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.

Lorentz transformations, graphically

Lee’s program Similarity with rotations How to choose + vs –

Note: for HW problems, you can use Lee’s program to

check your answers—but not to DO your problems.