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Originally Posted by NQLD_Newby
Hmmmm.... I must be misunderstanding something then.
Let me try to explain what I mean, in a hope that you can help me see where I am going wrong.
There are three observers, 1, 2, and 3.
Obs1 is 10 light minutes away from you, obs 2 is 20 light minutes away and obs 3 is 30 light minutes away.
You are travelling at the speed of light, and at exactly 10.00am you turn on your lights.
Because you are travelling at the speed of light, none of the observers can see you until you pass them. They cannot see your lights until then either as you and the photons are travelling at the same speed.
It takes 10 minutes for you and the photons from your lights to reach obs1, therefore he says you turned your lights on at 10.10am.
It takes 20 minutes to reach obs2 so he says 10.20am is the time you turned them on.
Likewise obs3 says 10.30am is when you turned them on.
So between you and the three observers you have four different times for the same event. Each of you is correct, as your measurements were made relative to your position in time-space.
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Rex,
What you're describing is the elapsed time, not the time ordinate as defined by a specific event in space time. An event in space time is defined by the coordinates (x,y,z,t).
Since the three observers are in the same frame of reference, they agree on a synchronized time as to when the headlights were turned on. In other words the t value is the same for each observer.
Plugging in v=0 (since each observer is stationary) in
t' = (t - (v/csquared)x)/(square root of1 - vsquared/csquared)
Gives t'=t which proves the event is synchronized.
Suppose this time is 10.00am. If the car travels at the speed of light, the headlights are turned on at each location of the observer (as we both agree to). Each observer however has noted that the lights are turned on at 10.00am and therefore concludes the car has passed their locations at 10.00am.
Compare this when the car is travelling at more conventional speeds.
The time when the car passes each location is simply 10.00am plus the time it takes for the car to reach each destination.
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The difference is, similar to the way the deeper into space you look, the further back in time you go, obs1 is looking 10 minutes back in time obs2 20 minutes and obs3 is looking 30 minutes back in time. But relative to their positions the event happened at the times they have stated.
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What it means is that the signal for the event has taken 10, 20 or 30 minutes to reach the observers. If all the observers are travelling at the same velocity (<< c) or are stationary you get the same synchronized result irrespective of the distance of the observers from the source.
If the observers are travelling at different velocites (and at high velocities for the effects to be noticeable), the event is no longer synchronized.
Hope this is useful.
Regards
Steven