby_\hexpbyb [[ ]p_e_gZkhq_gb^_ckl\by´ RZoiZjhgh\kj\bk  Baoh^gZ lhqdZ gZ bake_^\ZgbylZ fm \tjom ijbgpbiZ gZ gZc-fZedhlh ^_ckl\b_ _ _^gh g_]h\h h[h[s_gb_ ³ijhlbqZl kZfh l_ab g_h[jZlbfb ijhp_kb dhblh ijb aZ^Z^_gb \tgrgb mkeh\by O M  gZc-[tjah ^h\_`^Zl kbkl_fZlZ ^h l_jfh^bgZfbqgh jZ\gh\_kb_´ RZoiZjhgh\  -44)26 B lhc ³ij_^klZ\ey\Z h[h[s_gb_ gZ ijbgpbiZ gZ gZc-fZedhlh ^_ckl\b_ gZ f_oZgbqgbl_ ijhp_kb ijhlbqZsb\fZdjhl_eZlZ\ mkeh\bylZdh]Zlh_ijbeh`bfijbgpbiZgZehdZeghlh jZ\gh\_kb_´ RZoiZjhgh\  519)27 GZj_q_gbyl hl g_]h ijbgpbi ³gZ

ktklhygb_ gZ kbkl_fZlZ kthl\_lkl\m\Z fbgbfZegh ijhba\h^kl\h gZ _gljhiby :dh lZdb\Z ij_iylkl\by gyfZ lh ijhba\h^kl\hlh gZ _gljhiby ^hklb]Z k\hy Z[khexl_g fbgbfmf gmeZ >hdZaZgZ _ hl Ijb]h`bg ij_a ] hl hlghr_gbylZ gZ HgkZ]_j \` ke_^\ [_e _d\b\Ze_glgZ _ gZ ^hdZaZgby hl HgkZ]_j ijbgpbi gZ gZc-fZedh jZak_c\Zg_ gZ _g_j]bylZ L_hj_fZlZ _ \ kbeZ Zdh dbg_lbqgbl_ dh_nbp_glb \ hlghr_gbylZ gZ HgkZ]_j kZ ihklhyggb Ijhba\h^kl\hlh gZ _gljhiby _ ijbjZkltl gZ _gljhiby \t\ nbabq_kdZlZ kbkl_fZ aZ _^bgbpZ \j_f_ \ j_amelZl gZ ijhlbqZsbl_ \ g_y g_jZ\gh\_kgb ijhp_kb 25 Hkgh\Z\Zl k_ gZ l_hj_fZlZ gZ HgkZ]_j _^gZ hl hkgh\gbl_ l_hj_fb gZ l_jfh^bgZfbdZlZ gZ g_jZ\gh\_kgbl_ ijhp_kb < l_jfh^bgZfbqgb kbkl_fb \ dhblh bfZ ]jZ^b_glb gZ l_fi_jZlmjZlZ gZ dhgp_gljZpbbl_ gZ dhfihg_glbl_ gZ obfbqgbl_ ihl_gpbZeb \tagbd\Zl g_h[jZlbfb ijhp_kb gZ lhiehijh\h^ghkl ^bnmaby obfbq_kdb j_Zdpbb L_ab ijhp_kb k_ oZjZdl_jbabjZl k lhiebggb b ^bnmabhggb ihlhpb kdhjhklb gZ obfbqgbl_ j_Zdpbb b ij L_ k_ gZjbqZl k h[sby l_jfbg ihlhpb b k_ hagZqZ\Zl J ,Z ij_^ba\bd\Zsbl_ ]b ijbqbgb hldehg_gbylZ gZ l_jfh^bgZfbqgbl_ iZjZf_ljb hl jZ\gh\_kgbl_ klhcghklb – l_jfh^bgZfbqgb kbeb O <jtadZlZ f_`^m J b O Zdh l_jfh^bgZfbqgbl_ kbeb kZ fZedb \t\ \b^Z gZ ebg_cgb mjZ\g_gby J = X (i,k = 1,2, … m), dt^_lh dbg_lbqgbl_ dh_nbpb_glb L hij_^_eyl ijbghkZ gZ jZaebqgbl_ l_jfh^bgZfbqgb kbeb O \ kta^Z\Zg_lh gZ ihlhdZ J , =hjgbl_ jZ\_gkl\Z k_ gZjbqZl n_ghf_gheh]bqgb mjZ\g_gby Z L n_ghf_gheh]bqgb dh_nbpb_glb klhcghklbl_ gZ L k_ ij_kfylZl beb k_ gZfbjZl ih hibl_g itl L_jfh^bgZfbqgbl_ ihlhpb b kbeb fh]Zl ^Z [t^Zl kdZeZjb \_dlhjb b l_gahjb Kihj_^ l_hj_fZlZ gZ HgkZ]_j