PoS(Baldin ISHEPP XXII)047

Transcription

1 Lmaon of classcal mechancs an ways s expanson Vyacheslav Mchalovch Somskov Insue of Ionosphere Insue of Ionosphere, Kamenskoe Plao, 05000, Kazakhsan E-mal: vmsoms@rambler.ru The problem of rreversbly n he classcal mechancs s scusse. We have shown how hs problem can be solve n he frame of he mechancs of he srucural parcles (SP). A bref physcal jusfcaon for consrucng of he srucure parcles (SP) mechancs s offers. The SP s equlbrum sysems from suffcenly large number of poenally neracng maeral pons. Unlke of he maeral pon he SP has an nner energy. Therefore, he SP moon equaon obans from he prncple of ualy of symmery. The SP ynamcs s rreversble ue o ransform he SP moon energy no he nernal energy n he exernal forces. Irreversbly of he SP ynamcs allows nroucng he concep of ynamcal enropy an reveals s physcal naure uner he classcal mechancs laws. The SP mechanc enables srcly escrbe sspave processes of evoluon of nonequlbrum sysems. Some of problems from oher secons of physcs are scusse. XXII Inernaonal Baln Semnar on Hgh Energy Physcs Problems 5-0 Sepember 04 JIR, Dubna, Russa PoS(Baln ISHEPP XXII)047 Speaker Copyrgh owne by he auhor(s) uner he erms of he Creave Commons Arbuon-onCommercal-ShareAlke Lcence. hp://pos.sssa./

2 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov. Inroucon Symmery s he key concep pcure of he worl. I has eep ancen roos. Accorng o he eas of Plao, he symmery of forms efnes he srucure of maer. Toay, here s, perhaps, no branch of physcs n whch symmery oes no play a funamenal role. The elecroynamcs, quanum chromoynamcs, ec. are consruce base on he symmery [, ]. If he symmery s no broken, hen he escrpon many ynamcal processes n naure s possble. However, n ransonal an evoluonary processes, when he srucure of naural sysems s change, he symmery s broken. To escrbe hese processes all he exsng mehos of analyss sysems base on he laws of conservaon of symmery, are powerless. In hese cases he emprcal mehos for escrbng of he processes of symmery breakng are omnae. Wh he problems n explanng of he observe breakng of he me symmery n he ynamcs of sysems, apparenly frs encounere Bolzmann. He re o explan he secon law of hermoynamcs n he framework of he reversble Hamlonan formalsm [3, 4]. For oay a common mechansm of rreversbly n classcal mechancs s base on he hypohess of he exsence of ranom flucuaons n Hamlonan sysems. The exponenal nsably of he sysems n hs case leas o he rreversbly. Bu he hypohess of flucuaons oes no f n he eermnsc prncples of classcal mechancs. I.e. mus be noe ha src eermnsc mechansm of rreversbly whn he Hamlonan formalsm oes no exs [3, 4]. An snce all he heores n varous fels of physcs, one way or anoher, s base on he formalsm of classcal mechancs, he problem of explanaon of he mechansm of symmery breakng me s a serous obsacle o he evelopmen of physcs n general. Up o now hs problem was one of he mos mporan problems n physcs [5]. However, urne ou ha f you remove some of he resrcons uner whch he consruce formalsm of classcal mechancs, s possble o offer an explanaon of he mechansm of rreversbly n he framework of ewon's laws [6-9]. Inee, all naural boes have a srucure. Tha s, hey have he nheren ynamcs of he srucural elemens. In a general case, such a boy can be represene by a sysem of maeral pons (MP). Ths means ha he sysem has an nernal energy an he moon energy as a whole. The nernal energy eermne by he symmery of he boy. The moon energy s eermne by he symmery of space. Therefore, he moon of he boy s efne as he symmeres of space an he symmeres of he sysem. We shall call hs he prncple of ualy of symmery (PDS) [0]. From he PDS he ualsm of he energy s followe. Inee, he energy of he boy s mae up of he nernal energy an he moon energy. Only