The space time interval is defined by:
$$I\equiv x^2 - c^2t^2$$
Events with common space time intervals lie on a hyperbola of constant $I$.
**True or False:** A Lorentz boost (change to another inertial frame) can allow you to shift between different hyperbolas.
1. True
2. False
Note:
* Correct answer: B
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
$E_{tot}$ is conserved but not invariant. What does that mean?
1. It's the same at any time in every reference frame.
2. It's the same at a given time in every reference frame.
3. It's the same at any time in a given reference frame.
4. Something else
Note:
* Correct answer: C
$m$ is invariant but not conserved. What does that mean?
1. It's the same at any time in every reference frame.
2. It's the same at a given time in every reference frame.
3. It's the same at any time in a given reference frame.
4. Something else
Note:
* Correct answer: B
Charge is invariant and conserved. What does that mean?
1. It's the same at any time in every reference frame.
2. It's the same at a given time in every reference frame.
3. It's the same at any time in a given reference frame.
4. Something else
Note:
* Correct answer: A