L = L Zdh gyfZ fZ]gblgh ihe_ b \tjl_g_ gZ kbkl_fZlZ < kemqZy dh]Zlh gZ kbkl_fZlZ ^_ckl\m\Z \tgrgh fZ]gblgh ihe_ 7 beb kbkl_fZlZ k_ \tjlb k t]eh\Z kdhjhkl ω, L (ω)= L (-ω), L (7)= L (-7) L_ab jZ\_gkl\Z k_ gZjbqZl hlghr_gby gZ \aZbfghkl gZ HgkZ]_j b mklZgh\y\Zl \jtadZlZ f_`^m dbg_lbqgbl_ dh_nbpb_glb ijb djtklhkZgb ijhp_kb EZjk HgkZ]_j _ Zf_jbdZgkdb nbabd l_hj_lbd b nbabdh-obfbd jh^_g \ Hkeh ghj\_`_p ih ijhbaoh^ Hl ] `b\__ b jZ[hlb \ K:S hl ] ijhn_khj \ C_cekdby mgb\_jkbl_l Hkgh\gbl_ jZ[hlb kZ ih l_hjbylZ gZ g_h[jZlbfbl_ ijhp_kb l_hjbylZ gZ nZah\bl_ ij_oh^b l_hjbylZ gZ _e_dljheblbl_ AZ hlghr_gbylZ gZ \aZbfghkl ihemqZ\Z Gh[_eh\ZlZ gZ]jZ^Z ih obfby aZ ] 26 Ijbf_jb G_h[jZlbfb ijhp_kb ijb aZ^Z^_gb L b J ijhlbqZl gZc-[tjah Zdh k_ ba[bjZ itly ih dhclh [jhy gZ aZ^Z^_gbl_ d\Zglh\b ktklhygby gZ kbkl_fZlZ _ fZdkbfZegh RZoiZjhgh\ < bahebjZgZ kbkl_fZ ijb ihklhyggZ \tlj_rgZ _g_j]by ? b h[_f kZfhijhba\hegh ijhlbqZl kZfh l_ab g_h[jZlbfb ijhp_kb dhblh k_ ktijh\h`^Zl k fZdkbfZe_g ijbjZkl gZ _gljhibylZ gZ kbkl_fZlZ l _ ih gZc-djZltd gZqbg \h^yl ^h \tagbd\Zg_ gZ l_jfh^bgZfbqgh jZ\gh\_kb_ RZoiZjhgh\ 27 Ih-lhqgZ nhjfmebjh\dZ gZ ijbgpbiZ ijb aZ^Z^_gb \tgrgb ijhf_geb\b x baf_g_gb_lh gZ \k_db l_jfh^bgZfbq_g ihl_gpbZe ∆Ψ \ bgl_j\ZeZ hl \j_f_ [t , t ], h[mkeh\_gh hl baf_g_gb_lh gZ 



















 

















































 



























































´





 























 

 9 ³

 







 

















ik









   



























 











kk









ik











ik







d



















































 















k



















 







´

d

















i









 



™/ik





















 i









ik







 

d 





















































































ik













kk













i 



ik













































  







 





















i





























  



































kk











































































´

 