he sum of hese energes s ynamcal nvaran of he boy. As we show bellow, rreversbly of he ynamcs s connece wh he possbly of ransformaon of he energy of moon no nernal energy of he boes. Therefore, he mechancs shoul be base on he equaons of sysems moon an no on MP or any oher nonsrucural elemens. Bu only accounng he srucurng boes s nsuffcen o escrbe he rreversble ynamcs. Aonally, he hypohess of he holonomc consrans shoul be exclung when he moon equaons for he sysems we wll be receve []. For consrucon of he formalsm escrbng he ynamcs of boes n he form of sysems MP, nee o use he fac ha her moon s eermne by he rajecory of he cener of mass (CM) an moons of he MP relave o CM. Ths can be one by assumng ha all boes can specfy as a se of neracng srucure parcles (SP) (SP - equlbrum sysem conssng from a large number of poenally neracng MP). In hs case, he moon equaon PoS(Baln ISHEPP XXII)047

3 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov shoul be erve from he SP ualy of he energy conservaon law, subme n accorance wh he PDS as he sum of he energy of moon an nernal energy [6-]. The man objecve of hs work s o enfy some of he general laws of he mechansms of symmery breakng n physcs on he bass of he PDS. For hs, we frs gve some examples of well-known mechansms of symmery breakng n physcs. We show why he sysems ynamcs of MP, eermne on he bass of Lagrange's equaons, s reversble. Afer ha, we conser he lmaons of classcal mechancs, whch preclue he escrpon of sspave processes. ex, we explan how o arrve a he eermnsc explanaon of he mechansm of rreversbly n mechancs usng of he PDS. Afer ha we conser an analogy beween he mechansms of symmery breakng n he mechancs an physcs of elemenary parcles.. VIOLATIOS OF SYMMETRY I PHYSICS The moern concep of symmeres an her volaon n physcs s recly relae o he mahemacal concep of symmery groups []. Group heory mehos use n physcs n hose cases when we analyses he processes, n whch here s no breakng of symmery, or when we are nerese n he nal an fnal sae of he sysem an he process of ranson s acually gven by he "hans" []. Only n hs way we are able o use a src an unversal mahemacal apparaus of he heory of groups. Symmery breakng s always assocae wh non-lnear processes. Inee, he formal symmery breakng s efne operaors ha epen on varables several rreucble symmery groups. For example, he ransformaon of he moon energy no he nernal energy of he sysem n an nhomogeneous fel of forces s eermne by he b-lnear erms ha epen on he macro an mcroparameers [8-]. I.e., he couplng funcons, whch eermne he ransformaon of one rreucble symmery group o anoher, mus epen on he elemens of he wo groups of symmery. There are currenly no unversal mehos for solvng nonlnear equaons. Therefore o escrbe he symmery breakng s necessary o resor o prvae mehos of solvng varous problems of ynamcs, whch are cae by her physcal saemen [0]. In quanum fel heory, quanum chromoynamcs, known processes of sponaneous symmery breakng. To escrbe her mechansms he meho of he renormalzaon group analyss s usng. Ths meho base on a funconal equaon []. Along wh he renormalzaon-group analyss n physcs evelope meho for solvng a farly we range of asks, base on he concep of supersymmery. The mos mporan propery of supersymmery s ha combnes connuous ransformaon (e.g., measures of ranslaon) wh a specal ype of scree ransformaons (reflecon-ype). Ths meho s applcable f here s a formal analogy beween wo of hese ypes of ransformaons ha are of a fferen naure. Avalably of hs analogy s he bass of supersymmery []. In hese cases, a possbly of reucng he problem of one or anoher meho o he problem wh a new ype of he expane symmery s use. Ofen, he nee o explan he symmery breakng leas o he evelopmen of he very founaons of physcs an physcal pcure of he worl as was n he case of sponaneous symmery breakng [3]. Thus, as a rule, now explan he mechansms of symmery breakngs are base on he phenomenologcal approaches n physcs. As usually, nerese nal an fnal sae of he sysems, bu he non-lnear process of symmery volaons, ofen no consere. Ths s one n quanum chromoynamcs by emprcal selecon of operaors of he creaon (annhlaon) of parcles, gauge fels, he nepenen varables n connecon wh he nal an fnal saes. An alhough he corresponng heory s no selom perfecly escrbe numerous expermenal PoS(Baln ISHEPP XXII)047 3

