Potential Energy of Length Contraction

[Albertgauss]

Is there any potential energy associated with length contraction? If I start with a rod at rest, and accelerate it to a relavsitic kinetic energy, the rod also length contracts, at least as viewed from the ground frame watching the rod go by. When the rod decelerates and comes to rest, it will extend to its rest frame length. Is there any release of energy associated with this? I presume there would be, since pieces in the rod move a length "dx" back into their "rest frame postions" and there is a Force Causing deceleration (though how this gets the energy out of the contracted rod, I'm not sure exactly), thus, there should be some kind of work associated with the process. Any ideas?

 

[Jonathan Scott]

Is there any potential energy associated with length contraction? If I start with a rod at rest, and accelerate it to a relavsitic kinetic energy, the rod also length contracts, at least as viewed from the ground frame watching the rod go by. When the rod decelerates and comes to rest, it will extend to its rest frame length. Is there any release of energy associated with this? I presume there would be, since pieces in the rod move a length "dx" back into their "rest frame postions" and there is a Force Causing deceleration (though how this gets the energy out of the contracted rod, I'm not sure exactly), thus, there should be some kind of work associated with the process. Any ideas?

No, there is no potential energy associated with length contraction.

Note that from the point of view of an observer on the rod, at any time when the rod is not being accelerated or decelerated (and has settled back into a stable shape) the rod looks exactly the same as it does in the original rest state, with exactly the same internal forces.