³

x















2



1















15

fZdkbfZegZ kdhjhkl gZ g_h[jZlbfbl_ ijhp_kb ih kts_kl\h ij_^klZ\ey\Z \ZjbZpbhg_g ijbgpbi gZ g_jZ\gh\_kgZlZ l_jfh^bgZfbdZ aZ n_ghf_gheh]bqgb dh_nbpb_glbLhcg_ijhbalbqZhlijbgpbiZgZehdZeghlhjZ\gh\_kb_bhl\lhjby aZdhg gZ l_jfh^bgZfbdZlZ Z ij_^klZ\ey\Z ihklmeZl ke_^\Zs hl ZgZeh]bylZ gZ _dki_jbf_glZegbl_ ^Zggb aZ j_^bpZ jZaebqgb l_jfh^bgZfbqgb ijhp_kb´ RZoiZjhgh\  Hkgh\ZlZ gZ g_]h\hlh jZa]e_`^Zg_ _ \t\_`^Zg_lh gZ eZ]jZg`bZg aZ h[h[s_gbl_ obfbqgbl_ j_Zdpbb28 dhclh bfZ ke_^gbl_ hkh[_ghklb   ijhkljZgkl\_gbl_ dhhj^bgZlb kZ aZf_g_gb k iteghlZlZ gZ _kl_kl\_gbl_ beb ghjfZegb obfbqgb j_Zdpbb   kdhjhklbl_ – ktk kdhjhklbl_ gZ obfbqgbl_ j_Zdpbb   \j_f_lh fh`_ ^Z k_ hlkljZgb Ijb g_jZ\gh\_kgbl_ j_Zdpbbdhblh k_ jZa]e_`^Zl dZlh gZitegh g_kbf_ljbqgb k_ baihea\Z b ijbgpbitl gZ Dxjb29 ijb dh_lh gZ \aZbfh^_ckl\b_lh gZ l_jfh^bgZfbqgb l_gahjgb ihlhpb k jZaebqgZ jZaf_jghkl fh`_ ^Z k_ ktihklZ\b kdZeZjgZlZ \_ebqbgZ kdhjhkl gZ obfbqgbl_ j_Zdpbb dhylh gZitegh ^Z ]h oZjZdl_jbabjZ AZ h[hkgh\Z\Zg_lh gZ y\e_gbylZ gZ kZfhhj]ZgbaZpby _\hexpbb b p_e_gZkhq_gb ^_ckl\by k_ baihea\Z ijbgpbitl gZ fZdkbfmfZgZIhgljy]bg30.

kl_i_gbl_ gZ iteghlZ gZ h[h[s_gbl_ j_Zdpbb {ξ} _ jZ\gh gZ gZc-fZedhlh ^_ckl\b_ D gZ kbkl_fZlZ aZ _^bgbpZ \j_f_ RZoiZjhgh\ 28


















































´























































 























-12 



    ³



 



 



























 













 





















´









 



´

 























´

















x





































 

 

























































 





 



















 











































´

















´





























´

























³



 





 



 

³







´

















 





  





































 

















 



















 





