4 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov resuls; quesons abou he mechansms of symmery breakng reman unclear. On he oher han, seems obvous ha f he symmery breakng permeaes all areas of physcs, he explanaon of he naure of such volaons shoul be unversally applcable, as n classcal mechancs, an oher branches of physcs. Consequenly, he queson of how o evelop generc mehos of analyss an escrpon of ynamc sysems subjec o symmery breakng s sll relevan. Here, we are ry o conser hs queson on example of a eermnsc mechansm of symmery breakng of he me whch was subme n he framework of he mechancs SP [0].. LIMITATIOS OF CLASSICAL MECHAICS Classcal mechancs s bul for moel he boy n he form of MP. MP oes no possess by he srucure. Therefore, he ynamcs of MP s eermne only by he symmery of space, an an nvaran of MP s only he energy of s moon n he fel of exernal forces. An hs nvaran eermnes all he moon laws of MP. To escrbe sysems of MP he canoncal Lagrangan an Hamlonan formalsms n classcal mechancs are use. Upon recep of he Lagrange equaons for MP sysems he hypohess holonomc consrans s use [4]. The usng of hs hypohess leas o he fac ha he Lagrangan an Hamlonan formalsms canno escrbe rreversble processes. Below brefly we wll show how hs hypohess exclues erms of he moon equaons whch are responsble for he non-lnear ransformaon of he energy beween varous egrees of freeom ha s he naure of he breakng of he symmery of he me [5]. Lagrange equaons for a sysem of MP oupu c usng he prncple of D Alember, prove ha he work of he reacon forces ue o knemac consrans s zero. Accorng o hs prncple, we have he followng equaon [4]: F Here -s acve force, whch ace on -h МP; -s neral force from -h МP; - s a vrual splacemen;,... R -s a number of МP n he sysem. In orer o negrae (), go o nepenen generalze varables. Mae n () he necessary ransformaons, we oban [4]: Here -s a me; -s a knec energy for all МP; - are he generalze nepenen varables; - s a vrual splacemen; l -s exernal force ace on l -h МP. For o oban from eq. () he canoncal equaon of Lagrange, we use he hypohess of holonomc consrans. Only n hs case oes no epen on k. I.e. he hypohess of holonomc consrans proves conons: l convere no a sysem of nepenen equaons: R R F p r 0 l l l l l ql q l p r R T T Q q 0 T ql q l Q q l 0, l. q () () Uner hese conons, he eq. () s PoS(Baln ISHEPP XXII)047 4

5 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov T T Ql 0 ql q l (3) Thus, he requremen of holonomc consrans allow us o move o a sysem of nepenen 0 equaons whch s eermne by he conon: l. aurally, ha removes he possbly of escrbng he ynamcs of sysems n cases when here s engagemen varables. Bu hs engagemen of he varables efnes a nonlnear ransformaon of energes of he fferen egrees of freeom. Suppose, moreover, ha he followng conon have a place: r Ql V q l. (4) Equaon (3) uner he conon (4) can be wren as [4]: L L 0 ql q l (5) where L T V s a Lagrange funcon. The eq. (5) s a Lagrange equaon. I allows eermnng he ynamcs of he sysem by calculang he ynamcs of each MT. Hamlon's equaons can be obane from he Lagrange equaons by replacng he veloces on momens [4, 6]. Conon holonomc consrans s equvalen o he poenaly of collecve forces (4) eermnng he moon of he