## Announcements * What's left? * Quiz 7 (Due Apr. 20) * Homework 13 (Due Apr. 20) * If we finish early, we finish early.

With Einstein's velocity addition rule, $$u = \dfrac{u' + v}{1+\frac{u'v}{c^2}}$$ what happens when $v$ is very small compared to $c$? 1. $u\rightarrow 0$ 2. $u\rightarrow c$ 3. $u\rightarrow \infty$ 4. $u \approx u' + v$ 5. Something else Note: * Correct Answer: D * denominator goes to 1 because second term is near zero - get back classical addition

With Einstein's velocity addition rule, $$u = \dfrac{u' + v}{1+\frac{u'v}{c^2}}$$ what happens when $u'$ is $c$? 1. $u\rightarrow 0$ 2. $u\rightarrow c$ 3. $u\rightarrow \infty$ 4. $u \approx u' + v$ 5. Something else Note: * Correct Answer: B * plug it in and you will get c; if something moves with c it does so in every frame - constant speed of light

With Einstein's velocity addition rule, $$u = \dfrac{u' + v}{1+\frac{u'v}{c^2}}$$ what happens when $v$ is $c$? 1. $u\rightarrow 0$ 2. $u\rightarrow c$ 3. $u\rightarrow \infty$ 4. $u \approx u' + v$ 5. Something else Note: * Correct Answer: B * if frame moves at c, all things move at c

I have seen the Einstein 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

**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