16

DZdlh fgh]hdjZlgh baltd\Z FZdk IeZgd \ k\hy l_dkl ^hdZlh bglmblb\gh agZq_gb_lhb\k_h[sghkllZgZijbgpbiZgZgZc-fZedhlh^_ckl\b_kZklZgZebykgb hs_ hl \j_f_gZlZ gZ EZc[gbp b Fhi_jlxb lh gZitegh dhj_dlgZlZ b \k_h[o\ZlgZ nhjfmebjh\dZ h[jtsZsZ \gbfZgb_ b gZ aZ^Z^_gbl_ mkeh\by dZlh h]jZgbqZ\Zsb kj_^ dhb \bjlmZegb ^\b`_gby ^Z k_ ltjkb fbgbfmfZ k_ m^Z\Z b lh ihkl_i_ggh _^\Z gZ EZ]jZg` OZfbeltg b O_efohep aZ ^Z ^hklb]g_ ljbmfn qZd \ d\Zglh\ZlZ f_oZgbdZ\hkgh\hiheZ]ZsZlZ\Z`ghklgZΨ-nmgdpbylZ Ke_^\Z q_ ZgZeh]bq_g itl s_ k_ gZeh`b ^Z [t^_ ba\tj\yg b ijb h[h[sZ\Zg_lhgZijbgpbiZIj_^eh`_gbylhlRZoiZjhgh\ijbgpbigZgZc-[tjahlh ^hklb]Zg_ ^h jZ\gh\_kgh iheh`_gb_ itj\h h[h[sZ\Z ijbgpbiZ gZ gZc-fZedh ^_ckl\b_ih^nhjfZlZgZ_dklj_fZe_gijbgpbihldhclh ihg_ nbabdhobfbqgbyl ZgZeh]gZijbgpbiZgZgZc-fZedhlh^_ckl\b__ke_^kl\b_KtsghkllZ_^Zk_fbkeb ijbgpbitlg_dZlhfbgbfmfgZkZfhlh^_ckl\b_ZgZ^_ckl\b_lhaZ_^bgbpZ\j_f_ K lh\Z nZdlbq_kdb ih^ ^_ckl\b_ k_ jZa[bjZ bgl_]jZe ih \j_f_lh hl ^_ckl\b_lh \ h[bqZ_g kfbkte < j_amelZl dZlh ke_^kl\b_ hl lZdt\ \ZjbZpbhg_g ijbgpbi gZ fyklhlh gZ aZdhgZ aZ aZiZa\Zg_ gZ _g_j]bylZ aZklZ\Z _^gh iheh`_gb_ aZ aZiZa\Zg_ gZ^_ckl\b_lhKtsghkllZh[Zq_ _\lh\Zq_kj_^\kbqdbijhp_kbijbdhgklZglgh ^_ckl\b_ijhlbqZlhg_abaZdhblh_gljhibylZgZjZaij_^_e_gb_lhgZ_g_j]bylZ\t\ \j_f_lh _ fbgbfZegZ j_ki _dklj_fZegZ  Lh]Z\Z ijhp_kbl_ ijhlbqZl ih hgZab djb\Z gZ _gljhibylZ gZ jZaij_^_e_gb_lh gZ _g_j]bylZ \t\ \j_f_lh dhylh _ k gZckljtf_g kdehg l_ aZ gZc-djZldh \j_f_ ^Z k_ mklZgh\b jZ\gh\_kgh ktklhygb_ l_ fZdkbfZegZ _dklj_fZegZ  _gljhiby gZ jZaij_^_e_gb_lh gZ _g_j]bylZ \ ijhkljZgkl\hlhKlh\ZijbgpbitlgZgZc-fZedhlh^_ckl\b_\t\nbabdh-obfbqgby fm\ZjbZgl_h[h[s_gb^hg_jZ\gh\_kgbkbkl_fbijhp_kbl_ijhlbqZlihhgabitl ih dhclh \g_k_ghlh g_jZ\gh\_kb_ k_ hlkljZgy\Z gZc-[tjah Lh]Z\Z \gZkyghlh g_jZ\gh\_kb_ hj]ZgbabjZ kbkl_fZlZ fZdkbfZegh hl _^gZ kljZgZ ijbgpbitl gZ Ihgljy]bghl^jm]ZlgZjq_l\tjlbaZdhggZl_jfh^bgZfbdZlZ 31.

Ihgljy]bg aZ ^mZeghkllZ dhclh k\tja\Z Z[kljZdlgZlZ l_hjby gZ ij_h[jZah\ZgbylZ gZ Nmjb_ k lhiheh]bylZ b ih-ki_pbZegh k dh[hj^bafbl_ Z hl ^jm]Z kljZgZ ijbgpbitl gZ fZdkbfmfZ \ hilbfZeghlh mijZ\e_gb_ Hl ]e_^gZ lhqdZ gZ nbabdZlZ ktsh b nbabdh-obfbylZ Z g_ gZ l_ogbq_kdbl_ ijbeh`_gby ijbgpbitl gZ fZdkbfmfZ gZ Ihgljy]bg h[h[sZ\Z ijbgpbiZ gZ gZcfZedhlh ^_ckl\b_ aZ kemqZbl_ gZ g_ebg_cgb hi_jZlhjb \ l q b lmd gZc-\Z`gh \tjom obe[_jlh\b ijhkljZgkl\Z dZlh hij_^_ey aZ dhc deZk [Zabkb gZ obe[_jlh\b j_ki lbih\_ [ZgZoh\b ijhkljZgkl\Z ijbgpbitl fh`_ ^Z k_ h[h[sb kthl\ kts_kl\m\Z hilbfZegh mijZ\e_gb_ 31 Kj\ b k nemdlmZpbhggh-^bkbiZlb\gZlZ l_jh_fZ \ klZlbklbq_kdZlZ nbabdZ dhylh k\tja\Z nemdlmZpbbl_ gZ nbabq_kdZlZ \_ebqbgZ \ jZ\gh\_kgh ktklhygb_ b g_jZ\gh\_kgbl_ k\hckl\Z gZ kbkl_fZlZ ijb \tgrgh \ta^_ckl\b_ 





















































³























 















 



















