On the trip to PA, I explained to my wife why faster than light communication implies communication backwards in time. It went something like this:
Start out by doing a lot of experiments with magnets and electric fields. So you discover things like moving magnets creates electric currents, and moving electrons create magnetic fields. Anyway, so a guy by the name of Maxwell puts these together and realizes that a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. So if you differentiate the equation for how a magnetic field changes an electric field, you can get a wave equation which travels at the speed of light. This is kind of surprising, since you take constants that come from experiments on magnets and wires, and you get an answer that matches experiments to determine the speed of light. So this gets you wondering, could light be an electromagnetic wave?
So later experiments with waving electrons back and forth on wires creates waves (radio waves) and they can use them to communicate back and forth. (For some reason my hand gestures on this were not appreciated (Maybe because I was driving the car at the time.).) The simplest antenna is just a wire that you put an oscillating current on. But in the 1800s technology was not capable of making currents oscillate anywhere near fast enough to make visible light, so it took some time before people started to believe that light was an electromagnetic wave.
Anyway, so you can calculate the speed of light from electromagnetic properties, that is things that you measure with wires and magnets. Then with the equations two funny things were noticed. First, they seem to predict that the speed of light is a constant. This is weird. If I throw a baseball forward from a car going 75 mph at 25 mph, then it will being going 100 mph compared to the ground. The equations for light seem to imply that if you turn on a light when going the 75 mph, it will still be going the speed of light from the ground.
So a guy by the name of Einstein noticed this, and some other things like if a hoop of wire on a railroad car goes through a magnet, it creates electricity, and the equations predict the same amount of current if you calculate it as a moving car and stationary magnet, or a moving magnet and stationary car.
Einstein takes seriously the possibility that the speed of light is a constant. This has even stranger implications. Einstein figures out a bunch of them, and experiments since then have shown that he was right. One of them is that events don't always happen in the same order depending on who is looking at them.
So, let us say that there are two lights, A and B. There is a train platform which has the lights. There is also a train going from B to A which we will call Alpha and a train going from A to B which we will call Beta. On the train platform, the lights A and B turn on at the same time. The lights are separated from each other.
So lets say someone stands on the platform in the center of the two lights. They then see the lights go on at the same time since they are the same distance from each.
Now, the Alpha train heading towards A. The lights go on. Since the train is heading towards A, and the speed of light is a constant, a person exactly in the middle between light A and B will be closer to A by the time that the light reaches them. Since the distance to each light is a the same when they go on, in their frame, Light A goes on before light B. So, lets say that the trains are long and fast enough that the difference is one second. This is not just a difference in when the light reaches them, this is a difference in what time they will calculate that the light goes on.
Now, the Beta train heading towards B. The lights go one. For similar reasons as with the Alpha, the train Beta train will calculate that B light goes on before the A light. So, in the Beta train frame, light B goes on a second before light A.
So, a recap. On the frame of reference for the station platform, lights A and B go off at the same time. On the Alpha train that is heading towards light A, light A goes off first by a second. On the Beta train that is heading towards B, light B goes off first by a second. This is both weird and somewhat mindblowing. This is not science fiction, this is the way the world works, and things like GPS satellites that have both varying relative motions and care about precision time have to deal with this type of stuff.
On to the science fiction. Some authors allow faster than light communication, some don't. Some authors also allow communication or travel back in time. For example, Douglas Adam's universe has both time travel and faster than light travel. Orson Scott Card's Ender Universe has faster than light communication, but no backwards in time communication. Carl Sagan's Contact universe has both time travel and faster than light travel. Ursala K. Leguin's universe has only faster than light communications.
Lets say we have practically instantaneous communication which is much faster than the speed of light. So, on the Alpha train, send a message from the location of B to the location of A near instantaneously. From the Beta train perspective, this message just went backwards in time by a second. Transfer the message to the Beta train. On the Beta train, transfer the message from the location of A to the location of B to the location of A. From the Alpha train's perspective, the message has traveled back in time by a second. So, then transfer the message back to the Alpha train. The Alpha train then receives the message before they sent it.
So, if there is faster than light communication, then there is also backwards in time communication. About the only exception is if the faster than light communication requires planet sized facilities. Ursala K. Leguin's universe might have this restriction, but the Ender universe does not. If the faster than light communication only can happen planet to planet, then it might be hard to get enough difference in velocity for the backwards in time communication to happen.
I, Josh Cogliati grant this to the public domain.