Fractal Relativity, Generalized Noether Theorem and New Research of Space-Time

Size: px

Start display at page:

Download "Fractal Relativity, Generalized Noether Theorem and New Research of Space-Time"

Lambert Heath
5 years ago
Views:

1 r Rei, Generize Noeher Theorem n New Reserh o Spe-Time Yi-ng Chng Deprmen o Phsis, Yunnn Unersi, Kunming 659, Chin (e-mi: inghng@homi.om) Absr irs, e he r imension D=n(ineger)+(eim), so he r imension mri ws represene b usu mri s spei eim row (oumn). We reserhe h mhemis, or empe, he r imension iner gebr, n phsis m be eeope o r n he ompe imension eene rom r. rom his he r rei is isusse, whih onnes wih se-simiri Unerse n he eense qunum heor. The spe imension hs been eene rom re number o superre n ompe number. Combining he quernion, e., he high imension ime i i j k is inroue. Suh he eor n irreersibii o ime re ere. Then he r imension ime is obine, n spe n ime possess ompee smmer. I m be onsrue preiminri h he higher imension, r, ompe n superompe spe-ime heor oers. We propose generize Noeher heorem, n irreersibii o ime shou orrespon o non-onserion o erin quni. Resume reersibii o ime n possibe erese o enrop re isusse. in, we obin he qunie reions beween energ-mss n spe-ime, whih is onsisen wih he spe-ime unerin reion in sring heor. Kewors: rei, spe-ime, r, ompe, irreersibii o ime. r n Is Deeopmen 975 B.Mnebro [,] propose n suie r whose orm is ereme irregur n/or rgmene ses. We hink h r possesses wo bsi hrers: he se-simiri or ieren ses n he r imension, whih m be non-ineger (rion or irrion number). Thereore, we eene he r imension D ino he ompe imension in boh spes o mhemis n phsis [], whose represenion is: D z D it. () When he ompe imension is ombine wih rei, whose imensions re hree re spes n n imginr ime. I m epress hnge o he r imension wih ime or energ, e., n eiss in he rs esripion o meeoroog, seismoog, meiine n he sruure o prie, e [4]. urher, r imension m be eene o superre n superompe imension [5]. We reserhe mn spes o eeopmen o r imension in mhemis n phsis [5]. Assume h he r imension D=n(ineger)+(eim). rom his he r imension iner gebr, nsis n se, e., m be eeope. or empe, he r imension mri ws h usu mri s spei eim row (oumn), whose D imension squre

2 mri is eine s:... n D n nn Dn D nd DD, () in whih he in row n oumn shou be unersoo s spei eim imension. So o iner gebr n be ppie b he sme w, bu ierene is on in row n oumn [5]. The r nsis rees o iereni, inegr n operion uus o non-ineger orer. The inegr operor is eene o n posie number power s:. () ( ) is he iereni operor s=/. Using he sme meho, we eene eor, ensor, e., o r imension, een eene rious regions o mhemis o he ompe number imension. Bse on he r mhemi eeopmen, we m reserh h he r imension n is eeopmen re ppie o mehnis, sisis n eeronmis, e. The r qunum heor n is mening in he prie phsis were isusse [5].. r Rei The bsi mhemi represenion o he spei rei is inrine o he iner s. Using meho o iner gebr his is inrine o he snr quri orm uner iner rnsormion. This iner rnsormion o he iner s is: '. (4) I is he Lorenz rnsormion (LT) o < or he imeike iner, or he generize Lorenz rnsormion (GLT) o > or he speike iner [4,6]. irs, we isuss he r spei rei wih D=n+ imension spe n imension ime. Le 4 i, LT o moing spee ong n ireion [7] in +-imension spe is: R / R / R /, (5) in whih / ( R n is he spee in eim imension spe. / ), Ne, i =, i is he sme wih usu LT, on. I, =, in + =

3 imension spe-ime,, (6) i.e., ' ( ), ' ( ). (7) This is LT o. Moreoer, we m ere he orresponing GLT o : ' ( / ), ' ( / ), ( / ( In gener rei, i imension o spe is D, so he iner is: / ) ), (8) D s g. (9), Corresponing quniies n ormus shou be eene. This onnes wih some r sruures o he unerse [8,9]. or insne, hese isribuions on gies n users o gies n superusers he simiri; he wo je srems on he uromp sr n he rio qusrs, whih re ew miion imes rger hn he ormer, he so simiri. We oun h he erge isnes (he Tiius-Boe w) beween he Sun n pnes m be represene s new orm [,]: r n n, () in whih n is ineger n is wo onsns, respee, or erresri n Join pnes. I is simir ompee wih he Bohr om moe. rom his we obine he qunum onsns H ( GM ) / o he sor ssem, n orresponing qunum heor. Suh mn quniies o he sor ssem n be qunize. urher, we ere he sronomi Shroinger equion, n he isne w is sisi resu o pne eouion. This shou be he eense qunum heor, whih hs ieren qunum onsns bu simir ormuions. I is nme uners qunum heor. We ompre qunie he wo simir regions: he sor ssem n he omi sruure, n oun h he wo mie ues o geomeri series re.86m or isne, n kg or mss. Boh re bou he heigh o mnkin house n bou humn weigh, respee []. This no on orrespons o he nhropi prinipe [], bu so is e. Combining he sronomi qunum heor, he nure shows se-simir embee sruure.. High Dimension Time, r Time n Irreersibii o Time In rei he hree-imension spe is re number, n one-imension ime is imginr number 4 i, so h uniiion o spe-ime orrespons o ompe number. When ompe number is eeope o he quernion (one o he superompe), ime shou be hree imension orm: i i. () j k

4 In he eense spei rei on b h, noher inrin eoi h m be ieren eoiies, whih onsru new rie o spe-ime ssems [4]. This is onnee possib wih he mn unerse propose b ere [], n er mn wors [4]. In q.() i onne possib wih ieren eoiies. When, q.() is simpiie s: i T ( i ) j k. () This se is si imension superompe spe-ime. Sine he superompe is ring, i oes no obe he ommue w o muipiion, i.e., T T TT. The hree-imension ime possesses eor hrerisi. This shows h T is q number in qunum heor, n hs he irreersibii on he sequene o ing ime. I i,j n k re hree oorine is, T is hree imension ime, in whih he simunei is represene b n equipoeni sure T (,, ) C. In his se, ime possesses hrer o eor. Dere o union or ime orrespons he ireion ere: T os os os, () whose mimum is gruion or ime: gr i j k. (4) This is eor, whih is perpeniur o he equipoeni sure T=C, n poins o ireion o union inrese. We suppose h i m esribe rrow o ime, n orresponing he irreersibii o ime. I he union is enrop, he gruion m eine ireion o ime. Moreoer, we m eine ergene o ime T,, ) : ( T z. (5) This seems o represen h high-imension ime m be ergen. We m so eine roion o ime: rot ( ) i ( ) j ( ) k z z. (6) This onnes possib o h high imension ime m be spir eeopmen. A presen rious higher imension heories re inrese o spe. We he inrese imension o ime o hree [5]. I spe-ime heor ombines biquernion, ime wi be be o higher imension. I is onsisen wih he Kuz-Kein heor n supersring. Bu, hese imensions beween spe n ime m be re-oe n eeope or higher imension supersmmer heor, supersring n rious uniie heories. or empe, we ere some 4

5 new represenions o he supersmmeri rnsormions, n inroue he supermuipes. So rious ormuions (inues equions, ommuion reions, propgors, Jobi ieniies, e.) o bosons n ermions m be uniie [5]. Suh he mhemi hrerisi o pries is propose: bosons orrespon o re number, n ermions orrespon o imginr number, respee. ermions o een (or o) number orm bosons (or ermions), whih is jus onsisen wih reion beween imginr n re number. The imginr number is on inue in he equions, orms, n mries o ermions. This is onnee wih rei. The uniie orms o supersmmer re so onnee wih he sisis uniing Bose-insein n ermi-dir sisis [6]. Thereore, possibe ireion o eeopmen is he higher imension ompe spe. urher, in he higher imension ime we inroue simir r ime: T n, (7) D whih m be. or.7 imension ime, e. This m be eeope o he ompe ime whose imension is hngebe, een superompe imension ime. Suh spe n ime possess ompee smmer. r possesses he se-simiri o sruure, n simir he r ime possesses bioogi Heke re-eouion w. The higher imension n r ime inroue wi ere rious eeopmens o ieren heories. or empe, hese ourh omponens whih orrespon ime in he our-imension eors, energ, requen n ensi, e., m een o he higher imension n r. In wor, i m be onsrue preiminri h he higher imension, r, ompe n superompe spe-ime heor oers [5]. L.Noe suie r spe-ime n prinipe o se rei, oring o whih he ws o phsis mus be suh h he pp o oorine ssems wheer heir se o se, whose mhemi rnsion is he requiremen o se orine o he equions o phsis [7]. 4. Generize Noeher Theorem n New Reserh o Spe-Time In nure here re rious rrows o ime [8,9], whih re nme irreersibii o ime. The Noeher heorem onnes ose spe-ime, n poine ou: i ssem uner erin rnsormion group is inrine, he smmer wi proue neessri erin onsere quni. or he oninuous smmeri groups, n ssem, whih m be represene b Lgrngin L, orrespons o oninuous equion,. (8) Here he our-imension eor L L ( L ), (9) n is inegr re onsere. A we-known empe is h uniorm spe-ime orrespons o onserion o momenum-energ. We eeop he Noeher heorem o generize ormuion: 5