´ 







































































































17

Ih gZqbgZ ih dhclh ij_nhjfmebjZo ijbgpbiZ gZ RZoiZjhgh\ lhc \_q_ fh`_ ^Z k_ jZa]e_`^Z dZlh h[h[s_gb_ gZ ijbgpbiZ gZ gZc-fZedhlh ^_ckl\b_ aZ d\Zglh\h  f_oZgbqgb kbkl_fb Ijb aZ^Z^_gh ^_ckl\b_ _gljhibylZ gZ jZaij_^_e_gb_lh gZ _g_j]bylZ \t\ \j_f_lh _ fbgbfZegh _dklj_fZegh  H[h[s_gb_lh k_ ktklhb \ lh\Z q_   k_ jZa]e_`^Z _gljhibylZ gZ _g_j]bylZ \t\ \j_f_lh b q_   ly k_ h[_^bgy\Z k h[bqZcgZlZ _gljhiby gZ _g_j]bylZ \ ijhkljZgkl\hlh ?lh _^bg ijbf_j k dhjimkdmeyjgh-\tegh\by ^mZebatf \ d\Zglh\ZlZ f_oZgbdZ Kihj_^ ijbgpbiZ – ktsh b jZa]e_`^Zcdb fbdjhh[_dlZ dZlh ³g_jZ\gh\_kb_´ ³kfms_gb_´  \g_k_gh \t\ \j_f_ijhkljZgkl\hlh – mklhcqb\b s_ [t^Zl ktklhygbylZ k gZc-fZedZ b gZc-]heyfZ _gljhiby gZ jZaij_^_e_gb_lh gZ _g_j]bylZ \ ijhkljZgkl\h-\j_f_lh kthl\_lgh qZklbpZ gZitegh ehdZebabjZg _g_j]by-bfimek  b \tegZ  gZitegh g_ehdZebabjZg _g_j]by-bfimek  ?dki_jbf_gltlbih-lhqghg_]h\ZlZ³ih^]hlh\dZ´gZkhq\Zfbdjhh[_dlZdtf_^ghhl ^\_l__dklj_fZegbktklhygbybebdtfgydh_f_`^bggh\kthl\_lkl\b_kijbgpbiZ aZg_hij_^_e_ghkl ?lh ^jm] ijbf_j k ³]he_fby \ajb\´ \ dhkfh]hgbylZ b dhkfheh]bylZ G_jZ\gh\_kgh ³\g_k_gZlZ´ _g_j]by bfZ ^\_ mklhcqb\b _dklj_fZegb ktklhygby gZ fZdkbfmfl_ijhkljZgkl\_gh-\j_f_\ZlZehdZebaZpbygZkZfby³]heyf\ajb\´bgZ fbgbfmfl_³lhiebgZlZkftjl´gZ\k_e_gZlZLy\ktsghklk_dhe_[Z_f_`^ml_ab ^\_ k\hb mklhcqb\b h[Zq_ g_kt\f_klbfb ktklhygby b ltdfh lh\Z dhe_[Zgb_ ij_^klZ\ey\Z ijhkljZgkl\h-\j_f_lh b ³\kbqdh hklZgZeh´ H[Zq_ ij_^klZ\Z aZ ³\gZkyg_´ ke_^h\Zl_egh ³hl\tg´  _^\Z eb fh`_ eh]bq_kdh kt]eZkm\Zgh ^Z k_ ijbeh`b dtf ³\k_e_gZlZ´ dhylh [b^_cdb ³\kbqdh´ g_ ^himkdZ k\h_ ³hl\tg´  Lh]Z\Z ke_^kl\b_lh hl ijbgpbiZ aZ ihklhygkl\h gZ ^_ckl\b_lh ij_^iheZ]Z q_ _g_j]bylZ g_ k_ \gZky Z \tagbd\Z \t\ \k_e_gZlZ k\b^_l_ekl\hlh aZ dh_lh _ bahljhighlh nhgh\h baetq\Zg_ gZ g_[_kgby k\h^ k l_fi_jZlmjZ ° D b ly ih aZdhgbl_ gZ l_jfh^bgZfbdZlZ k_ jZaij_^_ey \ ijhkljZgkl\h-\j_f_lh \b^bfh \ _dki_jbf_glbl_dZlh³q_j\_ghij_f_kl\Zg_´b_fibjbqghh[h[s_ghdZlh³aZdhggZ OZ[te´  klj_f_cdb k_ dtf ^\_l_ mklhcqb\b b ijhlb\hiheh`gb ktklhygby gZ ³]he_fby\ajb\´bgZ³lhiebggZlZkftjl´Ke_^h\Zl_egh³]he_fbyl\ajb\´_lhqgh lhedh\Zobihl_lbq_gdhedhlh³lhiebggZlZkftjl´bZdhitj\bylk_ij_^klZ\ydZlh ³gZmq_g nZdl´ lh\Z e_`b \ Zgljhihfhjnghlh ijbibk\Zg_ gZ ^_ckl\bl_eghkl gZ fbgZehlh beb gZ hgh\Z dh_lh gb k_ kljm\Z dZlh fbgZeh b g_]eb`bjZg_ gZ [t^_s_lh

