Information traveling faster than light?

[Joza]

If I am correct, information cannot travel faster than the speed of light?

So, let's say a rod, longer than the distance light can travel in a second was constructed in space. It is rigid and firm, and not bendable. At one end, is a button, and when the rod is tilted, it presses this button. If I then tilt the rod from the other end, thereby pressing the switch at the other end instantaneously, has information traveled faster than light?


Is this a valid argument? Like, are there effects which would prevent the rod from being completely rigid at such massive lengths?

 

[JesseM]

If I am correct, information cannot travel faster than the speed of light?

So, let's say a rod, longer than the distance light can travel in a second was constructed in space. It is rigid and firm, and not bendable. At one end, is a button, and when the rod is tilted, it presses this button. If I then tilt the rod from the other end, thereby pressing the switch at the other end instantaneously, has information traveled faster than light?


Is this a valid argument? Like, are there effects which would prevent the rod from being completely rigid at such massive lengths?

It's impossible to have a perfectly rigid object in relativity--all objects behave like springs or slinkies, where if you push one one there's a compression wave that travels along it until it reaches the other end, and only then does the other end move. Physically this makes sense, since solid objects are made up of atoms which are held together by electromagnetic forces, so if you push one atom the electromagnetic field in the vicinity of other atoms won't be affected until an electromagnetic wave traveling at the speed of light reaches them. In fact the actual speed of the compression wave will be less than the speed of light--the speed will be equal to the speed of sound waves in that material.

For more on this, see this page or this one.

 

[Joza]

Bingo. I knew it couldn't be true.

I guess I'll have to wait until my relativity course!

 

[Anonym]

If I am correct, information cannot travel faster than the speed of light?

No, the information rate cannot travel faster than the speed of light. According to SR the speed of light is the upper bound for the group velocity of the signal propagation.

Regards, Dany.

 

[JesseM]

No, the information rate cannot travel faster than the speed of light. According to SR the speed of light is the upper bound for the group velocity of the signal propagation.

There are weird materials with "anomolous dispersion" where the group velocity can be faster than light, although of course in these materials information still cannot move faster than light--as this page says:

Unfortunately we frequently read in the newspapers about how someone has succeeded in transmitting a wave with a group velocity exceeding c, and we are asked to regard this as an astounding discovery, overturning the principles of relativity, etc. The problem with these stories is that the group velocity corresponds to the actual signal velocity only under conditions of normal dispersion, or, more generally, under conditions when the group velocity is less than the phase velocity. In other circumstances, the group velocity does not necessarily represent the actual propagation speed of any information or energy. For example, in a regime of anomalous dispersion, which means the refractive index decreases with increasing wave number, the preceding formula shows that what we called the group velocity exceeds what we called the phase velocity. In such circumstances the group velocity no longer represents the speed at which information or energy propagates.

 

[rbj]

No, the information rate cannot travel faster than the speed of light. According to SR the speed of light is the upper bound for the group velocity of the signal propagation.

what does information "rate" (bits per unit time?) have anything to do with this? bits per unit time and length per unit time are not dimensionally the same and can't be directly compared (or added or equated, etc.).

what relativity says is that if some event happens over here and you are over there, you won't know about it (and react) until after a period of

$$\frac{\left| \mathrm{locus}(here) - \mathrm{locus}(there) \right|}{c}$$

as view by a third observer who is equi-distant from here and there.

it could be a single bit of information. or a bunch of bits.