Einstein s theory of special relativity

Transcription

1 Einstein s theory of speial relatiity Announements: First homework assignment is online. You will need to read about time dilation (1.8) to answer problem #3 and for the definition of γ for problem #4. First problem soling session will be Tuesday 3-4 and 5-6. Homework is due Wednesday at 1:50pm in wood box in physis help room (GB90). No lass on Monday (MLK) Albert Einstein ( ): Today we will introdue the speial relatiity postulates and think about simultaneity. Physis 170 Spring 009 1

2 From Maxwell s equations, light is an eletromagneti wae with speed: = 1 µ ε 0 0 = m/s Conentional wisdom: Waes must hae a medium to trael in sound in air, tsunami in water, et. Therefore it was belieed light traeled in stationary ether where the speed was m/s. If the ether exists, it is an inompressible, inisible, and non-isous medium whih permeates the unierse (like The Fore). Physis 170 Spring 009

3 The ether Cliker question 1 Set frequeny to DA Suppose the earth moes through the fixed ether with speed. A light wae traeling at speed with respet to the ether is heading in the opposite diretion. Aording to Galilean relatiity, what is the speed of the light wae as iewed from the earth? A) B) + C) Physis 170 Spring 009 3

4 Physis 170 Spring = = + + = + 1 ) ( ) ( d d d d t t down up Boat traels bak and forth aross rier with width How long does it take to omplete eah trip? Up & down rier: Aross rier: d t aross = d t up = d t down + = Boat traels at speed on a rier with urrent at eloity Boat traels up and down a rier a distane of d d 1 d d t t return away = = + You get different results depending on the route taken!

5 Mihelson-Morley experiment in 1887 to see ether effet Earth goes around sun at 30 km/s must be going through ether Measure speed of light in perpendiular diretions Floated in merury so ould rotate to see effet. Also took data at different times of year. Should see ether flow as small as 1 km/s and saw nothing! Physis 170 Spring 009 5

6 Present View: There is no ether Eletromagneti waes are speial. A time-hanging eletri field indues a magneti field, and ie-ersa. A medium ( ether ) is not neessary. Physis 170 Spring 009 6

7 Einstein s relatiity postulate # The speed of light is the same in all inertial frames of referene. The speed of light is the same in all inertial frames of referene. Physis 170 Spring 009 7

8 Cliker question Set frequeny to DA Suppose the earth moes through spae with speed. A light wae traeling at speed with respet to faraway stars is heading in the opposite diretion. Aording to Einstein s relatiity, what is the speed of the light wae as iewed from the earth? A) B) + C) Physis 170 Spring 009 8

9 Time to talk about time Measuring time in different frames Synhronization of loks What time is it? How do you know? Physis 170 Spring 009 9

10 Cliker question 3 Set frequeny to DA Q. The speed of light in a auum is 3.00 x 10 8 m/s. About how long does it take light to trael the length of your arm? A. 1 ms (10-3 s) B. 1 µs (10-6 s) C. 1 ns (10-9 s) D. 1 ps (10-1 s) Speed of light = 3.0 X 10 8 m/s E. 1 fs (10-15 s) = 0.3 m/ns = 300 m/µs (Note also, ~ 1 foot/ns, whih is something I use all the time) Physis 170 Spring

11 Cliker question 4 Set frequeny to DA Q. In a gien referene frame, the time at whih in eent takes plae is gien by: A. The time an obserer at the origin of the referene frame obseres the eent. B. The time anyone in the referene frame obseres the eent. C. The time gien by a loal obserer s lok loated at the eent. D. The time gien by a properly synhronized loal obserer s lok loated at the eent. We hae argued that to desribe a physial eent, we must speify both where it is (in some inertial oordinate system) and what time it ours (aording to some lok). But whih lok? Physis 170 Spring

12 More on referene frames An obserer at (0,0) has a lok; eents there are oered. An obserer at (3m,m) had better hae a lok, too, if you want to know about eents there. And, the two loks had better show the same time. Physis 170 Spring 009 1

13 Synhronizing loks At the origin, at three o lok, the lok sends out a light signal to tell eerybody it s three o lok Time passes as the signal gets to the lok at x = 3m. When the signal arries, the lok at x=3m is set to 3:00 plus the 10 ns delay. This is a properly synhronized lok Physis 170 Spring