18

< aZdexq_gb_ [bo bkdZe ^Z ih^q_jlZy dZlh gZc-\Z`gZ b^_ylZ q_ ]jZgbpZlZ gZ gZc-fZedhlh b gZc-]heyfhlh _ _^gZ b ktsZ dh_lh _^bghktsb_ ijhbaebaZ hl lhlZeghkllZ ?^ghlh gZ \k_e_gZlZ dZlh pyeh b fgh]hlh gZ fbdjhh[_dlbl_ ij_^klZ\ey\Zllh\Z_^bghktsb_H[eZkllZ³hl^hem´gZkdhjhkllZgZk\_lebgZlZ\t\ \Zdmmf _ h[eZkl ³hl^hem´ b kijyfh dhgklZglZlZ gZ IeZgd H[eZkllZ ³hl]hj_´ gZ^ Z[khexlgZlZ gmeZ _ h[eZkl ³hl]hj_´ kijyfh dhgklZglZlZ gZ IeZgd B gZc-k_lg_ ^\_l_h[eZklb- (1) v • c b  L!– kZ_^gZbktsZbk_h[_^bgy\Zlhl_dklj_fZe_g ijbgpbigZ_gljhibylZ Nbehkhnkdbyl kfbkte gZ _dklj_fZeghlh _ q_ fbgbfZeghlh b fZdkbfZeghlhkZ_^ghbktshblZdZb_^ghlhgZp_ehkllZbfgh]hlhgZg_cghlh kt^tj`Zgb_ BlZdZbdjZyl_bgZqZehlhO_jZdeblh\hlh³_^ghfgh]h´bOZc^_]_jh\ZlZ nbehkhnby EBL?J:LMJ:

;Z_j = Wg_j]by wdk_j]by Zg_j]by - < Wg_j]by b wdk_j]by Fhkd\Z Fbj -27. ;hevpfZg E H f_oZgbq_kdhf kfuke_ \lhjh]h gZqZeZ l_hjbb l_iehlu - Ba[jZggu_ ljm^u. Fhkd\Z GZmdZ -29. ;hevpfZg E H k\yab f_`^m \lhjuf gZqZehf f_oZgbq_kdhc l_hjbb l_iehlu b l_hjby \_jhylghkl_c \ l_hj_fZo h l_ieh\hf jZ\gh\_kbb - Ba[jZggu_ ljm^u Fhkd\Z GZmdZ -235. ;hevpfZg E Hl\_l gZ aZf_qZgb_ P_jf_eh ih ih\h^m l_hjbb l_iehlu - Ba[jZggu_ ljm^u. Fhkd\Z GZmdZ -452. ;hevpfZg E H g_dhlhjuo \hijhkZo l_hjbb ]Zah\ – < kts Z\l KlZlvb b j_qb Fhkd\Z GZmdZ -76. ;hj G AZdhgu khojZg_gby \ d\Zglh\hc l_hjbb – < Ba[jZggu_ gZmqgu_ ljm^u Fhkd\Z GZmdZ -203. ;hrgydh\bq N Hp_gdZ l_iehl_ogbq_kdbo ijhp_kkh\ k ihfhsvx wdk_j]bb – < Wg_j]by b wdk_j]by Fhkd\Z Fbj -11. =b[[k rel="nofollow">` L_jfh^bgZfbdZ KlZlbklbq_kdZy f_oZgbdZ Fhkd\Z GZmdZ =bga[mj] < L_hj_lbq_kdZy nbabdZ b ZkljhnbabdZ Fhkd\Z GZmdZ A\hgdbg : E E_\bg Keh`ghklv dhg_qguo h[t_dlh\ b h[hkgh\Zgb_ ihgylbc bgnhjfZpbb b kemqZcghklb k ihfhsvx l_hjbb Ze]hjblfh\ – Mki_ob fZl_fZlbq_kdbo gZmd L XXV, \ui -127. DZimklbgkdbc : FZdk IeZgd dZd l_jfh^bgZfbd b nbabdh-obfbd – < K[hjgbd d klhe_lbx kh ^gy jh`^_gby FZdkZ IeZgdZ Fhkd\Z B-\h :G KKKJ DZp F <_jhylghklv b kf_`gu_ \hijhku \ nbabd_ Fhkd\Z Fbj Dhghie_\Z G < Ihih\ DZeb[jh\hqgu_ ihey Fhkd\Z :lhfba^Zl Dhghie_\Z G = Khdhebd Kbf_ljbb b lbiu nbabq_kdhc l_hjbb –
 



