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Georges Braque, Man with Guitar

History: Special Relativity ‘ s impact on 20 th century art.

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Georges Braque, Man with Guitar

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  1. History: Special Relativity‘s impact on 20th century art “In the intellectual atmosphere of 1905 it is not surprising that Einstein and Picasso began exploring new notions of space and time almost coincidentally.….Just as relativity theory overthrew the absolute status of space and time, the cubism of Georges Braque and Picasso dethroned perspective in art.” Georges Braque, Man with Guitar

  2. Relativistic addition of velocities example (part a) A spaceship moving away from earth at 0.900c fires a robot probe at 0.700c relative to the spaceship. What is the probe’s velocity relative to the earth ? Let S and S’ be the reference frames of the Earth and the Spaceship. Their relative velocity of S’ and S are u=0.900c. Note the sgn

  3. Relativistic addition of velocities example (part b) A scoutship is sent to catch up at 0.950 relative to the earth. What is the velocity of the scoutship relative to the spaceship ? Let S and S’ be the reference frames of the Scoutship and the Spaceship. Their relative velocity of S’ and S are u=0.900c. Note the sgn

  4. What is the Doppler effect for electromagnetic waves ? “Blueshift” “Redshift” Source moving towards observer Source moving away from observer

  5. Doppler effect for electromagnetic waves M87 Source approaching observer, “blue shift”, u is the speed of the source relative to the observer. The frequency of the source in its rest frame is f0 Jet being ejected from a black hole. (f0 =6.7 x 1014Hz f=5.6 x 1013Hz) Red shift or blue shift ? Source moving away from observer, “red shift”, u is the speed of the source relative to the observer. The frequency of the source in its rest frame is f0

  6. Doppler effect (non-relativistic case) Source approaching observer, “blue shift”, u is the speed of the source relative to the observer. The frequency of the source in its rest frame is f0 What should I do next ? Why ?

  7. Doppler effect for electromagnetic waves (non-rel) Use the binomial expansion ! Uum what’s that ? What happened to u2/c2 ? Warning !!: Only works for the non-relativistic case u<<c

  8. Applications of Doppler effect for EM waves Many examples of Youtube videos for ambulance and police sirens (please pay attention to the Doppler effect for sound !) https://www.youtube.com/watch?v=YxlMvxEs2H8

  9. Example of Doppler effect for EM waves (blue shift) How fast must you be approaching a red traffic light (λ=675 nm) for it to appear green (λ=575 nm) ? Not a good excuse for a speeding ticket

  10. Relativistic momentum From our discussion of Lorentz transformations, velocities depend on the reference frame. Hence classical momentum will not be conserved in all inertial reference frames. This is a serious problem. What can we do ? Ans: define relativistic momentum (and later energy)

  11. Relativistic momentum (cont’d) Now introduce relativistic mass

  12. Relativistic Force (on our way to E=mc2) If v is along the x-axis and acceleration is constant, then can obtain a simple form for F. Use d/dx(xn)=nxn-1

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