Consider the product of the speed of light and the proper time: $c\,d\tau$. Is this quantity invariant? 1. Yes 2. No 3. I don't know how to tell Note: * Correct Answer: A

Is this "4-velocity" a contravariant 4-vector? $$\eta^{\mu} \equiv \dfrac{dx^{\mu}}{d\tau}$$ 1. Yes 2. No 3. I don't know how to tell Note: * Correct Answer: A

What is $\dfrac{dt}{d\tau}$? 1. $\gamma$ 2. $1/\gamma$ 3. $\gamma^2$ 4. $1/\gamma^2$ 5. Something else Note: * Correct Answer: A

With $\eta^0 = c\gamma$ and $\vec{\eta}=\gamma\vec{u}$, what is the square of $\eta$? $$\eta^2 \equiv \eta \cdot \eta = \eta_{\mu}\eta^{\mu}$$ 1. c^2 2. u^2 3. -c^2 4. -u^2 5. Something else Note: * Correct Answer: C

The momentum vector $\vec{p}$ is given by, $$\vec{p} = \dfrac{m\vec{u}}{\sqrt{1-u^2/c^2}}$$ What is $|\vec{p}|$ as $u$ approaches zero? 1. zero 2. $m\,u$ 3. $m\,c$ 4. Something else Note: * Correct Answer: B

Are energy and rest mass Lorentz invariants? 1. Both energy and mass are invariants 2. Only energy is an invariant 3. Only rest mass is an invariant 4. Neither energy or mass are invariants

$$E-E_{rest} = (\gamma - 1) mc^2$$ What happens to the difference in the total and rest energies when the particle speed ($u$) is much smaller than $c$? 1. It goes to zero 2. It goes to $m\,c^2$ 3. It goes to $1/2\,m\,u^2$ 4. It depends Note: * Correct answer: C

What's $p_{\mu} p^{\mu}$? 1. $\gamma mc^2$ 2. -$\gamma mc^2$ 3. $mc^2$ 4. -$mc^2$ 5. Something else Note: * Correct answer: D