Same time in both locations, assuming the message is sent in full exactly at the midpoint.
OK... let's replace the message with a baseball. Hypothetically speaking, say you can instantaneously accelerate a baseball to the speed of light. You fire one forward and one backward. Would the one going forward appear to be moving at half the speed of light from your point of view? If that's so (which seems logical), then the one going backwards would appear to be moving at 1.5 times the speed of light, right?
Not worth the conjecture...even hypothetically, a baseball can't travel at the speed of light. I know I'm supposed to accept the premise that it can, but that's basically like me asking you to do math under the premise that 1 + 1 = 4. You could try, but your solutions would be all fucked up.
Same here. By ignoring the fact that a material object can't travel at light speed, we could come up with all sorts of thought experiments like the one you propose, but all of them would end up being fucked up.
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