Uniid Absolu Rlaiiy Thory Anónio Saraia 9-4- ajps@hoail.o Inroduion Eryhing is rlai, inluding ligh spd. Fro a pariular and idn propry o h Lornz s quaions ha drid a hory ha agrs ih all knon prinal daa and orks or aoi and sub aoi sals, bu i also orks or graiy a arosopi sals. Basis o h hory Fro h Lornz s quaions: / / / For n rlai ras ih n rlai spds: / / / n,, n n,
/ / / n n n n n n n n n n / / / n n n n So: n n k n n (Consan) Th orhodo rlaiiy us S k as a ariabl, bu as ha donsra k is a onsan ih only on alu or all a parils. As an gi indpndn alus o and h spa-i dosn is. and ar no spa and i bu alngh and priod o a lroagni a. On dir onsqun is ha auu ligh spd is ariabl ih h rquny. Driaion and Gnralizaion o h Plank s Forula Th Plank s orula h E is no orr or all lroagni spru. Magni a quaion: ( ) 4 sin B B π
Enrgy o h agni ild: E B µ E B µ sin 4π ( ) and k 6π k 4 E B µ 4 4 6B π k E µ And E h Gnral Plank s orula: E k h 7 B.95 s ; E 5 8.8 s Ea alu o k Equalling h ors o h lron: 4 kh q F and 4πε R R 7 π q π k 4 4ε h7 k 4.955598 Ea ass o h proon: Enrgy: E.5776 J E ke h.6778 h 7 kg
Th Uniid Absolu Rlaiiy Thory prdis h ass o h lron: Anohr orula or k: hq π 7 ε h k k 4 8π µ h7 ( 7 ε ) Elron alngh: (7 ε ) µ h 7 6 π q 4 ε Hydrogn-Duriu Abundan ( ) H Abundan o h duriu; D.678 7 D - Duriu ass; H - Hydrogn ass D H H 7.678 7.677 6 5 4 Th rong abundan o h duriu is. o kp h rong Einsin s 7 ass o.676. Wrong orula: Righ orula: E E Th righ abundan is no ro h ariabl abundan in a pariular sa ar, bu ro h unirs abundan. 4
Spd o h lroagni as k M i For M k Mar rquny --.6674 M 5 Hz As an s or lo rquny as, lik ligh, h spd appars as a onsan bu h spd hangs a lo aly or h rqunis rlad ih subaoi parils, h sal hr lassi rlaiiy ails. Th sall ariaion o spd or lo rqunis is allod by all knon prinal daa. For rqunis grar hn M h as ha iaginary spds and alnghs ha an hy ar longiudinal as. Walngh o a a-paril k 5
i k M i k λ.8478 k 7 Enrgy o a a paril h E and E k h h k 6
Mass o a a paril ransrsa l.. phoons z..boson..boson nuron proon longiudin al.. phoons nurino lron M To plain all h ising parils, rqunis and asss us b posii and ngai. Th su o all ha iss is qual o zro. Th asss o h longiudinal phoons ar ngai. Th ass has h signal o h harg. Enrgy o a a paril E i89. 58GV M ie Th nrgis o h longiudinal phoons ar iaginary. 7
Gnral a paril syry ngai..proon ngai..lron posii..lron posii..proon Uniid or Aording o our hory h ligh spd is ariabl, so around h parils iss a ild o spd ariaion or an alraion ild. Th ariaion o spd ih i is quialn o h ariaion o h squard spd ih spa. Th ors us b plaind by only on hanis and only on orula. For apl, h proons ha only on or no h lri and h srong. k k Alraion: d g d k g For: h F g and 8
For bn o qual parils: 4 kh F or 4 kh( ) F ( )( ) Uniid or bn o lrons F 4 hk kh and.46 k F.4 N Elri or: F 4 q hk ε 4 πε R R.4 8 Rydbrg onsan: R H 7.968 Rydbrg alngh: λ H 8 R H 9.74 λ H. π.r This is a proo ha h lri or is qual o h uniid or or h lron. 9
For in hydrogn ao Rydbrg onsan: R H 7.96776 Rydbrg alngh: λ H 8 R H 9.76 Rydbrg rquny: H λ H.885 5 Hz Orbial rquny: OR H Orbial spd: 7 and OR.46 Bohr radius: R B π. OR 5. Cnrip alraion: g R 9.5.46 9. g.478 8 p. 5 p.678 7 g p 7. 7 g g g p 9.5 F g 8. 8 N This is anohr proo o h alidiy o h uniid or.
Uniid or Srong or To proons: To nurons: FPP P g P. 97N FNN N g N. 4N A proon and a nuron: FPN P g N. N Wha abou h lri or? q 5 R 4. 4πε R This is prisly h disan bn h proon and h nuron in a duron. Th srong or is qual o h lri or, ha ans ha h srong or dosn is. Th nurons bhas as a ngaily hargd parils, i is only nural or arosopi disans. πr n P and 5 P. (Copon alngh o h proon) n Alraion: 7 g 7.755 R 5.758 6 Th binding nrgy is no kini or ponial. Elri ild o h nuron Ch arg.. dnsiy _ 5 Radius
Th Paril Valus h h k h h 4k k Z ν N P M Nuron: 7.6749 kg ;.756 Hz.99775 8 k s 5.969 ; g k 7 s 7.7865 Proon:.677 7 ;.6858.9977565 8 ;.4 5 g 7.75574 7
Nurino: 4 6 h 4 5 ;.4557 k 4 9.7768 ; 5.555467 7 g.6 E i9. GV Boson Z h E k.8 8 5 i s.5 Hz 7 5 i.6.4 kg Boson W E 8. 4GV. 8 s 5 7.4 Hz.54.95 5 kg Top quark E 74. GV.5 8.9 5 7.766 8 6.9 5
E. 599898MV Elron.559.467 k 5.7 s 9.989 g k 8 s.5 F g.4 N Monopol F 4 q kh h q 4 πµ q q -- Elri harg; µ -- Vauu prabiliy.47 7.75 5.58455 8.65 5 E 99. 8GV Mass and Enrgy Rlaion h E For high nrgy parils E h h h ke ke 4
For hargd parils ih lo nrgy: E For high nrgy parils: E h k E Absolu Rlaiiy Kinais / / / A (Consan) / and / A And h h / A and h / A As / / /( / ) / ( / ) ( / ) h / E h ( / ) 5
E E / / Kini nrgy E k E and E E E / / E E k ( / ) / For and << E k Monu p p and ( / ) / ( / ) p / Binding nrgy o o quarks 8 9 q E F µ 6.4TV For h on hr s no paril alraor ih nough nrgy o spara o quarks or onopols. 6
N paril W ound a n paril ha is h quanu o auu and is nrgy is qual o h ponial nrgy o h paril in h unirs graiaional ild. Sral prins sho a issing ass prisly qual o MV. ε E MV µ ε Vauu priiiy; µ Vauu prabiliy Graiaional ponial nrgy: E GM R U U G Graiaional onsan; M U ass o our unirs R Radius o our unirs ( la a h sura o our unirs) U E h ; 7.5 Hz h 5.5 Thos propris pro h rlaion bn lroagnis and graiy. 8 kg Driaion o h Lornz s quaions and hir ru aning Transrs propagaion spd: 7
a.. ron ir Approiaion: ( ) A A ( ) A A ( ) Wih and / B B ( ) B B ( ) ( ) / Subsiuing h alu o : / / 8
9 / / Sparaion: / / / All h soluions o h syss ihou : C ) ( C D D ) (
On possibl gnral or o h Lornz s quaions: α os / / os / os α α / / os / os ) / ( sn α α α For h our quaions: α / / / 9 α / /........ or or........ or or / / / / / /
N gnral rlaiiy alulaions Ligh dlion by h sun As h spa onraion and i dilaaion orulas ar no qual onlud ha ligh spd is ariabl, so donsra ha h alus o on s o gnral rlaiiy an b alulad i onsidr ha h ligh spd in graiaional ilds bhas as in h opial dius. This s onid by Einsin ry o alula h diaion o a ligh ray ro a disan sar ha passs nar h Sun sura and is obsrd on h Earh. / / and / and / and () Sun nr R l R S R S Sun suri l i r dα i Earh
On h pla dind by h disan l, ro h Sun sura, h ligh ray ha passs nar h Sun has an inidn angl i, a rraion angl r and an angl shi dα Th rraion plan diid o zons o h spa ih propagaion spds and. Aording o h las o rraion: sni snr ; sni R S ; l RS snr l R S R S osi l ; r i dα ; l R S sn( i dα ) l R S R S sni.os d i sndα S α os. l R S R R S l. dα RS d R S α dα.s l R l and RS dα d () l. I an o pu graiy in h rlaiiy quaions us hang h linar loiy by h sap spd as h graiaional ponial: GM S ; M S -- Sun ass R GM S 4 l RS d GM S l ( l R ) S 5 / 4 dl Subsiuing and d in () g: GM S RS dl dα ( l R ) 6 / 4 S D ES GM S RS dl α ; D 6 / 4 ES Earh Sun disan ( l R ) S W ha only onsidr h angl diaion o h ligh ray ha os ro h Sun. Considring also h ligh ray ha gos o h Sun, h diaion angl ill b doubl: δ α
4GM R δ S S RS δ 4GM R S S δ 8.48856 6 rad.75" Thus, ha alulad h orr diaion. Shapiro i dlay This s o gnral rlaiiy onid by Irin Shapiro innds o asur h dlay o a radar signal ro h Earh o Mars, hn h suprior onjunion, rld on Mars and dd on h Earh. Th signal passs nar h Sun s sura and du o h spa-i bnding i surs a dlay. Our alulaions onsidr h spa absolu and h ligh spd ariabl. D MS.79 -- Mars Sun disan; DMT.779 --Mars Earh disan; 8 R S 6.95 -- Sun s radius. D TS.5 --Earh Sun disan; M S.989 -- Sun s ass D MT D MT i dlay ; slor ligh spd DMT / / and / ; / ; DMT Esap spd: GM S i and R
Sun MS R S D TS R S D Mars l R R S Earh ( l ) R D MS R S i GM ( l D ) R MS S S Arag : DMT GM ( l D ) D MS MT S dl R S GM S 4D MS DTS log and D D MT MT RS GM S 4D log MS D RS TS 47.µs Th prinal alu o is a lil lor han 5 µ s. Corrion o Mrury s prihlion prssion W do h driaion and h alulaion o h gnral rlaiiy orrion o h Mrury s prihlion prssion, onsidring ha h spa is absolu and h ligh spd is ariabl in graiaional ilds. 4
Corrion o h graiaional or Fro h orulas o h spa onraion and i dilaaion: / / A ( A onsan ) Doing / / A Th a nrgy is gin: E and h E h h and A A As / ( / ) / This quaion is dirn ro h Einsin s orula. Bu his on is ohrn ih h o quaions o i dilaaion and spa onraion. No on an plain hy h Einsin s orula only an b drid ro h i quaion, dnying h spa orula. W hink hr is an inrpraion probl o h prinal daa. All h prins gi no h rlaion bn h asss bu h rlaion bn h raio o h ass by h lri harg. q q / I onsidr ha h harg is also ariabl: q q / Thus, / ( / ) 5
ih GM ( r all spd ro ininiy ) r GM r GM GM G M F F F r r r GM G M F r r Orbial on quaion Doing u ha h lassial quaion o an llipi orbi r d d u u F θ GMa( ε ) u Subsiuing h alu o F d u dθ GM ( ε ) u a a( ε ) () GM As a( ε ) an us h lassial soluion d u u dθ a( ε ) ε osθ u a ( ε ) Subsiuing h alu o u in () du GM GM a ( ε ) θ θ εsnθ εsnθ C () dθ a( ε ) a( ε ) a orbi ajor si ais ; ε orbi nriiy As an s h rs o his quaion ar angls and h r rsponsibl or h orrion is: 6
δ GM θ a( ε ) To obain h alu oδ or a opl orbi doθ π, hus 6π. GM δ a( ε ) G 6.67 ; M.989 ; 8 ; a 5.787 ; ε. 56 7 δ 5.7 Radians/roluion Th alu o h shi in sonds pr on hundrd yars is: 8 δ 6 π.48 roluion priod in yars 4.94".48 Thus, ha h alu o h Mrury s prssion. Saying, ar all, ha h ligh spd is onsan in h auu is als baus h auu ihou a graiaional ild dosn is. All h spa is a hug graiaional ild. Pound-Rbka prin Th ral gnral rlaiiy alulaions ar ry sipl. In his prin a gaa ray is id ro h ground o h op o a or and h graiaional rdshi o h ray is anlld in h dor ih a Dopplr shi du o h spd V. So, h spd V is a asur o h graiaional rdshi hn h rquny is h sa. 8.6 ; R h. 6 γ V V 7 V 7.6 s Graiaional rdshi: 7
/ And GM GM / R R R GM R R gh (G graiaional onsan; M arh ass; R arh radius; g 9.8s ). 5 Dopplr : V V. 5 Rlaiisi Flyby Anoaly W ound ha h lyby anoaly o h arh orbis o sallis an b plaind by a rlaiisi orrion ro Th Uniid Absolu Rlaiiy Thory. This anoaly onsiss o an inras o h spd o h sallis during arh lybys, ha an b plaind ih Non s physis. As h Einsin s gnral rlaiiy hory dosn prdi his orrion, i is a proo ha suppors our hory. 8
Orbial on quaion ro UART du GMθ GMε sin θ a dθ a( ε ) a( ε ) ( ε ) θ ε sin θ C As du ε sin θ d θ a ( ε ) and doing: C θ GMθ GMε sinθ a( ε ) a( ε ) a ajor si ais; ε nriiy; M ass; G graiaional onsan; ligh spd; θ angl Th irs orrion is h godi or h prihlion prssion orrion. Th o s ar h sa. Th graioagnis dosn is. Th sond orrion is h lyby anoaly. As s h anls or a opl orbi. Mrury s Prihlion Prssion θ GMθ a( ε ) ; For on orbi θ π 6π. GM θ a( ε ) M kg ; a 5.8 ; ε. 56 7 θ 5 radians/roluion 9
Th alu o h shi in sonds pr on hundrd yars is: 8 α θ 6 ;.48 Roluion priod in yars π.48 α 4.94 ar sonds (Th sa alu as Einsin) Godi E 6π. GM θ a( ε ) ε.4 ; 6 a 7 ; 4 M 6 ; T.84 4 yars 8 6 α θ π.t α.4 ar sonds/yar.4 Th Einsin alu is α 6. 6, 6.6 Flyby Anoaly GMε sin θ θ a( ε ) For θ π θ Th anls or a opl orbi.
