Announcements 11/20/12 Prayer Lab 10, HW 36 due tonight Exam 3 starts Monday after break Exam 3 review: Monday, 4:30 – 6 pm, this room Close to Home

From warmup Extra time on? Other comments? a. a.You might know this already, but the Mythbusters did an experiment where they shot a soccer ball out of a cannon positioned at the back of a truck to illustrate the effects of the Galilean velocity transformation equation, and they succeeded in canceling out the two velocities. Here's a link to the video

About the Exam…

Clicker question: From my point of view, objects which experience no force don’t accelerate. What type of reference frame am I in? a. a.An “Einsteinian” reference frame b. b.An “enlightened” reference frame c. c.An “inertial” reference frame d. d.A “null” reference frame e. e.A “unique” reference frame

Fictitious forces Toss a ball straight up, in car. Slam on the brakes. What happens? Throw a ball to a friend on a merry-go-round (as it’s spinning). What path does the ball take? Reference frames where Newton’s Laws apply: “inertial frames”

Galilean Relativity Credit: this slide and next one from Dr. Durfee v 1 = 80 mph v 2 = 100 mph

Galilean Relativity v 1 = 0 mph v 2 = 20 mph Reference frame moving with car 1

HW 37-3 A 1 kg object (m 1 ) collides with a 2 kg object (m 2 ) on a frictionless surface. Before the collision, m 1 is traveling at 9 m/s to the right and m 2 is at rest with respect to the ground. The collision is elastic and m 1 bounces straight back to the left. a. a.Figure out the final velocities of both masses after the collision. [Hint given.] b. b.A bicycle rider moving at 5 m/s to the right (relative to the ground) observes the collision. Show that both kinetic energy and momentum are also conserved in her frame of reference. All valid physical laws are true in all inertial reference frames

Bike lights I’m riding my bike at 1  10 8 m/s. I turn on my front bike light (c=3  10 8 m/s). a. a.How fast does someone on the ground see the light waves go away? b. b.How fast do I see the light waves go away? Changing magnetic field  electric field Changing electric field  magnetic field Nothing in equations says anything about the flashlight!!! (the source of waves) Maxwell Eqns: speed of waves is

Compare to Sound Source stationary: sound waves travel at 343 m/s (as measured by both source and observer) Source moving at 100 m/s: ?  sound waves still travel at 343 m/s (as measured by both source and observer). Only frequency will be changed. Why is it a Big Deal that light waves do the same thing?

Einstein: There is no problem Postulate 1: The laws of physics apply in all inertial reference frames. Postulate 2: The speed of light is the same for all inertial observers, regardless of motion of the light source or observer. The “Big Deal”: these two simple statements have some crazy implications, as we shall see. Michelson-Morley experiment

From warmup The Galilean velocity transformation equation, Eqn 39.2 (8th edition), is simple--much simpler than its name implies. It's also sometimes called the "classical velocity addition" formula. It's "obviously" true. Use it to answer this question: A pickup truck is traveling at 5 m/s. A man standing in the back of the truck throws a ball forward at 10 m/s (relative to himself). How fast will someone on the ground measure the ball to be traveling? What is the faulty assumption on which the equation relies? a. a.The person on the ground would measure the speed to be 15 m/s (speed of frame + speed of ball). I believe that the faulty assumption in this equation is that time is the same in each frame, not dependent on their velocity.

From warmup Explain in your own words (in language that your non- physics-major roommates could understand) how the Galilean velocity transformation equation and the 2nd postulate of special relativity are at odds with each another. a. a.The Galilean velocity transformation equation assumes that speed will always add up, so if you switched on a flashlight while on a pickup truck moving forward with speed v, you would get c + v as the speed of the light. However, the second postulate states that nothing can move faster than the speed of light...unless you have a Lorentzian manifold which allows you to warp space-time to create a warp bubble (Go Dr. White!).

Example: Light Ray on a Train If height of train car inside is h, how long did that take (to me, inside the train)? Credit: animations from Dr. Durfee Answer: t = 2h/c

As seen from ground If height of train car inside is h, how long did that take (to you, on the ground)? Train is traveling at speed v Answer: t = 2h/c  (1-v 2 /c 2 ) -1/2 How long did it take, really? Why doesn’t this “problem” exist with sound waves?

Notation Time measured by me, on train:  t Time measured by you, on ground:  t  Answer 2 (measured on ground): t = 2h/c  (1-v 2 /c 2 ) -1/2 Answer 1 (measured on train): t = 2h/c For v = 0.9c:  = 0.9  = 2.3 v/cv/c 

Think about this… Suppose I, Dr. Colton (in the train), measure a time interval to be 1 second, presumably through lots and lots of light bounces or something along those lines. If the train is moving at 0.9c, you, the class (on the ground) measure that time interval to be 2.3 s. To you, it looks like things in the train are running in slow motion. However, what if you on the ground are the one that is bouncing light rays back and forth. If you measure a time interval to be 1 s, how long will that interval look like, to me on the train? a. a.1 s. That is, to Dr. Colton, it looks like things on the ground are running normally b. b.(1/2.3) s. That is, to Dr. Colton, it looks like things on the ground are sped up c. c.2.3 s. That is, to Dr. Colton, it looks like things on the ground are running in slow motion. To you, my time appears to be slowed. To me, your time appears to be slowed. Who is right?

Twin “Paradox” Speedo & Goslo…which twin is older?

Simultaneity Dr. Colton on train, again Turn the flashlights on at the same time, the photons reach the walls simultaneously. OK?

Simultaneity Viewed from the ground; train moving to right. Which light ray travels farther? Which light ray hits the wall first? Events which happen simultaneously in one “reference frame” do NOT happen simultaneously in any other reference frame

A different effect Light from which lightning bolt will reach Jim first? Jim Slide credit: Dr Durfee, again

Jim

Jim’s friends all record the actual times in Jim’s reference frame Or equivalently, Jim is just smart enough to factor out the time the light took while traveling. An “array” of observers Jim Jim’s friends