sysem. Ths follows from he fac ha one an he same Lagrange equaon can come as by he varaonal meho, an by negraon of he D Alember equaon wh respec o me prove poenal exernal forces. Inee, negrang he D Alember equaon wh fxe nal an fnal me of he rajecory of he sysem, we have [6]: w L A, (6) A L where -s acon. From here we have [6]: A 0 (7) Expresson (7) s he prncple of leas acon of Hamlon. In accorance wh he moon of he sysem occurs n such a way ha he efne negral becomes saonary value wh respec o any possble varaons n he poson of he sysem wh s fxe nal an fnal posons. Thus, he hypohess of holonomc consrans whch use n he ervaon of he canoncal Lagrange an Hamlon equaons preclues he use of hese equaons for he escrpon of rreversble processes. In he general case, when he hypohess of holonomcy s no applcable, nsea of equaon (7) we wll have: PoS(Baln ISHEPP XXII)047 5

6 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov A A (8) Here A - s a erm, cause by non-holonomc consrans an eermne by he non-lnear ransformaon of he energes for fferen egrees of freeom. In he smples case A s blnear funcon. For SP he A s eermne he ransformaon of he moon energy no he nernal energy. To unersan he naure of A, le us explan how he SP moon equaon was obane, an wha are s man feaures..3 O THE MECHAICS OF STRUCTURED PARTICLES Snce all boes n naure have a srucure, wheher s an aom, or wha use o be calle elemenary parcles, her ynamcs s eermne by he relave movemens of he componens, an he movemen of boes as a whole n he fel of exernal forces. The relave moon of boy pars s eermne by s symmeres an fel nhomogeney of he exernal forces. The boy moon as a whole s eermne by he space symmery. These boy moon an relave moon pars of he boy are wo nepenen ypes of moon. Therefore, he boy ynamcs s eermne by s nernal symmeres an symmeres of space. Ths s he essence of PDS. The boy moon s eermne f he relave moon of he boy elemens an he CM moon n he fel of exernal forces are enfe. The nvaran of he boy moon s he sum of he moon energy an he nernal energy. I.e., he boy s moon equaon mus sasfy conservaon law of he sum of he nernal energy an he energy of moon. In general, he sysem s moon equaon wll be eermne by he PDS, uner he conon ha each MT obeys he ewon laws. Hence s clear ha he varables ha eermne he boy moon are he poson an velocy of he CM of he sysem an he coornaes an veloces of all MP relave o he CM. Varables eermnng he boy moon s calle macro varables. The varables eermnng he moon of all MP relave o he CM are he mcro varables. The boy moon equaon, whch sasfes all hese requremens, obane by fferenang he ual energy over me, akng no accoun s preservaon [8]: M V F (Φ + E )V / V ns, (9) VR (/ ) Here r - s a velocy of CM; =,,3... -are he number of ns M MP; = m F ; F (R,r ) E ; = - s a varaon of he nernal Φ energy; vf (R,r ) F, (R,r ) - s a force whch ace on he -h MP from he r se of exernal fel of forces; = R +r r, - are he coornaes of he -h MP relave o he CM. The frs erm n he rgh-han se of eq. (9) s a poenaly force apple o he CM. Ths force changes he knec energy of he SP. The secon erm s non-lnear an epens on boh he mcro an macro varables. Ths erm changes he nernal energy of he SP. The hypohess of holonomc consrans o erve he eq. (9) oes no use. As was shown n [5], hs hypohess exclues he possbly of escrpon of he ransformaon of he SP moon energy no nernal energy n he frame of canoncal formalsm of classcal mechancs. Such a ransformaon s eermne by he nonlnear erms n he eq. (9) whch PoS(Baln ISHEPP XXII)047 6