Earh Flyby Daa Mission Da a () ε (/s) Galilo D9 6 5.47.9 Nar Jan98 6 8.57.8.46 Cassini Aug99 6.58 5.8. 4 Rosa Mar5 7.55..8 Angl or h aiu Orbial spd: GM R a and sin θ ( ε ) R a ε osθ GM a ( ε ) ε ε osθ sin θ d dθ ε ± osθ ( ε ) 6ε ε Galilo θ.657rad ε sin θ R a( ε ) θ and ( ε osθ ) 5GMε sinθ θ a( ε ) R.85 ;.9
Th ariaion o R and bn h: is along h sa dirion, and hr s a dir rlaion R W don kno ho o dri h alu o h i or priod. For Galilo:. 777 Nar θ.9 ; R 6.6.47 Cassini θ.744 6. 6 Rosa θ. 4. For Galilo and Nar ound h rlaion: 4 a / GM. ε 8 For Cassini and Rosa: 4 a / GM. ε 8 ; π 4 4 Bu h alu o us b drid.
Unis uniiaion in S. I. sys Eryhing is ad o spd and disan. Ti dosn is in naur. Thr ar only disan dinsions. Diniion o ass Walngh o h lron: Ligh spd.46 Pariular lron rlaions: Elron harg -- q Plank s onsan -- h 5 Magni lu quanu -- Φ Inrs prabiliy -- µ Priiiy -- ε Elron nrgy -- E 4 4 Elron ass -- 4 Bolzann onsan -- k B Using: disan L and spd V So, h ass is qual: M L 4 V
Lis o unis Mass -- M L 4 V Ti -- T LV Elri harg -- q L V Elri dipol on -- d ql M L 4 V Th lri dipol on is a ass. Magni harg -- h L V q q Φ Plank s onsan -- h L 5 V Magni lu quanu -- Φ q M Inrs prabiliy Dnsiy Elri ponial LV µ Magni urrn -- Magni ild -- Elri ild -- I LV B V (Magni lu dnsiy) E V Elri urrn Magni olag -- I L V Priiiy -- For -- ε F L V 4 L Magni ponial Inrs rsisan -- A Ω LV Cirulaion Graiaional onsan -- Prssur -- Farad -- L 4 LV G L 4
Hnry -- Enrgy -- V Mon -- Wa -- E L 4 V 4 L V 5 L 4 V Magni ild srngh -- H LV Elri lu -- L V Enrgy Alraion Magni urrn dnsiy -- a J M L V Enrgy -- ε E µ Elri urrn dnsiy -- J E V Elri displan ild -- D LV µ Magni urrn -- I LV G G Bolzann onsan -- k B L Th praur is an nrgy sura dnsiy: For h Sun: T k 58K ; Sura -- E T k L Enrgy -- E ST.5 k 4 L V S π 8 4 R 6 J Por sura dnsiy a arh -- P.W Toal por or arh sun disan: 5
4 D.8 A π ES P T.6 W --- E.6 J Unis abl L- L L L L L4 L5 V- Thral Rsisan; Elri Rsisan V V V V V4 Frquny; Voriiy Alraion; Currn Dnsiy Sound Rsisan Spd; Magni Fild Elri Fild; Inrs Induan Elri Currn Dnsiy; Ponial Voriiy V5 Luinan Spral Irradian Ti; Inrs Frquny Disan; Priiiy Magni Ponial; Conduan; Cirulaion Magni Currn; Elri Volag; Inrs Prabiliy Magni Fild Srngh Prssur; Enrgy Dnsiy Innsiy; Irradian Sura; Capaian; Bolzann Consan Magni Charg; Magni Flu Elri Flu; Q.M. Probabiliy Magni Volag; Elri Currn Tpraur; Sura Tnsion Volu; Inrs Graiaional Consan Tru Magni Dipol Mon Elri Charg For Por Mass; Elri Dipol Mon Monu; Fals Magni Mon Enrgy; Torqu Plank Consan; Angular Monu Th isn Thr s h nohing. Bu, i so, h nohing an iss. On h logial lii, i nohing iss h nohing an is. Tha ans h nohing has an inrinsi insabiliy, i an allos h isn o i sl, so h nohing prpually osilla bn his syri oponns lik ( ) ( ). This osillaion ih no iniial nrgy is h isn. So h su ha all ha iss is qual o zro. 6
Th nohing and ryhing Th isn iss orr. Th nohing and ryhing is ad o o hings: spd and disan. Spd is qual o agni ild and disan is qual o priiiy. Th nohing: B ρ B ρ ρ ε ρ ε ρ ε ρ ε B ρ B ρ B ρ B ρ ρ ε ρ ε ρ ε ρ ε B ρ B ρ Th nohing days o our yps o a-parils: B ρ B ρ ε ρ ε ρ ε ρ ε ρ B ρ B ρ ε ρ ε ρ B ρ B ρ ε ρ B ρ B ρ ε ρ Th oal spd and disan rains qual o zro as h nrgy. To parils has posii ass and h ohr o ngai ass. 7
To hargd parils and o nural. A h sura o our unirs Th il ans ha his is no h only on. Th ulipliiy o hings is a la o h naur. Our unirs an b jus a sipl subaoi paril o anohr ga unirs. Th orhodo physis sas ha h unirs has no nr, bu his orrsponds o anohr hiddn nralisi i o our posiion, baus hn h physiiss ak h alulaions, hy alays pu us in h nr o h obsrabl unirs. This unirs has a nr and ar no liing a h nr o i, ar liing a h sura o our unirs, jus lik ar liing a h sura o h arh. I iss alrady a pro o ha. Th Hubbl onsan is no onsan ih h dirion o obsraion. W ar liing a h sura o a blak hol ha roas a ligh spd. Variabl Hubbl Consan in an Epanding Unirs Th Hubbl onsan is ariabl ih disan and ls oordinas, baus ar no liing a h nr o our unirs. Wih a righ asurn produr an ind h loaion o h unirs nr. 8
V B α θ R d θ R U A α Loal..obsrr W us i a rrn disan d: R U 5 d.57 ; U 5 R Loal unirs radius 5.4 R d R U dr U osα d sin α θ Ar sin R Rlai pansion spd bn A and B: V RgU os( α θ ) osα g Unirs alraion U 8.74 ; ligh spd Hubbl rquny: H V R U All sky obsraion: 9
5 9 45 8 8 8 H.6 ; Unirs rquny -- H U.9 Hz H 8 45.66 H 8 9 5.5 H 8 5 5.4 H 8 8.4 In an alrad panding unirs h Hubbl onsan is ariabl. Roaing Unirs Our unirs is rnal as all h isn, i has no bginning. Hubbl onsan: H. 8 Hz Loal graiaional alraion: g U H 6.9 Our unirs is roaing ih a onsan angular spdω : ω πh U ; ωru πh U RU H π 9 H U.66 -- Frquny o h unirs 4
Th loal orbial spd is qual o ligh spd. R Radius o h loal unirs U ω Toal..unirs R U Loal..unirs Visibl..unirs Unirs priod: 8 TU.7 s 86. 5Gy H U Radius: H R U 6 Th loal orbial spd is ligh spd:. GM R U U 5 M U.76 kg So orulas: 4
T U π U R GM U GM g U R U U πr U T U Apparn linar pansion Th rd shi is du o h rlaiisi dilaaion o h alnghs by ransrs rlai spd. R α α D H R H R osα C U R U θ α osα Rlai longiudinal spd H Rsin α sin α H Rsin α sinθ and sin α sin θ R R U H RU sin θ sinθ and H R U 4
Rlai ransrs spd R R U D R U D osθ H R osα os α R U R D DR U osα osα R D RD R U H R D RU D osθ H ( D RU osθ ) osθ DH W ound h Hubbl la bu his spd is ransrs. Transrs rd shi / ( ) is h rlai spd; For a loal spd qual o h ransrs rd shi bhas as a longiudinal rd shi: So, a roaing unirs ih a onsan angular spd appars o b panding. In i h Hubbl onsan is prisly a onsan. 4
44 Ligh disprsion in h inrsllar diu and h Pulsar disan Ligh disprsion in h inrsllar diu o our galay, allo us o kno h a disan o Pulsars and ohr ariabl ission objs by asuring h i dlay bn ligh o dirn rqunis. Fro Lornz s quaions: / / / For n rlai ras: n n k n n (Consan) and ar h priod and h alngh o h ligh a, and k us b dirn ro zro sin kno ha ligh spd in h auu o our galay is ariabl ih h rquny du o h isn o r lrons. is h ligh spd in pr auu. Doing h propagaion spd qual o: and h rquny: W g h gnral propagaion spd orula:
± k Th disprsion i dlay bn o dirn rqunis along h disan D is: D A B Dk( B A ) ± Th disan o h Pulsar is: D k B A I is h arag rquny and B h bandidh in Hrz, h disan in r is ( all S.I. unis ): D kb Aording ih h daa analysis ha don or a gra nubr o Pulsars ound h rlaion:.7 k.7, so: 4 D 7. ; (.788) B This is h a orula o h disan o a Pulsar or a ariabl sar in our galay. Th inrsllar diu ss o b alos unior. Ousid o our galay his orula is no orr. 45
Gnral orulas o ligh propagaion in spa k n kn n D ; D D D kn n In our galay: n.7 ; k.7.7.7 / In inrgalai spa: n.7 ; k.8 9 9.7.8 / Th aning o h in sruur onsan Norally h in sruur onsan is sn as a rlaion bn lri and graii ors. As ar going o s ha is no h ru aning as h ors us b qual. 46
Th inrs o h in sruur onsan is h nubr o is ha h alngh o h lron aks h prir o i orbi. Angular onu: h L R n and n π h πr Elri and nrip ors bn h proon and h lron: F R F ε q 4πε R R q and 4πε R h πr h ε R π q and h lri nrgy is: q E so, 8πε R 4 q E and 8ε h E h λ W g h Rydbrg onsan, hih is an prinal onird alu: R M 4 q 7.974 8ε h 47
So, h radius o h orbi o h lron is: h ε R π q 5. And h spd: h π R 6. s Th alngh o h lron is:.46 W s ha h prir: πr 7 πr α Th alu is no a pr ingr baus h orbi is no prly irular. Maning o h a union ro quanu hanis Th a aning o h a union Ψ is no a probabiliy apliud bu a agni ponial A. In h Shrodingr quaion: dψ d dψ π i πψ and i Ψ d λ Th lri and agni ilds ro agni ponial ar: 48
ρ da E d and ρ da B d I Ψ A : ρ E iπψ ρ π B i Ψ λ ρ E ρ λ B ρ E ρ B (Ligh spd) And kno ha or an lroagni a: ρ E ρ M B M So, THE WAVE FUNCTION IS A MAGNETIC POTENTIAL. Spd o h For ro Absolu Rlaiiy k ± k V d and d V d ± d 49
Vor Paril Modl A ru undanal paril is a or o nohing, ad o spd and disan. B ρ E ρ Th agni ild B ρ is a spd. Th lri ild E ρ is a squard spd. Elri harg q E ρ Volu Magni harg q B ρ Ara Oulo Mass q Magni ponial A Cirulaion Γ For h lron: Th rrn lngh.4 ρ E ρ 8.4 s 9 B 7.9 s 4 A 7. s Fro luid hanis: Γ T πr ρ E A n 5
Asronoial Abrraion Th Einsin s abrraion orula is rong and aording o rlaiiy hory abrraion an is. Einsin s abrraion orula: osθ / osθ ' osθ. / Einsin s spd oposiion orula: ' So: ' os θ ' and os θ And osθ ' Aording o Einsin os θ ' θ ' Thr s no abrraion. L s s h as ha h sar is on h znih, as and ak 9 dgrs on or us b iaginary: os θ ' and iv iv osθ ' iv 5
