PH 103 Dr. Cecilia Vogel Lecture 10

Review Outline  Interference  2-slit  Diffraction grating  spectra  Relativity  classical relativity  constants  velocity addition  when is it a good approx

Relativity  means comparing physical quantities measured by observers in different states of motion (aka reference frames).  maybe the values are the same  maybe the values are different  if different, look for patterns,  relationships between the values of the same thing measured by different observer  What is your reference frame?  Doesn’t matter where you are  Just how you are moving

Classical Relativity  Historical  Common experience  Applicable ONLY when all speeds are much less than the speed of light in vacuum.  The following classical relativity ideas hold when v<<c:  Different observers measure same time intervals  Different observers measure same lengths  Different observers measure different velocities...  of each other. Pattern: v AB = -v BA  of another object. Pattern: v 13 = v 12 + v 23

Relative Velocities  Earth is a convenient reference frame  but it is not special  Anyone moving relative to the Earth will observe that the Earth is moving !  If you want to know the velocity of something relative to some observer,  Consider that observer to be at rest,  (pretend you are them)  and ask how does the position of that thing change relative to them?

Relative Velocities  What direction is the water moving in photo?  The water is moving South – relative to Earth.  However, relative to the boy, S  the edge of the water is North of him  and it is getting farther North of him  SO…. it is moving North relative to the boy.

Vector Addition of Velocities  1, 2, & 3 stand for reference frames  (NOT velocities!)  So if v 13 = velocity of Fred relative to Earth, then 1 is Fred and 3 is Earth  Pay attention to the sign : v has direction  Pay attention to order of subscripts:  If car goes North relative to cows,  then cows go South past car v AB = -v BA

Using Vector Addition  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 THE SIGN when you trade subscripts  Step 5: Plug v 12 and v 23 into eqn to get v 13  Step 6: Check that your answer makes sense!

Postulate of Classical Relativity Laws of Mechanics same in all inertial reference frames  What is an inertial frame? One in which Newton’s first law holds  When doesn’t it?! Accelerating frame  Do objects at rest remain at rest when you stop, start, turn corner in your car?  In practice, inertial frame moves at constant velocity.

Different but the Same Laws of Mechanics same in all inertial reference frames  Means: Same mechanics experiment repeated in two different reference frames will yield the same outcome.  Example: Throw a pretzel up and catch it  on Earth  on smoothly flying airplane  same result  Why smooth? -- no acceleration

Different but the Same Laws of Mechanics same in all inertial frames  Means: Same mechanical process observed by observers in different reference frames will  not look the same  but will follow the same laws  Example: Throw a pretzel up and catch it on an airplane in smooth flight  as viewed on plane  as viewed on Earth SAME law of gravity applies to both

Postulate  If all frames yield same laws, then How do you tell whether or not you are moving?  You don’t!  There is NO preferred frame  No frame can claim to be at absolute rest.  All frames at rest relative to themselves.  Relative to the trees, the cars are moving, but relative to the cars, the trees are moving. (Earth is a convenient reference frame for us, but it’s not special in the laws of physics )

Tempted to extend that rule  If there really is no preferred reference frame, then ALL laws of physics should be same for all inertial observers  That’s Einstein’s first postulate of special relativity.