Undergrad Velocity u > c? Faster Than Light Comm?

[f todd baker]

On my website (unnamed since I have been previously reprimanded for "promoting" the site!) I got a question, pretty straightforward, the essence of which is: Two long wires are not parallel and make an angle θ with each other; they cross at one point and one wire is moving with velocity v perpendicular to the first; the point where they cross moves with a velocity u.

It is easy to show that u=v/tanθ and u may be larger than c. But this point has no mass and carries no information so, no problem with special relativity (just like a sweeping laser spot moving across the moon with v>c). But then I got a followup question suggesting having an array of moving wires the spacing of which is coded information. What am I missing?

 

[FactChecker]

If the distance between the wires changes, that change can not travel along the wire at infinite speed. In fact it is limited to c or less.

 

[f todd baker]

All wires but one are moving with the same velocity and are parallel. The distance between any two of them does not change.

 

[FactChecker]

Oh. I missed that. There is nothing that says that information set up earlier can not be read fast. The wires that you describe can not be set up over a distance faster than c. It would take a long time to set up the parallel wires of that length. Your example is just a more complicated case of sending information and storing it in a safe in a distant location. Then the safe can be opened and read instantly. That does not mean that the information was transmitted instantly.

 

[Dale]

I second @FactChecker here. The information is transmitted at the time of setting up the spacing between the wires. The diagonal wire is actually completely irrelevant.

 

[Ibix]

No information is being transmitted in the u direction - it's being transmitted in the v direction. It's just that observers spaced perpendicular to that get the information with different delays. The only way to communicate in the u direction is to poke one of the wires as it passes, and then this is just a complicated variant on "can I communicate faster than light by pushing a rigid rod".

 

[Herman Trivilino]

But then I got a followup question suggesting having an array of moving wires the spacing of which is coded information. What am I missing?

The coding can't travel faster than $c$.

 

[DaveC426913]

Though this is an idealized thought experiment: here's some practical cold water tossed on it:

The speed of transmission will be far slower than c; it is limited to the speed of sound in the material that the wires are made of.

Even if they were made of the hardest substance currently known - diamond - their best transmission speed will be only 12km/s - the speed of sound in diamond.