# Simultaneity question

1. Jul 24, 2013

### Solarmew

i'm reading over the GRE prep book and i just got to the question:
"System S' travels with constant velocity v≠0 w.r.t. system S. If two events, separated by a distance x≠0, occur simultaneously at time t in S, do they occur simultaneously in S'?"
the answer is "No, never". But the "never" part kind of bothers me. If you held two flashlights in your hands and they both lit up at the same time while your friend was driving away from you maintaining the same distance to both lights, wouldn't the events also occur at the same time in their frame of reference?

2. Jul 24, 2013

### WannabeNewton

In the book example the separation is along the direction of motion; in your example the separation is perpendicular to the direction of motion.

3. Jul 24, 2013

### Solarmew

errr... where does it say the separation is along the direction of motion? :uhh:

4. Jul 24, 2013

### WannabeNewton

It's assuming that the Lorentz boost is along the $x$-direction of frame $S$ with the two events having a non-zero spatial separation $x\neq 0$ in frame $S$. If the separation is purely perpendicular to the direction of motion (such as me holding a flashlight in each arm exactly side by side) then there won't be an anomaly. If the car is traveling along the $x$-direction in my frame and the separation between the flash lights is $\Delta y$ i.e. $\Delta x = 0$ and I turn them both on so that $\Delta t = 0$ then $\Delta t' = 0$ trivially by the Lorentz transformations for a boost along the $x$-direction.

5. Jul 24, 2013

### Solarmew

what i typed up was the whole question ... i dunno what kind of assumptions are supposed to be made based on that information :\ ... maybe it's just poorly worded ...

6. Jul 24, 2013

### WannabeNewton

Well solarmew (mew from pokemon? xD) I would have to agree that it isn't exactly worded in the most unambiguous fashion. As long as the direction of the Lorentz boost isn't exactly perpendicular to the direction of separation of the simultaneous events in frame $S$, you can agree with the text.

7. Jul 24, 2013

### Solarmew

fair enough :P and no, no pokemons XD just "mew" as in the sound a kitty makes :3

8. Jul 24, 2013

### WannabeNewton

D'aww the pokemon is cooler :p xD

9. Jul 24, 2013

### WannabeNewton

Good luck on your GRE by the way!

10. Jul 24, 2013

### Solarmew

thanks, i'm gonna need it X.X ... considering i have to take it this september, the same time the three-quarter quantum sequence starts ... -___________-

11. Jul 24, 2013

### micromass

Staff Emeritus
[Broken]

Last edited by a moderator: May 6, 2017