7 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov epene from he mcro an macro varables. I.e. n conras o he canoncal Lagrange equaons, he eq. (9) akes no accoun he non-lnear ransformaon of he moon energy no nernal energy. Ths ransformaon s responsble for he symmery breakng of he me [7]. Magnue of he change n nernal energy s proporonal o he graens of exernal fel of force [4]. The responsble role of he nonlnear erms for he symmery breakng of he me, clearly emonsrae hrough he numercal calculaon of he passage of he oscllaor hrough a poenal barrer [8, 0]. I urne ou ha only hrough he nonlnear erms, provng an exchange of energy beween fferen egrees of freeom, n parcular, he muual ransformaon of he oscllaor moon energy an nernal energy, he oscllaor may pass hrough he poenal barrer, even f he barrer hegh s more han he moon energy of he oscllaor. If we neglec he non-holonomc consrans, hs effec sappears. When SP s moon n a nonunform fel of exernal forces, he energy of moon can ransform no he nernal energy, bu no vce versa. The reason he breakng of he me symmery connece wh he fac ha he SP consss from he suffcenly large number of MP an n frs approxmaon can be consere equlbrum. In hs case, he ncrease of he SP moon energy ue o s nernal energy s mpossble..4 UCERTAITY OF SYSTEM DYAMICS I CLASSICAL MECHAICS Le us show how o fn he value A (see. eq. (8)) for he SP moon. Eq. (8) for SP can be obane by negraon, base on he prncple of D Alember equaons an he SP moon equaon [6]. In accorng o he prncple of D Alember, we wll have for he MP sysem: F ( m v ) r 0. () Here, he nex runs hrough all he mcro an macro varables. Mulply he on an negrae n he nerval from o. We wll have: F ( mv ) r. () In accorance wh he SP moon equaon, he forces, whch responsble for he change n nernal energy, epen on he velocy an canno be efne as graen of a scalar funcon. Monogenc naure of he acve forces wll only be for a poenal componen of he force ha eermnes he SP moon. Ths means ha he power funcon s exs only for he force whch responsble for he moon of he CM of SP. In accorance SP moon equaon, can be wren as follows: F r U U Performng a sanar converson, for example, as was one n [6], we wre: (3) PoS(Baln ISHEPP XXII)047 7

8 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov M V v U m r Fs r, (4) ns F where s (Φ + E )V / V - s a forces whch responsble for he change of he SP nernal energy. L Usng he noaon: T U T, where ( M V ) /, we wll have: r If s requre ha o vansh a he ens of he nerval, an we wll have: A L where. v s L m r F r A F r s (5), (6) A Fs r F r s Hence we have:. I.e. he negral (6) s zero when =0. Bu hs s possble only when he nernal energy oes no change along he rajecory of he sysem,.e. when he SP moon energy s an nvaran. Thus, he symmery breakng of he me n classcal mechancs assocae wh a change n he nernal energy of he sysem. Ths s equvalen o he energy sspaon. I s only possble ue o he srucural boy. R r Le we have he nequaly:. I means ha he scale of he nhomogeney of he F exernal forces s much larger han he characersc scale of he SP. Then he force n (9) can be expane n he small parameer. Keepng n he expanson of he zero-an frs-orer F F ( r ) F erms, we can wre: R R. Takng no accoun ha v r F и F F, we wll have [0]: ns V ( M V ) E ( ) V F 0 r F v R. (7) The secon erm n he rgh-han se of (7), eermnes he change n nernal energy. He s a non-lnear, epens on he mcro an macro varables an s proporonal o he fference beween he forces exere on he acon, fferen areas of he sysem. Is magnue s much smaller han he frs erm of he rgh se. Then, accorng o (7) we have for SP: PoS(Baln ISHEPP XXII)047 A [ V { ( r ) }/ ] F v V r R (8) 8