 

³

















³



´







´



 





 









 

³































³







´





´



³

 



 

















 













´



 

³



















´



 





³













































Dmag_ph\Z H





 

118-127.

































 



´

´







 















³

³





 

















 

 









 















´







³

´













FZdk\_ee b ]jZgbpb ijbf_gbfhklb \lhjh]h gZqZeZ l_jfh^bgZfbdb

 















<

–



FZdk\_eebjZa\blb_nbabdbXIX-XX \_dh\Fhkd\Z³GZmdZ´-166. EZg^ZmEEbrnbp?KlZlbklbq_kdZynbabdZQZklFhkd\Z³GZmdZ´ G_l_j W  Bg\ZjbZglgu_ \ZjbZpbhggu_ aZ^Zqu – <
Fhkd\Z =hkba^nbafZlebl -630. IZmeb < Ijbgpbi aZij_lZ ]jmiiZ Ehj_gpZ hljZ`_gb_ ijhkljZgkl\Z \j_f_gb b aZjy^Z – < Gbevk ;hj b jZa\blb_ nbabdb Fhkd\Z BE -73. I_j_i_ebpZ < Ijbgpbi ijbqbgghklb l_hjby hlghkbl_evghklb b k\_jok\_lh\u_ kb]gZeu – < Nbehkhnkdb_ ijh[e_fu ]bihl_au k\_jok\_lh\uo kdjhkl_c Fhkd\Z GZmdZ IhieZ\kdbc J >_fhg FZdk\_eeZ b khhlghr_gby f_`^m bgnhjfZpb_c b wgljhib_c – Mki_ob nbabq_kdbo gZmd L \ui fZc -176. 







 





















 



























































