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it would take 4 billion years for light to travel from our planet to their planet and then back to our planet again. so if we had to communicate with them, there would be a 4-billion-years lag time between responses.
however, the distance between us is still 2 billion light years. so if we look at them, we'll see their civilization as it was 2 billion years ago, and if they look at us, they'll see us as we were the same 2 billion years ago.
you know how in the beginning of Contact the camera is traveling through the universe and there's the sound of the radio stations? the further it travels, the older the programs become. so if there was a civilization capturing our signals 64 light years away from here, they'd soon hear announcements about germany invading poland... and if they were to instantaneously move 6 years closer to earth, they'd hear announcements about the end of WWII
there might be advanced civilizations on the distant planets we're looking at, the problem is that neither we nor they can see each other because of this light lag.
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