( V ) i( V V ) osθ ' 4 V osθ ' ( V ) 4 V ( V V ) Aording o Einsin os θ ' θ ' No abrraion. Th lassial alu: θ ' arg and 4 s θ '.6" I ligh spd, aording o Einsin, is no addii is obious ha, in Einsin s rlaiiy hory, h abrraion us b alays zro. And kno ha his is no ru. Th Copon saring is no a rlaiisi phnona Th rlaiiy hory blirs brak, i i s nssary, all ahaial ruls o pro ha h hory is alid as or h Copon saring. Bu h ruh is only on: h Copon saring is no a rlaiisi phnona. Th Copon saring phnona 5
Whn a phoon sriks a rs lron, h phoon hangs o dirion and is alngh inrass (is nrgy drass) and h lron gs so spd: E / E h / λ α E h / λ Epirial Copon orula: h λ λ ( osα ) Oiial and rong rlaiisi driaion (Wikipédia) Ciaion: W us ha: (Consraion o nrgy, hr E γ is h nrgy o a phoon bor h ollision and E is h nrgy o an lron bor ollision is rs ass). Th ariabls ih a pri ar usd or hos ar h ollision. And: (Consraion o onu, ih h p baus assu ha h lron is a rs.) W hn us E h p: 5
Th os(θ) r appars baus h ona ar spaial ors, all o hih li in a singl D plan, hus hir innr produ is h produ o hir nors uliplid by h osin o h angl bn h. subsiuing p γ ih and p γ' ih, dri No ill in or h nrgy par: W sol his or p ' : Thn ha o quaions or, hih qua: No i's jus a qusion o rriing: 54
End o iaion. Th inroduion o os θ i s jus a ahaial rror. Righ driaion Consraion o h nrgy: E E and p E p E p ( E E) Consraion o h onu: p p p α p p pp osα p p p pp osα ( E E) and p and E p E p p pp osα ( p p) and h p and λ p h λ hosα λ λ λ ( hosα λ ) h λ h( h λ ) This is h a quaion or Copon saring. Finding, ih a driaion, a pirial quaion an b jus a qusion o luk. As pro, his quaion is alos quialn o h Copon on ( h absolu rlaiiy inrodu so, no sd, lil orrions ): 55
For 9. kg and λ λ Copon..alu ; λ our.. alu α λ λ...54.544 6.74.94 9.4648.467.69.6998 5.45754.45756 8.48596.48568 Eidn rrors o h horial basis o h rlaiiy hory This papr is basd on h original Einsin s book Rlaiiy: h spial and gnral hory. To h book iaion ha addd so onaris abou h isn o sral idn rrors in h driaions o h basis o h rlaiiy hory. Curiously h rlaiisi physiians oninu o sa ha h Lornz s ransoraions riy h Einsin s posulas hn i s possibl o pro larly h onrary. W hink, hor, ha h rlaiiy hory is parially orr, as pros h prins, bu is nssary o rorula is horial basis. APPENDIX I Rlaiiy: h spial and gnral hory (Th donload o his book an b don a Proj Gunbrg) SIMPLE DERIVATION OF THE LORENTZ TRANSFORMATION (SUPPLEMENTARY TO SECTION ) z' 56
z y' y k k' ' For h rlai orinaion o h o-ordina syss indiad in Fig., h -as o boh syss prannly oinid. In h prsn as an diid h probl ino pars by onsidring irs only ns hih ar loalisd on h -ais. Any suh n is rprsnd ih rsp o h o-ordina sys K by h absissa and h i, and ih rsp o h sys K by h absissa ' and h i '. W rquir o ind ' and ' hn and ar gin. A ligh-signal, hih is proding along h posii ais o, is ransid aording o h quaion or -... (). Sin h sa ligh-signal has o b ransid rlai o K ih h loiy, h propagaion rlai o h sys K ill b rprsnd by h analogous orula ' - ' O... () Thos spa-i poins (ns) hih saisy () us also saisy (). Obiously his ill b h as hn h rlaion (' - ') l ( - )... (). is ulilld in gnral, hr l indias a onsan; or, aording o (), h disapparan o ( - ) inols h disapparan o (' - '). I apply qui siilar onsidraions o ligh rays hih ar bing ransid along h ngai -ais, obain h ondiion (' ') µ( )... (4). By adding (or subraing) quaions () and (4), and inroduing or onnin h onsans a and b in pla o h onsans l and µ, 57
hr and obain h quaions W should hus ha h soluion o our probl, i h onsans a and b r knon. Ths rsul ro h olloing disussion. For h origin o K ha prannly ', and hn aording o h irs o h quaions (5) I all h loiy ih hih h origin o K is oing rlai o K, hn ha ( Conary: W onsidr ha all horial argunaion usd by Einsin is rong ro h bginning bu, or no priing any doubs only onnra on h ahaial idn rrors. I ' a b a Bu ' ' so ' a Fro h sond quaion (5) a b b b Equlling boh quaions b a a b a b As b a 58
So his rsul dosn allo h driaion o h Lornz s ransoraions. Or sill b and a b a Bu so L s ignor his rsul and oninu ih h iaion. ) Th sa alu an b obaind ro quaions (5), i alula h loiy o anohr poin o K rlai o K, or h loiy (dird oards h ngai -ais) o a poin o K ih rsp o K'. In shor, an dsigna as h rlai loiy o h o syss. Furhror, h prinipl o rlaiiy ahs us ha, as judgd ro K, h lngh o a uni asuring-rod hih is a rs ih rrn o K us b aly h sa as h lngh, as judgd ro K', o a uni asuring-rod hih is a rs rlai o K. In ordr o s ho h poins o h -ais appar as id ro K, only rquir o ak a snapsho o K ro K; his ans ha ha o insr a pariular alu o (i o K),.g.. For his alu o hn obain ro h irs o h quaions (5) ' a To poins o h '-ais hih ar sparad by h disan D' I hn asurd in h K sys ar hus sparad in our insananous phoograph by h disan Bu i h snapsho b akn ro K'(' ), and i liina ro h quaions (5), aking ino aoun h prssion (6), obain Fro his onlud ha o poins on h -ais sparad by h disan I (rlai o K) ill b rprsnd on our snapsho by h disan 59
Bu ro ha has bn said, h o snapshos us b idnial; hn D in (7) us b qual o D' in (7a), so ha obain ( Conary: On or i onsidr ha all idologial argunaion is jus a big onusion. Ls onnra on ahaial prssions: and ' a b ' a bu as so ' ' a b so ' a Again and again Einsin ignor his iniial san ignor his rror. and ' '. L s ' a ' a bu ' a also ' and ' a b b and ' a b a ' b a b a a bu b a b so a ' a hus ' a bu ' a 6
hror as and a a as ' Again didn rah h driaion o h Lornz s ransoraions. Einsin also sas ha ', bu all kno ha ' Ls oninu) Th quaions (6) and (7b) drin h onsans a and b. By insring h alus o hs onsans in (5), obain h irs and h ourh o h quaions gin in Sion. Thus ha obaind h Lornz ransoraion or ns on h -ais. I saisis h ondiion ' - ^' - ^... (8a). Th nsion o his rsul, o inlud ns hih ak pla ousid h -ais, is obaind by raining quaions (8) and supplning h by h rlaions In his ay saisy h posula o h onsany o h loiy o ligh in auu or rays o ligh o arbirary dirion, boh or h sys K and or h sys K'. This ay b shon in h olloing annr. W suppos a ligh-signal sn ou ro h origin o K a h i. I ill b propagad aording o h quaion 6
or, i squar his quaion, aording o h quaion y z ^... (). I is rquird by h la o propagaion o ligh, in onjunion ih h posula o rlaiiy, ha h ransission o h signal in qusion should ak pla -- as judgd ro K -- in aordan ih h orrsponding orula or, r' ' ' y' z' - ^'... (a). In ordr ha quaion (a) ay b a onsqun o quaion (), us ha ' y' z' - ^' s ( y z - ^) (). Sin quaion (8a) us hold or poins on h -ais, hus ha s I. I is asily sn ha h Lornz ransoraion rally saisis quaion () or s I; or () is a onsqun o (8a) and (9), and hn also o (8) and (9). W ha hus drid h Lornz ransoraion. Th Lornz ransoraion rprsnd by (8) and (9) sill rquirs o b gnralisd. Obiously i is iarial hhr h as o K b hosn so ha hy ar spaially paralll o hos o K. I is also no ssnial ha h loiy o ranslaion o K ih rsp o K should b in h dirion o h -ais. A sipl onsidraion shos ha ar abl o onsru h Lornz ransoraion in his gnral sns ro o kinds o ransoraions, iz. ro Lornz ransoraions in h spial sns and ro purly spaial ransoraions, hih orrsponds o h rplan o h rangular o-ordina sys by a n sys ih is as poining in ohr dirions. Mahaially, an hararis h gnralisd Lornz ransoraion hus: I prsss ', y', ', ', in rs o linar hoognous unions o, y,,, o suh a kind ha h rlaion ' y' z' - ^' y z - ^ (a). is saisid idnially. Tha is o say: I subsiu hir prssions in, y,,, in pla o ', y', ', ', on h l-hand sid, hn h l-hand sid o (a) agrs ih h 6
righ-hand sid. (Conary: ' ' / / / roing ' ' and ' ' ' ' or and ' ' ha ans, h i is a union o and no an indpndn oordina as appars in h prssion o h spa-i: y z y z Thus, pro ha h spa-i quaion is an rror, baus ha quaion sas ha h i is indpndn o h spa. I i is a union o h spa, so hing is rong. ) War and ligh as Ligh as bhas aly lik ar sura as. B B V A A W ha a boa A oing a h ar sura ih loiy rlai o h ar. Insid h boa hr s ar and h obsrr A asurs h onsan spd V. Th A 6
loiy o h a in h ar ou o h boa rains V so hr s no addiion o spds. Th rlai loiy bn h a and h boa is V A bu h obsrr in h boa an asur his spd. Any obsrr soppd rlai o h ar alays asurs a onsan spd V. I hr s a oing rpor, boa B, oing ih spd B h rlai spd o h a o h boa is V B bu h B obsrr an asur his spd. Insid h boa B hr s ar oo and insid h boa h obsrr asur a onsan spd V. Th spd o h a insid h boa B rlai o h ar is V B. Ligh bhas aly h sa ay. For ligh h V V B B spd bos i h spd is rquny dpndn V B and baus h rquny hangs bn h ar ou and insid h boa. So, h rlais V ± spds iss a h sa i ha h propagaion spd rains onsan. Many is h Lornz s orula is usd on a rong ay. Thr ar no ysris in h unirs. Classial Enangln To parils ro an plosion ral in opposi ays: Th quaion o h nangl onu is: p p Thy ar nangld. I asur h onu o on kno h onu o h ohr. I hang h alu o ons onu, h ohr says h sa. Th sa as quanu nangln. Th no inoraion la says ha an no pu h sond paril in a pris sa ha an b asurd. So, ha s h probl? Th probl is ha in quanu hanis suppos ha h asur ss h sa. So ar sing h sa o h sond paril a a big disan and insananous. 64
