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
## 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 (next 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)
Which of the following equations is the correct way to write out the Lorentz scalar product? 1. $a \cdot b = -a^0b^0 + a^1b^1 + a^2b^2 + a^3b^3$ 2. $a \cdot b = a_0b^0 + a_1b^1 + a_2b^2 + a_3b^3$ 3. $a \cdot b = a_{\nu}b^{\nu}$ 4. None of these 5. All three are correct Note: * Correct Answer: E
Velocity is a defined quantity: $$\mathbf{u}=\dfrac{\Delta\mathbf{r}}{\Delta t} = \langle \dfrac{\Delta x}{\Delta t},\dfrac{\Delta y}{\Delta t},\dfrac{\Delta z}{\Delta t}\rangle$$ In another inertial frame, seen to be moving to the right, parallel to x, observers see: $$\mathbf{u'}=\dfrac{\Delta\mathbf{r'}}{\Delta t'} = \langle \dfrac{\Delta x'}{\Delta t'},\dfrac{\Delta y'}{\Delta t'},\dfrac{\Delta z'}{\Delta t'}\rangle$$ Is velocity a 4-vector? 1. Yes 2. No Note: * Correct answer: B
Imagine this quantity: $$u^{\mu} \equiv \begin{pmatrix}c\\\ \frac{\Delta x}{\Delta t}\\\ \frac{\Delta y}{\Delta t}\\\ \frac{\Delta z}{\Delta t}\end{pmatrix} $$ Is this quantity a 4-vector? 1. Yes, and I can say why. 2. No, and I can say why. 3. None of the above. Note: * Correct answer: B
Imagine this quantity: $$\eta^{\mu} \equiv \frac{1}{\Delta \tau}\begin{pmatrix}ct\\\ \Delta x\\\ \Delta y\\\ \Delta z\end{pmatrix} $$ Is this quantity a 4-vector? 1. Yes, and I can say why. 2. No, and I can say why. 3. None of the above. Note: * Correct answer: A
In my frame ($S$) I measure two events which occur at the same place, but different times $t_1$ and $t_2$ (they are NOT simultaneous) Might you (in frame $S'$) measure those SAME two events to occur simultaneously in your frame? 1. Possibly, if he’s in the right frame! 2. Not a chance 3. Definitely need more info! 4. ??? Note: * Correct Answer: B
Two events have a timelike separation. In a "1+1"-dimensional spacetime (Minkowski) diagram (x horizontal, ct vertical), the magnitude of the slope of a line connecting the two events is 1. Greater than 1 2. Equal to 1 3. Less than 1 Note: * Correct Answer: A