Consider some material object, more or less rigid, with two ends, A and B, like

A---B

It is at rest at a point in time t_0 in my reference frame. Now I kick it a bit, i.e. I apply some force for a limited amount of time at A in the direction of B. After the kick, the whole object has a speed v in the direction A->B. I reckon that the speed of B, v_B, is never larger than that of A, v_A, before, during and after the whole experiment.

Now I consider how, during application of the force, the force propagates through the object from A to B. The speed of propagation is limited by the speed of light c.

As a consequence it seems that during the force application, there is a small time interval where v_B<v_A. Integration of this delta-speed translates into a reduction of the distance between A and B at the end of the experiment.

If I did not make a mistake, the reduction factor is (1-v/c).

This is a stronger reduction even than the relativistic length contraction factor. How can I get the object longer again to match the relativistic contraction?

Ideas?

Harald.

Harald---

You must remember that special relativity only applies when the acceleration is zero. While the force is being applied, the acceleration is greater than zero, and you must use the full machinery of general relativity, which I know much less about.

Hi Harald,

Relativistic length contraction and the fact that causality forbids perfectly rigid bodies are two different things since the latter involves forces, or more generally, limits on the speeds with which information can be transmitted.

...special relativity only applies when the acceleration is zero. While the force is being applied, the acceleration is greater than zero, and you must use the full machinery of general relativity, which I know much less about.


Excuse me? I think you should take a look at your special relativity book. I guarantee you that it will have a chapter on relativistic dynamics. In fact einstein used this to discover how to formulate a relativistic theory of gravition by inventing the principle of equivalence. The idea is that if you want to know how a system will behave in a gravitational field, you just think in terms of acceleration in the absence of a gravitational field.

Ugh. You're right. I should quit responding before I've had coffee.

I generally allow myself one stupid mistake a month, and it's been a clean december otherwise...

Harald---p-brane is right and I'm an idiot:)

Don`t sweat it. I say dumb things all the time.:)

Now I consider how, during application of the force, the force propagates through the object from A to B. The speed of propagation is limited by the speed of light c.
I'm no expert here, but I'd guess it's a compression wave that propagates at the material's speed of sound, followed by a decompression wave (if you didn't kick the object so hard it deformed permanently).
As a consequence it seems that during the force application, there is a small time interval where v_B<v_A. Integration of this delta-speed translates into a reduction of the distance between A and B at the end of the experiment.
As p-brane said, this doesn't have anything to do with relativistic length contraction, which is independent of how an object attains its final velocity. Also notice that, by your reasoning, pulling one end of an object instead of pushing it would cause it to stretch rather than contract.