6 A priur se o he boe resus is h pe o smmer is ireion o ime. Suh irreersibii o ime shou orrespon o non-onserion o erin quni, or empe, enrop. The simpes empe is h when hnge o energ hs ireion, he rrow o ime m be eine rom his. urher, hnge eiss in ime, so hnge o n quni wih he ireion m be ppie o eine he rrow o ime. Beuse he inrine uner ime reeion nno obin onsn, i nno so obin einie non-onsere quni when ime reeion oes no ho. The irreersibii o ime in ieren regions seems o be ue o ieren non-onsere quniies in hese ses. Suh ieren rrows o ime re proue. Reen, Hurh n Skeneris reserhe qunum Noeher meho []. In boe semen, we isuss irreersibii o ime in high imension ime. Here we propose noher uners mhemi orm on rrow o ime: Assume h erin quni is non-onsere, so Q, () where Q is issipe erm. In he ie heor represens -imension ergene. Aoring o he -imension Guss w,... V... S... QV. () im. ( ) im. im. or onserion proess u hrough ose ( -)-imension ur e sur is zero. Whie or he non-onserion proess he u is no zero, i.e., is hngebe. This impies h neessr oniion o onserion quni (inuing onserion o energ) is n isoe ssem. urher, we hink h he wo neessr oniions or he onserion o energ n or reersibii o ime shou inue: (). An riion ores mus be negee; (b). Ssem is isoe, whih is se eep b he heor o he issipe sruure. The oniion (b) is inene gener. Isoe ssems n orresponing reersibii o ime re ew ieize ses in mrosopi wor. Bu, (b) is neessr. Beuse erin ow eiss or n open ssem, rom his ireion m be eine. A rjeor is inee reersibe or ime, bu 6

7 inpu n oupu re wo ieren ireions. Thereore, nure is mos irreersibe. Reersibii o ime orrespons o eisene o inerse eemen, n irreersibii o ime orrespons o Mrko proess n semigroup. A or e or generize eouionr operor U e L eines issipe semigroup. Combining some known resus, we propose unmen operor [4,], p i ( i ), () where n re orree or n ie erm, respee, n boh m be noniner orms. rom orresponing equion HU i ( i ) U, () or qunum heor, orm o o ime. U m be soe when, n H re no obious unions The mos known-we rrow o ime is he seon w o hermonmis n inresing enrop. Bu, i is bse on sisi inepenene, e. We propose h i inerions n uuions eis mong rious subssems o n isoe ssem, hese prerequisies wi no ho. nrop is no n ie quni, n he erese o enrop on he isoe ssem is possibe []. Sine uuions n be mgniie ue o inern inerions uner erin oniion, he equ-probbii oes no ho, n enrop wou be eine s S ( ) k P ( )n P ( ). rom his we ue erese o enrop in spei inern r r r onense proess []. Inern inerions, whih bring bou inppibii o he sisi inepenene, use possib ereses o enrop in n isoe ssem. This possibii is reserhe or re proess, inern energ, ssem enrop, n noniner inerions, e []. In hese ses, he sisis n he seon w o hermonmis shou be ieren. An isoe ssem m orm se-orgnize sruure, whose enrop is smer, n be orme. urher, we in nege emperure is onriion wih usu mening o emperure n wih some bsi oneps o phsis n mhemis. Nege emperure is bse on he Kein se n he oniion U> n S<. Conerse, here is so nege emperure or U< n S>. I wi ere neessri erese o enrop [4]. When erese o enrop is possibe, no on he rrow o ime on enrop wi be n opposie ireion, n gener reersibii o ime wi be resume. urher, PCT inrine n some eouions o mn ssems rom prie n bioog o sr n osmoog wi open up new prospes. In he spei rei, energ is m / ( ), he ime iner he sme posiion is, n spe iner he sme insn is / ( ) ( ). rom his we ere neessri resu: energ is in ire proporion o 7

