Intersection of bars moving at v>c

[Waxbear]

I have two metal bars positioned in space so that, when viewed in the xy-plane, they intersect each other at some point P.

One of the rods are parallel with the x-axis and at rest, while i move the other rod downwards, in the -y direction, with a speed u. The speed of the point P, called U_P, should then be u/Tan(Theta). Since i can choose Theta to be as small as i like, i can make P move at a speed greater than light, and thus having made U_P > c.

I then stand at one end of the rod at rest and manipulate the rods like mentioned above, and my friend is standing on the other end of the rod at rest and sees the intersection arrive. Now consider that, before the experiment, i told my friend that when he sees the intersection arrive, it means "go!". Haven't i then sent the go-code to him at a speed faster than light, and thus transmitted an information carrying signal at a speed faster than light?

Of course i know that i haven't because SR doesn't allow this. But what part of the thought experiment is wrong?

 

[Doc Al]

Of course i know that i haven't because SR doesn't allow this. But what part of the thought experiment is wrong?

Your assumption that you can move the entire bar from rest to some speed u instantly.

Once the bar is moving at speed u, it's true that the intersection can move at v > c, but that's of no use for transmitting a signal.

 

[Waxbear]

Considering that the bars are very long, so that the time it takes me to accelerate the bar to some speed u, is insignificantly small, compared to the time it takes the light emitted from when i started moving the bar to reach my friend. Wouldn't my "intersection signal" then be able to catch up with the light, so that it arrives at my friend before the light?

I'm sorry if the whole question seems silly, I'm merely trying to understand why this cannot happen, to gain a better understanding of SR.

 

[Doc Al]

Considering that the bars are very long, so that the time it takes me to accelerate the bar to some speed u, is insignificantly small, compared to the time it takes the light emitted from when i started moving the bar to reach my friend. Wouldn't my "intersection signal" then be able to catch up with the light, so that it arrives at my friend before the light?

No. When you start to move one end of the bar, the other end won't begin to move until the mechanical impulse travels the length of the bar. And that impulse travels much less than the speed of light.

 

[JesseM]

Considering that the bars are very long, so that the time it takes me to accelerate the bar to some speed u, is insignificantly small, compared to the time it takes the light emitted from when i started moving the bar to reach my friend.

If you accelerate one end of the bar by pushing it, other points on the bar won't start accelerating until a sound wave starting from the point you pushed has reached them (see here), and the sound wave will travel slower than the light wave, so your friend will get the light signal before he sees any movement of the part of the bar nearest to him. As long as you are accelerating the bar by pushing from a single point, there's no way the time needed to accelerate the whole bar can be insignificantly small relative to the time for the light to reach your friend (you could accelerate the whole bar quickly by having a set of coordinated pushes at different points along its length, but the pushes would have to happen at a prearranged time, so this wouldn't be useful for sending a signal that some event whose time you didn't know in advance had happened near you, like sending your friend a signal that a radioactive particle had decayed or that you had finally beat Donkey Kong or something)

 

[Dale]

Considering that the bars are very long, so that the time it takes me to accelerate the bar to some speed u, is insignificantly small, compared to the time it takes the light emitted from when i started moving the bar to reach my friend.

It is not insignificantly small in any circumstance; it is always much greater than the time it takes the light to reach your friend. The time it takes to accelerate the bar depends on the size of the bar and the speed of sound in the bar, which is always less than c.

 

[Waxbear]

Ah yes, thank you! The reason i ask this is because in the book I'm reading for my SR course it was used as an example on how "movements" can travel at v > c, but movements carrying information cannot. The book used the sweeping of a laser beam across the surface of moon, by a person standing on Earth as an example, and i can see why that can never be used to transmit signals. But the book also mentions this whole rod thing, and it was less clear to me why that couldn't be used.

I guess you can say that you would have to already have sent a v < c signal to all parts of the rod (this being the mechanical wave that "carries" the pushing on the rod) before you can send the v > c signal, thus making the entire signal operation happen at v < c.

Thank you for clearing that up for me :)

 

[Waxbear]

Reading a little further in the book i found this: "One consequence of SR is that rigid objects can no longer exist, not even as idealized objects. Since keeping an object rigid would imply sending a signal instantaneously." which is basically exactly what all of you said :)