If two events happen at different times and at different places in two different reference frames (observers) couldn't the observers work backwards (considering the finite speed of light) to find out when and where the events took place ? Is this God's-eye perspective correct ?


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  • $\begingroup$ If an event takes place in front of me but behind you, can't we work backwards to figure out where it took place? $\endgroup$ – WillO Jul 18 at 11:03
  • $\begingroup$ If a series of events happen in a single reference frame, couldn't the observer work backwards to find out when and where the events took place relative to them? It's not clear to me why you expect this to be any different than most observations. $\endgroup$ – JMac Jul 18 at 12:08

Yes, they could, and they should. The result, according to the theory of special relativity, is that the two observers will (probably) get that the time between the two events differ. They might even get different results about in which order the two events occurred.

You are certainly not alone thinking that the relativity of simultaneity is just because the light reaches the observers at different times. This is a common misunderstanding among people who start trying to learn about special relativity. But what the theory says is that time still differs after "working backwards".

  • $\begingroup$ Yes. As you say, the results of special relativity are already "corrected" for the speed of light. $\endgroup$ – Chet Miller Jul 20 at 1:55

I think you have misunderstood relativity of simultaneity of events.

Assume that observer A is next to the earth. Let's say that event $E_1$ took place in earth at $t_1=0$ according to A, while event $E_2$ happens at $t_2$ in the sun. Of course, A should consider the distance between earth and sun to measure the time of event $E_2$ correctly. That's, if he has received a signal from sun at let's say $t_{2i}=8~min$ he should subtract it by $8~min$ as well. So he will asume that $E_2$ took place at $t_2=0$ in reality. (This is "couldn't the observers work backwards (considering the finite speed of light) to find out when and where the events took place?" sure they can. They should.). So according to A, $E_1$ and $E_2$ are "simultaneous" even though he has not received their signal simultaneously. As you can see, location of A doesn't matter, because he can always measure the distance between himself and the event and by substracting the time that light crosses this distance, he will find the "real" time of events.

Now let's assume another observer, B, who is moving at velocity $v$ w.r.t. A. Just like A, position of B doesn't matter, he can substract extra times easily. However, there is something weird about B. according to Lorentz transformation, you can see that B will disagree with A about simultaneously of events. B says that although $E_1'$ happened at $t'_1=0$, $E'_2$ took place at $t_2'=-\gamma vD/c^2$ where D indicate the distance between A and the sun. Why is that? Well that's another question. But as for your question, they can, and they should, but in the end of the day, they will disagree.


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