The Proof That There are no Invariabilities of Lorentz Transformations in the Interaction Theories of Micro-particle Physics

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Roland Goodwin
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1 Th Poo Tht Th o Ivblts o ot Tsotos th Itcto Thos o Mco-tcl Phscs M Xoch Isttt o Iovtv Phscs Fho Ch bstct It s ov ths tht th t lst v sttos th tcto thos o co-tcl hscs tht th ot tsotos hv o vblts.. I th ol to clclt tsto obblts tcl hscs th so-cll vblt cto o hs sc s ot vbl ctll th ot tsotos. Ol th stto o o-sol oto wth t s vbl.. Th olto vctos o qt lctogtc ls th sto ols hv o vblt o ot tsoto.. Th ogto cto o so l qt tho o l hs o ot vblt. I th tsoto wht s s th cto th th bt ct clclto ts whch ls to wog slt.. Thogh th oto qtos o qt ls th tcto Hlto chg th ot tsoto th oto qto o tbto whch s s to clclt th tsto obblt th tcto stto hs o vblt. 5. Th tctos btw bo stt s tcls hv o ot vblt. I ct th cl o ltvt hs o oto t hols. 6. Th clclto thos o hgh o tbtos olto ocsss qt tho o ls volt th vblt o ot tsoto. Th coclsos bov ctv o stog w lctogtc tctos so o. Tho th cl o ltvt os ot hol th co-tcl s tctos. O th oth h th vblt cl o lght s s s stll ctv. So th ols o scl ltvt stll hol bt w shol cos th wth bsolt sgccs. Wos: Pcl o ltvt ot vblt volto Qt tho o l Qt chcs Phs sc cto Pogto cto Nolto CMBR Cosolog. Itocto Th st s scl ltvt s bs o two otol cls. O s th cl o ltvt oth s th vblt o lght s s. ccog to th cl o ltvt oto s ltv coct. W c ot t whth c s ovg o s o t st b hscl ts. Wth o stct sg th os o hscl lws lt to th chocs o c s. To ch ths hscl qtts shol b covt ot tsotos. Bcs ost co-hscs volv low s s ocsss scl ltvt s l s co-hscs ocsss. Mco-hscs cls ltvt qt tho o l o-ltvt qt chcs. Bcs th oto qtos tctos Hltos qt tho o l cos vbl ot tsoto hscsts blvs tht tcto ocsss o co-tcls sts th cl o ltvt.

2 Howv stooc obsvtos o tht th cosc cowv bcgo to CMBR ws sotoc sc stbto. I w t th c whch CMBR s sotoc s bsoltl sttc c obsvtos cts tht o sol sst s ovg s bot 9 s log ct cto th coot sst o clstl sh. Ths vloct c b cos s th bsolt vloct o sol sst. I ct Bg Bg cosolog s bsoltl sttc c. W c th tht ll tl vlocts o tls th vs w cs b th ccltg ocsss Bg Bg. So hscs s l stto t st. Cosolog ltvt cosstt. Ths s sos obl. I ths w ov tht th cl o ltvt s ol sbjctv scos jgt coscoc low s s cotos jst s Gllo s ttol ts clos sh. U coscoc hgh s s cotos th cl o ltvt os ot hol. I ct th cl o ltvt hs v b cctl v b ts. Phscsts hv v c ot ts c wth hgh ogh s to v th coctss o ltvt cl! I th ocsss o co-tcl s cs collsos th tsto obblts cos hvg othg to o c s. Qt tho o l s costct ths cl th tcto thos o co-tcls cos stsg th cl o ltvt. Howv ths w cll s th oto qtos th tcto Hltos o co-tcls qt tho o l s tht t lst v sttos th tcto thos o co-tcls hv o vblt ot tsoto.. Th so-cll vblt cto o hs sc th ols o tsto obblt hs o vblt o ot tsoto ctll. Ol th o-sol oto ocss wth t s vbl. Th slt cts tht ll tsto ocsss o co-tctos hv o vblts ot tsoto. Th cotto ltos o l otos hv o vblt to ths slt.. Th olto vctos o qt lctogtc ls th sto ols hv o vblt o ot tsoto so tht ll co-tcto ocsss lt to hotos hv o ot vblt.. Th ogto cto o so l hs o ot vblt ctll. Wht s th tsoto s th s o ot ctos wh th. Bt th ct clclto w t. Th coso o sbsct s osto ls to sos st.. Thogh th oto qtos o gg ls so ls th tcto Hltos chg ot tsoto th oto qto o tbto tho s to ctcll clclt th tsto obblts tcto stto hs o ot vblt. I ct v th ost otol olto ols o obblt wv qt tho o l qt chcs hv o vblt o ot tsoto too. Uottl ths obls glct t st. 5. Th tctos btw bo stt s tcls volt th vblt o ot tsoto. I ct so-cll ltvt qt tho o l ol scbs tcto ocsss whch tcls t th tl l stts. Th Hltos o tctos costct b tcl s wv ctos. Wht s ts tcls t l stts. Bcs th wv ctos th octs q o o-sol ot o tcls vbl qtts o ot tsotos th obblt lts o tstos vbl.

