Can you guess. 1/18/2016. Classical Relativity: Reference Frames. a x = a x

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Nelson Long
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1 /8/06 PHYS 34 Modern Phsis Speial relaii I Classial Relaii: Referene Frames Inerial Frame of Referene (IFR): In suh frame, he Newons firs and seond laws of moion appl. Eample: A rain moing a a Consan eloi. Todas Conens: a) Classial Relaii and Galilean Transform b) Einsein s Posulaes ) The relaii of ime and lengh d) Loren Transform e) The relaii of eloi Non-Inerial Frame of Referene: An aeleraing or deeleraing objes. Eample: A ake-off phase of a roke. For an asronau siing in he hair F up > 0, bu aeleraion relaie o he roke a = 0 F up > m*a, Newon s seond law fails in he roke frame. Classial Relaii: Cornersone of Classial Phsis The Newon s Laws hae he same forma in all inerial frames of referene (IFR). a = a Classial Relaii: Cornersone of Classial Phsis Galilean Transformaion Time and spae ransformaion, ensuring Newon s laws are he same in all IFRs. Can ou guess. F = ma = ma = F The laws of E&M, inluding speed of ligh, are also he same in all inerial frames of referene., deermined onl b auum permeabili (magnei onsan) and auum permiii (eleri onsan)

/8/06 Eperimens of Ligh Speed: Alwas C Assume he ar is he earh, he ligh speed in all direions is = 9979458m/s. This eperimen is done b Mihelson, he firs US iien o win he Nobel Prie in phsis.

(guessing) The ligh speed is independen of he frame of he referene. (eperimenal fa) Based on phsis ha ou hae learned, do ou feel omforable o aep boh argumens simulaneousl?

2 /8/06 Eperimens of Ligh Speed: Alwas C Assume he ar is he earh, he ligh speed in all direions is = m/s. This eperimen is done b Mihelson, he firs US iien o win he Nobel Prie in phsis. hps:// Le us hink from guessing and fa The law of all phsis are he same in all inerial frames of referene. (guessing) The ligh speed is independen of he frame of he referene. (eperimenal fa) Based on phsis ha ou hae learned, do ou feel omforable o aep boh argumens simulaneousl? I indiaes wo possibiliies: eiher he earh has no relaie speed o he ligh propagaion medium, or he ligh speed is independen of he frame of he referene. Disuss and Debae! Le us hink from guessing and fa The law of all phsis are he same in all inerial frames of referene. The ligh speed is independen of he frame of he referene. Einsein s Posulaes of Relaii The form of eah phsis law is he same in all inerial frames of referene. Feel unomforable beause of Galilean Transformaion. Ligh moes a he same speed relaie o all frames of referene. Einsein ( )

3 /8/06 Mus modif Galilean Transformaion Ligh Clok Ligh pulse bounes beween wo mirrors perpendiular o direion of moion. A one-wa rip is one uni of ime Δ = d/ Einsein found ha he definiion of ime is ambiguous. We need o redefine ime using a phsial sandard. Moing ligh lok has longer ineral beween ligh round rips. Moing lok is slower han he res one! Ligh Clok Sai Ligh Clok Consider pulse of ligh bouning beween wo mirrors hp://galileoandeinsein.phsis.irginia.edu/more_suff/flashles/lighlok.swf d Δ o = d / Aknowledgemen: The eperimen slides from PRAVEEN MOHAN 3

4 /8/06 Moing Clok Moing Clok Consider pah of pulse of ligh in moing frame of referene: Ligh Clok Eleaor moing upward a a onsan eloi,. Δ d uδ Aknowledgemen: The eperimen slides from PRAVEEN MOHAN Aknowledgemen: The eperimen slides from PRAVEEN MOHAN Calulae Time Dilaion The Conep Reoluion of Time ( Δ) = d + (u Δ) d = ( Δ) -(u Δ) d / = Δ -(u / ) Δ d / = Δ [ - (u / )] / Δ d uδ Noie ha d = Δ o for sai lok. hps:// We hae he relaion of ime duraions beween he sai lok and he moing lok. Δ o = Δ [- (u / )] / Δ o < Δ, sai lok faser 4

5 /8/06 Lengh Transformaion L = L 0 (?) Lengh Conraion Δ o = L 0 / (L 0, Δ o in mirror frame) L 0 Δ = L+ u Δ Δ= Δ + Δ = L/ [- (u / )] - (L, Δ in lab frame) Δ o = Δ [- (u / )] / (ime relaion) Δ = L- u Δ L = L 0 [- (u / )] / Δ= Δ + Δ = L/ [- (u / )] - Objes look shorer when he moe! Lengh Conraion Sole Muon Parado Conraion akes plae onl in he direion of moion. If an obje is moing horionall, no onraion akes plae eriall. 5

/8/06 ICP3 (0 mins): ICP3 (0 mins): Quesion A (in he Earh Frame of Referene) Calulae he muon life ime in he Earh frame of referene, and alulae how far muon an rael before i deas in he Earh frame.

6 /8/06 ICP3 (0 mins): ICP3 (0 mins): Quesion A (in he Earh Frame of Referene) Calulae he muon life ime in he Earh frame of referene, and alulae how far muon an rael before i deas in he Earh frame. (hin: earh is moing owards muon, so he earh lok is slower han he lok in muon s own lok) Δ o = Δ [- (u / )] / Quesion B (in he muon frame of referene) Calulae he disane from he op amosphere o he Earh s surfae (3 Km in he Earh frame) in he muon s own frame of referene. To rael his disane, how muh ime does muon needs in erms of he muon s own frame of referene? Does muon has enough ime o reah he Earh s surfae before i deas? L = L 0 [- (u / )] / Rehek he Relaii Coordinae Transformaion Δ = Δ o / [- (u / )] / L = L o [- (u / )] / Δ o is he ime duraion in he moing obje own frame. Δ is he ime duraion in he lab frame. L 0 is he spae separaion in he moing obje own frame. L is he spae separaion in he lab frame. Δ o = -, L o = - Δ= -, L= - Hendrik Loren (853-98) 6

7 /8/06 7 Loren Transformaion where - ICP4 (0 mins): Proe ime dilaion and lengh onraion from Loren ransformaion. where -? Δ o = -, L o = - Δ= -, L= - L = L o [- (u / )] / Δ = Δ o / [- (u / )] /

The Special Theory of Relativity Chapter II

The Special Theory of Relativity Chapter II The Speial Theory of Relaiiy Chaper II 1. Relaiisi Kinemais. Time dilaion and spae rael 3. Lengh onraion 4. Lorenz ransformaions 5. Paradoes? Simulaneiy/Relaiiy If one obserer sees he eens as simulaneous,