Is ry sipl o sol his. Th parils ha a dinii sa n ar asurn. Ho is possibl ha bli ha a pariular absra orula prdis all h inoraion abou a a-paril. I s obious ha hr ar hiddn ariabls ha Shrodingr orula dosn ar ih. All h irdnss s o quanu hanis ar inrpraion rrors. Th naur has no parados. Thoris ih parados us b rong. Th quanu hanis is no a hory bu a alulaion hod ha or obain any obji soluion nds alays h hlp o h lassial hanis. Sagna Aording o h Lornz s orulas ( ipos ha ligh spd is onsan baus hos orulas don ha ha propry): R πr ωr / ; / R / And πr R 4πR As R 4πR Aording o lassial i (ligh spd is ariabl): R π ; πr 4πR C As 4πR C 65
I s alos ipossibl o asur h dirn bn h lassial and h rlaiisi alus. As, h Sagna pros nohing. R C Vloir o graiaional rrn This papr onsiss on a dsripion o an prin, ih a spial inrror, o asur h spd o a hil, ih h di insid, rlaily o h Earh graiaional ild. W an o pro ha h o basi posulas o h rlaiiy hory ar rong: s posula an disinguish h sa o unior on ro h rs in a losd lab ih any kind o prin don insid i Bu hr ar no losd labs or graiy. I h hr is h Earh graiaional ild i s possibl o asur h spd rlaily o i. This hypohsis is ohrn ih h rsuls o h Mihlson s prin. Conrary o ha is hough h Mihlson s prin gis h sa rsul i h hr iss and is soppd rlaily o h Earh, ha is h as i i is h graiaional ild o h Earh. nd posula -- h spd o ligh is onsan and dosn dpnd o h on o h ir or h rpor. As pros h phnonon o asronoi abrraion h ligh has rlai spd. Our prin pros ha h ligh spd is addii as all ohrs. Eprin dsripion 66
MIRROR PIPE. WITH. WATER MIRROR..5 BEAMSPLITTER D.5 DET LASER VACUUM.PIPE MIRROR V Th di has a lasr diod ( λ 6.5 7, P.5W ), a 5% - 5% ba splir, hr irrors, a pip illd o ar ih o glass indos, anohr on ih auu and a ligh dor DET. Th lasr ba is diidd on h splir and rals in o dirions in h irrors irui. Thn hy ar joind again and n o h dor hr h ariabl inrrn parn gnras h olag V. Th nir di is prod ro isibl ligh and inrards by a alli bo. Tis o h ligh rays: Insid h auu ub, i h ligh propagas in h arh graiaional ild, on ay h spd ill b and h ohr ay : D D k D D k and D 8 ; D. ; 7.4 Spa phas shi: 67
8 9 7.4 and. Volag ariaion on h dor: V V ih λ 6.5 7 λ / V V 6.8 In our div 46V, so or a k / h 7.8 / s : V V 8. 7V ; 9% V Variabl Sura Mahin I h praur is an nrgy sura dnsiy an g ork by hanging h sura o a body. W an do ha by onrolling lrially and agnially h shap o a rury body or a plasa. T T Changing h shap h praur also hangs: E T A T T T < T T T 68
Changing h shap again: T T T > T Mihlson prin and ohr hings Th Mihlson prin as ad or ding h rlai spd o h prinal di o h auu. W kno ha h arh is oing in h spa so, i h ligh spd is rlai, an b abl o d his on. So, is nssary ha h ligh in h di propagas in h auu. Bu ha is ipossibl a arh sura baus h ligh os in h arh graiaional ild ha is a rs rlaily o h di. Bu hr s anohr probl ih h prin. Th ligh is no oing in h auu nihr in h arh graiaional ild, i is oing in h air. Ho an d h on rlaily o h auu i h ligh propagas in h air. And his prin is h only prinal basis or ligh spd onsany. Tha s h probl ih null rsul prins. Th prin an b rong and sill g h pd rsul. Dark ar Thorial ass o h unirs: M 5 U.76 kg Obsrd ass o h unirs: 5 M O ( 7% ) W hink ha h dark nrgy dosn is, bu in any as i has no ass. Nubr o nurinos in h unirs: 69
88 n Arag ass o h r yps o h nurinos: M U M n O.5 5 Th lron nurino ass: ν 4 6 Th uon and au nurinos ha grar asss. Tpraur Th praur is an nrgy sura dnsiy: E T A Bu h ara is alays rlai o a sphr: A 4πR Volu: V 4 R π, so: T E 6π. V For h nrgy o h sun a h arh disan or an obj load in h auu: T.9 E 6π. V Monopol h only lnary paril 7
W s lrons oing ro h nulus ba day, and s lrons nring h nulus lron apur. Is i orr ha hy an is insid h nulus? Cnrip or o h lron: F R Elri or or hydrogn: F 4πε q R I ligh spd is a lii ( approiaion ): R q q R 4πε R 4πε R.8 5 Th proon radius:. 5 So, i ss ha h lron an is insid h nulus, bu ro h poin o i o h proon: Th ass o h lron bos inini / ( / ) q Th harg o h lron bos inini q / Cuing h ininis: q R 4πε R.6 6 So, h lrons an is insid o h nulus. Th graiaional or is also inini. Th o onopols lron A roaing onopol ras an lri ild. 7
ρ E q R E ρ N S E ρ Th lron is ad o o syri onopols roaing a h sa ais. Binding nrgy o h onopols: q E µ 6.4TV h q 5 q. ( T Wb ) Magni harg µ Vauu prabiliy 9 8 -- Monopol alngh 7
Th nurino N S Th nurino is ad o o syri onopols ih paralll ais. Sun s Corona Tpraur Probl Th ral probl is no h orona high praur bu insad h lo praur o h sura. Th sura praur is is lor ha i should b. A arh in auu spa: Tpraur -- T E 9K Disan --.5 D E Toal nrgy -- E.9 6 J Sura o h sphr -- A E 4π. DE T E.5 E A E A h arag orona: 6 T C 5 K. 9 D C E E 7
9. A C T C.5 E A C A h Sun s sura: T S 578K 8 D S 7 8 6. A S E E T S.5 E A S B B T S Earh agni ild: B T 4µ T Sun : BS BT So, hink ha h lo praur o h sura is du o h high agni ild o h sun a h sura. And hr s a aor o du o h raal sura o h sun, h ral sura is is grar hn h sura o a sphr. 74
Sral spds Ligh bhas lik ar as. A B air air Vauu Th spd in air is alos. I air os h ransrsal ransir A produs a shi /. Bu h spd is no ransid o h auu as. Thr s also a Dopplr shi. Th rlai spd o h as in auu o air is. Bu his spd is ipossibl o b asurd by an obsrr insid air. Th only ay is by obsring h abrraion. In air h shid a has h spd alos. On ohr spd: ligh glass Th Sagna spd aording Wikipdia: 75
V ± Rω Bu hy orgo ha R ω, a linar loiy. So, in a inrial sys h ligh spd an b ± Ininiy is Equal o Zro Hypohsis: log log( ) log( ) log( ) log( ) log( ) i π So, ha prod ha ininiy is qual o zro. 76
Ho naur dals ih ahaial ininis Dopplr or sound: (Frquny ans nrgy) Mahaial graphi Ral graphi a a y n y ( ) a 77
78 Th ral graphi gis a sipl planaion or h doubl soni boo. Variaion o h Rrai Ind ih Frquny Lornz s quaions: ; ) ( d d ; ) ( This is an approiaion baus is a union o, bu or isibl ligh alos onsan. d d ; k ; k d d A log log log ) ( ) ( ) ( ) ( A A ; k ; n
Rrai Ind B n ; B is an prinal onsan. B n Ral graphi a slo ligh prins n Mahaial ininis don is in naur. W ha prod ha Lornz s quaions adi spds dirn hn ligh spd. 79
Th Spd o h Fors Th parils ar no as. Thy ar loalizd a irs. V For h lron: 5. 5 s This spd is ariabl ih h disan gnraing an alraion ild. Th inraions ih h as ransi o h paril, lling i hr o go. Th osillaing nr an b diidd, or apl, on o hal parils ha passs an obsal and hn ronsruing h paril ar. Th a ounias ih h paril a h spd orula or h spd o h ors. V / ha is h gnral k k V d d For h lron: V 5. 5 s Th inraion a is oposd o agni phoons ha ar undabl and ar longiudinal as. This spd is alays grar hn ligh spd. 8
Abrraion o h ors Th ors, ih ini spds, ha no abrraion baus h inraion happns a hal disan o h parils and so h i dlay iss bu is qual o boh parils. I i iss abrraion also h orbis o h lrons in h aos should b insabl, and ha dosn happns. Graiy spd V and M h M h k 6.6 4 h ; 8 ;.9 4 k, M ass V. 4 h k M Sun graiy spd: M kg V S. 6 s Unirs graiy spd: 5 M U.8 V U. 47 Craion o Ngai Mass A ass is an lri dipol on: qd 8
So, i harg a apaior gnra a ass. Whn h dipol is nural h ass is ngai. Using a suprapaior: C Farad ; V. 5Vol q CV CVd Th arag disan d is: d 9. 5g So, a apaior loss igh hn hargd. This ill b h uur propulsion sys. Brokn Syry k ; h Plank s onsan k Thr ar alays o ras or ligh: is h pah in our unirs ra and is h pah in h loal ra. 8
k R U k α R U. -- Loal radius o our unirs R U 6 4 RU ( RU k ) 6.45 sin α α 4.77 rad R U.5 4 s Loal uraur -- 7 7.7 R U Casiir and Uniid Fors Uniid or ro Absolu Rlaiiy is siilar o Casiir or. Uniid or: 4 kh F ; 4 4 F 4 4 kh 8
Casiir or: F hπa 48. 4 Rrn ara: 48. k A ; π k h π 48. h A. π Hydrogn Classial Walnghs and Innsiis Walnghs: R H ; λ n n R H.9776 7 n n Rlai innsiy Walngh (n) 9 5 8.584 8 6 88.949 7 8 97.7 6 5 4.74 5 44.47 4 8 486. 8 656.85 7 4 5 65.5 84
6 4 8 65.5 5 4 5 45.6 7 5 4 465.5 6 5 6 7457.8 7 6 68.5 Aording o Absolu Rlaiiy: Innsiy -- 5.55. λ I λv I.5. 6 n. n For in a nozzl 85
A irular pip ors a losd loop ih o dirn sions and spds. W ill dri h orula o h or gnrad in h nozzls or pansion habrs, using h on onsraion prinipl. W assu a unior lo and a onsan spd. 86
On Dinsional Mall Equaions de ρ E d ε db ρ M d de d db 4 d E B db d J de d M µ J E k ; k For h lron: B ; E 87