3 Howv hscs o th tctos btw bo tcls whch th wv ctos gs ots hv o sts o tcls. W hv so tht th oct q s ot th vbl qtt o ot tsoto g. Th tcto Hltos c ot b costct b tcl s wv ctos hscl qtts. Th tho o qt tho o l b ctv. I ths w ov tht th tctos btw bo stt s tcls hv o ot vblt b svl ls jst s th scttg ocss o lctos tl l th stct o hog toc g lvls th sso bsoto o hotos tos. ccog to ct stg ltvt qt tho o l scbs stbl tcls wth hgh s o-ltvt ot qt chcs scbs stbl tcls wth low ss. Ths clsscto s stbl o th cl o ltvt cl. Th cl o ltvt hs o oto. I th cl o ltvt s coct t shol lso b ctv o th co-tcls wth low ss. I ct clsscl Nwto tho lso stss th cl o ltvt. Th oto qtos o Nwto chcs chg th Gllo s tsoto. Howv th oto qtos Hltos o o-ltvt qt chcs c ot chg o tt th Gllo s tsoto o th ot s tsoto. Ths ct cts tht co-tcl hscs hs o ltvt ssc! So cll o-ltvts o oto qto tcto Hltos qt chcs ot cs b th oto thos o sctos. Th tth s tht ltvt os ot st co-hscs t ll! 6. Th olto ocsss o hgh o tbtos qt tho o ls volt th vblt o ot tsoto. W t th b sht o hog toc g lvls s coct l t st th ov th coclso gll. Th coclsos bov gll ctv o stog w lctogtc tctos. Tho th cl o ltvt os ot hol th ls o co-tcl s tctos. Howv th vblt cl o lght s s s stll ctv. It s tht th ols o scl ltvt c stll hol. Bt th shol b l wth bsolt sgcc. I ths w th ts o co-tcls th obsvtos o co-cosolog bco cosstt th cotcto btw cosolog scl ltvt c b lt thooghl.. Th ot tsoto o hs sc cto. Th vbl qtts o ot tsoto tcl hscs I tcl hscs th bsc ol to clclt th c obblt tcl hscs s W P Q B M Th bsc ol to clclt th collso coss-sctos s W P Q B M J I th ols th obblt lt M s th cto o cs oths tc ctos. s th cto o hs sc t l stt. ll tt boos hscl octs cos ths cto s th vbl qtts o ot tstos. Howv t s ot lss o-sol oto wth.

4 Bo ovg t w to th vbl qtt o ot tsoto. I scl ltvt hscl qtts tso th os o covc. Sos tht th s hscl qtt t coos o sc-t coots vloct th tl c. It b scl vcto o tso sbscts glct. W tso t to th c whch ovs o s ltv to. I obt ' t cots ltv s w s tht th hscl qtt s ot th vbl qtt o ot tsoto. I t os ot cot th lto tht ' t s o ' t s th s s tht t s o t w s tht t s th vbl qtt o ot tsoto. W t svl ls cool g tcl hscs. Sos tht ovs log th ostv cto o s ltv to th ot coot tsotos st c t t t Th vs tsoto o s t t t Th ot tsotos o vlocts 5 So t vlocts ot th vbl qtts o ot tsoto bt sc coot chg. I c ot g o tcl wth ss Sbstttg 5 6 w obt th ot tsotos o ot g 6 7 So th vbl qtts o ot tsotos bt Wtg th th o-sol os wth w hv ot. 8 s th vbl qtts o ot tsoto thoght t s ql to costt. Th cto J s lso th ot vbl qtt wth J 9 W c ov t sl. ccog to 6 w hv

