# Communication between two observers moving at the same relative velocity

Let's say we have two ships moving at, for example, .8c. Let's put them 1 light-year apart and give them exactly the same velocity. I want to point a laser from one ship and hit the other ship.

My initial thought is that since the speed of light is constant I'll have to aim the light ahead, so that the beam is still moving forward at .8c, and toward the other ship at .6c so they add up to $.6^2 + .8^2 = 1^2$, meaning that the maximum speed of communication between these two ships is .6c.

Someone has pointed out to me that this is wrong, since one of the core principles of relativity is that velocities are relative. Because of this we should not be able to tell that we are going .8c and communication between the two ships should be completely normal.

How does this work out? I imagine that I am correct from the perspective of a stationary observer, but time dilation will make it appear that .6c is actually 1c onboard either of the ships.

To clarify, my main question is: which direction the will the light beam have to be directed from the transmitter to the receiver. Can I point the beam directly at the receiving ship or will I have to lead it? If it can be pointed directly at the receiving ship, how can you reconcile the frame of reference of a stationary observer with the frame of reference moving with the two ships?

• Whenever you talked about speed, you must also say w.r.t whom? In your question this part is missing. If you are clear on this, then, by applying [link] (physics.stackexchange.com/questions/103907/…) special relativity formula for relative speed, you will get to know that information would flow at the same speed for all the ships, i.e. c. – Vikash Kumar Dec 28 '17 at 10:01
• Obviously you have to aim your laser pointer straight into the target - receiver. The beam will move at straight line towards the receiver in your frame. However , in the frame of the "stationary" observer this beam will have the same x- velocity as you. It's x- coordinate will always be the same as yours, so it will go through the laser's tube perfectly well. Look at episode 1 in this video youtube.com/watch?v=FQKp3FU8vR8. – Albert Dec 28 '17 at 16:12

## 2 Answers

If they're moving at the same relative velocity, then there's a reference frame at which they're not moving at all. In this reference frame (since nothing's moving), light is clearly going to travel at speed c. Things only get interesting in relativity when something is moving relative to something else!

• That was my understanding as well, can you clarify what happens from a stationary 3rd party's perspective and how that translates into the ships' perspective? – bendl Dec 28 '17 at 12:56
• Read this link: hyperphysics.phy-astr.gsu.edu/hbase/Relativ/tdil.html Length contraction: things will shrink in the direction of motion (so you need to find how close and far away the object is moving towards the third party and apply a length contraction to that. The same can be done with time contraction (listed lower in the link). As for the signal traveling at c....I guess it would look "redshifted" in one direction and "blueshifted" in the other...but I would recommend writing another question more specifically about what the third-party sees. (and where it is!) – Steven Sagona Dec 30 '17 at 4:11

You are wrong and the answer on worldbuilding is correct. The ships are only moving at 0.8c relative to an external observer, the light that is emitted from 1 ship to the other from this external observer's perspective will move at c but the distance between the 2 ships will appear smaller here than on the 2 ships. When looking at it from the perspective on one of the ships, the ships are not moving relative to each other and the light will move at c. You will correct for the difference from the perspective from the ships and the external observer with time dilation and space contraction. You do not need any time dilation when dealing with things moving at the same speed.

The speed of light is constant in all reference frames so the communication is c for all cases. However there will be a difference in how far the ships are from each other as well as how fast they are moving when compared with an external observer.

Also note that moving at 0.8c does not have any special relativistic effect on the ship when looking at it from the ship's perspective. In actual perspective on the ship, they can go faster than the speed of light no problem as their time dilates. The difference shows up when the ship makes is compared with a reference frame that did not experience the relativistic journey. This is the reason why you can compare 2 ships traveling together at 0.8c as if they were standing still.