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
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* 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