Students act out the classic light clock scenario for deriving time dilation.
This is a kinesthetic activity to help derive the expression for time dilation.
2 people are needed for this skit. It helpts to have each person toss a small ball in the air to represent a photon in the light clock.
Have one person walking with their light clock and one person standing still with their light clock.
“For each light clock, consider two events: the photon is emitted and the photon is detected. How would each person describe these events for a tick of my light clock? For hers?
How do the time intervals for your light clock in (1) your reference frame \(\Delta t\) and (2) your friend's reference frame \(\Delta t'\) compare?
assignment_ind Small White Board Question
10 min.
group Small Group Activity
30 min.
energy conservation mass conservation collision
Groups are asked to analyze the following standard problem:
Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?
assignment Homework
computer Computer Simulation
30 min.
face Lecture
120 min.
Planck distribution blackbody radiation photon statistical mechanics
These notes from the fourth week of Thermal and Statistical Physics cover blackbody radiation and the Planck distribution. They include a number of small group activities.assignment Homework
Writing an operator in matrix notation in its own basis is easy: it is diagonal with the eigenvalues on the diagonal.
What if I want to calculate the matrix elements using a different basis??
The eigenvalue equation tells me what happens when an operator acts on its own eigenstate. For example: \(\hat{S}_y\left|{\pm}\right\rangle _y=\pm\frac{\hbar}{2}\left|{\pm}\right\rangle _y\)
In Dirac bra-ket notation, to know what an operator does to a ket, I needs to write the ket in the basis that is the eigenstates of the operator (in order to use the eigenvalue equation.)
One way to do this to stick completeness relationships into the braket: \begin{eqnarray*} \left\langle {+}\right|\hat{S_y}\left|{+}\right\rangle = \left\langle {+}\right|(I)\hat{S_y}(I)\left|{+}\right\rangle \end{eqnarray*}
where \(I\) is the identity operator: \(I=\color{blue}{\left|{+}\right\rangle _{yy}\left\langle {+}\right|}\;+\;\color{blue}{\left|{-}\right\rangle _{yy}\left\langle {-}\right|}\). This effectively rewrite the \(\left|{+}\right\rangle \) in the \(\left|{\pm}\right\rangle _y\) basis.
Find the top row matrix elements of the operator \(\hat{S}_y\) in the \(S_z\) basis by inserting completeness relations into the brakets. (The answer is already on the Spins Reference Sheet, but I want you do demonstrate the calculation.)
group Small Group Activity
30 min.
group Small Group Activity
30 min.
assignment_ind Small White Board Question
10 min.
Special Relativity Spacetime Diagrams Worldlines Postulates of Relativity
Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.