title, topic, keyword
Small group, whiteboard, etc
Required in-class time for activities
Leave blank to search both

Activities

Small White Board Question

10 min.

##### Possible Worldlines
Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.
• Found in: Theoretical Mechanics course(s)

Kinesthetic

5 min.

##### Time Dilation Light Clock Skit
Students act out the classic light clock scenario for deriving time dilation.

Small White Board Question

10 min.

##### Time Dilation
• Found in: Theoretical Mechanics course(s)

Lecture

30 min.

##### Lorentz Transformation (Geometric)
In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.
• Found in: Theoretical Mechanics course(s)

Small Group Activity

5 min.

##### Events on Spacetime Diagrams
Students practice identifying whether events on spacetime diagrams are simultaneous, colocated, or neither for different observers. Then students decide which of two events occurs first in two different reference frames.
• Found in: Theoretical Mechanics course(s)

Small Group Activity

30 min.

##### Right Angles on Spacetime Diagrams
Students take the inner product of vectors that lie on the spacetime axis to show that they are orthogonal. To do the inner product, students much use the Minkowski metric.
• Found in: Theoretical Mechanics course(s)

Problem

5 min.

##### Events on Spacetime Diagrams
1. Which pairs of events (if any) are simultaneous in the unprimed frame?

2. Which pairs of events (if any) are simultaneous in the primed frame?

3. Which pairs of events (if any) are colocated in the unprimed frame?

4. Which pairs of events (if any) are colocated in the primed frame?

1. For each of the figures, answer the following questions:
1. Which event occurs first in the unprimed frame?

2. Which event occurs first in the primed frame?

• Found in: Theoretical Mechanics course(s)

Problem

##### Energy of a relativistic Fermi gas

For electrons with an energy $\varepsilon\gg mc^2$, where $m$ is the mass of the electron, the energy is given by $\varepsilon\approx pc$ where $p$ is the momentum. For electrons in a cube of volume $V=L^3$ the momentum takes the same values as for a non-relativistic particle in a box.

1. Show that in this extreme relativistic limit the Fermi energy of a gas of $N$ electrons is given by \begin{align} \varepsilon_F &= \hbar\pi c\left(\frac{3n}{\pi}\right)^{\frac13} \end{align} where $n\equiv \frac{N}{V}$ is the number density.

2. Show that the total energy of the ground state of the gas is \begin{align} U_0 &= \frac34 N\varepsilon_F \end{align}

• Found in: Thermal and Statistical Physics course(s)