5 5 ccog to 7 w gt ] [ I tcl hscs sl vbl qtts S t Mwhl w hv t t t t t So th wv cto o tcl s lso th vbl qtts o ot tsoto wth t t t t Th to o cto tcl hscs s 5 Tsog t to c bcs chg w ol to clclt th lto btw t t. B sg th Jcob s t o tgl tsoto w hv t t t t t t t t 6 So 6 lso th vbl qtt o ot tsoto wth.. Th ot tsoto o hs sc cto I hs sc cto s th vbl qtt o ot tsoto t shol sts 7 W wll ov tht 7 ol hols th stto o o-sol oto wth. I gl stto wh 7 s tbl. ccog to 6 w hv

6 8 Fo th o-sol oto wth B tso to c ccog to 5 w hv 8 c b wtt s 9 Sbstttg 9 w gt Tho t s ov tht th stto o o-sol oto th hs sc cto c ot b vbl th ot tsoto. Howv th ct qt tho o l gl ths slt to th stto o th-sol oto wthot oo. It s ov blow tht ths s ossbl. I th th-sol oto wth ccog to 5 8 w hv Cog wth t s obvos tht c ot chg th ot tsoto. Th slt c b v ctl. Fo th o-sol oto wth w sbsttt th ltos th ght s o gt tl. Th ccog to 7.. w gt o Fo th coct clclto b cosg 7 w hv 6

7 7 5 W obt 6 B sg th Jcob s ol w gt 7 H. Sos tht th tg cto s chg wth w gt c c 8 Th ow lts o tgl sgls bot c. Th so s tht wh w hv c.. Th ot tsotos o th oto qto o so l th Hlto o lctogtc tcto. Th ot tsoto t o o-sol sc-t coots I scl ltvt w t t wt s wth 9 H. Th vs tsoto s. ccog to th vblt cl o lght s s w hv so w hv. W shol ttto to th ostos o s. ccog to 9 w hv o wh. B wtg th ot cll w hv

8 Th oths o. Ths slt s v sgct o o scssos blow. It s ov tht wht s th ot tsoto o ogto ctos o so ls s wh th th. Bt th ct clclto w t. Th coso o sbsct s osto ls to wog slt so tht w th tht ogto ctos o so ls s ot vbl.. Th ot tsotos o so l ts oto qto Th Dc qto o so l c s B tsog t to c cosg ltos o w hv ollowg tl Th covt l o tl oto s cosstt wth tht o coot tsoto. W s sbsct stg ct ot tsoto stg th ct ot tsotos o coots cto. Sbstttg lt st w gt B tocg t ctg t o th lt s o w gt Sos tht th sts vsl t lt o 5 It hs b ov cosh sh wth cosh sh qt tho o l. It c b wtt s th o o t Dg w wv cto wth cosh sh cosh sh sh cosh 6 sh cosh 7 o 8 c b wtt s 9 9 hv th s o so w s tht th oto qto o so l s vbl th ot tsoto. Howv cots th s o ltv oto. Th c 8

9 9 sts ctcll. Th ct qt tho o l glct ths c l to th vblt o th ot tsoto. O th oth h t ws ov qt tho o l []. Bs o t w gt. B cosg lto 6 w obt O. Th ot tsoto o th Hlto o lctogtc tcto I qt tho o l b cosg th tcto btw lctogtc l so l th oto qto c s J T T T J H J H H s th Hlto o tcto. ccog to th covt l o vcto scl ltvt sl to th coot tsoto th covt ol o o-sol lctogtc ottl s : v v W wt ot th coct slts 5 Th oto qto o o- so tcl cots th t. B ocg t o th lt s cosg 5 7 w gt 6 So th oto qto o o- so tcl ss to b ot vbl scll bt th slt cots th ltv s. Sll w hv 7 Bcs ltv s s cot th tso wv ctos th tcto Hlto s chg th ot tsoto. Jst bcs qt tho o l ss th ctos o

