geistkiesel
Valued Senior Member
Another AE gedunken gets gedunked.
2vt + x = ct after RP reflects from RMC.
A platform has mirrors and clocks, LMC and RMC, located at the extreme ends of platform and are separated by the midpoint of the platform at M. M has a light emitter which emits pulses, LP and RP, simultaneously towards the respective LMC and RMC (or the pulses could be located on the embankment). When the platform is stationary wrt the embankment the round trip travel of both pulses are ct, where ct is the distance M to LMC and M to RMC. Likewise, the arrival times of both pulses at LMC and RMC are the same.
When the platform moves to the right the round trip time of the pulses arriving simultaneously at M is increased by an amount t’ = 2vt/(c – v). There are two pieces of information available to platform observers that the platform is moving and the embankment is stationary.
1. When the platform is in motion with v > 0 wrt the embankment, the arrival times of the pulses at LMC and RMC will be different as the LMC is heading toward an oncoming LP and when arriving at LP after moving ct, the RP is still 2vt from RMC - two different distances for light travel. RP must travel and additional 2vt plus a distance vt’ to catch the RMC. In clear form ct’ = 2vt + vt’, or t’ = 2vt/(c – v), therefore the clocks will indicate different arrival times at LMC and RMC.
2. Very briefly [t’], as LP reflects and RP continues toward RMC both pulses are moving in the same direction – which accounts for the extended time/distance for the round trips of the pulses for the moving platform. After LP reflects at LMC and returns to the origin of the pulses, not returning to M, or after traveling another ct, LP is now at the origin of the pulses and is 2vt from M due to the platform motion now totaling 2vt, and like RP earlier, requires t’ = 2vt/(c – v) additional time to arrive at M. I leave it for an exercise to show that RP and LP arrive simultaneously at M. When measured t’, when the platform v > 0, then t’ > 0, otherwise v = 0.
Code:
LMC LP <---|---> RP RMC
[B]|________________________M________________________|[/B]
|<---------ct------|-----ct -----------><--vt2--->|light after ct
| vt [B]|__________________|______M_______________________|[/B]frame after ct
|--------ct------->|<--2vt-->|<--2vt+-->|<----x---|light after 2ct
| <--2vt[B]->|_____________|___________M_______________________|[/B]frame after 2ct
M shown just as LP reaches [I]the origin of pulses[/I], M having moved 2vt.
A platform has mirrors and clocks, LMC and RMC, located at the extreme ends of platform and are separated by the midpoint of the platform at M. M has a light emitter which emits pulses, LP and RP, simultaneously towards the respective LMC and RMC (or the pulses could be located on the embankment). When the platform is stationary wrt the embankment the round trip travel of both pulses are ct, where ct is the distance M to LMC and M to RMC. Likewise, the arrival times of both pulses at LMC and RMC are the same.
When the platform moves to the right the round trip time of the pulses arriving simultaneously at M is increased by an amount t’ = 2vt/(c – v). There are two pieces of information available to platform observers that the platform is moving and the embankment is stationary.
1. When the platform is in motion with v > 0 wrt the embankment, the arrival times of the pulses at LMC and RMC will be different as the LMC is heading toward an oncoming LP and when arriving at LP after moving ct, the RP is still 2vt from RMC - two different distances for light travel. RP must travel and additional 2vt plus a distance vt’ to catch the RMC. In clear form ct’ = 2vt + vt’, or t’ = 2vt/(c – v), therefore the clocks will indicate different arrival times at LMC and RMC.
2. Very briefly [t’], as LP reflects and RP continues toward RMC both pulses are moving in the same direction – which accounts for the extended time/distance for the round trips of the pulses for the moving platform. After LP reflects at LMC and returns to the origin of the pulses, not returning to M, or after traveling another ct, LP is now at the origin of the pulses and is 2vt from M due to the platform motion now totaling 2vt, and like RP earlier, requires t’ = 2vt/(c – v) additional time to arrive at M. I leave it for an exercise to show that RP and LP arrive simultaneously at M. When measured t’, when the platform v > 0, then t’ > 0, otherwise v = 0.
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