Announcements 4/4/11 Prayer Exam 3 ongoing Project final reports & “Show & Tell”

Reading Quiz Which of these topics related to relativity

was in today’s reading assignment?a. “length contraction”b. “Lorentz transformations”c. “rest energy”d. “relativistic momentum”e. “velocity addition”

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. Delayed observation due to time of light travel

a. 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

Twin paradoxa. Resolved because the equations we’ll discuss only

apply to inertial reference frames (no acceleration). Simultaneous events

a. Things that happen at same time in one reference frame will NOT be simultaneous in another one.

b. Dr. Colton with flashlights in train

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)

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 experienced such a short trip because…

a. time was slowed down for himb. the distance shrank for him

1ground point of view:

train groundx x

1train point of view:

ground trainx x

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

It took Dr. Colton so little time because…a. time was slowed down for himb. the distance shrank for him

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

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

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

What do the symbols all stand for?

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?