Michelson Morley Experiment

Transcription

1 Mihelson Morley Eperimen Mihelson Morley Eperimen Relaiiy and Asrophysis Leure 09 Terry Herer Ouline Worked Problems 3-: Mihelson-Morley Eperimen Spaelike and Timelike inerals Simulaneiy Eample Sample problem L- (pg ) Problem L-, page (due Friday/Monday) Will hand bak on Monday if you hand i in on Friday Prelim Wednesday, Sep. 3 Closed book and noes Will oer maerial hrough Friday (9/) Should know Spaeime ineral, fundamenal posulaes of Speial Relaiiy, simulaneiy and oher issues raise by relaiiy Will hae boh qualiaie and quaniaie quesions Lorenz Transformaion equaions will be proided (if needed) A90-09 Mihelson Morley Eperimen A90-09

2 Mihelson Morley Eperimen Mihelson-Morley Ep. (Prob. 3-) Suppose we hae a plane flying from poin A o poin wih eloiy Le he disane from A o be L, hen he ime o rael bak and forh wih no wind is Traeling along wind direion n L For a wind blowing wih eloiy,, blowing from A o, he rael ime from A o (wih he wind) is L A Flying bak agains he wind, he rael ime is A L A L Summing gies he oal ime AA L L A A L Relaie o he no wind ime, we hae AA L L n AA L / Noe ha his is highly non-linear, if > you an fly bak from o a! A90-09 Mihelson Morley Eperimen 3 Problem 3-b Now suppose he plane flies from A o C wih he wind perpendiular o he direion of moion. The air speed is sill u he plane has o fly ino he wind wih a eloiy omponen equal o or i will go off rak, ha is, y Le be he eloiy omponen in he direion (A-C direion), hen y The rael ime from A o C is The reurn rip akes he same ime, so ha AC ACA L L AC CA L Relaie o he no wind ime, we hae ACA L n L Traeling o wind direion A ACA L L / Noe, you may no make if > you an ge from A o C or C o A! C A90-09 Mihelson Morley Eperimen 4 A90-09

3 Mihelson Morley Eperimen Problem 3- AA o wind L / o wind L Le us ompare he wo round rip imes for AA and ACA Assuming <<, we an us he epansion z n nz if z The for moing parallel o he wind (AA) L AA And for perpendiular o he wind (ACA) L ACA Thus ACA akes less ime and he ime differene is: L ACA AA L is round rip disane ACA / A90-09 Mihelson Morley Eperimen 5 Problem 3-d Suppose a Souh Pole saion send ou 4 planes rael as shown o weaher saions loaed 300 km away. The planes are raeling a 300 km/hr The ime differene beween he firs and las plane reurning is 4 seonds Wha is he wind speed? Assume ha he wind is blowing horizonally in he diagram We hae from our preious slide 300 km L L / Souh Pole saion wih by weaher saions loaed 300 km away in loaions shown. Thus / 0 km/hr The wind is blowing along he pah whih akes he longes ime. The direion is no known wih addiional info. A90-09 Mihelson Morley Eperimen 6 A

4 Mihelson Morley Eperimen Problem 3-e Mihelson and Morley designed an eperimen o look for a hange in he speed of ligh due o moion (of he Earh) relaie o he eher They used an inerferomeer whih diided an inoming ligh beam ino wo pars The beams rael in perpendiular direions, unil hey hi a and rerae heir seps The reurning beams inerfere wih one anoher Numbers The oal pah lengh (L) was m for heir eperimen The orbial speed of he Earh is 30 km/se We hae for he ime differene L So ha m m/se se Whih is indeed ery, ery shor beam splier elesope eye Correor o ge same opial pah lengh Mihelson inerferomeer used in Mihelson-Morley eperimen A90-09 Mihelson Morley Eperimen 7 Problem 3-f Sine his iming is oo shor o measure (een by oday s sandards, hey used a Na ligh Emis a speifi waelengh, 59 nm Thus for a period ( yle) T f m 5 0 se 30 m/se beam splier The eperimen was done o /00 of his alue ( dark fringe o anoher) 7 0 se ep Now Mihelson and Morley roaed he able so hey were looking for wie he effe (ompued in par e) ep 7 0 se se The eloiy auray relaie o Earh moion is (era faor of for roaion): / L 30 m ep L 37 elesope eye Correor o ge same opial pah lengh Mihelson inerferomeer used in Mihelson-Morley eperimen. Round rip pah, L = m. Earh speed 30 km/se 0 / 7 5 km/ se A90-09 Mihelson Morley Eperimen A

5 Mihelson Morley Eperimen Problem 3-g No effe was deeed wih he eperimen A null resul he eperimen ould no ell ha he Earh is moing hrough an eher Does he Mihelson-Morley eperimen by iself disproe ha ligh is propagaed hrough an eher? No quie bu i is lose. One ould hae lengh onraion (only) of he inerferomeer along he direion of moion This ould ompensae for he a slower rael ime by he ligh (phoons) making he arm shorer. This looks like relaiiy bu i is no, he speed of ligh is no a onsan in his ase A modified eperimen wih arms of unequal lengh (see problem 3-3) sill shows here is no moion Requires boh lengh onraion and ime dilaion for no fringe shif (as predied by Relaiiy). A90-09 Mihelson Morley Eperimen 9 Spaelike Inerals In lab frame we see wo eens (een A and een ) separaed by a disane (= A ) and ime (= A ) Can we find a roke frame in whih he eens are simulaneous? Le he oordinaes for een A be zero in boh frames. Then we hae A = A = 0 = known = unknown A = A = 0 = known = 0 We wan he speed rel of he roke suh ha = 0. We use he Lorenz ransformaion equaions rel rel = 0 rel rel is he required speed of he roke so ha = 0. Noe ha sine rel <, we mus hae > Thus - < 0 (he spaeime ineral is spaelike) A90-09 Mihelson Morley Eperimen 0 A

6 Mihelson Morley Eperimen Timelike Inerals In lab frame we see wo eens (een A and een ) separaed by a disane (= A ) and ime (= A ) Can we now find a roke frame in whih he eens our a he same loaion? Le he oordinaes for een A be zero in boh frames. Then we hae A = A = 0 = known = 0 A = A = 0 = known = unknown We wan he speed rel of he roke suh ha = 0. We use he Lorenz ransformaion equaions rel rel = 0 rel Again rel is he required speed of he roke so ha = 0. Noe ha sine rel <, we mus hae < Thus - > 0 (he spaeime ineral is imelike) A90-09 Mihelson Morley Eperimen A