Equations from Relativistic Transverse Doppler Effect. The Complete Correlation of the Lorentz Effect to the Doppler Effect in Relativistic Physics

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1 Equtins m Rltiisti Tnss ppl Et Th Cmplt Cltin th Lntz Et t th ppl Et in Rltiisti Physis Cpyight 005 Jsph A. Rybzyk Cpyight Risd 006 Jsph A. Rybzyk Fllwing is mplt list ll th qutins usd in did in th Rltiisti Tnss ppl Et pp. Eh qutin is idntiid by th sm numb usd in th thy nd gin nly n in th d its ist us. Als inludd th iginl illusttins nd Appndis usd in th iginl wk.. Clssil ppl Et Lin--Sight Mtin Wh in n t Figu, A, O, nd B pints in th sttiny m (SF), Light Emittd t Pint O A O St B FIGURE St Rding m A whil Apphing B is th spd light, is th spd th su, nd th mittd wlngth nd quny sptily nd nd th bsd wlngth nd quny sptily: F bs A th ppl t will h th ms () Clssil ppl Et Rssin Fmul Wlngth () Clssil ppl Et Rssin Fmul Fquny whil bs B th ppl t will h th ms: (3) Clssil ppl Et Apph Fmul Wlngth (4) Clssil ppl Et Apph Fmul Fquny

2 A. Millnnium Vsin Einstin Tnsmtin Fmuls Wh in n t Figu, A, O, nd B pints in th SF-S nd Y is pint in ming intil m (MF)-S, S Y A O T T t St B S FIGURE Einstin Rltinship btwn Intil Fms St nd Obss is th spd light, is th spd th su, t is th tim intl in th ming intil m S nd T is th spnding tim intl in th sttiny m S : ( t) T T (5) Pythgn Rltinship istns ( t) T T (6) ( t) T ( ) (7) t T (8) t T (9) Einstin Tim Tnsmtin t Simpliid T t (0) Einstin Tim Tnsmtin T Simpliid B. Spil Rltiity Vsin Einstin Tnsmtin Fmuls t T () t T ()

3 t T (3) Einstin s Tim Tnsmtin t T t (4) Einstin s Tim Tnsmtin T C. Millnnium Vsin Einstin Tnsmtin Fmuls Still ing t Figu, d is distn in th ming intil m S nd is th spnding distn in th sttiny m S th bss: d t (5) Ming Intil Fm istn T (6) Cspnding Sttiny Fm istn d (7) Einstin istn Cnttin d Simpliid t T (8) F dditinl n, th mplt tnsmtin ltinships gin in Figu 3. S Y A T O T t St B S Cntt Int Cil FIGURE 3 Int Cil btwn Epnding Light Sphs 3. Th Tnsmtin Et Wlngth nd Fquny Wh d is distn in th ming intil m th su, is th spnding distn in th sttiny m th bs, is th spd light, is th spd th su, nd th lssil symbls wlngth nd quny sptily, nd th mittd 3

4 wlngth nd quny sptily, nd nd th tnsmd wlngth nd quny sptily: d (9) Einstin istn Tnsmtin Simpliid (0) Wlngth Tnsmtin UF t SF () Clssil Wlngth t Fquny Rltinship () Emittd Wlngth t Emittd Fquny Rltinship (3) Tnsmd Wlngth t Tnsmd Fquny Rltinship (4) Emittd Fquny t Emittd Wlngth Rltinship (5) Tnsmd Fquny t Tnsmd Wlngth Rltinship (6) (7) (8) (9) Fquny Tnsmtin UF t SF 4. Th Cmplt Rltiisti Lin--Sight ppl Et Wh is th spd light, is th spd th su nd is ssin nd pph (wh inditd), nd th mittd wlngth nd quny sptily, nd th tnsmd wlngth nd quny sptily, nd nd th bsd wlngth nd quny sptily: 4

5 (30) Clssil Lin--Sight ppl Et Wlngth (R, A) (3) Clssil Lin--Sight ppl Et Fquny (R, A) (3) Rltiisti Lin--Sight ppl Et Wlngth (R, A) (33) Rltiisti Lin--Sight ppl Et Fquny (R, A) (34) (35) Rltiisti Lin--Sight ppl Et Wlngth (R, A) (36) (37) Rltiisti Lin--Sight ppl Et Fquny (R, A) 5. Th Rltiisti Tnss ppl Et Initil Wlngths nd Fqunis Wh in ing t Figus 4, nd 5 FIGURE 4 Clssil Tnss ppl Et ind Rssin Rssin 90 gs Apph s s s s A B C 5

