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rajark
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It all started when I read that different inertial observers from the same place at the same time should see same things.
Say there are two clocks C1 and C2 in a stationary frame of reference S. C1 is at X=0 and C2 at X=X (some positive X) and both are syncronized in this frame. Say there is an observer named Mary located at X=0
Let's say Tom is an observer in a moving frame of reference S' located at X' = 0 with a clock C'. Let its relative velocity w.r.t frame S be V and moving towards positive X direction. When Mary and Tom are at the same place i.e., X=0 & X'=0 coincides in space, Clocks C1 and C' are synchronised and the reading is C1=C'=0. The second clock is at X' = X√(1-(V/C)^2) in Tom's frame. Now what the second clock C2 reads to Mary and Tom?
C2 reads zero to Mary as it is synchronised with C1 in Mary's frame. If Mary sees the second clock reading zero, then Tom should also see the same. But then how Tom reconciles the reading with the concept of unsynchronised clocks C1 and C2 in his own reference frame?
The point is that the clock C2 is moving towards Tom in his frame and the light from the clock should have left some time before. This "sometime: turns out to be (VX/C^2)/√(1-(V/C)^2) time units in his frame. But Tom also knows only (VX/C^2) time units should have passed in the moving clocks. So Tom concludes that the current time of the clock C2 is (VX/C^2).
The clock C2 is at X' in Tom's frame but it is showing the time what it was sometimes before when it was not at X'. In that case, should not Tom see the clock itself located at the point where it was located sometimes before? But he is not seeing so. If he sees it located at X' only, then it was the location of clock soemtimes before. So he should also conclude the clock is located more closer to him i.e., it should have had moved some distance towards him in this "sometime". So he should concludes that
X' = { X√[(1-(V/C)^2)] - V [(VX/C^2)/√(1-(V/C)^2)].
Please explain me why the above conclusion about C2 location is not right.
Say there are two clocks C1 and C2 in a stationary frame of reference S. C1 is at X=0 and C2 at X=X (some positive X) and both are syncronized in this frame. Say there is an observer named Mary located at X=0
Let's say Tom is an observer in a moving frame of reference S' located at X' = 0 with a clock C'. Let its relative velocity w.r.t frame S be V and moving towards positive X direction. When Mary and Tom are at the same place i.e., X=0 & X'=0 coincides in space, Clocks C1 and C' are synchronised and the reading is C1=C'=0. The second clock is at X' = X√(1-(V/C)^2) in Tom's frame. Now what the second clock C2 reads to Mary and Tom?
C2 reads zero to Mary as it is synchronised with C1 in Mary's frame. If Mary sees the second clock reading zero, then Tom should also see the same. But then how Tom reconciles the reading with the concept of unsynchronised clocks C1 and C2 in his own reference frame?
The point is that the clock C2 is moving towards Tom in his frame and the light from the clock should have left some time before. This "sometime: turns out to be (VX/C^2)/√(1-(V/C)^2) time units in his frame. But Tom also knows only (VX/C^2) time units should have passed in the moving clocks. So Tom concludes that the current time of the clock C2 is (VX/C^2).
The clock C2 is at X' in Tom's frame but it is showing the time what it was sometimes before when it was not at X'. In that case, should not Tom see the clock itself located at the point where it was located sometimes before? But he is not seeing so. If he sees it located at X' only, then it was the location of clock soemtimes before. So he should also conclude the clock is located more closer to him i.e., it should have had moved some distance towards him in this "sometime". So he should concludes that
X' = { X√[(1-(V/C)^2)] - V [(VX/C^2)/√(1-(V/C)^2)].
Please explain me why the above conclusion about C2 location is not right.
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