


Prayer
Exam 3 ongoing
Project final reports & “Show & Tell”


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”





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 light waves travel at c .
still see
“Time dilation”
  v c g 
1
1
  2 g v / c ground point of view:
  train
 g   ground train point of view: ground
 g   train




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 paradox a. 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

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


Albert, Henry, and simultaneity (expanding spheres of light)


Dr. Colton takes his rocket (0.9 c, planet Zyzyx, 1 light year away. g = 2.29) to

Earth frame: how long does it take?
x=vt: t=1.11 year




Earth frame: how much does Dr. Colton age?
0.485 year
Colton frame: how much does Dr. Colton age?
0.485 year
Colton frame: how fast was planet Zyzyx
“approaching”?
0.9 c
Do you see a problem?
x = vt

ground point of view:
  train
 g
1   ground train point of view: ground
 g
1   train

Which is correct?: Dr. Colton experienced such a short trip because… a. time was slowed down for him b. the distance shrank for him


The length of an object measured by someone at rest with respect to the object is called the object’s: a. Lorentz length b. proper length c. relativistic length d. zeit-length
The term I prefer: “rest length”


It took Dr. Colton so little time because… a. time was slowed down for him b. the distance shrank for him


Who measures Dr. Colton’s trip’s “proper time”?
Who measures Dr. Colton’s trip’s “rest length”?

Thought question: Does Dr. Colton fit inside the barn?
a. Yes b. No
Dr. Colton c. It depends doors
Barn frame:
Colton frame:



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 f
  f c v or...
f
  f
1

1



What do the symbols all stand for?




wavelength l
, frequency f v
 source of red light waves
Dr. Colton c
Source frame: after Dr. Colton hits one wave crest, how fast does the gap between him and next crest “close”?
v+c
Source frame: what’s the time between wave crests for Dr.
Colton?
t = dist./vel. = l s
/(v+c)
Colton frame: is the time between wave crests faster or slower than that? (and by how much?)
Faster, by factor of g
Colton frame: therefore, time between wave crests = … period


 l v source
 c

 g


What’s an event?


When did that happen?
Where did that happen?