I have seen the Eisntein summation notation before: $$\mathbf{a}\cdot\mathbf{b} \equiv a_{\mu}b^{\mu}$$ 1. Yes and I'm comfortable with it 2. Yes, but I'm just a little rusty with it 3. Yes, but I don't remember it it all 3. Nope

## Announcements * Poster printing (Free!) * Send your poster (PDF or PPT) to coeprint@msu.edu * Tell them you are in PHY 482 * Make sure to give a couple of days for the print! (No weekends) * Last Quiz (this Friday) * Use special relativity to investigate the effects of particle detection * Compare two events observed from different frames

**True or False:** The dot product (in 3 space) is invariant to rotations. $$\mathbf{a}\cdot\mathbf{b} \equiv a_{\mu}b^{\mu}$$ 1. True 2. False 3. No idea Note: * Correct answer: A (when Galilean relativity is ok)

Displacement is a defined quantity $$\Delta x^{\mu} \equiv \left(x^{\mu}_A - x^{\mu}_B\right)$$ Is the displacement a contravariant 4-vector? 1. Yes 2. No 3. Umm...don't know how to tell 4. None of these. **Be ready to explain your answer.** Note: * Correct Answer: A

The displacement between two events $\Delta x^{\mu}$ is a contravariant 4-vector. Is $5 \Delta x^{\mu}$ also a 4-vector? 1. Yes 2. No Note: * Correct Answer: A

The displacement between two events $\Delta x^{\mu}$ is a contravariant 4-vector. Is $\Delta x^{\mu}/\Delta t$ also a 4-vector (where $\Delta t$ is the time between in events in some frame)? 1. Yes 2. No Note: * Correct Answer: B

The displacement between two events $\Delta x^{\mu}$ is a contravariant 4-vector. Is $\Delta x^{\mu}/\Delta \tau$ also a 4-vector (where $\Delta \tau$ is the proper time)? 1. Yes 2. No Note: * Correct Answer: A