9 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov Thus, he sspaon s proporonal o he graen of he exernal forces. Snce he sspaon s mpossble for neracng srucureless boes, an he formaon of new srucures s mpossble whou sspave processes, hen we come o a concluson abou he nfne vsbly of maer. Consequenly, ue o ewon's laws an herarchy of funamenal forces, he naural sysems have a herarchy srucure. Therefore, sspaon an symmery breakng of he me are he nheren properes of maer. Ths concluson follows srcly from he PDS an ewon's laws. Snce he nernal energy an he moon energy are nepenen, he poson of he sysem n space ambguous eermne by he value of he fel of forces a he pon where he CM of he sysem s. Ths means he egeneracy of phase rajecory of he SP, an volaon of he symmery of me. Almos any objec n naure s a nonequlbrum sysem (S). Any S n he approxmaon of local hermoynamc equlbrum can be represene by a se of moon relave o each oher SP [8]. Then he sae of S wll be eermne by he 6R- coornaes an veloces of each SP, where R s he number of SP. The corresponng phase space we call an S-space n orer o sngush from he usual phase space for a se of MP [9]. S-space s compressble, because he moon energy of SP s ransforme rreversbly no her nernal energy as a resul of her neracons wh each oher. Thus, he sae of he S s efne by wo ypes of energy, each of whch can be assocae wh s subspace. The SP moon energy correspons o he subspace of macro varables. An he nernal energy correspons o he subspace of all mcro varables for each MP. Ths means ha each pon of he S-space correspons o he some regon of mcro varables subspace. Ths corresponence s eermne by he sum's nvarance of he nernal energes an moon energes of he all SP. Tha s, beween he pon of he convenonal phase space efne by he coornaes an momens of all SP, an he sae of he S no bjecon because of he ambguy of he nernal energy. If he change n nernal energy of each SP nsgnfcanly an can be neglece, hen he equaon (9) s ransforme no a reversble ewon's equaon. In hs case, S-space s equvalen o he ornary phase Space. The moon energes of each SP are rreversbly ransforme no s nernal energy. Ths s makes possble o nrouce he concep of ynamcal enropy n classcal mechancs. The change of hs enropy s eermne by he relave ncremen of he nernal energes all SP. In accorng wh such eermnaon, he change of he ynamcal enropy S of S s gven by [0]: R L L ks k L S [ F L v ] / E L k s EL -s nernal energy for L -SP; L - s a number of MP n he L -SP; L =,,3 R - s L a number of SP no S; s - s exernal MP whch nerace wh k -h МP of L F -СЧ; ks -s a force, ace on k -h МP of SP from s -h МP anoher SP; k -s a velocy k -h МP. From (9) follows ha he S comes no equlbrum when all he energy of he relave moon of SP go no her nernal energy. Ths concluson s n full complance wh he sascal naure of he equlbrum esablshmen. I also follows from he eq. (7). Inee, accorng o he eq. (7) he ransformaon of he moon energy no he nernal energy of he SP s only possble when he exernal fel for her s nonhomogenous. For each SP such fel s a fel from he oher SP. Snce he rae of ncrease of he SP nernal energy s proporonal o v (9) PoS(Baln ISHEPP XXII)047 9

10 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov he graen of he exernal forces, hs rae ecreases wh ecreases of he energy of he relave moon of SP. When he SP relave veloces are reuce, he S approaches o he equlbrum. Equlbrum correspons o he homogeney of he fel of nernal forces. Such a scenaro s conssen wh he esablshmen of he equlbrum n connecon wh he eq. (7), accorng o whch an ncrease n he nernal energy of he SP n a unform fel s no possble. oe ha he S for a sysem from a small number of MPs oppose o he hermoynamc enropy can be negave. I can be seen from numercal calculaons [5] an also follows from he fac ha he concep of equlbrum of he sysem s applcable only for he case of a suffcenly large number of MP n he sysem. An only for he sysem whch can be consere as equlbrum [9] he S conces wh he hermoynamc enropy..5 ABOUT VIOLATIO OF THE TIME SYMMETRY I ELEMETARY PARTICLE PHYSICS Praccally all he basc equaons of he quanum mechancs, he physcs of elemenary parcles, nclung