PHY61 Eried Psis Letre Notes Reltiit 3 Reltiit 3 Dislimer: Tese letre otes re ot met to reple te orse tetbook. Te otet m be iomplete. Some topis m be ler. Tese otes re ol met to be std id d spplemet to or ow otes. Plese report iries to te proessor. Additio o Veloities Now tt we kow tt te Glile trsormtio mst be modiied, it s time to reisit te topi o ddig eloities. Cosider two iertil rmes S d S wit reltie eloit. S ' S' ' d i rme S' dt + i Glile trsormtio, wi wold impl ' > i Cosider te ierse Loret Trsormtio: γ + t d, t γ t + / Tke dieretils: d γ d + dt dt γ dt + / d D. Aost Pge 1 8/17/4
PHY61 Eried Psis Letre Notes Reltiit 3 Diide oe b te oter: d d + dt dt dt + / d d dt + d / dt d Note tt dt Te eloit dditio ormle re: + / γ / e γ / e were we e diided b dt j j Note tt ee tog d, tt d Emple: Cosider spert tt trels t.8 rom Ert d tt les projetile wit reltie eloit o.8. Wt is te eloit o te projetile rom Ert? Glile: 8. + 8. 16. >! 16. Loret:. 976< 1 + 8. I isted o projetile we tred o ligt bem, bot obserers o te spert d o Ert wold gree tt te eloit o te ligt bem is, s reqired b Eistei s d postlte. Te dditio o eloit ormle tell s tt otig eeed te speed o ligt. D. Aost Pge 8/17/4
PHY61 Eried Psis Letre Notes Reltiit 3 Doppler Eet Te Doppler eet is ge i reqe o trelig we we te sore is moig towrd or w rom reeier, like te ge i pit o r s egie we it trels b o. We derie te ge i pit or ligt sig wt we e lered i Speil Reltiit. Cosider ligt we trelig log te -is. It emits we rests i time T i te rest rme o te emitter. Frme S Sore ere rest λ rest 1 Frme S Reeier Legt o wetri L λ T T λ For ligt, λ λ T reqe o ligt i rest rme Te reqe is rests per time T Now osider reeier i dieret iertil rme S. Sppose tt te trsmitter i rme S is moig towrd te reeier t eloit. Let s ompte te reqe reeied gie tt te speed o ligt is lws ostt or ll rmes. L λ T T λ T legt o wetri i rme S Now rom time diltio we kow tt T γ T Diste treled b rest 1 mis diste sore moes b te time o te lst rest. λ γt γ T γ Sie / T D. Aost Pge 3 8/17/4
PHY61 Eried Psis Letre Notes Reltiit 3 Now we sbstitte i or γ: / So te Doppler sit eqtios re: Sore d reeier pproig Sore d reeier reedig Ts, we sore d reeier ppro e oter, te reqe is sited iger. We s tt te ligt is ble-sited. We sore d reeier reede rom e oter, te reqe is sited lower. We s tt te ligt is red-sited. Red ligt s lower reqe t ble ligt. Moder eletrois llow s to determie reqeies er rtel, so we mesre reltie eloities rtel s well sig tis eet. Emples ilde Doppler weter rdr, polie rdr, d ee te epsio o te ierse! Loret Irie We e see tt some qtities ge rom oe iertil rme to oter (legt, time, eloit, reqe). A qtit wi does ot ge ter Loret trsormtio is sid to be Loret Irit. Oe speil irit is te Spe-time Iterl: t + + t t t et. 1 1 Tis is te geerlitio o Crtesi diste or 4-dimesiol spe-time. Te sme le or s is obtied or iertil rme. So ltog legt d time seprtel re ot irit rom oe rme to oter, tis prtilr ombitio is. We proe tt tis is tre b pplig te Loret trsormtio. For emple, osider sbtomi prtile wi des i time τ i its rest rme. D. Aost Pge 4 8/17/4
PHY61 Eried Psis Letre Notes Reltiit 3 I te rest rme S : t, t τ, 1 1 1 τ Now mke Loret trsormtio to oter rme S moig t eloit : γ + t t γ t + / γτ, γτ 1 t γτ, t1 t γτ γ τ γ τ γ τ 1 / τ / 1 / τ s i te rest rme Some termiolog: > time - like A rme eists were eets or i oe ple, seprted b time. ligt - like eets re seprted b te speed o ligt. < spe - like No ligt sigl oet te eets. D. Aost Pge 5 8/17/4