Lecture1-2

O the kinecc energy of our electron is 1000000 ev or

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Unformatted text preview: pCon lines due to cool gas in the galaxy. o  these lines are shi^ed in wavelength if the galaxy is moving relaCve to the earth. u༇ In the Hydra galaxy 200 million light years away, the line is shi^ed from 394 nm to 475 nm in wavelength. 42 Compute velocity from red- shi^ u༇  λ/λ’=394/475=0.8295 u༇  β=0.1848 u༇  Galaxy is moving away with a very large velocity (due to the Hubble expansion of the universe). 43 The Twin Paradox u༇ A twin making a round trip to a nearby star comes back younger than his twin remaining on earth. o  Why is there any difference when the relaCve velociCes are the same? o  We can analyze this with Time DilaCon o  or with the Doppler Shi^. Doppler Shi^ Analysis if the Twin Paradox 44 Example: Time DilaCon Assume the muon lifeCme is τ. If it has a velocity of 0.999c, how far does it travel before it decays? start in a frame at rest with the muon the muon is at the origin assume the muon decays at time τ now boost to the frame in which the earth is at rest x ' = γ ( x − vt ) v # t' = γ %t − 2 $ c γ= x ' = γ ( x − vt ) = γ ( vτ ) 1 v2 1− 2 c t ' = γ (τ ) 1 1 1 1 1 γ= = ≈ ≈ ≈ ≈ 22 2 2 1 − .998 0.002 0.002 v 1 − .999 1− 2 c E = mc 2 in rest frame E = γ mc 2 in earth frame 45 & x( ' Problem: Muon LifeCme u༇  The mean muon lifeCme is about 2 microseconds. Without the Cme dilaCon of SR, how far would a muon moving at a velocity of 0.999c typically travel before it decays? A) 6 m B) 60 m C) 600 m D) 6000 m E) Not enough info to answer. 46 Tough Problem: Muon LifeCme u༇  The mean muon lifeCme is about 2 microseconds. According to SR, how far would a muon moving at a velocity of 0.999c typically travel before it decays? A) 13000 m B) 1300 m C) 130 m D) 13 m E) 1.3 m 47 Minkowski Space (1907) u༇ Hermann Minkowski proposed that special relaCvity could be best expressed in 4 dimensions o  With a new and unusual dot product o  (Important that c=1 or else t→ct ) u༇ We do not noCce this geometry because we move at very small angles from the t axis. o  v/c<<1 Note: I am using a different (sign) convenCon than the book does, but the book makes liole use of 4- vectors… 48 Future, past and light- cone u༇  Humans move almost directly along the Cme axis. Our path through space- Cme is nearly on Cme axis o  Photons move on the light- cone o  We can shoot other parCcles close to the lig...
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