10 tcls to costct th Hlto th tcto stto ls wth th obls o bo stts. s show th ctos o tcls chg so w c cos 7 s vbl. Howv s ov blow th qt ctos o lctogtc ls ol vctos th ols o sto ot vbl. I th obls o bo stts volv ltv ss c ot b lt gl th tcto Hlto. I ths css th o ot vblt.. Th ot tsoto o bsc qto o tbto th Nolto Fol o Pobblt Wv Howv qt tho o l w clclt tcl s tsto obblts tcto stto. Th bsc qto o tbto s ctcll s t H t 8 t I ct th obblt lt M c bs o 7. It s s to s tht 7 hs o vblt v thogh th tcto Hlto s chg th ot tsoto b so s tht oto t c ot chg. t t st th ot tsoto o t ccog to w hv th ot tsoto o 8 s t t H t 9 Usg 9 to o clclto th tsto obblt s ctl t o tht bs o 7. Uottl ths obl s glct qt tho o l t st.. Th ot tsotos o olto vctos o qt lctogtc ls sto ols I qt tho o l th qt lctogtc l s st 5 I th ol th o-sol olto vctos. Sos tht th lctogtc wv ogts log th cto th tos o olto vctos : 5 H othogol ch oth wth 5 Bs o 5 5 th ollowg sto ltos o olto vctos.

11 5 5 s s th clcltos o tsto obblts btw hotos oth tcls. Howv t s to ov tht 5 hs o vblt o ot tsoto. Th ot tsotos o hoto s o-sol ot : 5 B cosg 5 w hv t t t t 55 t t 56 Th th ot tsotos t t t t

12 59 so o. 5 c ot chg th tsotos. s show blow th cosog tsto obblts hv o vblt. 5. Th ot tsotos o cotto ltos o l otos ogto ctos 5. Th ot tsotos o cotto ltos ogto ctos o scl ls I qt tho o l th otos o scl ls c b wtt s: 6 b b 6 Th cotto ltos ] [ 6 ] [ 6 s to bo s ot ot vbl qtt so th cotto ltos o scl ls hv o ot sts. Th ogto cto o scl l s t t t t F 6 ccog to 7 s vbl ot tsoto. Th oth qtts 6 ot vbl. So th ogto ctos o scl ls chg th ot tsoto. Th sttos o lctogtc l sl to scl ls wth. Th cotto ltos hv o sts bt th ogto ctos hv ot tsotos. 5. Th ot tsotos o cotto ltos th ogto ctos o so ls I qt tho o l th otos o so ls c b wtt s

13 65 b v v b 66 Th cotto ltos } { 67 } { 68 H 69 Sll bcs s ot th vbl qtt o ot tsoto lt s th ct ot tsoto o sc-t coot o w hv 7 B tsog to th oto c ccog to 8 w hv. B sg } { to st th ct ot tsoto o 67 cosg w gt } { } { ] [ 7 ccog to 5 cosg wh w hv v 7 Cosg w hv } { 7 Th st th clclto o ths obl ct qt tho o l. Pls s o tl. Sll th tsoto o 68 s } { 7

14 Tho th cotto ltos o so ls hv o ot st too. Th ogto cto o so l s s S F t t{ } t t{ } 75 F ccog to 7 7 th sco ql sg 76 os ot hol b th ot tsoto. W hv S 76 F F SF Th ogto cto o so l hs o vblt th ot tsoto. t π F It s s to ow tht 77 s chg th ot tsoto. W hv F F Th ot tsoto o th ogto cto o so l s S F F π π 79 It s ot vblt o ot tsoto. 6. Th ot tsotos o obblt lts th low o ocsss o qt tho o l 6. Th ot tsoto o st o c ocsss Th st o ocss scbs tcl s c qt tho o l. I th ol s tcl s g. Bcs s ot vbl qtt ot tsoto s ot _ vbl too. I ct th lto btw tcl s l c obblt s W. ccog to ~ scl ltvt t s s o c. I th c whch tcl s t st tcl s l s logst. Ol b ths ct w c s tht th c ocsss o co-tcls hv o st o ot tsoto. I to s ot vbl qtt whch lso ls to th st volto o ot tsoto th st o c ocss. 6. Th ot tsoto o sco o collso ocsss

