Communication between two ships moving at relativistic speed

Disclaimer: I'm asking for a friend on Wordbuilding.SE, and since many people there seem to have a great misconception on the matter, it thought it will be helpful for everyone. The full question is this one, but I'll summarize it here. I'll rely on you guys to explain it better than me, on a site that is more suited for this kind of question than on the comment section of Worldbuilding.

Let's say that 2 ships are travelling at 0.8c (originally the asker seems to consider it as an absolute speed in a fixed frame reference, we can consider it's relative to Earth). Both are going in the same direction, so they are immobile relative to each other, only seperated by around 1AU. They want to communicate via a laser beam.

The question is : how their speed will affect the laser beam?

My take on this is that their speed only exists relative to external things (the Earth, their destination and probably some space dust in between), but since they are at rest relative to each other, the laser beam will travel just fine since light travels at $c$ as seen from any point of reference (no redshift, no "aiming formard" needed, and only a small 8 minute delay in communication due to the distance between the two ships).

However, some people seem to think of speed as an absolute thing, and that, for example the laser can't go faster than $0.2c$. While this is wrong, I'm not really good at explaining and I though it would be an interesting question for Physics.SE.

Again, the goal is not to pick the right answer, but to explain it so that everyone can understand (for Science, you know).

• The speed of light is the same in every inertial frame of reference... – CooperCape Dec 28 '17 at 10:55
• Yes, that's what I'm saying ^^ (maybe badly phrased, hence my request) – Keelhaul Dec 28 '17 at 10:58
• Oh I see, apologies (Derp :/) – CooperCape Dec 28 '17 at 11:03
• Related: physics.stackexchange.com/q/79331/2451 and links therein. – Qmechanic Dec 28 '17 at 12:46
• The error of the OP on Worldbuilding is the wrong thinking about the behavior of the point of origin of light. It is a bit counterintuitive, but in Special Relativity, the point of origin travels with the observer. For example, if you and I are flying apart at 0.99c and when we pass each other I flash a light, then, as we are flying away, I see my light going $360^o$ out from me while you see the same light going out $360^o$ out from you. It is because light does not move in time, but travels with time, whether it is my time or your time. – safesphere Dec 28 '17 at 17:31

The ships are stationary relative to each other, and so can communicate using lasers as normal. So you are correct that there is an 8 minute delay to the messages sent between the ships from the perspective of their crews, and they do not need to aim ahead.

From the reference frame of the Earth it is indeed true that the component of the velocity of the light that is parallel to the line between the ships will be less than c (3/5 c to be exact) and the light delay becomes $$8/(3/5)=40/3\approx13.3$$ minutes. But in this reference frame the passengers on the ship have their time dilated by a factor of $$\gamma=\frac{1}{\sqrt{1-\left(0.8\right)^2}}=\frac{5}{3}$$, and thus don't notice this, since the 13.3 minutes in the Earths frame is then the same as $$13.3.../\gamma=\left(\frac{40/3}{5/3}\right)=8$$ minutes in the ship frame.

In your question you are probably implicitly asking what will be one – way speed of light between the spaceships in their "moving" frame (in the direction of their travel or in opposite direction) and whether its value will be lesser or greater than $$c$$.

It is allowed to assume, that in the frame of these spaceships one – way speed of the beam is lesser than $$c$$ in “forward” direction and greater than $$c$$ in “opposite” direction.

But, if the astronauts would measure speed of light on a closed path using a single clock, the measured value would be equal precisely to $$c$$ in any direction anyway.

Lorentz Ether Theory admits that motion is absolute, but relativistic effects make it undetectable. This theory assumes that there is a preferred frame. Speed of light is isotropic only in preferred frame. In a moving frame speed of light is anisotropic, since this frame moves in a preferred frame. Clocks of moving obsrvers indicate so – called local time, which is different from absolute time.

This theory is empirically equivalent to Special Relativity. Special Relativity assumes, that there is no preferred frame and one - way speed of light one - way speed of light is isotropic an equal to constant $$c$$ in any frame.

It should be noted, that it is not possible even in principle to measure the one way speed of light. So, equality of speed of light in different directions and Einsten's method to synchronize clocks is a convention, which looks natural only in inertial frames. In rotating frames, even in special relativity, the non-transitivity of Einstein synchronisation diminishes its usefulness.

Reichenbach‘s synchrony convention allows anisotropic one – way speeds of light, but keeps average speed of light on closed path isotropic and equal to constant $$c$$.

Let‘s assume, that the spaceships move at equal velocities very close to $$c$$ and chase each other in preferred frame or Ether, so distance between them doesn't change. In the frame of these spaceships "real" speed of light between them will be different from $$c$$, because they also move with speed close to $$c$$.

From the point of view of an observer who is „at rest“ in the Ether, difference of velocities will be $$c-v$$ or $$c+v$$. But, it is necessary to keep in mind length contraction and time dilation. However, since astronauts do not know anything about their own movement, measured speed of light in one direction will depend on their clocks synchronization method.

If the astronauts compare round – trip speeds of light in different directions, they would measure, that roundtrip speed of light is isotropic and equal $$c$$ (Michelson - Morley experiment).

Since the astronauts know nothing about their velocity, they may ascribe value $$c$$ to one - way speed of light and synchronize front and rear clock accordingly. This way, due to discrepancy between the front and the rear clocks (they would show not “real absolute”, but “wrong local” time) it is clear that measured one – way speed of light will be equal exactly to $$c$$.

However, if somehow the astronauts at some instant were able to set time on the front clock and rear clock according to „absolute Etherian time“ they woud give different values for one – way speeds of light.

In forward direction it would tend towards $$c/2$$ and in the backward towards infinitely large value, so measured speed of light „back and forth“ will still be $$c$$.