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ryancomplete
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Einstein’s train-carriage example:
A train-carriage is moving at a constant velocity v relative to the ground. An observer is stationed on the ground perpendicular to the midpoint of the train at time x relative to the ground’s frame of reference. At this time, lightning strikes the front and back of the train-carriage which reflects and reaches the ground observer at the same time. The ground observer therefore concludes that the lightning struck the front and back of the train at the same time. But, for an observer who is stationed on the train at the midpoint of the train-carriage, the light from the front lightning strike will reach him/her before the back lightning strike and thus he/she will conclude that the front of the train carriage must have been struck first. And therefore, based on their respective observations, simultaneity is relative.
But what if clocks were used instead of observers in order to detect simultaneity? For example:
Two clocks that are stationary with respect to the ground’s frame of reference, clock gr1 and gr2, are synchronous, and two clocks that are stationary with respect to the train-carriage’s frame of reference, clock tc1 and tc2, are synchronous. Clock tc1 is at the very back of the train-carriage and clock tc2 is at the very front of the train carriage. Each clock is light sensitive and will immediately stop ticking the moment light reaches it. At a specific time with regard to the ground’s frame of reference, clock tc1 is at the exact position as clock gr1 and clock tc2 is at the same position as clock gr2. At this specific time with regard to the ground’s frame of reference, lightning strikes the back clocks, gr1 and tc1, and the front clocks, gr2 and tc2. As a result, clocks gr1 and gr2 stop ticking and each record the time to be x. The clocks tc1 and tc2 also stop ticking and both these clocks record the time to be y. Now the fact that the back and front clocks, tc1 and tc2, have recorded the same time would surely demonstrate simultaneity regardless of the differences in the times that the light from the front and back strikes took to reach the observer on the train-carriage.
A train-carriage is moving at a constant velocity v relative to the ground. An observer is stationed on the ground perpendicular to the midpoint of the train at time x relative to the ground’s frame of reference. At this time, lightning strikes the front and back of the train-carriage which reflects and reaches the ground observer at the same time. The ground observer therefore concludes that the lightning struck the front and back of the train at the same time. But, for an observer who is stationed on the train at the midpoint of the train-carriage, the light from the front lightning strike will reach him/her before the back lightning strike and thus he/she will conclude that the front of the train carriage must have been struck first. And therefore, based on their respective observations, simultaneity is relative.
But what if clocks were used instead of observers in order to detect simultaneity? For example:
Two clocks that are stationary with respect to the ground’s frame of reference, clock gr1 and gr2, are synchronous, and two clocks that are stationary with respect to the train-carriage’s frame of reference, clock tc1 and tc2, are synchronous. Clock tc1 is at the very back of the train-carriage and clock tc2 is at the very front of the train carriage. Each clock is light sensitive and will immediately stop ticking the moment light reaches it. At a specific time with regard to the ground’s frame of reference, clock tc1 is at the exact position as clock gr1 and clock tc2 is at the same position as clock gr2. At this specific time with regard to the ground’s frame of reference, lightning strikes the back clocks, gr1 and tc1, and the front clocks, gr2 and tc2. As a result, clocks gr1 and gr2 stop ticking and each record the time to be x. The clocks tc1 and tc2 also stop ticking and both these clocks record the time to be y. Now the fact that the back and front clocks, tc1 and tc2, have recorded the same time would surely demonstrate simultaneity regardless of the differences in the times that the light from the front and back strikes took to reach the observer on the train-carriage.