he Schrönger equaon, Paul, Drac ec. erve from he Hamlon formalsm [7, 8]. Bu hs formalsm s no accepable for he analyss of processes of symmery breakng of he me assocae wh he ransformaon of he moon energy of he parcles no her nernal energy or no he nernal energy of her ecay proucs. Le us conser neracon of he parcles, for whch s necessary o ake no accoun quanum effecs. For example, he scaerng of he elecron flux on nucleons. Le he new parcles are prouce n hs case. Ths means ha here may be a change n he nernal energy of he proucs of neracon prove ha he oal energy of a sysem of neracng parcles s consan. Snce n hs case he sysem s moon energy s ecreases ue o s ransformng no he nernal energy, he symmery breakng of he me s observe. I.e. he conon (8) has a place. Ths conon s equvalen o he uncerany prncple [8], bu he cononaly of he ransformaon of he moon energy of neracng parcles no he nernal energy of he reacon proucs. Then, accorng o (8) we wll have A h, (8) where h - s a Plank consan. Ths gves rse o quesons: how oes hs compare wh he Hesenberg uncerany prncple? Is somehow relae o he fac ha accorng o he SP mechancs, even he smalles parcle, have a srucure,.e. each parcle possess nernal energy wh he corresponng phase space? We remark ha f he uncerany prncple s ue o he srucure, he value of he wll eermne he parameers lowes parcles whch may exs. I.e., n hs case, he uncerany prncple can be nerpree so ha he accuracy of eermnng he ynamcs of a parcle canno excee he accuracy of eermnaon of he moon energy a each pon n he phase space, whch s resrce by he changes of he sysem s nernal energy. In connecon wh rases he queson abou he regon of resrcon of he basc equaons of quanum mechancs. Is necessary o expanson of he formalsm of quanum mechancs, by analogy wh he exenson of classcal mechancs on he bass of accounng srucurng parcles? Ths gves rse o quesons. How oes hs compare wh he Hesenberg uncerany prncple? Do no he h somehow relae o he fac ha, accorng o SP mechancs, even he smalles parcle o be srucural,.e. each parcle possess nernal energy wh he corresponng phase space? We remark ha f he uncerany prncple s ue o he srucure, PoS(Baln ISHEPP XXII)047 0

11 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov he value of he h wll eermne he parameers lowes parcles whch may exs. I.e., n hs case, he uncerany prncple can be nerpree so ha he accuracy of eermnng he ynamcs of a parcle canno excee he accuracy of eermnaon of he moon energy a each pon n he phase space, whch s resrce by he changes of he sysem s nernal energy. In connecon wh he queson abou he regon of resrcon of he basc equaons of quanum mechancs s rases. Is necessary o expanson of he formalsm of quanum mechancs, by analogy wh he expanson of classcal mechancs on he bass of accounng srucurng parcles? Thus, he problem of many-boy mechancs, of quanum mechancs, elemenary parcle physcs, he problem of symmery breakng n he processes of he parcle neracons, ec. requre analyss from he poson of PDS. Ths follows from he fac ha all parcles, nclung he so-calle elemenary parcles, have a srucure. Therefore, an accurae escrpon of he naure of neracon of boes, her ynamcs s mpossble whou akng no accoun he nonlnear ransformaon of he sysem s moon energy no her nernal energy..6 COCLUSIO The escrpon of he ynamcs of sysems n heerogeneous space mus be base on he PDS. Accorng o he PDS he sysem ynamcs s eermne by he sum of he moon energy an nernal energy of sysems. Invaran s he sum of hese energes. Ths nvaran s eermne n he nepenence of mcro an macro varables. The nernal energy s eermne n he mcro varables. The moon energy s eermne n he macro varables. Leanng on PDS, s possble o consruc he sysem s moon equaon whch escrbes he rreversble processes whn he laws of classcal mechancs. The ably o escrbe