15 5 Th tsto obblt o sco o collso ocss s scb b. Bcs th ogto cto o so l hs o vblt o ot tsoto th obblt lt M cotg th ogto ls o Fo volts th st o ot tsoto. Fo l o th Coto scttg ocss l l q q th tsto obblt lt s ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ l l l l q M s 8 H ˆ s ot vbl bt ˆ ˆ l l ˆ whch co o th ogto cto o lcto hv o sts o ot tsoto. W hv ˆ ˆ 8 so o o ˆ lˆ. So w hv M M. Th sco ocss o Coto scttg hs o ltvt. Fo th sco o ocss cotg th ogto l o bosos M s stc ot tsoto. Bt th o hgh o ocsss o Coto scttg th ogto l o o wll. Th ocsss stll hv o st o ot tsoto. 6. Th ot tsotos o obblt tsotos ltv to hoto s olto. Fo th tcto ocsss lt to hotos th tsto obblts lt to th sto o hoto s olto. Bcs th oltos o hotos ot tct ts w shol t th vg ov th olto o hoto th tl stts t th sto ov th olto o hoto th l stts. Bcs hotos tsvsl ol both logtl t hotos cos t. Th hv o cotbto o th tsto obblt. Th sto ol o olto s : l l l l l 8 It s s to wo wthot coct clclto tht th ol hs o ot vblt to th ct tht ol t th vls. ct ccog to th ct tho b cosg 7 7 w gt v v

16 v 8 v Fo l o th ocss o Coto scttg th slt s : l l v v v l v cos l l l l l 8 I th ol 7 s s. Bcs 7 hs o ot vblt 8 hs o vblt too. Tht s to s ll co-tcto ocsss lt hotos hv o ot vblt. 7.Th ot tsotos o tcto ocsss btw bo stt s tcls 7. Th oto qtos o bo tcls ccog to st clsscto th thos o co-hscs v to ltvt qt tho o l o-ltvt ot qt chcs. Qt tho o l scbs stbl tcls wth hgh ovg s l s th tcto ocsss btw lt tcls whch t th tl l stts. Th tcto Hltos c b costct b sg th wv ctos o tcls. s show 5 th wv cto o tcl s vbl ot tsoto. Th lts o tsto obblts c lso b st b th octs o o-sol g ots o tcls jst vbl qtt o ot tsoto. q whch th Howv tl tcls hscs s ol bch o hscs. Thss tcls ct lboto th c tl. So qt tho o l c ol lt sll t o hscs whch hs o clos lto wth l wol. Wht closl coct to ctcl wol s th tcto btw bo tcls o l tos ttg hotos scoctos cos tt so o. I ths obls th tcto Hltos c ot b costct b tcl s wv ctos. Fo o- tcls w hv. Th oct q s ot th vbl qtt o th ot tsoto. Th tho o qt tho o l ot b ctv gl. No-ltvt qt chcs scb stbl tcls wth low ovg s. Howv th cl o ltvt hs o oto. It s th tbl o ot tbl. I t s tbl t shol hol o th tcls ovg low ss. I ct th cl o ltvt s cos to b tbl clsscl Nwto chcs. Th ols o th Nwto chcs cos chg th Gllo s tsoto. Th oto qtos o o-ltvt qt chcs c ot chg th ot tsoto. C t b vbl th Gllo s tsoto? Th sw s glct. Fo l th Schog s qto s ˆ t t t t H t t t 85 It s ot vbl o tt o th ot tsoto o th Gll s tsoto. I ct o 6

17 tt qt chcs o qt tho o l v th ost otol olto ol o obblt wv th th-sol coots c hs o th vblt o ot tsoto. t t t t t t t 86 So gll sg qt thos o coo co-hscs hv o ltvt. So-cll th o-ltvt o bo tcl s oto qtos s ot to th ot scto thos w s. Th ssc s tht th hv o ltvt t ll! W t lcto s scttg tl l stct o hog toc g lvl lght s sso bsoto bo tos s ls to ov ths coclso blow. Th Dc qto o qt chcs s bs o scl ltvt. Howv t bcos o-ltvt wh t s s to scb th g lvls o bo hog tos. 7. Th ot tsoto o lcto s scttg tl l Sos tht th tl l s sttc lctc l wth o ˆ. Th tcto Hlto s H ˆ s ot th ot vbl qtt. Bs o t t s ov qt tho o l tht th ctv scttg scto s Th tsto obblt lt s Z U 88 s U T 89 H th g ot o ct tcl otgog tcl. W hv B tsog 88 to ovg c w hv tht o 9 9 So 9 s ot th ot vbl qtt. I to hs sc cto s ot chg too 88 hs o ltvt. 7. Th ot tsoto o stct o hog toc g lvl It s obvos tht th g lvls o hog to c ot b clclt b qt tho o l 7

18 thogh t c b s to clclt th hgh o vso s sht. B cosg ltvt qt chc th oto qto o lcto hog to s 9 H s lcto s ottl cto. Dc s 9 to o clclto obt th ol o stct o hog toc g lvl c 9 Howv s ot th ot vblt qtt wth t 9 t t th tsotoo slcto ol cosg ct ot tsoto wthot cosg th ltvt tsoto th ottl s lt to s t. It s ossbl o s to obt th g lvls w o clclto c b sg t s ottl. So th stct o hog toc g lvl hs o ltvt. 7. Th ot tsoto o lght s sso bsoto bo tos I th t ocss o coo tl tcto btw lctogtc wv bo lcto to s volv. Sos tht lctogtc wv tsts log s ccog to o-ltvt qt chcs th tcto Hlto s 5 : H ˆ [ t] [ t] 9 H l wv [ t] s ot vbl bt oto s ot. ccog to th ts tsoto s t 95 Th oto s ct o th wv cto o bo lcto th bo wv cto s ot ot vbl. Th slt hs o st o ot tsoto. Sll 9 s ot vbl th Gllo s coot tsotos. No t o wht gl th ocsss o lght s sso bsoto hv o ltvt too. I ct o ost ctcl obls o co-hscs w c ot s th tho o ltvt qt tho o l to l wth. W c ol clclt th b o-ltvt qt chcs. U th cotos o low ss thss thos v ctv. W c ot s th cs. Mo ott s tht thss obls hv o th sts o ot tsoto ssc w c ot os ltvt o th. 8. Th ot tsotos o hgh o tbtos 8

19 olto ocsss qt tho o l 8. Th ot tsoto o b sht Th hgh o tbto ocsss o qt tho o ls cot t to b ol. Th olto toc th st volto o ot tsoto. t st w t th b sht o hog to s g lvls s ls. B th olto clclto th b sht s 6 5 l H hv s th wv cto o bo lcto hog to. Fo th go stt s lcto w B tsog t to ovg c w gt 97 t 98 Nw cto s o t ltv s wthot ot vblt. Otos ot vbl too. Both vg vls ot stcl th ot tsoto. So th b sht hs o ltvt. 8. Th ot st voltos cs b tgl tsotos I th olto ocsss o hgh o tbtos ollowg tgls volv l b l c l b H. s w ow tht vbl b ot. B sg th Jcob s ol w hv 99 ot So s stll th vbl qtt o ot tsoto. Bcs s lso ot vbl 99 s chg th ot tsoto. Howv th ct clclto o 99 s clt. I o to colt th tgls w to ov th ogl ot o coot th toc tsoto obt s wll s. B tocg o-sol shcl coots wth [] cos s s cos 9

20 s s s s cos w gt s s I ths w o s sl sttos 99 c b tgt. Fo l b b b b J t s th ot tsoto o w hv ] [ So s ot th vbl qtt o ot tsoto 99 ot vbl g. Bcs 99 s th coo olto ocsss o hgh o tbtos cool th clclto thos o oltos volt th ot vblt gll. t s t svl ls blow. 8. Th ot tsoto o ss olto Th obblt lt o ss olto s 6 S B tocg cosg w hv D l D 8 s ll t bt 9 s t. Bcs s ot vbl bt s ot ccog to w hv

21 D 5 Th obblt lt o ss olto hs o vblt o ot tsoto. 8. Th ot tsoto o vc olto Th obblt lt o vc olto s 6 8 D S S D D D D 6 D CD H C s t w hv 6 5 D C 5 B tg svl slctos clg v v 6 w obt t th tgl o 7 s 5 8 Sll bcs s vbl bt s ot th ot tsoto. So 7 s ot vbl. W c ot obt 8 o 7 t ot tsoto. Bss cots. I w t cosogl w shol lt 7 so tht 7 8 s ot ot vbl g. Bt ths ot ws glct th

