I’m asking this because there is a scifi book I’m reading, and in the book there’s a scene where someone is communicating with a person in a spacecraft moving at lightspeed. I know their ability to communicate would probably not be possible, but let’s just put that aside for a second. Hypothetically, if you could communicate with someone moving lightspeed, would the time dilation make it so that they would appear to be moving and speaking very slowly relative to you?
One would have to be orbiting the other. I don’t think you’d get any doppler shift in that signal, because the distance between transmitter and receiver remain constant.
The fun part of that scenario is that emitted photons carry momentum from your motion. If you’re moving at a significant fraction of the speed of light, hopefully you’re using an omnidirectional transmitter.
Edit: hmm. I wonder if Terrell rotation comes into play here. Probably not in terms of the actual transmission, but it certainly would in terms of placement of a transmitter on a spacecraft.