Announcements. Lecture 5 Chapter. 2 Special Relativity. The Doppler Effect

Transcription

1 Announements HW1: Ch.-0, 6, 36, 41, 46, 50, 51, 55, 58, 63, 65 *** Lab start-u meeting with TA yesterday; useful? *** Lab manual is osted on the ourse web *** Physis Colloquium (Today 3:40m anelled *** Course Web Page *** htt://highenergy.hys.ttu.edu/~slee/40/ Leture Notes, HW Assignments, Shedule for thephysis Colloquium, et.. Outline: Basi Ideas Leture 5 Chater. Seial Relativity Consequenes of instein s Postulates The Lorenz Transformation quations The Twin Paradox The Doler ffet Veloity Transformation Momentum & nergy General Relativity & a 1 st Look at Cosmology The Doler ffet So far we learned about the transformation of: sae oordinates and time veloity Now, let s study the relativisti transformation of frequeny (how does the light aear in a moving referene frame? The veloity of light is onstant Light is a wave henomenon, i.e. eletromagneti field osillates with a ertain eriod (frequeny very eriod of osillation may be onsidered an event The time interval between two events aears of a different length in different referene frames (time dilation THN The frequeny of osillation must also hange under Lorentz transformation (freqeny ~ 1/ time-eriod

2 BUT this doesn t look like a simle time dilation where dt dt i.e. fobs fsoure / xet for os(" 90 deg. A light soure moves at angle with reset to the line onneting the observer and the soure, and emits a frequeny fsoure in the frame in whih it is at rest (S "t the time between the rodution of wave fonts at oint 1 and in the observer s frame "ta the time interval between the arrivals of the two fonts Seond front has more time to travel, beause the soure has moved away from the observer after 1 Seond front has more time to travel, beause the soure has moved away from the observer after 1 "ta > "t Time of rodution of two wave fronts "ta Differene in arrival times "t the time between the rodution of wave in the observer s frame (i.e. #Tsoure; dilation Time of rodution of two wave fronts "ta "t + v"tos/ (i.e. time it takes the nd font to travel the extra distane, v"tos

3 Seial Case: 0 The soure of light moves away from the observer Seial Case: 90 deg. The soure of light moves erendiular with reset to the observer (shift to lower frequenies Red Shift Transvere Red Shift The origin of the transverse Doler effet is time dilation, this is a ure relativisti effet, no ounterart in lassial mehanis. No lassial analog Doler ffet Relativisti Dynamis Outline: Relativisti Momentum Relativisti Kineti nergy Total nergy Momentum and nergy in Relativisti Mehanis General Theory of Relativity Next Week Quantum Physis

4 Relativisti Momentum the momentum of a artile, m is invariant (does not deend on the veloity Relativisti Kineti nergy Newton s nd Law: exressed in terms of 3-vetors, invariant under G.Tr. (but not L.Tr. Relativisti form of the nd Law (introdued by instein: where definition of the momentum in relativisti mehanis xamle: Calulate the momentum of an eletron moving with a seed of By ignoring relativisti effets, one would get Relativisti Kineti nergy In relativisti mehanis, the onet of energy is more useful than the fore : vv f 1 v0 Total and Rest nergies We exet this result to be redued to the lassial K at low seed: Let s rewrite the exression for K in the form: the total energy the rest energy Limit of small seed: We must use Rel. M. (rather than Cl. M. when K and 0 beome of the same order of magnitude. The energy and momentum are onserved (the onsequene of uniform and isotroi sae. For an isolated system of artiles: kineti energy of a artile of the mass m moving with seed v

5 Another xamle: xressions for (total nergy and Momentum of a artile of mass m, moving at veloity u Classial Limit Classial Limit 1 1 mu <<1 mu <<1 mu m + NW mu m + FAMILIAR kineti energ

6 Kineti nergy K nergy Matter nergy Matter Relativisti Kineti nergy Show that + m 4 follows from # u mu and # u m for momentum and energy in terms of m and u Atomi Bomb (Chater 10: nergy is CRATD From the Mass of Nulei (Internal energy is transformed into kineti energy

7 4 ' ' ' ' m INVARIANT z y x z y x z y x ( ( ( m m m + + TOTAL NRGY Revolutionary Conet What about m? (m + m? (m + TOTAL NRGY INTRNAL NRGY (when 0 INTRNAL m (m + TOTAL NRGY INTRNAL NRGY

8 xressions for (total nergy and Momentum of a artile of mass m, moving at veloity u 1 Classial Limit mu <<1 mu m + Classial Limit Kineti nergy K 1 mu <<1 NW mu m + FAMILIAR kineti energ

9 nergy Matter nergy Matter Atomi Bomb (Chater 10: nergy is CRATD From the Mass of Nulei (Internal energy is transformed into kineti energy # u " # u # "

10 # u # "