6 p s s su FIGURE 5 Clssil Tnss ppl Et Rltinships is th spd light, is th spd th su, is th ppl td initil wlngth, s is th stt pint missin th initil wlngth, p, is th pjtin ngl, s, is th stt ngl th initil wlngth,, is th ngl ssin, is th ngl pph, is th ngl bstin, (i) is th ppl t t initil wlngths, nd th mittd wlngth nd quny sptily, is th tnsmd wlngth, nd nd th bsd wlngth nd quny sptily: 80 dg (38) Rltinship Angl Rssin t Angl Apph 80 dg (39) Rltinship Angl Apph t Angl Rssin s (40) Fm Lw Csins Thm Initil Wlngth s s (4) ppl Etd Initil Wlngth ( i) s s (4) Clssil Tnss ppl Et Ft Initil Wlngth s s (43) Clssil Tnss ppl Et Initil Wlngth s s (44) Clssil Tnss ppl Et Initil Wlngth s s (45) Clssil Tnss ppl Et Initil Wlngth s s (46) Clssil Ft Tnss ppl Et, Initil Wlngth 6

7 s s (47) s s (48) Rltiisti Tnss ppl Et Rssin, Initil Wlngth s s (49) Rltiisti Tnss ppl Et Apph, Initil Wlngth s s (50) Rltiisti Tnss ppl Et Obsd, Initil Wlngth (R, A) (5) Obsd Fquny t Obsd Wlngth Rltinship s s (5) s s (53) s s (54) Rltiisti Tnss ppl Et Obsd, Initil Fquny (R, A) 6. Th Cmplt Rltiisti Tnss ppl Et Wlngths nd Fqunis Wh in ing t Figu 6 7

8 p S S p s s - su - s is stt pint missin S is lding dg w is nd pint missin S is tiling dg w dius S - dius S whl numb Figu 6 Etndd Rltinships - Clssil Tnss ppl Et is th spd light, is whl numb m t ppimtly 0 7.5, is th spd th su, is th ppl td wlngth, s is th stt pint missin ll wlngths, is th nd pint missin ll wlngths, p, is th pjtin ngl, s, is th stt ngl ll wlngths,, is th ngl ssin, is th ngl pph, is th ngl bstin, is th ppl t t wlngths, nd th mittd wlngth nd quny sptily, nd th bsd wlngth nd quny m ding su sptily, nd th bsd wlngth nd quny m n pphing su sptily, nd nd th bsd wlngth nd quny sptily: ( ) ( ) ( ) s (55) Fm Lw Csins Thm ( ) s s ( ) (56) s s ( ) (57) ppl Etd istn s s ( ) (58) Clssil Tnss ppl Et Ft Wlngth s s ( ) (59) Clssil Tnss ppl Et Wlngth 8

9 s s ( ) (60) Clssil Tnss ppl Et Wlngth s s ( ) (6) Clssil Tnss ppl Et Wlngth s s ( ) (6) Rltiisti Tnss ppl Et Rssin, Wlngth s s ( ) (63) Rltiisti Tnss ppl Et Apph, Wlngth s s ( ) (64) Rltiisti Tnss ppl Et Obsd, Wlngth (R, A) s s ( ) (65) Rltiisti Tnss ppl Et Obsd, Fquny (R, A) 7. Th Spil Rltiity Rltiisti Tnss ppl Et Fmuls (Nt: Th llwing tw muls th iginl muls m Einstin s 905 pp. Sin th uth nsids ths muls int in sl dint wys, th d shuld t th sus th pp dinitins th ibls usd.) ω ωβ ( l / ) sφ / ( / ). (Nt: Ept β nd β tht dind in Eqs. (7) nd (74) sptily, th ibls usd in th mining spil ltiity muls h th sm dinitins just gin in Stin 6. Ths muls, hw, ls nsidd t b int by th uth in dn with th indings th psnt wk nd th iginl Millnnium Thy Rltiity.) s (66) SR Rltiisti Tnss ppl Et Obsd Wlngth 9

10 s (67) SR Rltiisti Tnss ppl Et Rssin Wlngth s (68) SR Rltiisti Tnss ppl Et Apph Wlngth s (69) SR Rltiisti Tnss ppl Et Rssin Wlngth s (70) SR Rltiisti Tnss ppl Et Apph Wlngth β (7) β β s (7) SR Rltiisti Tnss ppl Et Rssin Fquny (73) SR Rltiisti Tnss ppl Et Rssin Wlngth β (74) β β s (75) SR Rltiisti Tnss ppl Et Apph Fquny (76) SR Rltiisti Tnss ppl Et Apph Wlngth (Nt: Ept ibl E tht psnts th Einstin t, nd ibls nd tht ppl td wlngths, th ibls usd in Figu 7 nd th mining muls h th sm dinitins gin in Stin 6 nd my b usd t lt th spil ltiity muls with th millnnium ltiity muls.) 0

11 Rssin s su Apph E FIGURE 7 Th 90 g Rltiisti Tnss ppl Et s (77) s 0 (78) s (79) s (80) s (8) s (8) Cspnding MR Angl Rssin SR 90 g Angl Initil Wlngth s (83) Cspnding Spd wh MR Angl SR 90 g Angl Initil Wlngth s (84) Angl Rssin Null Clssil Tnss ppl Et - All Wlngths s (85) Spd Null Clssil Tnss ppl Et All Wlngths Appndis Th llwing Appndis inludd s pt this pp: Appndi A- (Oll Anlysis) Appndi A- (Cnstnt Spd Rng Angls) Appndi A-3 (Cnstnt Angl Rng Spds) Appndis A-4 nd A-5 itin Fmuls

