How does E=1/2mv^2 work when dealing with relative velocities?

Question

For example, if Jack and Jill, who both weigh 20kg each, are moving in the same direction at 1m/s, they should both have 10J of kinetic energy each, and they are both moving at 0m/s relative to each other and so there is a difference of 0J of kinetic energy between Jack and Jill. If Jack accelerates to 2m/s, while Jill stays at 1m/s, Jack now has 40J of kinetic energy, while Jill still has 10J, so Jack has 30J more kinetic energy than Jill. However, relative to Jill, Jack is moving at 1m/s, and so should only have 10J more energy than her. What am I missing?

In: Physics

Answer 1

Kinetic energy is dependent on frame. In Newtonian physics, Newton assumed (and even argued for) a absolute universal coordinate system, then velocity are all relative to this absolute system. But in Einstein’s relativity, or even just Galileo’s relativity, there are no absolute velocity, so there are no absolute kinetic energy. But Einstein’s theory deal with this by only require total energy to be absolute but its make up can change, in different reference frame kinetic energy can turn into mass and vice versa.