22 ct tho o olto. 8.5 Th ot tsoto o th o vt gl ocss Th lt o th o vt gl ocss s 6 S 9 St w gt Sll D D s ot vbl bt s ot. W hv D Th olto o th th o vt gl ocss s ot vbl ot tsoto. It ots tht ths o st volto s cs b th clclto tho o tgl tsoto. I w o ot toc ths tsoto th s o st volto. W shol to s whth o ot th st volto s sstl? Th obl s tht w o ot lt th tgl c ot b colt so tht coct slts c ot b obt to co wth ts. W shol cos th tgl tsoto s t o olto clclto. Bcs th slts o oltos cosstt wth ts ths g w s tht th clclto tho whch ls to ot st volto hs th ctcl g hscs. I s th bsc oltos ocsss o lctogtc tcto volt th st o ot tsoto. Th coclso s lso stbl o oth tcto thos. 9. Dscsso B th lss bovw s tht th cl o ltvt c ot hol th tcto thos o co-tcls t ll! st s scl ltvt s l s coscoc hgh s ocsss. I ltvt cl os ot hol co-ocsss t os ot st t. Howv wh hscsts ot ths obl to ow? Ths qsto s woth o o thoght. Wh st t ow scl ltvt 95 scc cot hs ot t ch coo stg bot whth o ot tos st ot to to qt chcs lt tcl hscs. It ws th tt t ltvt ws cct wl wh t ws l lt tcl hscs. Phscsts blv ltvt ws coct so tht ot st volto co-hscs ws glct coscosl o coscosl. Sg oth wos th obls o ot st voltos co-tcl hscs w hl vgl. Howv s log s w gt to th botto o tt th obls stll g o th wt. I scl ltvt th vblt cl o lght s s th cl o ltvt t ch oth. Bt so sttos th coct. Th ot ol s c bs o th vblt cl o lght s s. ccog to th cl o ltvt th ot ol

23 hs ltv sgcc ol. Mwhl th cl o ltvt cls tht th os o hscl oto qtos o ot chg wth c s. To ch ths hscl qtts shol b tso covt os. s show covc s o gl hscl qtts ot tsoto s o sc-t coot. Both t cocts bt w ot o ot stgsh th. Bss o to th oto qto o so l chg w shol toc so tsoto. Howv s show 6 so tsoto s ot covt. Tht s to s o to th oto qto o qt chcs chg covc s ot ogh. Th obl s v col ctll. It s ov ths tht v thogh so tsoto s cos th tcto thos o co-tcls hv t o ltvt. O th oth h th vblt cl o lght s s hs obt lot o vctos scll th ts o hgh g ccltos. Fo l th t to s lght s s th ocss tht hgh g oto cs to so hoto CRN 96. Howv th cl o ltvt s ol o bl wthot ll stct vcto. Bcs coo ts ol volv low s otos sl to Gllo o hscsts th jgts ccog to coo ts. Th bls tht th cl o ltvt s lght. So th l sttos b tht th ctvss o th vblt cl o lght s s covs th ctvss o th cl o ltvt. I ct to ow s hscsts hv v ctcl sts th ovg c wth hgh ogh s to v th cl o ltvt. Th Mchlso tc t ss to ov tht th bsolt oto o th th c ot b s. Howv ltvt w s th vblt o lght s s to l th Mchlso tc t. I ths g th Mchlso tc t ol vs th vblt cl o lght s s wthot vg th cl o ltvt. Iocll os o ltvt clg Mchlso ot Poc Mch so o ot cct st s ltvt. Wht th oos ws th cl o ltvt th th th vblt cl o lght s s. Th so ws tht th cl o ltvt ls to vos logc os. I ct t s th obl o t whth o ot th vblt cl o lght s s c hol. I th s o th cl o ltvt w c stll ch th ot tsoto bs o th vblt cl o lght s s. I ths cs th ot tsoto bcos bsolt jst s ot hsl cos t. ll ols o scl ltvt stll ctv bt bco bsolt os. Th cts o scl ltvt lso bco bsolt os. Howv t s l logc obl whth o ot th cl o ltvt s tbl. So t s s to cs gts. Sc st stblsh scl ltvt o h s go ctcs hs v sto. Th gts so volt lst so log t tht t s wot th hsto o scc. Th gts coctt o th sc-t o obls jst s lgth o t o whch ot scos. Coctss sts togth so tht t s clt to obt coct jgt. Bcs ths obls o ot blog to th st o hscl sch t st t hscsts o ot ttto to th g. tc chg 96 s wh CMBR ws o. Th soto o CMBR ov choc o bsoltl sttc c o hscs. Th cl o ltvt s ot obl o logc g. It bc obl whch c b v thogh ts obsvto o stoo. I ct th Sgc ct o 9 h ct tht th ltvt o oto ws ossbl. Th t coso ts o cowv coctos thogh stllt btw X To chv