14 Simultaneity in one frame Using this proedure, it is now possible to say that all the loks in a gien inertial referene frame read the same time Een if I don t go out there to hek it myself. So we an hae obserers anywhere in the unierse (in the referene frame) with a properly synhronized lok From the loal obserers we an know when and where eents really happen, een if I don t find out until later (when the eent reports get filed). Physis 170 Spring

15 Simultaneity Now we e got loks under ontrol (in one inertial frame) Do eents our at the same time (i.e., simultaneously?) Says who? Physis 170 Spring

16 Cliker question 5 Set frequeny to DA 1 Luy Riky Two firerakers sitting on the ground explode. Luy, sitting on the ground halfway between the firerakers, sees eah explosion at the same time. She knows the loation of eah explosion and reasons that they exploded at the same time. Riky is sitting on the ground next to fireraker. Aording to Riky, whih fireraker explodes first? A. Both explode at the same time B. Fireraker 1 explodes first C. Fireraker explodes first Note that Riky knows how far away eah fireraker is so the fat that he sees # first does not mean he thinks # explodes first. Physis 170 Spring

17 Cliker question 6 Set frequeny to DA 1 Two firerakers sitting on the ground explode. Luy, sitting twie as lose to # as #1, sees the two explosions at the same time. Whih fireraker explodes first in her referene frame? A. Both explode at the same time B. Fireraker 1 explodes first C. Fireraker explodes first Luy If Luy sees the light from both at the same time and knows that #1 is further away, it must hae exploded first. Anyone else in her referene frame will ome to the same onlusion! Physis 170 Spring

18 Simultaneity in two frames A seond frame has its own loks, and moes past me. What happens now? Physis 170 Spring

19 L Luy R Now Luy is the middle of a railroad ar, and sets off a fireraker. Light from the explosion traels to both ends of the ar. Whih end does it reah first? After the fireraker explodes, a spherial wae front of light is emitted. Reahes both ends at the same time. This wae front reahes the two ends at the same time. Note that Luy doesn t find out until later when the obserers at eah end with their synhronized loks report in. But that is an unimportant detail. Physis 170 Spring

20 Cliker question 7 L Set frequeny to DA R Luy Riky Riky is standing still next to the traks, wathing the train moe to the right. Aording to Riky, whih end of the train ar does the light from the explosion reah first? A. Both ends at the same time B. Left end (L) first In Riky s frame, these eents C. Right end (R) first are not simultaneous. Really, they are not simultaneous! Physis 170 Spring 009 0

21 L Luy R Riky Suppose Luy s fireraker explodes at the origin of Riky s referene frame. Physis 170 Spring 009 1

22 L Luy R Riky The light spreads out in Riky s frame from the point he saw it explode. Beause the train ar is moing, the light in Riky s frame arries at the left end first. Loal obserers at ±.5 in Riky s frame say the light arried there at the same time but at this point only the left end of the ar is at.5, the front end is way off at 6 or so. Physis 170 Spring 009

23 L Luy R Riky Sometime later, in Riky s frame, the light athes up to the right end of the train (the light is going faster than the train). Physis 170 Spring 009 3

24 Simultaneity is relatie! Gien two eents loated at different positions: 1) light hits the right end of the train ar ) light hits the left end of the train ar Luy finds that the eents are simultaneous. Riky (in a different referene frame) finds that they are not simultaneous. And they re both right! Physis 170 Spring 009 4

25 Cliker question 8 L Luy Set frequeny to DA R Riky Suppose Luy s fireraker is just slightly toward the right end of the train, so slightly that Riky still measures the light hitting the left end first. Aording to Luy, whih end gets hit first? A. Both ends at the same time B. Left end (L) first C. Right end (R) first Physis 170 Spring 009 5

26 The order of eents isn t een absolute Not only an obserers in the two frames not agree whether the eents at different loations are simultaneous, they may not een agree whih eent ame first. And that s the relatiity of simultaneity. Physis 170 Spring 009 6

27 Exeutie Summary of Time Dilation The proper time t is the time between two eents in the referene frame where both eents take plae at the same loation. So, the proper time of a lok keeping time is the time in the referene frame where the lok is not moing. In an inertial referene frame in whih the lok is moing, the moing lok will be slower by a fator of γ : t = γ t where γ = 1 1 β and β = We will oer time dilation for real next Wednesday. Physis 170 Spring 009 7