he rreversbly appears ue o ha ha he SP moon equaon escrbes he nonlnear ransformaon of he sysem's moon energy no he nernal energy. The resrcon of he Hamlonan sysems connece wh ha ha oes no ake no accoun he possbly of ransformng he energy of moon no nernal energy. I s because ha n he ervaon of Lagrange equaon he hypohess of holonomc consrans s use. Tha s hs hypohess exclues from conseraon all he ynamc processes ha are accompane by a non-lnear ransformaon of he sysem s moon energy no oher ypes of energy, n parcular, no he nernal energy. Bu precsely such ransformaons of energy are necessary conon for symmery breakng of he me. Therefore, he formalsm of classcal mechancs s only suable for he escrpon of aabac processes n he sysems near equlbrum. Accorng o he SP moon equaon, he phase rajecory of he sysem s egenerae. Degeneracy ue o he fac ha each pon of he phase rajecory whch eermne by he moon of he cener of mass of SP correspons o a se of nernal saes of he SP. Tha s, each pon of he phase space s efne up o a value A. The A s eermne by a nonlnear ransformaon of he moon energy no nernal energy. In he smples case he A s a blnear funcon. The A s corresponence o he uncerany prncple n quanum mechancs. So he queson: s no connece hs he prncple wh ha ha all naural objecs, no maer how small hey were no, have an nernal srucure, whch causes uncerany n he phase rajecory when he srong neracons have a place? PoS(Baln ISHEPP XXII)047

12 Lmaon of classcal mechancs an ways s expanson Vyacheslav Somskov The eermnsc rreversbly allows us o use n he classcal mechancs he ynamcal enropy as he relave ncrease n he nernal energy of he SP. The ynamcal enropy n he lm of large number of MP n he sysem correspons o he Bolzmann an Clausus enropes. References [] V.F. Kovalev, D.V. Shrkov. Group of symmeres for soluons of bounary value problems. Phys Vol. 78. no.8. p [] G.Y. Lyubarsk. Group heory an s applcaons n physcs. Moscow. GIFML p. [3] G.M. Zaslavsky. Sochascy of ynamcal sysems. Moscow. Scence, 984, 73 p. [4] I. Prgogne. From Beng o Becomng. Moscow. Scence p. [5] V.L. Gnzburg. On superconucvy an superfluy (wha I have o o, an was no possble), as well as "physcal mnmum 'a he begnnng of he XXI cenury. UF. obel Lecure T p [6] V.M. Somskov. The equlbraon of an har-sks sysem. IJBC. 004.V 4.. p [7] V.M. Somskov. Thermoynamcs an classcal mechancs, Journal of physcs: Conference seres p.7-6. [8] V.M. Somskov. The resrcons of classcal mechancs n he escrpon of ynamcs of nonequlbrum sysems an he way o ge r of hem. ew Av. n Phys. Vol.. o. Sepember. p [9] V.M. Somskov. onequlbrum sysems an mechancs of he srucure parcles. Elsever. Chaos an Complex sysem. 03. XV. 58 p [0] V.M. Somskov. From he ewonan mechancs o he physcs of evoluon. Almay p. [] V.M. Somskov. Why I Is ecessary o Consruc he Mechancs of Srucure Parcles an How o o. Open Access Lbrary Journal. 04. p. -8. [] Genensheyn LE, I.V.Krve. Supersymmery n quanum mechancs. UF.985. V. 46. no. 4. p [3] Y. ambu. Sponaneous symmery breakng n parcle physcs: examples of fruful exchange of eas. Phys. T p [4] G. Golsen. Classcal mechancs. Moscow p. [5] V.M. Somskov, Mokhnakn A. on-lnear Forces an Irreversbly Problem n Classcal Mechancs, Journal of Moern Physcs, Vol. 5 o p. 7-. [6] С.Lanczos. The varaon prncples of mechancs. Unversy of Torono press p. [7] A.Schrönger. An unulaory heory of he mechancs of aoms an molecules. Physcal Revew. 8, 96 (December). p [8] J. Greensen, A.Zajac. Quanum call. Moern sues of he founaons of quanum mechancs. Recenly. Inellgence p. [9] Y.B.Rumer, M.Sh.Rvkn. Thermoynamcs, Sascal Physcs. an knemacs. Moscow. Scence, p. [0] V.M. Somskov, A.B. Anreev. Feaures of he ranson o he hermoynamc escrpon of he ynamc escrpon of he srucure parcles. PEOS, Vol p. 5-. PoS(Baln ISHEPP XXII)047