4π sin Magni ild: ( ) B B 4π Elri ild: E E sin ( ) 4π sin Magni ponial or irulaion: ( ) A A Ti Dosn Eis Ti is a raio o ransoraion: Q V Q Ti is h raio o h ariaion o any physial quaniy ih i spd o ariaion. So, i is no dind only ih spa, disan or lngh. Ti is ry usul o opar dirn phnona bu i is only a ahaial niy. I dosn is as a hing or a oordina. Ti dosn is in naur. Th loks don asur i; hy asur a ariaion o a physial quaniy lik posiion, ass olu or lri ild, ih hir inrinsi loiy o ransoraion. In rlaiiy and quanu hanis i dosn lo as an rnal i. Th inrinsi i is no a oordina bu a priod. Th a paks don sprad. W an ak an absolu lok by asuring h ariaion o a agni ild. Th spd aris ih spd: V V ( / ) 88
Magni ild also aris ih spd h sa ay: B B ( / ) Absolu lok: B V B B ( / ) B V ( / ) V B B Th rlaiiy spd onusion Th rlaiisi physiians us h spd addiion orula in rong ass: I -- Thr s no addiion Bu his orula is ru or only on as: ir A ' glass W ha a pa o glass oing a spd. Th spd o h ligh ih rquny is. Bu hn h ligh nrs h glass a h poin A i hangs h rquny o ' ih spd. This ligh is oally arrid by h glass so h oal spd is ' ' ' and ' 89
As ha said ound h orula o h ariaion o rquny hn h ligh nrs h glass. Thr is anohr orula ha h rlaiisi physiians dny: ± ir rpor Thos ar h rlais spds o ligh. aosr Earh A Earh an asur h rlai spd o h ligh baus i hangs o hn nrs h aosphr. Cold Fusion Th old usion has h sa planaion as h supronduiiy. Th lai bhas as a blak hol or lrons, so hir rpulsion or bos zro. 9
F kh( ( ) )( 4 ) G 6.45 7 9 D --.4 kg ;.64 Pd --.77 5 ;.6 n n.45 6 n n.9 -- DPd. 9 D / Pd. (nubr o aos) Th palladiu hargd ih duriu us b supronduor. Pionr Anoaly Th Pionr anoaly is a rlaiisi lyby anoaly. Thr s no nough daa ro Pionr. GMε sin θ θ a( ε ) Corrd orbial spd: GM ε ε osθ and θ 9 a ( ε ) 9
GM ( ε ) a ( ε ) Alraion: Daa ro Pionr : Pionr alraion: d( ) GM ( ε ) g da a ( ε ) a. ; ε. 7596 g 8.74 s ε ε ga GM ε. 76 Graiaional Fild ro a Roaing Magn Graioagnis dosn is. A roaing agn produs a graiaional ild ha an b posii or ngai: ρ g Bω g -- alraion; B -- agni ild; ω -- angular spd For a supronduor: ρ B q ω 9
-- ass o h lron; q -- harg o h lron g q ω ω s g 8. 6 s Magni urrn Thr ar onopols bu hy is a h ry inrior o h sub aoi parils. A a arosopi ll a agni harg is a Coopr pair. Coopr pairs ha no lri harg and hy ar h uni o agni harg. Magni harg: q M h q A agni olag is qual o a lri urrn: V M I E A agni urrn is qual o an lri olag: I M V E Magni rsisan: M R M RE I M V I V E E Th agni rsisan is qual o h agni ponial: R M A and A B 9
For a supronduor: R R E M A 4 kh F Unis ariaion ih spd Disan Ti / / / Spd ( / ) Magni ild B B ( / ) Elri ild E E ( / ) Priiiy Prabiliy ε ε µ µ / 5 / /( / ) Enrgy Mass Alraion For Spin E E F F h h / / / /( / ) a a / ( / ) ( / ) / Elri harg q q /( / ) Magni harg q q ( / ) 94
Magni ponial A A / ( / ) Monu p p / /( / ) Linar Sagna Eprin This prin is a rsion o h Sagna prin ad ih linar spd. So, h sys is an inrial rrnial. I ill pro i ligh spd has or no rlai spd. irror pip. ih. ar irror D d or basplir irror lasr V Th di has a lasr diod ( λ 6.5 7, P.5W ), a 5% - 5% ba splir, hr irrors, a pip illd o ar ih o glass indos, anohr on ih auu and a ligh dor. Th lasr ba is diidd on h splir and rals in o dirions in h irrors irui. Thn hy ar joind again and n o h dor hr h ariabl inrrn parn gnras h olag V. Th di os in h rior o a ar so, h on rlai o h rs air ill su and subra o ligh spd. Aording o rlaiiy hory his is ipossibl. Tis o h ligh rays: 95
D D k D D k and D 8 ; D. ; 7.4 Spa phas shi: 8 9 7.4 and. Volag ariaion on h dor: V V ih λ 6.5 7 λ / V V 6.8 In our div 6V, so or a k / h 7.8 / s : V V. V ; 9% V W ha ad h prin (8-6-), ad asurs and ound alays a olag ariaion o V. So, ha prod ha ligh spd is no onsan and ha i sus o h spd o h rpor. Rlaiiy addiion loiy is no a rlai spd 96
97 ) )( ( ) )( ( ; R is no h rlai spd bn and, so: is no h rlai spd Th spd ariaion in a oing diu happns baus o h rquny Dopplr ariaion: and k
Laboraory dion o graiaional as Any rlai uni ha hangs ih spd or graiy an b usd o d graiaional as. W hink ha h asir on is lri olag. V V / / V V and GM R GM / R R V GM V R R Volag ariaion ih h disan ariaion o a ass. For R ; V V ; M kg ; R. V 7.4 9 V For M 8 kg ; R Ly 9.5 ; R.5 V.5 9 V Why using galai or ragalai sours i an rah h sa auray in a laboraory? 98
Lab. Graiaional Wa Dion Thr ar o yps o inraion o ar ih ligh: h usual orhogonal inraion and h linar inraion. orhogonal linar ligh..ray ass ass ligh..ray Orhogonal orula or rquny: / Linar : Orhogonal as: ; GM R GM GM ; R / R R R For M, R, R, 9 Linar as: 7.4 9 Hz ; R / GM R.44 5 Hz I s ry asy o d h linar graiaional in a lab. 99
Graiy spd asurn Frquny ariaion ih graiy: and / GM R GM R R 9 Hz ; M kg ; R ; R. 7.4 5 Hz I s possibl o pro, in laboraory, ha graiy spd is grar han ligh spd. W us o dirn asss, osillaing oghr, and o dors o graiaional as. Thn d h i dirn bn h o as. Aording o Einsin s his alu is zro. M V D V D M V 9 M 9 M ; V R M M 9 M M R ; M g ; M g ;. 9 s
Sound and ligh spd liis Mahaially i s ipossibl o oro h sound and h ligh barrir. Th argun or h ipossibiliy o oro ligh spd is h sa usd or sound and kno ha ah is possibl. For sound, prssur Dopplr orula: P V P V P prssur; V sound spd; P noral prssur; airplan spd. Mahaial graphi: P P Ral graphi: % P P % Wha happns or ligh us also happns or ligh. Tpraur: Radiaion prssur: T 4 T P 4 P
Rs nrgy: E E / E E Oro h ligh barrir is asir han oro h sound on. Group and phas spds V PH. VGR and V PH k d V GR and k d d d V PH M iv PH V GR iv GR
Th group spd or h ru spd o ransission o inoraion an b inini. Group spd o graiy M. h. h. M k h. k M k V GR M h. V GR V GR 9 M M ass o h body Th spd o h ransission o h graiy is ariabl ih h ass o h body and i is asr han ligh spd. Iaginary rqunis Thr ar also iaginary rqunis. and i i i i / Spd: k
I s ipossibl o iola ausaliy I ound a phnonon as hn ligh spd h ausaliy is no iolad baus ha phnonon ill din a n ausaliy. Causaliy dosn say aahd o ligh, bu o h ass phnonon. A spara has no spd lii A ligh spd h ass o h ra is inini bu h raion ass is also inini, so ha inini nrgy. In h rrn ra o h ra ryhing says h sa as lassial physis prdi. Graiaional onsan H R G M U U Hubbl onsan -- H. 8 Hz Ligh spd Mass o h unirs --.76 5 M U kg Radius o h unirs --. 6 R U Elron and nurino All h lrons ar binding o a nurino. λ 7.4 ; lron alngh h λ 6.65 4
Arag ass o h nurino: ν 4.85 5 Unirs ass -- M U.76 5 Obsrabl ass -- 5 M O (%) M.56 5 Nubr o nurinos -- n.76 87 Arag ass o h nurino: M ν n 5.65 5 Tau nurino: T 5 5.5 4 Ho an h orbi o an lron b sabl? Th inraion o an lron ha orbis a proon propagas a ligh spd. Du o abrraion h orbi us b unsabl and kno ha s no h as. Why? Baus h i dlay is qual or boh parils. Th inraion happns a nar hal disan o h o parils, so boh parils ar dlayd an qual aoun. In his as h orbi is sabl. Th sa happns ih graiy and all h ors. So, h no abrraion o graiy dosn pro ha h spd o graiy is grar han ligh spd. W kno ha i has a grar spd bu h no abrraion is no a pro. 5
Th Magni Mon Probl Linar onu o h lron in hydrogn: 4 p.995 kg. / s 7 Tru agni on ( unis: Wbr.r ): M q h q 5. 7 W Usual agni on or only linar onu: µ q 4π 9.7 4 A ( kg. / s N. s) So, ha ar h physiians asuring? h Plank s onsan Mass o h lron Ligh spd q Uniary agni harg q Uniary lri harg Walngh o h lron 6
S.I. Unis Uniiaion II Eryhing is ad only o disan (L) and spd (V). L- L L L L L4 L5 V- Thral Rsisan; Elri Rsisan V V V V V4 Frquny; Voriiy Alraion; Currn Dnsiy Sound Rsisan Spd; Magni Fild Elri Fild; Inrs Induan Elri Currn Dnsiy; Ponial Voriiy V5 Luinan Spral Irradian Ti; Inrs Frquny Disan; Priiiy Magni Ponial; Conduan; Cirulaion Magni Currn; Elri Volag; Inrs Prabiliy Magni Fild Srngh Prssur; Enrgy Dnsiy Innsiy; Irradian Sura; Capaian; Bolzann Consan Magni Charg; Magni Flu Elri Flu; Q.M. Probabiliy Magni Volag; Elri Currn Tpraur; Sura Tnsion Volu; Inrs Graiaional Consan Tru Magni Dipol Mon Elri Charg For Por Mass; Elri Dipol Mon Monu; Fals Magni Mon Enrgy; Torqu Plank Consan; Angular Monu Ha apaiy L Spii ha apaiy Voluri ha apaiy Ha Enrgy L V L V L G µ ; G Graiaional onsan; Mass Magni Volag Magnooi For Elri urrn 7
Enropy L Kinai isosiy Magni ponial Elri rsisan Inrs agni ponial Magni rsisan Magni ponial Dnsiy Sound ipdan Inrs prabiliy Elri displan ild Dynai isosiy Elri urrn Tpraur Enrgy sura dnsiy Magni harg Oulo Vauu nrgy ε µ Magni rsisan inrs lri rsisan Jrk L V Quanu hanis aunion agni ponial Disan priiiy Spd Magni ild Supronduiiy Th Coopr-pairs ar ord du o an arai or bn lrons hn h diu bhas as a blak hol. Uniid or bn o lrons: 4 kh( ) F ( )( ) 8
