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This is a fairly simple question, but one that I'm a bit confused on. I have five lamps at positions $x_A,x_B,x_C,x_D,x_E$ which turn on at times $ct_A, ct_B, ct_C, ct_D,ct_E$ in the ground's rest frame.

The problem is, given a space-time diagram of these events, what order does the observer on the ground at $x=0$ see the lamps turn on? The lamps are at rest in the ground's rest frame, and so is the observer.

Intuition leads to three possible interpretations, and I'm not sure which is correct.

  1. What order does the line $y=t$ intersect each of the lamps' events on the space-time diagram? That is, draw a horizontal line on the diagram, and move the line up, noting the order it reaches each event. This seems the simplest interpretation. diagram 1

  2. What order do the lines with gradient $-c$ intersect the $y$ axis of the space-time diagram for each event? This seems more logical, considering that the speed of light is finite, and the observer has to wait for the light from the lamp to reach them. diagram 2

    1. The same as 2), but with lines of +c from the line $x=0$.
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Let's talk the difference between the 1st and the 2nd scenario. The third one will be discussed later.

The observer can see the lights only when it travels to him passing through the spacetime. So, obviously the observer will "see" the lamps when the light rays follow Second Scenario and reaches him. That is the order he will see them.

But your observer has one piece of information. And that is, he knows the position of each lamp at t=0. So, he can easily calculate how much time it really took for the light to reach him after they were turned on. And then he can extrapolate the first picture. This is not the order he'd see but the order he can guess the First Scenario if he knows the distances beforehand.

The third picture actually never helps him anyway. Because now the light rays are travelling from him to the lamps. This does not help in anyway to observe the lamps.

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  • $\begingroup$ Perfect! Thanks Ari, that makes a lot of sense. It's that idea of observing vs. inferring that I was getting lost on. As for the third scenario, my idea was "send a ray of light to observe the interaction, wait for return ray of light", but obviously this is too complicated. $\endgroup$
    – Eleanor
    Aug 27, 2016 at 5:26

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