Closed systems and relativity

From Momchil Velkovsky:

I was teaching "Conservation Laws and Relativity" (ch 6.8) and I think that one should stress more , that energy change is the same in any inertial frame only for isolated systems. Although 6.54,6.55,6.56 all imply it, it was 2 pages before, when it was mentioned that Delta p_sys =0. Energy change in non-isolated systems is problematic. A system made of a box with attached spring that pushes from a wall is a closed one in the ground reference frame and gets its kinetic energy change from the elastic energy of the spring. We can conclude that this system is closed. In the reference frame that moves with the final velocity of the box, the kinetic energy change (but not the total energy change of the system!) is due to the work done by the wall. The spring potential energy change goes towards changing the kinetic energy of the wall (non-zero, even for infinitely massive one), together with the work done on the wall (if it has finite mass). Of course, if the wall plus our system form a bigger isolated one, then all accounting is fine. But an inevitable conclusion is that the potential energy of the spring, even if it looks that it belongs to the spring-box system, really belongs to the bigger system. The other conclusion is that it is meaningless to speak about a closed system, if it is not isolated. The system is closed only in a particular reference frame. This is really confusing for many people and I had several physicists, who can not understand it.

ericmazur / PnPbook

Closed systems and relativity #179