What Causes Acceleration in a Collision Under Special Relativity?

[analyst5]

I have a quick question regarding causality in SR and some specific examples. Collision between two bodies is one of the examples when one event causes another, let's say that a body travels towards another which is at rest and hits it. Now my question may seem strange, but what is really the cause of the acceleration of the second body after the hit. Does the first body as a whole cause the second one to move, or can we consider only the surface of the first body the cause of the event 'the second body starts to move', since only the surface had the interaction with it and therefore we are speaking of two time-like events? But this still sounds confusing since the body as a whole has its mass and force and it seems that when speaking in those terms, we should somehow consider that the body as a whole had something to do with the start of the motion of the second body.

I appreciate your help, thanks in advance.

 

[Dale]

Does the first body as a whole cause the second one to move, or can we consider only the surface of the first body the cause of the event 'the second body starts to move', since only the surface had the interaction with it.

It is a little more complicated than either of those options. The effect of the collision starts at the surface where the first body contacts the second body, but after it starts there is a compression wave which travels through the material of the second body at the speed of sound in the material. This wave inside the body is what ultimately causes the rest of the second body to move.

 

[analyst5]

So does the surface of the first body have the same force as the first body as a whole while interacting?

 

[Dale]

I am not certain that I know what you are asking, but I believe that you are asking if the net force on the first body is equal to the force on the surface of the first body. If that is what you are asking, then yes, provided there are no other forces involved.

Note, the force acting on the surface of the body causes an acceleration of the center of mass of the body, even while the compression wave is still traveling through the body.

 

[analyst5]

But the second body 'starts to move' point by point, starting from the sid which underwent collision, right? Since it cannot be rigid. How does the compression wave cause each point to move?

 

[Dale]

But the second body 'starts to move' point by point, starting from the sid which underwent collision, right? Since it cannot be rigid.

Yes.

How does the compression wave cause each point to move?

The internal stresses change as the compression wave passes.

Suppose that the compression wave is a perfectly sharp rectangular wave, meaning that where the wave is located there is a constant compressive stress and there is 0 stress elsewhere. Then if you consider an infinitesimal cube of material which crosses the border of the wave it is clear that the forces are unbalanced and therefore it accelerates.

 

[Bill_K]

This is all just basic Newtonian continuum mechanics. It has nothing to do with relativity.

 

[Dale]

Yes.

 

[AlephZero]

What Bill-K said, but the OP might not know these effects are very slow compared with the speed of light. In most common materials on earth, the speed of the compression wave is between 1 and 10 km/s. It is quite straightforward to measure these effects in lab-bench-sized experiments.

 

[analyst5]

I'm sorry, I didn't know that it was basic Newtonian mechanics, I thought it was connected with SR since in it there is no real rigid bodies. Anyway, thanks.

 

[Dale]

No worries. This does fall under Newtonian mechanics, in other words, if you are analyzing the motion of a non-rigid body in Newtonian mechanics then you would get all of the compression waves etc. which we have discussed.

The difference between relativity and Newtonian mechanics is not in the treatment of realistic non-rigid bodies, but simply the fact that idealized rigid bodies are incompatible with relativity while they are compatible with Newtonian mechanics.