Exploring Special Relativity Concepts

Special Relativity Contents: The End of Physics Michelson Morley Postulates of Special Relativity Time Dilation

The End Of Physics 1900 +/- 5 The End of physics Black Body Radiation -> Quantum mechanics Velocity of light With Respect to ether Maxwell s Equations 1 = c o o But what does light move through? Ether

Michelson Morley Path parallel to ether should take a bit longer Tried it in January Tried it in June The Earth is at rest in ether Or the path parallel to the ether shrinks Or, there is no ether So what does light travel through ?

Einsteins Gedanken If we caught up to an EM wave what would we see: B and E fields with nothing to create them This is impossible Therefore we cannot catch up to light waves

Postulates of Special Relativity First Postulate: The laws of physics are the same in all inertial frames of reference There is no experiment you can do to ascertain whether you are moving. (i.e. all motion is relative) Second Postulate: The speed of light is the same no matter what speed the source or observer is going (i.e the speed of light is a law of physics) (examples of this with cars/observers/galilean vs relativistic transforms)

The speed of the photons was independent of the speed of the pion

Time Dilation How the clock works What proper time is

Time Dilation Earth observer sees light traveling at speed of light Time is longer (i.e the clock runs slower) Derive Moving clocks run slower Examples: (time elapsed, velocity, factor of c)

Lorentz factor: Factor Vs V 8 7 6 5 Factor 4 3 2 1 0 0 0.5 1 1.5 Speed in c You can safely ignore relativistic effects to about .2 c

Example 1: If you drive by the school at 40.0 m/s, how long do we see your watch take to register 10.0 seconds? What about 40,000. m/s? .200 c? .500 c? ?, ?, 10.2 s, 11.5 s

Example 2: If we see your watch take 12 seconds to register 10. seconds, how fast are you going? (Show solution for c) .55c

Length Contraction l lo Moving objects shrink in the direction of motion 2 v = 1 L L o 2 c This reconciles the frames of reference

Mass Dilation Electron with 1.0 MeV Ke: m = 1.00 MeV + 0.511 MeV =1.511 MeV Electron at rest mo = 0.511 MeV e e Moving objects gain mass m = o m 2 v 1 2 c (The gained mass is energy mass as in E = mc2)

Example 3: A car that is 5.0 m long is going .60 c past us. How long is the car in our frame of reference? 4.0 m

Example 4: What is the speed of an electron if it has a mass of 0.634 MeV. (Its rest mass is 0.511 MeV) (What is its kinetic energy? through what potential was it accelerated?) 0.592 c

Whiteboards: Time Dilation, Length Contraction, Mass Dilation 1 | 2 | 3 | 4

Moe and Joe have clocks that tick every 10.00 seconds. Joe is flying by at .85 c. What time does Moe see Joe s clock take to tick? (trick with c) 19 s

Two stopwatches, one sitting still, one moving in a very large circle. The clock at rest ticks every .800 s, the moving one ticks every 1.200 s. What speed is the moving watch going? Show the general solution .75 c or 2.24 x 108 m/s

Moe and Joe both have identical watches. Joe is moving with respect to Moe at .85c. If 15 s elapse on Moe s clock, how much time has elapsed on Joe s clock? answer 7.9 s

Muons have a mean life of 2.2 x 10-6 s at rest. What speed are they traveling if they they have an average lifetime of 2.6 x 10-6 s? How far would they travel before decaying on the average? answer .53c, 1.6 x 108 m/s, 415 m

An electron has a rest mass of 0.511 MeV, and a moving mass of 1.511 MeV. What is its speed ? answer 0.941 c

What speed does a 45 foot long bus need to go to fit exactly into a tunnel that is 40. feet long? answer 0.46 c

Paradoxes Planet X Joe stays on earth Moe goes to planet x that is 30 Ly away at .99 c Comes back How old Moe is/Joe is Does this violate Special relativity? Inertial means no acceleration What they see

Paradoxes Planet X Planet X It s all relative Moe sees our clocks slow down too Postulates only apply to inertial frames of reference