2. Planet Earth Einstein’s Theory of Special Relativity

3. Classical Physics Review Length and Time –Define a standard for each and compare the unknowns to them. Kinematics –derive from length and time velocity and acceleration –v =  x/  t –a =  v/  t If a is constant –v = at and x = 1/2 a t 2 –as t goes to infinity v goes to infinity

4. Dynamics Newton’s Laws (existence and strength of all forces –Law of inertia –F = ma –Law of mutual interaction Conservation laws –Momentum –Energy Electricity and Magnetism –Maxwell’s equations for the dynamics of charged particles

5. Implicit Assumption All the laws of nature have the same form in all frames of reference moving at constant velocity with respect to each other. Transformation Laws between frames. S S’ vt x X’X’ X ’ = x - vt and V’ = V - v

6. Trouble All observers can use the same laws, and communicate! Michelson-Morley Experiment –to study the nature of light - particle or wave –if it is a wave - what is the nature of the medium? –search for the ether –the experiment was null

7. Einstein’s Postulates All the laws of nature have the same form in all frames of reference moving at constant velocity with respect to each other. The speed of light is a constant for all observers moving at constant velocity with respect to each other.

8. New Transformation Equations  t =  t 0 / (1 - v 2 /c 2 ) 1/2  x =  x 0  (1 - v 2 /c 2 ) 1/2 m = m 0 / (1 - v 2 /c 2 ) 1/2 V’ x = (V x - v) / (1 - V x  v/c 2 )

9. Time dilation  t =  t 0 / (1 - v 2 /c 2 ) 1/2 A space ship goes by at v =.8c. Someone on the ship drops a ball 16 ft. and measures a time of flight of 1 sec (  t 0 ). What does a stationary observer measure (  t )?  t =  t 0 / (1 - v 2 /c 2 ) 1/2 = 1/(1 -.64) 1/2 = 1.67 sec. 16 ft.

10. Length Contraction  x =  x 0  (1 - v 2 /c 2 ) 1/2 If the ball on the spaceship has a diameter of 5 cm (  x 0 ) as measured by someone on the ship. What is its diameter as measured by a stationary observer (  x )?  x =  x 0  (1 - v 2 /c 2 ) 1/2 = 5  (1 -.64) 1/2 = 5 .6 = 3cm 16 ft.

11. Mass Increase m = m 0 /(1 - v 2 /c 2 ) 1/2 Same ball has a mass of 10 gm as measured by someone on the ship( m 0 ). What is the mass as measured by the stationary observer (m)? m = m 0 /(1 - v 2 /c 2 ) 1/2 = 10/(1 -.64) 1/2 = 10/.6 = 16.7 gm 16 ft.

12. Addition of velocity V’ x = (V x - v) / (1 - V x  v/c 2 ) A space ship goes by at.8c (v) and watches someone on earth turn on a flashlight. What is the speed of the light as measured by the observer on the ship? Note the result is independent of v! V’ x = (V x - v) / (1 - V x  v/c 2 ) = ( c -.8c)/(1 - c .8c/c 2 ) = c SS’ V =.8c

13. Compare fictitious space ship speed with actual escape speed Fictitious speed of.8 c gives the results on the previous slides. Actual escape speed is about 7 mi/sec. The speed of light is 186,000 mi/sec. The escape speed can be written as.00004c try to redo the previous slides with this speed instead of.8c! For everyday experience v/c is very small and Einstein’s equations reduce to the ones on slide 4

14. Implications of variable mass The faster an object moves the harder it is to move it any faster. Kinetic energy is not the total energy of a moving object –E = KE + m 0  c 2 = m  c 2 –Rest energy exist. A particle has energy by virtue of its existence. We have already discussed many applications of this fact!

15. Suppose the ultimate speed was 100 miles/hour What would the three equations predict for a speed of 80 miles/hour or.8c? The same as already predicted but you would see it!

16. Trends Graph of ratios of masses times and lengths