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Relativity of Simultaneity
We tend to think of the word simultaneous as being fairly easy to define... two things either happen at the same time (simultaneously) or at different times.  
For example, if you are standing near two people and these two people clap their hands once.
You either hear one sound (if they clap their hands simultaneously) or two separate sounds.  
   
However things are not quite so simple if  
a) the two events (hand claps in this example) happen at a great distance from the observer (imagine trying to decide if one hand clap next to you is simultaneous with a hand clap on a planet orbiting alpha centauri!)  
b) two observers in relative motion are making measurements on the same events.  
 
In what follows we will concentrate on possibility b) above.  
   
Observer A carries a long support on which are fixed two mirrors, p and q.  
 
The mirrors a placed equidistant from A.  
   
At a certain instant, A sends two flashes of light, one towards each mirror.  
 
The light pulses are reflected by the mirrors (which could be quite a long way away from A).  
 
Hopefully you will agree that A should expect to see the two returning light pulses at the same time t later (next diagram).  
 
Now, even though the two events: light pulse hitting mirror p and light pulse hitting mirror q, occurred a long way from A, he/she can confidently conclude that (according to his/her observations) they occurred simultaneously.  
   
Now, say hello to observer B.  
B carries a long measuring rod (a ruler).  
 
Let's put B and A very close to each other, as shown below.  
 
What will B say about the light pulses hitting the mirrors? Clearly, all that we said before is still applicable to B. He/she will come to the same conclusion, namely that the pulses of light hit the two mirrors simultaneously.  
   
However, now imagine that A and B have a very high relative velocity (along the line parallel to the measuring rod).  
At this stage we must also assume that B has some means of detecting where the mirror was when the light pulse hit it.  
This is easier said than done but, so what, this is just a "thought experiment"! As long as we don't propose any measurements/observations that would be impossible to make, we're ok.  
We again start from the instant when A sends out the light pulses and B and A are very close together but now, a short time later, the situation could be as shown in the next diagram (which is drawn from B's point of view).  
 
B sees A and the mirrors moving to the right so B says that the light hitting mirror p has a shorter distance to cover than that hitting mirror q.  
   
B must therefore conclude that the two events (light hitting p and light hitting q) were not simultaneous.  
   
You might now be tempted to ask the question "who is right, A or B" ?  
   
They are both right.  
For A the events occurred simultaneously; for B they were not simultaneous.  
   
Simultaneity is a relative concept.  
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