I stumbled across a paradox in special relativity for which I have found no answer. In the twin paradox, the loss of symmetry in time dilation is usually explained by the reversal of movement of the second twin. In the following thought experiment, this does not occur:
(And for the overzealous censors here: The following is an example that I made up myself. No one needs to calculate anything here. My question comes at the end of this post.)
My alien friend speeds past earth at 0,66c. From the moment he passes over my home, we send radar pulses every second. How many of my pulses reach him until he leaves the range of our radars, which is 15 light seconds? And how many of his radar pulses reach me? No matter how I calculate, the number of pulses that reach him seems to be fewer than the number of pulses that reach me, because he is "running away" from my signal. [My signals reach him every 3s, I get a signal every 1,66s.] This would, however, produce an asymmetry: In my world, I would receive more pulses, and in his world, he would receive more pulses, which should be impossible. Even if I include his time dilation, I cannot get a symmetrical number of pulses. [His time runs at 0,75 of mine, so I still get a signal every 2,21s.]
My question is the following: If there should not be two different worlds after this event (one in which I received more pulses and one in which he received more pulses) there must be something that I am missing, but what? Or is this really a paradox? If so, how does Relativity explain this paradox?