Question about length contraction.

[cragar]

Lets say I have 2 charged spheres that are connected by a spring and they are a distance d apart. The spring is made of a material that will not allow the charge to evenly distribute. And each sphere has the same charge q on it. Now I move with respect to this object and I should see the spring length contracted. Now the charged spheres are closer together but why wouldn't the now stronger coulomb repulsion want to push the spring back out in my frame. And I guess there in now a B field because the charges are moving. Does the B field affect it though? There is probably something I don't understand about length contraction and where would the energy come from to push it back apart. Any help will be much appreciated.

 

[DaveC426913]

You are assuming the charged field itself somehow remains spherical. It too is length contracted, putting the spheres at the correct distance for the amount of charge they experience.

Make it simpler; remove the spheres and charges and just examine the spring. It's a foot long, but length contracted, its only half that. Why does it not bounce back? Because, at a half foot in length, it is in equilibrium.

 

[cragar]

OK thanks for your answer. Why can we say the spring is in equilibrium at a half of foot? Is it just because in our frame that is the springs rest length. Not that this would make a difference but if instead of charged spheres we had electrons at each end, that we could treat as point particles.

 

[DaveC426913]

Why can we say the spring is in equilibrium at a half of foot?

The atoms and their bonds are length-contracted. A spherical field of any sort, when seen at relativistic speeds, is going to be lozenge-shaped - shorter along the direction of motion. All physical processes (such as solid material matrices) will be likewise squished.