Announcements 11/28/11 Prayer Exam 3 ongoing, ends on Saturday Next Wednesday: Project “Show & Tell”

a. I’ll pick 4 groups to do 10 min presentationsb. If you volunteer, you get 3 extra credit ptsc. If I select you, you get 6 more extra credit ptsd. If I pick you, but you then back out, you get docked

ptse. To volunteer, send me an email by Wed night. Tell me

why I should pick you: what is especially cool about your project that other students will be interested in?

Foxtrot

What we learned last time Einstein’s postulates Light: like sound, speed of wave doesn’t depend

on speed of source Light: unlike sound, there is no medium… if

source is in an enclosed train car, observer on ground will still see light waves travel at c.

“Time dilation”

v/c

2

1

1

v

c

train point of view:ground train

t t

ground point of view:train groundt t

What we learned last time, cont. Twin paradox

a. Resolved because the equations we’ll discuss only apply to inertial reference frames (no acceleration).

Simultaneous eventsa. Things that happen at same time in one reference

frame will NOT be simultaneous in another one.b. Dr. Colton with flashlights in train

Delayed observation due to time of light travela. We’ll ignore, unless specifically stated in problem. b. I.e., if problem says “Joe measures such-and-such to

occur at t = 5 s,” that means he has already accounted for that time delay somehow

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

Video Albert, Henry, and simultaneity (expanding

spheres of light) (1:35)

Considering space travel… Dr. Colton takes his rocket (0.9 c, = 2.29)

to planet Zyzyx, 1 light year away.

Earth frame: how long does it take?

Earth frame: how much does Dr. Colton age?

Colton frame: how much does Dr. Colton age?

Colton frame: how fast was planet Zyzyx “approaching”?

Do you see a problem?

x=vt: t=1.11 year

0.485 year

0.485 year

0.9 c

x = vt

Length contraction

Which is correct?: Dr. Colton aged so little because…

a. time was slowed down b. the distance shrank

1ground point of view:

train groundx x

1train point of view:

ground trainx x

Earth F.O.R.

Colton F.O.R.

Video

Twin paradox (3:40)

Reading quiz

The length of an object measured by someone at rest with respect to the object is called the object’s:

a. Lorentz lengthb. proper lengthc. relativistic lengthd. zeit-length

The term I prefer: “rest length”

Proper time & Rest length

Dr. Colton aged so little because…a. time was slowed down for him (Earth

view)b. the distance shrank for him (Colton view)

Who measures Dr. Colton’s trip’s “rest length”?

Who measures Dr. Colton’s trip’s “proper time interval”?

Barn paradox

doors

Barn frame:

Colton frame:

Dr. Colton

Thought question: Does Dr. Colton fit inside the barn?

a. Yesb. Noc. It depends

Relativistic Doppler effect

A.k.a. “Doppler effect for light”a. Must be relativistic, because you don’t get

a measurable frequency/wavelength shift until source/observer speed is close to speed of light wave

Equation, used back in HW 19-4

If moving towards each other: num: + den: -

c vf f

c v

1or...

1f f

Relativistic Doppler effect: Derivation

Source frame: after Dr. Colton hits one wave crest, how fast does the gap between him and next crest “close”?

Source frame: what’s the time between wave crests for Dr. Colton?

Colton frame: is the time between wave crests faster or slower than that? (and by how much?)

Colton frame: therefore, time between wave crests = …

v

Dr. Coltonsource of red light waves c

wavelength , frequency f

v+c

t = dist./vel. = s/(v+c)

Faster, by factor of

1sourceperiodv c

Events

What’s an event?

When did that happen? Where did that happen?