Annoucements

• Last Quiz (This Friday)
  • Use special relativity to determine the time between signals
  • Discuss if events are timelike or spacelike separated and how you know
  • Explain why two events could occur at the same place (or time)
• Last Homework
  • Due next Friday NOT Monday! No project problem
• Rest of class
  • Finish up Relativity (next Monday-ish) and discuss E&M in general (next Wednesday-ish)
  • Extra credit assessment (next Friday)

Points that lie outside the light cone for a given event are:

1. accessible no matter where they are
2. accessible for given world lines (trajectories)
3. always inaccessible

The space time interval is defined by:

$$I\equiv x^2 + c^2t^2$$

Events with common space time intervals lie on a hyperbole of constant $I$.

True or False: A Lorentz boost can allow you to shift between different hyperboles.

1. True
2. False

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

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

What is $\dfrac{dt}{d\tau}$?

1. $\gamma$
2. $1/\gamma$
3. $\gamma^2$
4. $1/\gamma^2$
5. Something else

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

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