# Another FTL thought experiment: spaceships in opposite directions

I’m sure this has been covered before, but there are a lot of threads to wade thru, so here goes:

Two spaceships are traveling in opposite directions (to an outside observer) at 0.6 c.

To the observer, the distance between the spaceships is increasing at 1.2 c (more or less), right?

Now, one of the spaceships shoots a laser at the other. The laser beam is still traveling at c, so, to the observer, it will be gaining on the other spaceship at a a rate of .4 c, right?

What would the crew aboard the other ship receive in the form of a laser? Would it be Doppler shifted into a radio wave or something when it reached the other ship?

Correct, as observed in his reference frame.

The observer will see the laser frequency redshifted by a factor of 2 compared to what the “emitter crew” sees, and the “receiver crew” will see it as redshifted by another factor of 2 compared to what the observer sees. Or in other words, if the laser emits at frequency F, the observer will see it as F/2, and the receiving spaceship will see it as F/4.

A factor of 4 isn’t enough to make an optical laser (if that’s what your thought experiment is using) seem like a radio laser — but that just means you need to increase the speeds until it does.

No. No such thing as >1.0c in Einstein’s universe. To the observer, it’s increasing at 1.0c. Relativity is seriously weird.

The distance between the spaceships, as measured in the Observer’s reference frame, is indeed increasing at a rate of 1.2c. That is what he observes. Maybe a better way to put it is: the sum of the two distances that the observer measures between himself and the ships is increasing at 1.2c.

This is not a claim that something is moving faster than light. No one is observing the speed between himself and another object as being faster than c.

Yes, indeed. Just as, if you sweep a laser pointer very fast across a distant screen, the dot of light can be moving at comfortably faster than c. The point there is that “the dot” doesn’t exist as an entity - it’s just the point at which the screen is intersecting the beam - and nothing is being carried along from place to place faster than light.

If the observer is on Spaceship A, what would he observe about the speed between himself and Spaceship B? Or would he just not be able to see B at all?

If the spaceships are moving in opposite directions away from a stationary observer at 0.6c, then an observer on A would see B moving away at about 0.88c.

For this we use the equation:

Vr = (V1 - V2)/(1 - V1*V2/c^2)

where V1 and V2 are the velocities relative to an independent observer and Vr is the velocity the two movers see relative to each other.

If they are each moving at 0.6c away from each other this becomes:

Vr = (0.6c + 0.6c)/(1 + 0.36c^2/c^2) = 1.2c/1.36 = 0.88c

Note that one of the velocities was chosen to be negative since they are moving in opposite directions.

But if this were possible, couldn’t you use it to transfer infomation between two places at faster than c?

Nope, because no information moves along with the dot. The information comes from the light source and moves in different directions at c. For example, the as I move the dot from point A to point B, when it reaches point B there is no way to tell if I had been changing the frequency of the laser when it was at point A. All you have is the information I am giving when I shoot the laser at point B. You have to wait for the light from the laser hitting the target at A to reach B to get any information out of it.

But if you flicked the dot back and forth between A & B could you not convey some sort of message between the two of them? In morse maybe?! I know there’s something wrong with this . . .

Think about what’s actually happening here, though. A isn’t sending a message to B. You are sending messages to both A and B (messages like “I’m shining a laser at you… and now I’m not”). And how are those messages traveling? Along a beam of light, at the convenient speed of c.

If A could instantaneously (or at least, very quickly) cause B to begin receiving light from your laser beam, then yes, that would constitute FTL transmission of information. But it’s impossible for A to do that: A has to signal to you first that it has a message to send, and then you have to transmit the message to B. Assuming you’re using light waves to communicate, at every point the information is traveling at c.

For it to be a message from A to B, A would have to have some sort of control over what the dot is doing. But the only way he could do that would be to transmit some sort of message to the guy holding the laser pointer, which would invariably result in the message being at most the speed of light.

Ok, my head’s sorting itself out now. Thanks guys.

I know that since nothing can travel faster than speed of light, and since, radio waves also travel at speed of light, we cannot pass an information faster than the speed of light.

That is when I thought, that, suppose if we have a 186,282 mile long metal rod (weird - but just an assumption) out in free space. Now, let there be a radio-wave transmitter at its one end and a receiver at other.
If we transmit, suppose, Morse Code on this radio-wave transitter-receiver system, it will take one second for the information to flow from one end to another (speed of light = 186,282 miles per second).

Now, if we can push the 186,282 mile-long metal rod, the other end will respond immediately (pushed or pulled, as done on its one end), in less than second.

Doesn’t this demonstrate the information-flow, faster than speed of light? Or, Is there any basic flaw in this thought experiment and the underlying understanding?

Diagram: http://goo.gl/SeGyH

The flaw is that there is no such thing as an infinitely rigid object. When you push on one end of the rod the impulse goes through the rod at some speed less than the speed of light, so the other end of the rod would not move until a second or more had passed.

Nope, your push wouldn’t propagate through the material instantaneously.

Oh, on preview I see Lumpy beat me.

The pulse will travel through the rod at the speed of sound in the rod. If the rod is made of steel the pulse will take almost 14 hours to make it from one end to the other.