# If two spaceships are traveling closely to the speed of light in different directions, how can they communicate?

Supposed we have two spaceships at a speed close to lightspeed relative to each other, what would communication look like, for example with a laser beam, taking special relativity into consideration?

Special relativity tells us that we can assume spaceship A to be stationary, and spaceship B traveling away at dV. From the point of spaceship A, there should be a time dilation effect in spaceship B. On the other hand we can also assume spaceship B to be stationary and spaceship A traveling at speed dV.

Seems seems to be a paradox situation, how is it resolved?

• I think this was closed in error... lightspeed, or FTL travel is a different thing entirely to sublight travel, and the answers to the linked question aren't helpful here. That said, it is a standard relativity question, and I'm surprised that you haven't found a simple answer or example elsewhere. Nov 14, 2022 at 18:09
• My question is different from the linked question. Because
– Mark
Nov 16, 2022 at 9:29
• They can still communicate because from one ship's perspective the other is traveling less than lightspeed. Due to relativity, big speeds don't add up the way little ones do. Two ships moving at 0.9 lightpeed away from each other will observe each other moving at 0.994 lightspeed. I think this is the formula for big speeds. It always gives something less than c. Nov 16, 2022 at 10:36
• I am aware of that and I wrote that in the question. The question is not if they communicate but how that communication would work because of the "paradoxon" which I am sure, is not a paradoxon, I just don't know how to resolve it.
– Mark
Nov 16, 2022 at 10:49
• You're looking for the relativistic doppler effect.
– g s
Nov 26, 2022 at 21:20

There are, I think, two different issues you may be asking about here:

One is how can they communicate using light, etc, if they are both moving away from each other at near the speed of light. One of the features of special relativity is that the speed of an object depends on the reference frame, so even if ship A is travelling at, say, 0.9 times the speed of light away from point X, and ship B is travelling in the other direction away from X at 0.9 times the speed of light, from ship A's perspective, ship B is moving away from it at only 0.9945 times the speed of light (not, as one might expect, 1.8 times).

Therefore, a light beam travelling from one to the other of the ships will still travel faster than they are moving away from each other (barely), so it is still possible to send signals from one to the other that way. It will just happen a lot slower than if they were not moving away from each other so fast (and the round-trip time will obviously get longer and longer over time).

The other issue you bring up is basically the "Twin Paradox" (which you may want to look up in more detail). The issue is that from A's perspective, B's time should be moving slower than A, but from B's perspective, A's time should be moving slower than B. There is actually no paradox here, though. All A knows about B's state is what they receive from B's light communications, and vice-versa, so really what this means is that the communications that A receives from B will "look" like B's time is slowed down, but conversely the communications that B receives from A will also "look" like A's time is slowed down. This actually makes sense if you think about the fact that they're moving away from each other very fast, so the light that is travelling from one to the other will be taking a longer and longer time to get there, which will actually present the appearance of the sender being slowed down relative to the receiver (no matter who is the sender or receiver). Both will see what they expect to see, it just won't actually agree with what the other one sees (but that's ok, because it doesn't actually affect anything if the people on A and B have different opinions about what appears to be going on with time).

The Wikipedia article on the Twin Paradox actually covers some of this as well: