# Speed of information

1. Jul 29, 2007

### louk

Assume there is Police space ship that did catch a Bandit space ship by a thin, light but strong high-tech line which is one light minute long. The Police space tries to pull the Bandit Space into prison but the Bandit space reverses its engines so that both space ships now stand still – say relative our sun.

Suddenly the line brakes apart close to the Police ship. Will the Bandit space ship notice this immediately – which means that this information is transmitted faster than the speed of light, or will something still pull the Bandit space ship for a minute (since the distance was one light minute). If the last case is true – from where comes the energy that pulls the Bandit Space ship for a minute??

(If needed, an observatory space ship may be placed in between the two space ship. )

2. Jul 29, 2007

### Staff: Mentor

This question is similar to that of a star and planet where the star's mass goes to zero instantaneously. When does the planet experience the loss of gravity (from the star)?

We understand that the effect of any natural phenomenon like light or gravity is constrained by the 'speed of light'.

What about the tension in the line?

3. Jul 29, 2007

### louk

I guess that the "spring energy" from the tension in the now broken line will not be able to pull the Bandit ship for one minute with the same force as before. This energy will be released in the movements of the line when moving around, probably also partly as heat radiation.

I guess that the Bandit ship should be able to notice a decrease of the pulling force very quickly.

4. Jul 29, 2007

### mgb_phys

If you pull on the end of a string, how quickly does the 'pull' get to the other end? ( hint - what carries sound in a string )

5. Jul 29, 2007

### rbj

when i was a student at the University of North Dakota, one interesting "coincidence" was that the University was next door to the State School for the Blind. (it was because they were both "land grant schools", the State of ND had some land allocated and both schools where built on adjacent parcels of that reserved land.) behind the school for blind there was a 60 yard track for races. between each lane was a suspended cable that the runner could reach out and touch to guide them in their lane (they could hold little rings that would slide on the suspended cables nearly friction free). but the cool thing about these suspended cables was that they had no middle supports (that would be a hazard for the runner in the middle of his/her race) and to be reasonable straight, they had pretty high tension on them (and the track was slightly bowed down in the middle by use of a slight excavation, matching the catenary shape of the slightly drooping steel cable, so that the height of the cable was constant above the track).

these 7 cables (there were six lanes) were like giant guitar strings and it was fun and instructional to send waves down the cable and watch them get reflected at the terminals. you could also set up standing waves for the first, second, all the way to the 9th harmonic, if i recall. it was cool, because at the same time i was taking Applied Mathematics (post-calc math for engineers) where i was first learning partial diff-eq and Fourier Series where the waves on a string was the main application (going from the wave equation to a solution). you could visually see both d'Alembert's formula for the solution (that is the pulse you create by whacking the line goes down the line and reflects back) and the Fourier Series solutions (each standing wave mode).

if you ever get an opportunity to wiggle a cable suspended between distant terminating posts, you should try this.

6. Jul 29, 2007

### louk

When the Police space ship attaches the line to the Bandit Space ship and starts pulling – then I agree that it will take some time for the pulling force to reach the Bandit ship – corresponding to the speed of sound for that line.

However, the situation is that line breaks close to the Police ship and the question is from where the energy comes that will pull the Bandit ship with the same constant force for one minute. And if the pulling force is not constant for one minute then the information of the broken line has been passed to the Bandit ship faster than the speed of light. (The Police ship will directly notice the broken line and may switch off its engines).

Since the line is very light then the "spring force" in the line ought to pull the line to the Bandit ship and the net pulling force on the Bandit ship would directly be much less than before the line was broken.

(As for the analogy for a star losing its mass, the major difference is that no gravitational force is involved in this example. For the star case - maybe nature does not allow a gravitational source to momentarily disappear, or maybe it takes time (speed of light) until the planet will notice the force difference )

Last edited: Jul 29, 2007
7. Jul 30, 2007

### louk

But there are several things that do not make sense for me.

a) If the information of the broken line is transmitted with the speed of sound for the material of the line – say it is 1% of the light speed – then we end up in the situation that some force is pulling the Bandit space ship for 100 minutes. It seems to be even harder to explain what force that could be.

b) If the spring effect in the line makes effect – then we have the situation that in order to take account for the full length of the line in an integral, then the information of the broken line has to be spread immediately over the full line – ie faster than light. Otherwise we end up with the case a). Also, the equation – I think – will be second order differential equations which will solve into some kind of a damped oscillation. A change in the pulling force will in that case be felt directly at the Bandit ship. I am not aware of any solution that gives a constant pull for 1 minute and then transfers into a damped oscillation.

c) The only way that the Bandit ship cannot retrieve any information from the pulling force of the line faster than light is that the line will pull the ship with a constant force – and with the same force as before the line was broken - for at least one minute. But what force is pulling the line for this minute??

8. Jul 31, 2007

### louk

As for the suspended line and standing waves contributed by user rjb – there is a variation of the space ship problem.

Assume a cable car suspended by a cable in the middle between two cable towers. The cable car sends a radio signal at t0 to the two towers which makes them release the cable at the same time. The time for the radio signal to reach the towers is dt.

Now, will the cable car starts falling directly when the cable is released at the two towers at time t0+dt (case a) – or will it take the time corresponding to the speed of light (or maybe the speed of sound for the cable) from the towers back to the cable car before it starts falling – at t0+2dt or later (case b)?

In case a) - the information of the released line is passed faster than the speed of light. For case b) - I have to ask what is keeping the cable car up during the time a signal is transferred from the towers to the cable car.

Or does one have to include some kind of relativistic effect – but please notice that no involved object is moving.