³







´ 









19

IhieZ\kdbc J L_jfh^bgZfbdZ bgnhjfZpbhgguo ijhp_kkh\ Fhkd\Z GZmdZ Ijb]h`bg B <\_^_gb_ \ l_jfh^bgZfbdm g_h[jZlbfuo ijhp_kkh\ Fhkd\Z BE Julh\ K <\_^_gb_ \ klZlblbklbq_kdZy jZ^bhnbabdZ QZkl Fhkd\Z GZmdZ L_je_pdbc Y Ijbgpbi ijbqbgghklb b \lhjh_ gZqZeh l_jfh^bgZfbdb – >hdeZ^u :dZ^_fbb gZmd KKKJ L ‹ -332. N_cgfZg J : Ob[k D\Zglh\Zy f_oZgbdZ b bgl_]jZeu ih ljZ_dlhjbyf Fhkd\Z Fbj Nj_gd_ev Y KlZlbklbq_kdZy nbabdZ Fhkd\Z E_gbg]jZ^ Ba^Zl_evkl\h :G KKKJ P_jf_eh W H[ h^ghf iheh`_gbb ^bgZfbdb \ k\yab k f_oZgbq_kdhc l_hjb_c l_iehlu - < E ;hevpfZg KlZlvb b j_qb Fhkd\Z GZmdZ -83. RZj]ml Y =jZgbpu \hafh`gh]h ijbf_g_gby ihgylby wdk_j]bb – < Wg_j]by b wdk_j]by. Fhkd\Z Fbj -185. RZoiZjhgh\ F H \hafh`ghklb nhjfmebjh\db gh\h]h ijbgpbiZ g_jZ\gh\_kghc l_jfh^bgZfbdb b g_dhlhjuo _]h ke_^kl\byo – @mjgZe nbabq_kdhc obfbb l ‹ -3046. RZoiZjhgh\ F Ijbgpbi Dxjb nexdlmZpbb b l_hjby n_ghf_gheh]bq_kdbo dhwnbp_glh\ g_jZ\gh\_kghc l_jfh^bgZfbdb – @mjgZe nbabq_kdhc obfbb L ‹ -1637. RZoiZjhgh\ F Ijbgpbi gZbf_gvr_]h ^_ckl\by b aZdhgu l_jfh^bgZfbdb – @mjgZe nbabq_kdhc obfbb L ‹ -2882. RZoiZjhgh\ F Z Ijbgpbi gZbf_gvr_]h ^_ckl\by w\hexpby b p_e_gZijZ\e_ggu_ baf_g_gby fZdjhkdhibq_kdbo kbkl_f – @mjgZe nbabq_kdhc obfbb L ‹ -2884. RZoiZjhgh\ F H \hafh`ghklb nhjfmebjh\db gh\h]h ijbgpbiZ g_jZ\gh\_kghc l_efh^bgZfbdb. II. H[h[s_gb_ ijbgpbiZ gZbf_gvr_]h ^_ckl\by gZ g_f_oZgbq_kdb_ ijhp_ku – @mjgZe nbabq_kdhc obfbb L ‹ -522. RZoiZjhgh\ F G_jZ\gh\_kgZy l_jfh^bgZfbdZ b ijbgpbi gZbf_gvr_]h ^_ckl\by – < L_jfh^bgZfbdZ g_h[jZlbfuo ijhp_kkh\ Fhkd\Z GZmdZ -96. R_gghg D JZ[hlu ih l_hjbb bgnhjfZpbb b db[_jg_lbdZ Fhkd\Z BE Rj_^bg]_j W Ki_pbZevgZy l_hjby hlghkbl_evghklb b d\Zglh\Zy f_oZgbdZ - < Wcgrl_cgh\kdbc k[hjgbd. 1982Fhkd\Z GZmdZ -270. Wcgrl_cg : Ijbgpbi =ZfbevlhgZ b h[sZy l_hjby hlghkbl_evghklb - < ` I >h[_j Kbf_ljby \ nbabd_ L - Fhkd\Z Fbj 











 























³

´

















³











 

³





´





 





´



















´

















 



















































³

























´

















 

















































 





































 



   

















  























 







 











³





´













³













 

 





 









































 



 

³

´

Jarmer, M. 1974. The philosophy of quantum mechanics. Ney York, etc. John Wiley&Sons. Khrennikov, A. 2001.Linear representations of probabilistic transformations induced by context transitions. – Journal of Physics A. 34, 9965-9981. Khrennikov, A. 2003. Interference of probabilities and number field structure of quantum models. Annalen der Physik. Vol. 12, N. 10, 575-585. DeWitt, B. 1968. The Everett-Wheeler Interpretation of Quantum Mechanics. – In: Battelle Rencontres. 1967. Lectures in mathematics and physics. (eds. C. DeWitt, J. Wheeler). New York/ Amsterdam: W.A.Benjamin, 318-332. DeWitt, B. 1970.Quantum mechanics and reality. – Physics Today, September, 32-35. Lloyd, S. 1997. Quantum-mechanical Maxwell’s demon. – Physical Review A. Vol. 56, N. 5, 3374(9). Masanes. L., A. Acin, N. Gisin. 2006. General properties of nonsignaling theories. – Physical Review A. 73 012221(9). Maxwell, J. (1871). Theory of heat. – In: Maxwell’s Demon: Entropy, Information, Computing (eds. H. Leff, A. Rex). Bristol: Adam Hilger, 1990. Mehra, J. 1974. Einstein, Hilbert and the theory of gravitation. Historical origins of general relativity theory. Dordrecht. Planck, M. 1979. Das Prinzip der kleinsten Wirkung. – In: (ders.) Vorträge und Erinnerungen. Darmstadt. Wissenshaftliche Buchgesellschaft, 95-105. Sumiyoshi Abe, A. Rajagopal. 2003. Validity of the Second Law in Nonextensive Quantum Thermodynamics. – Physical Review Letters. Vol. 91, N 12, 120601(3).

20

Related Documents