8 he ime-iner he sme posiion in spe, n is in inerse proporion o he spe-iner he sme insn o ime. The resu m een o he gener rei, whih is so eeopmen o spe-ime h epens o mss n is moe. Combining he e Brogie reion in qunum heor, he sme onusion m be obine, n hese qunie reions re [4]: h n h. (4) nerg is qunum, so spe n ime re so qunum. Le h h n h h, (5) he minimum spe iner (spe qunum) n he minimum ime iner (ime qunum) whih orrespon o qunum energ re respee: n. (6) I boh re he Pnk spe se P G.6 m n he Pnk ime se 4 P P.5 se, n ssume P,, here wi be uniing P. We hink h his is eeopmen o Noeher heorem. The spe is qunum sruure or he sring heor n he oop qunum gri. urher, i is onsisen wih he spe-ime unerin reion X T s, whih is propose b Yone in 989 bse on he pi spi eension X~ s o srings wih energ. This impies he simpe reion or he ineerminies o he spe n ime enghs. I n be ere s ire onsequene o he wor-shee onorm inrine. Li n Yone isusse h he spe-ime unerin reion o he orm X T or he obserbii o he isnes wih respe o ime is uners i in sring heor inuing D-brnes. This reion, ombine wih he usu qunum mehni unerin prinipe, epins he ke quie eures o D-prie nmis [5]. Moreoer, here is he Bekensein s boun or inormion. In eeromgnei ie, he energ m e m( e / m) (7) eres ure spe-ime. Bu, he seon orree erm hos on or hrge boies, n orreion is he sme or he sme rio o hrge o mss e/m. I is nme he prinipe o equene or he eeromgnei ie [6]. This proes possibii on he eisene o eeromgnei spe-ime. Combining he boe onusion, he eeromgnei ime shou be: e / m ). (8) ( 8

9 The mos bsi energ-mss n spe-ime in nure re onnee qunie. The onsru uniie bkgroun or rious sienii esripions. Reerenes.B.Mnebro, rs, (reemn, Sn rniso, 977)..B.Mnebro, The r Geomer o Nure, (reemn, Sn rniso, 98)..Yi-ng Chng, porion o Nure (Chin). 7()-(988). 4.Yi-ng Chng, New Reserh o Prie Phsis n Rei, (Yunnn Siene n Tehnoog Press. 989). Phs.Abs. 9,7(99). 5.Yi-ng Chng, porion o Nure (Chin). ()49-54(99). 6.Yi-ng Chng, Gien eronmis. 8(): 8-9(7). 7.P.G.Bergmn, Inrouion o he Theor o Rei, (New York, 947). 8.A.S.Sz & D.N.Shrmm, Nure,4,78-79(985). 9. J.Mo, Nure, 9,95(987)..Yi-ng Chng, Pub. Beijing Asron.Obs. 6,6(99)..Yi-ng Chng, Phsis sss, 5()-7().. B.J.Crr & M.J.Rees, Nure, 78,65-6(979)..H.ere, Re.Mo.Phs., 9,454(957). 4.J.Grrig & A.Vienkin, Phs.Re., D64,45(). 5.Yi-n Chng, Journ o Yunnn Unersi. 5()7-4(). 6.Yi-ng Chng, Hroni J. 7(5)8-(984). 7.L.Noe, r Spe-Time n Mirophsis, Towrs Theor o Se Rei. (Wor Sienii. 99). 8.A.S.ingon, The Nure o he Phsi Wor, (Ann Arbor: Un. o Mihign Press. 958). 9.S.W. Hwking, Phs.Re. D() (985).. T.Hurh, K.Skeneris, Nu.Phs. B54() (999)..Yi-ng Chng, Hroni J. () 57-68(999)..Yi-ng Chng, Apeiron. 4(4)97-99(997)..Yi-ng Chng, nrop, 7()9-98(5). 4.Yi-ng Chng, rx. Phsis.gen-ph Mio Li & T.Yone, Phs.Re.Le.78,9- (997). 6.Yi-ng Chng, Gien eronmis. 6(5)9-96(5). 9

Released Assessment Questions, 2017 QUESTIONS

Released Assessment Questions, 2017 QUESTIONS Relese Assessmen Quesions, 17 QUESTIONS Gre 9 Assessmen of Mhemis Aemi Re he insruions elow. Along wih his ookle, mke sure ou hve he Answer Bookle n he Formul Shee. You m use n spe in his ook for rough