G -- Esap spd o h diu R For F< arai or > or > No and ; ], [ k 4.78 For 6kh F 7 4 Binding nrgy: 4 6kh L E.6 J 7.65 E 4( ) 7 Criial praur: E d.7 ( ) 4 T C T C 4.7 T C and G R G R.7 4 T C.4 R Th riial praur is ariabl ih h aoi ass and aoi radius o h diu. 9
Tabl o h aoi ass/aoi radius/n o h lns N S 4.6-6 Y 4. -6 Lu 5.6-6 Ti 5.4-6 Zr 4.7-6 H 6. -6 V 6. -6 Cr 6.7-6 Ru 6. -6 Rh 6.4-6 Ir 7.8-6 P 7.8-6 Cu 8. -6 Ag 6. -6 Au 7.6-6 Zn 8. -6 Cd 6. -6 Hg 7. -6 Ga 7.6-6 G 9.9-6 Sn 6. -6 Pb 6.6-6 Sb 7. -6 Bi 6.4-6 Fundanal orbi o h lron Absra Th in sruur onsan is no ll undrsood. 7 In his aril sho h ral aning o h nubr 7 ( h prir o h orbi o h lron is 7 is h Copon alngh o h lron ) and jusiy hy is his nubr and no anohr. Aording o lassial physis h spd o h lron in his orbi is: ; ligh spd 7 Th prir o h orbi:. π. R 7. ;.46 B RB -- Bohr s radius ; -- Copon alngh o h lron Th aning o h nubr 7 is ry sipl: or his nubr h oal nrgy o h lron ( su o h ponial nrgy and kini nrgy ) is iniu:
Ponial nrgy: E gr P B q g 4πε RB -- lron ass; g alraion; q -- lron harg; ε -- auu priiiy. E P q. ε 7. Kini nrgy: E K 7 Toal nrgy union o h nubr o alnghs ( i s possibl o donsra ha h ponial nrgy is allays ngai ): q E n ε n For a nrgy iniu de dn de dn q ε n n ε n q
n 7. 8 For a sabl orbi h nubr us b an ingr. Th parils ha no inrinsi osillaion Th osillaion o h a-parils i s no inrinsi bu is du o his on. Th orula o h lri ild: E E Is rong or h. Th ru orula is: 4π sin ( ) and k 4π k E E and Also or sall alus o. E s Th nrgy o a paril has lroagni origin and is du only o on ild, h agni or h lri no h su o h o. Mass: h k 4 4 8π ε k k 4 5 8π ε k h Mass o h lron:
4 8π k µ Enrgy o h Unirs Th oal nrgy o h unirs is qual o zro, baus h ponial nrgy is alays ngai and qual o h kini nrgy. For h unirs: M M U U g U R U GM and g U R U U GM R U U Th unirs is roaing loally a ligh spd. Mu ass o h unirs Ru radius o h unirs ligh spd gu graiaional alraion o h unirs For h arh: M M G T S E P and DTS E M K T V O
V O GM D TS S M arh ass; Ms sun ass; G graiaional onsan Ds disan arh sun; Vo orbial spd A Nural Roaing Mass Gnras a Magni Fild Ho is possibl ha a nural paril has a agni on? Magni on or only onu: p IA ass; spd; I lri urrn; A ara I πr Magni ild o a urrn loop: µ I B R µ B For h lron: πr 4π µ B 4 7.7T For arosopi bodis: M B µ TR For Mrury, Earh and Jupir: ; M ass; T priod o roaion; R radius 4
B.5 For Uranus, Npun and Sun: B 4.6 5 4 µ M TR TR µ M Cold Fusion and Supronduiiy Th o phnona ha h sa planaion. Th diu bhas as a blak hol so h or bn qual parils ba arai. Uniid or: F 4 kh( ) ( )( ) Esap spd: G Th palladiu hargd ih duriu us b a supronduor. Graiaional onsan o h lron: q G 4πε R R G q 4πε.78 Mass and lai disan o h diu: 5
G.6 6 For Zn: 8. 6 GPS and Rlaiiy Th GPS dosn nd rlaiisi orrions baus h sallis ar onsanly synhronizd by arh saions. Bu rlaiisi orrions is and ha dirn alus han usually laid. Orbial spd shi: O GM R.9 s O M 4 7 6 kg ; R O.66 / Ti shi pr day: 4 6 4.6µ s Graiaional shi: ; GM 4 6. ; R T 6.4 R T GM 5.84 R O 5.7 ; 4 6.4µ s 6
Toal shi pr day: T.4 4.6 6.8µs For bn a agn and a supronduor For a shor disan h or is rpulsi (). For a long disan h or is arai (-). For and orbial spd: F 4 kh( ) and ( )( ) G d G ; ; d d 4 4kh F ( )( ) G For F d d Magn d Suprondu or F 7
_ d Absurdiy Fro h Einsin s and Plank s orulas o h nrgy: E and E h h For a isibl phoon: 4 6 5 Hz.686 kg Monu: p Ho an h phoon has onu i i has zro ass? Ho an h phoons l graiy? Th Uniid Absolu Rlaiiy Thory plains his: Th phoon has ass baus his spd is no bu. 8
k k For h sa phoon: 8. 4 s Th Duron Orbi o h proon and h nuron: P 4. 5 N Mass and rquny o h nr o ass: 7 D.4 ; h h 4k k D D 4.5 Alraion: k 8 g 6. ;. π. ; n 9 g n p Kini nrgy o h proon: E k.mv p 7.45.5 7 n ;. p R 4.. π 5 5 p. -- Walngh o h proon n -- Nubr o alnghs in h prir o h orbi 9
W an riy h alus by h orula: For H : p R h.π.6mv p. 7 n 7 p 5 ; 6.8 9 g. ; n R.7 5 For 4 H : 7 MV n 7.66 ; 8 4 7 6.7 ; 9. ; g 4.94 9 n 9 8 ; R.7 5 Elron graiaional onsan G q 4. π. ε.78 G ; R 7 B 7 R B π
; ; Elron agni on Thorial alu: µ T 9.7 4 Eprinal alu: µ 9.84764 4 µ µ T /.5 This is h orbial spd o h proon in duron. 7 Wak For Th ak or is ha bn quarks, diad by h bosons W and Z. Th ak or is h srongs on. W, Z
qk qk Th quarks u and d ar onopols: Magni and uniid ors F 4 q kh 4. π. µ ; q h q q -- agni harg; q -- lri harg 7.4 ;.75 5 8.58 ; 5.6 ; E 99. 8GV Wak or: F.8 N ; g.6. π. n n g 8 ; n R π 8 5.9 Binding nrgy o o quarks: E B FR 4TV Th lron has agni hargs Magni on µ µ 4 in rinsi µ orbial 9.8
Orbial: qr µ R 5. ;. 6 Inrinsi: R 8 µ. qr 4 Th lron o has his inrinsi agni on us roa a his spd. I i is ipossibl hr is only on planaion: h lron us has o agni hargs. q h q Th Non s or orula is alid in h iroorld F G ; G Variabl graiaional onsan R For bn o lrons 4 kh F N ;. Hz ; F G ; R G q 4πε.78 Rydbrg onsan -- R H λ H ; R H λh R ; π λ H 7 F N
For bn o proons 4 kh F. N p F G p. N ; R p G p q 4πε p 8. 5 5 ; R p 4. F 8. For bn a proon and an lron 8 p N p F G p ; G p G pg R G.78 ; G p 8.4 5 Rp RB Bohr' s.. radius Linar Sagna Eprin II This prin is a rsion o h Sagna prin ad ih linar spd. So, h sys is an inrial rrnial. I ill pro i ligh spd has or no rlai spd. irror pip. ih. ar irror D d or basplir A B irror lasr V 4
Th di has a lasr diod ( λ 6.5 7, P.5W ), a 5% - 5% ba splir, hr irrors, a pip illd o ar ih o glass indos and a ligh dor. Th lasr ba is diidd on h splir and rals in o dirions in h irrors irui. Thn hy ar joind again and n o h dor hr h ariabl inrrn parn gnras h olag V. Th di os in h rior o a ar so, h on rlai o h rs air ill su and subra o ligh spd. Aording o rlaiiy hory his is ipossibl. I s iporan o no ha h diu, h air, is a rs ha is oing is h i dor and h ir ha hr ar h poins A and B. Tis o h ligh rays: D D k D D k and D 8 ; D. ; 7.4 Spa phas shi: 8 9 7.4 and. Volag ariaion on h dor: V V ih λ 6.5 7 λ / V V 6.8 5
In our div 6V, so or a k / h 7.8 / s : V V. V ; 9% V W ha ad h prin (8-6-), ad asurs and ound alays a olag ariaion o V. So, ha prod ha ligh spd is no onsan and ha i sus o h spd o h rpor. Furhr planaions Th poins A and B ork as ir-dor and dor-ir. W an s ho ligh spd is addii in his prin: d or ir d D d D ( ) This prin is ry dirn ro h Fizau prin hr ha is oing is h diu. For insan an no do h prin ih h di a rs and h air oing ih a an. In his as h orula us us is: And h spd ariaion is ry lil. 6
Roo-Tpraur Supronduor Condiion or h isn o a supronduor: G R Th orbial spd o h parils us b qual o ligh spd. ; R G G q 4πε.78 G -- Graiaional onsan o h lron A R. 6 Supronduor oposi subsan: n. R Rn R ; V n nv R n nr R nr n. R A R nr AR ; y 6 A R 8n n ny AR > 7
On Roo-praur Supronduor O -- 6.66 kg ; R.4 Zn --. 5 ; R.4 n.6 OZn.6 or ZnO Th zin oid dopd ih o or oygn aos is a roo-praur supronduor. Th palladiu hargd ih duriu is no a supronduor. Ohr apls: ZnF CuO. 8
Tabl o and R o h lns H.67-7.99 Li.5-6.6 Na.8-6.9 K 6.49-6 4. Rb.4-5 4.94 Cs. -5 5.9 B.5-6.56 Mg 4.4-6.45 Ca 6.65-6.4 Sr.45-5 4.9 Ba.8-5 4.89 S 7.46-6.86 Y.48-5.5 Lu.9-5 4.4 Ti 7.95-6.56 Zr.5-5.4 H.96-5.46 V 8.46-6.5 Nb.54-5.9 Ta. -5. Cr 8.6-6.6 Mo.59-5.75 W.5-5.6 Mn 9. -6.9 T.64-5.66 R.9-5. F 9.7-6. Ru.68-5.66 Os.6-5.98 Co 9.78-6. Rh.7-5.65 Ir.9-5. Ni 9.74-6.4 Pd.77-5.6 P.4-5.95 Cu.5-5. Ag.79-5.77 Au.7-5.7 Zn.9-5.8 Cd.87-5. Hg. -5.46 B.79-6.5 Al 4.48-6. Ga.6-5.6 In.9-5. Tl.9-5.66 C.99-6.6 Si 4.66-6.6 G. -5.7 Sn.97-5.4 Pb.44-5.74 N. -6.5 P 5.4-6.6 As.4-5.68 Sb. -5.7 Bi.47-5.96 O.66-6.4 S 5. -6.57 S. -5.9 T. -5.5 Po.47-5 4.6 F.5-6.7 Cl 5.88-6.9 Br. -5.4 I. -5.8 A H 6.64-7.59 N.5-6.8 Ar 6.6-6.5 Kr.9-5.67 X.8-5 4.5 Rn Eapl: Hydrogn 7.67 ; R.99 Calulaion o R: Dnsiy ρ 4 R R 4 πρ π Graiaional alraion and ass oposiion (A orrion o Non s hory) Wrong oposiion o h alraion: G G g R R n. g g and 9
G g ( n ) g( n ) R For: F g g g g n. and n n or This is h rong rdud ass. I orks in bu is rong. Tru alraion oposiion: g g g g n Tru ass oposiion: n n F F G R g g g For h sys arh-sun 4 M S ; M T 6 ; GM T 8 g T.78 ; D TS g S D TS.5 GM S 5.9 D TS M M S F G.56 D T TS N g 5 g g T S. ; M 7 M M T S.46
F Mg.56 N Ponial ild o orbial spd Th parils don osilla, so hy don i nrgy. Thy ha a sai lroagni ild. Thy ha a ponial ild o orbial spd ha gnras h graiaional alraions. Th ariaions o h ild nd nrgy, irual phoons. And propaga a / or / h group spd. Mirosopi alraion: d( ) g ; d G R k Marosopi alraion: d( ) g ; dr G R Graiaional onsan o h lron: G q.78 4πε G 5 ; R.8 R Classial radius o h lron: R ;.46 π7
Enrgy: q E 4πε R R q 4πε.8 5 For h proon: p q 8 R p Rp.54 π7 4 πε p p G p R p p Tru Plank unis Plank unis ar rong baus an i h arosopi graiaional onsan ih ohr irosopi unis. Plank sal is a yh. I hang h graiaional onsan by h alu or h lron ryhing orks in. G 6.67 G q 4πε.78 Vauu nrgy paril: ε E MV µ 7π. h. 5.5 G hg 4 7π. 5 8 kg
hg. 5 7π. s Elron harg: q G 7 π ε 9.6 Elron ass: h 7π. G 9. q G 7.56 4πε 6 G G 7 π E E.5 π7 Enrgy o h lron: E ε π.7µ Mass o h proon: p µ ε ε p µ h h h p 4k k
Enrgy o h proon: E p µ ε Th lron s onu orula Th lron agni on is no a agni on bu only a onu. Th ru agni on is h agni harg is h alngh o h lron as h lri dipol on (h lri dipol on is a ass). MM h 7 4 q 5.65 s q W don kno hy bu h lron onu in hydrogn ao has our oponns rlad ih a paril ih h nrgy: Monu orula: ε E MV µ µ ε 4 7 µ 9.848 7 s ε q Uniary agni harg Elron s alngh h Plank s onsan q Uniary lri harg ε Vauu priiiy µ Vauu prabiliy Elron s ass Ligh spd 4
7 Elron s orbial spd Quarks u, d and Monopol Thr quarks bondd oghr gis h proon ass. Th ass o h quark is uh grar hn h proon. Binding nrgy: E ( qk p ) FR 4 kh F ; n R ; n π k k π Walngh o h quark:. 8 h k 4 qk 6.4 kg Binding nrgy o h quarks: kh E FR. 68TV π k Th ass has h sign o h harg. 5
Monopol Magni and uniid ors: q kh µ R 4 ; R ; π q h q kµ q k. π h Quarks ar ad o o onopols lik lrons and nurinos. MP 7. kg For bn a proon and an lron Non s or: F p G p 8. R p B 8 N Elri or: F p q 4 πε R B 8. 8 N F p g p 8. 8 N Graiaional onsan: G p G G p 6
G q ; G p πε q 4πε 4 p Alraion: g p g g p g k 8.5 ; g p p k 7.77 7 g p k p ; p p RB Bohr s radius Soni Boo Prssur Th quaion o h ariaion o h prssur ih h spd gos o ininiy hn. Bu ininiy dosn is in naur. Th graphi rprsns h doubl soni boo. P P M P M a a P P PM P ( ) a 7
P P ; P P P P sound spd 4 s ; 4 P aosphri prssur kg / P M ( a) 76kg / ; Prssur is a olu is a onsan P M 7 ( ) kg / P P P a ± a M ( ) a.7 s P P P M 8
Hydrogn Innsiis and Frqunis I ( n. π. R H 4 ) ( n ) ( W ) ; R H.974 7 n\ n 4 5 6 7 8 9.9E 5 7.4E 4.97E 4.4E 4 7.74E 4.54E.8E.86E.E 4.E 4 6.7E.4E.E.5E 85. 7.4E.58E.9E.4E 79.6 46. 4.8E.4E 76. 445.5 97. 5 858. 5.6.5 4.5 6 6.. 5.8 7 8.5 5.5 8 9.4 9 R n n H n > n n\n 4 5 6 7 8 9.47 5.9 5.8 5.6 5. 5. 5.4 5.5 5 4.57 4 6.7 4 6.9 4 7. 4 7.55 4 7.7 4 7.8 4.6 4.4 4.74 4.98 4.4 4.5 4 4 7.4.4 4.8 4.54 4.65 4 5 4. 6.44 8. 9. 6.4 4. 5. 7.57.65 8.8 9 I I 9 8 I 9 49 ; I 8 I I 48 I I 8 5 I I 48 45 9
Sal Consan o Aogadro Aogadro onsan is a sal aor bn h iro osos and h aro osos. Graiaional onsan: G H M 6.67 U ligh spd ; H -- Hubbl onsan ; G λ G.5 4πλ G M U -- ass o h unirs λ alngh o h unirs ; G R U -- Radius o h unirs H nλ π -- Quanizaion ondiion G R U n 6 -- Aogadro onsan Quanu o ass: M 4 G 9 λ 5 kg -- Arag sar Nubr o sars: M n M U 6 Th unirs has a ol o sars Aogadro onsan: N A PV k T B P prssur; V olu; k B -- Bolzann s onsan; T praur PV aro nrgy ; k B T -- iro nrgy PV -- aro nropy ; T k B -- iro nropy 4
Eprin o praur ariaion ih sura Tpraur is an nrgy sura dnsiy. E T S T ST S W ha so ar in a up ih h dinsions: T h R R. and h. 4 a h praur T º C W ransr h ar o anohr up: T h R R. 5 and h. 5 And h ar praur riss.8ºc, so: T.8º C 4
Magni harg unis Magni/lri hargs quanizaion: q q h q kg.. s. C kg.. s. A Wbr q agni harg; q lri harg; h Plank s onsan Wikipdia Magni onopol In SI unis, hr ar o onliing onnions in us or agni harg. In on, agni harg has unis Wbr, hil in h ohr, agni harg has unis o Apr-r. Magni dipol on (d): d q. d ; d disan Md Wbr-r Wrong agni dipol on: µ I πr Apr r. squard Apr. q. d Apr r This is rong baus h usual agni on is only a linar onu. q Iπ R p kg.. s q Wbr agnilu oulo 4
Diniion o ass Th ass is an lri dipol on. Elron: q K B q K B.8 -- Bolzan onsan; ass o h lron q Uniary lri harg; Copon alngh Proon: q 5 p K B ; p. p Boson : q 7 K B ;.54 h h K q B Wikipdia Ligh Ligh rquny Whn a ba o ligh rosss h boundary bn o dirn dia, h alngh o h ligh hangs bu h rquny rains onsan. Fals, h rquny also hangs. n n ; n 4
/ / n n n n Elroagni Longiudinal Was Th auu, or rqunis > 6 Hz bhas as a plasa o lrons and posirons. Cu o rquny M nq k ε n.5 47 Dby lngh ε E k q n ; E. 5MV Spd o h longiudinal as k ; -- rquny Th alngh is a onsan k.4 7 44
Mass h k Enrgy is also a onsan h E 89. 6GV k Cosi Miroa Bakground Radiaion Th osi bakground radiaion is gnrad by h unirs roaion. k and k 4.9 ; ; k d k d R H k k BT π h ligh spd; H -- Hubbl onsan H π. -- rquny o roaion o h unirs; k B -- Bolzann onsan h Plank onsan T praur o bakground radiaion.7k 8 Hz 45
T h k B 5 π. kgm U.7K G graiaional onsan; Mu ass o h unirs Magni ponial quaion II da A d A d d A agni ponial; lri ponial or graiaional ponial k ; d d da d A Fr paril: d d Soluion: 4π A A sin 4π ( ) A k Wih an lri ponial: da d A and d d q 5. s 4πε RB Soluion: A A 4π k A and A, or h lron 4π k A 5.66 5 A s or da B A B d and B.95 7 s A 7. 5 B Rrn agni ild 46
47 Th Einsin s spa-i dosn is Th Lornz s quaions ar h ahaial basis o h rlaiiy hory. Fro h Lornz s quaions: / / / ) ( ) ( ) ( ) ( 4 Equalling h oiins ro h ariabl : 4 ) ( ) ( This is h inarian quaion. For n rlai ras ih n rlai spds: / / / n,, n n,
48 / / / n n n n n n n n n n -- Rlai spd bn and n aording ih rlaiiy. Th alu o h spd dosn ar, only nd ha i iss. / / / n n n n So: n n k n n (Consan) Aording o Einsin k is a ariabl, ha is an rror. So and ar no indpndn ariabls spa and i. Th rlaiiy hory says ha k or ligh, bing h alngh and h priod o an lroagni a. Tha ans ha and ar alays alngh and priod. So, h spa-i dosn is. A dir onsqun is ha h auu ligh spd is ariabl ih h rquny: k W an alula h alu o k: 4.9 k So h rlaiiy hory is a pariular as o our hory ihou spa-i.
Phoons o h graiaional ild Th bakground radiaion phoons ar h irual phoons o h graiaional ild o h unirs. Graiaional ild o h unirs: g U GM U 6.9 R U Frquny o h bakground radiaion: k B.7 5.6 h Alraion ild o h phoon: k and k.9 4 d k g and d Th alraion ild o h phoon is qual o h alraion o h unirs: g U π k Phoons o h arh graiaional ild: k 4 g 9.8.48 Hz 49
Doubl soni boo prssur In naur hr ar no ininis. Prssur orula: P P P P MX ( / ) ( MX ) ( ) ( MX ) P MX -- Posii aiu; -- Vrial asypo spd P -- Noral prssur; -- Spd MX -- Spd or posii aiu, P Prssur P P MX P P MX MX P MX 5
Longiudinal Was ro Parils Th parils, inluding phoons, i o yps o as: ransrs as ih spd lor han ligh spd and longiudinal as ih suprluinal spd. Enrgy o a a-paril: h h E And k ; k 4.9 Frquny: h ± h 4k k Transrs as: h h 4k A k Longiudinal as: h h 4k B k A B M ; M -- Frquny o h arosopi ar k 5
M A M B For h isibl phoon: 4 A 5 Hz 5 B 9.8 Hz Spd: B 9. s Enrgy: h E B 89. 5GV For h lron: A. B.9 B 5.4 5
Classial and Quanu Enangln Th lassial and quanu nangln bhas h sa ay. All h ysris o quanu hanis ar rrors. W ha a ass o ha ris a onu o. I diids in o pis ih asss and and spds and. p p ; Th rsuling onus ar nangld. L s us h Bll s inqualiy: Propry A p > 5 Propry B > 5 Propry C p > 5 ( A, B ) ( B, C ) ( A, C ) ( p >, < 5) ( > 5, p < 5) ( p > 5, p 5) 5 < ( 5% 5% ) ( 5% 5% ) ( % ) 4 4 As h onus ar nangld h Bll s inqualiy is iolad. Firs, a quanu asurn o spin or polarizaion is no a asurn. Th nangld (or no) parils ha a pris alu o spin or polarizaion bor h asurn. Thr is no panding a-union baus and in h Shrödingr quaion ar no spa and i bu alngh and priod. 5
Massi urrn Massi urrn: I MS L V Magni. pol. srngh Por and assi rsisan: P R MS I MS R MS L V Inrs. ru. agni. dipol. on Th assi olag is an lri ild: Enrgy: V MS R MS I MS V ρ E Elri -- E q V (Elri harg and lri olag) Magni -- Massi -- E q V (Magni harg and agni olag) ρ E VMS E (Massi harg and assi olag) Massi rsisan o h auu: R MS 4.8 ε 4 ε Magni dipol on o h auu Massi apaiy o h lron: C Massi priiiy: 47 4 MS L ε L MS G Walngh-rquny 54
For an lroagni a on a diu ransiion hn h alngh aris also aris h rquny: k k ( k ) / For isibl ligh -- 7 6 8.4 In Shrodingr quaions and ar no spa and i bu alngh and priod o a a-paril. Vauu nrgy o h osi bakground radiaion 5.6 Hz -- rquny 4 E h. V -- nrgy Nubr o bakground phoons in h unirs: n 4 πr 88 U. 9 / ; R U radius o h unirs Toal nrgy: E T En /.5MV / Nubr o lrons in h unirs: n 79 4 πru / 55
Th oal nrgy o h bakground phoons pr ubi r is qual o h nrgy o on lron. Elri ild ro a roaing agni harg ρ q E R Nurino Th rquny o h lron nurino is qual o h rquny o h isibl ligh. 56
Doubl sli quanu rasr a n prin Orhodo prin: o nangld phoons, s and p, ar produd a a ba-bariu bora rysal by sponanous parari don onrsion. Th s phoon passs by a hih-ay arkr, o quarr-a plas, and o a doubl sli. Thn i gos o h dor d. Th p phoon passs o a linar polarizr and gos o h dor d. Th oinidn ounr rgiss h n. Aording o h orhodo planaion g a iag o inrrn baus h linar polarizr rass h hih-ay knoldg, n i h phoon p nrs h polarizr ar h phoon s passs h doubl sli. d pol lasr bbo p s qp qp doubl..sli oinidn ounr d W hink ha h rsul is du o i ariaions a h dors baus o h polarizr. Bu hr s a ay o proing ha: I h orhodo planaion is ru us g h sa rsul ih anohr prin. phoograi.. pla I hr s a insananous or ro h uur ouniaion bn h phoons should g a inrrn piur. W hink ha h rsul ould b no inrrn. 57
Insananous Couniaion pol qp ir p s doubl..sli qp d or W ha an ir o nangld phoons s and p. Th s phoon passs a hih-ay arkr, o quarr-a polarizrs, and a doubl sli. Thn ha a phoo dor plad a h posiion o a dark ring. Whn hr s inrrn i ds no ligh, a digial zro. Th p phoon passs a linar polarizr ha an b rod o produ a digial on a h dor. Wih i plad a h ba ha a digial zro. Aording o h orhodo inrpraion o quanu hanis his us ork. W hink ha his dosn ork. Aording o our hory h spd o ouniaion bn isibl phoons is: Frquny: B M ; A 4 M ; A 5 Hz k 5 B 9.4 Hz Spd: B k B B 9. s 58
Doubl orbi o h lron n n R rquny ; R Rydbrg rquny R. 7 5 Hz Orbial rquny: O Prir 6.6 7 5 Hz O R R O Th Rydbrg priod is o is h orbial priod. Tha ans ha h lron has a doubl orbi. Prir o on orbi: P 7. 6 Copon alngh o h lron I s h rason hy h inrs in sruur onsan is no an ingr. I s hy h giroagni raio is o is h lassial alu: 59
γ onu q angular.. onu g ( Th orhodo agni on is only a linar onu ) g. -- Landé g aor ; g 7π Angular onu h 4π h spin ; R angular onu π γ L.76 ; 5.68 γ 5.68.4 q Virual Phoons Virual phoons us is o ranspor h ors bu hy ar undabl. Thy ar longiudinal as o gra rquny and onsan alngh ih spds grar han ligh spd. Th lron has a ild o roaion: ;. Hz ;.46 For irual phoons h quoin bn lri and agni ilds is grar han ligh spd: E > B Virual phoons o h lron: B M.9 Hz ; M ; k k 4.9 6
Spd o h irual phoons: B k B 5.4 s This is h spd o h lri or. For h nurino: B 5 4 8.9 Hz ; 5. Hz 6 B 7 ; Nurino ass:.9 kg Th alngh o h irual phoons is a onsan: k.84 7 Th rs nrgy is also a onsan: h E 89. 6GV k God dosn is Th nohing is rnal. Th nohing dosn adi i sl, so h nohing is unsabl. I diids in syri spds and disans as: V(-V) and L(-L) This is h isn and h isn is rnal. Th unirs is no panding. I is roaing ih onsan angular spd. Th bigbang nr happns so no on is ndd o sar h isn. Th loal linar spd o h unirs is ligh spd. Th obsrd rd shi o h galais is a ransrs rd shi. Th irs physial raliy, ar h spd and h disan, is h agni or ponial or irulaion: A VL Th nubr o sars o h loal unirs is qual o Aogadro onsan. Th unirs has a nr o roaion and ar no a h nr. Mar and aniar is dind by h sign o h ass. Aniar has a ngai ass. Th ass has h sign o h harg. Th lron is aniar. Marosopi graiaion aras boh ar and aniar. Th parils ar all oposd o onopols and hy ar spd and disan ors. Th iroos is qual o h aroos. Th ao is qual o h solar sys. 6
W ill nr kno i ligh propagas in h auu baus hr ar graiaional ilds ryhr. Th ru auu is h graiaional ild o h unirs. I is a suprluid and a supronduor (.7K). Th spin o h parils is du o h roaion o h unirs, so h spin is quanizd. Elron Spin Spd Spin R h 4π Classial radius o h lron: 5 R.8 π7 7.5 s Th lron is oposd o o roaing onopols. E n s E Rrn lri ild o h lron: π q E s R 5 5 8.8 5 Copon alngh;.7 Wbr Magni.. harg q 4 sin π E E s 4 7 ( ) π k E. 6
Longiudinal Was and Absolu Ti For Einsin ligh is god. I s hy ligh us b absolu. Transrs ligh is rlai. Causaliy is rlad no ih ransrs ligh bu ih longiudinal ligh ih spds asr han. Ti dosn is in naur. Ti is a drid uni ro disan and spd. Disan an b rplad by any physial quaniy. For longiudinal as i is absolu. Transrs and longiudinal as li. / / / Transrs spd For ransrs as h priod (i) is ariabl ih h ariaion o h ransrs spd o h ransission o h nrgy. 6
Is Ligh Spd Rlai Or No? This is a s o h rlaiiy posula o ligh spd onsany, basd on h phnonon o h asronoial abrraion. 8 α β V α V sin(8 α) sin β β Asronoial abrraion sin β sin α V Classial V: Rlaiisi V: V C osα V R W ha a aiu β or α π / 4 ; 4 V C.99867 8 V R.9979458 8 β C VC sin( π / 4) 7.7546 5 rad 4.594" β R sin( π / 4) 7.7596 5 rad 4.595" β " I i s possibl o asur hos angls ih his prision, an or h irs i o s h ligh spd onsany posula. 64
Corrion o h Uniid Alraion W ha dind h uniid graiaional alraion as: d g ; k d k And i gis: k g ; k 4.9 Copon rquny; Spd o h a This orula is orr or h lron baus Bu i us b rplad by anohr orula: d( ) k g g ; d Th quialn arosopi alraion is: k d( V ) g ; dr V GM R V Esap spd Th alraion ild is gnrad by h spd ariaion o h graions ih disan. So, hr is only on hanis o gnraion o h graiaional ild o h parils or h arosopi asss. Th graions ar phoons o ry lo phas spd. For h Earh: h 5 ; M.66 Hz k 4 M 6 M M Copon rquny o h ar M k g 9.8 G M 7 M 4.9 s ; G Group spd o h alraion ild: 5 4.5 s 65
V G 4 s G Copon alngh o h graions: M 4 5.6 ; G. All ass spru arh lron proon M ransrs graions as longiudinal.. as ( irual.. parils) ass odul ; Copon rquny g Graiaional alraion.87 M M Fild spd: 66
M Rlai alraion k g ; ; k ( )( g 4 ( ) For a blak hol: g A h sura o a blak hol h or is zro. ) / Uniid rlai or (bn qual parils) 4 kh ( ) F ( ) ( ) Mhod o Soling Any Equaion W us h progra QBASIC o sol h quaions. Equaion a: 9 6 4 67
FOR N TO STEP ( 9 6 4) / 4 PRINT NEXT N FOR N TO STEP 4 /( 9 6) PRINT NEXT N ( 9) 6 4 ( 4 6) /( 9) / So quaions onrg o h soluions. Th iniial is any alu, bu so alus don onrg. Equaion b: -------------------------- Log ( ) FOR N TO STEP LOG( ) 7. 994 PRINT NEXT N -------------------------- Equaion : ----------------------- Sin ( ) Log( ) 4 FOR N TO STEP 4 SIN( ) LOG( ). 47575 PRINT NEXT N 68
Th hod also orks or syss: ---------------------------- ------------------------------- y y 4 y y 5 y FOR N TO STEP y ( y 4) / y 7. 9765 ( y 5) / / y / 5. 9994 PRINT, y NEXT N This hod us b br sudy. Try o ind ohr soluions. Mhod o h Soluions Equaions Only or ral soluions. Insad o soling h quaion sol h soluions quaions. 5 6 ; soluions: a, b Progra: a b 5 ab 6 a FOR n TO STEP b 6 / a a 5 b PRINT a, b NEXT n 9 6 4 ; soluions a, b, 69
Progra: a b 9 ab a b 6 ab 4 a b FOR n TO STEP 9 a b b ( 6 a) /( a ) a 4 / b / PRINT a, b, NEXT n Progra: 4 5 5 4 ; soluions a, b,, d a b d ab a ad b bd d 5 ( a b) d ab( d) 5 abd 4 a b FOR n TO STEP d a b ( 5 ab bd ad) /( a b d) b ( 5 ad) /( d a( d)) a 4 / b / / d PRINT a, b,, d NEXT n Copl soluions: n n ; soluions: a iy, b iy 7
7 y 4 n n n ; soluions: a, iy b, iy 4 ) ( y a y a a 4 4 4 4 n n n n ; soluions: a, b, iy, iy d 4 ) ( 4 ) )( ( 4 y ab ab y b a y b a ab b a
Absolu oion Th roaional on o a poin is alays rlai. Th roaional on o a sys ih dinsions is absolu. This is also ru or linar on. ) ( A dirn o spd is alays absolu: Cons an K 7
Magni Dipol Mon Error Th agni dipol on is only a linar onu. IA p ; I Elri urrn; A Ara Th ru agni dipol on o h lron: µ q ; q - Magni harg; - Copon alngh q h ; q 7 4 µ 5 s Monu: p IA ; I q ; N N A 4π q p 4π Elron: g 4 p 9. ; g q 4π Proon: Nuron: g p p 6 p P.4 ; g p 5. 6 q 4π Copon alngh o h proon p p N N 7.8 q 4π 9.66 Muon: g µ µ 6 p µ 4.5 ; g µ q 4π 7
Gyroagni raio onu p γ angular.. onu h / π Elron: γ g q.76 h Proon: γ p g q p p 8.675 h Th rlai spd is also rlai / / Monu: p / / Angular onu: h R ; h h π 74
h / / ) ( / ) / π R ( Ligh spd ariaion ih graiy Enrgy: E E / ε µ ε µ / ; ε µ εµ Spd: ( / ) Priiiy and prabiliy ariaion: ε ( / ε ; µ 9 / 8 7 / 8 ) µ ( / ) Wih graiy: ε GM R µ GM R ε ; µ 9 / 8 7 / 8 75
Hliu and Lihiu Enrgy Equaions II I a-paril dualiy is alid i us is a orr planaion or aoi physis ih lrons as lassial parils. This planaion i s bs and asir han h quanu hanis on. Th iroos is qual o h aroos, h aos ar jus lik solar syss. For h hliu ao, h orbis o h lrons ar o inius o h nrgy: de dn ( N)( N ( N N ) N NN ) For h hydrogn N 7.6, h inrs in sruur onsan. On parial nrgy (kini plus ponial): E N de ( N) 5 dn N N Ionizaion nrgis: de dn ( N N ) N N 4 5 N N N N NN C N N 4N E 4 Couning ro h nulus: 8 8 E 8.7 J ; E.94 J N E 6N 4( N N ) N 4.65 N C E 6N 4( N N ) N 5 4.8 N C C ; C ; C. 6V 7 76
.65 4.8 4 5 N N N N N N 7 N 54.7 ; 4 N 99. Ei harg: 7 Z N.5. 4 Orbial rquny o h rior lron: OR N.5 6 Hz ligh spd ; Copon alngh o h lron Rydbrg rquny or hliu: R OR 6.5 5 Th lron has a doubl orbi lik in hydrogn λ R R. 7 On spral alngh: λ 7. 8 ; λ 498.7 9 Eprinal alu: λ 5.5n Elron radius: º --- N R. π º --- R.8 77
78 Th o lrons ar no in h sa orbi. B Z R R ; B R Bohr radius Lihiu ) ) ( ) ( )( ( N N N N N N N N N N N N N N N N dn de ) )( ( N N N N N N J E 7.96 ; J E 7. ; J E 9 8.64 5 4 4 ) ( 6.6 ) ( 6.48 ) ( 6.4 C N N N N N N N N N N N C N N N N N N N N N N N C N N N N N N N N N N N C ; 7 C ; 7 C 48 N ; 4 4. N ; 4. N Ei harg: Th innr lron has lor nrgy han h sond on. 4 9. 96.