12 Appndi A- Rltiisti Tnss ppl Et Rltiisti Tnss ppl Et W Thy.md Fbuy, 006 Jsph A. Rybzyk Spd : : : : km/h 000 MR Rltiisti Tnss ppl Et - is Angl Rssin, is Angl Apph, nd is Angl Obstin in dg. : 90 dg : 80 dg 90dg : 0 0 : s s s : s : Lin-- Sight gin t ight s( ) l : s l : : 000 l istn t bs km m ( ) ( ) s : s ( ) ( ) p : s ( ) l Angl Pjtin (0-0-0 dg) Angl Stt (0-80 dg) Angl Rssin (0-80 dg) Angl Apph (0-80 dg) p 30dg s dg 90dg 90dg Emittd Tnsmd Obsd R Obsd App MR muls inding whn is gin, inding whn is gin t mk s nd t mk sid (-d) sid St t t mk s St t t mk s : s dg : s ( ) Spil Rltiity Fmuls Fmuls gd m 0 t 80 dg. Spil Rltiity mul nd in MTR SR Rssin ( 0-80) SR Apph ( 0-80) s E : s E : s E : s E : 0 90dg 90dg E E E E β : β E3 : β s E E3 : E3 E β : β E3 : β s E E3 : E3 E

13 Appndi A- Rltiisti Tnss ppl Et Rltiisti Tnss ppl Et using Angl Rssin Spd/Su Ft ist/obs m m :.9 : : 0 4 F 80,000km/s us Fbuy, 006 Jsph A. Rybzyk MR Emittd MR Tnsmd Rssin Angl MR mul SR Fmul MR Obsd SR Obsd E & E : 0 dg s : s : 30 dg : 60 dg : 90 dg s : s : 0 dg s : s : 50 dg s : s : 80 dg s : s : 80 dg s : s s : s s : s s E : s E : s E : s E : s E : s E : s E : s E : Cmpisn / E Cmpisn / E Cmpisn / E Cmpisn / E Cmpisn / E Cmpisn / E Cmpisn / E Cmpisn / E E E E E E E E E E E E E E E E E 3

14 Appndi A-3 Rltiisti Tnss ppl Et Rltiisti Tnss ppl Et using Angl Rssin Fbuy, 006 Jsph A. Rybzyk Rssn Angl Ft ist/obs m m MR Emittd MR Tnsmd int h. Gin : 90 dg : by SR 90 dg, Su Spd MR Fmul SR Fmul MR Obsd SR Obsd E & E : 0 s s s : E : E :.6 s s s : E : E :.7 s s s : E : E :.8 s s s : E : E :.9 s s s : E : E : s s s : E : E :. s ( ) s ( ) s ( ) : E : E :. s ( ) s ( ) s ( ) : E : E :.3 s s s : E : 9.48 E 9.48 s s s : E : E :.4 s ( ) s ( ) s ( ) E : E : :.5 4

15 Appndi A-4 Rltiisti Tnss ppl Et itin mul lssil tnss ppl distn d using Lw Csins : 90 dg s :.9 Wh d ( ) ( ) d d s( ) s ( ) s ( ) s ( ) s d : s( ) s ( ) s s s s itin mul lssil tnss ppl ssin using Lw Csins s s s s itin mul ltiisti tnss ppl ssin using Lw Csins s s s s itin muls lssil nd ltiisti tnss ppl pph using Lw Csins Chng sign t - wh shwn nd hng t nd t s s s ( ) s itin mul lssil nd ltiisti tnss ppl Stt Angl using Lw Csins ( ) ( ) ( ) s ( s ) ( ) s( s ) ( ) ( ) ( ) s ( s ) ( ) ( ) s( s ) ( ) ( ) ( ) s ( ) ( ) s ( ) itin mul lssil nd ltiisti tnss ppl Pjtin Angl using Lw Csins ( ) ( ) ( ) ( ) ( ) ( ) s ( p ) s ( p ) ( ) ( ) s( p ) ( ) ( ) ( ) ( ) s ( p ) ( ) ( ) ( ) ( ) p ( ) ( ) s ( ) ( ) Appndi A-5 5

16 Rltiisti Tnss ppl Et itin mul Angl Rssin t qul Stt Angl s Substituting, nd d (-) w h m th Lw sins, d s s I s Thn d Th th b n b sttd s s whih n b sld t btin s s s s s s giing s ( s ) nd s s Substituting bk in pl gis s ( s ) nd s s inl sins. Rltiisti Tnss ppl Et Th Cmplt Cltin th Lntz Et t th ppl Et in Rltiisti Physis Cpyight 005 Jsph A. Rybzyk Cpyight Risd 006 Jsph A. Rybzyk All ights sd inluding th ight pdutin in whl in pt in ny m withut pmissin. Nt: I yu ntd this pg ditly duing sh, yu n isit th Millnnium Rltiity sit by liking n th Hm link blw: Hm 6