Classical Relativity Review and Application in Physics

1. PH 301 Dr. Cecilia Vogel Lecture 1

2. Review • PH 201-3 • Mechanics • Relative motion • Optics • Wave optics • E&M • Changing E and B fields Outline • Relativity • classical relativity

3. Relativity • Comparing physical quantities measured by observers in different states of motion. • Maybe measure the same value • Maybe measure different values • if different, look for patterns or equations relating the values

4. Classical Relativity • Historical • Relative motion in PH 201 • Applicable ONLY if all speeds are much less than the speed of light in vacuum

5. Classical Relativity • True (or very close to true) when v<<c: • Different observers measure same distance between objects • Different observers measure same time • Different observers measure different position and velocity • of each other. Pattern: • of another object. Pattern: DEMO

6. Vector Addition of Velocities • u and u’ are velocities of same object • measured by different observers • So if u = velocity of ___ relative to ___, then u’ is = velocity of ___ relative to ___. • v is relative velocity of those two observers • Pay attention to the sign: forward or back? • Pay attention to order: • If Fred goes North relative to Earth, then Earth goes South relative to Fred.

7. Using Vector Addition • Step 1: Let u = answer you seek. • Step 2: u = velocity of A rel to B, so A and B are determined. • Step 3: Identify frame C -- what’s left? • Step 4: Determine u’ • u’= velocity of A rel to C • If you have C rel to A, use opposite sign • Step 5: Determine v • v = velocity of C rel to B • If you have B rel to C, use opposite sign • Step 6: Plug in the numbers to compute u. • Step 7: Check that your answer makes sense!

8. Example Red car is traveling at 65 mph in the positive direction relative to the road. Blue car is behind the red car traveling in the same direction at 60 mph. Find the velocity of the blue car relative to the red car.

9. Different but the Same Laws of Mechanics same in all inertial reference frames • Means: Same experiment repeated in two different reference frames will yield • different numbers, • but the same laws. • Example: Throw a pretzel up and catch it during a smooth airplane flight (Why smooth?a = 0, inertial frame)

10. Different but the Same Laws of Mechanics same in all inertial frames • Example: Throw a pretzel up and catch it on an airplane in smooth flight • plane observer sees straight up and down • Earth observer see parabolic motion • as viewed on plane as viewed on ground • Both observe same acceleration of gravity!

11. Postulate • If all frames yield same laws, then • How do you tell whether or not you are moving? • No mechanics experiment will determine whether you are moving at constant v or at rest. • There is NO preferred reference frame • there is no absolute rest. • there is no absolute motion. • must give velocity relative to something. • Earth is convenient for us, but not special for laws of physics.

12. Extend that rule • If there really is no preferred reference frame, then • ALL laws of physics should be same in all inertial reference frame • Mechanics, thermo, E&M, optics, … • That’s Einstein’s first postulate.

13. Electricity and Magnetism • Laws of E & M determine the speed of electromagnetic waves in a vacuum, i.e. “the speed of light.” • So if all laws of physics are the same for all inertial observers, then • the laws of E& M are the same • so the speed of light is the same • That’s Einstein’s 2nd postulate • How can that be?

14. Conundrum If Einstein’s postulate is true: • speed of light is same for all • sunlight relative to the sun would have speed c • and relative to spaceship would also have speed c If classical relativity were true: • u = u’ + v would hold • sunlight relative to the sun would have speed c • but relative to spaceship would have speed c + v