24 lso vl th s coclso 7. Bt wht c ll ov bsoltl sttc c o hscs s jst th soto o CMBR. Bcs t cotcts th ltvt cl o oto ctl hscs s ww osto t st. O th oth h ll gts bot ltvt cl sch s sc-t o Sgc ct o th soto o CMBR co-ho. Bt cocos s coos o co-tcls. I th hscl lws o co-tcls hv ltvt hscsts hv so to blv th cl o ltvt. Bt th hscl lws o co-tcls hv o vblt th ot tsotos t s tht co-hscs hs o ltvt hscsts hv o so to stc to th ltvt cl o oto g. Th oos ths cl ct wthot scosss. So th s ol w o hscs. Tht s to gv th cl o ltvt bt sv th vblt cl o lght s s. I ths w ll ols o scl ltvt c b sv bt w to l th bsolt os. Th tho wll scss ths obl lt. bot th h s go Nwto stblsh clsscl chcs. Nwto thoght tht bsolt sc st bt h ot ow wh t ws. Mo cosolog o bsolt c o hscs. Ptcl hscs wll lso ov ts jgt o bsolt oto. Both co-hscs cohscs ch t coclso g. :Th sts th oo o th ot tsoto vblt o so l s qt tho o l I th ttboo Itoc to Qt Tho o Fl 5 7. b o Chg th to o S 5 { } S 6 t W hv Sbstttg 6 t s obt { } { } [ ] [ ]

25 Cosg th ot tsoto vblt o th cotto lto o scl l Usg th ol 5 ths t c b obt So t s cos to hv th vblt o ot tsoto } S 5 { Th o sts th oo bov. s wog. ccog th to o so tsoto coct o s Sbstttg 6 th ol 6 ths s obt. } { } { Tho s wog. [ ]. s ov ths th hs sc cto s ot vblt o ot so os ot hol.. ccog to o Zhg s boo th ol 55b. 6 th st ql sg s wog. Coct o s. ccog to o Zhg s boo th ol 5. 6 th sco ql sg s wog. Coct o s I ct hol th st osts ch oth. Bt bcs vbltos ot hol so tht 5 s stll tbl. s ot It s ot th o s ttboo tht th tsotos c ot th ts. Fo o ogto ctos to ogto cto th to o ogto cto g. Wh? I th ths tho s s to th tsoto o tcto Hlto ccog to 5 w gt 5

26 6 5 5bcos tcl lto. So th tsoto s glss. I ct scssg th tsoto o ogto to o cto w shol stt o6wth } { S 6 It ots tht th sg 6 s. Th t th tsoto 7 8 It c b ov tht 6 hs o vblt o ot tsoto. Rcs. Cho Gog Itoc to Qt tho o Fl Scc Pblshg Co o Chg Itoc to Qt tho o Fl Pblshg Co o Sh Nol Uvst C Shsh H Clsscl lctocs Pblshg Co o F Uvst Zho Jg Qt Mchcs Scc Pblshg Co Zho Sh Qt Mchcs Hgh cto Pblshg Co Zh Hog Qt Tho o Fl Scc Pblshg Co S Hogw Zhgg Sc Nvgto Mst Tcholog No

Stabilizing gain design for PFC (Predictive Functional Control) with estimated disturbance feed-forward

Stabilizing gain design for PFC (Predictive Functional Control) with estimated disturbance feed-forward Stblzg g sg o PFC Pctv Fctol Cotol wth stt stbc -ow. Zbt R. Hb. och Dtt o Pocss Egg Plt Dsg Lboto o Pocss Atoto Colog Uvst o Al Scc D-5679 öl Btzo St. -l: hl.zbt@sl.h-ol. {obt.hb l.och}@ h-ol. Abstct: