1. PH 103 Dr. Cecilia Vogel Lecture 16

2. Review Outline  Relativistic Energy  mass energy  kinetic energy  More consequences of constancy of speed of light  velocity transformation  not vector addition

3. Velocity Transformation  Velocity is distance/time  Since time and distance are different in Einstein’s relativity than classical relativity,  expect velocity transformation is different, too  Velocity transformation:  Differs from text

4. About Your Answer  Note:  Answer will never be bigger than c.  If |v 12 |and |v 23 | are < c, then |v 13 | < c  If |v 12 | or |v 23 | = c, then |v 13 | = c  speed of light the same for both observers  Numerator is classical answer.

5. Using Velocity Transformation  Step 1: Let v 13 = answer you seek.  Step 2: Identify frames 1 and 3 with person or object.  Step 3: Identify frame 2 -- what’s left?  Step 4: Determine value of v 12 and v 23  If you have v 21 or v 32 : change sign & switch  Step 5: Plug in v 12 and v 23 to get v 13  Step 6: Check your answer makes sense!  Big or small? Forward or backward?

6. Speed of Light is c!! Suppose “1” is a beam of light. Stan measures the light to travel at c (i.e. v 12 = c ). If Lou travels at 0.5 c relative to Stan, use the velocity transformation eqn below to prove that the light moves at speed c relative to Lou, too.

8. EXAMPLE A spaceship is approaching the planet Zorgon at a speed of 0.85 c. A diplomatic shuttle is sent ahead to arrive at the planet earlier. How fast should the shuttle be launched relative to the ship, in order to approach the planet at a rate of 0.95 c ? Step 1: Let v 13 = answer you seek. v 13 = shuttle relative to ship Step 2: Identify 1 and 3 with person or object. 1 is shuttle, 3 is ship Step 3: What’s left? 2 is Zorgon Step 4: Determine value of v 12 and v 23 v 12 is v of shuttle relative to Zorgon v 12 = +0.95c v 23 is v of Zorgon relative to ship = -(ship relative to Zorgon) v 23 = -0.85c

9. Step 5: Plug in: Step 6: Check: Numerator is classical answer? 0.1 c. Positive? Should be launched forward Small? Just need to add a bit more to make it head toward planet faster.