- #1
Kreizhn
- 743
- 1
Hey all,
Simple question, so hopefully it gets answered quickly.
I hate SR, but am marking an assignment on it. Here's the set-up
Alice is standing still on a train traveling at 3/5c and Bob is on the platform at rest. A series of lights are set up along the track, yada yada. Bob sees the lights flash every [itex] T_0 [/itex] seconds, so what is the time measured by Alice?
So clearly, Alice will see a slower time by a factor of [itex] \gamma = \frac45 [/itex] and will measure [itex] \frac45 T_0 [/itex]. However, I have a student who is using Lorentz transformations. If Alice's frame is (t',x') and Bob's is (t,x) then
[tex] \Delta t' =\gamma(\Delta t-\frac v{c^2} \Delta x ) [/tex]
He claims that [itex] \Delta x = 0 [/itex] since Bob is not moving, and calculates the time difference to be [itex] \frac54 T_0 [/itex] instead. Clearly this must be wrong because Alice should experience a slower amount of time. Is the assumption that [itex] \Delta x = 0 [/itex] wrong because in Alice's frame, Bob is in fact moving?
Simple question, so hopefully it gets answered quickly.
I hate SR, but am marking an assignment on it. Here's the set-up
Alice is standing still on a train traveling at 3/5c and Bob is on the platform at rest. A series of lights are set up along the track, yada yada. Bob sees the lights flash every [itex] T_0 [/itex] seconds, so what is the time measured by Alice?
So clearly, Alice will see a slower time by a factor of [itex] \gamma = \frac45 [/itex] and will measure [itex] \frac45 T_0 [/itex]. However, I have a student who is using Lorentz transformations. If Alice's frame is (t',x') and Bob's is (t,x) then
[tex] \Delta t' =\gamma(\Delta t-\frac v{c^2} \Delta x ) [/tex]
He claims that [itex] \Delta x = 0 [/itex] since Bob is not moving, and calculates the time difference to be [itex] \frac54 T_0 [/itex] instead. Clearly this must be wrong because Alice should experience a slower amount of time. Is the assumption that [itex] \Delta x = 0 [/itex] wrong because in Alice's frame, Bob is in fact moving?