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Old May 25th 2009, 12:25 AM   #1
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relativistic confusion

A lighthouse and a spaceship have synchronized clocks and are separated by a distance d. At t = 0, a beam is directed towards the spaceship and is received by it at t = T1. If the same thing is repeated except that at t = 0, the spaceship starts moving away from the lighthouse with a velocity v and receives the beam at say T2. Despite its motion, since the speed of light is the same from the space ship would T1 = T2?
According to Newtonian physics, if the relative velocity between two objects is the same, in two different cases, the distance separating them also changes at the same rate.
Is it that the speed of light remains constant because both length contraction and time dilation occur and hence their ratio remains constant?


Spaceships A & B have synchronized clocks. If they then start moving relative to each other As clock appears slow to B and vice versa. After some time, if A sees his clock read 10.15 am and Bs read 10.am, what does B see? From his frame As clock should read 10.am while his should read 10.15 am . Now the reading on a digital clock being a number cannot be relative. I mean the number 10.15 is 10.15; there cant be two opinions about that!
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Old May 26th 2009, 07:43 AM   #2
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Originally Posted by physicsquest View Post
A lighthouse and a spaceship have synchronized clocks and are separated by a distance d. At t = 0, a beam is directed towards the spaceship and is received by it at t = T1. If the same thing is repeated except that at t = 0, the spaceship starts moving away from the lighthouse with a velocity v and receives the beam at say T2. Despite its motion, since the speed of light is the same from the space ship would T1 = T2?

No. Although the speed is the same the distance has changed and therefore T1 is different than T2. The spaceship's frame of reference is a non-inertial one so one has to be careful. For this reason one can't think of the distance from emission point to spaceship as being constant, in case that's what you had in mind.
According to Newtonian physics, if the relative velocity between two objects is the same, in two different cases, the distance separating them also changes at the same rate. Is it that the speed of light remains constant because both length contraction and time dilation occur and hence their ratio remains constant?

Yes.
Spaceships A & B have synchronized clocks. If they then start moving relative to each other As clock appears slow to B and vice versa. After some time, if A sees his clock read 10.15 am and Bs read 10.am, what does B see?

It depends on how they started moving relative to each other. When they started moving they became non-inertial frames of reference and special relativity no longer applies. In general clocks are no longer synchronized in such cases.
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Old May 26th 2009, 11:58 AM   #3
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Thanks for the insight, but i think i messed up the questions a bit .So am trying again.

A lighthouse and two spaceships , all three have synchronized clocks .Both spaceships are separated by a distance d from the lighthouse at t =0. However spaceship 2 is in steady relative motion with respect to the lighthouse with a velocity v while 1 is stationary with respect to the lighthouse. At t = 0, a beam is directed towards the spaceships and is received by 1 at t = T1 and 2 at t = T2 Is T1 = T2?
My idea of synchronization is explained in the problem below.

Spaceships A & B have synchronized clocks. If they are moving relative to each other with a constant speed v, As clock appears slow to B and vice versa. After some time, if A sees his clock read 10.15 am and Bs read 10.am, what does B see?
From his frame As clock should read 10.am while his should read 10.15 am . Now the reading on a digital clock being a number cannot be relative. I mean the number 10.15 is 10.15; there cant be two opinions about that!
Maybe the synchronization could be done by having them pass really close (after the constant speed has been attained) and the clocks activated by a signal from a source equidistant from both such that the ray from the source is perpendicular to the direction of motion. This should eliminate any effects due to aceleration etc. i hope and bring us back into the realm of special relativity.


No. Although the speed is the same the distance has changed and therefore T1 is different than T2.

Here the confusion is that in newtonian physics the relative vel can remain same only if the approaching beam also increases its vel to c + v which is forbidden by relativity. But time dilation and length contraction are also there to ensure constancy.
Aargh! im going around in circles again!
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