Announcements 12/1/10 Prayer Exam 3 ongoing Friday’s lecture: no reading assignment Project Show & Tell – only 3 volunteers so far. Up to
15 extra credit points available! (for each group member) Email me by Saturday night.
All late homework & extra credit papers due Sat, Dec 11
Very Important Definitions
“gamma” is sometimes called “the Lorentz factor” or “the time dilation factor”
v
c 2
1
1
Space-time diagrams
Example: me slamming the book on the table
Example: me slamming the book on the table again
Example: measuring the time between book slams
Example: measuring the length of the book
“World lines” for Dr. Colton, book, & for space traveler passing by earth
a. When/where do these events occur?
t vs. ct
Quick Writing
Back to Dr. Colton’s trip to Zyzyx (Dr. Colton traveling at 0.9 c). Draw, as accurately as you can, these four world-lines:
a. The planet Earthb. The planet Zyzyxc. Dr Colton, as he travels to Zyzyxd. Leaving from the Earth at the same
time/place, a light beam that travels to Zyzyx
Draw, as accurately as possible, the same four world-lines, from Dr. Colton’s point of view.
Light cones
Present Possible futures Possible pasts “Elsewhere” Terminology: “timelike” vs “spacelike”
Example
Dr. Colton, on a fast train, turns on a flashlight at ct=1. People on the ground watch. Draw worldlines for Dr. Colton and the people on the ground. Draw the light from the flashlight. Mark the “flashlight turned on” event.
Do this for both frames of reference.
Reading Quiz
The Lorentz transformation equations in the book assume objects only have relative motion in the +x or –x directions
a. Trueb. False
The Lorentz transformation equations for y and z are more complicated than the equations for x and t.
a. True b. False
Lorentz Transformations, derived
Not in this class! ;-)
Can be done by using properties we’ve discussed: length contraction, time dilation, gamma, basic worldline transformations
The Lorentz Transformations
As regular equations:
In matrix form:
frame2 frame1 frame1( )x x ct
frame2 frame1 frame1( ) ( )ct x ct
frame2 frame1
x x
ct ct
Differences between my equations & book’s equations
Disclaimer: I often reverse order of x and ct. That’s OK.